Edited by Jaegwon Kim and Ernest Sosa Brown University
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Blackwell Publishing
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Preface Acknowledgments
Part I
Existence
ix xi
1
Introduction
3
On What There Is W. V. Quine
4
2
Empiricism, Semantics, and Ontology Rudolf Carnap
13
3
Existence and Description Bertrand Russell
23
4
Referring to Nonexistent Objects Terence Parsons
36
5
Ontological Relativity W. V. Q!.Iine
45
Part II
Identity
63
Introduction
65
6
The Identity ofIndiscernibles Max Black
66
7
Identity and Necessity Saul Kripke
72
8
The Same F John Perry
90
Contents
9
10
Contingent Identity Allan Gibbard
100
Identity, Essence, and Indiscernibility Stephen Yablo
116
Part III
Modalities and Possible Worlds
131
Introduction
133
11
Modalities: Basic Concepts and Distinctions Alvin Plantinga
135
12
Identity through Possible Worlds Roderick M. Chisholm
149
13
Counterparts or Double Lives? David Lewis
154
14
Primitive Thisness and Primitive Identity Robert M. Adams
172
15
The Nature of Possibility D. M. Armstrong
184
Part IV
Universals, Properties, Kinds
195
Introduction
197
16
Universals as Attributes D. M. Armstrong
198
17
New Work for a Theory of Universals David Lewis
209
18
Natural Kinds W. V. Quine
223
19
On Properties Hilary Putnam
243
20
Causality and Properties Sydney Shoemaker
253
Part V
Things and their Persistence
269
Introduction
271
21
Identity through Time Roderick M. Chisholm
273
22
Identity, Ostension, and Hypostasis W. V. Quine
284
23
Scattered Objects Richard Cartwright
291
24
Parthood and Identity across Time Judith Jarvis Thomson
301
25
Temporal Parts of Four-Dimensional Objects Mark Heller
312
Contents
Part VI
The Persistence of the Self
327
Introduction
329
26
The Persistence of Persons Roderick M. Chisholm
331
27
Persons and their Pasts Sydney Shoemaker
338
28
The Self and the Future Bernard Williams
355
29
Personal Identity Derek Parfit
365
30
Personal Identity: The Dualist Theory Richard Swinburne
377
31
Human Beings Mark Johnston
393
Part VII
Causation
409
Introduction
411
32
Causes and Conditions ]. L. Mackie
413
33
Causal Relations Donald Davidson
428
34
Causation David Lewis
436
35
Causal Connections Wesley C. Salmon
444
36
The Nature of Causation: A Singularist Account Michael Tooley
458
Part VIII
Emergence, Reduction, Supervenience
483
Introduction
485
37
Mechanism and Emergentism C. D. Broad
487
38
Ontological Reduction and the World of Numbers W. V. Quine
499
39
Special Sciences Jerry A. Fodor
504
40
Multiple Realization and the Metaphysics of Reduction Jaegwon Kim
515
41
Physicalism: Ontology, Determination, and Reduction Geoffrey Hellman and Frank Thompson
531
42
Supervenience as a Philosophical Concept Jaegwon Kim
540
Contents
Part IX
Realism/ Antirealism
557
Introduction
559
43
Realism Michael Dummett
561
44
Pragmatic Realism Hilary Putnam
591
45
Putnam's Pragmatic Realism Ernest Sosa
607
46
Yes, Virginia, There Is a Real World William P. Alston
620
47
Morals and Modals Simon Blackburn
634
48
Realism, Antirealism, Irrealism, Quasi-realism Crispin Wright
649
Name index Subject index
666 671
Metaphysics is a philosophical inquiry into the most basic and general features of reality and our place in it. Because of its very subject matter, metaphysics is often philosophy at its most theoretical and abstract. But, as the works in this book show, simple, intuitive reflections on our familiar experiences of everyday life and the concepts that we use to describe them can lead us directly to some of the most profound and intractable problems of metaphysics. This anthology, intended as a companion to Blackwell's A Companion to Metaphysics, is a collection of writings chosen to represent the state of discussion on the central problems of contemporary metaphysics. Many of the selections are "contemporary classics," and many of the rest will likely join the ranks of the "classics" in due course. Throughout the selection process we tried to be responsive to the needs of students who are relatively new to metaphysics. Given the overall aim of the volume and the nature of the field, it is unavoidable that some of the writings included contain somewhat technical parts that demand close study; however, we believe that most of the essential selections are accessible to the attentive reader without an extensive background in metaphysics or technical philosophy. The selections are grouped in nine parts. Each part is preceded by a brief editorial introduction, including a list of works for further reading. These introductions are not intended as comprehensive
surveys and discussions of the problems, positions, and arguments on the topic of each part; for such guidance the reader is encouraged to consult A Companion to Metaphysics. Rather, their aim is to give the reader some orientation, by indicating the scope of the problems dealt with in the works included in that section, and what their authors attempt to accomplish. Part I, on the nature of existence, deals with the question of what it is for something to exist and what it is for us to acknowledge something as existing. Part II concerns the problem of identity - whether qualitative indiscernibility entails identity, whether identity is always necessary or can be contingent, whether identity is relative to sortals, and so on. Part III is on "modal" concepts like necessity and possibility, essence and essential property, necessary and contingent truth, and "possible worlds." The part that follows is devoted to age-old issues concerning universals, properties, and kinds - the items in terms of which we characterize things of this world. The central question of Part V is what it is for something to be a "thing," and, in particular, what makes one thing at one time to be "the same thing" as something at another time. This part is followed by a group of writings addressing the same question for persons: there is a clear and deep difference, most of us would feel, between our continuing to live till tomorrow and our being replaced by an exact "molecule-for-molecule" duplicate in our sleep
Preface
tonight; but in what does this difference consist? Part VII is devoted to the nature of causation, the relation that David Hume famously called "the cement of the universe." Major contemporary accounts of the nature of causation are represented here. This is followed by a part concerning the ways (besides the causal relation) in which things and phenomena of this world may hang together, and the topics dealt with here - emergence, reduction, and supervenience - are of critical importance to current debates in philosophy of mind and philosophy of science. The issue of realism/ antirealism has lately returned as a major philosophical problem, and the final part of the book includes discussions of realism and its major contemporary alternatives. It was often difficult to neatly segregate the works into separate parts; the reader should be aware that many of the selections are of relevance to problems dealt with in more than one part. This is especially true of the chapters in Parts II and III, and those in Parts V and VI. The topics represented in this book by no means exhaust the field of metaphysics. For reasons of space, we have had to leave out many important topics, among them the following: facts, events, and tropes; primary and secondary qualities; the status of abstract entities; parts and wholes; the objective and the subjective; time and becoming; determinism and agency; and the nature and possibility of metaphysics. Even on the topics included here, many important and worthy works have had to be left out, either on account of limited space or because of the difficulty of extracting from them something of reasonable length that would be selfcontained. In choosing the works to be included, our primary focus has been on seminal primary literature that represents the major contemporary positions on the issues involved. In consequence,
we have had to forgo many valuable follow-up discussions and elaborations, objections and replies, and expository surveys. We hope that the interested reader will pursue the threads of discussion inspired by the materials included here. During much of the middle half of the century, metaphysics was in the doldrums, at least within the analytic tradition. This was largely due to the anti-metaphysical influence of the two then dominant philosophical trends. Logical positivism and its formalistic, hyper-empiricist legacies lingered through the 1950s and 1960s in the United States, nourishing an atmosphere that did not encourage serious metaphysics, while in Britain the antimetaphysical animus derived from "ordinary language" philosophy and the later works of Wittgenstein. However, metaphysics began a surprisingly swift, robust comeback in the 1960s, and since then has been among the most active and productive areas of philosophy. It is now flourishing as never before, showing perhaps that our need for metaphysics is as basic as our need for philosophy itself. We believe that this collection gives a broad glimpse of metaphysics during the century that is now about to close. Maura Geisser, Brie Gertler, and Matt McGrath have helped us with this project in various ways, and we have received valuable advice from our Brown colleagues Victor Caston and Jamie Dreier. Also helpful were the comments and suggestions by the anonymous readers of the preliminary plan we submitted to Blackwell. Steve Smith, our editor, has been unfailingly supportive and helpful. We owe thanks to them all. Jaegwon Kim Ernest Sosa October 1998
The authors and publishers would like to thank the following for permission to use copyright material: American Philosophical Quarter~y for chapters 27, 32; The American Philosophy Association and William P. Alston for chapter 46; Blackwell Publishers for chapters 13 (with David Lewis), 30, 47 (with Simon Blackburn); Cambridge University Press for chapters 25, 42; Columbia University for chapters 5,10,14,24,31, 33,34 (with David Lewis), 38,41,45 (with Ernest Sosa); Cornell University Press for chapters 6, 8, 28, 29; Harvard University Press for chapter 22; Kluwer Academic Publishers for chapters 4,9, 18, 19,20,23,39,43; La Trobe University and David Lewis for chapter 17;
New York University Press for chapter 7; Open Court, a division of Carus Publishing, for chapters 21, 26, 44; Oxford University Press for chapter 11; Philosophy and Phenomenological Research and Brown University for chapter 40; Princeton University Press for chapter 35; Review of Metaphysics for chapter 1; Routledge and Kegan Paul for chapter 37; The Bertrand Russell estate for chapter 3; University of Calgary Press for chapters 15,36; University of Chicago Press for chapter 2; University of Minnesota Press for chapters 12, 48; Westview Press for chapter 16. Every effort has been made to trace the copyright holders, but if any have been inadvertently overlooked, the publishers will be pleased to make the necessary arrangements at the first opportunity.
PART I
Introduction
Introduction The concept of existence is probably basic and primitive in the sense that it is not possible to produce an informative definition of it in terms that are more clearly understood and that would tell us something important and revealing about what it is for something to exist. Rather, the primary conceptual question about existence has been this: What kind of concept is expressed by "existence" and its cognates? When we say of something that it exists, are we attributing to that thing a certain proper~y, the property of existing, much in the way we attribute the property red to this apple when we say it is red? Something is red as opposed to yellow or black - or, at any rate, not red. But something exists as opposed to what? Being nonexistent? But how is that possible? Is it coherent to suppose that some things exist and some things don't exist? As Qp.ine says in his "On What There Is" (chapter 1), isn't it a truism that everything exists, and nothing else does? But this doesn't seem to make the issues go away. For, as Terence Parsons points out in "Referring to Nonexistent Objects" (chapter 4), our ordinary discourse is full of apparent references to things that do not exist, like fictional characters (Sherlock Holmes, Hamlet), mythological creatures (Pegasus, centaurs), and the fountain of youth that Ponce de Leon sought to find. It seems natural and intelligible to say that there are things, like centaurs and the fountain of youth, that do not exist. Moreover, we
apparently can say things that are true of them and things that are false of them. It seems true to say that centaurs are mythical animals, that Sherlock Holmes was a detective and lived on Baker Street, and so on; and it seems false to say that Sherlock Holmes was a baseball player, or that the golden mountain is in Argentina. But how is it possible for us to refer to them to begin with - things with which we have no causal or epistemic contact? Are we forced to countenance these nonexistent objects as denizens of our ontology, or is it possible to explain them away by paraphrasing statements that are apparently about them into statements that are free of such references? These are among the questions addressed in the selections by Bertrand Russell and Terence Parsons. Quine's "On What There Is" and Carnap's "Empiricism, Semantics, and Ontology" (chapter 2) address some fundamental issues about what it is for something to exist, and, more importantly, what it is for us, or our theory, to recognize something as existing. Carnap's distinction between "internal questions" and "external questions" about existence - that is, questions about whether something exists within a scheme of language, on the one hand, and questions about whether or not to accept a scheme that posits its existence, on the other - introduces pragmatic and relativistic dimensions into questions of existence. This question of the possible relativity of ontology to conceptual schemes is the topic of Quine's "Ontological Relativity" (chapter 5).
Further reading Alston, William P., "Ontological commitment," Philosophical Studies 9 (1958), pp. 8-17. Butchvarov, Panayot, Being Qua Being (Bloomington: Indiana University Press, 1979). Chisholm, Roderick M., "Beyond being and nonbeing," Philosophical Studies 24 (1973), pp. 245-57. Evans, Gareth, The Varieties ofReference (Oxford: Oxford University Press, 1982). Fine, Kit, "The problem of non-existence: I. Internalism," Topoi 1(1982), pp. 97-140. Katz, Jerrold]., "Names without bearers," Philosophical Review 103 (1994), pp. 1-39. Lewis, David, "Truth in fiction," in Philosophical Papers, vol. I (New York: Oxford University Press, 1983).
Moore, G. E., "Is existence a predicate?," repro in Philosophical Papers (London: Allen and Unwin, 1959). Parsons, Terence, Nonexistent Objects (New Haven, Conn.: Yale University Press, 1980). Routley, Richard, Exploring Meinong's Jungle and Beyond (Canberra: Australian National University, 1980). Russell, Bertrand, "On denoting," repro in R. C. Marsh (ed.), Logic and Knowledge (London: George, Allen and Unwin, 1956). Walton, Kendall, Mimesis as Make-Believe (Cambridge, Mass.: Harvard University Press, 1990). Williams, C. J. F., What Is Existence? (Oxford: Oxford University Press, 1981).
w. V. Quine A curious thing about the ontological problem is its simplicity. It can be put in three Anglo-Saxon monosyllables: 'What is there?' It can be answered, moreover, in a word - 'Everything' - and everyone will accept this answer as true. However, this is merely to say that there is what there is. There remains room for disagreement over cases; and so the issue has stayed alive down the centuries. Suppose now that two philosophers, McX and I, differ over ontology. Suppose McX maintains there is something which I maintain there is not. McX can, quite consistently with his own point of view, describe our difference of opinion by saying that I refuse to recognize certain entities. I should protest, of course, that he is wrong in his formulation of our disagreement, for I maintain that there are no entities, of the kind which he alleges, for me to recognize; but my finding him wrong in his formulation of our disagreement is unimportant, for I am committed to considering him wrong in his ontology anyway. When I try to formulate our difference of opinion, on the other hand, I seem to be in a predicament. I cannot admit that there are some things which McX countenances and I do not, for in admitting that there are such things I should be contradicting my own rejection of them. It would appear, if this reasoning were sound, that in any ontological dispute the proponent of the negative side suffers the disadvantage of not
Originally published in the Review of Metaphysics 2/1 (Sept. 1948). reprinted with permission.
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being able to admit that his opponent disagrees with him. This is the old Platonic riddle of nonbeing. Nonbeing must in some sense be, otherwise what is it that there is not? This tangled doctrine might be nicknamed Plato's beard; historically it has proved tough, frequently dulling the edge of Occam's razor. It is some such line of thought that leads philosophers like McX to impute being where they might otherwise be quite content to recognize that there is nothing. Thus, take Pegasus. If Pegasus were not, McX argues, we should not be talking about anything when we use the word; therefore it would be nonsense to say even that Pegasus is not. Thinking to show thus that the denial of Pegasus cannot be coherently maintained, he concludes that Pegasus is. McX cannot, indeed, quite persuade himself that any region of space-time, near or remote, contains a flying horse of flesh and blood. Pressed for further details on Pegasus, then, he says that Pegasus is an idea in men's minds. Here, however, a confusion begins to be apparent. We may for the sake of argument concede that there is an entity, and even a unique entity (though this is rather implausible), which is the mental Pegasus-idea; but this mental entity is not what people are talking about when they deny Pegasus. McX never confuses the Parthenon with the Parthenon-idea. The Parthenon is physical; the Parthenon-idea is mental (according anyway to McX's version of ideas, and I have no better to offer). The Parthenon is visible; the Parthenon-
On What There Is
idea is invisible. We cannot easily imagine two things more unlike, and less liable to confusion, than the Parthenon and the Parthenon-idea. But when we shift from the Parthenon to Pegasus, the confusion sets in - for no other reason than that McX would sooner be deceived by the crudest and most flagrant counterfeit than grant the non being of Pegasus. The notion that Pegasus must be, because it would otherwise be nonsense to say even that Pegasus is not, has been seen to lead McX into an elementary confusion. Subtler minds, taking the same precept as their starting point, come out with theories of Pegasus which are less patently misguided than McX's, and correspondingly more difficult to eradicate. One of these subtler minds is named, let us say, Wyman. Pegasus, Wyman maintains, has his being as an unactualized possible. When we say of Pegasus that there is no such thing, we are saying, more precisely, that Pegasus does not have the special attribute of actuality. Saying that Pegasus is not actual is on a par, logically, with saying that the Parthenon is not red; in either case we are saying something about an entity whose being is unquestioned. Wyman, by the way, is one of those philosophers who have united in ruining the good old word 'exist'. Despite his espousal of unactualized possibles, he limits the word 'existence' to actuality thus preserving an illusion of ontological agreement between himself and us who repudiate the rest of his bloated universe. We have all been prone to say, in our common-sense usage of 'exist', that Pegasus does not exist, meaning simply that there is no such entity at all. If Pegasus existed he would indeed be in space and time, but only because the word 'Pegasus' has spatio-temporal connotations, and not because 'exists' has spatio-temporal connotations. If spatio-temporal reference is lacking when we affirm the existence of the cube root of 27, this is simply because a cube root is not a spatiotemporal kind of thing, and not because we are being ambiguous in our use of 'exist'. 1 However, Wyman, in an ill-conceived effort to appear agreeable, genially grants us the nonexistence of Pegasus and then, contrary to what we meant by nonexistence of Pegasus, insists that Pegasus is. Existence is one thing, he says, and subsistence is another. The only way I know of coping with this obfuscation of issues is to give Wyman the word 'exist'. I'll try not to use it again; I still have 'is'. So much for lexicography; let's get back to Wyman's ontology.
Wyman's overpopulated universe is in many ways unlovely. It offends the aesthetic sense of us who have a taste for desert landscapes, but this is not the worst of it. Wyman's slum of possibles is a breeding ground for disorderly elements. Take, for instance, the possible fat man in that doorway; and, again, the possible bald man in that doorway. Are they the same possible man, or two possible men? How do we decide? How many possible men are there in that doorway? Are there more possible thin ones than fat ones? How many of them are alike? Or would their being alike make them one? Are no two possible things alike? Is this the same as saying that it is impossible for two things to be alike? Or, finally, is the concept of identity simply inapplicable to unactualized possibles? But what sense can be found in talking of entities which cannot meaningfully be said to be identical with themselves and distinct from one another? These elements are well-nigh incorrigible. By a Fregean therapy of individual concepts, some effort might be made at rehabilitation; but I feel we'd do better simply to clear Wyman's slum and be done with it. Possibility, along with the other modalities of necessity and impossibility and contingency, raises problems upon which I do not mean to imply that we should turn our backs. But we can at least limit modalities to whole statements. We may impose the adverb 'possibly' upon a statement as a whole, and we may well worry about the semantical analysis of such usage; but little real advance in such analysis is to be hoped for in expanding our universe to include so-called possible entities. I suspect that the main motive for this expansion is simply the old notion that Pegasus, for example, must be because otherwise it would be nonsense to say even that he is not. Still, all the rank luxuriance of Wyman's universe of possibles would seem to come to naught when we make a slight change in the example and speak not of Pegasus but of the round square cupola on Berkeley College. If, unless Pegasus were, it would be nonsense to say that he is not, then by the same token, unless the round square cupola on Berkeley College were, it would be nonsense to say that it is not. But, unlike Pegasus, the round square cupola on Berkeley College cannot be admitted even as an unactualized possible. Can we drive Wyman now to admitting also a realm of unactualizable impossibles? If so, a good many embarrassing questions could be asked about them. We might hope even to trap Wyman in contradictions, by getting him to admit that certain
W. V. Quine of these entities are at once round and square. But the wily Wyman chooses the other horn of the dilemma and concedes that it is nonsense to say that the round square cupola on Berkeley College is not. He says that the phrase 'round square cupola' is meaningless. Wyman was not the first to embrace this alternative. The doctrine of the meaninglessness of contradictions runs away back. The tradition survives, moreover, in writers who seem to share none of Wyman's motivations. Still, I wonder whether the first temptation to such a doctrine may not have been substantially the motivation which we have observed in Wyman. Certainly the doctrine has no intrinsic appeal; and it has led its devotees to such quixotic extremes as that of challenging the method of proof by reductio ad absurdum - a challenge in which I sense a reductio ad absurdum of the doctrine itself. Moreover, the doctrine of meaninglessness of contradictions has the severe methodological drawback that it makes it impossible, in principle, ever to devise an effective test of what is meaningful and what is not. It would be forever impossible for us to devise systematic ways of deciding whether a string of signs made sense - even to us individually, let alone other people - or not. For it follows from a discovery in mathematical logic, due to Church,2 that there can be no generally applicable test of contradictoriness. I have spoken disparagingly of Plato's beard, and hinted that it is tangled. I have dwelt at length on the inconveniences of putting up with it. It is time to think about taking steps. Russell, in his theory of so-called singular descriptions, showed clearly how we might meaningfully use seeming names without supposing that there be the entities allegedly named. The names to which Russell's theory directly applies are complex descriptive names such as 'the author of Waverley', 'the present King of France', 'the round square cupola on Berkeley College'. Russell analyzes such phrases systematically as fragments of the whole sentences in which they occur. The sentence 'The author of Waverley was a poet', for example, is explained as a whole as meaning 'Someone (better: something) wrote Waverley and was a poet, and nothing else wrote Waverley'. (The point of this added clause is to affirm the uniqueness which is implicit in the word 'the', in 'the author of Waverley'.) The sentence 'The round square cupola on Berkeley College is pink' is explained as 'Something is round and square and is a cupola on Ber-
keley College and is pink, and nothing else is round and square and a cupola on Berkeley College'. The virtue of this analysis is that the seeming name, a descriptive phrase, is paraphrased in context as a so-called incomplete symbol. No unified expression is offered as an analysis of the descriptive phrase, but the statement as a whole which was the context of that phrase still gets its full quota of meaning - whether true or false. The unanalyzed statement 'The author of Waverley was a poet' contains a part, 'the author of Waverley', which is wrongly supposed by McX and Wyman to demand objective reference in order to be meaningful at all. But in Russell's translation, 'Something wrote Waverley and was a poet and nothing else wrote Waverley', the burden of objective reference which had been put upon the descriptive phrase is now taken over by words of the kind that logicians call bound variables, variables of quantification: namely, words like 'something', 'nothing', 'everything'. These words, far from purporting to be names specifically of the author of Waverley, do not purport to be names at all; they refer to entities generally, with a kind of studied ambiguity peculiar to themselves. These quantificational words or bound variables are, of course a basic part of language, and their meaningfulness, at least in context, is not to be challenged. But their meaningfulness in no way presupposes there being either the author of Waverley or the round square cupola on Berkeley College or any other specifically preassigned objects. Where descriptions are concerned, there is no longer any difficulty in affirming or denying being. 'There is the author of Waverley' is explained by Russell as meaning 'Someone (or, more strictly, something) wrote Waverley and nothing else wrote Waverley'. 'The author of Waverley is not' is explained, correspondingly, as the alternation 'Either each thing failed to write Waverley or two or more things wrote Waverley'. This alternation is false, but meaningful; and it contains no expression purporting to name the author of Waverley. The statement 'The round square cupola on Berkeley College is not' is analyzed in similar fashion. So the old notion that statements of non being defeat themselves goes by the board. When a statement of being or nonbeing is analyzed by Russell's theory of descriptions, it ceases to contain any expression which even purports to name the alleged entity whose being is in question, so that the meaningfulness of the statement no longer can be thought to presuppose that there be such an entity.
On What There Is
Now what of 'Pegasus'? This being a word rather than a descriptive phrase, Russell's argument does not immediately apply to it. However, it can easily be made to apply. We have only to rephrase 'Pegasus' as a description, in any way that seems adequately to single out our idea; say, 'the winged horse that was captured by Bellerophon'. Substituting such a phrase for 'Pegasus', we can then proceed to analyze the statement 'Pegasus is', or 'Pegasus is not', precisely on the analogy of Russell's analysis of 'The author of Waverley is' and 'The author of Waverley is not'. In order thus to subsume a one-word name or alleged name such as 'Pegasus' under Russell's theory of description, we must, of course, be able first to translate the word into a description. But this is no real restriction. If the notion of Pegasus had been so obscure or so basic a one that no pat translation into a descriptive phrase had offered itself along familiar lines, we could still have availed ourselves of the following artificial and trivialseeming device: we could have appealed to the ex hypothesi unanalyzable, irreducible attribute of being Pegasus, adopting, for its expression, the verb 'is-Pegasus', or 'pegasizes'. The noun 'Pegasus' itself could then be treated as derivative, and identified after all with a description: 'the thing that is-Pegasus', 'the thing that pegasizes'. If the importing of such a predicate as 'pegasizes' seems to commit us to recognizing that there is a corresponding attribute, pegasizing, in Plato's heaven or in the minds of men, well and good. Neither we nor Wyman nor McX have been contending, thus far, about the being or nonbeing of universals, but rather about that of Pegasus. If in terms of pegasizing we can interpret the noun 'Pegasus' as a description subject to Russell's theory of descriptions, then we have disposed of the old notion that Pegasus cannot be said not to be without presupposing that in some sense Pegasus is. Our argument is now quite general. McX and Wyman supposed that we could not meaningfully affirm a statement of the form 'So-and-so is not', with a simple or descriptive singular noun in place of 'so-and-so', unless so-and-so is. This supposition is now seen to be quite generally groundless, since the singular noun in question can always be expanded into a singular description, trivially or otherwise, and then analyzed out Ii la Russell. We commit ourselves to an ontology containing numbers when we say there are prime numbers larger than a million; we commit ourselves to an ontology containing centaurs when we say there are
centaurs; and we commit ourselves to an ontology containing Pegasus when we say Pegasus is. But we do not commit ourselves to an ontology containing Pegasus or the author of Waverley or the round square cupola on Berkeley College when we say that Pegasus or the author of Waverley or the cupola in question is not. We need no longer labor under the delusion that the meaningfulness of a statement containing a singular term presupposes an entity named by the term. A singular term need not name to be significant. An inkling of this might have dawned on Wyman and McX even without benefit of Russell if they had only noticed - as so few of us do - that there is a gulf between meaning and naming even in the case of a singular term which is genuinely a name of an object. The following example from Frege will serve. 3 The phrase 'Evening Star' names a certain large physical object of spherical form, which is hurtling through space some scores of millions of miles from here. The phrase 'Morning Star' names the same thing, as was probably first established by some observant Babylonian. But the two phrases cannot be regarded as having the same meaning; otherwise that Babylonian could have dispensed with his observations and contented himself with reflecting on the meanings of his words. The meanings, then, being different from one another, must be other than the named object, which is one and the same in both cases. Confusion of meaning with naming not only made McX think he could not meaningfully repudiate Pegasus; a continuing confusion of meaning with naming no doubt helped engender his absurd notion that Pegasus is an idea, a mental entity. The structure of his confusion is as follows. He confused the alleged named object Pegasus with the meaning of the word 'Pegasus', therefore concluding that Pegasus must be in order that the word have meaning. But what sorts of things are meanings? This is a moot point; however, one might quite plausibly explain meanings as ideas in the mind, supposing we can make clear sense in turn of the idea of ideas in the mind. Therefore Pegasus, initially confused with a meaning, ends up as an idea in the mind. It is the more remarkable that Wyman, subject to the same initial motivation as McX, should have avoided this particular blunder and wound up with unactualized possibles instead. Now let us turn to the ontological problem of universals: the question whether there are such entities as attributes, relations, classes, numbers, functions. McX, characteristically enough, thinks
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W. V. Quine there are. Speaking of attributes, he says: 'There are red houses, red roses, red sunsets; this much is prephilosophical common sense in which we must all agree. These houses, roses, and sunsets, then, have something in common; and this which they have in common is all I mean by the attribute of redness.' For McX, thus, there being attributes is even more obvious and trivial than the obvious and trivial fact of there being red houses, roses, and sunsets. This, I think, is characteristic of metaphysics, or at least of that part of metaphysics called ontology: one who regards a statement on this subject as true at all must regard it as trivially true. One's ontology is basic to the conceptual scheme by which he interprets all experiences, even the most commonplace ones. Judged within some particular conceptual scheme - and how else is judgment possible? - an ontological statement goes without saying, standing in need of no separate justification at all. Ontological statements follow immediately from all manner of casual statements of commonplace fact, just as - from the point of view, anyway, of McX's conceptual scheme - 'There is an attribute' follows from 'There are red houses, red roses, red sunsets'. Judged in another conceptual scheme, an ontological statement which is axiomatic to McX's mind may, with equal immediacy and triviality, be adjudged false. One may admit that there are red houses, roses, and sunsets, but deny, except as a popular and misleading manner of speaking, that they have anything in common. The words 'houses', 'roses', and 'sunsets' are true of sundry individual entities which are houses and roses and sunsets, and the word 'red' or 'red object' is true of each of sundry individual entities which are red houses, red roses, red sunsets; but there is not, in addition, any entity whatever, individual or otherwise, which is named by the word 'redness', nor, for that matter, by the word 'househood', 'rosehood', 'sunsethood'. That the houses and roses and sunsets are all of them red may be taken as ultimate and irreducible, and it may be held that McX is no better off, in point of real explanatory power, for all the occult entities which he posits under such names as 'redness'. One means by which McX might naturally have tried to impose his ontology of universals on us was already removed before we turned to the problem of universals. McX cannot argue that predicates such as 'red' or 'is-red', which we all concur in using, must be regarded as names each of a single universal entity in order that they be meaningful at
all. For we have seen that being a name of something is a much more special feature than being meaningful. He cannot even charge us - at least not by that argument - with having posited an attribute of pegasizing by our adoption of the predicate 'pegasizes' . However, McX hits upon a different strategem. 'Let us grant,' he says, 'this distinction between meaning and naming of which you make so much. Let us even grant that "is red", "pegasizes", etc., are not names of attributes. Still, you admit they have meanings. But these meanings, whether they are named or not, are still universals, and I venture to say that some of them might even be the very things that I call attributes, or something to much the same purpose in the end.' For McX, this is an unusually penetrating speech; and the only way I know to counter it is by refusing to admit meanings. However, I feel no reluctance toward refusing to admit meanings, for I do not thereby deny that words and statements are meaningful. McX and I may agree to the letter in our classification oflinguistic forms into the meaningful and the meaningless, even though McX construes meaningfulness as the having (in some sense of 'having') of some abstract entity which he calls a meaning, whereas I do not. I remain free to maintain that the fact that a given linguistic utterance is meaningful (or significant, as I prefer to say so as not to invite hypostasis of meanings as entities) is an ultimate and irreducible matter of fact; or, I may undertake to analyze it in terms directly of what people do in the presence of the linguistic utterance in question and other utterance similar to it. The useful ways in which people ordinarily talk or seem to talk about meanings boil down to two: the having of meanings, which is significance, and sameness of meaning, or synonomy. What is called giving the meaning of an utterance is simply the uttering of a synonym, couched, ordinarily, in clearer language than the original. If we are allergic to meanings as such, we can speak directly of utterances as significant or insignificant, and as synonymous or heteronymous one with another. The problem of explaining these adjectives 'significant' and 'synonymous' with some degree of clarity and rigor - preferably, as I see it, in terms of behavior is as difficult as it is important. 4 But the explanatory value of special and irreducible intermediary entities called meanings is surely illusory. Up to now I have argued that we can use singular terms significantly in sentences without presup-
On What There Is
posing that there are the entities which those terms purport to name. I have argued further that we can usc general terms, for example, predicates, without conceding them to be names of abstract entities. I have argued further that we can view utterances as significant, and as synonymous or heteronymous with one another, without countenancing a realm of entities called meanings. At this point McX begins to wonder whether there is any limit at all to our ontological immunity. Does nothing we may say commit us to the assumption of universals or other entities which we may find unwelcome? I have already suggested a negative answer to this question, in speaking of bound variables, or variables of quantification, in connection with Russell's theory of descriptions. We can very easily involve ourselves in ontological commitments by saying, for example, that there is something (bound variable) which red houses and sunsets have in common; or that there is something which is a prime number larger than a million. But this is, essentially, the only way we can involve ourselves in ontological commitments: by our use of bound variables. The use of alleged names is no criterion, for we can repudiate their namehood at the drop of a hat unless the assumption of a corresponding entity can be spotted in the things we affirm in terms of bound variables. Names are, in fact, altogether immaterial to the ontological issue, for I have shown, in connection with 'Pegasus' and 'pegasize', that names can be converted to descriptions, and Russell has shown that descriptions can be eliminated. Whatever we say with the help of names can be said in a language which shuns names altogether. To be assumed as an entity is, purely and simply, to be reckoned as the value of a variable. In terms of the categories of traditional grammar, this amounts roughly to saying that to be is to be in the range of reference of a pronoun. Pronouns are the basic media of reference; nouns might better have been named propronouns. The variables of quantification, 'something', 'nothing', 'everything', range over our whole ontology, whatever it may be; and we are convicted of a particular ontological presupposition if, and only if, the alleged presupposition has to be reckoned among the entities over which our variables range in order to render one of our affirmations true. We may say, for example, that some dogs are white and not thereby commit ourselves to recognizing either doghood or whiteness as entities. 'Some dogs are white' says that some things that are dogs are white; and, in order that this statement
be true, the things over which the bound variable 'something' ranges must include some white dogs, but need not include doghood or whiteness. On the other hand, when we say that some zoological species are cross-fertile, we are committing ourselves to recognizing as entities the several species themselves, abstract though they are. We remain so committed at least until we devise some way of so paraphrasing the statement as to show that the seeming reference to species on the part of our bound variable was an avoidable manner of speaking. 5 Classical mathematics, as the example of primes larger than a million clearly illustrates, is up to its neck in commitments to an ontology of abstract entities. Thus it is that the great medieval controversy over universals has flared up anew in the modern philosophy of mathematics. The issue is clearer now than of old, because we now have a more explicit standard whereby to decide what ontology a given theory or form of discourse is committed to: a theory is committed to those and only those entities to which the bound variables of the theory must be capable of referring in order that the affirmations made in the theory be true. Because this standard of ontological presupposition did not emerge clearly in the philosophical tradition, the modern philosophical mathematicians have not on the whole recognized that they were debating the same old problem of universals in a newly clarified form. But the fundamental cleavages among modern points of view on foundations of mathematics do come down pretty explicitly to disagreements as to the range of entities to which the bound variables should be permitted to refer. The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentiethcentury surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism. Realism, as the word is used in connection with the medieval controversy over universals, is the Platonic doctrine that universals or abstract entities have being independently of the mind; the mind may discover them but cannot create them. Logicism, represented by Frege, Russell, Whitehead, Church, and Carnap, condones the use of bound variables to refer to abstract entities known and unknown, specifiable and unspecifiable, indiscriminately.
W. V. Quine Conceptualism holds that there are universals but they are mind-made. Intuitionism, espoused in modern times in one form or another by Poincare, Brouwer, Weyl, and others, countenances the use of bound variables to refer to abstract entities only when those entities are capable of being cooked up individually from ingredients specified in advance. As Fraenkel has put it, logicism holds that classes are discovered while intuitionism holds that they are invented - a fair statement indeed of the old opposition between realism and conceptualism. This opposition is no mere quibble; it makes an essential difference in the amount of classical mathematics to which one is willing to subscribe. Logicists, or realists, are able on their assumptions to get Cantor's ascending orders of infinity; intuitionists are compelled to stop with the lowest order of infinity, and, as an indirect consequence, to abandon even some of the classical laws of real numbers. The modern controversy between logicism and intuitionism arose, in fact, from disagreements over infinity. Formalism, associated with the name of Hilbert, echoes intuitionism in deploring the logicist's unbridled recourse to universals. But formalism also finds intuitionism unsatisfactory. This could happen for either of two opposite reasons. The formalist might, like the logicist, object to the crippling of classical mathematics; or he might, like the nominalists of old, object to admitting abstract entities at all, even in the restrained sense of mind-made entities. The upshot is the same: the formalist keeps classical mathematics as a play of insignificant notations. This play of notations can still be of utility - whatever utility it has already shown itself to have as a crutch for physicists and technologists. But utility need not imply significance, in any literal linguistic sense. Nor need the marked success of mathematicians in spinning out theorems, and in finding objective bases for agreement with one another's results, imply significance. For an adequate basis for agreement among mathematicians can be found simply in the rules which govern the manipulation of the notations - these syntactical rules being, unlike the notations themselves, quite significant and intelligible. 6 I have argued that the sort of ontology we adopt can be consequential - notably in connection with mathematics, although this is only an example. Now how are we to adjudicate among rival ontologies? Certainly the answer is not provided by the seman tical formula 'To be is to be the value of a
variable'; this formula serves rather, conversely, in testing the conformity of a given remark or doctrine to a prior ontological standard. We look to bound variables in connection with ontology not in order to know what there is, but in order to know what a given remark or doctrine, ours or someone else's, says there is; and this much is quite properly a problem involving language. But what there is is another question. In debating over what there is, there are still reasons for operating on a seman tical plane. One reason is to escape from the predicament noted at the beginning of this essay: the predicament of my not being able to admit that there are things which McX countenances and I do not. So long as I adhere to my ontology, as opposed to McX's, I cannot allow my bound variables to refer to entities which belong to McX's ontology and not to mine. I can, however, consistently describe our disagreement by characterizing the statements which McX affirms. Provided merely that my ontology countenances linguistic forms, or at least concrete inscriptions and utterances, I can talk about McX's sentences. Another reason for withdrawing to a semantical plane is to find common ground on which to argue. Disagreement in ontology involves basic disagreement in conceptual schemes; yet McX and I, despite these basic disagreements, find that our conceptual schemes converge sufficiently in their intermediate and upper ramifications to enable us to communicate successfully on such topics as politics, weather, and, in particular, language. Insofar as our basic controversy over ontology can be translated upward into a seman tical controversy about words and what to do with them, the collapse of the controversy into question-begging may be delayed. It is no wonder, then, that ontological controversy should tend into controversy over language. But we must not jump to the conclusion that what there is depends on words. Translatability of a question into seman tical terms is no indication that the question is linguistic. To see Naples is to bear a name which, when prefixed to the words 'sees Naples', yields a true sentence; still there is nothing linguistic about seeing Naples. Our acceptance of an ontology is, I think, similar in principle to our acceptance of a scientific theory, say a system of physics: we adopt, at least insofar as we are reasonable, the simplest conceptual scheme into which the disordered fragments of raw experience can be fitted and arranged. Our ontology is
On What There Is
determined once we have fixed upon the over-all conceptual scheme which is to accommodate science in the broadest sense; and the considerations which determine a reasonable construction of any part of that conceptual scheme, for example, the biological or the physical part, are not different in kind from the considerations which determine a reasonable construction of the whole. To whatever extent the adoption of any system of scientific theory may be said to be a matter of language, the same - but no more - may be said of the adoption of an ontology. But simplicity, as a guiding principle in constructing conceptual schemes, is not a clear and unambiguous idea; and it is quite capable of presenting a double or multiple standard. Imagine, for example, that we have devised the most economical set of concepts adequate to the play-by-play reporting of immediate experience. The entities under this scheme - the values of bound variables - are, let us suppose, individual subjective events of sensation or reflection. We should still find, no doubt, that a physicalistic conceptual scheme, purporting to talk about external objects, offers great advantages in simplifying our over-all reports. By bringing together scattered sense events and treating them as perceptions of one object, we reduce the complexity of our stream of experience to a manageable conceptual simplicity. The rule of simplicity is indeed our guiding maxim in assigning sense-data to objects: we associate an earlier and a later round sensum with the same so-called penny, or with two different so-called pennies, in obedience to the demands of maximum simplicity in our total world-picture. Here we have two competing conceptual schemes, a phenomenalistic one and a physicalistic one. Which should prevail? Each has its advantages; each has its special simplicity in its own way. Each, I suggest, deserves to be developed. Each may be said, indeed, to be the more fundamental, though in different senses: the one is epistemologically, the other physically, fundamental. The physical conceptual scheme simplifies our account of experience because of the way myriad scattered sense events come to be associated with single so-called objects; still there is no likelihood that each sentence about physical objects can actually be translated, however deviously and complexly, into the phenomenalistic language. Physical objects are postulated entities which round out and simplify our account of the flux of experience, just as the introduction of irrational
numbers simplifies laws of arithmetic. From the point of view of the conceptual scheme of the elementary arithmetic of rational numbers alone, the broader arithmetic of rational and irrational numbers would have the status of a convenient myth, simpler than the literal truth (namely, the arithmetic of rationals) and yet containing that literal truth as a scattered part. Similarly, from a phenomenalistic point of view, the conceptual scheme of physical objects is a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part. 7 Now what of classes or attributes of physical objects, in turn? A platonistic ontology of this sort is, from the point of view of a strictly physicalistic conceptual scheme, as much a myth as that physicalistic conceptual scheme itself is for phenomenalism. This higher myth is a good and useful one, in turn, insofar as it simplifies our account of physics. Since mathematics is an integral part of this higher myth, the utility of this myth for physical science is evident enough. In speaking of it nevertheless as a myth, I echo that philosophy of mathematics to which I alluded earlier under the name of formalism. But an attitude of formalism may with equal justice be adopted toward the physical conceptual scheme, in turn, by the pure aesthete or phenomenalist. The analogy between the myth of mathematics and the myth of physics is, in some additional and perhaps fortuitous ways, strikingly close. Consider, for example, the crisis which was precipitated in the foundations of mathematics, at the turn of the century, by the discovery of Russell's paradox and other antinomies of set theory. These contradictions had to be obviated by unintuitive, ad hoc devices; our mathematical myth-making became deliberate and evident to all. But what of physics? An antinomy arose between the undular and the corpuscular accounts oflight; and if this was not as out-and-out a contradiction as Russell's paradox, I suspect that the reason is that physics is not as outand-out as mathematics. Again, the second great modern crisis in the foundations of mathematics precipitated in 1931 by Giidel's proof that there are bound to be undecidable statements in arithmetic8 - has its companion piece in physics in Heisenberg's indeterminacy principle. In earlier pages I undertook to show that some common arguments in favor of certain ontologies are fallacious. Further, I advanced an explicit standard whereby to decide what the ontological commitments of a theory are. But the question
W. V. Quine what ontology actually to adopt still stands open, and the obvious counsel is tolerance and an experimental spirit. Let us by all means see how much of the physicalistic conceptual scheme can be reduced to a phenomenalistic one; still, physics also naturally demands pursuing, irreducible in toto though it be. Let us see how, or to what degree, natural science may be rendered independent of platonistic mathematics; but let us also pursue mathematics and delve into its platonistic foundations.
From among the vanous conceptual schemes best suited to these various pursuits, one - the phenomenalistic - claims epistemological priority. Viewed from within the phenomenalistic conceptual scheme, the ontologies of physical objects and mathematical objects are myths. The quality of myth, however, is relative; relative, in this case, to the epistemological point of view. This point of view is one among various, corresponding to one among our various interests and purposes.
Notes The impulse to distinguish terminologically between existence as applied to objects actualized somewhere in space-time and existence (or subsistence or being) as applied to other entities arises in part, perhaps, from an idea that the observation of nature is relevant only to questions of existence of the first kind. But this idea is readily refuted by counter-instances such as 'the ratio of the number of centaurs to the number of unicorns'. If there were such a ratio, it would be an abstract entity, viz., a number. Yet it is only by studying nature that we conclude that the number of centaurs and the number of unicorns are both 0 and hence that there is no such ratio. 2 Alonzo Church, 'A note on the Entscheidungsproblem', Journal oJSymbolic Logic I (1936), pp. 40-1,101-2. 3 Gottlob Frege, 'On sense and nominatum', in Herbert Feigl and Wilfrid Sellars (eds), Readings in Philosophtcal Analysts (New York: Appleton-CenturyCrofts, 1949), pp. 85-102.
4 See 'Two dogmas of empiricism' and 'The problem of meaning in linguistics', in W. V. Qt.iine, From a Logical Point oj View (Cambridge, Mass.: Harvard University Press, 1953). W. V. Quine, 'Logic and the reification of universals', in From a Logical Point oJ View. 6 See Nelson Goodman and W. V. Qt.iine, 'Steps toward a constructive nominalism', Journal oj Symbolic Logic 12 (1947), pp. 105-22. 7 The arithmetical analogy is due to Philip Frank, Modern Science and its Philosophy (Cambridge, Mass.: Harvard University Press, 1949), pp. 108f. 8 Kurt Giidel, 'Uber formal unertscheidbare Siitze der Principia Mathematica und verwandter Systeme', Monatshejie jiir Mathematik und Physik 38 (1931), pp. 173-98.
Rudolf Carnap
1 The Problem of Abstract Entities Empiricists are in general rather suspicious with respect to any kind of abstract entities like properties, classes, relations, numbers, propositions, etc. They usually feel much more in sympathy with nominalists than with realists (in the medieval sense). As far as possible they try to avoid any reference to abstract entities and to restrict themselves to what is sometimes called a nominalistic language, i.e., one not containing such references. However, within certain scientific contexts it seems hardly possible to avoid them. In the case of mathematics, some empiricists try to find a way out by treating the whole of mathematics as a mere calculus, a formal system for which no interpretation is given or can be given. Accordingly, the mathematician is said to speak not about numbers, functions, and infinite classes, but merely about meaningless symbols and formulas manipulated according to given formal rules. In physics it is more difficult to shun the suspected entities, because the language of physics serves for the communication of reports and predictions and hence cannot be taken as a mere calculus. A physicist who is suspicious of abstract entities may perhaps try to declare a certain part of the language of physics as uninterpreted and uninterpretable, that part which Originally published in Meaning and Necessity (Chicago: University of Chicago Press, 1956), pp. 205-21. Reprinted by permission of the University of Chicago Press.
refers to real numbers as space-time coordinates or as values of physical magnitudes, to functions, limits, etc. More probably he will just speak about all these things like anybody else but with an uneasy conscience, like a man who in his everyday life does with qualms many things which are not in accord with the high moral principles he professes on Sundays. Recently the problem of abstract entities has arisen again in connection with semantics, the theory of meaning and truth. Some semanticists say that certain expressions designate certain entities, and among these designated entities they include not only concrete material things but also abstract entities, e.g., properties as designated by predicates and propositions as designated by sentences. 1 Others object strongly to this procedure as violating the basic principles of empiricism and leading back to a metaphysical ontology of the Platonic kind. It is the purpose of this article to clarify this controversial issue. The nature and implications of the acceptance of a language referring to abstract entities will first be discussed in general; it will be shown that using such a language does not imply embracing a Platonic ontology but is perfectly compatible with empiricism and strictly scientific thinking. Then the special question of the role of abstract entities in semantics will be discussed. It is hoped that the clarification of the issue will be useful to those who would like to accept abstract entities in their work in mathematics, physics, semantics, or any other field; it may help them to overcome nominalistic scruples.
Rudolf Carnap
2
Linguistic Frameworks
Are there properties, classes, numbers, propositions? In order to understand more clearly the nature of these and related problems, it is above all necessary to recognize a fundamental distinction between two kinds of questions concerning the existence or reality of entities. If someone wishes to speak in his language about a new kind of entities, he has to introduce a system of new ways of speaking, subject to new rules; we shall call this procedure the construction of a linguistic framework for the new entities in question. And now we must distinguish two kinds of questions of existence: first, questions of the existence of certain entities of the new kind within the framework; we call them internal questions; and second, questions concerning the existence or reality of the system of entities as a whole, called external questions. Internal questions and possible answers to them are formulated with the help of the new forms of expressions. The answers may be found either by purely logical methods or by empirical methods, depending upon whether the framework is a logical or a factual one. An external question is of a problematic character which is in need of closer examination. The world of things. Let us consider as an example the simplest kind of entities dealt with in the everyday language: the spatio-temporally ordered system of observable things and events. Once we have accepted the thing language with its framework for things, we can raise and answer internal questions, e.g., "Is there a white piece of paper on my desk? ," "Did King Arthur actually live?," "Are unicorns and centaurs real or merely imaginary? ," and the like. These questions are to be answered by empirical investigations. Results of observations are evaluated according to certain rules as confirming or disconfirming evidence for possible answers. (This evaluation is usually carried out, of course, as a matter of habit rather than a deliberate, rational procedure. But it is possible, in a rational reconstruction, to lay down explicit rules for the evaluation. This is one of the main tasks of a pure, as distinguished from a psychological, epistemology.) The concept of reality occurring in these internal questions is an empirical, scientific, nonmetaphysical concept. To recognize something as a real thing or event means to succeed in incorporating it into the system of things at a particular spacetime position so that it fits together with the other
things recognized as real, according to the rules of the framework. From these questions we must distinguish the external question of the reality of the thing world itself. In contrast to the former questions, this question is raised neither by the man in the street nor by scientists, but only by philosophers. Realists give an affirmative answer, subjective idealists a negative one, and the controversy goes on for centuries without ever being solved. And it cannot be solved because it is framed in a wrong way. To be real in the scientific sense means to be an element of the system; hence this concept cannot be meaningfully applied to the system itself. Those who raise the question of the reality of the thing world itself have perhaps in mind not a theoretical question, as their formulation seems to suggest, but rather a practical question, a matter of a practical decision concerning the structure of our language. We have to make the choice whether or not to accept and use the forms of expression in the framework in question. In the case of this particular example, there is usually no deliberate choice because we all have accepted the thing language early in our lives as a matter of course. Nevertheless, we may regard it as a matter of decision in this sense: we are free to choose to continue using the thing language or not; in the latter case we could restrict ourselves to a language of sense-data and other 'phenomenal' entities, or construct an alternative to the customary thing language with another structure, or, finally, we could refrain from speaking. If someone decides to accept the thing language, there is no objection against saying that he has accepted the world of things. But this must not be interpreted as if it meant his acceptance of a beliefin the reality of the thing world; there is no such belief or assertion or assumption, because it is not a theoretical question. To accept the thing world means nothing more than to accept a certain form of language, in other words, to accept rules for forming statements and for testing, accepting, or rejecting them. The acceptance of the thing language leads, on the basis of observations made, also to the acceptance, belief, and assertion of certain statements. But the thesis of the reality of the thing world cannot be among these statements, because it cannot be formulated in the thing language or, it seems, in any other theoretical language. The decision of accepting the thing language, although itself not of a cognitive nature, will nevertheless usually be influenced by theoretical know-
Empiricism, Semantics, and Ontology
ledge, just like any other deliberate decision concerning the acceptance of linguistic or other rules. The purposes for which the language is intended to be used, for instance, the purpose of communicating factual knowledge, will determine which factors are relevant for the decision. The efficiency, fruitfulness, and simplicity of the use of the thing language may be among the decisive factors. And the questions concerning these qualities are indeed of a theoretical nature. But these questions cannot be identified with the question of realism. They are not yes-no questions but questions of degree. The thing language in the customary form works indeed with a high degree of efficiency for most purposes of everyday life. This is a matter of fact, based upon the content of our experiences. However, it would be wrong to describe this situation by saying: "The fact of the efficiency of the thing language is confirming evidence for the reality of the thing world"; we should rather say instead: "This fact makes it advisable to accept the thing language." The system of numbers. As an example of a system which is of a logical rather than a factual nature let us take the system of natural numbers. The framework for this system is constructed by introducing into the language new expressions with suitable rules: (1) numerals like "five" and sentence forms like "there are five books on the table"; (2) the general term "number" for the new entities, and sentence forms like "five is a number"; (3) expressions for properties of numbers (e.g., "odd," "prime"), relations (e.g., "greater than"), and functions (e.g., "plus"), and sentence forms like "two plus three is five"; (4) numerical variables ("m," "n," etc.) and quantifiers for universal sentences ("for every n, ... ") and existential sentences ("there is an n such that ... ") with the customary deductive rules. Here again there are internal questions, e.g., "Is there a prime number greater than a hundred?" Here, however, the answers are found, not by empirical investigation based on observations, but by logical analysis based on the rules for the new expressions. Therefore the answers are here analytic, i.e., logically true. What is now the nature of the philosophical question concerning the existence or reality of numbers? To begin with, there is the internal question which, together with the affirmative answer, can be formulated in the new terms, say, by "There are numbes" or, more explicitly, "There is an n such that n is a number." This statement follows
from the analytic statement "five is a number" and is therefore itself analytic. Moreover, it is rather trivial (in contradistinction to a statement like "There is a prime number greater than a million," which is likewise analytic but far from trivial), because it does not say more than that the new system is not empty; but this is immediately seen from the rule which states that words like "five" are substitutable for the new variables. Therefore nobody who meant the question "Are there numbers?" in the internal sense would either assert or even seriously consider a negative answer. This makes it plausible to assume that those philosophers who treat the question of the existence of numbers as a serious philosophical problem and offer lengthy arguments on either side, do not have in mind the internal question. And, indeed, if we were to ask them: "Do you mean the question as to whether the framework of numbers, if we were to accept it, would be found to be empty or not?," they would probably reply: "Not at all; we mean a question prior to the acceptance of the new framework." They might try to explain what they mean by saying that it is a question of the ontological status of numbers; the question whether or not numbers have a certain metaphysical characteristic called reality (but a kind of ideal reality, different from the material reality of the thing world) or subsistence or status of "independent entities." Unfortunately, these philosophers have so far not given a formulation of their question in terms of the common scientific language. Therefore our judgment must be that they have not succeeded in giving to the external question and to the possible answers any cognitive content. Unless and until they supply a clear cognitive interpretation, we are justified in our suspicion that their question is a pseudo-question, that is, one disguised in the form of a theoretical question while in fact it is nontheoretical; in the present case it is the practical problem whether or not to incorporate into the language the new linguistic forms which constitute the framework of numbers. The system ofpropositions. New variables, "p," "q," etc., are introduced with a rule to the effect that any (declarative) sentence may be substituted for a variable of this kind; this includes, in addition to the sentences of the original thing language, also all general sentences with variables of any kind which may have been introduced into the language. Further, the general term "proposition" is introduced. "p is a proposition" may be defined by "p or
Rudolf Carnap notp" (or by any other sentence form yielding only analytic sentences). Therefore, every sentence of the form " ... is a proposition" (where any sentence may stand in the place of the dots) is analytic. This holds, for example, for the sentence:
(a)
"Chicago is large is a proposition."
(We disregard here the fact that the rules of English grammar require not a sentence but a that-clause as the subject of another sentence; accordingly, instead of (a) we should have to say "That Chicago is large is a proposition".) Predicates may be admitted whose argument expressions are sentences; these predicates may be either extensional (e.g., the customary truth-functional connectives) or not (e.g., modal predicates like "possible," "necessary," etc.). With the help of the new variables, general sentences may be formed, e.g., (b) (c) (d)
"For every p, either p or not-p." "There is ap such thatp is not necessary and not-p is not necessary." "There is a p such that p is a proposition."
(c) and (d) are internal assertions of existence. The statement "There are propositions" may be meant in the sense of (d); in this case it is analytic (since it follows from (a» and even trivial. If, however, the statement is meant in an external sense, then it is noncognitive. It is important to notice that the system of rules for the linguistic expressions of the propositional framework (of which only a few rules have here been briefly indicated) is sufficient for the introduction of the framework. Any further explanations as to the nature of the propositions (i.e., the elements of the system indicated, the values of the variables "p," "q," etc.) are theoretically unnecessary because, if correct, they follow from the rules. For example, are propositions mental events (as in Russell's theory)? A look at the rules shows us that they are not, because otherwise existential statements would be of the form: "If the mental state of the person in question fulfils such and such conditions, then there is a p such that .... " The fact that no references to mental conditions occur in existential statements (like (c), (d), etc.) shows that propositions are not mental entities. Further, a statement of the existence of linguistic entities (e.g., expressions, classes of expressions, etc.) must contain a reference to a language. The fact
that no such reference occurs in the existential statements here shows that propositions are not linguistic entities. The fact that in these statements no reference to a subject (an observer or knower) occurs (nothing like: "There is a p which is necessary for Mr X") shows that the propositions (and their properties, like necessity, etc.) are not subjective. Although characterizations of these or similar kinds are, strictly speaking, unnecessary, they may nevertheless be practically useful. If they are given, they should be understood, not as ingredient parts of the system, but merely as marginal notes with the purpose of supplying to the reader helpful hints or convenient pictorial associations which may make his learning of the use of the expressions easier than the bare system of the rules would do. Such a characterization is analogous to an extra-systematic explanation which a physicist sometimes gives to the beginner. He might, for example, tell him to imagine the atoms of a gas as small balls rushing around with great speed, or the electromagnetic field and its oscillations as quasielastic tensions and vibrations in an ether. In fact, however, all that can accurately be said about atoms or the field is implicitly contained in the physical laws of the theories in question. 2 The system of thing properties. The thing language contains words like "red," "hard," "stone," "house," etc., which are used for describing what things are like. Now we may introduce new variables, say "f," "g," etc., for which those words are substitutable and furthermore the general term "property." New rules are laid down which admit sentences like "Red is a property," "Red is a color," "These two pieces of paper have at least one color in common" (i.e., "There is anfsuch that fis a color, and ... "). The last sentence is an internal assertion. It is of an empirical, factual nature. However, the external statement, the philosophical statement of the reality of properties - a special case of the thesis of the reality of universals - is devoid of cognitive content. The ~ystems of integers and rational numbers. Into a language containing the framework of natural numbers we may introduce first the (positive and negative) integers as relations among natural numbers and then the rational numbers as relations among integers. This involves introducing new types of variables, expressions substitutable for them, and the general terms "integer" and "rational number."
Empiricism, Semantics, and Ontology The system of real numbers. On the basis of the rational numbers, the real numbers may be introduced as classes of a special kind (segments) of rational numbers (according to the method developed by Dedekind and Frege). Here again a new type of variables is introduced, expressions substitutable for them (e.g., "v!z"), and the general term "real number." The spatia-temporal coordinate system for physics. The new entities are the space-time points. Each is an ordered quadruple of four real numbers, called its coordinates, consisting of three spatial and one temporal coordinates. The physical state of a spatio-temporal point or region is described either with the help of qualitative predicates (e.g., "hot") or by ascribing numbers as values of a physical magnitude (e.g., mass, temperature, and the like). The step from the system of things (which does not contain space-time points but only extended objects with spatial and temporal relations between them) to the physical coordinate system is again a matter of decision. Our choice of certain features, although itself not theoretical, is suggested by theoretical knowledge, either logical or factual. For example, the choice of real numbers rather than rational numbers or integers as coordinates is not much influenced by the facts of experience but mainly due to considerations of mathematical simplicity. The restriction to rational coordinates would not be in conflict with any experimental knowledge we have, because the result of any measurement is a rational number. However, it would prevent the use of ordinary geometry (which says, e.g., that the diagonal of a square with the side 1 has the irrational value v!z) and thus lead to great complications. On the other hand, the decision to use three rather than two or four spatial coordinates is strongly suggested, but still not forced upon us, by the result of common observations. If certain events allegedly observed in spiritualistic seances, e.g., a ball moving out of a sealed box, were confirmed beyond any reasonable doubt, it might seem advisable to use four spatial coordinates. Internal questions are here, in general, empirical questions to be answered by empirical investigations. On the other hand, the external questions of the reality of physical space and physical time are pseudo-questions. A question like "Are there (really) space-time points?" is ambiguous. It may be meant as an internal question; then the affirmative answer is, of course, analytic and trivial. Or it may be meant in the external sense:
"Shall we introduce such and such forms into our language?"; in this case it is not a theoretical but a practical question, a matter of decision rather than assertion, and hence the proposed formulation would be misleading. Or finally, it may be meant in the following sense: "Are our experiences such that the use of the linguistic forms in question will be expedient and fruitful?" This is a theoretical question of a factual, empirical nature. But it concerns a matter of degree; therefore a formulation in the form "real or not?" would be inadequate.
3 What does Acceptance of a Kind of Entities Mean? Let us now summarize the essential characteristics of situations involving the introduction of a new kind of entities, characteristics which are common to the various examples outlined above. The acceptance of a new kind of entities is represented in the language by the introduction of a framework of new forms of expressions to be used according to a new set of rules. There may be new names for particular entities of the kind in question; but some such names may already occur in the language before the introduction of the new framework. (Thus, for example, the thing language contains certainly words of the type of "blue" and "house" before the framework of properties is introduced; and it may contain words like "ten" in sentences of the form "I have ten fingers" before the framework of numbers is introduced.) The latter fact shows that the occurrence of constants of the type in question - regarded as names of entities of the new kind after the new framework is introduced - is not a sure sign of the acceptance of the new kind of entities. Therefore the introduction of such constants is not to be regarded as an essential step in the introduction of the framework. The two essential steps are rather the following. First, the introduction of a general term, a predicate of higher level, for the new kind of entities, permitting us to say of any particular entity that it belongs to this kind (e.g., "Red is a property," "Five is a number"). Second, the introduction of variables of the new type. The new entities are values of these variables; the constants (and the closed compound expressions, if any) are substitutable for the variables. 3 With the help of the variables, general sentences concerning the new entities can be formulated. After the new forms are introduced into the language, it is possible to formulate with their
Rudolf Carnap
help internal questions and possible answers to them. A question of this kind may be either empiricalor logical; accordingly a true answer is either factually true or analytic. From the internal questions we must clearly distinguish external questions, i.e., philosophical questions concerning the existence or reality of the total system of the new entities. Many philosophers regard a question of this kind as an ontological question which must be raised and answered before the introduction of the new language forms. The latter introduction, they believe, is legitimate only if it can be justified by an ontological insight supplying an affirmative answer to the question of reality. In contrast to this view, we take the position that the introduction of the new ways of speaking does not need any theoretical justification because it does not imply any assertion of reality. We may still speak (and have done so) of "the acceptance of the new entities," since this form of speech is customary; but one must keep in mind that this phrase does not mean for us anything more than acceptance of the new framework, i.e., of the new linguistic forms. Above all, it must not be interpreted as referring to an assumption, belief, or assertion of "the reality of the entities." There is no such assertion. An alleged statement of the reality of the system of entities is a pseudo-statement without cognitive content. To be sure, we have to face at this point an important question; but it is a practical, not a theoretical question; it is the question of whether or not to accept the new linguistic forms. The acceptance cannot be judged as being either true or false because it is not an assertion. It can only be judged as being more or less expedient, fruitful, conducive to the aim for which the language is intended. Judgments of this kind supply the motivation for the decision of accepting or rejecting the kind of entities. 4 Thus it is clear that the acceptance of a linguistic framework must not be regarded as implying a metaphysical doctrine concerning the reality of the entities in question. It seems to me due to a neglect of this important distinction that some contemporary nominalists label the admission of variables of abstract types as "Platonism."s This is, to say the least, an extremely misleading terminology. It leads to the absurd consequence that the position of everybody who accepts the language of physics with its real number variables (as a language of communication, not merely as a calculus) would be called Platonistic, even ifhe is a strict empiricist who rejects Platonic metaphysics.
A brief historical remark may here be inserted. The noncognitive character of the questions which we have called here external questions was recognized and emphasized already by the Vienna Circle under the leadership of Moritz Schlick, the group from which the movement of logical empiricism originated. Influenced by ideas of Ludwig Wittgenstein, the Circle rejected both the thesis of the reality of the external world and the thesis of its irreality as pseudo-statements;6 the same was the case for both the thesis of the reality of universals (abstract entities, in our present terminology) and the nominalistic thesis that they are not real and that their alleged names are not names of anything but merely flatus vocis. (It is obvious that the apparent negation of a pseudo-statement must also be a pseudo-statement.) It is therefore not correct to classify the members of the Vienna Circle as nominalists, as is sometimes done. However, if we look at the basic anti-metaphysical and pro-scientific attitude of most nominalists (and the same holds for many materialists and realists in the modern sense), disregarding their occasional pseudotheoretical formulations, then it is, of course, true to say that the Vienna Circle was much closer to those philosophers than to their opponents.
4
Abstract Entities in Semantics
The problem of the legitimacy and the status of abstract entities has recently again led to controversial discussions in connection with semantics. In a semantical meaning analysis certain expressions in a language are often said to designate (or name or denote or signify or refer to) certain extra-linguistic entities. 7 As long as physical things or events (e.g., Chicago or Caesar's death) are taken as designata (entities designated), no serious doubts arise. But strong objections have been raised, especially by some empiricists, against abstract entities as designata, e.g., against seman tical statements of the following kind: (I) (2) (3) (4) (5)
"The word 'red' designates a property of things." "The word 'color' designates a property of properties of things." "The word 'five' designates a number." "The word 'odd' designates a property of numbers." "The sentence 'Chicago is large' designates a proposition."
Empiricism, Semantics, and Ontology
Those who criticize these statements do not, of course, reject the use of the expressions in question, like "red" or "five"; nor would they deny that these expressions are meaningful. But to be meaningful, they would say, is not the same as having a meaning in the sense of an entity designated. They reject the belief, which they regard as implicitly presupposed by those seman tical statements, that to each expression of the types in question (adjectives like "red," numerals like "five," etc.) there is a particular real entity to which the expression stands in the relation of designation. This belief is rejected as incompatible with the basic principles of empiricism or of scientific thinking. Derogatory labels like "Platonic realism," "hypostatization," or "'Fido'-Fido principle" are attached to it. The latter is the name given by Gilbert Ryle to the criticized belief, which, in his view, arises by a naIve inference of analogy: just as there is an entity well known to me, viz., my dog Fido, which is designated by the name "Fido," thus there must be for every meaningful expression a particular entity to which it stands in the relation of designation or naming, i.e., the relation exemplified by "Fido"-Fido. 8 The belief criticized is thus a case ofhypostatization, i.e., of treating as names expressions which are not names. While "Fido" is a name, expressions like "red," "five," etc. are said not to be names, not to designate anything. Our previous discussion concerning the acceptance of frameworks enables us now to clarify the situation with respect to abstract entities as designata. Let us take as an example the statement: (a)
"'Five' designates a number."
The formulation of this statement presupposes that our language L contains the forms of expressions which we have called the framework of numbers, in particular, numerical variables and the general term "number." If L contains these forms, the following is an analytic statement in L: (b)
"Five is a number."
Further, to make the statement (a) possible, L must contain an expression like "designates" or "is a name of" for the seman tical relation of designation. If suitable rules for this term are laid down, the following is likewise analytic: (c)
"'Five' designates five."
(Generally speaking, any expression of the form "' ... ' designates ... " is an analytic statement provided the term " ... " is a constant in an accepted framework. If the latter condition is not fulfilled, the expression is not a statement.) Since (a) follows from (c) and (b), (a) is likewise analytic. Thus it is clear that if someone accepts the framework of numbers, then he must acknowledge (c) and (b) and hence (a) as true statements. Generally speaking, if someone accepts a framework for a certain kind of entities, then he is bound to admit the entities as possible designata. Thus the question of the admissibility of entities of a certain type or of abstract entities in general as designata is reduced to the question of the acceptability of the linguistic framework for those entities. Both the nominalistic critics, who refuse the status of designators or names to expressions like "red," "five," etc., because they deny the existence of abstract entities, and the skeptics, who express doubts concerning the existence and demand evidence for it, treat the question of existence as a theoretical question. They do, of course, not mean the internal question; the affirmative answer to this question is analytic and trivial and too obvious for doubt or denial, as we have seen. Their doubts refer rather to the system of entities itself; hence they mean the external question. They believe that only after making sure that there really is a system of entities of the kind in question are we justified in accepting the framework by incorporating the linguistic forms into our language. However, we have seen that the external question is not a theoretical question but rather the practical question whether or not to accept those linguistic forms. This acceptance is not in need of a theoretical justification (except with respect to expediency and fruitfulness), because it does not imply a belief or assertion. Ryle says that the "Fido"-Fido principle is "a grotesque theory." Grotesque or not, Ryle is wrong in calling it a theory. It is rather the practical decision to accept certain frameworks. Maybe Ryle is historically right with respect to those whom he mentions as previous representatives of the principle, viz., John Stuart Mill, Frege, and Russell. If these philosophers regarded the acceptance of a system of entities as a theory, an assertion, they were victims of the same old, metaphysical confusion. But it is certainly wrong to regard my seman tical method as involving a belief in the reality of abstract entities, since I reject a thesis of this kind as a metaphysical pseudostatement.
Rudolf Carnap
The critics of the use of abstract entities In semantics overlook the fundamental difference between the acceptance of a system of entities and an internal assertion, e.g., an assertion that there are elephants or electrons or prime numbers greater than a million. Whoever makes an internal assertion is certainly obliged to justify it by providing evidence, empirical evidence in the case of electrons, logical proof in the case of the prime numbers. The demand for a theoretical justification, correct in the case of internal assertions, is sometimes wrongly applied to the acceptance of a system of entities. Thus, for example, Ernest Nagel asks for "evidence relevant for affirming with warrant that there are such entities as infinitesimals or propositions.,,9 He characterizes the evidence required in these cases - in distinction to the empirical evidence in the case of electrons - as "in the broad sense logical and dialectical." Beyond this no hint is given as to what might be regarded as relevant evidence. Some nominalists regard the acceptance of abstract entities as a kind of superstition or myth, populating the world with fictitious or at least dubious entities, analogous to the belief in centaurs or demons. This shows again the confusion mentioned, because a superstition or myth is a false (or dubious) internal statement. Let us take as example the natural numbers as cardinal numbers, i.e., in contexts like "Here are three books." The linguistic forms of the framework of numbers, including variables and the general term "number," are generally used in our common language of communication; and it is easy to formulate explicit rules for their use. Thus the logical characteristics of this framework are sufficiently clear (while many internal questions, i.e., arithmetical questions, are, of course, still open). In spite of this, the controversy concerning the external question of the ontological reality of the system of numbers continues. Suppose that one philosopher says: "I believe that there are numbers as real entities. This gives me the right to use the linguistic forms of the numerical framework and to make semantical statements about numbers as designata of numerals." His nominalistic opponent replies: "You are wrong; there are no numbers. The numerals may still be used as meaningful expressions. But they are not names, there are no entities designated by them. Therefore the word 'number' and numerical variables must not be used (unless a way were found to introduce them as merely abbreviating devices, a way of
translating them into the nominalistic thing language)." I cannot think of any possible evidence that would be regarded as relevant by both philosophers, and therefore, if actually found, would decide the controversy or at least make one of the opposite theses more probable than the other. (To construe the numbers as classes or properties of the second level, according to the Frege-Russell method, does, of course, not solve the controversy, because the first philosopher would affirm and the second deny the existence of the system of classes or properties of the second level.) Therefore I feel compelled to regard the external question as a pseudo-question, until both parties to the controversy offer a common interpretation of the question as a cognitive question; this would involve an indication of possible evidence regarded as relevant by both sides. There is a particular kind of misinterpretation of the acceptance of abstract entities in various fields of science and in semantics that needs to be cleared up. Certain early British empiricists (e.g., Berkeley and Hume) denied the existence of abstract entities on the ground that immediate experience presents us only with particulars, not with universals, e.g., with this red patch, but not with Redness or Colorin-General; with this scalene triangle, but not with Scalene Triangularity or Triangularity-in-General. Only entities belonging to a type of which examples were to be found within immediate experience could be accepted as ultimate constituents of reality. Thus, according to this way of thinking, the existence of abstract entities could be asserted only if one could show either that some abstract entities fall within the given, or that abstract entities can be defined in terms of the types of entity which are given. Since these empiricists found no abstract entities within the realm of sense-data, they either denied their existence, or else made a futile attempt to define universals in terms of particulars. Some contemporary philosophers, especially English philosophers following Bertrand Russell, think in basically similar terms. They emphasize a distinction between the data (that which is immediately given in consciousness, e.g., sense-data, immediately past experiences, etc.) and the constructs based on the data. Existence or reality is ascribed only to the data; the constructs are not real entities; the corresponding linguistic expressions are merely ways of speech not actually designating anything (reminiscent of the nominalists' flatus vocis). We shall not criticize here this general conception. (As far as it is a
Empiricism, Semantics, and Ontology
principle of accepting certain entitles and not accepting others, leaving aside any ontological, phenomenalistic, and nominalistic pseudo-statements, there cannot be any theoretical objection to it.) But if this conception leads to the view that other philosophers or scientists who accept abstract entities thereby assert or imply their occurrence as immediate data, then such a view must be rejected as a misinterpretation. References to space-time points, the electromagnetic field, or electrons in physics, to real or complex numbers and their functions in mathematics, to the excitatory potential or unconscious complexes in psychology, to an inflationary trend in economics, and the like, do not imply the assertion that entities of these kinds occur as immediate data. And the same holds for references to abstract entities as designata in semantics. Some of the criticisms by English philosophers against such references give the impression that, probably due to the misinterpretaion just indicated, they accuse the semanticist not so much of bad metaphysics (as some nominalists would do) but of bad psychology. The fact that they regard a seman tical method involving abstract entities not merely as doubtful and perhaps wrong, but as manifestly absurd, preposterous and grotesque, and that they show a deep horror and indignation against this method, is perhaps to be explained by a misinterpretation of the kind described. In fact, of course, the semanticist does not in the least assert or imply that the abstract entities to which he refers can be experienced as immediately given either by sensation or by a kind of rational intuition. An assertion of this kind would indeed be very dubious psychology. The psychological question as to which kinds of entities do and which do not occur as immediate data is entirely irrelevant for semantics, just as it is for physics, mathematics, economics, etc., with respect to the examples mentioned above. 10
5 Conclusion For those who want to develop or use semantical methods, the decisive question is not the alleged ontological question of the existence of abstract entities but rather the question whether the use of abstract linguistic forms or, in technical terms, the use of variables beyond those for things (or phe-
nomenal data) is expedient and fruitful for the purposes for which semantical analyses are made, viz., the analysis, interpretation, clarification, or construction of languages of communication, especially languages of science. This question is here neither decided nor even discussed. It is not a question simply of yes or no, but a matter of degree. Among those philosophers who have carried out seman tical analyses and thought about suitable tools for this work, beginning with Plato and Aristotle and, in a more technical way on the basis of modern logic, with C. S. Peirce and Frege, a great majority accepted abstract entities. This does, of course, not prove the case. After all, semantics in the technical sense is still in the initial phases of its development, and we must be prepared for possible fundamental changes in methods. Let us therefore admit that the nominalistic critics may possibly be right. But if so, they will have to offer better arguments than they have so far. Appeal to ontological insight will not carry much weight. The critics will have to show that it is possible to construct a seman tical method which avoids all references to abstract entities and achieves by simpler means essentially the same results as the other methods. The acceptance or rejection of abstract linguistic forms, just as the acceptance or rejection of any other linguistic forms in any branch of science, will finally be decided by their efficiency as instruments, the ratio of the results achieved to the amount and complexity of the efforts required. To decree dogmatic prohibitions of certain linguistic forms instead of testing them by their success or failure in practical use, is worse than futile; it is positively harmful because it may obstruct scientific progress. The history of science shows exam pies of such prohibitions based on prejudices deriving from religious, mythological, metaphysical, or other irrational sources, which slowed up the developments for shorter or longer periods of time. Let us learn from the lessons of history. Let us grant to those who work in any special field of investigation the freedom to use any form of expression which seems useful to them; the work in the field will sooner or later lead to the elimination of those forms which have no useful function. Let us be cautious in making assertions and critical in examining them, but tolerant in permitting linguistic forms.
Rudolf Carnap
Notes The terms "sentence" and "statement" are here used synonymously for declarative (indicative, propositional) sentences. 2 In my book Meaning and Necessity (Chicago: University of Chicago Press, 1947) I have developed a semantical method which takes propositions as entities designated by sentences (more specifically, as intensions of sentences). In order to facilitate the understanding of the systematic development, I added some informal, extra-systematic explanations concerning the nature of propositions. I said that the term "proposition" "is used neither for a linguistic expression nor for a subjective, mental occurrence, but rather for something objective that mayor may not be exemplified in nature .... We apply the term 'proposition' to any entities of a certain logical type, namely, those that may be expressed by (declarative) sentences in a language" (p. 27). After some more detailed discussions concerning the relation between propositions and facts, and the nature of false propositions, I added: "It has been the purpose of the preceding remarks to facilitate the understanding of our conception of propositions. If, however, a reader should find these explanations more puzzling than clarifying, or even unacceptable, he may disregard them" (p. 31) (that is, disregard these extra-systematic explanations, not the whole theory of the propositions as intensions of sentences, as one reviewer understood). In spite of this warning, it seems that some of those readers who were puzzled by the explanations, did not disregard them but thought that by raising objections against them they could refute the theory. This is analogous to the procedure of some laymen who by (correctly) criticizing the ether picture or other visualizations of physical theories, thought they had refuted those theories. Perhaps the discussions in the present paper will help in clarifying the role of the system of linguistic rules for the introduction of a framework for entities on the one hand, and that of extra-systematic explanations concerning the nature of the entities on the other. 3 W. V. Quine was the first to recognize the importance of the introduction of variables as indicating the acceptance of entities. "The ontology to which one's use of language commits him comprises simply the objects that he treats as falling ... within the range of values of his variables" (W. V. Quine, "Notes on existence and necessity," Journal of Philosophy 40 (1943), pp. 113~27, at p. 118; compare also his "Designation and existence," Journal of Philosophy 36 (1939), pp. 702~9, and "On universals," Journal of Symbolic Logic 12 (1947), pp. 74-84. 4 For a closely related point of view on these questions see the detailed discussions in Herbert Feigl, "Existential hypotheses," Philosophy of Science 17 (1950), pp. 35~62.
Paul Bernays, "Sur Ie platonisme dans les mathematiques," L 'Enseignement math. 34 (1935), pp. 52~69. W. V. Quine, see previous note and a recent paper "On what there is," this volume, ch. I, Quine does not acknowledge the distinction which I emphasize above, because according to his general conception there are no sharp boundary lines between logical and factual truth, between questions of meaning and questions offact, between the acceptance of a language structure and the acceptance of an assertion formulated in the language. This conception, which seems to deviate considerably from customary ways of thinking, will be explained in his article "Semantics and abstract objects," Proceedings ofthe American Academy of Arts and Sciences 80 (1951), pp. 90-6. When Quine in the above article classifies my logicistic conception of mathematics (derived from Frege and Russell) as "platonic realism" (p. 9), this is meant (according to a personal communication from him) not as ascribing to me agreement with Plato's metaphysical doctrine of universals, but merely as referring to the fact that I accept a language of mathematics containing variables of higher levels. With respect to the basic attitude to take in choosing a language form (an "ontology" in Quine's terminology, which seems to me misleading), there appears now to be agreement between us: "the obvious counsel is tolerance and an experimental spirit" (ibid., p. 12). 6 See Rudolf Carnap, Scheinprobleme in der Philosophie; das Fremdpsychische und der Realismusstreit (Berlin, 1928); Moritz Schlick, Positivismu.1 und Realismus, repro in Gesammelte AU{siitze (Vienna:
1938). 7 See Rudolf Carnap, Introduction to Semantics (Cambridge, Mass.: Harvard University Press, 1942); idem, Meaning and Necessity. The distinction I have drawn in the latter book between the method of the namerelation and the method of intension and extension is not essential for our present discussion. The term "designation" is used in the present article in a neutral way; it may be understood as referring to the name-relation or to the intension-relation or to the extension-relation or to any similar relations used in other seman tical methods. 8 Gilbert Ryle, "Meaning and necessity," Philosophy 24 (1949), pp. 69~76. 9 Ernest Nagel, review ofRudolfCarnap, Meaning and Necessizy, 1st edn, Journal ofPhilosophy 45 (1948), pp. 467~72.
10 Wilfrid Sellars, "Acquaintance and description again," Journal of Philosophy 46 (1949), pp. 496~504, at pp. 502 f. analyzes clearly the roots of the mistake "of taking the designation relation of semantic theory to be a reconstruction of being present to an experience."
Bertrand Russell
General Propositions and Existence I am going to speak today about general propositions and existence. The two subjects really belong together; they are the same topic, although it might not have seemed so at the first glance. The propositions and facts that I have been talking about hitherto have all been such as involved only perfectly definite particulars, or relations, or qualities, or things of that sort, never involved the sort of indefinite things one alludes to by such words as 'all', 'some', 'a', 'any', and it is propositions and facts of that sort that I am coming on to today. Really all the propositions of the sort that I mean to talk of today collect themselves into two groupsthe first that are about 'all', and the second that are about 'some'. These two sorts belong together; they are each other's negations. If you say, for instance, 'All men are mortal', that is the negative of 'Some men are not mortal'. In regard to general propositions, the distinction of affirmative and negative is arbitrary. Whether you are going to regard the propositions about 'all' as the affirmative ones and the propositions about 'some' as the negative ones, or vice versa, is purely a matter of taste. For example, if! say 'I met no one as I came along', that, on the face of it, you would think is a negative
'Existence and description' is a new title for lectures V and VI of 'The Philosophy of Logical Atomism', first published in The Monist (1918), and reprinted with permission of the author's estate.
proposition. Of course, that is really a proposition about 'all', i.e., 'All men are among those whom I did not meet'. If, on the other hand, I say 'I met a man as I came along', that would strike you as affirmative, whereas it is the negative of 'All men are among those I did not meet as I came along'. If you consider such propositions as 'All men are mortal' and 'Some men are not mortal', you might say it was more natural to take the general propositions as the affirmative and the existence-propositions as the negative, but, simply because it is quite arbitrary which one is to choose, it is better to forget these words and to speak only of general propositions and propositions asserting existence. All general propositions deny the existence of something or other. If you say 'All men are mortal', that denies the existence of an immortal man, and so on. I want to say emphatically that general propositions are to be interpreted as not involving existence. When I say, for instance, 'All Greeks are men', I do not want you to suppose that that implies that there are Greeks. It is to be considered emphatically as not implying that. That would have to be added as a separate proposition. If you want to interpret it in that sense, you will have to add the further statement 'and there are Greeks'. That is for purposes of practical convenience. If you include the fact that there are Greeks, you are rolling two propositions into one, and it causes unnecessary confusion in your logic, because the sorts of propositions that you want are those that do assert the existence of something and general
Bertrand Russell
propositions which do not assert existence. If it happened that there were no Greeks, both the proposition that 'All Greeks are men' and the proposition that 'No Greeks are men' would be true. The proposition 'No Greeks are men' is, of course, the proposition 'All Greeks are not-men'. Both propositions will be true simultaneously if it happens that there are no Greeks. All statements about all the members of a class that has no members are true, because the contradictory of any general statement does assert existence and is therefore false in this case. This notion, of course, of general propositions not involving existence is one which is not in the traditional doctrine of the syllogism. In the traditional doctrine of the syllogism, it was assumed that when you have such a statement as 'All Greeks are men', that implies that there are Greeks, and this produced fallacies. For instance, 'All chimeras are animals, and all chimeras breathe flame, therefore some animals breathe flame.' This is a syllogism in Darapti, but that mood of the syllogism is fallacious, as this instance shows. That was a point, by the way, which had a certain historical interest, because it impeded Leibniz in his attempts to construct a mathematical logic. He was always engaged in trying to construct such a mathematical logic as we have now, or rather such a one as Boole constructed, and he was always failing because of his respect for Aristotle. Whenever he invented a really good system, as he did several times, it always brought out that such moods as Darapti are fallacious. If you say 'All A is B and all A is C, therefore some B is C' - if you say this, you incur a fallacy, but he could not bring himself to believe that it was fallacious, so he began again. That shows you that you should not have too much respect for distinguished men. 1 Now when you come to ask what really is asserted in a general proposition, such as 'All Greeks are men' for instance, you find that what is asserted is the truth of all values of what I call a propositional function. A propositional function is simply any expression containing an undetermined constituent, or several undetermined constituents, and becoming a proposition as soon as the undetermined constituents are determined. If! say 'x is a man' or 'n is a number', that is a propositional function; so is any formula of algebra, say (x + y)(x - y) = x2 - y2. A propositional function is nothing, but, like most of the things one wants to talk about in logic, it does not lose its importance through that fact. The only thing really that you can do with a propositional function is to assert either that it is
always true, or that it is sometimes true, or that it is never true. If you take: 'If x is a man, x is mortal', that is always true (just as much when x is not a man as when x is a man); if you take:
'x is a man', that is sometimes true; if you take: 'x is a unicorn',
that is never true. One may call a propositional function necessa~y, when it is always true; possible, when it is sometimes true; impossible, when it is never true.
Much false philosophy has arisen out of confusing propositional functions and propositions. There is a great deal in ordinary traditional philosophy which consists simply in attributing to propositions the predicates which only apply to propositional functions, and, still worse, sometimes in attributing to individuals predicates which merely apply to propositional functions. This case of necessary, possible, impossible, is a case in point. In all traditional philosophy there comes a heading of 'modality', which discusses necessary, possible, and impossible as properties of propositions, whereas in fact they are properties of propositional functions. Propositions are only true or false. If you take 'x is x', that is a propositional function which is true whatever 'x' may be, i.e., a necessary propositional function. If you take 'x is a man', that is a possible one. If you take 'x is a unicorn', that is an impossible one. Propositions can only be true or false, but propositional functions have these three possibilities. It is important, I think, to realize that the whole doctrine of modality only applies to propositional functions, not to propositions. Propositional functions are involved in ordinary language in a great many cases where one does not usually realize them. In such a statement as 'I met a man', you can understand my statement perfectly well without knowing whom I met, and the actual person is not a constituent of the proposition. You are really asserting there that a certain propositional function is sometimes true, namely the propositional function 'I met x and x is human'. There
Existence and Description
is at least one value of x for which that is true, and that therefore is a possible propositional function. Whenever you get such words as 'a', 'some', 'all', 'every', it is always a mark of the presence of a propositional function, so that these things are not, so to speak, remote or recondite: they are obvious and familiar. A propositional function comes in again in such a statement as 'Socrates is mortal', because 'to be mortal' means 'to die at some time or other'. You mean there is a time at which Socrates dies, and that again involves a propositional function, namely, that 't is a time, and Socrates dies at t' is possible. If you say 'Socrates is immortal', that also will involve a propositional function. That means that 'If t is any time whatever, Socrates is alive at time t', if we take immortality as involving existence throughout the whole of the past as well as throughout the whole of the future. But if we take immortality as only involving existence throughout the whole of the future, the interpretation of 'Socrates is immortal' becomes more complete, viz., 'There is a time t, such that if t' is any time later than t, Socrates is alive at t". Thus when you come to write out properly what one means by a great many ordinary statements, it turns out a little complicated. 'Socrates is mortal' and 'Socrates is immortal' are not each other's contradictories, because they both imply that Socrates exists in time, otherwise he would not be either mortal or immortal. One says, 'There is a time at which he dies', and the other says, 'Whatever time you take, he is alive at that time', whereas the contradictory of 'Socrates is mortal' would be true ifthere is not a time at which he lives. An undetermined constituent in a propositional function is called a variable.
Existence When you take any propositional function and assert of it that it is possible, that it is sometimes true, that gives you the fundamental meaning of 'existence'. You may express it by saying that there is at least one value of x for which that propositional function is true. Take 'x is a man'; there is at least one value of x for which this is true. That is what one means by saying that 'There are men', or that 'Men exist'. Existence is essentially a property of a propositional function. It means that that propositional function is true in at least one instance. If you say 'There are unicorns', that will mean that 'There is an x, such that x is a unicorn'. That is
written in phrasing which is unduly approximated to ordinary language, but the proper way to put it would be '(x is a unicorn) is possible'. We have got to have some idea that we do not define, and one takes the idea of 'always true', or of 'sometimes true', as one's undefined idea in this matter, and then you can define the other one as the negative of that. In some ways it is better to take them both as undefined, for reasons which I shall not go into at present. It will be out of this notion of sometimes, which is the same as the notion of possible, that we get the notion of existence. To say that unicorns exist is simply to say that '(x is a unicorn) is possible'. It is perfectly clear that when you say 'Unicorns exist', you are not saying anything that would apply to any unicorns there might happen to be, because as a matter of fact there are not any, and therefore if what you say had any application to the actual individuals, it could not possibly be significant unless it were true. You can consider the proposition 'Unicorns exist' and can see that it is false. It is not nonsense. Of course, if the proposition went through the general conception of the unicorn to the individual, it could not be even significant unless there were unicorns. Therefore when you say 'Unicorns exist', you are not saying anything about any individual things, and the same applies when you say 'Men exist'. If you say that 'Men exist, and Socrates is a man, therefore Socrates exists', that is exactly the same sort of fallacy as it would be if you said 'Men are numerous, Socrates is a man, therefore Socrates is numerous', because existence is a predicate of a propositional function, or derivatively of a class. When you say of a propositional function that it is numerous, you will mean that there are several values of x that will satisfy it, that there are more than one; or, if you like to take 'numerous' in a larger sense, more than ten, more than twenty, or whatever number you think fitting. If x, y, and z all satisfy a propositional function, you may say that that proposition is numerous, but x, y, and z severally are not numerous. Exactly the same applies to existence, that is to say that the actual things that there are in the world do not exist, or, at least, that is putting it too strongly, because that is utter nonsense. To say that they do not exist is strictly nonsense, but to say that they do exist is also strictly nonsense. It is of propositional functions that you can assert or deny existence. You must not run away with the idea that this entails consequences that it does not entail. If! say 'The things that there are in
Bertrand Russell
the world exist', that is a perfectly correct statement, because 1 am there saying something about a certain class of things; 1 say it in the same sense in which 1 say 'Men exist'. But 1 must not go on to 'This is a thing in the world, and therefore this exists'. It is there the falIacy comes in, and it is simply, as you see, a falIacy of transferring to the individual that satisfies a propositional function a predicate which only applies to a propositional function. You can see this in various ways. For instance, you sometimes know the truth of an existence-proposition without knowing any instance of it. You know that there are people in Timbuctoo, but 1 doubt if any of you could give me an instance of one. Therefore you clearly can know existencepropositions without knowing any individual that makes them true. Existence-propositions do not say anything about the actual individual but only about the class or function. It is exceedingly difficult to make this point clear as long as one adheres to ordinary language, because ordinary language is rooted in a certain feeling about logic, a certain feeling that our primeval ancestors had, and as long as you keep to ordinary language you find it very difficult to get away from the bias which is imposed upon you by language. When 1 say, e.g., 'There is an x such that x is a man', that is not the sort of phrase one would like to use. 'There is an x' is meaningless. What is 'an x' anyhow? There is not such a thing. The only way you can realIy state it correctly is by inventing a new language ad hoc, and making the statement apply straight off to 'x is a man', as when one says '(x is a man) is possible', or invent a special symbol for the statement that 'x is a man' is sometimes true. 1 have dwelt on this point because it realIy is of very fundamental importance. 1 shalI come back to existence in my next lecture: existence as it applies to descriptions, which is a slightly more complicated case than 1 am discussing here. 1 think an almost unbelievable amount of false philosophy has arisen through not realizing what 'existence' means. As 1 was saying a moment ago, a propositional function in itself is nothing: it is merely a schema. Therefore in the inventory of the world, which is what 1 am trying to get at, one comes to the question: What is there really in the world that corresponds with these things? Of course, it is clear that we have general propositions, in the same sense in which we have atomic propositions. For the moment 1 will include existence-propositions with
general propositions. We have such propositions as 'All men are mortal' and 'Some men are Greeks'. But you have not only such propositions; you have also such facts, and that, of course, is where you get back to the inventory of the world: that, in addition to particular facts, which 1 have been talking about in previous lectures, there are also general facts and existence-facts; that is to say, there are not merely propositions of that sort but also facts of that sort. That is rather an important point to realize. You cannot ever arrive at a general fact by inference from particular facts, however numerous. The old plan of complete induction, which used to occur in books, which was always supposed to be quite safe and easy as opposed to ordinary induction, that plan of complete induction, unless it is accompanied by at least one general proposition, will not yield you the result that you want. Suppose, for example, that you wish to prove in that way that 'All men are mortal', you are supposed to proceed by complete induction, and say 'A is a man that is mortal', 'B is a man that is mortal', 'C is a man that is mortal', and so on until you finish. You will not be able, in that way, to arrive at the proposition. 'All men are mortal' unless you know when you have finished. That is to say that, in order to arrive by this road at the general proposition 'All men are mortal', you must already have the general proposition 'All men are among those 1 have enumerated'. You never can arrive at a general proposition by inference from particular propositions alone. You will always have to have at least one general proposition in your premisses. That illustrates, 1 think, various points. One, which is epistemological, is that if there is, as there seems to be, knowledge of general propositions (I mean by that, knowledge of general propositions which is not obtained by inference), because if you can never infer a general proposition except from premisses of which one at least is general, it is clear that you can never have knowledge of such propositions by inference unless there is knowledge of some general propositions which is not by inference. 1 think that the sort of way such knowledge - or rather the belief that we have such knowledge - comes into ordinary life is probably very odd. 1 mean to say that we do habitually assume general propositions which are exceedingly doubtful; as, for instance, one might, if one were counting up the people in this room, assume that one could see all of them, which is a general proposition, and very doubtful as there may be people under the tables. But, apart from that sort of thing, you do have in any empiri-
Existence and Description
cal verification of general propositions some kind of assumption that amounts to this, that what you do not see is not there. Of course, you would not put it so strongly as that, but you would assume that, with certain limitations and certain qualifications, if a thing does not appear to your senses, it is not there. That is a general proposition, and it is only through such propositions that you arrive at the ordinary empirical results that one obtains in ordinary ways. If you take a census of the country, for instance, you assume that the people you do not see are not there, provided you search properly and carefully, otherwise your census might be wrong. It is some assumption of that sort which would underline what seems purely empirical. You could not prove empirically that what you do not perceive is not there, because an empirical proof would consist in perceiving, and by hypothesis you do not perceive it, so that any proposition of that sort, if it is accepted, has to be accepted on its own evidence. I only take that as an illustration. There are many other illustrations one could take of the sort of propositions that are commonly assumed, many of them with very little justification. I come now to a question which concerns logic more nearly, namely, the reasons for supposing that there are general facts as well as general propositions. When we were discussing molecular propositions I threw doubt upon the supposition that there are molecular facts, but I do not think one can doubt that there are general facts. It is perfectly clear, I think, that when you have enumerated all the atomic facts in the world, it is a further fact about the world that those are all the atomic facts there are about the world, and that is just as much an objective fact about the world as any of them are. It is clear, I think, that you must admit general facts as distinct from and over and above particular facts. The same thing applies to 'All men are mortal'. When you have taken all the particular men that there are, and found each one of them severally to be mortal, it is definitely a new fact that all men are mortal; how new a fact, appears from what I said a moment ago, that it could not be inferred from the mortality of the several men that there are in the world. Of course, it is not so difficult to admit what I might call existence-facts - such facts as 'There are men', 'There are sheep', and so on. Those, I think, you will readily admit as separate and distinct facts over and above the atomic facts I spoke of before. Those facts have got to come into the inventory of the world, and in that way propositional functions come in as involved in the study of
general facts. I do not profess to know what the right analysis of general facts is. It is an exceedingly difficult question, and one which I should very much like to see studied. I am sure that, although the convenient technical treatment is by means of propositional functions, that is not the whole ofthe right analysis. Beyond that I cannot go. There is one point about whether there are molecular facts. I think I mentioned, when I was saying that I did not think there were disjunctive facts, that a certain difficulty does arise in regard to general facts. Take 'All men are mortal'. That means: , "x is a man" implies "x is a mortal" whatever x may be.'
You can see at once that it is a hypothetical proposition. It does not imply that there are any men, nor who are men, and who are not; it simply says that if you have anything which is a man, that thing is mortal. As Mr Bradley has pointed out in the second chapter of his Principles of Logic, 'Trespassers will be prosecuted' may be true even ifno one trespasses, since it means merely that, if anyone trespasses, he will be prosecuted. It comes down to this that
'''x is a man" implies "x is a mortal" is always true' is a fact. It is perhaps a little difficult to see how that can be true if one is going to say that '''Socrates is a man" implies "Socrates is a mortal'" is not itself a fact, which is what I suggested when I was discussing disjunctive facts. I do not feel sure that you could not get round that difficulty. I only suggest it as a point which should be considered when one is denying that there are molecular facts, since, if it cannot be got round, we shall have to admit molecular facts. Now I want to come to the subject of completely general propositions and propositional functions. By those I mean propositions and propositional functions that contain only variables and nothing else at all. This covers the whole of logic. Every logical proposition consists wholly and solely of variables, though it is not true that every proposition consisting wholly and solely of variables is logical. You can consider stages of generalizations as, e.g., 'Socrates loves Plato'
Bertrand Russell 'x loves Plato' 'x lovesy'
'xRy.' There you have been going through a process of successive generalization. When you have got to xRy, you have got a schema consisting only of variables, containing no constants at all, the pure schema of dual relations, and it is clear that any proposition which expresses a dual relation can be derived from xRy by assigning values to x and R and y. So that that is, as you might say, the pure form of all those propositions. I mean by the form of a proposition that which you get when for every single one of its constituents you substitute a variable. If you want a different definition of the form of a proposition, you might be inclined to define it as the class of all those propositions that you can obtain from a given one by substituting other constituents for one or more of the constituents the proposition contains. E.g., in 'Socrates loves Plato', you can substitute somebody else for Socrates, somebody else for Plato, and some other verb for 'loves'. In that way there are a certain number of propositions which you can derive from the proposition 'Socrates loves Plato', by replacing the constituents of that proposition by other constituents, so that you have there a certain class of propositions, and those propositions all have a certain form, and one can, if one likes, say that the form they all have is the class consisting of all of them. That is rather a provisional definition, because as a matter of fact, the idea of form is more fundamental than the idea of class. I should not suggest that as a really good definition, but it will do provisionally to explain the sort of thing one means by the form of a proposition. The form of a proposition is that which is in common between any two propositions of which the one can be obtained from the other by substituting other constituents for the original ones. When you have got down to those formulas that contain only variables, like xRy, you are on the way to the sort of thing that you can assert in logic. To give an illustration, you know what I mean by the domain of a relation: I mean all the terms that have that relation to something. Suppose I say: 'xRy implies that x belongs to the domain of R', that would be a proposition of logic and is one that contains only variables. You might think it contains such words as 'belong' and 'domain', but that is an error. It is only the habit of using ordinary language that makes those words appear. They are not really
there. That is a proposition of pure logic. It does not mention any particular thing at all. This is to be understood as being asserted whatever x and Rand y may be. All the statements oflogic are of that sort. It is not a very easy thing to see what are the constituents of a logical proposition. When one takes 'Socrates loves Plato', 'Socrates' is a constituent, 'loves' is a constituent, and 'Plato' is a constituent. Then you turn 'Socrates' into x, 'loves' into R, and 'Plato' into y. x and Rand yare nothing, and they are not constituents, so it seems as though all the propositions oflogic were entirely devoid of constituents. I do not think that can quite be true. But then the only other thing you can seem to say is that the form is a constituent, that propositions of a certain form are always true: that may be the right analysis, though I very much doubt whether it is. There is, however, just this to observe, viz., that the form of a proposition is never a constituent of that proposition itself. If you assert that 'Socrates loves Plato', the form of that proposition is the form of the dual relation, but this is not a constituent of the proposition. If it were, you would have to have that constituent related to the other constituents. You will make the form much too substantial if you think of it as really one of the things that have that form, so that the form of a proposition is certainly not a constituent of the proposition itself. Nevertheless it may possibly be a constituent of general statements about propositions that have that form, so I think it is possible that logical propositions might be interpreted as being about forms. I can only say, in conclusion, as regards the constituents of logical propositions, that it is a problem which is rather new. There has not been much opportunity to consider it. I do not think any literature exists at all which deals with it in any way whatever, and it is an interesting problem. I just want now to give you a few illustrations of propositions which can be expressed in the language of pure variables but are not propositions of logic. Among the propositions that are propositions of logic are included all the propositions of pure mathematics, all of which cannot onl y be expressed in logical terms but can also be deduced from the premisses of logic, and therefore they are logical propositions. Apart from them there are many that can be expressed in logical terms, but cannot be proved from logic, and are certainly not propositions that form part oflogic. Suppose you take such a proposition as: 'There is at least one thing in the
Existence and Description
world'. That is a proposition that you can express in logical terms. It will mean, if you like, that the propositional function 'x = x' is a possible one. That is a proposition, therefore, that vou can express in logical terms; but you cann~t know from logic whether it is true or false. So far as you do know it, you know it empirically, because there might happen not to be a universe, and then it would not be true. It is merely an accident, so to speak, that there is a universe. The proposition that there are exactly 30,000 things in the world can also be expressed in purely logical terms, and is certainly not a proposition of logic but an empirical proposition (true or false), because a world containing more than 30,000 things and a world containing fewer than 30,000 things are both possible, so that if it happens that there are exactly 30,000 things, that is what one might call an accident and is not a proposition of logic. There are again two propositions that one is used to in mathematical logic, namely, the multiplicative axiom and the axiom of infinity. These also can be expressed in logical terms, but cannot be proved or disproved by logic. In regard to the axiom of infinity, the impossibility of logical proof or disproof may be taken as certain, but in the case of the multiplicative axiom, it is perhaps still open to some degree to doubt. Everything that is a proposition oflogic has got to be in some sense or other like a tautology. It has got to be something that has some peculiar quality, which I do not know how to define, that belongs to logical propositions and not to others. Examples of typical logical propositions are: 'If p implies q and q implies r, then p implies r.' 'If all a's are b's and all b's are c's, then all a's are c's.'
'If all a's are b's, and x is an a, then x is a b.' Those are propositions of logic. They have a certain peculiar quality which marks them out from other propositions and enables us to know them a priori. But what exactly that characteristic is, I am not able to tell you. Although it is a necessary characteristic of logical propositions that they should consist solely of variables, i.e., that they should assert the universal truth, or the sometimes-truth, of a propositional function consisting wholly of variables - although that is a necessary characteristic, it is not a sufficient one. I am sorry that I have had to leave so many problems unsolved. I always have to make this apology, but the world really is rather puzzling and I cannot help it.
Discussion Question: Is there any word you would substitute for 'existence' which would give existence to individuals? Are you applying the word 'existence' to two ideas, or do you deny that there are two ideas? Mr Russell: No, there is not an idea that will apply to individuals. As regards the actual things there are in the world, there is nothing at all you can say about them that in any way corresponds to this notion of existence. It is a sheer mistake to say that there is anything analogous to existence that you can say about them. You get into confusion through language, because it is a perfectly correct thing to say 'All the things in the world exist', and it is so easy to pass from this to 'This exists because it is a thing in the world'. There is no sort of point in a predicate which could not conceivably be false. I mean, it is perfectly clear that, if there were such a thing as this existence of individuals that we talk of it would be absolutely impossible for it not t~ apply, and that is the characteristic of a mistake.
2 Descriptions and Incomplete Symbols I am proposing to deal this time with the subject of descriptions, and what I call 'incomplete symbols', and the existence of described individuals. You will remember that last time I dealt with the existence of kinds of things, what you mean by saying 'There are men' or 'There are Greeks' or phrases of that sort, where you have an existence which may be plural. I am going to deal today with an existence which is asserted to be singular, such as 'The man with the iron mask existed' or some phrase of that sort, where you have some object described by the phrase 'The so-and-so' in the singular, and I want to discuss the analysis of propositions in which phrases of that kind occur. There are, of course, a great many propositions very familiar in metaphysics which are of that sort: 'I exist' or 'God exists' or 'Homer existed', and other such statements are always occurring in metaphysical discussions, and are, I think, treated in ordinary metaphysics in a way which embodies a simple logical mistake that we shall be concerned with today, the same sort of mistake that I spoke of last week in connection with the existence of kinds of things. One way of examining a proposition of that sort is to ask yourself what would happen if it were false. If you take such a proposition as
Bertrand Russell
'Romulus existed', probably most of us think that Romulus did not exist. It is obviously a perfectly significant statement, whether true or false, to say that Romulus existed. If Romulus himself entered into our statement, it would be plain that the statement that he did not exist would be nonsense, because you cannot have a constituent of a proposition which is nothing at all. Every constituent has got to be there as one of the things in the world, and therefore if Romulus himself entered into the propositions that he existed or that he did not exist, both these propositions could not only not be true, but could not be even significant, unless he existed. That is obviously not the case, and the first conclusion one draws is that, although it looks as if Romulus were a constituent of that proposition, that is really a mistake. Romulus does not occur in the proposition 'Romulus did not exist'. Suppose you try to make out what you do mean by that proposition. You can take, say, all the things that Livy has to say about Romulus, all the properties he ascribes to him, including the only one probably that most of us remember, namely, the fact that he was called 'Romulus'. You can put all this together, and make a propositional function saying 'x has such-and-such properties', the properties being those you find enumerated in Livy. There you have a propositional function, and when you say that Romulus did not exist you are simply saying that that propositional function is never true, that it is impossible in the sense I was explaining last time, i.e., that there is no value of x that makes it true. That reduces the non-existence of Romulus to the sort of non-existence I spoke of last time, where we had the non-existence of unicorns. But it is not a complete account of this kind of existence or non-existence, because there is one other way in which a described individual can fail to exist, and that is where the description applies to more than one person. You cannot, e.g., speak of 'The inhabitant of London', not because there are none, but because there are so many. You see, therefore, that this proposition 'Romulus existed' or 'Romulus did not exist' does introduce a propositional function, because the name 'Romulus' is not really a name but a sort of truncated description. It stands for a person who did such-and-such things, who killed Remus, and founded Rome, and so on. It is short for that description; if you like, it is short for 'the person who was called "Romulus" '. If it were really a name, the question of existence could not arise, because a name has got to name something or it is
not a name, and if there is no such person as Romulus, there cannot be a name for that person who is not there, so that this single word 'Romulus' is really a sort of truncated or telescoped description, and if you think of it as a name, you will get into logical errors. When you realize that it is a description, you realize therefore that any proposition about Romulus really introduces the propositional function embodying the description, as (say) 'x was called "Romulus" '. That introduces you at once to a propositional function, and when you say 'Romulus did not exist', you mean that this propositional function is not true for one value of x. There are two sorts of descriptions, what one may call 'ambiguous descriptions', when we speak of 'a so-and-so', and what one may call 'definite descriptions', when we speak of 'the so-and-so' (in the singular). Instances are: Ambiguous: A man, a dog, a pig, a Cabinet Minister. Definite: The man with the iron mask.
The last person who came into this room. The only Englishman who ever occupied the Papal See. The number of the inhabitants of London. The sum of 43 and 34. (It is not necessary for a description that it should describe an individual: it may describe a predicate or a relation or anything else.) It is phrases of that sort, definite descriptions, that I want to talk about today. I do not want to talk about ambiguous descriptions, as what there was to say about them was said last time. I want you to realize that the question whether a phrase is a definite description turns only upon its form, not upon the question whether there is a definite individual so described. For instance, I should call 'The inhabitant of London' a definite description, although it does not in fact describe any definite individual. The first thing to realize about a definite description is that it is not a name. We will take 'The author of Waverley'. That is a definite description, and it is easy to see that it is not a name. A name is a simple symbol (i.e., a symbol which does not have any parts that are symbols), a simple symbol used to designate a certain particular or by extension an object which is not a particular but is treated for the moment as if it were, or is falsely believed to be a particular, such as a person. This sort of phrase, 'The author of Waverley', is not a name because it is a complex symbol. It
Existence and Description
contains parts which are symbols. It contains four words, and the meanings of those four words are already fixed, and they have fixed the meaning of 'The author of Waverley' in the only sense in which that phrase does have any meaning. In that sense, its meaning is already determinate, i.e., there is nothing arbitrary or conventional about the meaning of that whole phrase, when the meanings of 'the', 'author', 'of, and 'Waverley' have already been fixed. In that respect, it differs from 'Scott', because when you have fixed the meaning of all the other words in the language, you have done nothing toward fixing the meaning of the name 'Scott'. That is to say, if you understand the English language, you would understand the meaning of the phrase 'The author of Waverley' if you had never heard it before, whereas you would not understand the meaning of 'Scott' if you had never heard the word before because to know the meaning of a name is to know who it is applied to. You sometimes find people speaking as if descriptive phrases were names, and you will find it suggested, e.g., that such a proposition as 'Scott is the author of Waverley' really asserts that 'Scott' and the 'the author of Waverley' are two names for the same person. That is an entire delusion; first of all, because 'the author of Waverley' is not a name, and, secondly, because, as you can perfectly well see, if that were what is meant, the proposition would be one like 'Scott is Sir Walter', and would not depend upon any fact except that the person in question was so called, because a name is what a man is called. As a matter of fact, Scott was the author of Waverley' at a time when no one called him so, when no one knew whether he was or not, and the fact that he was the author was a physical fact, the fact that he sat down and wrote it with his own hand, which does not have anything to do with what he was called. It is in no way arbitrary. You cannot settle by any choice of nomenclature whether he is or is not to be the author of Waverley, because in actual fact he chose to write it and you cannot help yourself. That illustrates how 'the author of Waverley' is quite a different thing from a name. You can prove this point very clearly by formal arguments. In 'Scott is the author of Waverley' the 'is', of course, expresses identity, i.e., the entity whose name is Scott is identical with the author of Waverley. But, when I say 'Scott is mortal', this 'is' is the 'is' of predication, which is quite different from the 'is' of identity. It is a mistake to interpret 'Scott is mortal' as meaning 'Scott is identical with one among mortals', because (among
other reasons) you will not be able to say what 'mortals' are except by means of the propositional function 'x is mortal', which brings back the 'is' of predication. You cannot reduce the 'is' of predication to the other 'is'. But the 'is' in 'Scott is the author of Waverley' is the 'is' of identity and not of predication? If you were to try to substitute for 'the author of Waverley' in that proposition any name whatever, say 'c', so that the proposition becomes 'Scott is c', then if 'c' is a name for anybody who is not Scott, that proposition would become false, while if, on the other hand, 'c' is a name for Scott, then the proposition will become simply a tautology. It is at once obvious that if 'c' were 'Scott' itself, 'Scott is Scott' is just a tautology. But if you take any other name which is just a name for Scott, then if the name is being used as a name and not as a description, the proposition will still be a tautology. For the name itself is merely a means of pointing to the thing, and does not occur in what you are asserting, so that if one thing has two names, you make exactly the same assertion whichever of the two names you use, provided they are really names and not truncated descriptions. So there are only two alternatives. If 'c' is a name, the proposition 'Scott is c' is either false or tautologous. But the proposition 'Scott is the author of Waverley' is neither, and therefore is not the same as any proposition of the form 'Scott is c', where 'c' is a name. That is another way of illustrating the fact that a description is quite a different thing from a name. I should like to make clear what I was saying just now, that if you substitute another name in place of 'Scott' which is also a name of the same individual, say, 'Scott is Sir Walter', then 'Scott' and 'Sir Walter' are being used as names and not as descriptions, your proposition is strictly a tautology. If one asserts 'Scott is Sir Walter', the way one would mean it would be that one was using the names as descriptions. One would mean that the person called 'Scott' is the person called 'Sir Walter', and 'the person called "Scott" is a description, and so is 'the person called "Sir Walter".' So that would not be a tautology. It would mean that the person called 'Scott' is identical with the person called 'Sir Walter'. But if you are using both as names, the matter is quite different. You must observe that the name does not occur in that which you assert when you use the name. The name is merely that which is a means of expressing what it is you are trying to assert, and when I say 'Scott wrote Waverley', the
Bertrand Russell
name 'Scott' does not occur in the thing I am asserting. The thing I am asserting is about the person, not about the name. So if I say 'Scott is Sir Walter', using these two names as names, neither 'Scott' nor 'Sir Walter' occurs in what I am asserting, but only the person who has these names, and thus what I am asserting is a pure tautology. It is rather important to realize this about the two different uses of names or of any other symbols: the one when you are talking about the symbol and the other when you are using it as a symbol, as a means of talking about something else. Normally, if you talk about your dinner, you are not talking about the word 'dinner' but about what you are going to eat, and that is a different thing altogether. The ordinary use of words is as a means of getting through to things, and when you are using words in that way the statement 'Scott is Sir Walter' is a pure tautology, exactly on the same level as 'Scott is Scott'. That brings me back to the point that when you take 'Scott is the author of Waverley' and you substitute for 'the author of Waverley' a name in the place of a description, you get necessarily either a tautology or a falsehood - a tautology if you substitute 'Scott' or some other name for the same person, and a falsehood if you substitute anything else. But the proposition itself is neither a tautology nor a falsehood, and that shows you that the proposition 'Scott is the author of Waverley' is a different proposition from any that can be obtained if you substitute a name in the place of 'the author of Waverley'. That conclusion is equally true of any other proposition in which the phrase 'the author of Waverley' occurs. If you take any proposition in which that phrase occurs and substitute for that phrase a proper name, whether that name be 'Scott' or any other, you will get a different proposition. Generally speaking, if the name that you substitute is 'Scott', your proposition, if it was true before will remain true, and if it was false before will remain false. But it is a different proposition. It is not always true that it will remain true or false, as may be seen by the example: 'George IV wished to know if Scott was the author of Waverley'. It is not true that George IV wished to know if Scott was Scott. So it is even the case that the truth or the falsehood of a proposition is sometimes changed when you substitute a name of an object for a description of the same object. But in any case it is always a different proposition when you substitute a name for a description.
Identity is a rather puzzling thing at first sight. When you say 'Scott is the author of Waverley', you are half-tempted to think there are two people, one of whom is Scott and the other the author of Waverley, and they happen to be the same. That is obviously absurd, but that is the sort of way one is always tempted to deal with identity. When I say 'Scott is the author of Waverley' and that 'is' expresses identity, the reason that identity can be asserted there truly and without tautology is just the fact that the one is a name and the other a description. Or they might both be descriptions. If I say 'The author of Waverley is the author of Marmion', that, of course, asserts identity between two descriptions. Now the next point that I want to make clear is that when a description (when I say 'description' I mean, for the future, a definite description) occurs in a proposition, there is no constituent of that proposition corresponding to that description as a whole. In the true analysis of the proposition, the description is broken up and disappears. That is to say, when I say 'Scott is the author of Waverley', it is a wrong analysis of that to suppose that you have there three constituents, 'Scott', 'is', and 'the author of Waverley'. That, of course, is the sort of way you might think of analysing. You might admit that 'the author of Waverley' was complex and could be further cut up, but you might think the proposition could be split into those three bits to begin with. That is an entire mistake. 'The author of Waverley' is not a constituent of the proposition at all. There is no constituent really there corresponding to the descriptive phrase. I will try to prove that to you now. The first and most obvious reason is that you can have significant propositions denying the existence of 'the so-and-so'. 'The unicorn does not exist.' 'The greatest finite number does not exist.' Propositions of that sort are perfectly significant, are perfectly sober, true, decent propositions, and that could not possibly be the case if the unicorn were a constituent of the proposition, because plainly it could not be a constituent as long as there were not any unicorns. Because the constituents of propositions, of course, are the same as the constituents of the corresponding facts, and since it is a fact that the unicorn does not exist, it is perfectly clear that the unicorn is not a constituent of that fact, because if there were any fact of which the unicorn was a constituent, there would be a unicorn, and it would not be true that it did not exist. That applies in this case of descriptions particu-
Existence and Description
larly. Now since it is possible for 'the so-and-so' not to exist and yet for propositions in which 'the so-and-so' occurs to be significant and even true, we must try to see what is meant by saying that the so-and-so does exist. The occurrence of tense in verbs is an exceedingly annoying vulgarity due to our preoccupation with practical affairs. It would be much more agreeable if they had no tense, as I believe is the case in Chinese, but I do not know Chinese. You ought to be able to say 'Socrates exists in the past', 'Socrates exists in the present' or 'Socrates exists in the future', or simply 'Socrates exists', without any implication of tense, but language does not allow that, unfortunately. Nevertheless, I am going to use language in this tenseless way: when I say 'The soand-so exists', I am not going to mean that it exists in the present or in the past or in the future, but simply that it exists, without implying anything involving tense. 'The author of Waverley exists': there are two things required for that. First of all, what is 'the author of Waverley'? It is the person who wrote Waverley, i.e., we are coming now to this, that you have a propositional function involved, viz., 'x writes Waverl~y', and the author of Waverley is the person who writes Waverley, and in order that the person who writes Waverley may exist, it is necessary that this propositional function should have two properties: 2
It must be true for at least one x. It must be true for at most one x.
If nobody had ever written Waverley, the author could not exist, and if two people had written it, the author could not exist. So that you want these two properties, the one that it is true for at least one x, and the other that it is true for at most one x, both of which are required for existence. The property of being true for at least one x is the one we dealt with last time: what I expressed by saying that the propositional function is possible. Then we come on to the second condition, that it is true for at most one x, and that you can express in this way: 'If x and y wrote Waverley, then x is identical with y, whatever x and y may be.' That says that at most one wrote it. It does not say that anybody wrote Waverley at all, because if nobody had written it, that statement would still be true. It only says that at most one person wrote it. The first of these conditions for existence fails in the case of the unicorn, and the second in the case of the inhabitant of London.
We can put these two conditions together and get a portmanteau expression including the meaning of both. You can reduce them both down to this: that '("x wrote Waverley" is equivalent to "x is e" whatever x may be) is possible in respect of e'. That is as simple, I think, as you can make the statement. You see, that means to say that there is some entity e, we may not know what it is, which is such that when x is e, it is true that x wrote Waverley, and when x is not e, it is not true that x wrote Waverley, which amounts to saying that e is the only person who wrote Waverley; and I say there is a value of e which makes that true. So that this whole expression, which is a propositional function about e, is possible in respect of e (in the sense explained last time). That is what I mean when I say that the author of Waverley exists. When I say 'The author of Waverley exists', I mean that there is an entity e such that 'x wrote Waverley' is true when x is e, and is false when x is not e. 'The author of Waverley' as a constituent has quite disappeared there, so that when I say 'The author of Waverley exists', I am not saying anything about the author of Waverley. You have instead this elaborate to-do with propositional functions, and 'the author of Waverley' has disappeared. That is why it is possible to say significantly 'The author of Waverley did not exist'. It would not be possible if 'the author of Waverley' were a constituent of propositions in whose verbal expression this descriptive phrase occurs. The fact that you can discuss the proposition 'God exists' is a proof that 'God', as used in that proposition, is a description and not a name. If 'God' were a name, no question as to existence could arise. I have now defined what I mean by saying that a thing described exists. I have still to explain what I mean by saying that a thing described has a certain property. Supposing you want to say 'The author of Waverl~y was human', that will be represented thus: '("x wrote Waverley" is equivalent to "x is e" whatever x may be, and e is human) is possible with respect to e.' You will observe that what we gave before as the meaning of 'The author of Waverley exists' is part of this proposition. It is part of any proposition in which 'the author of Waverley' has what I call a 'primary occurrence'. When I speak of a 'primary occurrence', I mean that you are not having a proposition about the author of Waverley occurring as a part of some larger proposition, such as
Bertrand Russell
'I believe that the author of Waverley was human' or 'I believe that the author of Waverley exists'. When it is a primary occurrence, i.e., when the proposition concerning it is not just part of a larger proposition, the phrase which we defined as the meaning of 'The author of Waverley exists' will be part of that proposition. If I say the author of Waverley was human, or a poet, or a Scotsman, or whatever I say about the author of Waverley in the way of a primary occurrence, always this statement of his existence is part of the proposition. In that sense all these propositions that I make about the author of Waverley imply that the author of Waverley exists. So that any statement in which a description has a primary occurrence implies that the object described exists. If I say 'The present King of France is bald', that implies that the present King of France exists. If I say, 'The present King of France has a fine head of hair', that also implies that the present King of France exists. Therefore unless you understand how a proposition containing a description is to be denied, you will come to the conclusion that it is not true either that the present King of France is bald or that he is not bald, because if you were to enumerate all the things that are bald you would not find him there, and if you were to enumerate all the things that are not bald, you would not find him there either. The only suggestion I have found for dealing with that on conventional lines is to suppose that he wears a wig. You can only avoid the hypothesis that he wears a wig by observing that the denial of the proposition 'The present King of France is bald' will not be 'The present King of France is not bald', if you mean by that 'There is such a person as the King of France and that person is not bald'. The reason for this is that when you state that the present King of France is bald, you say 'There is a c such that c is now King of France and c is bald', and the denial is not 'There is a c such that c is now King of France and c is not bald'. It is more complicated. It is: 'Either there is not a c such that c is now King of France, or, if there is such a c, then c is not bald.' Therefore you see that, if you want to deny the proposition. 'The present King of France is bald', you can do it by denying that he exists, instead of by denying that he is bald. In order to deny this statement that the present King of France is bald, which is a statement consisting of two parts, you can proceed by denying either part. You can deny the one part, which would lead you to suppose that the present King of France exists but is not bald, or the other part,
which will lead you to the denial that the present King of France exists; and either of those two denials will lead you to the falsehood of the proposition 'The present King of France is bald'. When you say 'Scott is human', there is no possibility of a double denial. The only way you can deny 'Scott is human' is by saying 'Scott is not human'. But where a descriptive phrase occurs, you do have the double possibility of denial. It is of the utmost importance to realize that 'the so-and-so' does not occur in the analysis of propositions in whose verbal expression it occurs; that when I say 'The author of Waverley is human', 'the author of Waverley' is not the subject of that proposition, in the sort of way that Scott would be if I said 'Scott is human', using 'Scott' as a name. I cannot emphasize sufficiently how important this point is, and how much error you get into in metaphysics if you do not realize that when I say 'The author of Waverley is human', that is not a proposition of the same form as 'Scott is human'. It does not contain a constituent 'the author of Waverley'. The importance of that is very great for many reasons, and one of them is this question of existence. As I pointed out to you last time, there is a vast amount of philosophy that rests upon the notion that existence is, so to speak, a property that you can attribute to things, and that the things that exist have the property of existence and the things that do not exist do not. That is rubbish, whether you take kinds of things, or individual things described. When I say, e.g., 'Homer existed', I am meaning by 'Homer' some description, say 'the author of the Homeric poems', and I am asserting that those poems were written by one man, which is a very doubtful proposition; but if you could get hold of the actual person who did actually write those poems (supposing there was such a person), to say of him that he existed would be uttering nonsense, not a falsehood but nonsense, because it is only of persons described that it can be significantly said that they exist. Last time I pointed out the fallacy in saying 'Men exist, Socrates is a man, therefore Socrates exists'. When I say 'Homer exists, this is Homer, therefore this exists', that is a fallacy of the same sort. It is an entire mistake to argue: 'This is the author of the Homeric poems and the author of the Homeric poems exists, therefore this exists'. It is only where a prepositional function comes in that existence may be significantly asserted. You can assert 'The so-and-so exists', meaning that there is just one c which has those properties, but when you get
Existence and Description
hold of a c that has them, you cannot say of this c that it exists, because that is nonsense: it is not false, but it has no meaning at all. So the individuals that there are in the world do not exist, or rather it is nonsense to say that they exist and nonsense to say that they do not exist. It is not a thing you can say when you have named them, but only when you have described them. When you say 'Homer exists', you mean 'Homer' is a description which applies to something. A description when it is fully stated is always of the form 'the so-and-so'. The sort of things that are like these descriptions in that they occur in words in a proposition, but are not in actual fact constituents of the proposition rightly analysed, things of that sort I call 'incomplete symbols'. There are a great many sorts of incomplete symbols in logic, and they are sources of a great deal of confusion and false philosophy, because people get misled by grammar. You think that the proposition 'Scott is mortal' and the proposition 'The author of Waverley is mortal' are of the same form. You think that they are both simple propositions attributing a predicate to a subject. That is an entire delusion: one of them is (or rather might be), and one of them is not. These things, like 'the author of Waverley', which I call incomplete symbols, are things that have absolutely no meaning whatsoever in isolation, but merely acquire a meaning in a context. 'Scott' taken as a name has a meaning all by itself. It stands for a certain person, and there it is. But 'the author of Waverley' is not a name, and does not all by itself mean anything at all, because
when it is rightly used in propositions, those propositions do not contain any constituent corresponding to it. There are a great many other sorts of incomplete symbols besides descriptions. These are classes, which I shall speak of next time, and relations taken in extension, and so on. Such aggregations of symbols are really the same thing as what I call 'logical fictions', and they embrace practically all the familiar objects of daily life: tables, chairs, Piccadilly, Socrates, and so on. Most of them are either classes, or series, or series of classes. In any case they are all incomplete symbols; i.e., they are aggregations that only have a meaning in use, and do not have any meaning in themselves. It is important, if you want to understand the analysis of the world, or the analysis of facts, or if you want to have any idea what there really is in the world, to realize how much of what there is in phraseology is of the nature of incomplete symbols. You can see that very easily in the case of 'the author of Waverley' because 'the author of Waverley' does not stand simply for Scott, nor for anything else. If it stood for Scott, 'Scott is the author of Waverley' would be the same proposition as 'Scott is Scott', which it is not, since George IV wished to know the truth of the one and did not wish to know the truth of the other. If 'the author of Waverley' stood for anything other than Scott, 'Scott is the author of Waverley' would be false, which it is not. Hence you have to conclude that 'the author of Waverley' does not, in isolation, really stand for anything at all; and that is the characteristic of incomplete symbols.
Notes I Cf. Louis Couturat, La Logique de Leibniz (Paris: F. Alean, 1901).
2 The confusion of these two meanings of , is' is essential to the Hegelian conception of identity- in-difference.
Terence Parsons
This paper has three parts. In part I I'm going to argue that there's a big difference between the way English speakers treat empty singular terms and the way they treat singular terms that refer to objects that don't exist. That is, the data of linguistic behavior suggest that referring to something that doesn't exist is very different from failing to refer to anything at alL Most AngloAmerican philosophers haven't believed in nonexistent objects, and so they've generally tried to treat singular terms which refer to nonexistent objects as if they were singular terms which fail to refer to anything at alL And I think that that is wrong; I'm going to argue that it's wrong in part I of the paper. In part II of the paper I'm going to describe for you a theory about nonexistent objects. I think people are generally opposed to nonexistent objects because they don't understand them, and because such objects have gotten a bad press from people like Russell and Quine, people who argue very eloquently. But I think that if we had a better understanding of nonexistent objects, then we wouldn't be persuaded by these arguments against them. So I am trying to bring about such an understanding by sketching a theory about nonexistent objects. The present paper only contains a sketch of such a theory; a more comprehensive development will be given elsewhere.!
Originally published in Theory and Decision 11 (1979). pp. 95-110. Copyright © by Reidel Publishing Company. Reprinted by permission of Kluwer Academic Publishers.
Finally, in part III I'm going to sketch a theory of singular terms. According to this theory, some of these terms will refer to existing objects, some of them will refer to nonexistent objects, and some of them just won't refer at alL
Part 1: Referring to Nonexistent Objects isn't Failing to Refer The first point I'd like to make is that people behave differently when they fail to refer than when they refer to something that doesn't exist that is, they react differently when they realize what they've done in each case. I'm going to give you two conversations. In each conversation there are two characters, A and B, plus one outsider. In the first conversation speaker B plays the devil's advocate; you're supposed to find speaker A's reactions normaL A: "The man in the doorway over there looks pretty silly." Outsider: "But there is no man in the doorway over there." A: (Looks again) "Oh! I thought there was; I was wrong." B: "Does he look anything like your department chairman?" A: "Who?" B: "The man in the doorway over there." A: "There isn't any man there; I was mistaken about that."
Referring to Nonexistent Objects
B: "Well, he doesn't exist, but he's there, isn't he?" A: "Look, I was talking about a guy who exists; that is I thought I was, but I was wrong, I wasn't talking about anybody. I can't tell you what 'he' looks like because there's no 'he' to describe." Now that was supposed to be a case of failure of reference. The speaker was trying to refer to someone, but he just made a mistake and failed to do so. When confronted with questions about the object he was referring to he treats the questions as spurious (i.e., he does this once he realizes his mistake). Now here's another case: A: "The unicorn I dreamed about last night
looked pretty silly." Outsider: "But there are no unicorns." A: "So what?" Outsider: "Well there aren't any unicorns, so there couldn't be any such thing as the unicorn you dreamed about last night, so 'it' couldn't possibly have looked silly." A: "Come on, it's not a real unicorn, it's one I dreamed about." B: "Did it look anything like your department chairman?" A: "No, actually it looked a little bit like my hairdresser. " In this conversation speaker A rejects the contention that he had failed to refer to anything, though he grants that what he is referring to doesn't exist. And he treats questions about it as perfectly reasonable. Some philosophers would criticize A for this; they'll say that he should have rejected the questions. But that won't work. The question was reasonable, and it had an answer, which A communicated to B. Now I know what many of you are thinking: sure, A managed to communicate some information to B, but did he do it by referring to a nonexistent object? The grammatical form of the English sentences being used suggests yes, but as Russell, and the early Wittgenstein, and Carnap, and Ryle, and Quine, and Chisholm, and half the rest of the philosophical world have been telling us for ages now, you can't trust the "surface" grammatical form of a sentence to reveal what's really going on. Since there aren't any nonexistent objects to be referred to, A's sentences must have a different logical form than their grammatical form suggests. And what we need to do to account for
what's going on is merely to show how to paraphrase A's sentences in such a way that we eliminate the apparent reference to an unreal object. Well I hate to be a spoilsport, but, as various people have pointed out, there's one major flaw in this idea: nobody knows how to produce the paraphrases. It hasn't been done. None of you know how to do it either. So here's the situation: speakers of English act as if they sometimes refer to nonexistent objects. We either have to take this at face value or explain it away. Nobody knows how to explain it away. I've tried to illustrate the situation with reference to a couple of lifelike conversations. If you're willing to supply the lifelike contexts yourselves, there are lots of other examples. You are all probably willing to assert each of the following sentences: (1)
(2)
(3)
(4) (5)
Ironically, a certain fictional detective (namely, Sherlock Holmes) is much more famous than any real detective, living or dead. Certain Greek gods were also worshipped by the Romans, though they called them by different names. For example, the Romans worshipped Zeus, though they called him "Jupiter." Any good modern criminologist knows much more about chemical analysis than Sherlock Holmes knew. Pegasus is the winged horse of Greek mythology. Pegasus is not the chief Greek deity; Zeus is.
I suggest that you are not only willing to assert these sentences, but you are also prepared to treat the singular terms in them as if they referred; you are willing to "refer back" to previous utterances of "Zeus" with pronouns, and you do not treat questions about the chief Roman deity as spurious; many of them you're willing to answer. Of course, I certainly haven't shown that all of this apparent reference to the nonexistent can't be paraphrased away. But some of the best minds have been trying for over fifty years now, without success. Maybe it's time to stop beating our heads against that wall. Besides, there's another wall that's more fun.
Part 2:
A Quasi-Meinongian View
Alexius Meinong is perhaps the most infamous believer in nonexistent objects. The theory to be
Terence Parsons
sketched here was inspired by him, though I think there are ways in which it diverges from his views. 2 I am going to assume that no two existing objects have exactly the same properties. This is not so much an assumption about the paucity of existing objects as it is an assumption about the variety of properties; in particular I assume that for any existing object there is at least one property (and probably many) that it has and that no other existing object has. Anyway, given this assumption, there's a natural one-one correlation between real, existing objects and certain non-empty sets of properties. For example, Madame Curie is a real object, and correlated with her is the set of properties that she has: Madame Curie {p: Madame Curie has p} Now, make a list of all existing objects. Correlated with each one is a set of properties - the set of all the properties it has: REAL OBJECTS 0] O2
SETS OF PROPERTIES {p: 0] has p} {p: O2 hasp}
{p: 0" hasp} The left-hand list now exhausts the ontology that people like Russell, QIine, Frege, and most of us find acceptable; the existing objects constitute all there is. But the theory now being presented says that there's a lot more, and it goes like this. It's not clear how to continue the left-hand list (that's our goal), but you can easily see how to continue the right-hand list - just write down any other nonempty set of properties. For example, write down: {goldenness, mountainhood,
... } filling in whatever properties for the dots that you like. Now the theory under discussion says that for any such set in the right-hand list, there is correlated with it exactly one object. So write in "0,,+]" in the left-hand list: {goldenness, mountainhood,
... } The object 0,,+] can't be an existing object, because it has the properties goldenness and mountainhood - it's a gold mountain - and there aren't any real gold mountains. But, as Meinong pointed out, that
doesn't stop there from being unreal gold mountains; although certain narrow-minded people object to this, that's just because they're prejudiced! (He called this 'the prejudice in favor of the actual. ') It's clear how to extend the right-hand list - just include any set of properties that isn't already there. Corresponding to each such set is a unique object, and vice versa - i.e., each object appears only once in the left-hand list. The two lists extend our original correlation, so that it is now a correlation between all objects and the sets of properties that they have. Actually we can dispense with talk of lists and correlations and present the theory in a more direct manner in terms of two principles. For reasons that will become apparent shortly, let me call the properties I have been discussing nuclear properties. The principles are:
2
No two objects (real or unreal) have exactly the same nuclear properties. For any set of nuclear properties, some object has all of the properties in that set and no other nuclear properties.
Principle 2 does most of the work; it's a sort of "comprehension" principle for objects. Notice that principle 2 does not require that objects be "logically closed"; e.g., an object may have the property of being blue and the property of being square without having the property of being blue-andsquare. This lack of logical closure is important in certain applications of the theory, particularly applications to fictional objects and objects in dreams. 3 Many nonexistent objects will be incomplete. By calling an object 'complete,' I mean that for any nuclear property, the object either has that property or it has its negation. This characterization presupposes that it makes sense to talk of the 'negation" of a nuclear property in a somewhat unusual sense. The assumption is that for any nuclear property, p, there is another nuclear property, q, which (necessarily) is had by all and only those existing objects which don't have p, and which I call the negation of p. The negation of a nuclear property,p, will not be a property that any object has if and only if it does not have p, for no nuclear property fits that description (by principle 2 any nuclear property, q, is such that some object has both p and q).4 Given this account of nuclear property negation, all existing objects are complete. Some nonexistent objects are complete too, but some aren't. Consider
Referring to Nonexistent Objects
the object whose sole nuclear properties are goldenness and mountainhood. It does not have the property of blueness, nor does it have the property of nonblueness either; I will say that it is indeterminate with respect to blueness. That object will in fact be indeterminate with respect to every nuclear property except goldenness and mountainhood. (The object in question may be the one that Meinong was referring to when he used the words "the gold mountain"; whether this is so or not involves questions of textual interpretation that I am unsure about.) Completeness is different from logical closure. Consider the set of properties got by taking all of my properties and replacing "hazel-eyed" by "non-hazel-eyed." According to principle 2 there is an object which has the resulting properties and no others. This object will be complete, but it will not be logically closed. For example, it has brownhairedness and it has non-hazel-eyedness, but it does not have the nuclear property of being bothbrown-haired-and-non-hazel-eyed. To get an object which is logically closed yet incomplete, add to "the gold mountain" all nuclear properties that are entailed by goldenness and mountainhood. Then it will have, e.g., the property of either-being-Iocated-in-North-America-ornot-being-Iocated-in-North-America, but it will not have either of those disjuncts; it will be indeterminate with respect to being located in North America. Some objects are impossible. By calling an object, x, possible, I mean that it is possible that there exists an object which has all of x's nuclear properties (and perhaps more besides).5 All existing objects are automatically possible objects by this definition. And some unreal ones are too, e.g., "the gold mountain." But consider the object whose sole nuclear properties are roundness and squareness (this may be Meinong's famous "round square"). This is an impossible object, since there could not be an existing object which has both of these properties. Still, as Meinong pointed out, that doesn't prevent there from being an impossible object which has them. Principles 1 and 2 yield a theory that has an important virtue: they not only tell us that there are nonexistent objects, they also in part tell us what nonexistent objects there are, and they tell us what properties they have. Nuclear properties anyway, which brings us to the following point:
Not all predicates can stand for nuclear properties.
Take "exists." In the theory I've sketched, if we allowed "exists" to stand for a nuclear property, there would be trouble. Because, suppose it did stand for a nuclear property, existence. Now consider this set of properties: {goldenness, mountainhood, existence} If existence were a nuclear property, then there would be an object correlated with this set of properties; call it "the existent gold mountain." Then the existent gold mountain would turn out to have the property existence; that is, the existent gold mountain would exist. But that's just false. Initially we were troubled by there being a gold mountain; Meinong placated us by pointing out that it's only an unreal object, it doesn't exist. But in the case of the existent gold mountain, this option doesn't seem open. Conclusion: "exists," at least as it is used above, does not stand for a nuclear property. I'll call "exists" an extranuclear predicate, and in general I'll divide predicates into two categories, those which stand for nuclear properties, which I'll call nuclear predicates, and the others, which I'll call extranuclear. Which are which? First, here are some examples: NUCLEAR PREDICATES:
"is blue," "is tall," "kicked Socrates," "was kicked by Socrates," "kicked somebody," "is golden," "is a mountain," ... EXTRANUCLEAR PREDICATES:
Ontological: Modal: Intentional: Technical:
"exists," "is mythical," "is fictional," ... "is possible," "is impossible," ... "is thought about by Meinong," "is worshipped by someone," ... "is complete," ...
I'd like to emphasize that this division of predicates into nuclear and extranuclear is not peculiar to Meinong at all, it's an old and familiar one. People like Frege and Russell distinguish predicates that stand for properties of individuals from those that don't. The extranuclear predicates listed above are mostly ones that Frege and Russell have been telling us all along do not stand for properties of individuals. For example, is "exists" a predicate? Some people say flatly "no." Frege tells us that it is a predicate, but not a predicate of individuals; it's a higher-order predicate, a predicate of concepts. Likewise, we all know that "is possible" is either
Terence Parsons
not a predicate at all, or it's a predicate not of individuals but of propositions or sentences. With the intentional predicates we're not sure what to say, but we are sure that there's trouble in supposing them to be properties of individuals. Our historical situation yields a very rough kind of decision procedure for telling whether a predicate is nuclear or extranuclear. It's this: if everyone agrees that the predicate stands for an ordinary property of individuals, then it's a nuclear predicate, and it stands for a nuclear property. On the other hand, if everyone agrees that it doesn't stand for an ordinary property of individuals (for whatever reason), or if there's a history of controversy about whether it stands for a property of individuals, then it's an extranuclear predicate, and it does not stand for a nuclear property. Of course, this "decision procedure" is a very imperfect one. Probably its main virtue is to give us enough clear cases of nuclear and extranuclear predicates for us to develop an intuitive feel for the distinction, so that we can readily classify new cases. I find that I have such a feel, and that other people pick it up quite readily, and even those who are skeptical about the viability of the distinction seem to agree about which predicates are supposed to be which. The theory itself will help by putting severe constraints on what can be nuclear. For example, it is a thesis of the theory that no nuclear property, F, satisfies: (:JX) (X is a set of nuclear properties & F rf. X & (x) (x has every member of X :J x has F».
This is because if F is nuclear and F rf. X, then the object which has exactly those nuclear properties in X has every member of X without having F. For similar reasons, no nuclear property, F, satisfies: (:JX) (X is a set of nuclear properties & F rf. X & (x) (x has every member of X :J x lacks F».
If we make some minimal assumptions about nuclear properties, then these principles will show that lots of properties are extranuclear. For example, suppose that we assume the following to be nuclear: being a unicorn, being a ball bearing, being round, being square. Then we can show that all of the paradigm extranuclear predicates listed above are indeed extranuclear. For example, for F = existence, pick as X the unit set of being a unicorn. Every object that has every member of X,
i.e., every object that is a unicorn, lacks existence. So existence is extranuclear. For each of the following choices of F, the corresponding choice of X can be used in one of the above theses to show that F is extranuclear: 6 F is mythical, is fictional is possible, is impossible is thought about by Meinong is worshipped by someone is complete
Part 3:
X {is a ball bearing} {is round, is square} {p: Jimmy Carter has
p} {is a ball bearing} {p: Madame Curie hasp}
Singular Terms
Now let me turn to singular terms, specifically definite descriptions and proper names. Ideally I would discuss these within the context of ordinary language, but I find it too complicated to say anything both precise and general and brief in that context. So instead I'll talk about a certain artificial language, one that's designed to allow us a lot of talk about objects. The language will look very much like the predicate calculus, and that's good, because we all know how to symbolize lots of English in that language. There are problems here, of course; for example, whether the English "if. .. then ... " means the same as the material conditional. But most of my examples will deal with atomic sentences, so we can avoid many of these issues. In fact, to avoid complexity, I'll just talk about the monadic part of the language? Here's what it looks like: We have nuclear predicates: pN, QN, R N , ... ; they are supposed to stand for nuclear properties. We have extranuclear predicates: pE, QE, RE, ... , and they are supposed to stand for extranuclear properties. And we have object names and object variables: a, b, c, ... , x, y, z, ... ; these are supposed to stand for objects. I've called a, b, c, . .. object "names," but don't take that too seriously because I really don't think that they behave very much like English proper names (one reason is that they're not allowed to lack reference, like Russellian "logically proper names"). In fact, eventually I won't use them at all; they're just a temporary expedient to help out in my exposition.
Referring to Nonexistent Objects
We make sentences as in the predicate calculus. For example, suppose that
DN stands for being a detective, £E stands for existing, and s stands for Sherlock Holmes. Then we can write:
JYvs for "Holmes is a detective" (which is true), and £E s for "Holmes exists" (which is false). I suppose that we also have some connectives, so that we can write things like: (JYI s & ~ £E s), meaning that Sherlock Holmes is a detective who doesn't exist. And this is a truth of the simplest sort; the name, s, refers to Sherlock Holmes, and we say of him, of that object, that he's a detective and that he doesn't exist. Quantifiers are nice to have too, so I'll suppose we have quantifiers. They range over objects, all objects of course, not just the ones that exist. So we can truly say things like: (::Ix)(JYvx & £Ex) & (::Ix) (DN X & ~ £b' x ), that is, "some detectives exist, and some don't." Now a certain amount of care is needed in symbolizing English here. For sometimes we don't say literally quite all that we mean. For example, forgetting nonexistent objects for the moment, if I tell someone "Every dish is broken," it would be wrong to symbolize this as (x) (Dx :::) Bx); because that says that every dish in the universe is broken, and I certainly didn't mean that. I only had certain dishes in mind. We can capture this by using a special predicate to symbolize my use of "dish," or else we can display what's going on by "expanding" the symbolization, something like this: (x) (Dx & Ox :::) Bx, which says "Every dish that we own is broken." Now we sometimes have to do something like this with respect to existence. For example, we are sometimes inclined to say "There are winged horses (Pegasus for example)," and this is easy to symbolize; it's: (::Ix)(WN x & HN x). But we're also sometimes inclined to say "There are no winged horses," and I don't think that we then contradict what we said earlier. We use the same words, but we mean something different. We mean, I suppose, that there are no existent winged horses: ~ (::Ix)(£Ex & W NX & HN x). Well now let me turn to definite descriptions. I'm going to write them just like everybody else, namely, if you have a formula, 0, then you can put an LX in front of it like this: (LX )0, and you read it 'the thing such that 0,' or words to this effect. For example, you read:
(Lx)(Wx&Hx) as "the thing such that it's winged and it's a horse," or just "the winged horse." And my semantical account of these definite descriptions is pretty ordinary: (Lx)0 refers to the unique object that satisfies 0, if there is one, and otherwise (Lx)0 just doesn't refer at all. Now we can make sentences with these things, and I'm going to do something just slightly unorthodox here - it's really just heuristic and not a matter of logic or semantics at all - but I want to put definite descriptions in front of the predicates they combine with, as we do it in English. So if we want to write "The man in the doorway is clever," we can write:
Now actually that isn't the way I'd be inclined to symbolize that English sentence if someone used it in an ordinary real-life situation. Because, if you remember how big our ontology is, you'll realize that there are lots of men in the doorway - and this is partly in answer to Quine's worries about what he called "the possible man in the doorway,,;8 there's no such thing as the possible man in the doorway, because there are lots of men there. There are fat men in the doorway, skinny ones, bald ones, and so on. But probably ifI say, in real life, "The man in the doorway is clever," I'm not talking about, them - they're all nonexistent men, and I'm talking about an existing one. So the right way to symbolize the most natural use of the sentence is like we did with the winged horses earlier, namely:
that is, "The existing man in the doorway is clever," but I don't say "existing" when I talk, because content makes it clear that that's what I mean. And now ifI'm lucky, my definite description will refer to someone, and that will happen if there's an existing man there, and if he's alone there (except for the unreal men who are there). And then maybe what I say will be true. When will it be true? Well this much is clear: if (Lx)0 refers to an object, then a sentence of the form (LX )0F will be true if the object referred to has property F, and false if it lacks property F. (It doesn't matter here whether F is nuclear or extranuclear.) But what if the definite description fails to refer? Well, for sure the
Terence Parsons sentence is untrue, but is it untrue because it's false, or untrue because it lacks truth-value altogether? Oh, I don't know. The data doesn't seem to tell us. I've said that the linguistic data tell us this: that if we believe that "the 0" fails to refer, and if someone asks us whether the 0 is F, then we generally regard the question as spurious; we won't answer it. But there are two ways this might be explained. First, maybe simple sentences with nonreferring definite descriptions lack truth-value; that would explain why the question is spurious it has no true or false answer. But maybe instead of lacking truth-value such sentences are false, automatically false, because of the failure of reference. Then literally the question has an answer - the answer is "no" - but the speaker will be reluctant to say this, for fear of encouraging the impression that the 0 has some property incompatible with F. In the first conversation I gave you, maybe speaker A won't say 'no' when speaker B asks if the man in the doorway looks like A's department chairman for fear of conveying the impression that the man in the doorway looks different from his department chairman. If this explanation were correct, it would be OK for A to precede his answer with the word "no," just as long as he went on to explain that there was no such man. And I think it would be natural for him to do this, but that doesn't show he thinks there literally is an answer to B's question, because we often say "no" just as a kind of generalized protest reaction. So I don't know what the right thing is to say here, but for present purposes I think I can remain neutral on this issue. So let me just stick with saying that when (Lx)0 fails to refer, then (Lx)0F is automatically untrue, without committing myself to which sort of untruth is in question. And that's really all I need to illustrate how failing to refer is different from referring to something nonexistent, because, for example, we can truly say that the fictional detective who lived at 22lB Baker Street was clever, but we can't ever say truly that the man in the doorway (i.e., the existing man in the doorway) is clever, when there exists no man in the doorway. (We can't even truly say that "he" is a man.) Before moving on to names, I should say one more thing about descriptions. Suppose that we have in our language some verbs of propositional attitude, such as believes or wonders whether. Then, as lots of people have pointed out, a sentence like: Agatha believes the tallest spy is a spy
is ambiguous. It has a de dicto reading, which can be symbolized:
aB{(Lx)0S} where (Lx)0 stands for "the tallest spy" (I don't really have the resources in this monadic fragment to represent the superlative construction, so just suppose it's done somehow). But the sentence also has a de re reading; Agatha believes ofthe tallest spy that he or she is a spy. So how is this to be written? Well, I'll use a technique here that Ron Scales has made much of. 9 First, we use abstraction to symbolize the de re property of being believed by Agatha to be a spy:
[AxaB{Sx}] and then we say that the tallest spy has that property:
(Lx)0[AxaB{ Sx }]. This gives us the effect of descriptions having scope, but without forcing us to consider them to be incomplete symbols. And that in turn lets us solve one of Russell's problems, a problem that Russell himself failed to solve; namely, we can symbolize the de dicto reading of "George IV wondered whether the author of Waverley was suchand-such" as:
g wondered whether {( LX) (X authored Waverley) was such-and-such} without insisting that this means the same as "George IV wondered whether one and only one person authored Waverley", and was such-andsuch.,10 Finally, what about proper names? Let me symbolize them with capital letters: A, B, C, . .. , and put them in sentences in the same places where definite descriptions go, just as in English. So we write "Pegasus flies" just as PF. Semantically, some names refer, and some don't; of those that refer, some refer to existing objects, and some to nonexistent objects. The rest of their semantics is just like definite descriptions. Now I want to deny some of the popular things that have been said recently about proper names. Well first I'll say (I've already said) that, contrary to popular opinion, names like "Pegasus" and "Sherlock Holmes" do refer; they refer to non-
Referring to Nonexistent Objects
existent objects. The former refers to a certain winged horse that appears in Greek mythology, and the latter to a certain fictional detective. My second denial: I deny that whether or not a name refers depends on whether our use of it can be traced back by means of a causal chain to something like a dubbing that takes place in the presence of its referent. I'm denying a popular version of the causal theory of names. Though in fact I think that the causal theory may come very close to being right in these cases; it only makes a small mistake (maybe) that isn't really relevant to the spirit of the theory. The mistake is to suppose that the referent of a name must itself be a causal agent in the chain. I don't think that's right even in the case of certain existing things. For example, the novel The Wind in the Willows has a certain name (namely, "The Wind in the Willows"); but if we trace back our present use of that name causal~y, we don't come to the novel, but rather to a copy of the novel. The novel itself is not a physical object, and doesn't enter into causal relations. But coming to a copy of the novel is good enough; we need one more link in the chain, but it's not a causal one; rather it consists of something like exemplification, or tokening. I think that reference to Sherlock Holmes is like this. We trace the name back causally to the Conan Doyle novels, but then instead of encountering what Keith Donnellan!! calls a "block," which is sort oflike a break in the chain, we make one more non-causal step to Sherlock Holmes.!2 If we couldn't reach Holmes through the novels in this way, probably we couldn't refer to him. Third, I have heard some people recently say that proper names do not manifest de rei de dicto ambiguities. This is thought to follow from the
claim that they are rigid designators. But it doesn't follow. A rigid designator is a name that names the same object in every possible world. But all that follows from this is that proper names do not manifest de rei de dicto ambiguities with respect to modal operators. It says nothing about what they do in the presence of, say, epistemic words. Agatha can believe de dicto that Plato is a famous philosopher without having any de re beliefs about Plato at all. Conversely, she can believe of Tully (i.e., de re) that he did such and such without believing de dicto that Tully did such and such. Lastly, I want to say that proper names have sense. Or at least they're as good candidates for having sense as any other kind of word in our language. Their having sense would explain how it's possible for Agatha to believe (de dicto) that Cicero did such and such without her believing (again de dicto) that Tully did. The reason people have thought that proper names lacked sense is that they seem to think that if proper names do have sense, then they must be synonymous with certain definite descriptions. But there's no good reason to think this, any more than you should think that if definite descriptions have sense, then they must be synonymous with certain names. I know that both Frege and Russell suggested this - that names are synonymous with descriptions - and recently this has been rejected. And the view that names have sense has been maligned by being associated with this view. But it's a classic case of guilt by association. I think that people have failed to notice the need for senses because of their preoccupation with modalities, and the view that names are rigid designators.
Notes Work on this paper was supported by the University of Massachusetts and by a grant from the National Endowment for the Humanities. I am indebted to the University of California at Irvine for providing office facilities, and to Karel Lambert, Kit Fine, and David Woodruff Smith for criticism. A draft of this paper was read at a conference at Arizona State University, Tempe. Preliminary work on such a theory is found in my "A prolegomenon to Meinongian semantics," Journal of Philosophy 71116 (1974), pp. 561-80, hereafter PMS; "A Meinongian analysis of fictional objects," Grazer Philosophische Studien 1 (1975), pp. 73-86, hereafter MAFO; and "Nuclear and extranuclear properties,
Meinong and Leibniz," Nous 12 (1978), pp. 147-51. A more comprehensive treatment is being developed in a book entitled Nonexistent Objects (New Haven: Yale University Press, 1980), hereafter NO. In none of these works are objects taken to be sets of properties. 2 Many of Meinong's views can be found in A. Meinong, "The theory of objects," in R. Chisholm (ed.) Realism and the Background of Phenomenology (Glencoe, III.: Free Press, 1960), and in J. Findlay, Meinong's Theory of Objects and Values (Oxford: Clarendon Press, 1963). For purposes of comparing my views with Meinong's, interpret my "exists" as his "exists or subsists".
3 Cf. MAFO and NO, 3 and 7.
Terence Parsons 4 Perhaps for this reason I shouldn't use the term "negation," but should use something like "complement." It isn't certain that "the" negation of p is unique, but the discussion of incomplete objects in the text doesn't suffer from this. Cf. NO, chs 5 and 6. 5 Many other notions may have an equal right to the title "possible." E.g., we might want to reserve the term for objects which are both possible in the sense defined and also complete. Or we might use it to denote those objects which are such that they might have existed (in a de re sense of "might have"). Cf. NO, chs I and 5. 6 By "is mythical" I mean "occurs in an actual myth"; similarly for "is fictional." For certain of the predicates we might have to appeal to the stronger, modalized principle: ('lX) (X is a set of nuclear properties & F fi X & possibly (x) (x has every member of X ~ x lacks F)).
7
S 9 10 II 12
Ultimately the distinction between nuclear and extranuclear properties should gain viability by being incorporated into a general theory of objects and properties; that is the task of most of NO. Relations are very important; they, together with the other constructions discussed below in the text, are developed throughout NO. In W. V. Quine, From a Logical Point o{ View (New York: Harper & Row, 1961), p. 4. R. Scales, "Attribution and existence" (Ph.D. diss., University of California, Irvine, 1969). Cf. L. Linsky, Referring (London: Routledge and Kegan Paul, 1967). K. Donnellan, "Speaking of nothing," Philosophital Reriew 83 (1974), pp. 3-32, sect. 6. The nature of the noncausal step from the story to Sherlock Holmes is discussed tersely in MAFO and in somewhat more detail in NO, ch. 7.
W. V. Quine
I I listened to Dewey on Art as Experience when I was a graduate student in the spring of 1931. Dewey was then at Harvard as the first William James Lecturer. I am proud now to be at Columbia as the first John Dewey Lecturer. Philosophically I am bound to Dewey by the naturalism that dominated his last three decades. With Dewey I hold that knowledge, mind, and meaning are part of the same world that they have to do with, and that they are to be studied in the same empirical spirit that animates natural science. There is no place for a prior philosophy. When a naturalistic philosopher addresses himself to the philosophy of mind, he is apt to talk of language. Meanings are, first and foremost, meanings of language. Language is a social art which we all acquire on the evidence solely of other people's overt behavior under publicly recognizable circumstances. Meanings, therefore, those very models of mental entities, end up as grist for the behaviorist's mill. Dewey was explicit on the point: "Meaning ... is not a psychic existence; it is primarily a property ofbehavior."J Once we appreciate the institution oflanguage in these terms, we see that there cannot be, in any useful sense, a private language. This point was Originally published in W. V. Quine Ontological Relativity and other Essays (1969), pp. 26-68. Copyright © by W. V. Quine. Reprinted by permission of Columbia University Press.
stressed by Dewey in the twenties. "Soliloquy," he wrote, "is the product and reflex of converse with others.,,2 Further along he expanded the point thus: "Language is specifically a mode of interaction of at least two beings, a speaker and a hearer; it presupposes an organized group to which these creatures belong, and from whom they have acquired their habits of speech. It is therefore a relationship.,,3 Years later, Wittgenstein likewise rejected private language. When Dewey was writing in this naturalistic vein, Wittgenstein still held his copy theory of language. The copy theory in its various forms stands closer to the main philosophical tradition, and to the attitude of common sense today. Uncritical semantics is the myth of a museum in which the exhibits are meanings and the words are labels. To switch languages is to change the labels. Now the naturalist's primary objection to this view is not an objection to meanings on account of their being mental entities, though that could be objection enough. The primary objection persists even if we take the labeled exhibits not as mental ideas but as Platonic ideas or even as the denoted concrete objects. Semantics is vitiated by a pernicious mentalism as long as we regard a man's semantics as somehow determinate in his mind beyond what might be implicit in his dispositions to overt behavior. It is the very facts about meaning, not the entities meant, that must be construed in terms of behavior. There are two parts to knowing a word. One part is being familiar with the sound of it and being able
W. V. Quine to reproduce it. This part, the phonetic part, is achieved by observing and imitating other people's behavior, and there are no important illusions about the process. The other part, the semantic part, is knowing how to use the word. This part, even in the paradigm case, is more complex than the phonetic part. The word refers, in the paradigm case, to some visible object. The learner has now not only to learn the word phonetically, by hearing it from another speaker; he also has to see the object; and in addition to this, in order to capture the relevance of the object to the word, he has to see that the speaker also sees the object. Dewey summed up the point thus: "The characteristic theory about B's understanding of A's sounds is that he responds to the thing from the standpoint of A."4 Each of us, as he learns his language, is a student of his neighbor's behavior; and conversely, insofar as his tries are approved or corrected, he is a subject of his neighbor's behavioral study. The semantic part of learning a word is more complex than the phonetic part, therefore, even in simple cases: we have to see what is stimulating the other speaker. In the case of words not directly ascribing observable traits to things, the learning process is increasingly complex and obscure; and obscurity is the breeding place of mentalistic semantics. What the naturalist insists on is that, even in the complex and obscure parts of language learning, the learner has no data to work with but the overt behavior of other speakers. When with Dewey we turn thus toward a naturalistic view of language and a behavioral view of meaning, what we give up is not just the museum figure of speech. We give up an assurance of determinacy. Seen according to the museum myth, the words and sentences of a language have their determinate meanings. To discover the meanings of the native's words, we may have to observe his behavior, but still the meanings of the words are supposed to be determinate in the native's mind, his mental museum, even in cases where behavioral criteria are powerless to discover them for us. When on the other hand we recognize with Dewey that "meaning ... is primarily a property of behavior," we recognize that there are no meanings, nor likenesses nor distinctions of meaning, beyond what are implicit in people's dispositions to overt behavior. For naturalism the question whether two expressions are alike or unlike in meaning has no determinate answer, known or unknown, except insofar as the answer is settled in principle by people's speech dispositions, known
or unknown. If by these standards there are indeterminate cases, so much the worse for the terminology of meaning and likeness of meaning. To see what such indeterminacy would be like, suppose there were an expression in a remote language that could be translated into English equally defensibly in either of two ways, unlike in meaning in English. I am not speaking of ambiguity within the native language. I am supposing that one and the same native use of the expression can be given either of the English translations, each being accommodated by compensating adjustments in the translation of other words. Suppose both translations, along with these accommodations in each case, accord equally well with all observable behavior on the part of speakers of the remote language and speakers of English. Suppose they accord perfectly not only with behavior actually observed, but with all dispositions to behavior on the part of all the speakers concerned. On these assumptions it would be forever impossible to know of one of these translations that it was the right one, and the other wrong. Still, if the museum myth were true, there would be a right and wrong of the matter; it is just that we would never know, not having access to the museum. See language naturalistically, on the other hand, and you have to see the notion of likeness of meaning in such a case simply as nonsense. I have been keeping to the hypothetical. Turning now to examples, let me begin with a disappointing one and work up. In the French construction "ne ... rien" you can translate "rien" into English as "anything' or as "nothing" at will, and then accommodate your choice by translating "ne" as "not" or by construing it as pleonastic. This example is disappointing because you can object that I have merely cut the French units too small. You can believe the mentalistic myth of the meaning museum and still grant that "rien" of itself has no meaning, being no whole label; it is part of "ne ... rien," which has its meaning as a whole. I began with this disappointing example because I think its conspicuous trait - its dependence on cutting language into segments too short to carry meanings - is the secret of the more serious cases as well. What makes other cases more serious is that the segments they involve are seriously long: long enough to be predicates and to be true of things and hence, you would think, to carry meanings. An artificial example which I have used elsewhere 5 depends on the fact that a whole rabbit is
Ontological Relativity
present when and only when an undetached part of a rabbit is present; also when and only when a temporal stage of a rabbit is present. If we are wondering whether to translate a native expression "gavagai" as "rabbit" or as "undetached rabbit part" or as "rabbit stage," we can never settle the matter simply by ostension - that is, simply by repeatedly querying the expression "gavagai" for the native's assent or dissent in the presence of assorted stimulations. Before going on to urge that we cannot settle the matter by non-ostensive means either, let me belabor this ostensive predicament a bit. I am not worrying, as Wittgenstein did, about simple cases of ostension. The color word "sepia," to take one of his examples,6 can certainly be learned by an ordinary process of conditioning, or induction. One need not even be told that sepia is a color and not a shape or a material or an article. True, barring such hints, many lessons may be needed, so as to eliminate wrong generalizations based on shape, material, etc., rather than color, and so as to eliminate wrong notions as to the intended boundary of an indicated example, and so as to delimit the admissible variations of color itself. Like all conditioning, or induction, the process will depend ultimately also on one's own inborn propensity to find one stimulation qualitatively more akin to a second stimulation than to a third; otherwise there can never be any selective reinforcement and extinction of responses. 7 Still, in principle nothing more is needed in learning "sepia" than in any conditioning or induction. But the big difference between "rabbit" and "sepia" is that whereas "sepia" is a mass term like "water," "rabbit" is a term of divided reference. As such it cannot be mastered without mastering its principle of individuation: where one rabbit leaves off and another begins. And this cannot be mastered by pure ostension, however persistent. Such is the quandary over "gavagai": where one gavagai leaves off and another begins. The only difference between rabbits, undetached rabbit parts, and rabbit stages is in their individuation. If you take the total scattered portion of the spatiotemporal world that is made up of rabbits, and that which is made up of undetached rabbit parts, and that which is made up of rabbit stages, you come out with the same scattered portion of the world each of the three times. The only difference is in how you slice it. And how to slice it is what ostension or simple conditioning, however persistently repeated, cannot teach.
Thus consider specifically the problem of deciding between "rabbit" and "undetached rabbit part" as translation of "gavagai." No word of the native language is known, except that we have settled on some working hypothesis as to what native words or gestures to construe as assent and dissent in response to our pointings and queryings. Now the trouble is that whenever we point to different parts of the rabbit, even sometimes screening the rest of the rabbit, we are pointing also each time to the rabbit. When, conversely, we indicate the whole rabbit with a sweeping gesture, we are still pointing to a multitude of rabbit parts. And note that we do not have even a native analogue of our plural ending to exploit, in asking "gavagai?" It seems clear that no even tentative decision between "rabbit" and "undetached rabbit part" is to be sought at this level. How would we finally decide? My passing mention of plural endings is part of the answer. Our individuating of terms of divided reference, in English, is bound up with a cluster of interrelated grammatical particles and constructions: plural endings, pronouns, numerals, the "is" of identity, and its adaptations "same" and "other." It is the cluster of interrelated devices in which quantification becomes central when the regimentation of symbolic logic is imposed. If in his language we could ask the native "Is this gavagai the same as that one?" while making appropriate multiple ostensions, then indeed we would be well on our way to deciding between "rabbit," "undetached rabbit part," and "rabbit stage." And of course the linguist does at length reach the point where he can ask what purports to be that question. He develops a system for translating our pluralizations, pronouns, numerals, identity, and related devices contextually into the native idiom. He develops such a system by abstraction and hypothesis. He abstracts native particles and constructions from observed native sentences and tries associating these variously with English particles and constructions. Insofar as the native sentences and the thus associated English ones seem to match up in respect of appropriate occasions of use, the linguist feels confirmed in these hypotheses of translation what I call analytical hypotheses. 8 But it seems that this method, though laudable in practice and the best we can hope for, does not in principle settle the indeterminancy between "rabbit," "undetached rabbit part," and "rabbit stage." For if one workable overall system of analytical hypotheses provides for translating a given native
w. V. Quine expression into "is the same as," perhaps another equally workable but systematically different system would translate that native expression rather into something like "belongs with." Then, when in the native language we try to ask, "Is this gavagai the same as that?," we could as well be asking "Does this gavagai belong with that?" Insofar, the native's assent is no objective evidence for translating "gavagai" as "rabbit" rather than "undetached rabbit part" or "rabbit stage." This artificial example shares the structure of the trivial earlier example "ne ... rien." We were able to translate "rien" as "anything" or as "nothing," thanks to a compensatory adjustment in the handling of "ne." And I suggest that we can translate "gavagai" as "rabbit" or "undetached rabbit part" or "rabbit stage," thanks to compensatory adjustments in the translation of accompanying native locutions. Other adjustments still might accommodate translation of "gavagai" as "rabbithood," or in further ways. I find this plausible because of the broadly structural and contextual character of any considerations that could guide us to native translations of the English cluster of interrelated devices of individuation. There seem bound to be systematically very different choices, all of which do justice to all dispositions to verbal behaviour on the part of all concerned. An actual field linguist would of course be sensible enough to equate "gavagai" with "rabbit," dismissing such perverse alternatives as "undetached rabbit part" and "rabbit stage" out of hand. This sensible choice and others like it would help in turn to determine his subsequent hypotheses as to what native locutions should answer to the English apparatus of individuation, and thus everything would come out all right. The implicit maxim guiding his choice of "rabbit," and similar choices for other native words, is that an enduring and relatively homogeneous object, moving as a whole against a contrasting background, is a likely reference for a short expression. If he were to become conscious of this maxim, he might celebrate it as one of the linguistic universals, or traits of all languages, and he would have no trouble pointing out its psychological plausibility. But he would be wrong; the maxim is his own imposition, toward settling what is objectively indeterminate. It is a very sensible imposition, and I would recommend no other. But I am making a philosophical point. It is philosophically interesting, moreover, that what is indeterminate in this artificial example is not just meaning, but extension; reference. My
remarks on indeterminacy began as a challenge to likeness of meaning. I had us imagining "an expression that could be translated into English equally defensibly in either of two ways, unlike in meaning in English." Certainly likeness of meaning is a dim notion, repeatedly challenged. Of two predicates which are alike in extension, it has never been clear when to say that they are alike in meaning and when not; it is the old matter of featherless bipeds and rational animals, or of equiangular and equilateral triangles. Reference, extension, has been the firm thing; meaning, intension, the infirm. The indeterminacy of translation now confronting us, however, cuts across extension and intension alike. The terms "rabbit," "undetached rabbit part," and "rabbit stage" differ not only in meaning; they are true of different things. Reference itself proves behaviorally inscrutable. Within the parochial limits of our own language, we can continue as always to find extensional talk clearer than intensional. For the indeterminacy between "rabbit," "rabbit stage," and the rest depended only on a correlative indeterminacy of translation of the English apparatus of individuation ~ the apparatus of pronouns, pluralization, identity, numerals, and so on. No such indeterminacy obtrudes so long as we think of this apparatus as given and fixed. Given this apparatus, there is no mystery about extension; terms have the same extension when true of the same things. At the level of radical translation, on the other hand, extension itself goes inscrutable. My example of rabbits and their parts and stages is a contrived example and a perverse one, with which, as I said, the practicing linguist would have no patience. But there are also cases, less bizarre ones, that obtrude in practice. In Japanese there are certain particles, called "classifiers," which may be explained in either oftwo ways. Commonly they are explained as attaching to numerals, to form compound numerals of distinctive styles. Thus take the numeral for 5. If you attach one classifier to it, you get a style of "5" suitable for counting animals; if you attach a different classifier, you get a style of "5" suitable for counting slim things like pencils and chopsticks; and so on. But another way of viewing classifiers is to view them not as constituting part of the numeral, but as constituting part of the term ~ the term for "chopsticks" or "oxen" or whatever. On this view the classifier does the individuative job that is done in English by "sticks of" as applied to the mass term "wood," or "head of" as applied to the mass term "cattle."
Ontological Relativity
What we have on either view is a Japanese phrase tantamount say to "five oxen," but consisting of three words; 9 the first is in effect the neutral numeral "5," the second is a classifier of the animal kind, and the last corresponds in some fashion to "ox." On one view the neutral numeral and the classifier go together to constitute a declined numeral in the "animal gender," which then modifies "ox" to give, in effect, "five oxen." On the other view the third Japanese word answers not to the individuative term "ox" but to the mass term "cattle"; the classifier applies to this mass term to produce a composite individuative term, in effect "head of cattle"; and the neutral numeral applies directly to all this without benefit of gender, giving "five head of cattle," hence again in effect "five oxen." If so simple an example is to serve its expository purpose, it needs your connivance. You have to understand "cattle" as a mass term covering only bovines, and "ox" as applying to all bovines. That these usages are not the invariable usages is beside the point. The point is that the Japanese phrase comes out as "five bovines," as desired, when parsed in either of two ways. The one way treats the third Japanese word as an individuative term true of each bovine, and the other way treats that word rather as a mass term covering the un individuated totality of beef on the hoof. These are two very different ways of treating the third Japanese word; and the threeword phrase as a whole turns out all right in both cases only because of compensatory differences in our account of the second word, the classifier. This example is reminiscent in a way of our trivial initial example, "ne ... rien." We were able to represent "rien" as "anything" or as "nothing," by compensatorily taking "ne" as negative or as vacuous. We are able now to represent a Japanese word either as an individuative term for bovines or as a mass term for live beef, by compensatorily taking the classifer as declining the numeral or as individuating the mass term. However, the triviality of the one example does not quite carryover to the other. The early example was dismissed on the ground that we had cut too small; "rien" was to short for significant translation on its own, "and 'ne ... rien" was the significant unit. But you cannot dismiss the Japanese example by saying that the third word was too short for significant translation on its own and that only the whole three-word phrase, tantamount to "five oxen," was the significant unit. You cannot take this line unless you are prepared to call a word too short for significant translation even when it is long enough to be a
term and carry denotation. For the third Japanese word is, on either approach, a term: on one approach a term of divided reference, and on the other a mass term. If you are indeed prepared thus to call a word too short for significant translation even when it is a denoting term, then in a backhanded way you are granting what I wanted to prove: the inscrutability of reference. Between the two accounts of Japanese classifiers there is no question of right and wrong. The one account makes for more efficient translation into idiomatic English; the other makes for more of a feeling for the Japanese idiom. Both fit all verbal behavior equally well. All whole sentences, and even component phrases like "five oxen," admit of the same net overall English translations on either account. This much is invariant. But what is philosophically interesting is that the reference or extension of shorter terms can fail to be invariant. Whether that third Japanese word is itself true of each ox, or whether on the other hand it is a mass term which needs to be adjoined to the classifier to make a term which is true of each ox - here is a question that remains undecided by the totality of human dispositions to verbal behavior. It is indeterminate in principle; there is no fact of the matter. Either answer can be accommodated by an account of the classifier. Here again, then, is the inscrutability of reference - illustrated this time by a humdrum point of practical translation. The inscrutability of reference can be brought closer to home by considering the word "alpha," or again the word "green." In our use of these words and others like them there is a systematic ambiguity. Sometimes we use such words as concrete general terms, as when we say the grass is green, or that some inscription begins with an alpha. Sometimes, on the other hand, we use them as abstract singular terms, as when we say that green is a color and alpha is a letter. Such ambiguity is encouraged by the fact that there is nothing in ostension to distinguish the two uses. The pointing that would be done in teaching the concrete general term "green" or "alpha" differs none from the pointing that would be done in teaching the abstract singular term "green" or "alpha." Yet the objects referred to by the word are very different under the two uses; under the one use the word is true of many concrete objects, and under the other use it names a single abstract object. We can of course tell the two uses apart by seeing how the word turns up in sentences: whether it takes an indefinite article, whether it takes a plural
W. V. Quine ending, whether it stands as singular subject, whether it stands as modifier, as predicate complement, and so on. But these criteria appeal to our special English grammatical constructions and particles, our special English apparatus of individuation, which, I already urged, is itself subject to indeterminacy of translation. So, from the point of view of translation into a remote language, the distinction between a concrete general and an abstract singular term is in the same predicament as the distinction between "rabbit," "rabbit part," and "rabbit stage." Here then is another example of the inscrutability of reference, since the difference between the concrete general and the abstract singular is a difference in the objects referred to. Incidentally we can concede this much indeterminacy also to the "sepia" example, after all. But this move is not evidently what was worrying Wittgenstein. The ostensive indistinguishability of the abstract singular from the concrete general turns upon what may be called "deferred ostension," as opposed to direct ostension. First let me define direct ostension. The ostended point, as I shall call it, is the point where the line of the pointing finger first meets an opaque surface. What characterizes direct ostension, then, is that the term which is being ostensively explained is true of something that contains the ostended point. Even such direct ostension has its uncertainties, of course, and these are familiar. There is the question how wide an environment of the ostended point is meant to be covered by the term that is being ostensively explained. There is the question how considerably an absent thing or substance might be allowed to differ from what is now ostended, and still be covered by the term that is now being ostensively explained. Both of these questions can in principle be settled as well as need be by induction from multiple ostensions. Also, if the term is a term of divided reference like "apple," there is the question of individuation: the question where one of its objects leaves off and another begins. This can be settled by induction from multiple ostensions of a more elaborate kind, accompanied by expressions like "same apple" and "another," if an equivalent of this English apparatus of individuation has been settled on; otherwise the indeterminacy persists that was illustrated by "rabbit," "undetached rabbit part," and "rabbit stage." Such, then, is the way of direct ostension. Other os tension I call deferred. It occurs when we point at the gauge, and not the gasoline, to show that there
is gasoline. Also it occurs when we explain the abstract singular term "green" or "alpha" by pointing at grass or a Greek inscription. Such pointing is direct ostension when used to explain the concrete general term "green" or "alpha," but it is deferred ostension when used to explain the abstract singular terms; for the abstract object which is the color green or the letter alpha does not contain the ostended point, nor any point. Deferred ostension occurs very naturally when, as in the case of the gasoline gauge, we have a correspondence in mind. Another such example is afforded by the GOdel numbering of expressions. Thus if7 has been assigned as Godel number of the letter alpha, a man conscious of the Godel numbering would not hesitate to say "Seven" on pointing to an inscription of the Greek letter in question. This is, on the face of it, a doubly deferred ostension: one step of deferment carries us from the inscription to the letter as abstract object, and a second step carries us thence to the number. By appeal to our apparatus of individuation, if it is available, we can distinguish between the concrete general and the abstract singular use of the word "alpha"; this we saw. By appeal again to that apparatus, and in particular to identity, we can evidently settle also whether the word "alpha" in its abstract singular use is being used really to name the letter or whether, perversely, it is being used to name the Godel number of the letter. At any rate we can distinguish these alternatives if also we have located the speaker's equivalent of the numeral "7" to our satisfaction; for we can ask him whether alpha is 7. These considerations suggest that deferred ostension adds no essential problem to those presented by direct ostension. Once we have settled upon analytical hypotheses of translation covering identity and the other English particles relating to individuation, we can resolve not only the indecision between "rabbit" and "rabbit stage" and the rest, which came of direct ostension, but also any indecision between concrete general and abstract singular, and any indecision between expression and Godel number, which come of deferred ostension. However, this conclusion is too sanguine. The inscrutability of reference runs deep, and it persists in a subtle form even if we accept identity and the rest of the apparatus of individuation as fixed and settled; even, indeed, if we forsake radical translation and think only of English. Consider the case of a thoughtful protosyntacticiano He has a formalized system of first-order
Ontological Relativity
proof theory, or protosyntax, whose universe comprises just expressions, that is, strings of signs of a specified alphabet. Now just what sorts of things, more specifically, are these expressions? They are types, not tokens. So, one might suppose, each of them is the set of all its tokens. That is, each expression is a set of inscriptions which are variously situated in space-time but are classed together by virtue of a certain similarity in shape. The concatenate x ~ y of two expressions x and y, in a given order, will be the set of all inscriptions each of which has two parts which are tokens respectively of x and y and follow one upon the other in that order. But x ~ y may then be the null set, though x and yare not null; for it may be that inscriptions belonging to x andy happen to turn up head to tail nowhere, in the past, present, or future. This danger increases with the lengths of x and y. But it is easily seen to violate a law of proto syntax which says that x = z whenever x ~ y = z ~ y. Thus it is that our thoughtful protosyntactician will not construe the things in his universe as sets of inscriptions. He can still take his atoms, the single signs, as sets of inscriptions, for there is no risk of nullity in these cases. And then, instead of taking his strings of signs as sets of inscriptions, he can invoke the mathematical notion of sequence and take them as sequences of signs. A familiar way of taking sequences, in turn, is as a mapping of things on numbers. On this approach an expression or string of signs becomes a finite set of pairs each of which is the pair of a sign and a number. This account of expressions is more artificial and more complex than one is apt to expect who simply says he is letting his variables range over the strings of such and such signs. Moreover, it is not the inevitable choice; the considerations that motivated it can be met also by alternative constructions. One of these constructions is GOdel numbering itself, and it is temptingly simple. It uses just natural numbers, whereas the foregoing construction used sets of one-letter inscriptions and also natural numbers and sets of pairs of these. How clear is it that at just this point we have dropped expressions in favor of numbers? What is clearer is merely that in both constructions we were artificially devising models to satisfy laws that expressions in an unexplicated sense had been meant to satisfy. So much for expressions. Consider now the arithmetician himself, with his elementary number theory. His universe comprises the natural numbers outright. Is it clearer than the protosyntactician's? What, after all, is a natural number? There
are Frege's version, Zermelo's, and von Neumann's, and countless further alternatives, all mutually incompatible and equally correct. What we are doing in anyone of these explications of natural number is to devise set-theoretic models to satisfy laws which the natural numbers in an unexplicated sense had been meant to satisfy. The case is quite like that of protosyntax. It will perhaps be felt that any set-theoretic explication of natural number is at best a case of obscurum per obscurius; that all explications must assume something, and the natural numbers themselves are an admirable assumption to start with. I must agree that a construction of sets and set theory from natural numbers and arithmetic would be far more desirable than the familiar opposite. On the other hand, our impression of the clarity even of the notion of natural number itself has suffered somewhat from Gbdel's proof of the impossibility of a complete proof procedure for elementary number theory, or, for that matter, from Skolem's and Henkin's observations that all laws of natural numbers admit nonstandard models.lO We are finding no clear difference between specifying a universe of discourse - the range of the variables of quantification - and reducing that universe to some other. We saw no significant difference between clarifying the notion of expression and supplanting it by that of number. And now to say more particularly what numbers themselves are is in no evident way different from just dropping numbers and assigning to arithmetic one or another new model, say in set theory. Expressions are known only by their laws, the laws of concatenation theory, so that any constructs obeying those laws - Gbdel numbers, for instanceare ipso facto eligible as explications of expression. Numbers in turn are known only by their laws, the laws of arithmetic, so that any constructs obeying those laws - certain sets, for instance - are eligible in turn as explications of number. Sets in turn are known only by their laws, the laws of set theory. Russell pressed a contrary thesis, long ago. Writing of numbers, he argued that for an understanding of number the laws of arithmetic are not enough; we must know the applications, we must understand numerical discourse embedded in discourse of other matters. In applying number, the key notion, he urged, is Anzahl: there are n soand-so's. However, Russell can be answered. First take, specifically, Anzahl. We can define "there are n so-and-so's" without ever deciding what numbers are, apart from their fulfillment of arithmetic.
W. V. Quine That there are n so-and-so's can be explained simply as meaning that the so-and-so's are in one-toone correspondence with the numbers up to n. II Russell's more general point about application can be answered too. Always, if the structure is there, the applications will fall into place. As paradigm it is perhaps sufficient to recall again this reflection on expressions and Godel numbers: that even the pointing out of an inscription is no final evidence that our talk is of expressions and not of Godel numbers. We can always plead deferred ostension. It is in this sense true to say, as mathematicians often do, that arithmetic is all there is to number. But it would be a confusion to express this point by saying, as is sometimes said, that numbers are any things fulfilling arithmetic. This formulation is wrong because distinct domains of objects yield distinct models of arithmetic. Any progression can be made to serve; and to identify all progressions with one another, e.g., to identify the progression of odd numbers with the progression of evens, would contradict arithmetic after all. So, though Russell was wrong in suggesting that numbers need more than their arithmetical properties, he was right in objecting to the definition of numbers as any things fulfilling arithmetic. The subtle point is that any progression will serve as a version of number so long and only so long as we stick to one and the same progression. Arithmetic is, in this sense, all there is to number: there is no saying absolutely what the numbers are; there is only arithmetic. 12
II I first urged the inscrutability of reference with the help of examples like the one about rabbits and rabbit parts. These used direct ostension, and the inscrutability of reference hinged on the indeterminacy of translation of identity and other individuative apparatus. The setting of these examples, accordingly, was radical translation: translation from a remote language on behavioral evidence, unaided by prior dictionaries. Moving then to deferred ostension and abstract objects, we found a certain dimness of reference pervading the home language itself. Now it should be noted that even for the earlier examples the resort to a remote language was not really essential. On deeper reflection, radical translation begins at home. Must we equate our neigh-
bor's English words with the same strings of phonemes in our own mouths? Certainly not; for sometimes we do not thus equate them. Sometimes we find it to be in the interests of communication to recognize that our neighbor's use of some word, such as "cool" or "square" or "hopefully," differs from ours, and so we translate that word of his into a different string of phonemes in our idiolect. Our usual domestic rule of translation is indeed the homophonic one, which simply carries each string of phonemes into itself; but still we are always prepared to temper homophony with what Neil Wilson has called the "principle of charity.,,13 We will construe a neighbor's word heterophonically now and again if thereby we see our way to making his message less absurd. The homophonic rule is a handy one on the whole. That it works so well is no accident, since imitation and feedback are what propagate a language. We acquired a great fund of basic words and phrases in this way, imitating our elders and encouraged by our elders amid external circumstances to which the phrases suitably apply. Homophonic translation is implicit in this social method of learning. Departure from homophonic translation in this quarter would only hinder communication. Then there are the relatively rare instances of opposite kind, due to divergence in dialect or confusion in an individual, where homophonic translation incurs negative feedback. But what tends to escape notice is that there is also a vast mid-region where the homophonic method is indifferent. Here, gratuitously, we can systematically reconstrue our neighbor's apparent references to rabbit stages, and his apparent references to formulas as really references to Godel numbers, and vice versa. We can reconcile all this with our neighbor's verbal behavior, by cunningly readjusting our translations of his various connecting predicates so as to compensate for the switch of ontology. In short, we can reproduce the inscrutability of reference at home. It is of no avail to check on this fanciful version of our neighbor's meanings by asking him, say, whether he really means at a certain point to refer to formulas or to their Godel numbers; for our question and his answer - "By all means, the numbers" - have lost their title to homophonic translation. The problem at home differs none from radical translation ordinarily so called except in the willfulness of this suspension of homophonic translation. I have urged in defense of the behavioral philosophy oflanguage, Dewey's, that the inscrutability
Ontological Relativity
of reference is not the inscrutability of a fact; there is no fact of the matter. But if there is really no fact of the matter, then the inscrutability of reference can be brought even closer to home than the neighbor's case; we can apply it to ourselves. If it is to make sense to say even of oneself that one is referring to rabbits and formulas and not to rabbit stages and Giidel numbers, then it should make sense equally to say it of someone else. After all, as Dewey stressed, there is no private language. We seem to be maneuvering ourselves into the absurd position that there is no difference on any terms, inter linguistic or intralinguistic, objective or subjective, between referring to rabbits and referring to rabbit parts or stages; or between referring to formulas and referring to their Giidel numbers. Surely this is absurd, for it would imply that there is no difference between the rabbit and each of its parts or stages, and no difference between a formula and its Giidel number. Reference would seem now to become nonsense not just in radical translation but at home. Toward resolving this quandary, begin by picturing us at home in our language, with all its predicates and auxiliary devices. This vocabulary includes "rabbit," "rabbit part," "rabbit stage," "formula," "number," "ox," "cattle"; also the two-place predicates of identity and difference, and other logical particles. In these terms we can say in so many words that this is a formula and that a number, this a rabbit and that a rabbit part, this and that the same rabbit, and this and that different parts. Injust those words. This network of terms and predicates and auxiliary devices is, in relativity jargon, our frame of reference, or coordinate system. Relative to it we can and do talk meaningfully and distinctively of rabbits and parts, numbers and formulas. Next, as in recent paragraphs, we contemplate alternative denotations for our familiar terms. We begin to appreciate that a grand and ingenious permutation of these denotations, along with compensatory adjustments in the interpretations of the auxiliary particles, might still accommodate all existing speech dispositions. This was the inscrutability of reference, applied to ourselves; and it made nonsense of reference. Fair enough; reference is nonsense except relative to a coordinate system. In this principle of relativity lies the resolution of our quandary. It is meaningless to ask whether, in general, our terms "rabbit," "rabbit part," "number," etc. really refer respectively to rabbits, rabbit parts, numbers, etc., rather than to some ingeniously
permuted denotations. It is meaningless to ask this absolutely; we can meaningfully ask it only relative to some background language. When we ask, "Does 'rabbit' really refer to rabbits?," someone can counter with the question: "Refer to rabbits in what sense of 'rabbits'?," thus launching a regress; and we need the background language to regress into. The background language gives the query sense, if only relative sense; sense relative in turn to it, this background language. Querying reference in any more absolute way would be like asking absolute position, or absolute velocity, rather than position or velocity relative to a given frame of reference. Also it is very much like asking whether our neighbour may not systematically see everything upside down, or in complementary color, forever undetectably. We need a background language, I said, to regress into. Are we involved now in an infinite regress? If questions of reference of the sort we are considering make sense only relative to a background language, then evidently questions of reference for the background language make sense in turn only relative to a further background language. In these terms the situation sounds desperate, but in fact it is little different from questions of position and velocity. When we are given position and velocity relative to a given coordinate system, we can always ask in turn about the placing of origin and orientation of axes of that system of coordinates; and there is no end to the succession of further coordinate systems that could be adduced in answering the successive questions thus generated. In practice of course we end the regress of coordinate systems by something like pointing. And in practice we end the regress of background languages, in discussions of reference, by acquiescing in our mother tongue and taking its words at face value. Very well; in the case of position and velocity, in practice, pointing breaks the regress. But what of position and velocity apart from practice? what of the regress then? The answer, of course, is the relational doctrine of space; there is no absolute position or velocity; there are just the relations of coordinate systems to one another, and ultimately of things to one another. And I think that the parallel question regarding denotation calls for a parallel answer, a relational theory of what the objects of a theories are. What makes sense is to say not what the objects of a theory are, absolutely speaking, but how one theory of objects is interpretable or reinterpretable in another.
W. V. Quine The point is not that bare matter is inscrutable: that things are indistinguishable except by their properties. That point does not need making. The present point is reflected better in the riddle about seeing things upside down, or in complementary colors; for it is that things can be inscrutably switched even while carrying their properties with them. Rabbits differ from rabbit parts and rabbit stages not just as bare matter, after all, but in respect of properties; and formulas differ from numbers in respect of properties. What our present reflections are leading us to appreciate is that the riddle about seeing things upside down, or in complementary colors, should be taken seriously and its moral applied widely. The relativistic thesis to which we have come is this, to repeat: it makes no sense to say what the objects of a theory are, beyond saying how to interpret or reinterpret that theory in another. Suppose we are working within a theory and thus treating of its objects. We do so by using the variables of the theory, whose values those objects are, though there be no ultimate sense in which that universe can have been specified. In the language of the theory there are predicates by which to distinguish portions of this universe from other portions, and these predicates differ from one another purely in the roles they play in the laws of the theory. Within this background theory we can show how some subordinate theory, whose universe is some portion of the background universe, can by a reinterpretation be reduced to another subordinate theory whose universe is some lesser portion. Such talk of subordinate theories and their ontologies is meaningful, but only relative to the background theory with its own primitively adopted and ultimately inscrutable ontology. To talk thus of theories raises a problem of formulation. A theory, it will be said, is a set of fully interpreted sentences. (More particularly, it is a deductively closed set: it includes all its own logical consequences, insofar as they are couched in the same notation.) But if the sentences of a theory are fully interpreted, then in particular the range of values of their variables is settled. How then can there be no sense in saying what the objects of a theory are? My answer is simply that we cannot require theories to be fully interpreted, except in a relative sense, if anything is to count as a theory. In specifying a theory we must indeed fully specify, in our own words, what sentences are to comprise the theory, and what things are to be taken as values
of the variables, and what things are to be taken as satisfying the predicate letters; insofar we do fully interpret the theory, relative to our own words and relative to our overall home theory which lies behind them. But this fixes the objects of the described theory only relative to those of the home theory; and these can, at will, be questioned in turn. One is tempted to conclude simply that meaninglessness sets in when we try to pronounce on everything in our universe; that universal predication takes on sense only when furnished with the background of a wider universe, where the predication is no longer universal. And this is even a familiar doctrine, the doctrine that no proper predicate is true of everything. We have all heard it claimed that a predicate is meaningful only by contrast with what it excludes, and hence that being true of everything would make a predicate meaningless. But surely this doctrine is wrong. Surely self-identity, for instance, is not to be rejected as meaningless. For that matter, any statement of fact at all, however brutally meaningful, can be put artificially into a form in which it pronounces on everything. To say merely of Jones that he sings, for instance, is to say of everything that it is other than Jones or sings. We had better beware of repudiating universal predication, lest we be tricked into repudiating everything there is to say. Carnap took an intermediate line in his doctrine of universal words, or Allwijrter, in The Logical Syntax of Language. He did treat the predicating of universal words as "quasi-syntactical" - as a predication only by courtesy, and without empirical content. But universal words were for him not just any universally true predicates, like "is other than Jones or sings." They were a special breed of universally true predicates, ones that are universally true by the sheer meanings of their words and no thanks to nature. In his later writing this doctrine of uni versal words takes the form of a distinction between "internal" questions, in which a theory comes to grips with facts about the world, and "external" questions, in which people come to grips with the relative merits of theories. Should we look to these distinctions ofCarnap's for light on ontological relativity? When we found there was no absolute sense in saying what a theory is about, were we sensing the in-factuality of what Carnap calls "external questions"? When we found that saying what a theory is about did make sense against a background theory, were we sensing the factuality of internal questions of the background
Ontological Relativity
theory? I see no hope of illumination in this quarter. Carnap's universal words were not just any universally true predicates, but, as I said, a special breed; and what distinguishes this breed is not clear. What I said distinguished them was that they were universally true by sheer meanings and not by nature; but this is a very questionable distinction. Talking of "internal" and "external" is no better. Ontological relativity is not to be clarified by any distinction between kinds of universal predication - unfactual and factual, external and internal. It is not a question of universal predication. When questions regarding the ontology of a theory are meaningless absolutely, and become meaningful relative to a background theory, this is not in general because the background theory has a wider universe. One is tempted, as I said a little while back, to suppose that it is; but one is then wrong. What makes ontological questions meaningless when taken absolutely is not universality but circularity. A question of the form "What is an F?" can be answered only by recourse to a further term: "An F is a G." The answer makes only relative sense: sense relative to the uncritical acceptance of "G." We may picture the vocabulary of a theory as comprising logical signs such as quantifiers and the signs for the truth functions and identity, and in addition descriptive or nonlogical signs, which, typically, are singular terms, or names, and general terms, or predicates. Suppose next that in the statements which comprise the theory, that is, are true according to the theory, we abstract from the meanings of the nonlogical vocabulary and from the range of the variables. We are left with the logical form of the theory, or, as I shall say, the theory form. Now we may interpret this theory form anew by picking a new universe for its variables of quantification to range over, and assigning objects from this universe to the names, and choosing subsets of this universe as extensions of the oneplace predicates, and so on. Each such interpretation of the theory form is called a model of it, if it makes it come out true. Which of these models is meant in a given actual theory cannot, of course, be guessed from the theory form. The intended references of the names and predicates have to be learned rather by ostension, or else by paraphrase in some antecedently familiar vocabulary. But the first of these two ways has proved inconclusive, since, even apart from indeterminacies of translation affecting identity and other logical vocabulary, there is the problem of deferred ostension. Para-
phrase in some antecedently familiar vocabulary, then, is our only recourse; and such is ontological relativity. To question the reference of all the terms of our all-inclusive theory becomes meaningless, simply for want of further terms relative to which to ask or answer the question. It is thus meaningless within the theory to say which of the various possible models of our theory form is our real or intended model. Yet even here we can make sense still of there being many models. For we might be able to show that for each of the models, however unspecifiable, there is bound to be another which is a permutation or perhaps a diminution of the first. Suppose, for example, that our theory is purely numerical. Its objects are just the natural numbers. There is no sense in saying, from within that theory, just which of the various models of number theory is in force. But we can observe even from within the theory that, whatever 0, 1,2,3, etc. may be, the theory would still hold true if the 17 of this series were moved into the role of 0, and the 18 moved into the role of 1, and so on. Ontology is indeed doubly relative. Specifying the universe of a theory makes sense only relative to some background theory, and only relative to some choice of a manual of translation of the one theory into the other. Commonly of course the background theory will simply be a containing theory, and in this case no question of a manual of translation arises. But this is after all just a degenerate case of translation still - the case where the rule of translation is the homophonic one. We cannot know what something is without knowing how it is marked off from other things. Identity is thus of a piece with ontology. Accordingly it is involved in the same relativity, as may be readily illustrated. Imagine a fragment of economic theory. Suppose its universe comprises persons, but its predicates are incapable of distinguishing between persons whose incomes are equal. The interpersonal relation of equality of income enjoys, within the theory, the substitutivity property of the identity relation itself; the two relations are indistinguishable. It is only relative to a background theory, in which more can be said of personal identity than equality of income, that we are able even to appreciate the above account of the fragment of economic theory, hinging as the account does on a contrast between persons and incomes. A usual occasion for ontological talk is reduction, where it is shown how the universe of some theory can by a reinterpretation be dispensed with in favor
w. V. Quine of some other universe, perhaps a proper part of the first. I have treated elsewhere 14 of the reduction of one ontology to another with help of a proxy Junction: a function mapping the one universe into part or all of the other. For instance, the function "Gbdel number of" is a proxy function. The universe of elementary proof theory or protosyntax, which consists of expressions or strings of signs, is mapped by this function into the universe of elementary number theory, which consists of numbers. The proxy function used in reducing one ontology to another need not, like Gbdel numbering, be one-to-one. We might, for instance, be confronted with a theory treating of both expressions and ratios. We would cheerfully reduce all this to the universe of natural numbers, by invoking a proxy function which enumerates the expressions in the Gbdel way and enumerates the ratios by the classical method of short diagonals. This proxy function is not one-to-one, since it assigns the same natural number both to an expression and to a ratio. We would tolerate the resulting artificial convergence between expressions and ratios, simply because the original theory made no capital of the distinction between them; they were so invariably and extravagantly unlike that the identity question did not arise. Formally speaking, the original theory used a two-sorted logic. For another kind of case where we would not require the proxy function to be one-to-one, consider again the fragment of economic theory lately noted. We would happily reduce its ontology of persons to a less numerous one of incomes. The proxy function would assign to each person his income. It is not one-to-one; distinct persons give way to identical incomes. The reason such a reduction is acceptable is that it merges the images of only such individuals as never had been distinguishable by the predicates of the original theory. Nothing in the old theory is contravened by the new identities. If on the other hand the theory that we are concerned to reduce or reinterpret is straight protosyntax, or a straight arithmetic of ratios or of real numbers, then a one-to-one proxy function is mandatory. This is because any two elements of such a theory are distinguishable in terms of the theory. This is true even for the real numbers, even though not every real number is uniquely specifiable; any two real numbers x and yare still distinguishable, in that x < y or y < x and never x < x. A proxy function that did not preserve the distinctness of
the elements of such a theory would fail of its purpose of reinterpretation. One ontology is always reducible to another when we are given a proxy functionJthat is oneto-one. The essential reasoning is as follows. Where P is any predicate of the old system, its work can be done in the new system by a new predicate which we interpret as true of just the correlates Jx of the old objects x that P was true of. Thus suppose we take Jx as the Gbdel number of x, and as our old system we take a syntactical system in which one of the predicates is "is a segment of." The corresponding predicate of the new or numerical system, then, would be one which amounts, so far as its extension is concerned, to the words "is the Gbdel number of a segment of that whose Gbdel number is." The numerical predicate would not be given this devious form, of course, but would be rendered as an appropriate purely arithmetical condition. Our dependence upon a background theory becomes especially evident when we reduce our universe U to another V by appeal to a proxy function. For it is only in a theory with an inclusive universe, embracing U and V, that we can make sense of the proxy function. The function maps U into Vand hence needs all the old objects of U as well as their new proxies in V. The proxy function need not exist as an object in the universe even of the background theory. It may do its work merely as what I have called a "virtual class," 15 and Gbdel has called a "notion.,,16 That is to say, all that is required toward a function is an open sentence with two free variables, provided that it is fulfilled by exactly one value of the first variable for each object of the old universe as value of the second variable. But the point is that it is only in the background theory, with its inclusive universe, that we can hope to write such a sentence and have the right values at our disposal for its variables. If the new objects happen to be among the old, so that Vis a subclass of U, then the old theory with universe U can itself sometimes qualify as the background theory in which to describe its own ontological reduction. But we cannot do better than that; we cannot declare our new ontological economies without having recourse to the uneconomical old ontology. This sounds, perhaps, like a predicament: as if no ontological economy is justifiable unless it is a false economy and the repudiated objects really exist after all. But actually this is wrong; there is
Ontological Relativity
no more cause for worry here than there is in reductio ad absurdum, where we assume a falsehood that we are out to disprove. If what we want to show is that the universe U is excessive and that only a part exists, or need exist, then we are quite within our rights to assume all of U for the space of the argument. We show thereby that if all of U were needed, then not all of U would be needed; and so our ontological reduction is sealed by reductio ad absurdum. Toward further appreciating the bearing of ontological relativity on programs of ontological reduction, it is worthwhile to reexamme the philosophical bearing of the Liiwenheim-Skolem theorem. I shall use the strong early form of the theorem, 17 which depends on the axiom of choice. It says that if a theory is true and has an indenumerable universe, then all but a denumerable part of that universe is dead wood, in the sense that it can be dropped from the range of the variables without falsifying any sentences. On the face of it, this theorem declares a reduction of all acceptable theories to denumerable ontologies. Moreover, a denumerable ontology is reducible in turn to an ontology specifically of natural numbers, simply by taking the enumeration as the proxy function, if the enumeration is explicitly at hand. And even if it is not at hand, it exists; thus we can still think of all our objects as natural numbers, and merely reconcile ourselves to not always knowing, numerically, which number an otherwise given object is. May we not thus settle for an all-purpose Pythagorean ontology outright? Suppose, afterward, someone were to offer us what would formerly have qualified as an ontological reduction - a way of dispensing in future theory with all things of a certain sort S, but still leaving an infinite universe. Now in the new Pythagorean setting his discovery would still retain its essential content, though relinquishing the form of an ontological reduction; it would take the form merely of a move whereby some numerically unspecified numbers were divested of some property of numbers that corresponded to S. Blanket Pythagorean ism on these terms is unattractive, for it merely offers new and obscurer accounts of old moves and old problems. On this score again, then, the relativistic proposition seems reasonable: that there is no absolute sense in speaking of the ontology of a theory. It very creditably brands this Pythagorean ism itself as meaningless. For there is no absolute sense in saying that all the
objects of a theory are numbers, or that they are sets, or bodies, or something else; this makes no sense unless relative to some background theory. The relevant predicates - "number," "set," "body," or whatever - would be distinguished from one another in the background theory by the roles they play in the laws of that theory. Elsewhere I urged in answer to such Pythagoreanism that we have no ontological reduction in an interesting sense unless we can specify a proxy function. Now where does the strong Liiwenheim-Skolem theorem leave us in this regard? If the background theory assumes the axiom of choice and even provides a notation for a general selector operator, can we in these terms perhaps specify an actual proxy function embodying the LowenheimSkolem argument? The theorem is that all but a denumerable part of an ontology can be dropped and not be missed. One could imagine that the proof proceeds by partitioning the universe into denumerably many equivalence classes of indiscriminable objects, such that all but one member of each equivalence class can be dropped as superfluous; and one would then guess that where the axiom of choice enters the proof is in picking a survivor from each equivalence class. If this were so, then with help of Hilbert's selector notation we could indeed express a proxy function. But in fact the Liiwenheim-Skolem proof has another structure. I see in the proof even of the strong Liiwenheim-Skolem theorem no reason to suppose that a proxy function can be formulated anywhere that will map an indenumerable ontology, say the real numbers, into a denumerable one. On the face of it, of course, such a proxy function is out of the question. It would have to be oneto-one, as we saw, to provide distinct images of distinct real numbers; and a one-to-one mapping of an indenumerable domain into a denumerable one is a contradiction. In particular it is easy to show in the Zermelo-Fraenkel system of set theory that such a function would neither exist nor admit even of formulation as a virtual class in the notation of the system. The discussion of the ontology of a theory can make variously stringent demands upon the background theory in which the discussion is couched. The stringency of these demands varies with what is being said about the ontology of the object theory. We are now in a position to distinguish three such grades of stringency.
W. V. Quine The least stringent demand is made when, with no view to reduction, we merely explain what things a theory is about, or what things its terms denote. This amounts to showing how to translate part or all of the object theory into the background theory. It is a matter really of showing how we propose, with some arbitrariness, to relate terms of the object theory to terms of the background theory; for we have the inscrutability of reference to allow for. But there is here no requirement that the background theory have a wider universe or a stronger vocabulary than the object theory. The theories could even be identical; this is the case when some terms are clarified by definition on the basis of other terms of the same language. A more stringent demand was observed in the case where a proxy function is used to reduce an ontology. In this case the background theory needed the unreduced universe. But we saw, by considerations akin to reductio ad absurdum, that there was little here to regret. The third grade of stringency has emerged now in the kind of ontological reduction hinted at by the Liiwenheim-Skolem theorem. If a theory has by its own account an indenumerable universe, then even by taking that whole unreduced theory as background theory we cannot hope to produce a proxy function that would be adequate to reducing the ontology to a denumerable one. To find such a proxy function, even just a virtual one, we would need a background theory essentially stronger than the theory we were trying to reduce. This demand cannot, like the second grade of stringency above, be accepted in the spirit of reductio ad absurdum. It is a demand that simply discourages any general argument for Pythagoreanism from the Liiwenheim-Skolem theorem. A place where we see a more trivial side of ontological relativity is in the case of a finite universe of named objects. Here there is no occasion for quantification, except as an inessential abbreviation; for we can expand quantifications into finite conjunctions and alternations. Variables thus disappear, and with them the question of a universe of values of variables. And the very distinction between names and other signs lapses in turn, since the mark of a name is its admissibility in positions of variables. Ontology thus is emphatically meaningless for a finite theory of named objects, considered in and of itself. Yet we are now talking meaningfully of such finite ontologies. We are able to do so precisely because we are talking, however vaguely and implicitly, within a
broader containing theory. What the objects of the finite theory are, makes sense only as a statement of the background theory in its own referential idiom. The answer to the question depends on the background theory, the finite foreground theory, and, of course, the particular manner in which we choose to translate or embed the one in the other. Ontology is internally indifferent also, I think, to any theory that is complete and decidable. Where we can always settle truth values mechanically, there is no evident internal reason for interest in the theory of quantifiers nor, therefore, in values of variables. These matters take on significance only as we think of the decidable theory as embedded in a richer background theory in which the variables and their values are serious business. Ontology may also be said to be internally indifferent even to a theory that is not decidable and does not have a finite universe, if it happens still that each of the infinitely numerous objects of the theory has a name. We can no longer expand quantifications into conjunctions and alternations, barring infinitely long expressions. We can, however, revise our semantical account of the truth conditions of quantification, in such a way as to turn our backs on questions of reference. We can explain universal quantifications as true when true under all substitutions; and correspondingly for existential. Such is the course that has been favored by Lesniewski and by Ruth Marcus. ls Its nonreferential orientation is seen in the fact that it makes no essential use of namehood. That is, additional quantifications could be explained whose variables are place-holders for words of any syntactical category. Substitutional quantification, as I call it, thus brings no way of distinguishing names from other vocabulary, nor any way of distinguishing between genuinely referential or value-taking variables and other place-holders. Ontology is thus meaningless for a theory whose only quantification is substitutionally construed; meaningless, that is, insofar as the theory is considered in and of itself. The question of its ontology makes sense only relative to some translation of the theory into a background theory in which we use referential quantification. The answer depends on both theories and, again, on the chosen way of translating the one into the other. A final touch of relativity can in some cases cap this, when we try to distinguish between substitutional and referential quantification. Suppose again a theory with an infinite lot of names, and suppose
Ontological Relativity
that, by Giidel numbering or otherwise, we are treating of the theory's notations and proofs within the terms of the theory. If we succeed in showing that every result of substituting a name for the variable in a certain open sentence is true in the theory, but at the same time we disprove the universal quantification of the sentence/ 9 then certainly we have shown that the universe of the theory contained some nameless objects. This is a case where an absolute decision can be reached in favor of referential quantification and against substitutional quantification, without ever retreating to a background theory. But consider now the opposite situation, where there is no such open sentence. Imagine on the contrary that, whenever an open sentence is such that each result of substituting a name in it can be proved, its universal quantification can be proved in the theory too. Under these circumstances we can construe the universe as devoid of nameless objects and hence reconstrue the quantifications as substitutional, but we need not. We could still construe the universe as containing nameless objects. It could just happen that the nameless ones are inseparable from the named ones, in this sense: it could happen that all properties of nameless objects that we can express in the notation of the theory are shared by named objects. We could construe the universe of the theory as containing, e.g., all real numbers. Some of them are nameless, since the real numbers are indenumerable while the names are denumerable. But it could still happen that the nameless reals are inseparable from the named reals. This would leave us unable within the theory to prove a distinction between referential and substitutional quantification. 2o E very expressible quantification that is true when referentially construed remains true when substitutionally construed, and vice versa. We might still make the distinction from the vantage point of a background theory. In it we might specify some real number that was nameless in the object theory; for there are always ways of strengthening a theory so as to name more real numbers, though never all. Further, in the background theory, we might construe the universe of the object theory as exhausting the real numbers. In the background theory we could, in this way, clinch the quantifications in the object theory as referential. But this clinching is doubly relative: it is relative to the background theory and to the interpretation or translation imposed on the object theory from within the background theory.
One might hope that this recourse to a background theory could often be avoided, even when the nameless reals are inseparable from the named reals in the object theory. One might hope by indirect means to show within the object theory that there are nameless reals. For we might prove within the object theory that the reals are indenumerable and that the names are denumerable and hence that there is no function whose arguments are names and whose values exhaust the real numbers. Since the relation of real numbers to their names would be such a function if each real number had a name, we would seem to have proved within the object theory itself that there are nameless reals and hence that quantification must be taken referentially. However, this is wrong; there is a loophole. This reasoning would prove only that a relation of all real numbers to their names cannot exist as an entity in the universe of the theory. This reasoning denies no number a name in the notation of the theory, as long as the name relation does not belong to the universe of the theory. And anyway we should know better than to expect such a relation, for it is what causes Berry's and Richard's and related paradoxes. Some theories can attest to their own nameless objects and so claim referential quantification on their own; other theories have to look to background theories for this service. We saw how a theory might attest to its own nameless objects, namely, by showing that some open sentence became true under all constant substitutions but false under universal quantification. Perhaps this is the only way a theory can claim referential import for its own quantifications. Perhaps, when the nameless objects happen to be inseparable from the named, the quantification used in a theory cannot meaningfully be declared referential except through the medium of a background theory. Yet referential quantification is the key idiom of ontology. Thus ontology can be multiply relative, multiply meaningless apart from a background theory. Besides being unable to say in absolute terms just what the objects are, we are sometimes unable even to distinguish objectively between referential quantification and a substitutional counterfeit. When we do relativize these matters to a background theory, moreover, the relativization itself has two components: relativity to the choice of background theory and relativity to the choice of how to translate the object theory into the back-
W. V. Quine ground theory. As for the ontology in turn of the background theory, and even the referentiality of its quantification - these matters can call for a background theory in turn. There is not always a genuine regress. We saw that, if we are merely clarifying the range of the variables of a theory or the denotations of its terms, and are taking the referentiality of quantification itself for granted, we can commonly use the object theory itself as background theory. We found that when we undertake an ontological reduction, we must accept at least the unreduced theory in order to cite the proxy function; but this we were able cheerfully to accept in the spirit of reductio ad absurdum arguments. And now in the end we have found further that if we care to question quantification itself, and settle whether it imports a universe of discourse or turns merely on substitution at the linguistic level, we in some cases have genuinely to regress to a background language endowed with additional resources. We seem to have to do this unless the nameless objects are separable from the named in the object theory. Regress in ontology is reminiscent of the now familiar regress in the semantics of truth and kindred notions - satisfaction, naming. We know from
Tarski's work how the semantics, in this sense, of a theory regularly demands an in some way more inclusive theory. This similarity should perhaps not surprise us, since both ontology and satisfaction are matters of reference. In their elusiveness, at any rate - in their emptiness now and again except relative to a broader background - both truth and ontology may in a suddenly rather clear and even tolerant sense be said to belong to transcendental metaphysics. 21 Note added in proof Besides such ontological
reduction as is provided by proxy functions (cf. pp. 55-7), there is that which consists simply in dropping objects whose absence will not falsify any truths expressible in the notation. Commonly this sort of deflation can be managed by proxy functions, but R. E. Grandy has shown me that sometimes it cannot. Let us by all means recognize it then as a further kind of reduction. In the background language we must, of course, be able to say what class of objects is dropped, just as in other cases we had to be able to specify the proxy function. This requirement seems sufficient still to stem any resurgence of Pythagoreanism on the strength of the Liiwenheim-Skolem theorem.
Notes 1 2 3 4 5 6 7 8
9 10
11
12
J.
Dewey, Experience and Nature (La Salle, Ill.: Open Court, 1925; repro 1958), p. 179. Ibid., p. 170. Ibid., p. 185. Ibid., p. 178. W. V. Quine, Word and Object (Cambridge, Mass.: MIT Press, 1960), sect. 12. L. Wittgenstein, Philosophical Investigations (New York: Macmillan, 1953), p. 14. Cf. Quine, Word and Object, sect. 17. Quine, Word and Object, sect. 15. For a summary of the general point of view see also sect. 1 of "Speaking of objects," in W. V. Quine, Ontological Relativity and Other Essays (New York: Columbia University Press, 1969). To keep my account graphic, I am counting a certain postpositive particle as a suffix rather than a word. See Leon Henkin, "Completeness in the theory of types," Journal of Symbolic Logic 15 (1950), pp. 8191, and references therein. For more on this theme see W. V. Quine, Set Theory and its Logic (Cambridge, Mass.: Harvard University Press, 1963, repro 1969), sect. II. Paul Benacerraf, "What numbers cannot be," Philosophical Review 74 (1965), pp. 47-73, develops this
l3 14
15 16
17
18
point. His conclusions differ in some ways from those I shall come to. N. L. Wilson, "Substances without substrata," Review (if Metaphysics 12 (1959), pp. 521-39, at p. 532. W. V. Quine, The Ways of Paradox (New York: Random House, 1966), pp. 204ff; or see "Ontological reduction and the world of numhers," this volume, ch.38. Quine, Set Theory and its Logic, sects 2f. Kurt Giidel, The Consistency oflhe Continuum Hypothesis (Princeton: Princeton University Press, 1940), p. 11. ThoralfSkolem, "Logisch-komhinatorische Untersuchungen ilber die Erfilllharkeit oder Beweisharkeit mathematischer Satze nehst cinem Theorem ilber dichte Mengen," Skrifter utgit av Videnskapsselskapel i Kristiania (1919); trans. in Jean van Heijenoort (cd.) From Frege to Gilde!: Source Book in the History (if' Mathematical Logic (Camhridge, Mass.: Harvard University Press, 1967), pp. 252-63. Ruth B. Marcus, "Modalities and intensional languages," .~ynthese 13 (1961), pp. 303-22. I cannot locate an adequate statement of Stanislaw Lesniewski's philosophy of quantification in his writings; I have it from his conversations. E. C. Luschei, in
Ontological Relativity The Lo!!.iwl Systems of Lesniewski (Amsterdam: North-Holland, 1962), pp. 108f, confirms my attribution but still cites no passage. On this version of quantification see further "Existence and quantification," in Quine, Ontolo!!.ical Relativity and Other Essays.
19 Such is the typical way of a numerically in segregative system, misleadingly called "w-inconsistent." See W.
v. Quine, Selected Lo!!.ic Papers (New York: Random House, 1966), pp. 118f, or "w-inconsistency and a socalled axiom of infinity," Journal of Symbolic Logic 18 (1953), pp. 122f. 20 This possibility was suggested by Saul Kripke. 21 In developing these thoughts I have been helped by discussions with Saul Kripke, Thomas Nagel, and especially Burton Dreben.
PART II
Introduction Introduction On the face of it, identity seems like the simplest of concepts: everything is identical with itself and with nothing else. But, as philosophers have long been aware, the concept of identity gives rise to some complex and difficult problems. One of these is the so-called Leibniz' law, or the identity of indiscernibles: Things with the same properties are one and the same. (The converse of this principle, also sometimes called "Leibniz' law," is uncontroversial: Identical things have the same properties.) In his "The Identity ofIndiscernibles" (chapter 6), Max Black presents a possible objection to Leibniz' law, by presenting a by-now famous counterexample involving two distinct spheres that nonetheless appear to have exactly the same properties. (Black's example is discussed further by A. ]. Ayer and D. ]. O'Connor; see Further reading, below.) Another question that has recently been much discussed is whether all statements of identity are metaphysically necessary or whether they can be contingent. The Evening Star is identical with the Morning Star. Given this, could or might the Evening Star not have been the Morning Star? It was long assumed that some identities, especially those that can be known only empirically, were only contingently true or contingently false, not necessarily true or necessarily false. Saul Kripke's challenge to this assumption, in "Identity and Necessity" (chapter 7), is among the more important developments in contemporary metaphysics, and has generated much discussion.
In "The Same F" (chapter 8), John Perry explores the claim, due to Peter Geach (see Further reading), that identities are relative to a sortal. That is, it is not proper to say simply 'x is identical with y'; one should rather say 'x is the same F as y," where 'F' is a sortal term denoting a kind. The following sort of example has been used in support of the doctrine of 'relative identity': although the chairman of the school board is not the same official as the postmaster, they are the same person. (This issue is further discussed in works by Fred Feldman and David Wiggins; see Further reading.) In "Contingent Identity" (chapter 9), Allan Gibbard makes a case for contingent identities, and carefully and systematically investigates some complex issues involved in allowing identities that are not necessary. The issue of sortal relativity of identity reappears in this context. Stephen Yablo, too, is concerned, in his "Identity, Essence, and Indiscernibility" (chapter 10), with the problem of making sense of identities and related relations that are not necessary, and develops a scheme that is interestingly different from that of Gibbard. The distinction between essential and contingent properties of an object plays a large role in Yablo, and his distinctions between "categorical" and "hypothetical" properties, and between "coincidence" and "identity," are worthy of note. (Modal concepts, such as necessity and contingency, which are used prominently in some of the chapters in this section, are treated more fully in Part III, "Modalities and Possible Worlds.")
Further reading Ayer, A. J., "The identity of indiscernibles," in Philosophical Essays (New York: St Martin's Press; London: Macmillan, 1954). Cartwright, Richard, "Identity and substitutivity," in Philosophical Essays (Cambridge, Mass.: MIT Press, 1987). Feldman, Fred, "Geach and relative identity," Review of Metaphysics 22 (1968/9), pp. 547-55. Geach, Peter, "Identity" and "Identity - a reply," in Logic Matters (Oxford: Basil Blackwell, 1972).
Kripke, Saul, Naming and Necessity (Cambridge, Mass.: Harvard University Press, 1980). Lowe, E. J., "What is a criterion of identity?," Philosophical QJ<arterly 39 (1989), pp. 1-21. O'Connor, D. J., "The identity of indiscernibles," Analysis 14 (1954), pp. 102-10. Salmon, Nathan, Frege's Puzzle (Cambridge, Mass.: MIT Press, 1986). Wiggins, David, Sameness and Substance (Cambridge, Mass.: Harvard University Press, 1980).
Max Black
A: The principle of the Identity ofIndiscernibles seems to me obviously true. And I don't see how we are going to define identity or establish the connection between mathematics and logic without using it. B: It seems to me obviously false. And your troubles as a mathematical logician are beside the point. If the principle is false, you have no right to use it. A: You simply say it's false ~ and even if you said so three times, that wouldn't make it so. B: Well, you haven't done anything more yourself than assert the principle to be true. As Bradley once said, 'assertion can demand no more than counter-assertion; and what is affirmed on the one side, we on the other can simply deny.' A: How will this do for an argument? If two things, a and b, are given, the first has the property of being identical with a. Now b cannot have this property, for else b would be a, and we should have only one thing, not two as assumed. Hence a has at least one property, which b does not have, that is to say the property of being identical with a. B: This is a roundabout way of saying nothing, for 'a has the property of being identical with a' means no more than 'a is a'. When you begin to say 'a is .. .' I am supposed to know what thing you are referring to as 'a', and I expect to be told something about that thing. But when you end the sentence Originally published in Mind 51 (1952), and reprinted in Max Black, Problems of Analysis (1954), pp. 204-16. Copyright © N. Black and by Cornell University. Reprinted here by permission of the Cornell University Press.
with the words' ... is a', I am left still waiting. The sentence 'a is a' is a useless tautology. A: Are you as scornful about difference as about identity? For a also has, and b does not have, the property of being different from b. This is a second property that the one thing has but not the other. B: All you are saying is that b is different from a. I think the form of words 'a is different from b' does have the advantage over 'a is a' that it might be used to give information. I might learn from hearing it used that 'a' and 'b' were applied to different things. But this is not what you want to say, since you are trying to use the names, not mention them. When I already know what 'a' and 'b' stand for, 'a is different from b' tells me nothing. It, too, is a useless tautology. A: I wouldn't have expected you to treat 'tautology' as a term of abuse. Tautology or not, the sentence has a philosophical use. It expresses the necessary truth that different things have at least one property not in common. Thus different things must be discernible; and hence, by contraposition, indiscernible things must be identical. QE.O. B: Why obscure matters by this old-fashioned language? By 'indiscernible' I suppose you mean the same as 'having all properties in common' Do you claim to have proved that two things having all their properties in common are identical? A: Exactly. B: Then this is a poor way of stating your conclusion. If a and b are identical, there is just one thing having the two names 'a' and 'b'; and in that case it is absurd to say that a and b are two. Conversely, once you have supposed there are two
The Identity of Indiscernibles
things having all their properties in common, you can't without contradicting yourself say that they are 'identical'. A: I can't believe you were really misled. I simply meant to say it is logically impossible for two things to have all their properties in common. I showed that a must have at least two properties - the property of being identical with a and the property of being different from b - neither of which can be a property of b. Doesn't this prove the principle of identity of indiscernibles? B: Perhaps you have proved something. If so, the nature of your proof should show us exactly what you have proved. If you want to call 'being identical with a' a 'property' I suppose I can't prevent you. But you must then accept the consequences of this way of talking. All you mean when you say 'a has the property of being identical with a' is that a is a. And all you mean when you say 'b does not have the property of being identical with a' is that b is not a. So what you have 'proved' is that a is a and b is not a; that is to say, b and a are different. Similarly, when you said that a, but not b, had the property of being different from b, you were simply saying that a and b were different. In fact you are merely redescribing the hypothesis that a and b are different by calling it a case of 'difference of properties'. Drop the misleading description and your famous principle reduces to the truism that different things are different. How true! And how uninteresting! A: Well, the properties of identity and difference may be uninteresting, but they are properties. If I had shown that grass was green, I suppose you would say I hadn't shown that grass was coloured. B: You certainly would not have shown that grass had any colour other than green. A: What it comes to is that you object to the conclusion of my argument following from the premiss that a and b are different. B: No, I object to the triviality of the conclusion. If you want to have an interesting principle to defend, you must interpret 'property' more narrowly - enough so, at any rate, for 'identity' and 'difference' not to count as properties. A: Your notion of an interesting principle seems to be one which I shall have difficulty in establishing. Will you at least allow me to include among 'properties' what are sometimes called 'relational characteristics' - like being married to Caesar or being at a distance from London? B: Why not? If you are going to defend the principle, it is for you to decide what version you wish to defend.
In that case, I don't need to count identity and difference as properties. Here is a different argument that seems to me quite conclusive. The only way we can discover that two different things exist is by finding out that one has a quality not possessed by the other or else that one has a relational characteristic that the other hasn't. If both are blue and hard and sweet and so on, and have the same shape and dimensions and are in the same relations to everything in the universe, it is logically impossible to tell them apart. The supposition that in such a case there might really be two things would be unverifiable in principle. Hence it would be meaningless. B: You are going too fast for me. A: Think of it this way. If the principle were false, the fact that I can see only two of your hands would be no proof that you had just two. And even if every conceivable test agreed with the supposition that you had two hands, you might all the time have three, four, or any number . You might have nine hands, different from one another and all indistinguishable from your left hand, and nine more all different from each other but indistinguishable from your right hand. And even if you really did have just two hands, and no more, neither you nor I nor anybody else could ever know that fact. This is too much for me to swallow. This is the kind of absurdity you get into, as soon as you abandon verifiability as a test of meaning. B: Far be it from me to abandon your sacred cow. Before I give you a direct answer, let me try to describe a counter-example. Isn't it logically possible that the universe should have contained nothing but two exactly similar spheres? We might suppose that each was made of chemically pure iron, had a diameter of one mile, that they had the same temperature, colour, and so on, and that nothing else existed. Then every quality and relational characteristic of the one would also be a property of the other. Now if what I am describing is logically possible, it is not impossible for two things to have all their properties in common. This seems to me to refute the Principle. A: Your supposition, I repeat, isn't verifiable and therefore can't be regarded as meaningful. But supposing you have described a possible world, I still don't see that you have refuted the principle. Consider one of the spheres, a, ... B: How can I, since there is no way of telling them apart? Which one do you want me to consider? A: This is very foolish. I mean either of the two spheres, leaving you to decide which one you A:
Max Black
wished to consider. If I were to say to you 'Take any book off the shelP, it would be foolish on your part to reply 'Which?' B: It's a poor analogy. I know how to take a book off a shelf, but I don't know how to identify one of two spheres supposed to be alone in space and so symmetrically placed with respect to each other that neither has any quality or character the other does not also have. A: All of which goes to show as I said before, the unverifiability of your supposition. Can't you imagine that one sphere has been designated as 'a'? B: I can imagine only what is logically possible. Now it is logically possible that somebody should enter the universe I have described, see one of the spheres on his left hand and proceed to call it 'a'. I can imagine that all right, if that's enough to satisfy you. A: Very well, now let me try to finish what I began to say about a ... B: I still can't let you, because you, in your present situation, have no right to talk about a. All I have conceded is that if something were to happen to introduce a change into my universe, so that an observer entered and could see the two spheres, one of them could then have a name. But this would be a different supposition from the one I wanted to consider. My spheres don't yet have names. If an observer were to enter the scene, he could perhaps put a red mark on one of the spheres. You might just as well say 'By "a" I mean the sphere which would be the first to be marked by a red mark if anyone were to arrive and were to proceed to make a red mark!' You might just as well ask me to consider the first daisy in my lawn that would be picked by a child, if a child were to come along and do the picking. This doesn't now distinguish any daisy from the others. You are just pretending to use a name. A: And I think you are just pretending not to understand me. All I am asking you to do is to think of one of your spheres, no matter which, so that I may go on to say something about it when you give me a chance. B: You talk as if naming an object and then thinking about it were the easiest thing in the world. But it isn't so easy. Suppose I tell you to name any spider in my garden: if you can catch one first or describe one uniquely, you can name it easily enough. But you can't pick one out, let alone 'name' it, by just thinking. You remind me of the mathematicians who thought that talking about an Axiom of Choice would really allow
them to choose a single member of a collection when they had no criterion of choice. A: At this rate you will never give me a chance to say anything. Let me try to make my point without using names. Each of the spheres will surely differ from the other in being at some distance from that other one, but at no distance from itself - that is to say, it will bear at least one relation to itself - being at no distance from, or being in the same place as - that it does not bear to the other. And this will serve to distinguish it from the other. B: Not at all. Each will have the relational characteristic being at a distance ~(two miles, say, from the centre of a sphere one mile in diameter, etc. And each will have the relational characteristic (if you want to call it that) of being in the same place as itself. The two are alike in this respect as in all others. A: But look here. Each sphere occupies a different place; and this at least will distinguish them from one another. B: This sounds as if you thought the places had some independent existence, though I don't suppose you really think so. To say the spheres are in 'different places' is just to say that there is a distance between the two spheres; and we have already seen that that will not serve to distinguish them. Each is at a distance - indeed the same distance from the other. A: When I said they were at different places, I didn't mean simply that they were at a distance from one another. That one sphere is in a certain place does not entail the existence of any other sphere. So to say that one sphere is in its place, and the other in its place, and then to add that these places are different seems to me different from saying the spheres are at a distance from one another. B: What does it mean to say 'a sphere is in its place'? Nothing at all, so far as I can see. Where else could it be? All you are saying is that the spheres are in different places. A: Then my retort is, What does it mean to say 'Two spheres are in different places'? Or, as you so neatly put it, 'Where else could they be?' B: You have a point. What I should have said was that your assertion that the spheres occupied different places said nothing at all, unless you were drawing attention to the necessary truth that different physical objects must be in different places. Now if two spheres must be in different places, as indeed they must, to say that the spheres occupy different places is to say no more than they are two spheres.
The Identity of Indiscernibles
A: This is like a point you made before. You won't allow me to deduce anything from the supposition that there are two spheres. B: Let me put it another way. In the two-sphere universe, the only reason for saying that the places occupied were different would be that different things occupied them. So in order to show the places were different, you would first have to show, in some other way, that the spheres were different. You will never be able to distinguish the spheres by means of the places they occupy. A: A minute ago, you were willing to allow that somebody might give your spheres different names. Will you let me suppose that some traveller has visited your monotonous 'universe' and has named one sphere 'Castor' and the other 'Pollux'? B: All right - provided you don't try to use those names yourself. A: Wouldn't the traveller, at least, have to recognize that being at a distance of two miles from Castor was not the same property as being at a distance of two miles from Pollux? B: I don't see why. If he were to see that Castor and Pollux had exactly the same properties, he would see that 'being at a distance of two miles from Castor' meant exactly the same as 'being at a distance of two miles from Pollux'. A: They couldn't mean the same. If they did, 'being at a distance (If two miles from Castor and at the same time not being at a distance of two miles from Pollux' would be a self-contradictory description.
But plenty of bodies could answer to this description. Again, if the two expressions meant the same, anything which was two miles from Castor would have to be two miles from Pollux - which is clearly false. So the two expressions don't mean the same, and the two spheres have at least two properties not III common. B: Which? A: Being at a distance of two miles from Castor and being at a distance of two miles from Pollux. B: But now you are using the words 'Castor' and
'Pollux' as if they really stood for something. They are just our old friends 'a' and 'b' in disguise. A: You surely don't want to say that the arrival of the name-giving traveller creates spatial properties? Perhaps we can't name your spheres and therefore can't name the corresponding properties; but the properties must be there. B: What can this mean? The traveller has not visited the spheres, and the spheres have no names - neither 'Castor', nor 'Pollux', nor 'a', nor 'b', nor any others. Yet you still want to say they
have certain properties which cannot be referred to without using names for the spheres. You want to say 'the property of being at a distance from Castor', though it is logically impossible for you to talk in this way. You can't speak, but you won't be silent. A: How eloquent, and how unconvincing! But since you seem to have convinced yourself, at least, perhaps you can explain another thing that bothers me: I don't see that you have a right to talk as you do about places or spatial relations in connection with your so-called universe. So long as we are talking about our own universe - the universe I know what you mean by 'distance', 'diameter', 'place' and so on. But in what you want to call a universe, even though it contains only two objects, I don't see what such words could mean. So far as I can see, you are applying these spatial terms in their present usage to a hypothetical situation which contradicts the presuppositions of that usage. B: What do you mean by 'presupposition'? A: Well, you spoke of measured distances, for one thing. Now this presupposes some means of measurement. Hence your 'universe' must contain at least a third thing - a ruler or some other measuring device. B: Are you claiming that a universe must have at least three things in it? What is the least number of things required to make a world? A: No, all I am saying is that you cannot describe a configuration as spatial unless it includes at least three objects. This is part of the meaning of 'spatial' - and it is no more mysterious than saying you can't have a game of chess without there existing at least thirty-five things (thirty-two pieces, a chessboard, and two players). B: If this is all that bothers you, I can easily provide for three or any number of things without changing the force of my counter-example. The important thing, for my purpose, was that the configuration of two spheres was symmetrical. So long as we preserve this feature of the imaginary universe, we can now allow any number of objects to be found in it. A: You mean any even number of objects. B: Quite right. Why not imagine a plane running clear through space, with everything that happens on one side of it always exactly duplicated at an equal distance in the other side. A: A kind of cosmic mirror producing real images. B: Yes, except that there wouldn't be any mirror! The point is that in this world we can imagine any
Max Black
degree of complexity and change to occur. No reason to exclude rulers, compasses and weighing machines. No reason, for that matter, why the Battle of Waterloo shouldn't happen. A: Twice over, you mean - with Napoleon surrendering later in two different places simultaneously! B: Provided you wanted to call both of them 'Napoleon'. A: So your point is that everything could be duplicated on the other side of the non-existent Looking Glass. I suppose whenever a man got married, his identical twin would be marrying the identical twin of the first man's fiancee? B: Exactly. A: Except that 'identical twins' wouldn't be numerically identical? B: You seem to be agreeing with me. A: Far from it. This is just a piece of gratuitous metaphysics. If the inhabitants of your world had enough sense to know what was sense and what wasn't, they would never suppose all the events in their world were duplicated. It would be much more sensible for them to regard the 'second' Napoleon as a mere mirror image - and similarly for all the other supposed 'duplicates'. B: But they could walk through the 'mirror' and find water just as wet, sugar just as sweet, and grass just as green on the other side. A: You don't understand me. They would not postulate 'another side'. A man looking at the 'mirror' would be seeing himself, not a duplicate. If he walked in a straight line toward the 'mirror', he would eventually find himself back at his starting point, not at a duplicate of his starting point. This would involve their having a different geometry from ours - but that would be preferable to the logician's nightmare of the reduplicated universe. B: They might think so - until the twins really began to behave differently for the first time! A: Now it's you who are tinkering with your supposition. You can't have your universe and change it too. B: All right, I retract. A: The more I think about your 'universe', the queerer it seems. What would happen when a man crossed your invisible 'mirror'? While he was actually crossing, his body would have to change shape, in order to preserve the symmetry. Would it gradually shrink to nothing and then expand again? B: I confess I hadn't thought of that.
A: And here is something that explodes the whole notion. Would you say that one of the two Napoleons in your universe had his heart in the right place - literally, I mean? B: Why, of course. A: In that case his 'mirror-image' twin would have the heart on the opposite side of the body. One Napoleon would have his heart on the left of his body, and the other would have it on the right of his body. B: It's a good point, though it would still make objects like spheres indistinguishable. But let me try again. Let me abandon the original idea of a plane of symmetry and suppose instead that we have only a centre of symmetry. I mean that everything that happened at any place would be exactly duplicated at a place an equal distance on the opposite side of the centre of symmetry. In short, the universe would be what the mathematicians call 'radially symmetrical'. And to avoid complications, we could suppose that the centre of symmetry itself was physically inaccessible, so that it would be impossible for any material body to pass through it. Now in this universe, identical twins would have to be either both right-handed or both left-handed. A: Your universes are beginning to be as plentiful as blackberries. You are too ingenuous to see the force of my argument about verifiability. Can't you see that your supposed description of a universe in which everything has its 'identical twin' doesn't describe anything verifiably different from a corresponding universe without such duplication? This must be so, no matter what kind of symmetry your universe manifested. B: You are assuming that in order to verify that there are two things of a certain kind, it must be possible to show that one has a property not possessed by the other. But this is not so. A pair of very close but similar magnetic poles produce a characteristic field of force which assures me that there are two poles, even if I have no way of examining them separately. The presence of two exactly similar stars at a great distance might be detected by some resultant gravitational effect or by optical interference - or in some such similar way - even though we had no way of inspecting one in isolation from the other. Don't physicists say something like this about the electrons inside an atom? We can verify that there are two, that is to say a certain property of the whole configuration, even though there is no way of detecting any character that uniquely characterises any element of the configuration.
The Identity of Indiscernibles
A: But if you were to approach your two stars one would have to be on your left and one on the right'. And this would distinguish them. B: I agree. Why shouldn't we say that the two stars are distinguishable - meaning that it would be possible for an observer to see one on his left and the other on his right, or more generally, that it would be possible for one star to come to have a relation to a third object that the second star would not have to that third object. A: So you agree with me after all. B: Not if you mean that the two stars do not have all their properties in common. All I said was that it was logically possible for them to enter into different relationships with a third object. But this would be a change in the universe. A: If you are right, nothing unobserved would be observable. For the presence of an observer would always change it, and the observation would always be an observation of something else. B: I don't say that every observation changes what is observed. My point is that there isn't any being to the right or being to the left in the two-sphere universe until an observer is introduced, that is to say until a real change is made. A: But the spheres themselves wouldn't have changed. B: Indeed they would: they would have acquired new relational characteristics. In the absence of any asymmetric observer, I repeat, the spheres would
have all their properties in common (including, if you like, the power to enter into different relations with other objects). Hence the principle of identity of indiscernibles is false. A: So perhaps you really do have twenty hands after all? B: Not a bit of it. Nothing that I have said prevents me from holding that we can verify that there are exactly two. But we could know that two things existed without there being any way to distinguish one from the other. The Principle is false. A: I am not surprised that you ended in this way, since you assumed it in the description of your fantastic 'universe'. Of course, if you began by assuming that the spheres were numerically different though qualitatively alike, you could end by 'proving' what you first assumed. B: But I wasn't 'proving' anything. I tried to support my contention that it is logically possible for two things to have all their properties in common by giving an illustrative description. (Similarly, if I had to show it is logically possible for nothing at all to be seen, I would ask you to imagine a universe in which everybody was blind.) It was for you to show that my description concealed some hidden contradiction. And you haven't done so. A: All the same I am not convinced. B: Well, then, you ought to be.
Saul Kripke
A problem which has arisen frequently in contemporary philosophy is: "How are contingent identity statements possible?" This question is phrased by analogy with the way Kant phrased his question "How are synthetic a priori judgments possible?" In both cases, it has usually been taken for granted in the one case by Kant that synthetic a priori judgments were possible, and in the other case in contemporary philosophical literature that contingent statements of identity are possible. I do not intend to deal with the Kantian question except to mention this analogy: After a rather thick book was written trying to answer the question how synthetic a priori judgments were possible, others came along later who claimed that the solution to the problem was that synthetic a priori judgments were, of course, impossible and that a book trying to show otherwise was written in vain. I will not discuss who was right on the possibility of synthetic a priori judgments. But in the case of contingent statements of identity, most philosophers have felt that the notion of a contingent identity statement ran into something like the following paradox. An argument like the following can be given against the possibility of contingent identity statements: 1 First, the law of the substitutivity of identity says that, for any objects x and y, if x is identical to y, then if x has a certain property F, so does y: Originally published in Milton K. Munitz (ed.), Identity and Individuation (1971), pp. 135-64. Reprinted by permission of New York University Press © Copyright by New York University.
(I)
(x)(y)[(x =y):::> (Fx:::> fy)]
On the other hand, every object surely is necessarily self-identical:
(2)
(x)[] (x
=
x)
But
(3) (x)(y)(x = y) :::> [[](x = x) :::> [](x = y)] is a substitution instance of (I), the substitutivity law. From (2) and (3), we can conclude that, for every x andy, if x equalsy, then, it is necessary that x equalsy:
(4)
(x)(y)((x =y):::> [](x =y))
This is because the clause [] (x = x) of the conditional drops out because it is known to be true. This is an argument which has been stated many times in recent philosophy. Its conclusion, however, has often been regarded as highly paradoxical. For example, David Wiggins, in his paper, "Identity-Statements," says: Now there undoubtedly exist contingent identity-statements. Let a = b be one of them. From its simple truth and (5) [=(4) above] we can derive "[](a = b)". But how then can there be any contingent identity-statements?2 He then says that five various reactions to this argument are possible, and rejects all of these reac-
Identity and Necessity
tions, and reacts himself. I do not want to discuss all the possible reactions to this statement, except to mention the second of those Wiggins rejects. This says: We might accept the result and plead that provided 'a' and 'b' are proper names nothing is amiss. The consequence of this is that no contingent identity-statements can be made by means of proper names. And then he says that he is discontented with this solution, and many other philosophers have been discontented with this solution, too, while still others have advocated it. What makes the statement (4) seem surprising? It says, for any objects x and y, if x is y, then it is necessary that x isy. I have already mentioned that someone might object to this argument on the grounds that premise (2) is already false, that it is not the case that everything is necessarily selfidentical. Well, for example, am I myself necessarily self-identical? Someone might argue that in some situations which we can imagine I would not even have existed, and therefore the statement "Saul Kripke is Saul Kripke" would have been false, or it would not be the case that I was selfidentical. Perhaps, it would have been neither true nor false, in such a world, to say that Saul Kripke is self-identical. Well, that may be so, but really it depends on one's philosophical view of a topic that I will not discuss: that is, what is to be said about truth-values of statements mentioning objects that do not exist in the actual world or any given possible world or counterfactual situation. Let us interpret necessity here weakly. We can count statements as necessary if, whenever the objects mentioned therein exist, the statement would be true. If we wished to be very careful about this, we would have to go into the question of existence as a predicate and ask if the statement can be reformulated in the form: For every x it is necessary that, if x exists, then x is self-identical. I will not go into this particular form of subtlety here because it is not going to be relevant to my main theme. Nor am I really going to consider formula (4). Anyone who believes formula (2) is, in my opinion, committed to formula (4). If x and yare the same things and we can talk about modal properties of an object at all, that is, in the usual parlance, we can speak of modality de re and an object necessarily having certain properties as such, then formula (I), I think, has to hold. Where x is any
property at all, including a property involving modal operators, and if x and yare the same object and x had a certain property F, then y has to have the same property F. And this is so even if the property F is itself of the form of necessarily having some other property G, in particular that of necessarily being identical to a certain object. Well, I will not discuss the formula (4) itself because by itself it does not assert, of any particular true statement of identity, that it is necessary. It does not say anything about statements at all. It says for every object x and objecty, if x andy are the same object, then it is necessary that x and yare the same object. And this, I think, if we think about it (anyway, if someone does not think so, I will not argue for it here), really amounts to something very little different from the statement (2). Since x, by definition of identity, is the only object identical with x, "(y)(y = x ~ Fy)" seems to me to be little more than a garrulous way of saying "Fx," and thus (x) (y) (y = x ~ Fx) says the same as (x)Fx no matter what "F" is - in particular, even if "F" stands for the property of necessary identity with x. So if x has this property (of necessary identity with x), trivially everything identical with x has it, as (4) asserts. But, from statement (4) one may apparently be able to deduce that various particular statements of identity must be necessary, and this is then supposed to be a very paradoxical consequence. Wiggins says, "Now there undoubtedly exist contingent identity-statements." One example of a contingent identity statement is the statement that the first Postmaster General of the United States is identical with the inventor of bifocals, or that both of these are identical with the man claimed by the Saturday Evening Post as its founder (falsely claimed, I gather, by the way). Now some such statements are plainly contingent. It plainly is a contingent fact that one and the same man both invented bifocals and took on the job of Postmaster General of the United States. How can we reconcile this with the truth of statement (4)? Well, that, too, is an issue I do not want to go into in detail except to be very dogmatic about it. It was, I think, settled quite well by Bertrand Russell in his notion of the scope of a description. According to Russell, one can, for example, say with propriety that the author of Hamlet might not have written Hamlet, or even that the author of Hamlet might not have been the author of Hamlet. Now here, of course, we do not deny the necessity of the identity of an object with itself; but we say it is true concerning a certain man that he in fact was the unique person to have
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written Hamlet and secondly that the man, who in fact was the man who wrote Hamlet, might not have written Hamlet. In other words, if Shakespeare had decided not to write tragedies, he might not have written Hamlet. Under these circumstances, the man who in fact wrote Hamlet would not have written Hamlet. Russell brings this out by saying that in such a statement, the first occurrence of the description "the author of Hamlet" has large scope. 3 That is, we say, "The author of Hamlet has the following property: that he might not have written Hamlet." We do not assert that the following statement might have been the case, namely that the author of Hamlet did not write Hamlet, for that is not true. That would be to say that it might have been the case that someone wrote Hamlet and yet did not write Hamlet, which would be a contradiction. Now, aside from the details of Russell's particular formulation of it, which depends on his theory of descriptions, this seems to be the distinction that any theory of descriptions has to make. For example, if someone were to meet the President of Harvard and take him to be a Teaching Fellow, he might say: "I took the President of Harvard for a Teaching Fellow." By this he does not mean that he took the proposition "The President of Harvard is a Teaching Fellow" to be true. He could have meant this, for example, had he believed that some sort of democratic system had gone so far at Harvard that the President of it decided to take on the task of being a Teaching Fellow. But that probably is not what he means. What he means instead, as Russell points out, is "Someone is President of Harvard and I took him to be a Teaching Fellow." In one of Russell's examples someone says, "I thought your yacht is much larger than it is." And the other man replies, "No, my yacht is not much larger than it is." Provided that the notion of modality de re, and thus of quantifying into modal contexts, makes any sense at all, we have quite an adequate solution to the problem of avoiding paradoxes if we substitute descriptions for the universal quantifiers in (4) because the only consequence we will draw,4 for example, in the bifocals case, is that there is a man who both happened to have invented bifocals and happened to have been the first Postmaster General of the United States, and is necessarily selfidentical. There is an object x such that x invented bifocals, and as a matter of contingent fact an object .y, such that'y is the first Postmaster General of the United States, and finally, it is necessary, that x is .y. What are x and .y here? Here, x and 'yare both
Benjamin Franklin, and it can certainly be necessary that Benjamin Franklin is identical with himself. So, there is no problem in the case of descriptions if we accept Russell's notion of scope. 5 And I just dogmatically want to drop that question here and go on to the question about names which Wiggins raises. And Wiggins says he might accept the result and plead that, provided a and b are proper names, nothing is amiss. And then he reject this. Now what is the special problem about proper names? At least if one is not familiar with the philosophicalliterature about this matter, one naively feels something like the following about proper names. First, if someone says "Cicero was an orator," then he uses the name "Cicero" in that statement simply to pick out a certain object and then to ascribe a certain property to the object, namely, in this case, he ascribes to a certain man the property of having been an orator. If someone else uses another name, such as, say, "Tully," he is still speaking about the same man. One ascribes the same property, if one says "Tully is an orator," to the same man. So to speak, the fact, or state of affairs, represented by the statement is the same whether one says "Cicero is an orator" or one says "Tully is an orator." It would, therefore, seem that the function of names is simply to refer, and not to describe the objects so named by such properties as "being the inventor of bifocals" or "being the first Postmaster General." It would seem that Leibniz' law and the law (I) should not only hold in the universally quantified form, but also in the form "if a = band Fa, then Fb," wherever "a" and "b" stand in place of names and "F" stands in place of a predicate expressing a genuine property of the object: (a = b· Fa) ~ Fb
We can run the same argument through again to obtain the conclusion where "a" and "b" replace any names, "If a = b, then necessarily a = b." And so, we could venture this conclusion: that whenever "a" and "b" are proper names, if a is b, that it is necessary that a is b. Identity statements between proper names have to be necessary if they are going to be true at all. This view in fact has been advocated, for example, by Ruth Barcan Marcus in a paper of hers on the philosophical interpretation of modallogic. 6 According to this view, whenever, for example, someone makes a correct statement of identity between two names, such as, for example, that Cicero is Tully, his statement has to be necessary if it is true. But such a conclusion seems plainly
Identity and Necessity
to be false. (I, like other philosophers, have a habit of understatement in which "it seems plainly false" means "it is plainly false." Actually, I think the view is true, though not quite in the form defended by Mrs Marcus.) At any rate, it seems plainly false. One example was given by Professor Quine in his reply to Professor Marcus at the symposium: "I think I see trouble anyway in the contrast between proper names and descriptions as Professor Marcus draws it. The paradigm of the assigning of proper names is tagging. We may tag the planet Venus some fine evening with the proper name 'Hesperus'. We may tag the same planet again someday before sunrise with the proper name 'Phosphorus'." (Quine thinks that something like that actually was done once.) "When, at last, we discover that we have tagged the same planet twice, our discovery is empirical, and not because the proper names were descriptions." According to what we are told, the planet Venus seen in the morning was originally thought to be a star and was called "the Morning Star," or (to get rid of any question of using a description) was called "Phosphorus." One and the same planet, when seen in the evening, was thought to be another star, the Evening Star, and was called "Hesperus." Later on, astronomers discovered that Phosphorus and Hesperus were one and the same. Surely no amount of a priori ratiocination on their part could conceivably have made it possible for them to deduce that Phosphorus is Hesperus. In fact, given the information they had, it might have turned out the other way. Therefore, it is argued, the statement "Hesperus is Phosphorus" has to be an ordinary contingent, empirical truth, one which might have come out otherwise, and so the view that true identity statements between names are necessary has to be false. Another example which Quine gives in Word and Object is taken from Professor Schriidinger, the famous pioneer of quantum mechanics: A certain mountain can be seen from both Tibet and Nepal. When seen from one direction, it was called "Gaurisanker"; when seen from another direction, it was called "Everest"; and then, later on, the empirical discovery was made that Gaurisanker is Everest. (Quine further says that he gathers the example is actually geographically incorrect. I guess one should not rely on physicists for geographical information.) Of course, one possible reaction to this argument is to deny that names like "Cicero," "Tully," "Gaurisanker," and "Everest" really are proper names. Look, someone might say (someone has
said it: his name was "Bertrand Russell"), just because statements like "Hesperus is Phosphorus" and "Gaurisanker is Everest" are contingent, we can see that the names in question are not really purely referential. You are not, in Mrs Marcus's phrase, just "tagging" an object; you are actually describing it. What does the contingent fact that Hesperus is Phosphorus amount to? Well, it amounts to the fact that the star in a certain portion of the sky in the evening is the star in a certain portion of the sky in the morning. Similarly, the contingent fact that Guarisanker is Everest amounts to the fact that the mountain viewed from such and such an angle in Nepal is the mountain viewed from such and such another angle in Tibet. Therefore, such names as "Hesperus" and "Phosphorus' can only be abbreviations for descriptions. The term "Phosphorus" has to mean "the star seen ... ," or (let us be cautious because it actually turned out not to be a star), "the heavenly body seen from such and such a position at such and such a time in the morning," and the name "Hesperus" has to mean "the heavenly body seen in such and such a position at such and such a time in the evening." So, Russell concludes, if we want to reserve the term "name" for things which really just name an object without describing it, the only real proper names we can have are names of our own immediate sense-data, objects of our own "immediate acquaintance." The only such names which occur in language are demonstratives like "this" and "that." And it is easy to see that this requirement of necessity of identity, understood as exempting identities between names from all imaginable doubt, can indeed be guaranteed only for demonstrative names of immediate sense-data; for only in such cases can an identity statement between two different names have a general immunity from Cartesian doubt. There are some other things Russell has sometimes allowed as objects of acquaintance, such as one's self; we need not go into details here. Other philosophers (for example, Mrs Marcus in her reply, at least in the verbal discussion as I remember it - I do not know if this got into print, so perhaps this should not be "tagged" on her 7) have said, "If names are really just tags, genuine tags, then a good dictionary should be able to tell us that they are names of the same object." You have an object a and an object b with names "John" and "Joe." Then, according to Mrs Marcus, a dictionary should be able to tell you whether or not "John" and "Joe" are names of the same object.
Saul Kripke
Of course, I do not know what ideal dictionaries should do, but ordinary proper names do not seem to satisfy this requirement. You certainly can, in the case of ordinary proper names, make quite empirical discoveries that, let's say, Hesperus is Phosphorus, though we thought otherwise. We can be in doubt as to whether Gaurisanker is Everest or Cicero is in fact Tully. Even now, we could conceivably discover that we were wrong in supposing that Hesperus was Phosphorus. Maybe the astronomers made an error. So it seems that this view is wrong and that if by a name we do not mean some artificial notion of names such as Russell's, but a proper name in the ordinary sense, then there can be contingent identity statements using proper names, and the view to the contrary seems plainly wrong. In recent philosophy a large number of other identity statements have been emphasized as examples of contingent identity statements, different, perhaps, from either of the types I have mentioned before. One of them is, for example, the statement "Heat is the motion of molecules." First, science is supposed to have discovered this. Empirical scientists in their investigations have been supposed to discover (and, I suppose, they did) that the external phenomenon which we call "heat" is, in fact, molecular agitation. Another example of such a discovery is that water is H 2 0, and yet other examples are that gold is the element with such and such an atomic number, that light is a stream of photons, and so on. These are all in some sense of "identity statement" identity statements. Second, it is thought, they are plainly contingent identity statements, just because they were scientific discoveries. After all, heat might have turned out not to have been the motion of molecules. There were other alternative theories of heat proposed, for example, the caloric theory of heat. If these theories of heat had been correct, then heat would not have been the motion of molecules, but instead, some substance suffusing the hot object, called "caloric." And it was a matter of course of science and not of any logical necessity that the one theory turned out to be correct and the other theory turned out to be incorrect. So, here again, we have, apparently, another plain example of a contingent identity statement. This has been supposed to be a very important example because of its connection with the mind -body problem. There have been many philosophers who have wanted to be materialists, and to be materialists in a particular form, which is known today as "the identity theory." According to this
theory, a certain mental state, such as a person's being in pain, is identical with a certain state of his brain (or, perhaps, of his entire body, according to some theorists), at any rate, a certain material or neural state of his brain or body. And so, according to this theory, my being in pain at this instant, ifI were, would be identical with my body's being or my brain's being in a certain state. Others have objected that this cannot be because, after all, we can imagine my pain existing even if the state of the body did not. We can perhaps imagine my not being embodied at all and still being in pain, or, conversely, we could imagine my body existing and being in the very same state even if there were no pain. In fact, conceivably, it could be in this state even though there were no mind "back of it," so to speak, at all. The usual reply has been to concede that all of these things might have been the case, but to argue that these are irrelevant to the question of the identity of the mental state and the physical state. This identity, it is said, is just another contingent scientific identification, similar to the identification of heat with molecular motion, or water with H 2 0. Just as we can imagine heat without any molecular motion, so we can imagine a mental state without any corresponding brain state. But, just as the first fact is not damaging to the identification of heat and the motion of molecules, so the second fact is not at all damaging to the identification of a mental state with the corresponding brain state. And so, many recent philosophers have held it to be very important for our theoretical understanding of the mind-body problem that there can be contingent identity statements of this form. To state finally what I think, as opposed to what seems to be the case, or what others think, I think that in both cases, the case of names and the case of the theoretical identifications, the identity statements are necessary and not contingent. That is to say, they are necessary if true; of course, false identity statements are not necessary. How can one possibly defend such a view? Perhaps I lack a complete answer to this question, even though I am convinced that the view is true. But to begin an answer, let me make some distinctions that I want to use. The first is between a rigid and a nonrigid designator. What do these terms mean? As an example of a nonrigid designator, I can give an expression such as "the inventor of bifocals." Let us suppose it was Benjamin Franklin who invented bifocals, and so the expression, "the inventor of bifocals," designates or refers to a certain man, namely, Benjamin Franklin. However, we can
Identity and Necessity
easily imagine that the world could have been different, that under different circumstances someone else would have come upon this invention before Benjamin Franklin did, and in that case, he would have been the inventor of bifocals. So, in this sense, the expression "the inventor of bifocals' is nonrigid: Under certain circumstances one man would have been the inventor of bifocals; under other circumstances, another man would have. In contrast, consider the expression "the square root of 25." Independently of the empirical facts, we can give an arithmetical proof that the square root of 25 is in fact the number 5, and because we have proved this mathematically, what we have proved is necessary. If we think of numbers as entities at all, and let us suppose, at least for the purpose of this lecture, that we do, then the expression "the square root of 25" necessarily designates a certain number, namely 5. Such an expression I call "a rigid designator." Some philosophers think that anyone who even uses the notions of rigid or nonrigid designator has already shown that he has fallen into a certain confusion or has not paid attention to certain facts. What do I mean by "rigid designator"? I mean a term that designates the same object in all possible worlds. To get rid of one confusion, which certainly is not mine, I do not use "might have designated a different object" to refer to the fact that language might have been used differently. For example, the expression "the inventor of bifocals" might have been used by inhabitants of this planet always to refer to the man who corrupted Hadleyburg. This would have been the case, if, first, the people on this planet had not spoken English, but some other language, which phonetically overlapped with English; and if, second, in that language the expression "the inventor of bifocals" meant the "man who corrupted Hadleyburg." Then it would refer, of course, in their language, to whoever in fact corrupted Hadleyburg in this counterfactual situation. That is not what I mean. What I mean by saying that a description might have referred to something different, I mean that in our language as we use it in describing a counterfactual situation, there might have been a different object satisfying the descriptive conditions we give for reference. So, for example, we use the phrase "the inventor of bifocals," when we are talking about another possible world or a counter factual situation, to refer to whoever in that counterfactual situation would have invented bifocals, not to the person whom people in that counterfactual situation would have called "the inventor of bifocals." They might have spoken a
different language which phonetically overlapped with English in which "the 'inventor of bifocals" is used in some other way. I am not concerned with that question here. For that matter, they might have been deaf and dumb, or there might have been no people at all. (There still could have been an inventor of bifocals even if there were no people - God, or Satan, will do.) Second, in talking about the notion of a rigid designator, I do not mean to imply that the object referred to has to exist in all possible worlds, that is, that it has to necessarily exist. Some things, perhaps mathematical entities such as the positive integers, if they exist at all, necessarily exist. Some people have held that God both exists and necessarily exists; others, that he contingently exists; others, that he contingently fails to exist; and others, that he necessarily fails to exist: 8 all four options have been tried. But at any rate, when I use the notion of rigid designator, I do not imply that the object referred to necessarily exists. All I mean is that in any possible world where the object in question does exist, in any situation where the object would exist, we use the designator in question to designate that object. In a situation where the object does not exist, then we should say that the designator has no referent and that the object in question so designated does not exist. As I said, many philosophers would find the very notion of rigid designator objectionable per se. And the objection that people make may be stated as follows: Look, you're talking about situations which are counterfactual, that is to say, you're talking about other possible worlds. Now these worlds are completely disjoint, after all, from the actual world which is not just another possible world; it is the actual world. So, before you talk about, let us say, such an object as Richard Nixon in another possible world at all, you have to say which object in this other possible world would be Richard Nixon. Let us talk about a situation in which, as you would say, Richard Nixon would have been a member of SDS. Certainly the member of SDS you are talking about is someone very different in many of his properties from Nixon. Before we even can say whether this man would have been Richard Nixon or not, we have to set up criteria of identity across possible worlds. Here are these other possible worlds. There are all kinds of objects in them with different properties from those of any actual object. Some of them resemble Nixon in some ways, some of them resemble Nixon in other ways. Well, which of these objects is
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Nixon? One has to give a criterion of identity. And this shows how the very notion of rigid designator runs in a circle. Suppose we designate a certain number as the number of planets. Then, if that is our favorite way, so to speak, of designating this number, then in any other possible worlds we will have to identify whatever number is the number of planets with the number 9, which in the actual world is the number of planets. So, it is argued by various philosophers, for example, implicitly by Q!Iine, and explicitly by many others in his wake, we cannot really ask whether a designator is rigid or nonrigid because we first need a criterion of identity across possible worlds. An extreme view has even been held that, since possible worlds are so disjoint from our own, we cannot really say that any object in them is the same as an object existing now but only that there are some objects which resemble things in the actual world, more or less. We, therefore, should not really speak of what would have been true of Nixon in another possible world but, only of what "counterparts" (the term which David Lewis uses 9) of Nixon there would have been. Some people in other possible worlds have dogs whom they call "Checkers." Others favor the ABM but do not have any dog called Checkers. There are various people who resemble Nixon more or less, but none of them can really be said to be Nixon; they are only counterparts of Nixon, and you choose which one is the best counterpart by noting which resembles Nixon the most closely, according to your favorite criteria. Such views are widespread, both among the defenders of quantified modal logic and among its detractors. All of this talk seems to me to have taken the metaphor of possible worlds much too seriously in some way. It is as if a "possible world" were like a foreign country, or distant planet way out there. It is as if we see dimly through a telescope various actors on this distant planet. Actually David Lewis's view seems the most reasonable if one takes this picture literally. No one far away on another planet can be strictly identical with someone here. But, even if we have some marvelous methods of transportation to take one and the same person from planet to planet, we really need some epistemological criteria of identity to be able to say whether someone on this distant planet is the same person as someone here. All of this seems to me to be a totally misguided way of looking at things. What it amounts to is the view that counterfactual situations have to be described purely qualitatively. So, we cannot say,
for example, "If Nixon had only given a sufficient bribe to Senator X, he would have gotten Carswell through," because that refers to certain people, Nixon and Carswell, and talks about what things would be true of them in a counterfactual situation. We must say instead "If a man who has a hairline like such and such, and holds such and such political opinions had given a bribe to a man who was a senator and had such and such other qualities, then a man who was a judge in the South and had many other qualities resembling Carswell would have been confirmed." In other words, we must describe counterfactual situations purely qualitatively and then ask the question, "Given that the situation contains people or things with such and such qualities, which of these people is (or is a counterpart of) Nixon, which is Carswell, and so on?" This seems to me to be wrong. Who is to prevent us from saying "Nixon might have gotten Carswell through had he done certain things"? We are speaking of Nixon and asking what, in certain counterfactual situations, would have been true of him. We can say that if Nixon had done such and such, he would have lost the election to Humphrey. Those I am opposing would argue, "Yes, but how do you find out if the man you are talking about is in fact Nixon?" It would indeed be very hard to find out, if you were looking at the whole situation through a telescope, but that is not what we are doing here. Possible worlds are not something to which an epistemological question like this applies. And if the phrase "possible worlds" is what makes anyone think some such question applies, he should just drop this phrase and use some other expression, say "counterfactual situation," which might be less misleading. If we say "If Nixon had bribed such and such a senator, Nixon would have gotten Carswell through," what is given in the very description of that situation is that it is a situation in which we are speaking of Nixon, and of Carswell, and of such and such a senator. And there seems to be no less objection to stipulating that we are speaking of certain people than there can be objection to stipulating that we are speaking of certain qualities. Advocates of the other view take speaking of certain qualities as unobjectionable. They do not say, "How do we know that this quality (in another possible world) is that of redness?" But they do find speaking of certain people objectionable. But I see no more reason to object in the one case than in the other. I think it really comes from the idea of possible worlds as existing out there, but very far off, viewable only through a special telescope. Even
Identity and Necessity
more objectionable is the view of David Lewis. According to Lewis, when we say "Under certain circumstances Nixon would have gotten Carswell through," we really mean "Some man, other than Nixon but closely resembling him, would have gotten some judge, other than Carswell but closely resembling him, through." Maybe that is so, that some man closely resembling Nixon could have gotten some man closely resembling Carswell through. But that would not comfort either Nixon or Carswell, nor would it make Nixon kick himself and say "/ should have done such and such to get Carswell through." The question is whether under certain circumstances Nixon himself could have gotten Carswell through. And I think the objection is simply based on a misguided picture. Instead, we can perfectly well talk about rigid and nonrigid designators. Moreover, we have a simple, intuitive test for them. We can say, for example, that the number of planets might have been a different number from the number it in fact is. For example, there might have been only seven planets. We can say that the inventor of bifocals might have been someone other than the man who in fact invented bifocals. lO We cannot say, though, that the square root of 81 might have been a different number from the number it in fact is, for that number just has to be 9. If we apply this intuitive test to proper names, such as for example "Richard Nixon," they would seem intuitively to come out to be rigid designators. First, when we talk even about the counter factual situation in which we suppose Nixon to have done different things, we assume we are still talking about Nixon himself. We say, "If Nixon had bribed a certain senator, he would have gotten Carswell through," and we assume that by "Nixon" and "Carswell" we are still referring to the very same people as in the actual world. And it seems that we cannot say "Nixon might have been a different man from the man he in fact was," unless, of course, we mean it metaphorically: He might have been a different sort of person (if you believe in free will and that people are not inherently corrupt). You might think the statement true in that sense, but Nixon could not have been in the other literal sense a different person from the person he, in fact, is, even though the thirty-seventh President of the United States might have been Humphrey. So the phrase "the thirty-seventh President" IS nonrigid, but "Nixon," it would seem, is rigid. Let me make another distinction before I go back to the question of identity statements. This dis-
tinction is very fundamental and also hard to see through. In recent discussion, many philosophers who have debated the meaningfulness of various categories of truths, have regarded them as identical. Some of those who identify them are vociferous defenders of them, and others, such as Quine, say they are all identically meaningless. But usually they're not distinguished. These are categories such as "analytic," "necessary," "a priori," and sometimes even "certain." I will not talk about all of these but only about the notions of aprioricity and necessity. Very often these are held to be synonyms. (Many philosophers probably should not be described as holding them to be synonyms; they simply use them interchangeably.) I wish to distinguish them. What do we mean by calling a statement necessary? We simply mean that the statement in question, first, is true, and, second, that it could not have been otherwise. When we say that something is contingently true, we mean that, though it is in fact the case, it could have been the case that things would have been otherwise. If we wish to assign this distinction to a branch of philosophy, we should assign it to metaphysics. To the contrary, there is the notion of an a priori truth. An a priori truth is supposed to be one which can be known to be true independently of all experience. Notice that this does not in and of itself say anything about all possible worlds, unless this is put into the definition. All that it says is that it can be known to be true of the actual world, independently of all experience. It may, by some philosophical argument, follow from our knowing, independently of experience, that something is true of the actual world, that it has to be known to be true also of all possible worlds. But if this is to be established, it requires some philosophical argument to establish it. Now, this notion, if we were to assign it to a branch of philosophy, belongs, not to metaphysics, but to epistemology. It has to do with the way we can know certain things to be in fact true. Now, it may be the case, of course, that anything which is necessary is something which can be known a priori. (Notice, by the way, the notion a priori truth as thus defined has in it another modality: it can be known independently of all experience. It is a little complicated because there is a double modality here.) I will not have time to explore these notions in full detail here, but one thing we can see from the outset is that these two notions are by no means trivially the same. If they are coextensive, it takes some philosophical argument to establish it. As stated, they belong to
Saul Kripke
different domains of philosophy. One of them has something to do with knowledge, of what can be known in certain ways about the actual world. The other one has to do with metaphysics, how the world could have been; given that it is the way it is, could it have been otherwise, in certain ways? Now I hold, as a matter of fact, that neither class of statements is contained in the other. But all we need to talk about here is this: Is everything that is necessary knowable a priori or known a priori? Consider the following example: the Goldbach conjecture. This says that every even number is the sum of two primes. It is a mathematical statement, and if it is true at all, it has to be necessary. Certainly, one could not say that though in fact every even number is the sum of two primes, there could have been some extra number which was even and not the sum of two primes. What would that mean? On the other hand, the answer to the question whether every even number is in fact the sum of two primes is unknown, and we have no method at present for deciding. So we certainly do not know, a priori or even a posteriori, that every even number is the sum of two primes. (Well, perhaps we have some evidence in that no counterexample has been found.) But we certainly do not know a priori anyway, that every even number is, in fact, the sum of two primes. But, of course, the definition just says "can be known independently of experience," and someone might say that if it is true, we could know it independently of experience. It is hard to see exactly what this claim means. It might be so. One thing it might mean is that if it were true we could prove it. This claim is certainly wrong if it is generally applied to mathematical statements and we have to work within some fixed system. This is what Godel proved. And even if we mean an "intuitive proof in general," it might just be the case (at least, this view is as clear and as probable as the contrary) that though the statement is true, there is just no way the human mind could ever prove it. Of course, one wayan infinite mind might be able to prove it is by looking through each natural number one by one and checking. In this sense, of course, it can, perhaps, be known a priori, but only by an infinite mind, and then this gets into other complicated questions. I do not want to discuss questions about the conceivability of performing an infinite number of acts like looking through each number one by one. A vast philosophical literature has been written on this: Some have declared it is logically impossible; others that it is logically possible; and some do not know. The
main point is that it is not trivial that just because such a statement is necessary it can be known a priori. Some considerable clarification is required before we decide that it can be so known. And so this shows that even if everything necessary is a priori in some sense, it should not be taken as a trivial matter of definition. It is a substantive philosophical thesis which requires some work. Another example that one might give relates to the problem of essentialism. Here is a lectern. A question which has often been raised in philosophy is: What are its essential properties? What properties, aside from trivial ones like self-identity, are such that this object has to have them if it exists at all, II are such that if an object did not have it, it would not be this object?12 For example, being made of wood, and not of ice, might be an essential property of this lectern. Let us just take the weaker statement that it is not made of ice. That will establish it as strongly as we need it, perhaps as dramatically. Supposing this lectern is in fact made of wood, could this very lectern have been made from the very beginning of its existence from ice, say frozen from water in the Thames? One has a considerable feeling that it could not, though in fact one certainly could have made a lectern of water from the Thames, frozen it into ice by some process, and put it right there in place of this thing. If one had done so, one would have made, of course, a different object. It would not have been this very lectern, and so one would not have a case in which this very lectern here was made of ice, or was made from water from the Thames. The question of whether it could afterward, say in a minute from now, turn into ice is something else. So, it would seem, if an example like this is correct - and this is what advocates of essentialism have held - that this lectern could not have been made of icc, that is in any counterfactual situation of which we would say that this lectern existed at all, we would have to say also that it was not made from water from the Thames frozen into ice. Some have rejected, of course, any such notion of essential property as meaningless. Usually, it is because (and I think this is what Quine, for example, would say) they have held that it depends on the notion of identity across possible worlds, and that this is itself meaningless. Since I have rejected this view already, I will not deal with it again. We can talk about this very object, and whether it could have had certain properties which it does not in fact have. For example, it could have been in another room from the room it in fact is in, even at this very time, but it
Identity and Necessity
could not have been made from the very beginning from water frozen into ice. If the essentialist view is correct, it can only be correct if we sharply distinguish between the notions of a posteriori and a priori truth on the one hand, and contingent and necessary truth on the other hand, for although the statement that this table, if it exists at all, was not made of ice, is necessary, it certainly is not something that we know a priori. What we know is that first, lecterns usually are not made of ice, they are usually made of wood. This looks like wood. It does not feel cold, and it probably would if it were made of ice. Therefore, I conclude, probably this is not made of ice. Here my entire judgment is a posteriori. I could find out that an ingenious trick has been played upon me and that, in fact, this lectern is made of ice; but what I am saying is, given that it is in fact not made of ice, in fact is made of wood, one cannot imagine that under certain circumstances it could have been made of ice. So we have to say that though we cannot know a priori whether this table was made of ice or not, given that it is not made of ice, it is necessarily not made of ice. In other words, if P is the statement that the lectern is not made of ice, one knows by a priori philosophical analysis, some conditional of the form "if P, then necessarily P." If the table is not made of ice, it is necessarily not made of ice. On the other hand, then, we know by empirical investigation that P, the antecedent of the conditional, is true - that this table is not made of ice. We can conclude by modus ponens: P~
OP
P
OP The conclusion - "OP" - is that it is necessary that the table not be made of ice, and this conclusion is known a posteriori, since one of the premises on which it is based is a posteriori. So, the notion of essential properties can be maintained only by distinguishing between the notions of a priori and necessary truth, and I do maintain it. Let us return to the question of identities. Concerning the statement "Hesperus is Phosphorus" or the statement "Cicero is Tully," one can find all of these out by empirical investigation, and we might turn out to be wrong in our empirical beliefs. So, it is usually argued, such statements must therefore be contingent. Some have embraced the other side of the coin and have held "Because of
this argument about necessity, identity statements between names have to be knowable a priori, so, only a very special category of names, possibly, really works as names; the other things are bogus names, disguised descriptions, or something of the sort. However, a certain very narrow class of statements of identity are known a priori, and these are the ones which contain the genuine names." If one accepts the distinctions that I have made, one need not jump to either conclusion. One can hold that certain statements of identity between names, though often known a posteriori, and maybe not knowable a priori, are in fact necessary, if true. So, we have some room to hold this. But, of course, to have some room to hold it does not mean that we should hold it. So let us see what the evidence is. First, recall the remark that I made that proper names seem to be rigid designators, as when we use the name "Nixon" to talk about a certain man, even in counterfactual situations. If we say, "If Nixon had not written the letter to Sax be, maybe he would have gotten Carswell through," we are in this statement talking about Nixon, Saxbe, and Carswell, the very same men as in the actual world, and what would have happened to them under certain counterfactual circumstances. If names are rigid designators, then there can be no question about identities being necessary, because "a" and "b" will be rigid designators of a certain man or thing x. Then even in every possible world, a and b will both refer to this same object x, and to no other, and so there will be no situation in which a might not have been b. That would have to be a situation in which the object which we are also now calling "x" would not have been identical with itself. Then one could not possibly have a situation in which Cicero would not have been Tully or Hesperus would not have been Phosphorus. 1.1 Aside from the identification of necessity with a priority, what has made people feel the other way? There are two things which have made people feel the other way.I4 Some people tend to regard identity statements as metalinguistic statements, to identify the statement "Hesperus is Phosphorus" with the metalinguistic statement" 'Hesperus' and 'Phosphorus' are names of the same heavenly body." And that, of course, might have been false. We might have used the terms "Hesperus" and "Phosphorus" as names of two different heavenly bodies. But, of course, this has nothing to do with the necessity of identity. In the same sense "2 + 2 = 4" might have been false. The phrases
Saul Kripke
"2 + 2" and "4" might have been used to refer to two different numbers. One can imagine a language, for example, in which "+," "2," and "="wereused in the standard way, but "4" was used as the name of, say, the square root of minus I, as we should call it, "i." Then "2 + 2 = 4" would be false, for 2 plus 2 is not equal to the square root of minus I. But this is not what we want. We do not want just to say that a certain statement which we in fact use to express something true could have expressed something false. We want to use the statement in our way and see if it could have been false. Let us do this. What is the idea people have? They say, 'Look, Hesperus might not have been Phosphorus. Here a certain planet was seen in the morning, and it was seen in the evening; and it just turned out later on as a matter of empirical fact that they were one and the same planet. If things had turned out otherwise, they would have been two different planets, or two different heavenly bodies, so how can you say that such a statement is necessary?' Now there are two things that such people can mean. First, they can mean that we do not know a priori whether Hesperus is Phosphorus. This I have already conceded. Second, they may mean that they can actually imagine circumstances that they would call circumstances in which Hesperus would not have been Phosphorus. Let us think what would be such a circumstance, using these terms here as names of a planet. For example, it could have been the case that Venus did indeed rise in the morning in exactly the position in which we saw it, but that on the other hand, in the position which is in fact occupied by Venus in the evening, Venus was not there, and Mars took its place. This is all counterfactual because in fact Venus is there. Now one can also imagine that in this counterfactual other possible world, the Earth would have been inhabited by people and that they should have used the names "Phosphorus" for Venus in the morning and "Hesperus" for Mars in the evening. Now, this is all very good, but would it be a situation in which Hesperus was not Phosphorus? Of course, it is a situation in which people would have been able to say, truly, "Hesperus is not Phosphorus"; but we are supposed to describe things in our language, not in theirs. So let us describe it in our language. Well, how could it actually happen that Venus would not be in that position in the evening? For example, let us say that there is some comet that comes around every evening and yanks things over a little bit. (That would be a very simple scientific way of imagining
it: not really too simple - that is very hard to imagine actually.) It just happens to come around every evening, and things get yanked over a bit. Mars gets yanked over to the very position where Venus is, then the comet yanks things back to their normal position in the morning. Thinking of this planet which we now call "Phosphorus," what should we say? Well, we can say that the comet passes it and yanks Phosphorus over so that it is not in the position normally occupied by Phosphorus in the evening. If we do say this, and really use "Phosphorus" as the name of a planet, then we have to say that, under such circumstances, Phosphorus in the evening would not be in the position in where we, in fact, saw it; or alternatively, Hesperus in the evening would not be in the position in which we, in fact, saw it. We might say that under such circumstances, we would not have called Hesperus "Hesperus" because Hesperus would have been in a different position. But that still would not make Phosphorus different from Hesperus; what would then be the case instead is that Hesperus would have been in a different position from the position it in fact is and, perhaps, not in such a position that people would have called it "Hesperus." But that would not be a situation in which Phosphorus would not have been Hesperus. Let us take another example which may be clearer. Suppose someone uses "Tully" to refer to the Roman orator who denounced Cataline and uses the name 'Cicero' to refer to the man whose works he had to study in third-year Latin in high school. Of course, he may not know in advance that the very same man who denounced Cataline wrote these works, and that is a contingent statement. But the fact that this statement is contingent should not make us think that the statement that Cicero is Tully, if it is true, and it is in fact true, is contingent. Suppose, for example, that Cicero actually did denounce Cataline, but thought that this political achievement was so great that he should not bother writing any literary works. Would we say that these would be circumstances under which he would not have been Cicero? It seems to me that the answer is no, that instead we would say that, under such circumstances, Cicero would not have written any literary works. It is not a necessary property of Cicero - the way the shadow follows the man - that he should have written certain works; we can easily imagine a situation in which Shakespeare would not have written the works of Shakespeare, or one in which Cicero would not have written the works of Cicero. What may be
Identity and Necessity
the case is that we fix the reference of the term "Cicero" by use of some descriptive phrase, such as "the author of these works." But once we have this reference fixed, we then use the name "Cicero" rigidzy to designate the man who in fact we have identified by his authorship of these works. We do not use it to designate whoever would have written these works in place of Cicero, if someone else wrote them. It might have been the case that the man who wrote these works was not the man who denounced Cataline. Cassius might have written these works. But we would not then say that Cicero would have been Cassius, unless we were speaking in a very loose and metaphorical way. We would say that Cicero, whom we may have identified and come to know by his works, would not have written them, and that someone else, say Cassius, would have written them in his place. Such examples are not grounds for thinking that identity statements are contingent. To take them as such grounds is to misconstrue the relation between a name and a description used to fix its reference, to take them to be synonyms. Even if we fix the reference of such a name as "Cicero" as the man who wrote such and such works, in speaking of counterfactual situations, when we speak of Cicero, we do not then speak of whoever in such counter factual situations would have written such and such works, but rather of Cicero, whom we have identified by the contingent property that he is the man who in fact, that is, in the actual world, wrote certain works. IS I hope this is reasonably clear in a brief compass. Now, actually I have been presupposing something I do not really believe to be, in general, true. Let us suppose that we do fix the reference of a name by a description. Even if we do so, we do not then make the name synonymous with the description, but instead we use the name rigidry to refer to the object so named, even in talking about counterfactual situations where the thing named would not satisfy the description in question. Now, this is what I think in fact is true for those cases of naming where the reference is fixed by description. But, in fact, I also think, contrary to most recent theorists, that the reference of names is rarely or almost never fixed by means of description. And by this I do not just mean what Searle says: "It's not a single description, but rather a cluster, a family of properties which fixes the reference." I mean that properties in this sense are not used at all. But I do not have the time to go into this here. So, let us suppose that at least one half of prevailing views about
naming is true, that the reference is fixed by descriptions. Even were that true, the name would not be synonymous with the description, but would be used to name an object which we pick out by the contingent fact that it satisfies a certain description. And so, even though we can imagine a case where the man who wrote these works would not have been the man who denounced Cataline, we should not say that that would be a case in which Cicero would not have been Tully. We should say that it is a case in which Cicero did not write these works, but rather that Cassius did. And the identity of Cicero and Tully still holds. Let me turn to the case of heat and the motion of molecules. Here, surely, is a case that is contingent identity! Recent philosophy has emphasized this again and again. So, if it is a case of contingent identity, then let us imagine under what circumstances it would be false. Now, concerning this statement I hold that the circumstances philosophers apparently have in mind as circumstances under which it would have been false are not in fact such circumstances. First, of course, it is argued that "Heat is the motion of molecules" is an a posteriori judgment; scientific investigation might have turned out otherwise. As I said before, this shows nothing against the view that it is necessary - at least if! am right. But here, surely, people had very specific circumstances in mind under which, so they thought, the judgment that heat is the motion of molecules would have been false. What were these circumstances? One can distill them out of the fact that we found out empirically that heat is the motion of molecules. How was this? What did we find out first when we found out that heat is the motion of molecules? There is a certain external phenomenon which we can sense by the sense of touch, and it produces a sensation which we call "the sensation of heat." We then discover that the external phenomenon which produces this sensation, which we sense, by means of our sense of touch, is in fact that of molecular agitation in the thing that we touch, a very high degree of molecular agitation. So, it might be thought, to imagine a situation in which heat would not have been the motion of molecules, we need only imagine a situation in which we would have had the very same sensation and it would have been produced by something other than the motion of molecules. Similarly, if we wanted to imagine a situation in which light was not a stream of photons, we could imagine a situation in which we were sensitive to
Saul Kripke
something else in exactly the same way, producing what we call visual experiences, though not through a stream of photons. To make the case stronger, or to look at another side of the coin, we could also consider a situation in which we are concerned with the motion of molecules but in which such motion does not give us the sensation of heat. And it might also have happened that we, or, at least, the creatures inhabiting this planet, might have been so constituted that, let us say, an increase in the motion of molecules did not give us this sensation but that, on the contrary, a slowing down of the molecules did give us the very same sensation. This would be a situation, so it might be thought, in which heat would not be the motion of molecules, or, more precisely, in which temperature would not be mean molecular kinetic energy. But I think it would not be so. Let us think about the situation again. First, let us think about it in the actual world. Imagine right now the world invaded by a number of Martians, who do indeed get the very sensation that we call "the sensation of heat" when they feel some ice which has slow molecular motion, and who do not get a sensation of heat - in fact, maybe just the reverse - when they put their hand near a fire which causes a lot of molecular agitation. Would we say, "Ah, this casts some doubt on heat being the motion of molecules, because there are these other people who don't get the same sensation"? Obviously not, and no one would think so. We would say instead that the Martians somehow feel the very sensation we get when we feel heat when they feel cold, and that they do not get a sensation of heat when they feel heat. But now let us think of a counterfactual situation. 16 Suppose the earth had from the very beginning been inhabited by such creatures. First, imagine it inhabited by no creatures at all: then there is no one to feel any sensations of heat. But we would not say that under such circumstances it would necessarily be the case that heat did not exist; we would say that heat might have existed, for example, if there were fires that heated up the air. Let us suppose the laws of physics were not very different: Fires do heat up the air. Then there would have been heat even though there were no creatures around to feel it. Now let us suppose evolution takes place, and life is created, and there are some creatures around. But they are not like us, they are more like the Martians. Now would we say that heat has suddenly turned to cold, because of the way the creatures of this planet
sense it? No, I think we should describe this situation as a situation in which, though the creatures on this planet got our sensation of heat, they did not get it when they were exposed to heat. They got it when they were exposed to cold. And that is something we can surely well imagine. We can imagine it just as we can imagine our planet being invaded by creatures of this sort. Think of it in two steps. First there is a stage where there are no creatures at all, and one can certainly imagine the planet still having both heat and cold, though no one is around to sense it. Then the planet comes through an evolutionary process to be peopled with beings of different neural structure from ourselves. Then these creatures could be such that they were insensitive to heat; they did not feel it in the way we do; but on the other hand, they felt cold in much the same way that we feel heat. But still, heat would be heat, and cold would be cold. And particularly, then, this goes in no way against saying that in this counter factual situation heat would still be the molecular motion, be that which is produced by fires, and so on, just as it would have been if there had been no creatures on the planet at all. Similarly, we could imagine that the planet was inhabited by creatures who got visual sensations when there were sound waves in the air. We should not therefore say, "Under such circumstances, sound would have been light." Instead we should say, "The planet was inhabited by creatures who were in some sense visually sensitive to sound, and may be even visually sensitive to light." Ifthis is correct, it can still be and will still be a necessary truth that heat is the motion of molecules and that light is a stream of photons. To state the view succinctly: we use both the terms "heat" and "the motion of molecules" as rigid designators for a certain external phenomenon. Since heat is in fact the motion of molecules, and the designators are rigid, by the argument I have given here, it is going to be necessa~y that heat is the motion of molecules. What gives us the illusion of contingency is the fact we have identified the heat by the contingent fact that there happen to be creatures on this planet - (namely, ourselves) who are sensitive to it in a certain way, that is, who are sensitive to the motion of molecules or to heat - these are one and the same thing. And this is contingent. So we use the description, 'that which causes such and such sensations, or that which we sense in such and such a way,' to identify heat. But in using this fact we use a contingent property of heat, just as we use the contingent
Identity and Necessity
property of Cicero as having written such and such works to identify him. We then use the terms "heat" in the one case and "Cicero" in the other rigidzv to designate the objects for which they stand. And of course the term "the motion of molecules" is rigid; it always stands for the motion of molecules, never for any other phenomenon. So, as Bishop Butler said, "everything is what it is and not another thing." Therefore, "Heat is the motion of molecules" will be necessary, not contingent, and one only has the illusion of contingency in the way one could have the illusion of contingency in thinking that this table might have been made of ice. We might think one could imagine it, but if we try, we can see on reflection that what we are really imagining is just there being another lectern in this very position here which was in fact made of ice. The fact that we may identify this lectern by being the object we see and touch in such and such a position is something else. Now how does this relate to the problem of mind and body? It is usually held that this is a contingent identity statement just like "Heat is the motion of molecules." That cannot be. It cannot be a contingent identity statement just like "Heat is the motion of molecules" because, if I am right, "Heat is the motion of molecules" is not a contingent identity statement. Let us look at this statement. For example, "My being in pain at such and such a time is my being in such and such a brain state at such and such a time," or "Pain in general is such and such a neural (brain) state." This is held to be contingent on the following grounds. First, we can imagine the brain state existing though there is no pain at all. It is only a scientific fact that whenever we are in a certain brain state we have a pain. Second, one might imagine a creature being in pain, but not being in any specified brain state at all, maybe not having a brain at all. People even think, at least prima facie, though they may be wrong, that they can imagine totally disembodied creatures, at any rate certainly not creatures with bodies anything like our own. So it seems that we can imagine definite circumstances under which this relationship would have been false. Now, if these circumstances are circumstances, notice that we cannot deal with them simply by saying that this is just an illusion, something we can apparently imagine, but in fact cannot in the way we thought erroneously that we could imagine a situation in which heat was not the motion of molecules. Because although we can say that we pick out heat contingently by the contingent prop-
erty that it affects us in such and such a way, we cannot similarly say that we pick out pain contingently by the fact that it affects us in such and such a way. On such a picture there would be the brain state, and we pick it out by the contingent fact that it affects us as pain. Now that might be true of the brain state, but it cannot be true of the pain. The experience itself has to be this experience, and I cannot say that it is a contingent property of the pain I now have that it is a pain.17 In fact, it would seem that the terms "my pain" and "my being in such and such a brain state" are, first of all, both rigid designators. That is, whenever anything is such and such a pain, it is essentially that very object, namely, such and such a pain, and wherever anything is such and such a brain state, it is essentially that very object, namely, such and such a brain state. So both of these are rigid designators. One cannot say this pain might have been something else, some other state. These are both rigid designators. Second, the way we would think of picking them out - namely, the pain by its being an experience of a certain sort, and the brain state by its being the state of a certain material object, being of such and such molecular configuration - both of these pick out their objects essentially and not accidentally, that is, they pick them out by essential properties. Whenever the molecules are in this configuration, we do have such and such a brain state. Whenever you feel this, you do have a pain. So it seems that the identity theorist is in some trouble, for, since we have two rigid designators, the identity statement in question is necessary. Because they pick out their objects essentially, we cannot say the case where you seem to imagine the identity statement false is really an illusion like the illusion one gets in the case of heat and molecular motion, because that illusion depended on the fact that we pick out heat by a certain contingent property. So there is very little room to maneuver; perhaps none. 18 The identity theorist, who holds that pain is the brain state, also has to hold that it necessarily is the brain state. He therefore cannot concede, but has to deny, that there would have been situations under which one would have had pain but not the corresponding brain state. Now usually in arguments on the identity theory, this is very far from being denied. In fact, it is conceded from the outset by the materialist as well as by his opponent. He says, "Of course, it could have been the case that we had pains without the brain states. It is a contingent identity." But that cannot be. He has to hold that
Saul Kripke
we are under some illusion in thinking that we can imagine that there could have been pains without brain states. And the only model I can think of for what the illusion might be, or at least the model given by the analogy the materialists themselves suggest, namely, heat and molecular motion, simply does not work in this case. So the materialist is up against a very stiff challenge. He has to show that these things we think we can see to be possible are in fact not possible. He has to show that these things which we can imagine are not in fact things we can imagine. And that requires some very dif-
ferent philosophical argument from the sort which has been given in the case of heat and molecular motion. And it would have to be a deeper and subtler argument than I can fathom and subtler than has ever appeared in any materialist literature that I have read. So the conclusion of this investigation would be that the analytical tools we are using go against the identity thesis and so go against the general thesis that mental states are just physical states. 19 The next topic would be my own solution to the mind~body problem, but that I do not have.
Notes This paper was presented orally, without a written text, to the New York University lecture series on identity which makes up the volume Identity and Individuation. The lecture was taped, and the present paper represents a transcription of these tapes, edited only slightly with no attempt to change the style of the original. If the reader imagines the sentences of this paper as being delivered, extemporaneously, with proper pauses and emphases, this may facilitate his comprehension. Nevertheless, there may still be passages which are hard to follow, and the time allotted necessitated a condensed presentation of the argument. (A longer version of some of these views, still rather compressed and still representing a transcript of oral remarks, has appeared in Donald Davidson and Gilbert Harman (eds), Semantics o[Natural Language (Dordrecht: Reidel, 1972).) Occasionally, reservations, amplifications, and gratifications of my remarks had to be repressed, especially in the discussion of theoretical identification and the mind~body problem. The notes, which were added to the original, would have become even more unwieldly if this had not been done. 2 R.]. Butler (ed.), Ana~ytical Philosophy, Second Series (Oxford: Blackwell, 1965), p. 41. 3 The second occurrence of the description has small scope. 4 In Russell's theory, F(zxGx) follows from (x)Fx and (3!x) Gx, provided that the description in F(zxGx) has the entire context for its scope (in Russell's 1905 terminology, has a "primary occurrence"). Only then is F(zxGx) "about" the denotation of"zxGx." Applying this rule to (4), we get the results indicated in the text. Notice that, in the ambiguous form O(zxGx = zxHx), if one or both of the descriptions have "primary occurrences," the formula does not assert the necessity of zxGx = zxHx; if both have secondary occurrences, it does. Thus in a language without explicit scope indicators, descriptions must be construed with the smallest possible scope ~ only
then will ~ A be the negation of A, OA the necessitation of A, and the like. 5 An earlier distinction with the same purpose was, of course, the medieval one of de dicto~de re. That Russell's distinction of scope eliminates model paradoxes has been pointed out by many logicians, especially Smullyan. So as to avoid misunderstanding, let me emphasize that I am of course not asserting that Russell's notion of scope solves Quine's problem of "essentialism", what it does show, especially in conjunction with modern model-theoretic approaches to modal logic, is that quantified modal logic need not deny the truth of all instances of (x)(y)(x = y.:J. Fx :J Fy), nor of all instances of "(x)(Gx :J Ga)" (where "a" is to be replaced by a non vacuous definite description whose scope is all of "Ga"), in order to avoid making it a necessary truth that one and the same man invented bifocals and headed the original Postal Department. Russell's contextual definition of description need not be adopted in order to ensure these results; but other logical theories, Fregean or other, which take descriptions as primitive must somehow express the same logical facts. Frege showed that a simple, non-iterated context containing a definite description with small scope, which cannot be interpreted as being "about" the denotation of the description, can be interpreted as about its "sense." Some logicians have been interested in the question of the conditions under which, in an intensional context, a description with small scope is equivalent to the same one with large scope. One of the virtues of a Russellian treatment of descriptions in modal logic is that the answer (roughly that the description be a "rigid designator" in the sense of this lecture) then often follows from the other postulates for quantified modal logic: no special postulates are needed, as in Hintikka's treatment. Even if descriptions are taken as primitive, special postulation of when scope is irrelevant can often be deduced from more basic axioms.
Identity and Necessity 6 R. B. Marcus, "Modalities and intensional languages," in Boston Studies in the Philosophy ofScience, vol. I (New York: Humanities Press, 1963), pp. 71ff. See also the "Comments" by Quine and the ensuing discussion. 7 It should. See her remark in Boston Studies in the Philosophy of Science, vol. I, p. liS, in the discussion following the papers. 8 If there is no deity, and especially if the nonexistence of a deity is necessary, it is dubious that we can use "he" to refer to a deity. The use in the text must be taken to be non literal. 9 David K. Lewis, "Counterpart theory and quantified modal logic," Journal of Philosophy 65 (1968), pp. 113ff. to Some philosophers think that definite descriptions, in English, are ambiguous, that sometimes "the inventor of bifocals" rigidly designates the man who in fact invented bif()cals. I am tentatively inclined to reject this view, construed as a thesis about English (as opposed to a possible hypothetical language), but I will not argue the question here. What I do wish to note is that, contrary to some opinions, this alleged ambiguity cannot replace the Russellian notion of the scope of a description. Consider the sentence "The number of planets might have been necessarily even." This sentence plainly can be read so as to express a truth; had there been eight planets, the number of planets would have been necessarily even. Yet without scope distionctions, both a "referential" (rigid) and a nonrigid reading of the description will make the statement false. (Since the number of planets is the rigid reading amounts to the falsity that 9 might have been necessarily even.) The "rigid" reading is equivalent to the Russellian primary occurrence; the nonrigid, to innermost scope - some, following Donnellan, perhaps loosely, have called this reading the "attributive" use. The possibility of intermediate scopes is then ignored. In the present instance, the intended reading of 0 D (the number of planets is even) makes the scope of the description D (the number of planets is even), neither the largest nor the smallest possible. II This definition is the usual formulation of the notion of essential property, but an exception must be made for existence itself: on the definition given, existence would be trivially essential. We should regard existence as essential to an object only if the object necessarily exists. Perhaps there are other recherche properties, involving existence, for which the definition is similarly objectionable. (I thank Michael Siote for this observation.) 12 The two clauses of the sentence noted give equivalent definitions of the notion of essential property, since D«3x)(x = a):::J Fa) is equivalent to D(x)(~ Fx :::J x = a). The second formulation, however, has served as a powerful seducer in favor of theories of "identification across possible worlds." For it sug-
gests that we consider 'an object b in another possible world' and test whether it is identifiable with a by asking whether it lacks any of the essential properties of a. Let me therefore emphasize that, although an essential property is (trivially) a property without which an object cannot be a, it by no means follows that the essential, purely qualitative properties of a jointly form a sufficient condition for being a, nor that any purely qualitative conditions are sufficient for an object to be a. Further, even if necessary and sufficient qualitative conditions for an object to be Nixon may exist, there would still be little justification for the demand for a purely qualitative description of all counterfactual situations. We can ask whether Nixon might have been a Democrat without engaging in these subtleties. 13 I thus agree with Quine, that "Hesperus is Phosphorus" is (or can be) an empirical discovery; with Marcus, that it is necessary. Both Quine and Marcus, according to the present standpoint, err in identifying the epistemological and the metaphysical issues. 14 The two confusions alleged, especially the second, are both related to the confusion of the metaphysical question of the necessity of "Hesperus is Phosphorus" with the epistemological question of its aprioricity. For if Hesperus is identified by its position in the sky in the evening, and Phosphorus by its position in the morning, an investigator may well know, in advance of empirical research, that Hesperus is Phosphorus if and only if one and the same body occupies position x in the evening and position y in the morning. The a priori material equivalence of the two statements, however, does not imply their strict (necessary) equivalence. (The same remarks apply to the case of heat and molecular motion.) Similar remarks apply to some extent to the relationship between "Hesperus is Phosphorus" and" 'Hesperus' and 'Phosphorus' name the same thing." A confusion that also operates is, of course, the confusion between what we say of a counterfactual situation and how people in that situation would have described it; this confusion, too, is probably related to the confusion between aprioricity and necessity. 15 If someone protests, regarding the lectern, that it could after all have turned out to have been made of ice, and therefore could have been made of ice, I would reply that what he really means is that a lectern could have looked just like this one, and have been placed in the same position as this one, and yet have been made of ice. In short, I could have been in the same epistemological situation in relation to a lectern made of ice as I actually am in relation to this lectern. In the main text, I have argued that the same reply should be given to protests that Hesperus could have turned out to be other than Phosphorus, or Cicero other than Tully. Here, then, the notion of "counterpart" comes into its own. For it is not this table, but an epistemic "counterpart," which was hewn from ice; not
Saul Kripke Hesperus-Phosphorus-Venus, but two distinct counterparts thereof, in two of the roles Venus actually plays (that of Evening Star and Morning Star), which are different. Precisely because of this fact, it is not this table which could have been made of ice. Statements about the modal properties of this table never refer to counterparts. However, if someone confuses the epistemological and the metaphysical problems, he will be well on the way to the counterpart theory Lewis and others have advocated. 16 Isn't the situation I just described also counterfactual? At least it may well be, if such Martians never in fact invade. Strictly speaking, the distinction I wish to draw compares how we would speak in a (possibly counterfactual) situation, if it obtained, and how we do speak of a counterfactual situation, knowing that it does not obtain - i.e., the distinction between the language we would have used in a situation and the language we do use to describe it. (Consider the description: "Suppose we all spoke German." This description is in English.) The former case can be made vivid by imagining the counterfactual situation to be actual. 17 The most popular identity theories advocated today explicitly fail to satisfy this simple requirement. For these theories usually hold that a mental state is a brain state, and that what makes the brain state into a mental state is its "causal role," the fact that it tends to produce certain behavior (as intentions produce actions, or pain, pain behavior) and to be produced by certain stimuli (e.g., pain, by pinpricks). If the relations between the brain state and its causes and effects are regarded as contingent, then being suchand-such-a-mental-state is a contingent property of the brain state. Let X be a pain. The causal-role identity theorist holds (I) that X is a brain state, (2) that the fact that X is a pain is to be analyzed (roughly) as the fact that X is produced by certain stimuli and produces certain behavior. The fact mentioned in (2) is, of course, regarded as contingent; the brain state X might well exist and not tend to produce the appropriate behavior in the absence of other conditions. Thus (I) and (2) assert that a certain pain X might have existed, yet not have been a pain. This seems to me self-evidently absurd. Imagine any pain: is it possible that it itselfcould have existed, yet not have been a pain? If X = Y, then X and Y share all properties, including modal properties. If X is a pain and Y the corresponding brain state, then being a pain is an essential property of X, and being a brain state is an essential property of Y. If the correspondence relation is, in fact, identity, then it must be necessary of Y that it corresponds to a pain, and necessary of X that it correspond to a brain state, indeed to this particular brain state, Y. Both assertions seem false; it seems clearly possible that X should have existed without the corresponding brain state; or that the brain state
should have existed without being felt as pain. Identity theorists cannot, contrary to their almost universal present practice, accept these intuitions; they must deny them, and explain them away. This is none too easy a thing to do. 18 A brief restatement of the argument may be helpful here. If "pain" and "C-fiber stimulation" are rigid designators of phenomena, one who identifies them must regard the identity as necessary. How can this necessity be reconciled with the apparent fact that Cfiber stimulation might have turned out not to be correlated with pain at all? We might try to reply by analogy to the case of heat and molecular motion; the latter identity, too, is necessary, yet someone may believe that, before scientific investigation showed otherwise, molecular motion might have turned out not to be heat. The reply is, of course, that what really is possible is that people (or some rational or sentient beings) could have been in the same epistemic situation as we actually are, and identify a phenomenon in the same way we identify heat, namely, by feeling it by the sensation we call "the sensation of heat," without the phenomenon being molecular motion. Further, the beings might not have been sensitive to molecular motion (i.e., to heat) by any neural mechanism whatsoever. It is impossible to explain the apparent possibility of C-fiber stimulations not having been pain in the same way. Here, too, we would have to suppose that we could have been in the same epistemological situation, and identify something in the same way we identify pain, without its corresponding to C-fiber stimulation. But the way we identify pain is by feeling it, and if a C-fiber stimulation could have occurred without our feeling any pain, then the C-fiber stimulation would have occurred without there being any pain, contrary to the necessity of the identity. The trouble is that although "heat" is a rigid designator, heat is picked out by the contingent property of its being felt in a certain way; pain, on the other hand, is picked out by an essential (indeed necessary and sufficient) property. For a sensation to be felt as pain is for it to be pain. 19 All arguments against the identity theory which rely on the necessity of identity, or on the notion of essential property, are, of course, inspired by Descartes's argument for his dualism. The earlier arguments which superficially were rebutted by the analogies of heat and molecular motion, and the bifocals inventor who was also Postmaster General, had such an inspiration: and so does my argument here. R. Albritton and M. Slote have informed me that they independently have attempted to give essentialist arguments against the identity theory, and probably others have done so as well. The simplest Cartesian argument can perhaps be restated as follows: Let "A" be a name (rigid designator) of Descartes's body. Then Descartes argues that since he could exist even if A did not,
H Goliath)
is true and
(12)
D(E Lumpl
---->
H Lumpl)
is false, so on the Carnapian account I am now giving, the open sentence D(Ex ----> Hx) is true of the Goliath-concept and false of the Lumplconcept. Indeed, just as, on Carnap's account, variables in modal contexts range over individual concepts, so on the account in section III, proper names in modal contexts can be construed as denoting individual concepts. Proper names work, in other words, roughly as Frege claims. Let the name "Goliath" in (11), for instance, denote the Goliath-concept, and suppose predicates shift in modal contexts as Carnap suggests. Then (11) attributes to the Goliath-concept the property
D(E_---->H_), that in every possible world W, if it assigns to Wan existing individual, then it assigns to Wan individual that is humanoid. The Goliath-concept has that property, and so (11) on this construal is true. The Lumpl-concept does not have that property, and so (12) on this construal is false. That is as it should be on the account in section III. Modal properties can be construed as attributing properties and relations to individual concepts, much as Frege claims.
VI What happens to identity on this account? Identity of individual concepts x andy is not now expressed as "x = y"; that, in modal contexts, means just that x and y are concepts of the same individual. The way to say that x and yare the same individual concept is
o [(Ex V Ey) ----> x = y]. I shall abbreviate this "x ~y". It could now be objected that the thesis of contingent identity has collapsed. Identity in the system here, it seems, is given not by "=," but by " ~ " and the relation " ~ " is never contingent: if it holds between two individual concepts, then it holds between them in every possible world. No genuine relation of identity, then, is contingent; the illusion that there are contingent identities came
Allan Gibbard
from using the identity sign "=" to mean something other than true identity. To this objection the following answer can be given. "=" indeed is the identity sign for individuals in the system, and if! am right that a piece of clay is an individual in the Carnapian sense, then "=" is the identity sign for pieces of clay. For consider: in nonmodal contexts, I stipulated, the variables range over individuals. Now "=" in such contexts holds only for identical individuals; it is the relation a piece of clay, for instance, bears to itself and only to itself. Moreover, applied to individuals, "=" satisfies Leibniz' Law: individuals related by it have the same properties in the strict sense, and stand in the same relations in the strict sense. The contexts where "=" is not an identity sign are modal contexts, but there the variables range not over individuals, but over individual concepts. "=" in the system, then, is the identity sign for individuals, and according to the system, "=" can hold contingently for individuals: A sentence of the form "a = b," then, asserts the identity of two individuals, and it may be contingent. Quine would object to this answer. It depends on a "curious double interpretation of variables": outside modal contexts they are interpreted as ranging over individuals; inside modal contexts, over individual concepts. "This complicating device," Qp.ine says, "has no essential bearing, and is better put aside. ,,22 "Since the duality in question is a peculiarity of a special metalinguistic idiom and not of the object-language itself, there is nothing to prevent our examining the object-language from the old point of view and asking what the values of its variables are in the old-fashioned non-dual sense of the term.,,23 The values in the old-fashioned sense, Quine says, are individual concepts, for "(\Ix) ~" is a logical truth, and on "the old point of view," that means that entities between which the relation ~ fails are distinct entities. In all contexts, then, the values of the variables are individual concepts, and identity is given by" ~." All this can be accepted, however, and the point I have made stands: "=" in the system expresses identity of individuals. "a = b," on Qp.ine's interpretation, says that a and b are concepts of the same individual. That amounts to saying that the individual of which a is the concept is identical with the individual of which b is the concept. Even on Quine's interpretation, then, "a = b" in effect asserts the identity of individuals, and does so in the most direct way the system allows.
On either Quine's interpretation or Carnap's, then, to assert (13)
Goliath = Lumpl
is in effect to assert the identity of an individual. For all Carnap's system says, (13) may be true, though Goliath might not have been identical with Lumpl. If (13) is true but contingent, then it seems reasonable to call it a contingent identity. The claim that there are contingent identities in a natural sense, then, is consistent with Carnap's modal system on either Carnap's or Quine's interpretation of values of variables.
VII One further Qp.inean objection needs to be answered. I am embracing "essentialism" for individual concepts. Essentialism, if I understand Quine, is the view that necessity properly applies "to the fulfillment of conditions by objects ... apart from special ways of specifying them. ,,24 Now what I have said, as I shall explain, requires me to reject essentialism for concrete things but accept it for individual concepts. That discriminatory treatment needs to be justified. First, a more precise definition of essentialism: Essentialism for a class of entities U, I shall say, is the claim that for any entity e in U and any condition rp which e fulfills, the question of whether e necessarily fulfills rp has a definite answer apart from the way e is specified. 25 Now according to what I have said, essentialism for the class of concrete things is false. In the clay statue example, I said, the same concrete thing fulfills the condition
necessarily under the specification "Goliath" and only contingently under the specification "Lump)"; whether that thing, apart from any special designation, necessarily fulfills that condition is a meaningless question. Essentialism for the class of individual concepts, on the other hand, must be true ifCarnap's system is to work. That is so because Carnap's system allows quantification into modal contexts without restriction. For let rp be a condition and e an individual concept which fulfills rp. Then Drpx is well formed and the variable "x" ranges over individual con-
Contingent Identity
cepts, so that e is in the range of "x." Thus e either definitely satisfies the formula 04>x or definitely fails to satisfy it. The question of whether e necessarily fulfills 4> must have a definite answer even apart from the way e is specified. Thus essentialism holds for individual concepts. Why this discriminatory treatment? Why accept essentialism for individual concepts and reject it for individuals? The point of doing so is this: my arguments against essentialism for concrete things rested not on general logical considerations, but on considerations that apply specifically to concrete things. I argued that it makes no sense to talk of a concrete thing as fulfilling a condition 4> in every possible world - as fulfilling 4> necessarily, in other words - apart from its designation. Essentialism, then, is false for concrete things because apart from a special designation, it is meaningless to talk of the same concrete thing in different possible worlds. For this last, I had two arguments, both of which apply specifically to concrete things. First I considered the clay statue example, gave reasons for saying that Goliath is identical to Lumpl, and showed that the same statue in a different situation would not be the same piece of clay. Second, in section III, I gave a theory of identity of concrete things across certain possible worlds, according to which such identity made sense only with respect to a kind. These arguments applied only to concrete things. 26 It makes good sense, on the other hand, to speak of the same individual concept in different possible worlds. An individual concept is just a function which assigns to each possible world in a set an individual in that world. There is no problem of what that function would be in a possible world different from the actual one. Whereas, then, there is no good reason for rejecting essentialism indiscriminately, there are strong grounds for rejecting essentialism for concrete things.
VIII An objection broached in section V remains to be tackled. There is, according to the system here, no such thing as de re modality for concrete things: in a formula of the form OFx, the variable ranges over individual concepts rather than concrete things. Now without de re modality for concrete things, the objection goes, our tongues will be tied: we will be left unable to say things that need to be said, both for scientific and for daily purposes.
In fact, though, the system here ties our tongues very little. It allows concrete things to have modal properties of a kind, and those permissible modal properties will do any job that de re modalities could reasonably be asked to do. To see how such legitimate modal properties can be constructed, return to the statue example. According to the theory given here, the concrete thing Goliath or Lumpl has neither the property of being essentially humanoid nor the property of being possibly nonhumanoid. There is a modal property, though, which it does have: it is essentially humanoid qua statue. That can be expressed in the Carnapian system I have given. Let 8 be the predicate "is a statue-rigid individual concept." 8 is intensional, then, in the sense that it applies to individual concepts, so that variables in its scope take individual concepts as values, just as they do in the scope of a modal operator. The sentence x is essentially humanoid qua statue,
then, means this:
(14)
(3y)[y
=
x &8y & O(Ey
-->
Hy)].27
Here the variable y is free within the scope of a modal operator, and hence ranges over individual concepts; but x occurs only outside the scope of modal operators, and hence ranges over individuals. In "y = x," then, the predicate "=" makes a compensating shift of the kind shown in section V, but only in its left argument. Thus "y = x" here means that y is a concept of an individual identical to x - in other words, y is a concept of x. (14), then, says the following: "There is an individual concept y which is a statue-concept, and is a concept of something humanoid in any possible world in which it is a concept of anything." That gives a property which applies to concrete things: only the variable x is free in (14), and since it occurs only outside the scope of modal operators, it ranges over individuals. (14), then, gives a property of the concrete thing Lumpl, a property which we might call "being essentially humanoid qua statue." Concrete things, then, in the system given here, have no de re modal properties - no properties of the form OF. They do, however, have modal properties of a more devious kind: modal properties qua a sortal. Such properties should serve any purpose for which concrete things really need modal properties.
Allan Gibbard (16)
IX Dispositional properties raise problems of much the same kind as do modal properties. At least one promising account of dispositions is incompatible with the system given here. Here is the account. A disposition like solubility is a property which applies to concrete things, and it can be expressed as a counterfactual conditional: "x is soluble" means "If x were placed in water, then x would dissolve." This counterfactual conditional in turn means something like this: "In the possible world which is, of all those worlds in which x is in water, most like the actual world, x dissolves."z8 Now this account is incompatible with the system I have given, because it requires identity of concrete things across possible worlds. For without such cross-world identity, it makes no sense to talk of "the possible world which is, of all those worlds in which x is in water, most like the actual world." For such talk makes sense only if there is a definite set of worlds in which x is in water, and there is such a definite set only if for each possible world, either x is some definite entity in that world - so that it makes definite sense to say that x is in water in that world - or x definitely does not exist in that world. The account of dispositions I have sketched, then, requires identity of concrete things across possible worlds, which on the theory in this paper is meaningless. The point is perhaps most clear in the statue example. It makes no sense to say of the concrete thing Goliath, or Lumpl, that if I squeezed it, it would cease to exist. If I squeezed the statue Goliath, Goliath would cease to exist, but if I squeezed the piece of clay Lumpl, Lumpl would go on existing in a different shape. Take, then, the property "If I squeezed x, then x would cease to exist," which I shall write
(15)
I squeeze x 0-> x ceases to exist.
That is not a property which the single concrete thing, Goliath or Lumpl, either has or straightforwardly lacks. Counterfactual properties, then, have much the same status as modal properties. A concrete thinga piece of salt, for instance - cannot have the counterfactual property
x is in water 0-> x dissolves, or as I shall write it,
Wx
0-> Dx.
Put more precisely, the point is this: a concrete thing can have no such property if, first, the account of counterfactuals which I have given is correct and, second, identity of concrete things across possible worlds makes no sense. Call a property of the form given in (15) and (16) a straightforward counterJactual property; then on the theories I have given, concrete things can have no straightforward counterfactual properties. Individual concepts, in contrast, can perfectly well have straightforward counterfactual properties, since they raise no problems of identity across possible worlds. Indeed we can treat the connective "0->" as inducing the same shifts as do modal operators: making the variables in its scope range over individual concepts, and shifting the predicates appropriately. On that interpretation, (15) is true of the Goliath-concept but false of the Lumplconcept; (15) says, "In the possible world which, of all those worlds in which I squeeze the thing picked out by concept x, is most like the actual world, the thing picked out by x ceases to exist." That holds of the Goliath-concept but not of the Lumpl-concept. Likewise on this interpretation, (16) is true not of a piece of salt, but of a piece-of-salt individual concept. (16) now says the following: "In the possible world which is, of all those worlds in which the thing picked out by x is in water, most like the actual world, the thing picked out by x dissolves." So far the situation is grave. The moral seems to be this: concrete things have no dispositional properties, but individual concepts do. Watersolubility, or something like it, may be a property of a piece-of-salt individual concept, but it cannot be a property of the concrete thing, that piece of salt. That is a sad way to leave the matter. On close examination, many seeming properties look covertly dispositional - mass and electric charge are prime examples. Strip concrete things of their dispositional properties, and they may have few properties left. Fortunately, though, individuals do turn out to have dispositional properties of a kind. The device used for modal properties in the last section works here too. A concrete thing like a piece of salt cannot, it is true, have the straightforward counterfactual property Wx 0-> Dx. Only an individual concept could have that property. A piece of salt does, though, have the more devious counterfactual property given by "Qua piece of salt, if x were in water then x would dissolve," which I shall write
Contingent Identity
(17)
(x qua piece)[Wx D-+ Dx].
This expands as follows: let .0/ mean "is a piecerigid individual concept"; then (17) means (18)
(:ly)[y
= x
&.9'y(Wy D-+ Dy)].
As in the corresponding formula (14) for modal properties, "x" here is free of modal entanglements, and so it ranges over concrete things. (18) seems a good way to interpret water solubility as a property of pieces of salt. Concrete things, then, can have dispositional properties. The dispositional property is watersoluble is not the straightforward counterfactual property given by (16), but the more devious counterfactual property given by (18). A system with contingent identity can still allow dispositions to be genuine properties of concrete things.
x From the claim that Goliath = Lumpl, I think I have shown, there emerges a coherent system which stands up to objections. Why accept this system? In section II, I gave one main reason: the system lets concrete things be made up in a simple way from entities that appear in fundamental physics. It thus gives us machinery for putting into one coherent system both our beliefs about the fundamental constitution of the world and our everyday picture of concrete things. Another important reason for accepting the system is one of economy. I think I have shown how to get along without de re modality for concrete things and still say what needs to be said about them. That may be especially helpful when we deal with causal necessity; indeed, the advantages of doing without de re causal necessity go far beyond mere economy. What I have said in this paper about plain necessity applies equally well to causal necessity, and the notion of causal necessity seems especially unobjectionable - even Quine thinks it may be legitimate. 29 Causally necessary truths are what scientists are looking for when they look for fundamental scientific laws, and it surely makes sense to look for fundamental scientific laws. Now we might expect fundamental scientific laws to take the form Dc.p, "It is causally necessary that .p," where .p is extensional - contains no modal operators. If so, then scientific laws contain de dicto causal necessity, but no de re necessity. To get significant de re
causal necessities, we would need to make metaphysical assumptions with no grounding in scientific law. If we can get along without de re physical necessity, that will keep puzzling metaphysical questions about essential properties out of physics. The system here shows how to do that. None of the reasons I have given in favor of the system here are conclusive. The system has to be judged as a whole: it is coherent and withstands objections; the remaining question is whether it is superior to its rivals. What, then, are the alternatives? Kripke gives an alternative formal semantics/o but no systematic directions for applying it. To use Kripke's semantics, one needs extensive intuitions that certain properties are essential and others accidental. Kripke makes no attempt to say how concrete things might appear in a theory of fundamental physics; whether such an account can be given in Kripke's system remains to be seen. One other alternative to the theory in this paper is systematic: statues and pieces of clay can be taken, not to be "individuals" in the Carnapian sense of the term which I have been using, but to be Carnapian "individual concepts." They may be regarded, that is, as functions from possible worlds, whose values are Carnapian individuals. 3 ! On such a view, a Carnapian individual would be regarded as a sort of "proto-individual" from which concrete things are constructed. Such a view has its advantages: it allows standard quantification theory, with no Carnapian shift of the range of variables in modal contexts. Indeed, as Q!ine points out, a Carnapian semantics can be interpreted so that variables always range over individual concepts. 32 One reason for preferring the Carnapian system is this. I expect that the variables used in expressing fundamental laws can most simply be interpreted as ranging over Carnapian individuals. If so, then I would be reluctant to regard those Carnapian individuals as mere proto-individuals, with genuine individuals as functions which take these protoindividuals as values at possible worlds. Fundamental physics, I would like to say, deals with genuine individuals. If the system I have given is accepted, the ramifications are wide. Take just one example: the question of whether a person is identical with his body. If there is no consciousness after death, then, it would seem, a person ceases to exist when he dies. A person's body normally goes on existing after he dies. Ordinarily, then, a person is not
Allan Gibbard
identical with his body. In some cases, however, a person's body is destroyed when he dies. In such cases, according to the system in this paper, there is no purely logical reason against saying the following: the person in this case is identical with his body, but had he died a normal death, he would have been distinct from his body. If there are reasons against such a view, they must be nonlogical reasons. Whether or not the system I have advocated is the best one, I have at least done the following. First, I have shown that there is a problem with identity across possible worlds, even in the simple case of possible worlds which branch after the entity in question begins to exist. In such cases, I
have shown, certain assumptions, not easily refuted, lead to contingent identity. Second, I have given a theory of proper names which fits much of what Kripke says about proper names when he considers examples, and which, in rare cases, allows contingent identity. Finally, I have shown how, while accepting contingent identity and rejecting de re modality for concrete things, we can still allow concrete things to have modal and dispositional properties. The system I advocate is worked out in more detail in the appendix. 33 In that system, I think, concrete things and possible worlds lose some of their mystery: they arise naturally from a systematic picture of the physical world.
Notes I am grateful for the comments and criticisms of many people. I was helped in the early stages of revision by discussion at the University of Pittsburgh philosophy colloquium, by the written comments of Richard Gale and Paul Teller, and by discussion with Allen Hazen, Robert Kraut, and Storrs McCall. I am especially grateful to Anil Gupta for his extensive help, both in the early and the late stages of revision.
2
3 4
6 7 8 9
Saul Kripke, "Identity and necessity," this volume, ch. 7; idem, "Naming and necessity," in D. Davidson and G. Harman (eds), Semantics of Natural Language (Dordrecht: Reidel, 1972). Gottlob Frege, "On sense and reference," trans. M. Black, in P. Geach and M. Black, Translations from the Philosophical Writings ofGottlob Frege (Oxford: Blackwell, 1966), pp. 55-78, at p. 57; orig. German pub. 1892. This volume, pp. 74-5; Kripke, "Naming and necessity," pp. 260-4. Bertrand Russell, "On denoting," in Robert Marsh (ed.), Logic and Knowledge (New York: Macmillan, 1956), pp. 41-56; orig. pub. 1905. Kripke, "Naming and necessity," pp. 254-60, 284308. W. V. O. Quine, "Identity, ostension, and hypostasis," this volume, ch. 22, sect. I. This fits the view put forth in ibid. Kripke, "Naming and necessity," pp. 269-70. David Lewis, "Counterparts of persons and their bodies," Journal of Philosophy 68 (1971), pp. 203-11, gives a theory very much like this. There are, according to Lewis, a diversity of counterpart relations which hold between entities in different possible worlds - the "personal" counterpart relation and the "bodily" counterpart relation are two (p. 208). The counterpart relation appropriate to a given modal
10
11 12 13 14 15 16
17
context may be selected by a term, such as "I" or "my body," or it may be selected by a phrase, "regarded as a ~," which works like one of my "qua" phrases. In these respects, then, my theory fits Lewis's. In other respects, it differs. My relation of being an F-counterpart is an equivalence relation, and it holds between any two entities in different worlds which are both F's and which share a common past. Lewis's counterpart relations "are a matter of overall resemblance in a variety of respects" (p. 208), and are not equivalence relations (p. 209). Peter Geach Reference and Generality (Ithaca, NY: Cornell University Press, 1962), sect. 34, contends that a proper name conveys a "nominal essence" "requirements as to identity" that can be expressed by a common noun. The name "Thames," for instance, conveys the nominal essence expressed by the common noun "river." In this respect, my theory follows Geach's. Geach, however, (sect. 31), thinks that even in the actual world, identity makes no sense except with respect to a general term. According to the theory in this paper, non-relative identity makes sense in talk of anyone possible world; it is only cross-world identity that must be made relative to a sortal. Kripke, "Naming and necessity," pp. 298-9. This volume, p. 74. Kripke, "Naming and necessity," p. 268. This volume, p. 74. Kripke, "Naming and necessity," pp. 271-2. Cf. W. V. O. Quine, "Reference and modality," in From a Logical Point of View, 2nd edn (New York: Harper & Row, 1961), pp. 139-59, sect. 2. See esp. Rudolf Carnap, Meaning and Necessity (Chicago: University of Chicago Press, 1947), sect. 41. I shall not follow Carnap in detail, nor, for the most part, shall I try to say in what precise ways I follow him and in what ways I deviate from what he says.
Contingent Identity 18 Aldo Bressan, A General Interpreted Modal Calculus (New Haven, Conn.: Yale University Press, 1972). 19 Frege, "On sense and reference," p. 59. 20 The original paper included an appendix, omitted here. 21 The talk of "shifts" is not Carnap's; it is part of my own informal reading of Carnap's semantics. Carnap does think "that individual variables in modal sentences ... must be interpreted as referring, not to individuals, but to individual concepts" (Meaning and Necessity, p. 180). He does not, however, allow variables to shift their ranges of values within a single language. Rather, he constructs two languages, a nonmodal language S) in which variables range over individuals and a modal language S2 in which variables range over individual concepts. Any sentence of S) is a sentence of S2 and is its own translation into S2 (see ibid., pp. 200-2). The semantics I give in the Appendix (not included in this volume) is roughly that ofCarnap's S2 (see ibid., pp. 183-4). In informal discussion in the body of this paper, though, I take a variable to range over individuals whenever such an interpretation is possible. Carnap does not talk of predicates shifting in the way I describe, but once variables are taken to range over individual concepts, such a reinterpretation of predicates allows a straightforward reading of Carnap's semantics. Quine discussed this point in his letter to Carnap (Meaning and Necessity, p. 197). 22 Quine, "Reference and modality," p. 153. 23 Letter in Carnap, Meaning and Necessity, p. 196. 24 Quine, "Reference and modality," p. 151.
25 For other characterizations of essentialism, see Terence Parsons, "Essentialism and quantified modal logic," Philosophical Review 78 (1969), pp. 35-52, sect. 2. 26 Quine objects to essentialism even for abstract entities. "Essentialism," he writes, "is abruptly at variance with the idea, favored by Carnap, Lewis, and others, of explaining necessity by analyticity" ("Reference and modality," p. 155). That, however, cannot be true: Carnap does explain his system in terms of analyticity, and his system involves essentialism, as I have explained. Carnap's system is thus a counterexample to Q]Jine's claim; it shows that one can consistently both accept essentialism for individual concepts and explain necessity by analyticity. 27 Anil Gupta has shown me a formula similar to this one, which he attributes to Nuel Belnap. 28 See Robert Stalnaker, "A theory of conditionals," in Studies in Logical Theory, American Philosophical Quarterly Monograph Series, no. 2 (1968), and Stalnaker and Richmond Thomason, "A semantic analysis of conditional logic," Theoria 36 (1970), pp. 23-42. For a somewhat different theory which raises similar problems, see David K. Lewis, Counterfactuals (Oxford: Blackwell, 1973). 29 See Quine, "Reference and modality," pp. 158-9. 30 Saul Kripke, "Semantical considerations on modal logic," Acta philosophica Fennica 16 (1963), pp. 83-94. 31 See Richmond Thomason and Robert Stalnaker, "Modality and reference," Nous 2 (1968) pp. 359-72. 32 Letter in Carnap, Meaning and Necessity, p. 196. 33 See n. 20 above.
10
Stephen Yablo
Can things be identical as a matter offact without being necessarily identical? Until recently it seemed they could, but now "the dark doctrine of a relation of 'contingent identity' ,,1 has fallen into disrepute. In fact, the doctrine is worse than disreputable. By most current reckonings, it is refutable. That is, philosophers have discovered that things can never be contingently identical. Appearances to the contrary, once thought plentiful and decisive, are blamed on the befuddling influence of a powerful alliance of philosophical errors. How has this come about? Most of the credit goes to a simple argument (original with Ruth Marcus, but revived by Saul Kripke) purporting to show that things can never be only contingently identical. Suppose that a and (3 are identical. Then they share all their properties. Since one of (3's properties is that necessarily it is identical with (3, this must be one of a's properties too. So necessarily a is identical with (3, and it follows that a and (3 cannot have been only contingently identical. 2
1
A Paradox of Essentialism
Despite the argument's simplicity and apparent cogency, somehow, as Kripke observes, "its conclusion ... has often been regarded as highly paradoxical.,,3 No doubt there are a number of bad reasons for this (Kripke himself has exposed sevOriginally published in Journal of Philosophy 84 (1987), pp. 293-314. Copyright~) byJournal of Philosophy, Inc. Reprinted by permission of Columbia University.
eral), but there is also a good one: essentialism without some form of contingent identity is an untenable doctrine, because essentialism has a shortcoming that only some form of contingent identity can rectify. The purpose of this paper is to explain, first, why contingent identity is required by essentialism and, second, how contingent identity is permitted by essentialism. Essentialism's problem is simple. Identicals are indiscernible, and so discernibles are distinct. Thus, if a has a property necessarily which (3 has only accidentally, then a is distinct from (3. In the usual example, there is a bust of Aristotle, and it is formed of a certain hunk of wax. (Assume for the sake of argument that the hunk of wax composes the bust throughout their common duration, so that temporal differences are not in question.) If the bust of Aristotle is necessari(y a bust of Aristotle and if the hunk of wax is only accidentalzy a bust of Aristotle, then the bust and the hunk of wax are not the same thing. Or suppose that Jones drives home at high speed. Assuming that her speeding home is something essential~y done at high speed, whereas her driving home only happens to be done at high speed, her speeding home and her driving home are distinct. So far, so good, maybe; but it would be incredible to call the bust and the wax, or the driving home and the speeding home, distinct, and leave the matter there. In the first place, that would be to leave relations between the bust and the hunk of wax on a par with either's relations to the common run of other things, for example, the Treaty of Versailles. Secondly, so far it seems an extraordi-
Identity, Essence, and Indiscernibility
narily baffling metaphysical coincidence that bust and wax, though entirely distinct, nevertheless manage to be exactly alike in almost every ordinary respect: size, weight, color, shape, location, smell, taste, and so on indefinitely. If distinct statues (say) were as similar as this, we would be shocked and amazed, not to say incredulous. How is such a coincidence possible? And, thirdly, if the bust and the wax are distinct (pure and simple), how is it that the number of middle-sized objects on the marble base is not (purely and simply) 2 (or more)? Ultimately, though, none of these arguments is really needed: that the bust and the wax are in some sense the same thing is perfectly obvious. Thus, if essentialism is to be at all plausible, non identity had better be compatible with intimate identity-like connections. But these connections threaten to be inexplicable on essentialist principles, and essentialists have so far done nothing to address the threat. 4 Not quite nothing, actually; for essentialists have tried to understand certain (special) of these connections in a number of (special) ways. Thus, it has been proposed that the hunk of wax composes the bust; that the driving home generates the speeding home; that a neural event subserves the corresponding pain; that a computer's structural state instantiates its computational state; that humankind comprises person kind; and that a society is nothing liver and above its members. Now all these are important relations, and each is importantly different from the others. But it is impossible to ignore the fact that they seem to reflect something quite general, something not adequately illuminated by the enumeration of its special cases, namely, the phenomenon of things' being distinct by nature but the same in the circumstances. And what is that if not the - arguedly impossible - phenomenon of things" being contingently identical but not necessarily so? The point is that, if essentialism is true, then many things that are obviously in slime sense the same will emerge as strictly distinct; so essentialism must at least provide for the possibility of intimate identity-like connections between distinct things; and such connections seem to be ways of being contingently identical. Essentialism, if it is to be plausible, has to be tempered by some variety of contingent identity. Hence, essentialism is confronted with a kind of paradox: to be believable, it needs contingent identity; yet its principles appear to entail that contingent identity is not possible. To resolve the
paradox, we have to ask: What is the "nature" of a particular thing?
2
Essence
Begin with a particular thing a. How should a be characterized? That is, what style of characterization would best bring out "what a is"? Presumably a characterization of any sort will be via certain of a's properties. But which ones? Why not begin with the set of all a's properties whatsoever, or what may be called the complete profile of a? Since a's properties include, among others, that of being identical with a, there can be no question about the sufficiency of characterization by complete profile. But there may be doubt about its philosophical interest. For the properties of a will generally be of two kinds: those which a had to have and those which it merely happens to have. And, intuitively, the properties a merely happens to have reveal nothing of what a is, as contrasted with what it happens to be like. As Antoine Arnauld explains in a letter to Leibniz, ... it seems to me that I must consider as contained in the individual concept of myself only that which is such that I should no longer be me if it were not in me: and that all that is to the contrary such that it could be or not be in me without my ceasing to be me, cannot be considered as being contained in my individual concept. s (Adding: "That is my idea, which I think conforms to everything which has ever been believed by all the philosophers in the world"!) If a's nonnecessary properties reveal nothing about what a is, nothing will be lost if they are struck from its characterization. Dropping a's non necessary properties from its complete profile yields the set of all properties that a possesses essentially, or what can be called the complete essence of 00. 6 Since a is essentially identical with a, the property of so being will be included in a's complete essence; so the sufficiency of the characterization is again beyond doubt. Nor can there be much question that complete essences do better than complete profiles at showing what particulars are by nature. But worries about philosophical interest remain. In the first place, the essence of an entity ought, one feels, to be an assortment of properties in virtue
Stephen Yablo of which it is the entity in question. But this
requirement is trivialized by the inclusion, in essences, of identity properties, like that of being identical with California. A thing does not get to be identical with California by having the property, alike, by having certain other properties. And it is these other properties that really belong in a thing's characterization. Another way of putting what is probably the same point is that identity properties and their ilk are not "ground floor," but dependent or supervenient. As a kind of joke, someone I know explains the difference between his two twin collies like this: "It's simple: this one's Lassie, and that one's Scottie." What makes this a joke is that that cannot be all there is to it; and the reason is that identity properties are possessed not simpliciter, but dependently on other properties. It is only these latter properties that ought, really, to be employed in a thing's characterization. Secondly, the essence of a thing is supposed to be a measure of what is required for it to be that thing. But, intuitively, requirements can be more or less. If the requirements for being (3 are stricter than the requirements for being Cl:, then (3 ought to have a "bigger" essence than Cl:. To be the Shroud of Turin, for instance, a thing has to have everything it takes to be the associated piece of cloth, and it has to have enshrouded Jesus Christ (this is assuming that the Cloth of Turin did, in fact, enshroud Jesus Christ). Thus, more is essential to the Shroud of Turin than to the piece of cloth, and the Shroud of Turin ought accordingly to have the bigger essence. So, if essences are to set out the requirements for being their possessors, it should be possible for one thing's essence to include another's.7 What is perhaps surprising, however, is that this natural perspective on things will not survive the introduction of identity properties and their ilk into individual essences. Think of the piece of cloth that makes up the Shroud of Turin (call it "the Cloth of Turin"): if the property of being identical with the Cloth of Turin is in the Cloth of Turin's essence, then, since that property is certainly not in the Shroud of Turin's essence, the inclusion is lost. Equivalently, it ought to be possible to start with the essence of the Cloth of Turin, add the property of having served as the burial shroud of Jesus Christ (along perhaps with others this entails), and wind up with the essence of the Shroud of Turin. But, if the property of being identical to the Cloth of Turin is allowed into the Cloth of Turin's essence, then adding the property of having served as Jesus's burial shroud produces a
sort of contradiction; for, obviously, nothing is both identical to the Cloth of Turin and necessarily possessed of a property - having served as Jesus's burial shroud - which the Cloth of Turin possesses only contingently. And the argument is perfectly general: if identity properties (or others like them) are allowed into things' essences, then distinct things' essences will always be incomparable. s Implicit in the foregoing is a distinction between two types of property. On the one hand, there are properties that can only 'build up' the essences in which they figure. Since to include such properties in an essence is not (except trivially) to keep any other property out, they will be called cumulative. On the other hand, there are properties that exercise an inhibiting effect on the essences to which they belong. To include this sort of property in an essence is always to block the entry of certain of its colleagues. Properties like these - identity properties, kind properties, and others - are restrictive. If restrictive properties are barred from essences, that will ensure that essences are comparable, and so preserve the intuition that each essence specifies what it takes to be the thing that has it. Essences constrained to include only cumulative properties will have two advantages. First, they will determine their possessors' inessential properties negatively, not by what they include but by what they leave out; and, as a result, things' essences will be amenable to expansion into the larger essences of things it is "more difficult to be," thus preserving the intuition that a thing's essence specifies what it takes to be that thing. And, second, things will be the things they are in virtue of having the essences they have. To put it approximately but vividly, they will be what they are because of what they are like (see Prop. 4).9 Our tactic will be to look first for properties suited to inclusion in cumulative essences and then to show that, under reasonable further assumptions, identity supervenes on cumulative essence.
3
Modeling Essence
To find a set of properties suitable for the construction of cumulative essences, one needs to know what "properties" are; especially because a totally unrestricted notion of property is incoherent, as Richard's and Grelling's paradoxes show. lO So it makes sense to look for a sharper formulation of the notion of property before pushing ahead with the search for cumulative essence. Such a
Identity, Essence, and Indiscernibility
formulation is provided by the apparatus of possible worlds. Let 2 be an ordinary first-order language with identity, and let 2(0) be 2 supplemented with the sentential necessity operator "0." To a first approximation, a model of 2(0) is just a set "fII of models W of 2 (to be thought of as possible worlds). But there is a qualification. Traditionally, a model's domain is simultaneously the set of things that can be talked about and the set of things that exist, i.e., the domain of discourse and the ontological domain. But, since one can talk about things that do not exist, W's domain of discourse should be allowed to contain things not in its ontological domain; and since there are not, mystical considerations to the side, things about which one cannot talk, W's ontological domain should be a subset of its domain of discourse. What this means formally is that with each model Win 1{/. is associated a subset fiJ( W) of its domain (intuitively, the set of things existing in J1I). Let W thus supplemented be known as afree model of 2. For simplicity's sake, every member of"fll will have the same domain fiJ, and fiJ will be the union of the fiJ( W)'s. And now a model of 2 ( 0) can be defined as a set 1fl" of free models of !t', such that the domain of discourse of each is the union of all their ontological domains. 11 Tempting though it is to define a property as any function P from worlds W to subsets P( W) of fiJ, there is reason not to. For when will a have P necessarily: when it has P in every world, or when it has it in every world in which it exists? Not the former, because then everything necessarily exists. 12 Nor the latter, first, because it permits a thing to possess only accidentally a property it must perish to lose and, second, because it upsets the principle that essence varies inversely with existence; i.e., the fewer the worlds a thing exists in, the more properties it has essentially. What this in fact points up is a difference between two kinds of characteristic: being human in every world where you exist is sufficient for being human everywhere (almost all characteristics are like this), but existing in every world where you exist is obviously not sufficient for existing everywhere (apparently only existence and characteristics involving existence are like this). From now on, an attribute is a function from worlds W to subsets of fiJ, and a proper~y is an attribute P such that anything having it wherever it exists has it everywhere. In general, an attribute is necessary to a thing if it attaches to the thing in every possible
world (preserving the intuition that existence is sometimes contingent). If the attribute is also a property, this reduces to the thing's having the attribute wherever it exists (preserving the intuition that humanity is necessary to Socrates if he cannot exist without it). In what follows, properties (rather than attributes in general) are the items under investigation. From the definition of property, it follows that, if P is a property, then so are pD : W -> {aEfiJ I 'v'W' mP( W')} (the property of being essentially P, or P's essentialization); pO: W -> {aEfiJ I :l W' mP( W')} (the property of being possibly P, or P's possibilization); and p"'-: W -> {mP( W) I :lW' art P(W')} (the property of being accidentally P, henceforth P's accidentalization). The essentialization XD (accidentalization X"'-) of a set X of properties is the set of its members' essentializations (accidentalizations). If a is in P( W) and exists in W, then it is in P[W] (note the square brackets). If for each P in X mP( W), then mX( W); if, in addition, a exists in W, then it is in X[W]. A set Y of properties is satisfiable in W, written Sat [Y, W], iff there is something in np,yp[W]. Given a set X of properties, a thing a's X-essence lEA a) is the set of all P in X which a possesses essentially, or {PEX I :lW(mpD(W))}. (3 is an X-refinement of a, written a ::; (3(X) - or just a ::; (3 if X is clear from context - iff a's Xessence is a subset of (3's, i.e., if IEAa) be a property-model of 2 ( 0) if "fII is a model of 2 (0) and X is a set of properties on "fII. A property-model fl is upwardclosed, or u-closed, iff: (U)
'v'a'v'Y (y)(x D y@t
== y #
x).
The old identity axiom is not so easily emended, however. That is, we obviously cannot replace it with
(x =y)
== (x
(CCI I )
(x tDz@tll One possible analogue of the old fusion axiom is, then, this: (CCI3)('lx) (x E S & x E @t) => ('ly)(y Fu S
(g)
t).
But that is only one of the possibilities. It is, after all, rather weak. It allows us to say, for example, that there is something that fuses Caesar's nose in 44 BC and that there is something that fuses Nixon's nose in 1979; but it does not allow us to conclude that there is something that both fuses Caesar's nose in 44 BC and fuses Nixon's nose in
1979. Admirers of the Calculus ofIndividuals will surely want that there be such a thing and will, therefore, regard the axiom I set out as too weak to be regarded as the appropriate analogue of the old fusion axiom. There are a number of available middle grounds, but I suspect that the truly devoted friends of fusions will want to go the whole distance. The simplest way of expressing their view is to take them to say that there is not one fusion axiom in the Cross-temporal Calculus of Individuals, but indefinitely many, the procedure for generating them being this. Take any set of n sets SI ... Sn For n = 1, write what I earlier called (CCI3)' For n = 2, write
[tl
f= tz
& ('lx)(x E SI & xE@tIl &
('ly)(y E Sz &yE@tz)] => ('lz)(zFuSI (Q)tl & zFuSz@tz) and so on. For my own part, I have no objection - it seems to me that one has only to live with fusions for a while to come to love them. But I shall not argue for all or even any of these fusion axioms. I do not know what an argument for them would look like. By the same token, however, I do not know what an argument against them would look like, "What an odd entity!" not seeming to me to count as an argument. So I shall leave it open which fusion axiom or axioms should be regarded as replacing the old fusion axiom. More precisely, I shall leave it open which fusion axiom or axioms should be regarded as replacing the old fusion axiom, so long as the axiom or axioms chosen do not guarantee the uniqueness of fusions. For we do not want an analogue of what I earlier called "the fusion principle" to be provable in the Cross-temporal Calculus ofIndividuals. The fusion principle, it will be remembered, says that, if anything is a member of S, then there is a unique thing that fuses the Ss. We do not want to have it provable that if anything is a member of Sand exists at t, then there is a unique entity that fuses the Ss at t: we want, precisely, to leave open that there may be more than one. My reason for saying that issues from the use to which I would like to be able to put these notions. Consider again the Tinkertoy house H. A Tinkertoy house is made only of Tinkertoys; and H is, at 1:15, made only of the Tinkertoys on the shelf at 1: 15. I would like, therefore, to be able to say that H fuses, at 1: 15, the Tinkertoys on the shelf at 1:15. And what about
Judith Jarvis Thomson
W', the wood on the shelf at 1:15? I would like to be able to say that that too fuses the Tinkertoys on the shelf at 1:15. But nothing can be true if it licenses our concluding from this that H is identical with W'. With fusions now relativized to times, we cannot single out a thing to call" W" as I did in section I above: (2)
W = the fusion of the Tinkertoys on the shelf at 1:15
now lacks a sense, for there now is no fusing simpliciter, there is only fusing-at-a-time. And, without an analogue of the fusion principle, we cannot even single out a thing to call "w" by drawing attention to the fact that there is something that fuses, at 1:15, the Tinkertoys on the shelf at 1:15: i.e., we cannot replace (2) with
W = the unique thing that fuses, at 1:15, the Tinkertoys on the shelf at 1: 15, for there may be more than one thing that does this. Indeed, I suggest we agree that there are at least two things which do this, viz., H and W'. Perhaps you have no taste for fusions, and regard the new fusion axioms (like the old one) as grossly overstrong. All the same, the difficulty we began with can be eliminated, and without appeal to temporal parts, if we say that parthood is a threeplace relation 11 and that the new identity axiom (interpreted as I indicated) is true. How is H related to W'? We can say, quite simply, that H
C: the proposition that if A were true, then C would also be true. The operation D--> is defined by a rule of truth, as follows. A D--> C is true (at a world w) iff either (1) there are no possible A-worlds (in which case A D--> Cis vacuous), or (2) some A-world where C holds is closer (to w) than is any A-world where C does not hold. In other words, a counterfactual is nonvacuously true iff it takes less of a departure from actuality to make the consequent true along with the antecedent than it does to make the antecedent true without the consequent. We did not assume that there must always be one or more closest A-worlds. But if there are, we can simplify: A D--> Cis non vacuously true iff C holds at all the closest A-worlds. We have not presupposed that A is false. If A is true, then our actual world is the closest A-world, so A D--> C is true iff C is. Hence A D--> C implies the material conditional A :::) C; and A and C jointly imply A D--> C. Let Al ,Az, . .. be a family of possible propositions, no two of which are compossible; let C I , Cz, . .. be another such family (of equal size). Then if all the counterfactuals Al D--> C I , A z D--> Cz, . .. between corresponding propositions in the two families are true, we shall say that
Causation the C's depend counterfactually on the A's. We can say it like this in ordinary language: whether C I or Cz or ... depends (counterfactually) on whether Al or A z or .... Counterfactual dependence between large families of alternatives is characteristic of processes of measurement, perception, or control. Let R I , R z, ... be propositions specifying the alternative readings of a certain barometer at a certain time. Let PI, P z, ... specify the corresponding pressures of the surrounding air. Then, if the barometer is working properly to measure the pressure, the R's must depend counterfactually on the P's. As we say it: the reading depends on the pressure. Likewise, if I am seeing at a certain time, then my visual impressions must depend counterfactually, over a wide range of alternative possibilities, on the scene before my eyes. And if I am in control over what happens in some respect, then there must be a double counter factual dependence, again over some fairly wide range of alternatives. The outcome depends on what I do, and that in turn depends on which outcome I want. 8
Causal Dependence among Events If a family CI , Cz, . .. depends counterfactually on a family AI,Az, ... in the sense just explained, we will ordinarily be willing to speak also of causal dependence. We say, for instance, that the barometer reading depends causally on the pressure, that my visual impressions depend causally on the scene before my eyes, or that the outcome of something under my control depends causally on what I do. But there are exceptions. Let G I , G z, ... be alternative possible laws of gravitation, differing in the value of some numerical constant. Let MI M z, ... be suitable alternative laws of planetary motion. Then the M's may depend counterfactually on the G's, but we would not call this dependence causal. Such exceptions as this, however, do not involve any sort of dependence among distinct particular events. The hope remains that causal dependence among events, at least, may be analyzed simply as counterfactual dependence. We have spoken thus far of counterfactual dependence among propositions, not among events. Whatever particular events may be, presumably they are not propositions. But that is no problem, since they can at least be paired with propositions. To any possible event e, there corres-
ponds the proposition O(e) that holds at all and only those worlds where e occurs. This O(e) is the proposition that e occurs.9 (If no two events occur at exactly the same worlds ~ if, that is, there are no absolutely necessary connections between distinct events ~ we may add that this correspondence of events and propositions is one to one.) Counterfactual dependence among events is simply counterfactual dependence among the corresponding propositions. Let CI, CZ, ... and el, ez, ... be distinct possible events such that no two of the c's and no two of the e's are compossible. Then I say that the family el, ez, ... of events depends causally on the family CI, cz, . .. iff the family O(ed, O(ez), . .. of propositions depends counter factually on the family O( C]), O( cz), . .. . As we say it: whether el or ez or. .. occurs depends on whether CI or Cz or ... occurs. We can also define a relation of dependence among single events rather than families. Let c and e be two distinct possible particular events. Then e depends causally on c iff the family O(e), ~ O(e) depends counterfactually on the family O(c), ~ O(c). As we say it: whether e occurs or not depends on whether c occurs or not. The dependence consists in the truth of two counterfactuals: O(c)->O(e) and ~ O(c)-> ~ O(e). There are two cases. If c and e do not actually occur, then the second counterfactual is automatically true because its antecedent and consequent are true: so e depends causally on c iff the first counterfactual holds. That is, iff e would have occurred if chad occurred. But if c and e are actual events, then it is the first counterfactual that is automatically true. Then e depends causally on c iff, if c had not been, e never had existed. I take Hume's second definition as my definition not of causation itself, but of causal dependence among actual events.
Causation Causal dependence among actual events implies causation. If c and e are two actual events such that e would not have occurred without c, then c is a cause of e. But I reject the converse. Causation must always be transitive; causal dependence may not be; so there can be causation without causal dependence. Let c, d, and e be three actual events such that d would not have occurred without c, and e would not have occurred without d. Then c is a cause of e even if e would still have occurred (otherwise caused) without c.
David Lewis
We extend causal dependence to a transItive relation in the usual way. Let c, d, e, ... be a finite sequence of actual particular events such that d depends causally on c, eon d, and so on throughout. Then this sequence is a causal chain. Finally, one event is a cause of another iff there exists a causal chain leading from the first to the second. This completes my counterfactual analysis of causation.
Counter factual versus Nomic Dependence It is essential to distinguish counter factual and causal dependence from what I shall call nomic dependence. The family C l , Cz, ... of propositions depends nomically on the family A I, Az, ... iff there are a nonempty set E of true law-propositions and a set IY of true propositions of particular fact such that £.I and IY jointly imply (but IY alone does not imply) all the material conditionals Al :J C l , Az :J Cz, . .. between the corresponding propositions in the two families. (Recall that these same material conditionals are implied by the counterfactuals that would comprise a counterfactual dependence.) We shall say also that the nomic dependence holds in virtue of the premise sets £.I and IY. Nomic and counterfactual dependence are related as follows. Say that a proposition B is counterfactually independent of the family AI, A z, ... of alternatives iff B would hold no matter which of the A's were true - that is, iff the counterfactuals Al D--> B, A z D--> B, ... all hold. If the C's depend nomically on the A's in virtue of the premise sets E and IY, and ifin addition (all members of) £.I and ~ are counterfactually independent of the A's, then it follows that the C's depend counterfactually on the A's. In that case, we may regard the nomic dependence in virtue of £.I and IY as explaining the counterfactual dependence. Often, perhaps always, counter factual dependences may be thus explained. But the requirement of counterfactual independence is indispensable. Unless E and ~ meet that requirement, nomic dependence in virtue of £.I and ~ does not imply counterfactual dependence, and, if there is counterfactual dependence anyway, does not explain it. Nomic dependence is reversible, in the following sense. If the family C l , Cz, ... depends nomically on the family AI, A z, ... in virtue of £.I and ~, then also AI, Az, ... depends nomically on the family ACI , ACz , ... , in virtue of E and ~, where A is
•
•
@ ••
Figure 34.1 the disjunction A I V A zV . . .. Is counterfactual dependence likewise reversible? That does not follow. For, even if E and ~ are independent of AI, A z, . .. and hence establish the counterfactual dependence of the C's on the A's, still they may fail to be independent of AC I , ACz, ... , and hence may fail to establish the reverse counterfactual dependence of the A's on the AC's. Irreversible counterfactual dependence is shown in figure 34.1: @ is our actual world, the dots are the other worlds, and distance on the page represents similarity "distance." The counterfactuals Al D--> C l , A z D--> Cz, and A3 D--> C3 hold at the actual world; wherefore the C's depend on the A's. But we do not have the reverse dependence of the A's on the AC's, since instead of the needed ACz D--> A z and AC] D--> A] we have ACz D--> Al and AC3 D--> AI. Just such irreversibility is commonplace. The barometer reading depends counterfactually on the pressure - that is as clear-cut as counterfactuals ever get - but does the pressure depend counterfactually on the reading? If the reading had been higher, would the pressure have been higher? Or would the barometer have been malfunctioning? The second sounds better: a higher reading would have been an incorrect reading. To be sure, there are actual laws and circumstances that imply and explain the actual accuracy of the barometer, but these are no more sacred than the actual laws and circumstances that imply and explain the actual pressure. Less sacred, in fact. When something must give way to permit a higher reading, we find it less of a departure from actuality to hold the pressure fixed and sacrifice the accuracy, rather than vice versa. It is not hard to see why. The barometer, being more localized and more delicate than the weather, is more vulnerable to slight departures from actuality. 10 We can now explain why regularity analyses of causation (among events, under determinism) work as well as they do. Suppose that event c causes event e according to the sample regularity analysis that I gave at the beginning of this paper, in virtue
Causation
of premise sets £! and ~. It follows that £!, ~, and ~ O(c) jointly do not imply O(e). Strengthen this: suppose further that they do imply ~ O(e). If so, the family O(e), ~ O(e) depends nomically on the family O(c), ~ O(c) in virtue of £! and !3'. Add one more supposition: that £! and !3' are counterfactually independent of O(c), ~ O(c). Then it follows according to my counterfactual analysis that e depends counterfactually and causally on c, and hence that c causes e. If I am right, the regularity analysis gives conditions that are almost but not quite sufficient for explicable causal dependence. That is not quite the same thing as causation; but causation without causal dependence is scarce, and if there is inexplicable causal dependence we are (understandably!) unaware of it. 11
Effects and Epiphenomena I return now to the problems I raised against regularity analyses, hoping to show that my counterfactual analysis can overcome them. The problem oj ~fJats, as it confronts a counterfactual analysis, is as follows. Suppose that c causes a subsequent event e, and that e does not also cause c. (I do not rule out closed causal loops a priori, but this case is not to be one.) Suppose further that, given the laws and some of the actual circumstances, c could not have failed to cause e. It seems to follow that if the effect e had not occurred, then its cause c would not have occurred. We have a spurious reverse causal dependence of con e, contradicting our supposition that e did not cause c. The problem oj epiphenomena, for a counterfactual analysis, is similar. Suppose that e is an epiphenomenal effect of a genuine cause c of an effect ! That is, c causes first e and then!, but e does not cause! Suppose further that, given the laws and some of the actual circumstances, c could not have failed to cause e; and that, given the laws and others of the circumstances,Jcould not have been caused otherwise than by c. It seems to follow that if the epiphenomenon e had not occurred, then its cause c would not have occurred and the further effectJof that same cause would not have occurred either. We have a spurious causal dependence of Jon e, contradicting our supposition that e did not cause! One might be tempted to solve the problem of effects by brute force: insert into the analysis a stipulation that a cause must always precede its effect (and perhaps a parallel stipulation for causal dependence). I reject this solution. (1) It is worth-
less against the closely related problem of epiphenomena, since the epiphenomenon e does precede its spurious effect! (2) It rejects a priori certain legitimate physical hypotheses that posit backward or simultaneous causation. (3) It trivializes any theory that seeks to define the forward direction of time as the predominant direction of causation. The proper solution to both problems, I think, is flatly to deny the counterfactuals that cause the trouble. If e had been absent, it is not that c would have been absent (and with it!, in the second case). Rather, c would have occurred just as it did but would have failed to cause e. It is less of a departure from actuality to get rid of e by holding c fixed and giving up some or other of the laws and circumstances in virtue of which c could not have failed to cause e, rather than to hold those laws and circumstances fixed and get rid of e by going back and abolishing its cause c. (In the second case, it would of course be pointless not to hold J fixed along with c.) The causal dependence of e on c is the same sort of irreversible counterfactual dependence that we have considered already. To get rid of an actual event e with the least overall departure from actuality, it will normally be best not to diverge at all from the actual course of events until just before the time of e. The longer we wait, the more we prolong the spatiotemporal region of perfect match between our actual world and the selected alternative. Why diverge sooner rather than later? Not to avoid violations oflaws of nature. Under determinism any divergence, soon or late, requires some violation of the actual laws. If the laws were held sacred, there would be no way to get rid of e without changing all of the past; and nothing guarantees that the change could be kept negligible except in the recent past. That would mean that if the present were ever so slightly different, then all of the past would have been different - which is absurd. So the laws are not sacred. Violation oflaws is a matter of degree. Until we get up to the time immediately before e is to occur, there is no general reason why a later divergence to avert e should need a more severe violation than an earlier one. Perhaps there are special reasons III special cases - but then these may be cases of backward causal dependence.
Preemption Suppose that C! occurs and causes e; and that C2 also occurs and does not cause e, but would have caused
David Lewis
e if CI had been absent. Thus C2 is a potential alternate cause of e, but is preempted by the actual cause CI. We may say that CI and C2 overdetermine e, but they do so asymmetrically.lZ In virtue of what difference does C] but not Cz cause e? As far as causal dependence goes, there is no difference: e depends neither on C] nor on C2. If either one had not occurred, the other would have sufficed to cause e. So the difference must be that, thanks to CI there is no causal chain from C2 to e; whereas there is a causal chain of two or more steps from CI to e. Assume for simplicity that two steps are enough. Then e depends causally on some intermediate event d, and d in turn depends on CI. Causal dependence is here intransitive: CI causes e
via d even though e would still have occurred without CI. SO far, so good. It remains only to deal with the objection that e does not depend causally on d, because if d had been absent, then C] would have been absent, and C2, no longer preempted, would have caused e. We may reply by denying the claim that if d had been absent, then CI would have been absent. That is the very same sort of spurious reverse dependence of cause on effect that we have just rejected in simpler cases. I rather claim that if d had been absent, C] would somehow have failed to cause d. But CI would still have been there to interfere with Cz so e would not have occurred.
Notes I thank the American Council of Learned Societies, Princeton University, and the National Science Foundation for research support. David Hume, An Enquiry Concerning Human Understanding, sec. 7. 2 Not one that has been proposed by any actual author in just this form, so far as I know. 3 I identify a proposition, as is becoming usual, with the set of possible worlds where it is true. It is not a linguistic entity. Truth-functional operations on propositions are the appropriate Boolean operations on sets of worlds; logical relations among propositions are relations of inclusion, overlap, etc. among sets. A sentence of a language expresses a proposition iff the sentence and the proposition are true at exactly the same worlds. No ordinary language will provide sentences to express all propositions; there will not be enough sentences to go around. 4 One exception: Ardon Lyon, "Causality," British Journal for the Philosophy oj Science, 18/1 (May 1967), pp. 1-20. S See, for instance, Robert Stalnaker, "A theory of conditionals," in Nicholas Rescher (ed.), Studies in Logical Theory (Oxford: Blackwell, 1968); and my Counter[actuals (Oxford: Blackwell, 1973). 6 Except that Morton G. White's discussion of causal selection, in Foundations oJHistorical Knowledge (New York: Harper & Row, 1965), pp. 105-81, would meet my needs, despite the fact that it is based on a regularity analysis. 7 That this ought to be allowed is argued in G. E. M. Anscombe, Causality and Determination: An Inaugural Lecture (Cambridge: Cambridge University Press, 1971); and in Fred Dretske and Aaron Snyder, "Causal irregularity," Philosophy oj Science, 39/1 (Mar. 1972), pp. 69-71.
8 Analyses in terms of counterfactual dependence are found in two papers of Alvin I. Goldman: "Toward a theory of social power," Philosophical Studies 23 (1972), pp. 221-68; and "Discrimination and perceptual knowledge," presented at the 1972 Chapel Hill Colloquium. 9 Beware: if we refer to a particular event e by means of SOme description that e satisfies, then we must take care not to confuse O(e), the proposition that e itself occurs, with the different proposition that some event or other occurs which satisfies the description. It is a contingent matter, in general, what events satisfy what descriptions. Let e be the death of Socrates the death he actually died, to be distinguished from all the different deaths he might have died instead. Suppose that Socrates had fled, only to be eaten by a lion. Then e would not have occurred, and O(e) would have been false; but a different event would have satisfied the description "the death of Socrates" that I used to refer to e. Or suppose that Socrates had lived and died just as he actually did, and afterwards was resurrected and killed again and resurrected again, and finally became immortal. Then no event would have satisfied the description. (Even if the temporary deaths are real deaths, neither of the two can be the death.) But e would have occurred, and O(e) would have been true. Call a description of an event e rigid iff (I) nothing but e could possibly satisfy it, and (2) e could not possibly occur without satisfying it. I have claimed that even such commonplace descriptions as "the death of Socrates" are nonrigid, and in fact I think that rigid descriptions of events are hard to find. That would be a problem for anyone who needed to associate with every possible event e a sentence (e) true at all and only those worlds where e occurs. But we need no such sentences - only propositions, which mayor may not have expressions in our language.
Causation 10 Granted, there are contexts or changes of wording that would incline us the other way . For some reason, "If the reading had been higher, that would have been because the pressure was higher" invites my assent more than "If the reading had been higher, the pressure would have been higher." The counterfactuals from readings to pressures are much less clear-cut than those from pressures to readings. But it is enough that some legitimate resolutions of vagueness give an irreversible dependence of readings on pressures. Those are the resolutions we want at present, even if they are not favored in all contexts.
II I am not here proposing a repaired regularity analysis. The repaired analysis would gratuitously rule out inexplicable causal dependence, which seems bad. Nor would it be squarely in the tradition of regularity analyses any more. Too much else would have been added. 12 I shall not discuss symmetrical cases of overdetermination, in which two overdetermining factors have equal claim to count as causes. For me these are useless as test cases because I lack firm naive opinions about them.
35
Wesley C. Salmon
Basic Problellls As a point of departure for the discussion of causality, it is appropriate for us to take a look at the reasons that have led philosophers to develop theories of explanation that do not require causal components. To Aristotle and Laplace it must have seemed evident that scientific explanations are inevitably causal in character. Laplacian determinism is causal determinism, and I know of no reason to suppose that Laplace made any distinction between causal and noncausallaws. It might be initially tempting to suppose that all laws of nature are causal laws, and that explanation in terms of laws is ipso facto causal explanation. It is, however, quite easy to find law-statements that do not express causal relations. Many regularities in nature are not direct cause--effect relations. Night follows day, and day follows night; nevertheless, day does not cause night, and night does not cause day. Kepler's laws of planetary motion describe the orbits of the planets, but they offer no causal account of these motions.! Similarly, the ideal gas law
PV = nRT relates pressure (P), volume (V), and temperature (7) for a given sample of gas, and it tells how these Originally published in Scientific Explanation and the Causal Structure of the World (1984). Copyright \0 by Princeton University Press. Reprinted by permission of Princeton University Press.
quantities vary as functions of one another, but it says nothing whatever about causal relations among them. An increase in pressure might be brought about by moving a piston so as to decrease the volume, or it might be caused by an increase in temperature. The law itself is entirely noncommittal concerning such causal considerations. Each of these regularities - the alternation of night with day; the regular motions of the planets; and the functional relationship among temperature, pressure, and volume of an ideal gas - can be explained causally, but they do not express causal relations. Moreover, they do not afford causal explanations of the events subsumed under them. For this reason, it seems to me, their value in providing scientific explanations of particular events is, at best, severely limited. These are regularities that need to be explained, but that do not, by themselves, do much in the way of explaining other phenomena. To untutored common sense, and to many scientists uncorrupted by philosophical training, it is evident that causality plays a central role in scientific explanation. An appropriate answer to an explanation-seeking why-question normally begins with the word "because," and the causal involvements of the answer arc usually not hard to find. 2 The concept of causality has, however, been philosophically suspect ever since David Humc's devastating critique, first published in 1739 in his Treatise ofHuman Nature. In the "Abstract" of that work, Hume wrote: Here is a billiard ball lying on the table, and another ball moving toward it with rapidity.
Causal Connections
They strike; the ball which was formerly at rest now acquires a motion. This is as perfect an instance of the relations of cause and effect as any which we know either by sensation or reflection. Let us therefore examine it. It is evident that the two balls touched one another before the motion was communicated, and that there was no interval betwixt the shock and the motion. ContiguiZy in time and place is therefore a requisite circumstance to the operation of all causes. It is evident, likewise, that the motion which was the cause is prior to the motion which was the effect. Priority in time is, therefore, another requisite circumstance in every cause. But this is not all. Let us try any other balls of the same kind in a like situation, and we shall always find that the impulse of the one produces motion in the other. Here, therefore, is a third circumstance, viz., that of constant conjunction betwixt the cause and the effect. Every object like the cause produces always some object like the effect. Beyond these three circumstances of contiguity, priority, and constant conjunction I can discover nothing in this cause. 3 This discussion is, of course, more notable for factors Hume was unable to find than for those he enumerated. In particular, he could not discover any 'necessary connections' relating causes to effects, or any 'hidden powers' by which the cause 'brings about' the effect. This classic account of causation is rightly regarded as a landmark in philosophy. In an oft-quoted remark that stands at the beginning of a famous 1913 essay, Bertrand Russell warns philosophers about the appeal to causality: All philosophers, of every school, imagine that causation is one of the fundamental axioms or postulates of science, yet, oddly enough, in advanced sciences such as gravitational astronomy, the word "cause" never occurs .... To me it seems that ... the reason why physics has ceased to look for causes is that, in fact, there are no such things. The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm. 4 It is hardly surprising that, in the light of Hume's critique and Russell's resounding condemnation,
philosophers with an empiricist bent have been rather wary of the use of causal concepts. By 1927, however, when he wrote The Analysis oj Matter, 5 Russell recognized that causality plays a fundamental role in physics; in Human Knowledge, four of the five postulates he advanced as a basis for all scientific knowledge make explicit reference to causal relations. 6 It should be noted, however, that the causal concepts he invokes are not the same as the traditional philosophical ones he had rejected earlier. 7 In contemporary physics, causality is a pervasive ingredient. s
Two Basic Concepts A standard picture of causality has been around at least since the time of Hume. The general idea is that we have two (or more) distinct events that bear some sort of cause - effect relations to one another. There has, of course, been considerable controversy regarding the nature of both the relation and the relata. It has sometimes been maintained, for instance, that facts or propositions (rather than events) are the sorts of entities that can constitute relata. It has long been disputed whether causal relations can be said to obtain among individual events, or whether statements about cause--effect relations implicitly involve assertions about classes of events. The relation itself has sometimes been taken to be that of sufficient condition, sometimes necessary condition, or perhaps a combination of the two. 9 Some authors have even proposed that certain sorts of statistical relations constitute causal relations. The foregoing characterization obviously fits J. L. Mackie's sophisticated account in terms of IN U s conditions - that is, insufficient but nonredundant parts of unnecessa~y but sufficient conditions. 10 The idea is this. There are several different causes that might account for the burning down of a house: careless smoking in bed, an electrical short circuit, arson, being struck by lightning. With certain obvious qualifications, each of these may be taken as a sufficient condition for the fire, but none of them can be considered necessary. Moreover, each of the sufficient conditions cited involves a fairly complex combination of conditions, each of which constitutes a nonredundant part of the particular sufficient condition under consideration. The careless smoker, for example, must fall asleep with his cigarette, and it must fall upon something flammable. It must not awaken the smoker by
Wesley C. Salmon
burning him before it falls from his hand. When the smoker does become aware of the fire, it must have progressed beyond the stage at which he can extinguish it. Anyone of these necessary components of some complex sufficient condition can, under certain circumstances, qualify as a cause. According to this standard approach, events enjoy the status of fundamental entities, and these entities are 'connected' to one another by cause-effect relations. It is my conviction that this standard view, in all of its well-known variations, is profoundly mistaken, and that a radically different notion should be developed. I shall not, at this juncture, attempt to mount arguments against the standard conception. Instead, I shall present a rather different approach for purposes of comparison. I hope that the alternative will stand on its own merits. There are, I believe, two fundamental causal concepts that need to be explicated, and if that can be achieved, we will be in a position to deal with the problems of causality in general. The two basic concepts are propagation and production, and both are familiar to common sense. When we say that the blow of a hammer drives a nail, we mean that the impact produces penetration of the nail into the wood. When we say that a horse pulls a cart, we mean that the force exerted by the horse produces the motion of the cart. When we say that lightning ignites a forest, we mean that the electrical discharge produces a fire. When we say that a person's embarrassment was due to a thoughtless remark, we mean that an inappropriate comment produced psychological discomfort. Such examples of causal production occur frequently in everyday contexts. Causal propagation (or transmission) is equally familiar. Experiences that we had earlier in our lives affect our current behavior. By means of memory, the influence of these past events is transmitted to the present. I I A sonic boom makes us aware of the passage of a jet airplane overhead; a disturbance in the air is propagated from the upper atmosphere to our location on the ground. Signals transmitted from a broadcasting station are received by the radio in our home. News or music reaches us because electromagnetic waves are propagated from the transmitter to the receiver. In 177 5, some Massachusetts farmers - in initiating the American Revolutionary War - "fired the shot heard 'round the world.,,12 As all of these examples show, what happens at one place and time can have significant influence upon what happens at other
places and times. This is possible because causal influence can be propagated through time and space. Although causal production and causal propagation are intimately related to one another, we should, I believe, resist any temptation to try to reduce one to the other.
Processes One of the fundamental changes that I propose in approaching causality is to take processes rather than events as basic entities. I shall not attempt any rigorous definition of processes; rather, I shall cite examples and make some very informal remarks. The main difference between events and processes is that events are relatively localized in space and time, while processes have much greater temporal duration, and in many cases, much greater spatial extent. In space-time diagrams, events are represented by points, while processes are represented by lines. A baseball colliding with a window would count as an event; the baseball, traveling from the bat to the window, would constitute a process. The activation of a photocell by a pulse of light would be an event; the pulse of light, traveling, perhaps from a distant star, would be a process. A sneeze is an event. The shadow of a cloud moving across the landscape is a process. Although I shall deny that all processes qualify as causal processes, what I mean by a process is similar to what Russell characterized as a causal line: A causal line may always be regarded as the persistence of something - a person, a table, a photon, or what not. Throughout a given causal line, there may be constancy of quality, constancy of structure, or a gradual change of either, but not sudden changes of any considerable magnitudeY Among the physically important processes are waves and material objects that persist through time. As I shall use these terms, even a material object at rest will qualify as a process. Before attempting to develop a theory of causality in which processes, rather than events, are taken as fundamental, I should consider briefly the scientific legitimacy of this approach. In Newtonian mechanics, both spatial extent and temporal duration were absolute quantities. The length of a rigid rod did not depend upon a choice of frame of reference, nor did the duration of a process (such as
Causal Connections
the length of time between the creation and destruction of a material object). Given two events, in Newtonian mechanics, both the spatial distance and the temporal separation between them were absolute magnitudes. A 'physical thing ontology' was thus appropriate to classical physics. As everyone knows, Einstein's special theory of relativity changed all that. Both the spatial distance and the temporal separation were relativized to frames of reference. The length of a rigid rod and the duration of a temporal process varied from one frame of reference to another. However, as Minkowski showed, there is an invariant quantity - the space-time interval between two events. This quantity is independent of the frame of reference; for any two events, it has the same value in each and every inertial frame of reference. Since there are good reasons for according a fundamental physical status to invariants, it was a natural consequence of the special theory of relativity to regard the world as a collection of events that bear space-time relations to one another. These considerations offer support for what is sometimes called an 'event ontology'. There is, however, another way (originally developed by A. A. Robb) of approaching the special theory of relativity; it is done entirely with paths of light pulses. At any point in space-time, we can construct the Minkowski light cone - a twosheeted cone whose surface is generated by the paths of all possible light pulses that converge upon the point (past light cone) and the paths of all possible light pulses that could be emitted from the point (future light cone). When all of the light cones are given, the entire space-time structure of the world is determined. 14 But light pulses, traveling through space and time, are processes. We can, therefore, base special relativity upon a 'process ontology'. Moreover, this approach can be extended in a natural way to general relativity by taking into account the paths of freely falling material particles; these moving gravitational test particles are also processes. IS It is, consequently, entirely legitimate to approach the space-time structure of the physical world by regarding physical processes as the basic types of physical entities. The theory of relativity does not mandate an 'event ontology'. Whether one adopts the event-based approach or the process-based approach, causal relations must be accorded a fundamental place in the special theory of relativity. As we have seen, any given event Eo occurring at a particular space-time point
Po, has an associated double-sheeted light cone. All events that could have a causal influence upon Eo are located in the interior or on the surface of the past light cone, and all events upon which Eo could have any causal influence are located in the interior or on the surface of the future light cone. All such events are causally connectable with Eo. Those events that lie on the surface of either sheet of the light cone are said to have a lightlike separation from Eo those that lie within either part of the cone are said to have a time/ike separation from Eo, and those that are outside of the cone are said to have a space/ike separation from Eo. The Minkowski light cone can, with complete propriety, be called "the cone of causal relevance," and the entire spacetime structure of special relativity can be developed on the basis of causal concepts. 16 Special relativity demands that we make a distinction between causal processes and pseudo-processes. It is a fundamental principle of that theory that light is a first signal - that is, no signal can be transmitted at a velocity greater than the velocity of light in a vacuum. There are, however, certain processes that can transpire at arbitrarily high velocities - at velocities vastly exceeding that of light. This fact does not violate the basic relativistic principle, however, for these 'processes' are incapable of serving as signals or of transmitting information. Causal processes are those that are capable of transmitting signals; pseudo-processes are incapable of doing so. Consider a simple example. Suppose that we have a very large circular building - a sort of super-Astrodome, if you will - with a spotlight mounted at its center. When the light is turned on in the otherwise darkened building, it casts a spot of light upon the wall. If we turn the light on for a brief moment, and then off again, a light pulse travels from the light to the wall. This pulse of light, traveling from the spotlight to the wall, is a paradigm of what we mean by a causal process. Suppose, further, that the spotlight is mounted on a mechanism that makes it rotate. If the light is turned on and set into rotation, the spot of light that it casts upon the wall will move around the outer wall in a highly regular fashion. This 'process' - the moving spot oflight - seems to fulfill the conditions Russell used to characterize causal lines, but it is not a causal process. It is a paradigm of what we mean by a pseudo-process. The basic method for distinguishing causal processes from pseudo-processes is the criterion of mark transmission. A causal process is capable of
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transmitting a mark; a pseudo-process is not. Consider, first, a pulse of light that travels from the spotlight to the wall. If we place a piece of red glass in its path at any point between the spotlight and the wall, the light pulse, which was white, becomes and remains red until it reaches the wall. A single intervention at one point in the process transforms it in a way that persists from that point on. If we had not intervened, the light pulse would have remained white during its entire journey from the spotlight to the wall. If we do intervene locally at a single place, we can produce a change that is transmitted from the point of intervention onward. We shall say, therefore, that the light pulse constitutes a causal process whether it is modified or not, since in either case it is capable of transmitting a mark. Clearly, light pulses can serve as signals and can transmit messages; remember Paul Revere, "One if by land and two if by sea." Now, let us consider the spot oflight that moves around the wall as the spotlight rotates. There are a number of ways in which we can intervene to change the spot at some point; for example, we can place a red filter at the wall with the result that the spot oflight becomes red at that point. But if we make such a modification in the traveling spot, it will not be transmitted beyond the point of interaction. As soon as the light spot moves beyond the point at which the red filter was placed, it will become white again. The mark can be made, but it will not be transmitted. We have a 'process', which, in the absence of any intervention, consists of a white spot moving regularly along the wall of the building. If we intervene at some point, the 'process' will be modified at that point, but it will continue on beyond that point just as if no intervention had occurred. We can, of course, make the spot red at other places if we wish. We can install a red lens in the spotlight, but that does not constitute a local intervention at an isolated point in the process itself. We can put red filters at many places along the wall, but that would involve many interventions rather than a single one. We could get someone to run around the wall holding a red filter in front of the spot continuously, but that would not constitute an intervention at a single point in the 'process'. This last suggestion brings us back to the subject of velocity. If the spot oflight is moving rapidly, no runner could keep up with it, but perhaps a mechanical device could be set up. If, however, the spot moves too rapidly, it would be physically impossible to make the filter travel fast enough to
keep pace. No material object, such as the filter, can travel at a velocity greater than that oflight, but no such limitation is placed upon the spot on the wall. This can easily be seen as follows. If the spotlight rotates at a fixed rate, then it takes the spot oflight a fixed amount of time to make one entire circuit around the wall. If the spotlight rotates once per second, the spot oflight will travel around the wall in one second. This fact is independent of the size of the building. We can imagine that without making any change in the spotlight or its rate of rotation, the outer walls are expanded indefinitely. At a certain point, when the radius of the building is a little less than 50,000 kilometers, the spot will be traveling at the speed of light (300,000 km/sec). As the walls are moved still farther out, the velocity of the spot exceeds the speed of light. To make this point more vivid, consider an actual example that is quite analogous to the rotating spotlight. There is a pulsar in the Crab nebula that is about 6,500 light-years away. This pulsar is thought to be a rapidly rotating neutron star that sends out a beam of radiation. When the beam is directed toward us, it sends out radiation that we detect later as a pulse. The pulses arrive at the rate of 30 per second; that is the rate at which the neutron star rotates. Now, imagine a circle drawn with the pulsar at its center, and with a radius equal to the distance from the pulsar to the earth. The electromagnetic radiation from the pulsar (which travels at the speed of light) takes 6,500 years to traverse the radius of this circle, but the 'spot' of radiation sweeps around the circumference of this circle in 1/30th of a second; at that rate, it is traveling at about 4 x 1013 times the speed oflight. There is no upper limit on the speed of pseudoprocesses. 17 Another example may help to clarify this distinction. Consider a car traveling along a road on a sunny day. As the car moves at 100 km/hr, its shadow moves along the shoulder at the same speed. The moving car, like any material object, constitutes a causal process; the shadow is a pseudo-process. If the car collides with a stone wall, it will carry the marks of that collision -- the dents and scratches - along with it long after the collision has taken place. If, however, only the shadow of the car collides with the stone wall, it will be deformed momentarily, but it will resume its normal shape just as soon as it has passed beyond the wall. Indeed, if the car passes a tall building that cuts it off from the sunlight, the shadow will be
Causal Connections
obliterated, but it will pop right back into existence as soon as the car has returned to the direct sunlight. If, however, the car is totally obliterated say, by an atomic bomb blast - it will not pop back into existence as soon as the blast has subsided. A given process, whether it be causal or pseudo, has a certain degree of uniformity - we may say, somewhat loosely, that it exhibits a certain structure. The difference between a causal process and a pseudo-process, I am suggesting, is that the causal process transmits its own structure, while the pseudo-process does not. The distinction between processes that do and those that do not transmit their own structures is revealed by the mark criterion. If a process - a causal process - is transmitting its own structure, then it will be capable of transmitting certain modifications in that structure. In Human Knowledge, Russell placed great emphasis upon what he called "causal lines," which he characterized in the following terms: A "causal line," as I wish to define the term, is a temporal series of events so related that, given some of them, something can be inferred about the others whatever may be happening elsewhere. A causal line may always be regarded as the persistence of something - a person, table, a photon, or what not. Throughout a given causal line, there may be constancy of quality, constancy of structure, or gradual change in either, but not sudden change of any considerable magnitude. IS He then goes on to comment upon the significance of causal lines: That there are such more or less self-determined causal processes is in no degree logically necessary, but is, I think, one of the fundamental postulates of science. It is in virtue of the truth of this postulate - if it is true - that we are able to acquire partial knowledge in spite of our . 19 enormous Ignorance. Although Russell seems clearly to intend his causal lines to be what we have called causal processes, his characterization may appear to allow pseudo-processes to qualify as well. Pseudo-processes, such as the spot oflight traveling around the wall of our Astrodome, sometimes exhibit great uniformity, and their regular behavior can serve as a basis for inferring the nature of certain parts of the pseudo-process on the basis of observation of
other parts. But pseudo-processes are not selfdetermined; the spot of light is determined by the behavior of the beacon and the beam it sends out. Moreover, the inference from one part of the pseudo-process to another is not reliable regardless of what may be happening elsewhere, for if the spotlight is switched off or covered with an opaque hood, the inference will go wrong. We may say, therefore, that our observations of the various phenomena going on in the world around us reveal processes that exhibit considerable regularity, but some of these are genuine causal processes and others are pseudo-processes. The causal processes are, as Russell says, self-determined; they transmit their own uniformities of qualitative and structural features. The regularities exhibited by the pseudoprocesses, in contrast, are parasitic upon causal regularities exterior to the 'process' itself - in the case of the Astrodome, the behavior of the beacon; in the case of the shadow traveling along the roadside, the behavior of the car and the sun. The ability to transmit a mark is the criterion that distinguishes causal processes from pseudo-processes, for if the modification represented by the mark is propagated, the process is transmitting its own characteristics. Otherwise, the 'process' is not self-determined, and is not independent of what goes on elsewhere. Although Russell's characterization of causal lines is heuristically useful, it cannot serve as a fundamental criterion for their identification for two reasons. First, it is formulated in terms of our ability to infer the nature of some portions from a knowledge of other portions. We need a criterion that does not rest upon such epistemic notions as knowledge and inference, for the existence of the vast majority of causal processes in the history of the universe is quite independent of human knowers. This aspect of the characterization could, perhaps, be restated nonanthropocentrically in terms of the persistence of objective regularities in the process. The second reason is more serious. To suggest that processes have regularities that persist "whatever may be happening elsewhere" is surely an overstatement. If an extremely massive object should happen to be located in the neighborhood of a light pulse, its path will be significantly altered. If a nuclear blast should occur in the vicinity of a mail truck, the letters that it carries will be totally destroyed. If sunspot activity reaches a high level, radio communication is affected. Notice that, in each of these cases, the factor cited does not occur or exist on the world line of the process in
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question. In each instance, of course, the disrupting factor initiates processes that intersect with the process in question, but that does not undermine the objection to the claim that causal processes transpire in their self-determined fashion regardless of what is happening elsewhere. A more acceptable statement might be that a causal process would persist even if it were isolated from external causal influences. This formulation, unfortunately, seems at the very least to flirt with circularity, for external causal influences must be transmitted to the locus of the process in question by means of other processes. We shall certainly want to keep clearly in mind the notion that causal processes are not parasitic upon other processes, but it does not seem likely that this rough idea could be transformed into a useful basic criterion. It has often been suggested that the principal characteristic of causal processes is that they transmit energy. While I believe it is true that all and only causal processes transmit energy, there is, I think, a fundamental problem involved in employing this fact as a basic criterion - namely, we must have some basis for distinguishing situations in which energy is transmitted from those in which it merely appears in some regular fashion. The difficulty is easily seen in the' Astrodome' example. As a light pulse travels from the central spotlight to the wall, it carries radiant energy; this energy is present in the various stages of the process as the pulse travels from the lamp to the wall. As the spot of light travels around the wall, energy appears at the places occupied by the spot, but we do not want to say that this energy is transmitted. The problem is to distinguish the cases in which a given bundle of energy is transmitted through a process from those in which different bundles of energy are appearing in some regular fashion. The key to this distinction is, I believe, the mark method. Just as the detective makes his mark on the murder weapon for purposes of later identification, so also do we make marks in processes so that the energy present at one space-time locale can be identified when it appears at other times and places. A causal process is one that is self-determined and not parasitic upon other causal influences. A causal process is one that transmits energy, as well as information and causal influence. The fundamental criterion for distinguishing self-determined energy-transmitting processes from pseudo-processes is the capability of such processes of transmitting marks. In the next section, we shall deal with the concept of transmission in greater detail.
Our main concern with causal processes is their role in the propagation of causal influences; radio broadcasting presents a clear example. The transmitting station sends a carrier wave that has a certain structure - characterized by amplitude and frequency, among other things - and modifications of this wave, in the form of modulations of amplitude (AM) or frequency (FM), are imposed for the purpose of broadcasting. Processes that transmit their own structures are capable of transmitting marks, signals, information, energy, and causal influence. Such processes are the means by which causal influence is propagated in our world. Causal influences, transmitted by radio, may set your foot to tapping, or induce someone to purchase a different brand of soap, or point a television camera aboard a spacecraft toward the rings of Saturn. A causal influence transmitted by a flying arrow can pierce an apple on the head of William Tell's son. A causal influence transmitted by sound waves can make your dog come running. A causal influence transmitted by ink marks on a piece of paper can gladden one's day or break someone's heart. It is evident, I think, that the propagation or transmission of causal influence from one place and time to another must playa fundamental role in the causal structure of the world. As I shall argue next, causal processes constitute precisely the causal connections that Hume sought, but was unable to find.
The 'At-At' Theory of Causal Propagation In the preceding section, I invoked Reichenbach's mark criterion to make the crucial distinction between causal processes and pseudo-processes. Causal processes are distinguished from pseudoprocesses in terms of their ability to transmit marks. In order to qualify as causal, a process need not actually be transmitting a mark; the requirement is that it be capable of doing so. When we characterize causal processes partly in terms of their ability to transmit marks, we must deal explicitly with the question of whether we have violated the kinds of strictures Hume so emphatically expounded. He warned against the uncritical use of such concepts as 'power' and 'necessary connection'. Is not the abili~y to transmit a mark an example of just such a mysterious power? Kenneth Sayre expressed his misgivings on this
Causal Connections
score when, after acknowledging the distinction between causal interactions and causal processes, he wrote: The causal process, continuous though it may be, is made up of individual events related to others in a causal nexus .... it is by virtue of the relations among the members of causal series that we are enabled to make the inferences by which causal processes are characterized .... if we do not have an adequate conception of the relatedness between individual members in a causal series, there is a sense in which our conception of the causal process itself remains deficient. 20 The 'at-at' theory of causal transmission IS an attempt to remedy this deficiency. Does this remedy illicitly invoke the sort of concept Hume proscribed? I think not. Ability to transmit a mark can be viewed as a particularly important species of constant conjunction - the sort of thing Hume recognized as observable and admissible. It is a matter of performing certain kinds of experiments. If we place a red filter in a light beam near its source, we can observe that the mark - redness - appears at all places to which the beam is subsequently propagated. This fact can be verified by experiments as often as we wish to perform them. If, contrariwise (returning to our Astrodome example of the preceding section), we make the spot on the wall red by placing a filter in the beam at one point just before the light strikes the wall (or by any other means we may devise), we will see that the mark - redness - is not present at all other places in which the moving spot subsequently appears on the wall. This, too, can be verified by repeated experimentation. Such facts are straightforwardly observable. The question can still be reformulated. What do we mean when we speak of transmission? How does the process make the mark appear elsewhere within it? There is, I believe, an astonishingly simple answer. The transmission of a mark from point A in a causal process to point B in the same process is the fact that it appears at each point between A and B without further interactions. If A is the point at which the red filter is inserted into the beam going from the spotlight to the wall, and B is the point at which the beam strikes the wall, then only the interaction at A is required. If we place a white card in the beam at any point between A and B, we will find the beam red at that point.
The basic thesis about mark transmission can now be stated (in a principle I shall designate MT for "mark transmission") as follows: MT:
Let P be a process that, in the absence of interactions with other processes, would remain uniform with respect to a characteristic Q which it would manifest consistently over an interval that includes both of the space-time points A and B (A i= B). Then, a mark (consisting of a modification ofQ into Q'), which has been introduced into process P by means of a single local interaction at point A, is transmitted to point B if P manifests the modification Q' at B and at all stages of the process between A and B without additional interventions.
This principle is clearly counterfactual, for it states explicitly that the process P would have continued to manifest the characteristic Q if the specific marking interaction had not occurred. This subjunctive formulation is required, I believe, to overcome an objection posed by Nancy Cartwright (in conversation) to previous formulations. The problem is this. Suppose our rotating beacon is casting a white spot that moves around the wall, and that we mark the spot by interposing a red filter at the wall. Suppose further, however, that a red lens has been installed in the beacon just a tiny fraction of a second earlier, so that the spot on the wall becomes red at the moment we mark it with our red filter, but it remains red from that point on because of the red lens. Under these circumstances, were it not for the counterfactual condition, it would appear that we had satisfied the requirement formulated in MT, for we have marked the spot by a single interaction at point A, and the spot remains red from that point on to any other point B we care to designate, without any additional interactions. As we have just mentioned, the installation of the red lens on the spotlight does not constitute a marking of the spot on the wall. The counterfactual stipulation given in the first sentence of MT blocks situations, of the sort mentioned by Cartwright, in which we would most certainly want to deny that any mark transmission occurred via the spot moving around the wall. In this case, the moving spot would have turned red because of the lens even if no marking interaction had occurred locally at the wall. A serious misgiving arises from the use of counterfactual formulations to characterize the
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distinction between causal processes and pseudoprocesses; it concerns the question of objectivity. The distinction is fully objective. It is a matter of fact that a light pulse constitutes a causal process, while a shadow is a pseudo-process. Philosophers have often maintained, however, that counterfactual conditionals involve unavoidably pragmatic aspects. Consider the famous example about Verdi and Bizet. One person might say, "If Verdi had been a compatriot of Bizet, then Verdi would have been French," whereas another might maintain, "If Bizet had been a compatriot of Verdi, then Bizet would have been Italian." These two statements seem incompatible with one another. Their antecedents are logically equivalent; if, however, we accept both conditionals, we wind up with the conclusion that Verdi would be French, that Bizet would be Italian, and they would still not be compatriots. Yet both statements can be true. The first person could be making an unstated presupposition that the nationality of Bizet is fixed in this context, while the second presupposes that the nationality of Verdi is fixed. What remains fixed and what is subject to change - which are established by pragmatic features of the context in which the counterfactual is uttered - determine whether a counterfactual is true or false. It is concluded that counterfactual conditional statements do not express objective facts of nature; indeed, van Fraassen 21 goes so far as to assert that science contains no counterfactuals. If that sweeping claim were true (which I seriously doubt),22 the foregoing criterion MT would be in serious trouble. Although MT involves an explicit counterfactual, I do not believe that the foregoing difficulty is insurmountable. Science has a direct way of dealing with the kinds of counterfactual assertions we require: namely, the experimental approach. In a well-designed controlled experiment, the experimenter determines which conditions are to be fixed for purposes of the experiment and which allowed to vary. The result of the experiment establishes some counterfactual statements as true and others as false under well-specified conditions. Consider the kinds of cases that concern us; such counterfactuals can readily be tested experimentally. Suppose we want to see whether the beam traveling from the spotlight to the wall is capable of transmitting the red mark. We set up the following experiment. The light will be turned on and off one hundred times. At a point midway between the spotlight and the wall, we station an experimenter with a random number generator. Without com-
municating with the experimenter who turns the light on and off, this second experimenter uses his device to make a random selection of fifty trials in which he will make a mark and fifty in which he will not. If all and only the fifty instances in which the marking interaction occurs are those in which the spot on the wall is red, as well as all the intervening stages in the process, then we may conclude with reasonable certainty that the fifty cases in which the beam was red subsequent to the marking interaction are cases in which the beam would not have been red if the marking interaction had not occurred. On any satisfactory analysis of counterfactuals, it seems to me, we would be justified in drawing such a conclusion. It should be carefully noted that I am not offering the foregoing experimental procedure as an analysis of counterfactuals; it is, indeed, a result that we should expect any analysis to yield. A similar experimental approach could obviously be taken with respect to the spot traversing the wall. We design an experiment in which the beacon will rotate one hundred times, and each traversal will be taken as a separate process. We station an experimenter with a random number generator at the wall. Without communicating with the experimenter operating the beacon, the one at the wall makes a random selection of fifty trials in which to make the mark and fifty in which to refrain. If it turns out that some or all of the trials in which no interaction occurs are, nevertheless, cases in which the spot on the wall turns red as it passes the second experimenter, then we know that we are not dealing with cases in which the process will not turn from white to red if no interaction occurs. Hence, if in some cases the spot turns red and remains red after the mark is imposed, we know we are not entitled to conclude that the mark has actually been transmitted. The account of mark transmission embodied in principle MT - which is the proposed foundation for the concept of propagation of causal influence may seem too trivial to be taken seriously. I believe such a judgment would be mistaken. My reason lies in the close parallel that can be drawn between the foregoing solution to the problem of mark transmission and the solution of an ancient philosophical puzzle. About 2,500 years ago, Zeno of Elea enunciated some famous paradoxes of motion, including the well-known paradox of the flying arrow. This paradox was not adequately resolved until the early part of the twentieth century. To establish an intimate
Causal Connections
connection between this problem and our problem of causal transmission, two observations are in order. First, a physical object (such as the arrow) moving from one place to another constitutes a causal process, as can be demonstrated easily by application of the mark method - for example, initials carved on the shaft of the arrow before it is shot are present on the shaft after it hits its target. And there can be no doubt that the arrow propagates causal influence. The hunter kills his prey by releasing the appropriately aimed arrow; the flying arrow constitutes the causal connection between the cause (release of the arrow from the bow under tension) and the effect (death of a deer). Second, Zeno's paradoxes were designed to prove the absurdity not only of motion, but also of every kind of process or change. Henri Bergson expressed this point eloquently in his discussion of what he called "the cinematographic view of becoming." He invites us to consider any process, such as the motion of a regiment of soldiers passing in review. We can take many snapshots - static views - of different stages of the process, but, he argues, we cannot really capture the movement in this way, for, every attempt to reconstitute change out of states implies the absurd proposition, that movement is made out of immobilities. Philosophy perceived this as soon as it opened its eyes. The arguments of Zeno of Elea, although formulated with a very different intention, have no other meaning. Take the flying arrow. 2.1 Let us have a look at this paradox. At any given instant, Zeno seems to have argued, the arrow is where it is, occupying a portion of space equal to itself. During the instant it cannot move, for that would require the instant to have parts, and an instant is kv definition a minimal and indivisible element of time. If the arrow did move during the instant, it would have to be in one place at one part of the instant and in a different place at another part of the instant. Moreover, for the arrow to move during the instant would require that during that instant it must occupy a space larger than itself, for otherwise it has no room to move. As Russell said:
This is what M. Bergson calls the cinematographic representation of reality. The more the difficulty is meditated, the more real it becomes. 24 There is a strong temptation to respond to this paradox by pointing out that the differential calculus provides us with a perfectly meaningful definition of instantaneous velocity, and that this quantity can assume values other than zero. Velocity is change of position with respect to time, and the derivative dxl dt furnishes an expression that can be evaluated for particular values of t. Thus an arrow can be at rest at a given moment - that is, dxl dt may equal 0 for that particular value of t. Or it can be in motion at a given moment - that is, dxl dt might be 100 km/hr for another particular value of t. Once we recognize this elementary result of the infinitesimal calculus, it is often suggested, the paradox of the flying arrow vanishes. This appealing attempt to resolve the paradox is, however, unsatisfactory, as Russell clearly realized. The problem lies in the definition of the derivative; dxl dt is defined as the limit as Llt approaches 0 of Llx/ Llt, where Llt represents a nonzero interval of time and Llx may be a nonzero spatial distance. In other words, instantaneous velocity is defined as the limit, as we take decreasing time intervals, of the noninstantaneous average velocity with which the object traverses what is - in the case of nonzero values - a nonzero stretch of space. Thus in the definition of instantaneous velocity, we employ the concept of noninstantaneous velocity, which is precisely the problematic concept from which the paradox arises. To put the same point in a different way, the concept of instantaneous velocity does not genuinely characterize the motion of an object at an isolated instant all by itself, for the very definition of instantaneous velocity makes reference to neighboring instants of time and neighboring points of space. To find an adequate resolution of the flying arrow paradox, we must go deeper. To describe the motion of a body, we express the relation between its position and the moments of time with which we are concerned by means of a mathematical function; for example, the equation of motion of a freely falling particle near the surface of the earth is
(1) It is never moving, but in some miraculous way the change of position has to occur between the instants, that is to say, not at any time whatever.
x
= f(t) =
1/2gt2 2
where g = 9 .8m/ sec . We can therefore say that this equation furnishes a function f(t) that relates
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the position x to the time t. But what is a mathematical function? It is a set of pairs of numbers; for each admissible value of t, there is an associated value of x. To say that an object moves in accordance with equation (I) is simply to say that at any given moment t it is at point x, where the correspondence between the values of t and of x is given by the set of pairs of numbers that constitute the function represented by equation (I). To move from point A to point B is simply to be at the appropriate point of space at the appropriate moment of time - no more, no less. The resulting theory is therefore known as "the 'at-at' theory of motion." To the best of my knowledge, it was first clearly formulated and applied to the arrow paradox by Russell. According to the 'at-at' theory, to move from A to B is simply to occupy the intervening points at the intervening instants. It consists in being at particular points of space at corresponding moments. There is no additional question as to how the arrow gets from point A to point B; the answer has already been given - by being at the intervening points at the intervening moments. The answer is emphatically not that it gets from A to B by zipping through the intermediate points at high speed. Moreover, there is no additional question about how the arrow gets from one intervening point to another - the answer is the same, namely, by being at the points between them at the corresponding moments. And clearly, there can be no question about how the arrow gets from one point to the next, for in a continuum there is no next point. I am convinced that Zeno's arrow paradox is a profound problem concerning the nature of change and motion, and that its resolution by Russell in terms of the 'at-at' theory of motion represents a distinctly nontrivial achievement. 25 The fact that this solution can - if I am right - be extended in a direct fashion to provide a resolution of the problem of mark transmission is an additional laurel. The 'at-at' theory of mark transmission provides, I believe, an acceptable basis for the mark method, which can in turn serve as the means to distinguish causal processes from pseudo-processes. The world contains a great many types of causal processes - transmission of light waves, motion of material objects, transmissions of sound waves, persistence of crystalline structure, and so forth. Processes of any of these types may occur without having any mark imposed. In such instances, the processes still qualify as causal. Abil-
ity to transmit a mark is the criterion of causal processes; processes that are actual~y unmarked may be causal. Unmarked processes exhibit some sort of persistent structure, as Russell pointed out in his characterization of causal lines; in such cases, we say that the structure is transmitted within the causal process. Pseudo-processes may also exhibit persistent structure; in these cases, we maintain that the structure is not transmitted by means of the 'process' itself, but by some other external agency. The basis for saying that the regularity in the causal process is transmitted via the process itself lies in the ability of the causal process to transmit a modification in its structure - a mark - resulting from an interaction. Consider a brief pulse of white light; it consists of a collection of photons of various frequencies, and if it is not polarized, the waves will have various spatial orientations. If we place a red filter in the path of this pulse, it will absorb all photons with frequencies falling outside of the red range, allowing only those within that range to pass. The resulting pulse has its structure modified in a rather precisely specifiable way, and the fact that this modification persists is precisely what we mean by claiming that the mark is transmitted. The counterfactual clause in our principle MT is designed to rule out structural changes brought about by anything other than the marking interaction. The light pulse could, alternatively, have been passed through a polarizer. The resulting pulse would consist of photons having a specified spatial orientation instead of the miscellaneous assortment of orientations it contained before encountering the polarizer. The principle of structure transmission (ST) may be formulated as follows: ST:
If a process is capable o.ftransmitting changes in structure due to marking interactions, then that process can be said to transmit its own structure.
The fact that a process does not transmit a particular type of mark, however, does not mean that it is not a causal process. A ball of putty constitutes a causal process, and one kind of mark it will transmit is a change in shape imposed by indenting it with the thumb. However, a hard rubber ball is equally a causal process, but it will not transmit the same sort of mark, because of its elastic properties. The fact that a particular sort of structural modification does not persist, because of some inherent tendency of the process to resume
Causal Connections
its earlier structure, does not mean it is not transmitting its own structure; it means only that we have not found the appropriate sort of mark for that kind of process. A hard rubber ball can be marked by painting a spot on it, and that mark will persist for a while. Marking methods are sometimes used in practice for the identification of causal processes. As fans of Perry Mason are aware, Lieutenant Tragg always placed 'his mark' upon the murder weapon found at the scene of the crime in order to be able to identify it later at the trial of the suspect. Radioactive traces are used in the investigation of physiological processes - for example, to determine the course taken by a particular substance ingested by a subject. Malodorous substances are added to natural gas used for heating and cooking in order to ascertain the presence of leaks; in fact, one large chemical manufacturer published full-page color advertisements in scientific magazines for its product "La Stink." One of the main reasons for devoting our attention to causal processes is to show how they can transmit causal influence. In the case of causal processes used to transmit signals, the point is obvious. Paul Revere was caused to start out on his famous night ride by a light signal sent from the tower of the Old North Church. A drug, placed surreptitiously in a drink, can cause a person to lose consciousness because it retains its chemical structure as it is ingested, absorbed, and circulated through the body of the victim. A loud sound can produce a painful sensation in the ears because the disturbance of the air is transmitted from the origin to the hearer. Radio signals sent to orbiting satellites can activate devices aboard because the wave retains its form as it travels from earth through space. The principle of propagation of causal influence (PCI) may be formulated as follows: PCI:
A process that transmits its own structure IS capable ojpropagating a causal influence from one space-time locale to another.
The propagation of causal influence by means of causal processes constitutes, I believe, the mysterious connection between cause and effect which Hume sought. In offering the 'at-at' theory of mark transmission as a basis for distinguishing causal processes from pseudo-processes, we have furnished an account of the transmission of information and propagation of causal influence without appealing
to any of the 'secret powers' which Hume's account of causation soundly proscribed. With this account we see that the mysterious connection between causes and effects is not very mysterious after all. Our task is by no means finished, however, for this account of transmission of marks and propagation of causal influence has used the unanalyzed notion of a causal interaction that produces a mark. Unless a satisfactory account of causal interaction and mark production can be provided, our theory of causality will contain a severe lacuna. 26 Nevertheless, we have made significant progress in explicating the fundamental concept, introduced at the beginning of the chapter, of causal propagation (or transmission). This chapter is entitled "Causal Connections," but little has actually been said about the way in which causal processes provide the connection between cause and effect. Nevertheless, in many common-sense situations, we talk about causal relations between pairs of spatiotemporally separated events. We might say, for instance, that turning the key causes the car to start. In this context we assume, of course, that the electrical circuitry is intact, that the various parts are in good working order, that there is gasoline in the tank, and so forth, but I think we can make sense of a causeeffect relation only if we can provide a causal connection between the cause and the effect. This involves tracing out the causal processes that lead from the turning of the key and the closing of an electrical circuit to various occurrences that eventuate in the turning over of the engine and the ignition of fuel in the cylinders. We say, for another example, that a tap on the knee causes the foot to jerk. Again, we believe that there are neutral impulses traveling from the place at which the tap occurred to the muscles that control the movement of the foot, and processes in those muscles that lead to movement of the foot itself. The genetic relationship between parents and offspring provides a further example. In this case, the molecular biologist refers to the actual process of information transmission via the DNA molecule employing the 'genetic code'. In each of these situations, we analyze the causeeffect relations in terms of three components - an event that constitutes the cause, another event that constitutes the effect, and a causal process that connects the two events. In some cases, such as the starting of the car, there are many intermediate events, but in such cases, the successive intermediate events are connected to one another by
Wesley C. Salmon
spatiotemporally continuous causal processes. A splendid example of multiple causal connections was provided by David Kaplan. Several years ago, he paid a visit to Tucson, just after completing a boat trip through the Grand Canyon with his family. The best time to take such a trip, he remarked, is when it is very hot in Phoenix. What is the causal connection to the weather in Phoenix, which is about 200 miles away? At such times, the air-conditioners in Phoenix are used more heavily, which places a greater load on the generators at the Glen Canyon Dam (above the Grand Canyon). Under these circumstances, more water is allowed to pass through the turbines to meet the increased demand for power, which produces a greater flow of water down the Colorado River. This results in a more exciting ride through the rapids in the Canyon. In the next chapter,27 we shall consider eventsespecially causal interactions - more explicitly. It will then be easier to see how causal processes constitute precisely the physical connections between causes and effects that Hume sought what he called "the cement of the universe." These causal connections will playa vital role in our account of scientific explanation. It is tempting, of course, to try to reduce causal processes to chains of events; indeed, people fre-
quently speak of causal chains. Such talk can be seriously misleading if it is taken to mean that causal processes are composed of discrete events that are serially ordered so that any given event has an immediate successor. If, however, the continuous character of causal processes is kept clearly in mind, I would not argue that it is philosophically incorrect to regard processes as collections of events. At the same time, it does seem heuristically disadvantageous to do so, for this practice seems almost inevitably to lead to the puzzle (articulated by Sayre in the quotation given previously) of how these events, which make up a given process, are causally related to one another. The point of the 'at-at' theory, it seems to me, is to show that no such question about the causal relations among the constituents of the process need arise - for the same reason that, aside from occupying intermediate positions at the appropriate times, there is no further question about how the flying arrow gets from one place to another. With the aid of the 'atat' theory, we have a complete answer to Hume's penetrating question about the nature of causal connections. For this heuristic reason, then, I consider it advisable to resist the temptation always to return to formulations in terms of events.
Notes
2
3
4
6
It might be objected that the alternation of night with day, and perhaps Kepler's "laws," do not constitute genuine lawful regularities. This consideration does not really affect the present argument, for there are plenty of regularities, lawful and nonlawful, that do not have explanatory force, but that stand in need of causal explanation. Indeed, in Italian, there is one word, perche, which means both "why" and "because." In interrogative sentences it means "why," and in indicative sentences it means "because." No confusion is engendered as a result of the fact that Italian lacks two distinct words. David Hume, An Inquiry Concerning Human Understanding (Indianapolis: Bobbs-Merrill, 1955), which also contains "An abstract of A Treatise of Human Nature," pp. 186-7. Bertrand Russell, Mysticism and Logic (New York: W. W. Norton, 1929), p. 180. Bertrand Russell, The Analysis of Matter (London: George Allen and Unwin, 1927). Bertrand Russell, Human Knowledge, Its Scope and Limits (New York: Simon and Schuster, 1948), pp.487-96.
7 In ibid., regrettably, Russell felt compelled to relinquish empiricism. I shall attempt to avoid such extreme measures. 8 Patrick Suppes, A Probabilistic Theory of Causality (Amsterdam: North-Holland, 1970), pp. 5-6. 9 See]. L. Mackie, The Cement ofthe Universe (Oxford: Clarendon Press, 1974), for an excellent historical and systematic survey of the various approaches. 10 Ibid., p. 62. 11 Deborah A. Rosen, "An argument for the logical notion of a memory trace," Philosophy ~r Science 42 (1975), pp. 1-10. 12 Ralph Waldo Emerson, "Hymn sung at the completion of the battle monument, Concord." 13 Russell, Human Knowledge, p. 459. 14 See John Winnie, "The causal theory of space-time," in John Earman, Clark Glymour, and John Stachel (eds), Minnesota Studies in the Philosophy of Science, vol. 8 (Minneapolis: University of Minnesota Press, 1977), pp. 134-205. 15 See Adolf Grunbaum, Philosophical Problems of Space and Time, 2nd edn (Dordrecht: D. Reidel, 1973), pp.735-50. 16 Winnie, "Causal theory."
Causal Connections 17 Milton A. Rothman, "Things that go faster than light," Scientific American 203/1 (July 1960), pp. 142-52, contains a lively discussion of pseudoprocesses. 18 Russell, Human Knowledge, p. 459. 19 Ibid. 20 Kenneth M. Sayre, "Statistical models of causal relations," Philosophy ofScience 44 (1977), pp. 203-14, at p.206. 21 Bas C. van Fraassen, The Scientific Image (Oxford: Clarendon Press, 1980), p. 118. 22 For example, our discussion of the Minkowski light cone made reference to paths of possible light rays; such a path is one that would be taken by a light pulse if it were emitted from a given space-time point in a given direction. Special relativity seems to be permeated with reference to possible light rays and possible causal connections, and these involve counterfactuals quite directly. See Wesley C. Salmon, "Foreword," in Hans Reichenbach, Laws, Modalities, and Counterfactuals (Berkeley/Los Angeles/London: University of California Press, 1976), pp. vii-xlii, for further
23 24 25
26
27
elaboration of this issue, not only with respect to special relativity but also in relation to other domains of physics. A strong case can be made, I believe, for the thesis that counterfactuals are scientifically indispensable. Henri Bergson, Creative Evolution (New York: Holt, Reinhart and Winston, 1911), p. 308. Russell, Mysticism and Logic, p. 187. Zeno's arrow paradox and its resolution by means of the 'at-at' theory of motion are discussed in Wesley C. Salmon, Space, Time, and Motion (Encino, Calif.: Dickenson, 1975; 2nd edn, Minneapolis: University of Minnesota Press, 1980), ch. 2. Relevant writings by Bergson and Russell are reprinted in idem, Zeno '.I Paradoxes (Indianapolis: Bobbs-Merrill, 1970); the introduction to this anthology also contains a discussion of the arrow paradox. Salmon offers an account of these notions in his Scientific Explanation and the Causal Structure of the World (Princeton: Princeton University Press, 1984), ch.6. Ibid.
36
Michael Tooley
Is a singularist conception of causation coherent? That is to say, is it possible for two events to be causally related, without that relationship being an instance of some causal law, either basic or derived, and either probabilistic or non-probabilistic? Since the time of Hume, the overwhelmingly dominant philosophical view has been that such a conception of causation is not coherent. In this paper, I shall attempt to show that that view is incorrect. The paper has three main sections. In the first, I argue that, although some traditional arguments in support of a singularist conception of causation are problematic, there are good reasons for trying to develop a singularist account. Then, in the second section, I consider a Humean objection to a singularist conception of causation. My central contention there is that while the argument has considerable force against any reductionist account, it leaves untouched the possibility of a realist approach according to which causal relations are neither observable, nor reducible to observable properties and relations. Finally, in the third section, I turn to the task of actually setting out a satisfactory singularist account of the nature of causation. There I shall offer both a general recipe for constructing a singularist account, and a specific version that incorporates my own views on the direction of causation.
Originally published in Canadian Journal of Philosophy, suppl. vol. 16 (1990), pp. 271-322. Reprinted by permission of University of Calgary Press.
1 Arguments in Support of a Singularist Conception of Causation A. Two problematic arguments in support of a singularist account What grounds might be offered for thinking that it is possible for one event to cause another, without the causal relation being an instance of any causal law? There are, I think, at least six lines of argument that are worth mentioning. Two of these I shall set aside as dubious. The other four, however, appear to be sound. Immediate knowledge of causal relations? One consideration that might be advanced starts out by appealing to the possibility of knowledge that two events are causally related, which is based upon nothing beyond perception of the two events and their more or less immediate surroundings. The thrust of the argument is then that, since experience of such a very limited sort can surely not provide one with any knowledge of the existence of a law, it must be possible to know that two events are causally related without knowing that there is any law of which that relation is an instance. But if that is possible, then is it not also reasonable to suppose that it is possible for two events to be causally related, even if there is no corresponding law? This general line of argument comes in different versions, corresponding to four slightly different claims concerning knowledge of causal relations. First, there is the claim that causal relations
The Nature of Causation
can be given in immediate experience, in the strong sense of actually being part of an experience itself. Second, there is the claim that, even if causal relations are not given in immediate experience, one can certainly have non-inferential knowledge that states of affairs are causally related. Third, there is the claim that causal relations are at least observable in many cases. Finally, there is the claim that there are situations where observation of a single case can provide one with grounds for believing that two events are causally related, and that it can do so even in the absence of any prior knowledge of causal laws. These four claims give rise to different arguments. But, while I shall not attempt to establish it here, I think that it is very doubtful that any of them can be sustained. The appeal to intuition A second line of thought involves the claim that if one simply examines one's ordinary concept of causation ~ of one event's bringing about, or giving rise to, another ~ one does not find any reference to the idea of a law. One's ordinary concept of causation is simply that of a relation between two events ~ that is to say, a relation that involves only two events, together with whatever causal intermediaries there may be, and nothing else. It cannot matter, therefore, what is the case in other parts of the universe, or what laws obtain. Is there anything in this argument? Perhaps. For if it is true that, no matter how carefully one inspects one's ordinary concept of causation, one cannot see any reason why only events that fall under laws can be causally related, then that may provide some support for a singularist conception. But it would seem that that support must be, at best, very limited. For, given the great difficulty, not only in arriving at a satisfactory analysis of the concept of causation, but even in determining the correct direction in which to look, the fact that no connection with laws is immediately apparent when one introspectively examines one's ordinary concept of causation can hardly provide much of a basis for concluding that no such connection exists. B.
More promising lines of argument
In this section, I want to mention four considerations that, though by no means compelling, constitute much more substantial reasons for accepting a singularist conception of causation. The four arguments consist of three that I have set out elsewhere, in a detailed way, 1 plus a natural variant.
My discussion of them here, consequently, will be comparatively brief. The four arguments all attempt to establish a singularist conception of causation by offering reasons for rejecting the alternatives. We need to consider, therefore, just what the alternatives are. The place to begin, clearly, is with the dominant, supervenience view. According to it, events cannot be causally related unless that relation is an instance of some law. Moreover, whether or not two events are causally related is logically determined by the non-causal properties of the two events, and the non-causal relations between them, together with the causal laws that there are in the world. The supervemence view of causal relations involves, in short, the following two theses:
2
Causal relations presuppose corresponding causal laws; Causal relations are logically supervenient upon causal laws plus the non-causal properties of, and relations between, events.
Traditionally, the supervenience view and the singularist view have been treated as the only alternatives on offer with respect to the question of the relation between causal relations and causal laws. It is clear, however, that there is a third alternative, since the first of the above theses is compatible with the denial of the second. There is, accordingly, a view that is intermediate between the singularist position and the supervenience position ~ the view, namely, that causal relations presuppose corresponding causal laws, even though causal relations are not logically supervenient upon causal laws together with the non-causal properties of, and relations between, events. The relevance of this for the present arguments is that each argument involves two distinct parts ~ one directed against the supervenience view and the other directed against the intermediate view. In the case of the supervenience alternative, the strategy is to describe a logically possible situation that is a counterexample to the supervenience account. The counterexamples have no force, however, against the intermediate view, so some other line of argument is called for, and what I shall argue is that the singularist view is to be preferred to the intermediate view on grounds of simplicity. The argument from the possibility of indeterministic laws The first argument starts out from the plausible ~ though by no means indubitable ~
Michael Tooley
assumption that indeterministic causal laws are logically possible. Granted that assumption, consider a world with only two basic causal laws: For any x, x's having property P is causally sufficient to bring it about that either x has property Q or x has property R; For any x, x's having property S is causally sufficient to bring it about that either x has property Q or x has property R. In such a world, if an object has property P, but not property S, and then acquires property Q, but not property R, it must be the case that the acquisition of property Q was caused by the possession of property P. Similarly, if an object has property S, but not property P, and then acquires property Q, but not property R, it must be the case that the acquisition of property Q was caused by the possession of property S. But what if an object has both property P and property S? If the object acquires only property Q, there will be no problem: it will simply be a case of causal overdetermination. Similarly, if it acquires only property R. But what if it acquires both property Q and property R? Was it the possession of property P that caused the acquisition of property Q, and the possession of property S that caused the possession of property R, or was it the other way around? Given a supervenience view of causation, no answer is possible, for the causal laws in question, together with the non-causal properties of the objects, do not entail that it was one way rather than the other. Can an advocate of a supervenience view argue successfully that this case is not really a counterexample? One try would be to say that in the case where an object has both property P and property S, and then acquires properties Qand R, there are no causal relations at all involved. But that won't do, since the first law, for example, implies that the possession of property P always causes something. Another attempted escape would be to argue that there are causal relations in the situation, but they are not quite as determinate as one might initially assume. Thus it is not the case either that the possession of property P causes the possession of property Q, or that it causes the possession of property R. What is true is that the possession of property P causes the state of affairs which involves either the possession of property Q, or the possession of property R.
But this, I believe, will not do either. The reason is that causal relations hold between states of affairs, and, while one may use disjunctive expressions to pick out states of affairs, states of affairs in themselves can never be disjunctive in nature. Accordingly, if the situation described is to involve causal relations falling under the relevant laws, it must be the case either that the possession of property P caused the acquisition of property Q, or that it caused the acquisition of property R, and similarly for property S. It would seem, then, that the possibility of indeterministic causal laws gives rise to a very strong objection to the supervenience view of causal relations. But what of the intermediate view? Obviously, the above argument leaves it unscathed, since, in the situation being considered, all of the causal relations fall under causal laws. So if the intermediate view is to be rejected, some other argument is needed. The only possibility that I can see here is a somewhat modest argument which turns upon the fact that the intermediate view involves a somewhat richer ontology than the other views. For consider, first, the supervenience view. Given that, according to it, causal relations between states of affairs are logically supervenient upon causal laws plus non-causal states of affairs, the only basic causal facts that need to be postulated are those that correspond to causal laws. (According to the view of causal laws that I have defended elsewhere, such facts are to be identified with certain contingent relations between universals. 2 ) Second, consider the singularist view. According to it, it is causal relations that are in some sense primary, rather than causal laws. So the singularist view is certainly committed to postulating basic causal facts which involve states of affairs standing in causal relations. But what account is to be offered of causal laws? If a regularity view of laws were tenable, nothing would be needed beyond regularities involving the relation of causation. However, as a number of philosophers have argued, regularity accounts of the nature of laws are exposed to very strong objections. 3 Let us suppose, therefore, that a singularist account of causation is combined with the view that laws are relations among universals. The result will be that a singularist approach involves, in the case of any world that contains causal laws, the postulation of two sorts of basic causal facts - consisting, on the one hand, of relations between particular states of affairs, and, on the other, of relations between universals.
The Nature of Causation
At first glance, then, the singularist approach might seem to have a more luxuriant ontology than the supervenience approach, since the latter postulates only one type of causal fact, whereas the former postulates two. But I think that further reflection undermines that conclusion. The reason is that both approaches need to leave room for the possibility of non-causal laws. When this is taken into account, it can be seen that both approaches need to postulate exactly two fundamental sorts of facts, in the general area oflaws and causation. For, on the one hand, the supervenience view needs to postulate two special types of facts in order to distinguish between causal laws and non-causal laws, while, on the other, the singularist approach can also account for everything while postulating only two special sorts of facts. For although it cannot reduce causal laws to causal relations between states of affairs, it can analyse the concept of a causal law in terms of the concept of a law causal or otherwise - together with the concept of causal relations. In short, the situation is this. Both approaches need an account of the nature of laws. Given that, the supervenience view then goes on to explain what it is that distinguishes causal laws from noncasual laws, and then uses the notion of a causal law to offer an analysis of what it is for two states of affairs to be causally related. The singularist view, on the other hand, has to explain what it is for two states of affairs to be causally related, and it then uses that concept, in conjunction with that of a law, to explain what a causal law is. The two approaches would seem, therefore, to be on par with respect to overall simplicity. But what of the intermediate account? The answer is that it is necessarily more complex. Since it denies that causal relations between events are logically supervenient upon causal laws together with the totality of non-causal facts, it is committed, like the singularist approach, to postulating a special relation that holds between states of affairs. But, unlike the singularist approach, it cannot go on to analyse causal laws as laws that involve the relation of causation. For the latter sort of analysis makes it impossible to offer any reason why it should be the case that events can be causally related only if they fall under some law. Accordingly, if the exclusion of anomic causation is to be comprehensible, given an intermediate view, one needs to offer a separate account of the nature of causallaws. 4 The upshot is that an intermediate account needs to postulate three special sorts of
facts: those corresponding to non-causal laws, those corresponding to causal laws, and those corresponding to causal relations between states of affairs. An intermediate account therefore involves a somewhat richer ontology than either a singularist approach or a supervenience approach. This completes the argument. For we have seen, first, that there are only two alternatives to a singularist conception of causation - namely, the supervenience view and the intermediate view. Second, one of the alternatives - the supervenience view - is ruled out by certain logically possible cases involving indeterministic causal laws. Third, the other alternative - the intermediate view - is ontologically less economical than the singularist view. Other things being equal, therefore, the singularist approach is to be preferred. The argument from the possibility of uncaused events and probabilistic laws The second argument is, in a
sense, a simpler version of the previous one. It does involve however, two additional assumptions namely, that both probabilistic laws and uncaused events are possible. Given those two assumptions, the argument runs as follows. Imagine a world where objects sometimes acquire property Q without there being any cause of that occurrence. Suppose, further, that the following is a law: For any x, x's having property P causally brings it about, with probability 0.75, that x has property Q. If objects sometimes acquire property Q even though there is no cause of their doing so, then why shouldn't this also be possible in cases where an object happens to have property P? Indeed, might there not be an excellent reason for thinking that there were such cases? For suppose that objects having property P went on to acquire property Q 76 per cent of the time, rather than 75 per cent of the time. That would not necessarily be grounds for entertaining doubts concerning the above law, since that law might be derived from a very powerful, simple, and well-confirmed theory. In that situation, one would have reason for believing that, over the long term, of the 76 out of 100 cases when an object with property P acquires property Q, 75 will be ones where the acquisition of property Q is caused by the possession of property P, while the other will be one where property Q is spontaneously acquired. But if one adopts a
Michael Tooley
supervenience view, what state of affairs serves to differentiate the two sorts of cases? No answer can be forthcoming, since, by hypothesis, there are no differences with respect to non-causal properties or relations. The above possibility is a counterexample, therefore, to a supervenience view of causal relations.
The argument from the possibility of exact replicas of causal situations The third argument runs as follows. Suppose that event P causes event M. There will, in general, be nothing impossible about there also being an event M* which has precisely the same properties 5 as M, both intrinsic and relational, but which is not caused by P. But is it logically possible for it to be the case that, in addition, either (I) the only relation between P and M is that of causation, or else (2) any other relation that holds between P and M also holds between P and M*? If either of these situations can obtain, we have a counterexample to the supervenience view. For assume that the supervenience approach is correct. That means that P's causing M is logically supervenient upon the non-causal properties of, and the non-causal relations between, P and M, together with the causal laws. But if M* has precisely the same non-causal properties as M, and also stands to P in the same non-causal relations as M does, then the supervenience thesis entails that P must also cause M* , contrary to our hypothesis. An advocate of the supervenience view might well challenge, of course, the assumption that situations of the above sort are possible. But I believe that the assumption can be sustained, and elsewhere I have advanced three sorts of cases in support of it,6 two of which I shall mention here. The first involves two assumptions; first, that there could be immaterial minds that were not located in space, but which could be causally linked - say, by 'telepathy'; second, that there could also be two such minds that were in precisely the same state at every instant. Granted these assumptions, one has a counterexample of the desired sort to the supervenience view: a case, namely, where a mind P is causally linked to a mind, M, but not to a qualitatively indistinguishable mind, M*. A second sort of case involves the following three assumptions: first, that it is logically possible for there to be worlds that exhibit, at least some of the time, rotational symmetry; second, that enduring objects have temporal parts, and that it is causal relations between those parts that unite them into
enduring objects; third, that the only external relations that hold between complete temporal slices of a universe, or between parts of diffe;ent complete temporal slices, are causal and temporal ones. Given those assumptions, consider, for example, a Newtonian world that contains only two neutrons, endlessly rotating in the same direction around their centre of gravity. Choose any time, t, and let U be the temporal part that contains events at t, together with all prior events, while V contains all later events. The thrust of the argument is then that the rotational symmetry that characterizes such a world at every moment means that a supervenience view cannot give a satisfactory account of the causal connections between the two temporal parts. For if P and P* are the earlier temporal parts of the two neutrons, and M and M* the later temporal parts, it will be impossible, given a supervenience view, to hold that P is causally linked to M, but not to M*, since M and M* have the same properties, both intrinsic and relational, and there is no non-causal relation that holds between P and M, but not between P and M*. If the subsidiary assumptions can be defended in either or both of these cases - and I believe that they can 7 - then one has another sort of counterexample to the supervenience view.
The argument from the possibility of inverted universes Let us say that two possible worlds are inverted twins if they are exactly the same except for the direction of time and for any properties or relations that involve the direction of time. Whether a possible world has an inverted twin depends upon what the laws of nature are. Some laws will exclude inversion; others will not. Consider, for example, any world that is governed by the laws of Newtonian physics. For any instantaneous temporal slice, S, of that world, there will be another possible Newtonian world that contains an instantaneous temporal slice, T such that Tinvolves precisely the same distribution of particles as S, but with velocities that are exactly reversed. Given that the laws of Newtonian physics are symmetric with respect to time, the course of events in the one world will be exactly the opposite of that in the other world. Any Newtonian world necessarily has, therefore, an inverted twin. Imagine, then, for purposes of illustration, that our world is a Newtonian world. There will then be a possible world that is just like our world, except that the direction of time, and the direction of causation, are, so to speak, reversed. That is to
The Nature of Causation
say, if we let A and B be any two complete temporal slices of our world, such that A is causally and temporally prior to B, then the other world will contain temporal slices A* and B* such that, first, A* and B* are indistinguishable from A and B, respectively, except with respect to properties that involve the direction of time, and second, B* is causally and temporally prior to A* . So there will be, for example, a complete temporal slice of the twin world that is just like a temporal slice of our own world in the year AD 1600 except that all properties that involve the direction of time such as velocity - will be reversed. Similarly, there will be a complete temporal slice that corresponds, in the same way, to a temporal slice of our own world in the year AD 1700. But both the causal and the temporal orderings will be flipped over, with the l700-style slice both causally prior to, and earlier than, the l600-style slice. The question now is this. What makes it the case that, in our world, A causes B, whereas in the inverted twin world, B* causes A*? If one adopts a supervenience account, then, in view of the fact that the two worlds have, by hypothesis, the same laws, the difference must be a matter either of some difference between A and A* , or between Band B* , with respect to non-causal properties, or else of some non-causal relation that holds between A and B, but not between A* and B*. Can such a difference be found? One difference is that while A is earlier than B, A* is later than B* , rather than earlier. But is this a non-causal difference? The answer depends upon the correct theory of the nature of time. In particular' it depends upon whether the direction of time is to be analysed in terms of the direction of causation. If, as I am inclined to believe, it is, then the causal difference between the two worlds cannot be grounded upon the temporal difference. But this, in turn, also means that A and A* cannot differ with respect to their non-causal properties, and similarly for Band B*. For, by hypothesis, A differs from A* only with respect to those properties that involve the direction of time, and those differences will not be non-causal differences if the direction of time is to be defined in terms of the direction of causation. The crux of this fourth and final argument, in short, is the assumption that the direction of time is to be analysed in terms of the direction of causation. If that assumption cannot be sustained, the argument collapses. But if it can be sustained, the argument appears to go through, since A will not
then differ from A* with respect to any non-causal properties, nor B from B*, nor will there be any non-causal relation that holds between A and B but not between A* and B*. The possibility of inverted universes will thus constitute another counterexample to the supervenience view of causation. To sum up, the four arguments that I have set out in this section constitute, I believe, a very strong case against the supervenience view. As we have seen, however, this is not to say that there is an equally strong case for the singularist conception of causation. For there is a third alternative the intermediate view - which escapes the objections to which the supervenience account is exposed. Nevertheless, with the field thus narrowed, there is at least some reason for preferring the singularist view, since it involves a more economical ontology.
2 Arguments against a Singularist Account? I have argued that, other things being equal, the singularist view is to be preferred. But are other things equal, or are there, on the contrary, strong objections to a singularist conception of causation? Given that very few philosophers indeed have embraced a singularist view, it is natural to suppose that very strong objections, if not out and about, must at least be lurking on the sidelines. But is that so? Perhaps, instead, it has simply been taken for granted that a singularist view cannot be right, that causal relations must fall under laws? That certainly seem to have been the feeling of Elizabeth Anscombe, as the following, somewhat caustic comment on Davidson, and others, testifies: Meanwhile in non-experimental philosophy it is clear enough what are the dogmatic slumbers of the day. It is over and over again assumed that any singular causal proposition implies a universal statement running 'Always when this, then that'; often assumed that true singular causal statements are derived from such 'inductively believed' universalities. Examples indeed are recalcitrant, but that does not seem to disturb. Even a philosopher acute enough to be conscious of this, such as Davidson, will say, without offering any reason at all for saying it, that a singular causal statement implies that there is such a true universal statement - though perhaps we can never have knowledge of it.
Michael Tooley
Such a thesis needs some reason for believing it!s Such a thesis does indeed need support. However, I believe that Anscombe is wrong in suggesting that the widespread philosophical acceptance of the view that causal relations presuppose laws does not rest upon any argument. For it seems to me that the reason that one rarely encounters any arguments bearing upon this thesis is that most philosophers have generally been convinced by Hume's argumentation on the matter, regardless of whether they have accepted or rejected his positive account of the nature of causation. We need to consider, therefore, the Humean line of argument. It has, in effect, two parts. The first involves the claim that causal relations are not observable in the relevant technical sense of being immediately given in experience. The second involves the claim that causal relations are not analytically reducible to observable properties and relations unless one looks beyond the individual case. How might it be argued that causal relations are not immediately given in experience? A standard empiricist argument might run as follows. First, to say that a property or relation is immediately given in an experience is to say that it is part of the experience itself, and where the latter is so understood that a property or relation can be part of an experience E only if it would also have to be part of any experience that was qualitatively indistinguishable from E. Second, given any experience E whatever - be it a perception of external events, or an introspective awareness of some mental occurrence, such as an act of willing, or a process of thinking - it is logically possible that appropriate, direct stimulation of the brain might produce an experience, E*, which was qualitatively indistinguishable from E, but which did not involve any causally related elements. So, for example, it might seem to one that one was engaging in a process of deductive reasoning, when, in fact, there was not really any direct connection at all between the thoughts themselves - all of them being caused instead by something outside of oneself. It then follows, from these two premisses, that causal relations cannot be immediately given in experience in the sense indicated. But what is the significance of this conclusion? The answer is that it then follows, according to traditional empiricism, that the concept of causation cannot be analytically basic. For one of the
central tenets of empiricism is that not all ideas can be treated as primitive. In particular, an idea can be treated as analytically basic only if it serves to pick out some property or relation with which one is directly acquainted. But what properties and relations can be objects of direct acquaintance? Within traditional empiricism, the answer is that one can be directly acquainted only with properties and relations that can be given within immediate experience. It therefore follows that if traditional empiricist views concerning what concepts can be treated as analytically basic are sound, the concept of causation cannot be treated as analytically basic. It stands in need of analysis. Is traditional empiricism right on these matters? I believe that it is. Arguing for that view would, however, take us rather far afield. For the way that I would want to proceed is by showing, first, that, pace Wittgenstein, a private language is unproblematic, and second, that while concepts that involve the ascription of secondary qualities to external objects can be analysed in terms of concepts that involve the ascription of qualia to experiences, analysis in the opposite direction is impossible. This brings us to the second stage of the Humean argument - the part which is directed to showing that a singularist conception of causation makes it impossible to analyse causation in terms of observable properties and relations. Hume's argument here involves asking one to try to identify, in any case where one event causes another, what it is that constitutes the causal connection. He suggests that when we do so, we will see, first, that the effect comes after the cause, and second, that cause and effect are contiguous, both temporally and spatically. But these two relations, surely, are not enough. Something more is needed, if events are to be causally related. But what can that something more possibly be? In response to this question, Hume argues that, regardless of what sort of instance one considers be it a case of one object's colliding with another, or a case of a person's performing some action - one will find that there is neither any further property, either of the cause or of the effect, nor any further relation between the two events, to which one can point. Hume therefore concludes that if one is to find something that answers to our concept of causation, one has to look beyond any single instance, and he then goes on to argue that if one has to look beyond single instances, the only situations that could possibly be relevant are ones involving events of similar sorts, similarly conjoined.
The Nature of Causation
Thus one is led, in the end, to the conclusion that our idea of causation is in some way necessarily linked with the idea of regularities, of constant conjunctions of events. 9 How might one attempt to rebut this argument? One line, which appears to be embraced by Anscombe,1O involves the attempt to move from the claim that causation is observable to the conclusion that the concept of causation can be treated as basic, and thus as not in need of any analysis in terms of other ideas. But it seems very unlikely that this response can be sustained. For, on the one hand, the fact that something is observable in the ordinary, non-technical sense of that term provides no reason at all for concluding that the relevant concept can be taken as analytically basic: electrons are, for example, observable in cloud chambers, but that does not mean that the term 'electron' does not stand in need of analysis. And, on the other hand, if one shifts to a technical sense of 'observation' that does license that inference ~ namely, that according to which a property or relation is observable only if it can be given in immediate experience ~ then, as was argued above, causation is not observable in that sense. Another possible singularist response is that advanced by C. J. Ducasse, who attempted to show that causation could be analysed in terms of relations which Hume granted are observable in the individual instance ~ the relations, namely, of spatial and temporal contiguity, and of temporal priority. Thus, according to Ducasse, to say that C caused K, where C and K are changes, is just to say:
2
3
The change C occurred during a time and through a space terminating at the instant I at the surface S. The change K occurred during a time and through a space beginning at the instant I at the surface S. No change other than C occurred during the time and through the space of C, and no change other than K during the time and through the space of K. 11
But this proposal cannot be sustained. One problem with it, which Ducasse himself discusses, is that causation is not just a relation between the totality of states of affairs existing during some interval, and terminating at some surface at some instant, and the totality of states of affairs beginning at that surface and at that instant, and existing throughout some interval. Causation is a relation that holds between different parts of two such
totalities. Thus, to use Ducasse's own illustration, if a brick strikes a window at the same time that sound waves emanating from a canary do so, one wants to be able to say that it is the brick's striking the window that causes it to shatter. But this is precluded by Ducasse's analysis. 12 Ducasse's account is open to a number of other objections. Is it not logically possible, for example, for there to be spatio-temporal events which are uncaused? And is it not possible for there to be immaterial minds that have no spatial location, but who can communicate with one another 'telepathically'? Ducasse's account appears to exclude such possibilities. The objection that I wish to focus upon here, however, concerns the question of whether there can be causal action at a distance ~ i.e., whether two events that are separated, either spatially, or temporally, or both, can be causally related even if there is no intervening causal process that bridges the spatial and/or temporal gap between the two events. Ducasse's account implies that causal action at a distance is logically impossible. But is that really so? Ducasse's account is by no means the only one which entails that causal action at a distance is logically impossible, since Hume's own account, for example, has precisely the same implication. But other, more recent accounts of the concept of causation ~ such as Wesley Salmon's ~ also involve the idea that gappy causal processes are logically impossible. 13 But though this idea has been embraced by various philosophers, it seems clearly untenable. For, as I have argued elsewhere, one can surely imagine, for example, a world where the laws governing the transmission of light waves entail that light particles will exist only at some of the places along the line of travel. Insert a mirror at certain points, and the light ray would be reflected. Insert it at other points, and there would be no effect at all. Nor would there be any other ways of intervening at those points which would interfere in any way with the transmission of the wave. 14 My reason for mentioning this objection to Ducasse's analysis is that the fact that discontinuous causal processes are logically possible adds force to Hume's objection to a singularist conception of causation. To see why, consider the responses that can be made to Hume's argument. Two possible replies have already been mentioned, and rejected ~ the response, namely, that causation is itself a directly observable relation, so that the whole idea that an analysis is needed is wrong, and the response that causation is just succession plus
Michael Tooley
continguity, contrary to what Hume contends. But if neither of these replies is satisfactory, what, then, is left? One idea is to uncover what Hume himself failed to find - that is, some further observable property or relation. It is at this point that the possibility of discontinuous causal processes is relevant. For while the situation does not seem very promising if one assumes, with Hume, that there cannot be any spatial or temporal gap between a cause and its effect, it surely looks desperate indeed if an event at one time can cause an event at a much later time, in a remote part of the universe, with no intervening causal process. If causal situations can be as unconstrained as this, what observable relation - beyond that of temporal priority - can possibly hold between two causally related events? The prospects for a singularist account of causation may well seem hopeless at this point. It may seem that, if one is to find an account of causation, one must look beyond a given pair of causally related events. But if causation is simply a relation between two individual events, this possibility is precluded. It would seem, therefore, that a singularist conception of causation must be rejected. This conclusion is, however, mistaken. To see why, one needs only to get clear about precisely what the Humean argument establishes. In the first place, then, it shows, I believe, that causation is not directly observable in the relevant technical sense, and therefore that it cannot be a primitive, unanalysable relation between events. In the second place, it makes it at least immensely plausible especially when one considers the possibility of radical causal gaps - that causation cannot be reduced to observable properties of, and relations between, individual pairs of events. These two conclusions, however, do not suffice to rule out a singularist conception of causation. For one possibility remains: the possibility, namely, that causation is simply a relation between individual events, but one that is neither observable, nor reducible to observable properties and relations. Hume's line of argument therefore requires supplementation, if a singularist conception of causation is to be refuted. Specifically, one must either show that there is something special about causation which makes it the case that only a reductionist account will do, or else one must defend the completely general thesis that all properties and relations are either observable or else reducible to observable properties and relations. But neither route seems at all promising. For as regards the
former, the problem is that there just do not seem to be any arguments of that sort, while, as regards the latter, the thesis that there are no theoretical properties or relations at all is not tremendously plausible in itself, and the arguments that have been offered in support of it all seem to appeal, either openly or covertly, to some form of verification ism. The conclusion, accordingly, is that a Humean argument does not refute a singularist approach to causation. It shows at most that a singularist account needs to be combined with the view that causation is a theoretical relation between events. Should an advocate of a singularist account of causation be troubled by this conclusion? Not if the arguments advanced in section I.B are correct. For those arguments are not only arguments in support of a singularist conception of causation: they are also arguments against any reductionist approach to causation, and indeed, more powerful ones, since a reductionist approach to causation is incompatible with both singularist accounts and intermediate accounts of causal relations. The case against a reductionist approach to causation does not rest, however, simply upon the arguments advanced in section LB. For, as I have argued elsewhere, there are other very strong reasons for holding that no reductionist account of causation can be tenable, and reasons that are completely independent of whether a singularist account of causation is correct. 15 In a passage quoted earlier, Anscombe says that contemporary philosophers, in holding that causal relations presuppose laws, are guilty of dogmatic slumber. Now even if she were right in thinking that philosophers were slumbering here, the characterization of that as 'dogmatic' would not be fair, since the most that would be involved would be an assumption which philosophers had not in fact examined, rather than one which they were unwilling to examine. But, as the discussion in the present section has shown, Anscombe is not right on this matter. For the idea that a singularist account of causation is untenable is not an assumption that philosophers have made without any supporting argument. There is an argument, and one that goes back to Hume's discussion. It is, moreover, an argument that is very difficult to resist, unless one has a viable account of the meaning of theoretical terms - something that, in addition to being unavailable to Hume, has become available only in this century. It is true, nevertheless, that there is an unexamined assumption that is endemic in the philosophy
The Nature of Causation
of causation, but Anscombe has misdiagnosed its location. For, rather than its being the idea that causal relations presuppose causal laws, it is, instead, an assumption that Anscombe herself shares with those whom she criticizes - the assumption, namely, that causal relations, rather than being theoretical relations, are either themselves observable, or else reducible to other properties and relations that are.
3
The Positive Theory
In the first part of this paper, I have tried to do two main things: first, to show that a singularist account of causation is preferable to the alternatives; second, to determine in what general direction one should look in attempting to develop such an account. My argument in support of the preferability of a singularist account involved three main points. First, supervenience accounts of causation must be set aside, since they are exposed to decisive counterexamples. Second, other things being equal, singularist accounts of causation are preferable to intermediate accounts, since the latter necessarily involve a more complicated ontology. Third, the Humean objection to singularist accounts - an objection that may initially appear very strong indeed - turns out to rest upon an unexamined assumption, and one which, I have argued elsewhere, will not stand up under critical scrutiny - the assumption, namely, that causal relations are reducible to non-causal properties and relations. What form should a singularist account take? The main points that emerged with respect to this question were these. First, causation cannot be treated as a primitive relation, for it is not directly observable in the relevant sense. Second, a singularist theory of causation cannot attempt to reduce causation to non-causal properties and relations, since, although the Humean argument is not successful in ruling out a singularist account, it is, I believe, a very plausible argument for the conclusion that if causation is conceived of in singularist terms, then no reductionist account is possible. Therefore, third, the only hope for a viable singularist account of causation involves treating causal relations as theoretical relations between events. But, fourth, there is nothing disturbing about this conclusion, since there are independent grounds for holding that no
reductionist account of causation can be satisfactory.
A.
The basic strategy, and the underlying ideas
How is the concept of causation to be analysed? If causal relations are theoretical relations, then the starting point must be some theory that can plausibly be viewed as implicitly defining the concept of causation. Given such a theory, the next task will then be to convert the implicit definition that the theory provides into an explicit analysis. Exactly how the latter task is best carried out need not concern us at this point. What is relevant is simply that no method of analysing any theoretical term can be employed until a relevant theory involving that term is at hand. We need to develop, accordingly, a theory of causation. The relevant theory of causation must, in addition, be analytically true. For the goal is to set out an analysis of the concept of causation, and not merely to offer an account that is true of causation as it is in the actual world. The theory must be true of causation in all possible worlds. So none of the statements in the theory can be merely contingently true. The remainder of the present section will be concerned with isolating the basic ideas that can be used to construct an appropriate, analytically true theory of causation. The material is organized as follows. I begin by raising the question of precisely which causal relation, or relations, one should focus upon. Is there a single, basic causal relation, to which all other causal relations can be reduced? Or does one have to recognize distinct causal relations that are equally basic? Having determined which causal relation (or relations) one should focus upon, I then go on to consider the formal properties of the basic causal relation (or relations) in question. That might appear, initially, to be a relatively straightforward task, but we shall see that that is not entirely so. In any case, given a decision as to the formal properties possessed by some basic causal relation, the idea is that the analytically true statements in question can form part of the desired theory of that relation. Those formal properties will not suffice, however, to differentiate the causal relation in question from a number of non-causal relations. Nor, if it turns out that there is more than one basic causal relation, will the formal properties provide one with any account of what it is that makes all of
Michael Tooley
those distinct relations causal relations. Something more is needed, then, before one has a theory that suffices to capture the concept of a causal relation, and the crucial question is what that something more IS. If one were setting out a non-singularist account of causation, a natural move at this point would be to appeal to the idea that events cannot be causally related unless the relation is an instance of some law, and then to try to exploit this connection between causal relations and causal laws in order to construct a sufficiently strong theory. But this avenue is closed if it is a singularist account that one is after. So what can one appeal to at this point? The more one reflects upon this problem of developing a theory of causation for the singularist case, the more intractable it is likely to seem. But there is, I believe, a possible solution. Suppose that a singularist view of causation is correct, so that it is logically possible for there to be causally related events that do not fall under any law. It is then very tempting to think that it must be possible to characterize causation as it is in itself, without any reference to laws of nature. But perhaps this is a mistake. Perhaps our grasp of causation is inextricably tied to the distinction between causal laws and non-causal laws, so that causal relations just are those relations which are such that any laws involving them have certain properties - properties not possessed by non-causal laws. The idea, in short, is that it may be that the only way we have of characterizing causal relations is an indirect one, and one that involves the concept of a law of nature. If so, then the concept of causation is parasitic upon the concept of a law of nature. But this sort of conceptual dependence need not entail any ontological dependence. Events could still be causally related without falling under any relevant law. To implement this general idea, one needs to be able to point to a difference between laws that involve causal relations and laws that do not. One needs to find some further condition, T - beyond that of involving causal relations - such that it is an analytic truth that a law is a causal law if and only if it satisfies T. For given such a condition, one would then be able to characterize causal relations as those relations such that any laws involving them must satisfy condition T. Moreover, such a characterization would be perfectly compatible with the possibility of there being events that were causally related, even though the relation was not an instance of any law, since the fact that the intrinsic
nature of some relation is such that any laws involving it would necessarily have certain properties does not entail that, in order for the relation to be instantiated, there need be any laws involving it. Given this general strategy, the basic challenge is to come up with a plausible candidate for condition T. The specific suggestion that I shall advance is one that I have defended elsewhere, in connection with supervenience and intermediate accounts of causal laws. Fundamental causal relations Before attempting to set out a theory of causation, one needs to get clear about which causal relation or relations should feature in the theory. Is there a single basic causal relation, to which all causal relations, in all possible worlds, can be reduced? Or is it necessary to recognize distinct causal relations that are equally basic? How might one attempt to reduce all causal relations to a single, basic, causal relation? Two possibilities immediately come to mind. One involves treating direct causation as the basic relation, and then defining other causal relations - such as indirect causation, and causation in general - in terms of it. The other involves treating causation in general as the basic relation, and then defining both direct causation and indirect causation in terms of it. Would either of these reductions be satisfactory? I think not. In the case of the first, the problem is that any acceptable account of causation must apply to continuous causal processes, and this will not be the case for any theory in which all causal relations are to be reduced to direct causation. For in a continuous causal process, there are no events standing in the relation of direct causation, and therefore no relation that is definable in terms of direct causation can be instantiated in such a process. But what about the reduction of all causal relations to the relation of causation in general? Initially, this programme may seem more promising, since it might seem to be a straightforward matter to define both the concept of a continuous causal process and the concept of direct causation, given the concept of causation in general. But this, I think, is a mistake. One way of seeing the problem is by noticing that there are two rather different concepts of direct causation. According to one, a sufficient condition of A's being a direct cause of B is that A is a cause of B and there is no causally intermediate event. Direct causation, so conceived, can be reduced to the relation of causation in
The Nature of Causation
general. But there is another possibility. Causation might, so to speak, be quantized, so that there were cases where A caused B, and where, rather than its merely happening to be the case that there was no causal intermediary between A and B, the causal relationship that obtained between A and B was itself such as to preclude there being any causally intermediate event. 16 This latter situation involves a stronger type of direct causation, and one that is not, it would seem, reducible to the relation of causation in general. For suppose that one offered the following account: A causes B directly if and only if the general relation of causation obtains between A and B, and the world is such that it is a law that if the general relation of causation holds between events X and Y, there is no event Z such that the general relation of causation holds both between X and Z and between Z and Y. That definition would secure the right formal properties for the relation of direct causation, but it would suffer from two defects. First, the relation of causation in general is necessarily transitive, whereas in the above definition of direct causation one is postulating a law which entails that causation in general is not transitive. Second, this definition of direct causation entails that in a world where some events are directly caused by others, absolutely all causal relations must be quantized. It therefore would preclude the possibility of a world where some causal relations were quantized, and others not. Given that the strong relation of direct causation - which precludes the existence of causally intermediate events - cannot be reduced to the relation of causation in general, or vice versa, the prospects for reducing all causal relations to some single, basic causal relation do not seem promising. It seems to me that one must recognize the possibility of at least two basic causal relations: first, that of direct causation, of the strong, quantized sort, and second, that of causation of the sort involved in continuous causal processes - what might be referred to as non-discrete causation. The approach that I shall adopt, accordingly, will be to set out a theory of causation that, rather than focusing upon some specific causal relation, functions simply to explain what it is to be a causal relation. Any specific causal relation can then be defined in terms of the additional properties that serve to distinguish it from other causal relations. Formal properties of causal relations What properties distinguish one causal relation from another? A
natural answer is that certain formal properties do so. Thus, it might seem to be true by definition, for example, that the relation of non-discrete causation is a dense relation, whereas the relation of direct, quantized causation is not. That is to say, for any states of affairs X and Y, if X stands in the relation of non-discrete causation to Y, then there must be some state of affairs, Z, such that X stands in that relation to Z, and similarly for Z and Y. Similarly, it might also seem to be a necessary truth that nondiscrete causation is transitive, while direct, quantized causation is not. The idea that different causal relations are to be individuated by reference to their differing formal properties may seem plausible. Some care is needed, however, on this matter. Consider, first, the question of transitivity. Is it really the case that non-discrete causation is transitive? Initially, an affirmative answer may seem obviously correct. But there is a somewhat subtle objection that can be directed against the proposition that nondiscrete causation is transitive - an objection that is perhaps best developed by considering an analogous case. Suppose that the correct account oflaws is in terms of relations among universals, and that, in particular, there is some second-order relation N such that if N holds between properties P and Q then it is a law that anything with property P has property Q Suppose, further, that N holds between P and Q and between Q and R. Then it will be a law that everything with property P has property Q and also that everything with property Q has property R. But if so, it must also be a law that everything with property P has property R. Does this mean that properties P and R must also stand in relation N? It is not easy to see any reason why this need be so. The conjunctive state of affairs consisting of P and Qs standing in relation N, together with Q and R's standing in relation N, would seem perfectly sufficient to make it a law that anything with property P has property R. This view may very well be correct in the case of laws. But if so, should not one adopt the same view in the case of the relation of non-discrete causation? That is to say, assume that that relation holds between events P and Q and also between Q and R. Is not that conjunctive fact sufficient to make it true to say that P caused R, without one's having to postulate that events P and R are themselves united by the relevant causal relation? This objection, though initially plausible, cannot be sustained. For, first of all, notice that one cannot maintain that whenever P causes R via some other
Michael Tooley
event Q, the relevant causal relation cannot hold between P and R. For that would entail that in a continuous causal process there would be no events that were causally related. There must, accordingly, be cases of three events - P, Q, and R where there is a causal relation that holds between P and Q, between Q and R, and also between P and R. Second, in such a case, how is one to think of the three instances of the causal relation? As three states of affairs that are unrelated except as involving the same individuals, and the same causal relation? This is not, I suggest, plausible, for it fails to capture the fact that the third state of affairs is logically supervenient upon the other two. A much more natural view, and one that does capture that supervenience, is to view the third state of affairs as containing the other two states of affairs as parts. An analogy may be helpful. Consider the relation between two points when there is some pathway connecting them, and suppose that points A and C are connected because, and only because, A is connected to B, and B to C. Then the path from A to C can be broken down into two parts, one of which is the path from A to B, and the other the path from B to C. In similar fashion, I am suggesting that when P causes R because, and only because, P causes Q, and Q causes R, the right way to think of the situation is to view the causal connection between P and R as decomposable into two parts - the causal connection of P to Q, and that of Q to R. But if, in a given case, the relation of non-discrete causation is thus decomposable into parts, then it would seem that composition of appropriately related parts should also result in an instance of the relation in question. That is to say, if the relation of non-discrete causation holds between P and Q, and between Q and R, then it must also hold between P and R, since the latter state of affairs need be nothing over and above the combination of the other two states of affairs. Non-discrete causation, considered as a real relation, as a genuine universal, must therefore be transitive. The relation of direct causation, on the other hand, obviously need not be transitive. But is it also true that it cannot be transitive? The problem with the latter claim is that there does not seem to be any reason why P's being a direct cause of Q, together with Q's being a direct cause of R, should be incompatible with P's also being a direct cause of R. For why might not one event cause another
event both directly and indirectly? But if this can sometimes be the case, then it would seem that there must be possible worlds in which it is always the case, and in which, therefore, direct causation is transitive. So transitivity will not always serve to distinguish between non-discrete causation and direct causation. But while transitivity itself will not do, the idea of there being, so to speak, different causal pathways connecting two states of affairs suggests that a slightly different property will serve to distinguish between direct causation and non-discrete causation. Consider some state of affairs in virtue of which event X stands in the relation of non-discrete causation to event Y, and where the state of affairs has no proper part that has that property, and similarly, a minimal state of affairs in virtue of which event Y stands in the relation of non-discrete causation to event Z. Then the combination of those two states of affairs necessarily makes it the case that event X stands in the relation of nondiscrete causation to event Z. The relation of non-discrete causation has what I shall refer to as the property of being intrinsically transitive. Direct causation, by contrast, lacks this property: the combination of a minimal state of affairs in virtue of which X directly causes Y with one in virtue of which Y directly causes Z is never in itself a state of affairs in virtue of which X directly causes Z. Direct causation can never be intrinsically transitive. What about the other property mentioned above - namely, that of being a dense relation? Will it serve to distinguish between the two causal relations? That non-discrete causation is necessarily dense seems unproblematic. But what about direct, quantized causation? Does it necessarily lack that property? The situation appears to be the same as with transitivity. That is to say, it would seem that while direct causation need not be a dense relation, one can describe possible worlds in which it would, as a matter of fact, have that property. But here, too, one can shift to a slightly different notion that of being intrinsical~y dense - where to say that a relation R is intrinsically dense is to say that any state of affairs, S, in virtue of which X stands in relation R to Y, can always be divided into proper parts, S1 and S2, such that, for some Z, X stands in relation R to Z, and Z in relation R to Y, in virtue of S1 and S2, respectively. One can then say that non-discrete causation is an intrinsically dense relation, whereas direct causation is not.
The Nature of Causation
It seems plausible, then, that different causal relations can be distinguished by reference to their different formal properties. But can a consideration of formal properties also playa role in the construction of the general account of what it is to be a causal relation? If this is to be so, there will presumably have to be formal properties that are common to all causal relations. That there are certain formal properties that any causal relation must necessarily possess is, I think, both a rather natural view, and one quite widely accepted in philosophical discussions of causation. In particular, I think that it is tempting to hold that all causal relations must have the following three formal properties. First, causal relations are irreflexive: no state of affairs can ever be the cause of itself. Second, causal relations are asymmetric: if A causes B, then it cannot be the case that B causes A. Third, causal loops are impossible. There cannot, for example, be three events, A, B, and C such that A causes B, B causes C, and C causes A. But this view can certainly be challenged. One way of doing so is by arguing that time-travel into the past is logically possible, and that if it is, then local causal loops must also be logically possible. For if Mary can travel back into the past, what prevents her from, say, marrying her maternal grandfather, and then later giving birth to her own mother?17 Alternatively, one can argue that global causal loops are possible - that is to say, that there could be a world where the total state of the universe at one time - call it A - would causally give rise to a sequence of total states which, though all qualitatively distinct for perhaps a very long time indeed, would lead, in the end, to a state that was not only qualitatively indistinguishable from A, but identical to it. 18 On the other hand, a number of philosophers, such as Antony Flew, Max Black, David Pears, Richard Swinburne, Hugh Mellor and others, have tried to show either that the idea of backwards causation is not coherent - thus ruling out the possibility of local causal loops - or, alternatively, that no causal loops at all are possible, be they local or global. 19 Some of the arguments appear either to be question-begging or to depend upon the assumption that a tensed view of time is correct, but others are both neutral on the question of the nature of time and more promising. Nevertheless, I think it is very doubtful whether any of the arguments succeeds in establishing the desired conclusion.
I cannot defend that judgement here, but let me illustrate it by reference to one of the more interesting arguments - that advanced by Hugh Mellor. The thrust of Mellor's argument is that the impossibility of backwards causation can be established by appealing to the proposition that a cause must raise the probability of its effect. An initial objection to this argument is that there are counterexamples to the general thesis that causes raise the probabilities of their effects. 2o This first objection, however, can be gotten around, since it is possible to set out postulates for causal laws that will enable one to derive modified versions of the claim that causes are positively relevant to their effects - versions which will not be exposed to any straightforward counterexamples, and which will still provide the basis for a proof that causal loops are impossible. 21 But now another objection can be pressed, for it can be argued that, if causal loops are possible, then one of the crucial postulates that is needed to establish the probability claim is not acceptable. 22 So the issue then becomes whether it is possible to offer grounds for accepting that postulate which will not beg the question of the possibility of causal loops. I shall not pursue this issue here. For while I think that the question of the possibility of causal loops is a fundamental one, it does not seem crucial with respect to the theory of causation that I am setting out here. For my general approach can, I believe, be tailored to either view. What I shall do, accordingly, is to adopt the position that seems to me most plausible - namely, the view that causal loops are not possible - and set out the account that is appropriate, given that assumption. I shall then indicate how the account would need to be modified, if it turned out that that assumption was incorrect.
The problem o/completing the theory In what follows it will be assumed, then, that all causal relations are irreflexive, asymmetric, and such as cannot enter into causal loops. These formal properties do not suffice, of course, to distinguish causal relations from a number of other relations. Consider, for example, the relation of temporal priority. If causal relations have the above formal properties, then I think it is plausible to hold that temporal priority does so as well. Or consider the inverse of any causal relation - such as the relation of being caused by. Since the inverse of any relation possessing the above properties must also possess those properties, the relation of being caused by must
Michael Tooley
also be irreflexive, asymmetric, and such as cannot enter into loops. What, then, can we add to the theory of causation so that it is satisfied by causal relations, but not by their inverses, or by any other relation? This is not an easy question, but one way of approaching it is by asking what account is to be given of the direction of causation, since, in distinguishing between causal relations and their inverses, the theory must necessarily incorporate some explanation of the direction of causation. Elsewhere, I have surveyed the main accounts that have been offered of the direction of causation, and I have argued that none of them is tenable. 23 But there is another account that can be offered an account to which I shall be turning shortly which is, I believe, satisfactory. For in addition to escaping the objections to which other accounts fall prey, it rests upon an underlying idea which has a strong intuitive basis, it can generate the desired formal properties for causal relations and causal laws, and it provides the basis for a satisfactory account of the epistemological justification of our causal claims. In Causation, I was only able to show how the alternative approach to the direction of causation could be carried through for the supervenience and intermediate views, for none of the avenues that I explored in an attempt to develop a singularist account proved successful. The problem was, however, that I was implicitly assuming that if causal relations do not presuppose causal laws, then an analysis of what it is to be a causal relation should not involve the concept of a law. But while this is a rather natural assumption, it is in fact false, and once it is set aside, there is no longer any barrier to developing a singularist account. Causal relations and causal laws: exploiting the conceptuallink The objective is to find a set of analy-
tical truths involving the concept of causation that, taken together, will constitute a theory which implicitly defines what it is to be a causal relation. Some analytical truths are already at hand namely, those concerning the formal properties of causation. But as they are obviously not sufficient, the problem is how to supplement them. As I indicated earlier, the solution that I am proposing is as follows. First, if a singularist account of causation is correct, then there is a connection between the concept of a causal law and that of causal relations. For on a singularist view, causal laws are nothing more than laws that
involve causal relations. As a consequence, given a singularist view, one can characterize causal relations as those relations whose presence in a law makes that law a causal one. Such a characterization will not, of course, shed any light upon causal relations if one cannot say anything about causal laws beyond the fact that they are laws involving causal relations. My second point, however, is that that is not the case. For one can specify an independent constraint T, such that something is a causal law if and only if it satisfies T. If the latter point can be sustained, then it will be possible to set out an analysis of the concept of causation. For causal relations will simply be those relations that have certain formal properties, and which are such that any laws involving them must satisfy condition T. Causal laws: the underlying intuition The problem of setting out a singularist analysis of causation reduces, therefore, to that of finding an appropriate constraint upon causal laws. But if that is right, then the prospects for a singularist account of causation would seem promising. For once one is dealing with causal laws, it would appear to be a straightforward matter to modify the basic account that I have offered elsewhere in the case of supervenience and intermediate approaches to causation. What is it that makes something a causal law? Reflection upon certain simplified situations suggests, I believe, a very plausible answer. Imagine, for example, the following possible world. It contains two radioactive elements, P and Q, that, in every sort of situation but one, exhibit half-lives of five minutes and ten minutes respectively. However, in one special sort of environment - characterized by some property R - an atom of type P undergoes radioactive decay when and on(y when one of type Q also decays. Now, given such facts, a natural hypothesis would be that the events in question are causally connected. Either (I) the decay of an atom of type P is, in the presence of property R, both causally sufficient and causally necessary for the decay of an atom of type Q, or (2) the decay of an atom of type Q, in the presence of property R, is both causally sufficient and causally necessary for the decay of an atom of type P, or (3) there is some property S which is, given property R, causally sufficient and causally necessary both for the decay of an atom of type P and for the decay of one of type Q. But which of these causal connections obtains? Given only the above informa-
The Nature of Causation
tion, there is no reason for preferring one causal hypothesis to the others. But suppose that the following is also the case: in the presence of property R, both clement P and element Qhave a halflife of five minutes. Then surely one has good grounds for thinking that, given the presence of property R, it is the decay of an atom of type P that is both causally sufficient and causally necessary for the decay of an atom of type Q, rather than vice versa, and rather than there being some other property that is involved. Conversely, if it turned out that, in the special situation, each element had a half-life of ten minutes, one would have good grounds for thinking instead that it was the decay of an atom of type Q that, given the presence of property R, was both causally sufficient and causally necessary for the decay of an atom of type P. In the former case, the observed facts suggest that atoms of type P have the same probability of decaying in a given time period in the special situation that they have in all other situations, while atoms of type Q do not. On the contrary, atoms of type Q appear to have, in the special situation, precisely the same probability of decay as atoms of type P. So the probability of decay has, so to speak, been transferred from atoms of type P to atoms of type Q It is this, I suggest, that makes it natural to say, in that case, that it is the decay of atoms of type P that is, in the presence of property R, both causally sufficient and causally necessary for the decay of atoms of type Q The direction of causation coincides, therefore, with the direction of transmission of probabilities. The basic idea, accordingly, is to characterize causal laws in terms of the transmission of probabilities. Talk about the 'transmission of probabilities' is, of course, a metaphor, and one needs to show that that metaphor can be cashed out in precise terms. I shall turn to that task in the next section.
B.
The theory
A brief recap may be helpful at this point, so that the overall structure of my approach is clear. If a singularist account of causation is to succeed, causation must be treated as a theoretical relation between events. We need, accordingly, a theory of causation. That theory, moreover, must consist of analytically true statements, if it is to provide the basis for an analysis of the concept of causation. The basic theory which I shall be proposing - at least in its initial formulation - will involve two
sorts of elements: first, statements concerning the formal properties of causal relations; second, statements that place constraints upon causal laws, by connecting causal laws with probabilities. Causal relations can then be defined as those relations that satisfy the theory question. Causal laws: capturing the intuition How can we express, in a precise way, the intuitive idea presented in the previous section concerning the relation between causal laws and relevant probabilities? The answer is provided, I believe, by the postulates described below. 24 In setting out those postulates, I think it will be best to proceed in two steps. First, I shall formulate a set of postulates that captures, in a simple and natural way, the fundamental intuition concerning causal laws. Second, I shall show how those postulates can be modified slightly to produce postulates that are equally natural, but more powerful. The first set of postulates would appear to be adequate for our purposes. For when combined with appropriate statements concerning the formal properties of causal relations, the result is a theory that can be used to explain what it is to be a causal relation. But the second set of postulates provides, I believe, an account that is in a certain respect more satisfying, since it allows one to dispense with any explicit reference to the formal properties that are shared by all causal relations. In order to set out the postulates in a more perspicuous fashion, it will be helpful to use a little notation. First, we need a way of representing the fact that two states of affairs (or events) are causally related. I shall use the term 'C' as the relevant predicate, and, to represent a state of affairs, I shall place square brackets around a sentence describing that state of affairs. 25 So, for example, the sentence 'C[Pa][Qb], will say that the state of affairs (or event) that consists of a's having property P causes the state of affairs (or event) that consists of b's having property Q Next, we need to have a perspicuous way of representing causal laws. Now on a singularist approach to causation, in contrast to a supervenience one, statements expressing causal laws involve reference to some causal relation, so that a typical statement of a causal law might be: 'It is a law that if anything, x, has property P, then x's having P causes it to be the case that there is some other thing,y, such thaty stands in relation R to x, andy has the intrinsic property I.' If we use standard logical notation, plus '0' as an abbreviation for
Michael Tooley
'it is a law that', together with the notation just introduced for the representation of causal relations between states of affairs, the preceding statement could be expressed as:
o (x)(Px :J C[Px][3y)(y # x & Ryx & Iy)]). But this is still very cumbersome. One way of improving things is to introduce predicates that attribute relational properties to individuals. Thus, if one defines 'Qx' as equivalent to
(3y)(y
# x & Ryx &
Iy),
the above statement can be rewritten as:
o (x)(Px :J C[Px][Qx]). Even with this simplification, however, the postulates needed for causal laws will still be rather messy. But further simplification is obviously possible, since all that the relevant expression really needs to do is to indicate that we are dealing with a statement of a causal law, and to refer to the intrinsic property P, and to the relational property Q I shall, accordingly, employ the expression 'P -> Q' as an abbreviation of the above statement. This will enable me to set out the postulates for causal laws in a considerably more perspicuous fashion. Not all causal laws need have the same finegrained logical structure as that of the above. There can, for example, be causal laws where the state of affairs that is the cause involves a number of individuals, having various intrinsic properties, and standing in various relations to one another. But statements of such laws can easily be viewed as having the same basic logical form as the above. For the individuals over which the variable, 'x', ranges need not, of course, be simple entities. They may, instead, be complex individuals, consisting of a large number of simpler individuals. Another possibility is that of causal laws of the following form:
D(x)(Px:J C[Px] (3y) (y
# x & Iy)]).
Here, in contrast to the type of causal law considered above, there is no specification of how x and y are related. But this does not make any difference with respect to the basic logical form of the statement, since by defining 'Qx' as equivalent to
(3y)(y
# x&
Iy),
the above statement can be seen to have the form:
D(x)(Px:J C[Px][Qx]). A final possibility worth mentioning is that of causal laws of the following form:
D(x)(Px:J C[Px][Ix]). Here, in contrast to the previous cases, the same individual is involved in the effect as in the cause: an individual's having property P causes it to have property I. But this, too, does not affect the basic logical form. For in the first place, one could simply allow property Q to be either a relational property or an intrinsic one. Alternatively - and this is the approach that I favour - one can argue that, properly viewed, laws of the present sort also involve relational properties. For, although I cannot defend these claims here, I believe that it can be shown, first, that a cause can never be simultaneous with its effect, and second, that enduring individuals are reducible to causally related, momentary individuals. If these two claims can be sustained, then causal relations between states of affairs involving a single enduring individual are, at bottom, causal relations between states of affairs that involve different temporal parts of that individual. A third thing that is needed is a way of referring to relations of logical probability. I shall use the expression 'Prob(Px, E) = k' to do that. It is to be interpreted as saying that the logical probability that x has property P, given only evidence E, is equal to k. Finally, we need to refer to information of a certain restricted sort - specifically, information that is either tautological, or that concerns only what causal laws there are. I shall use the term 'L' for that purpose. Given the above notation, one natural formulation of the desired postulates for causal laws is this:
(C 1): Prob(Px, P -> Q & L) = Prob(Px, L) (C2): Prob(Qx,P -> Q & L) = Prob(Px, L) + Prob(~ Px, L) x Prob(Qx, ~ Px & P -> Q & L) (C 3 ): Prob(Qx, ~ Px & P -> Q & L) = Prob(Qx,~ Px & L) (C4): Prob(Qx, P -> Q & L) = Prob(Px, L) + Prob(~ Px, L) x Prob(Qx, ~ Px & L)
The Nature of Causation
These postulates are essentially somewhat simplified versions of ones that I set out elsewhere in developing a supervenience account of causation. There I discussed, in a fairly detailed way, the line of thinking that leads to the specific postulates in question. 26 So perhaps it will suffice here simply to note the central considerations. Postulate (C 1) states that if the prior probability that some individual will have property P, given only information that is restricted to logical truths and statements of causal laws, has a certain value, then the posterior probability of that individual's having property P, given the additional information that the possession of property P causally gives rise to the possession of property Q, must have precisely the same value. Postulate (C 1) therefore asserts, in effect, that the posterior probability of a state of affairs of a given type is, in the situation described, not a function of the prior probability of any state of affairs of a type to which states of affairs of the first type causally give rise. Postulates (C2 ), (C3), and (C4 ) deal with the posterior probability of a state of affairs, given information to the effect that it is a state of affairs of a type that is causally brought about by states of affairs of some other type, together with prior information that is restricted in the way indicated above. The first of these three postulates asserts that, given the additional information that the possession of property P causally gives rise to the possession of property Q, the posterior probability that some individual has property Q is, in the way indicated, a function of the prior probability that that individual has property P. Postulate (C2 ) does not, however, express that dependence in the clearest way, since it involves, on the right-hand side, a probability that is also conditional upon the information that the possession of property P gives rise to the possession of property Q It is for this reason that postulate (C3) is part of the theory, for it makes it possible to derive a statement in which the relevant posterior probability is expressed in terms of prior probabilities alone. Postulate (C3 ) asserts that if the prior probability that some individual will have property Q, given only information that is either tautologous or else restricted to statements of causal laws, has a certain value, then the posterior probability of that individual's having property Q - given the additional information both that the possession of property P causally gives rise to the possession of property Q, and that the individual does not have property P
- must have precisely the same value as the prior probability. (C 3 ), together with (C2 ), then entails (C4 ), which does express the posterior probability that an individual will have property Q in a way that involves only prior probabilities. The crucial content of the above theory of causal laws is expressed, accordingly, by postulates (C 1) and (C4 ). For (C 1) expresses the fact that the logical probability that a given state of affairs will obtain, given information about the types of states of affairs that are caused by states of affairs of that type, does not differ from the prior probability, upon evidence of a certain restricted sort, that the state of affairs in question will obtain. Its posterior logical probability cannot, therefore, be a function of the prior logical probabilities of states to which it causally gives rise. But by contrast, as is indicated by postulate (C4 ), the posterior logical probability of a given state of affairs is a function of the prior logical probability of any state of affairs of such a type that states of affairs of that type causally give rise to states of affairs of the first type. The relation between posterior probabilities and prior probabilities is, in short, different for causes than for effects. The above theory of causal laws could be formulated more economically. For not only does (C4 ) follow from (C2 ) and (C3 ), as was noted above, but, in addition, (C2) is not an independent postulate either, since it follows from (C 1 ) by means of the probability calculus. One could, therefore, cut back to postulates (Cl) and (C3 ) if one wanted a more succinct formulation. However, it seems to me that, in the present context, explicit expression of the basic ideas is more important than economy. I have attempted to motivate postulates (Cd through (C4 ) by appealing to the idea that there is a connection between the direction of causation and what I have referred to as the direction of transmission of probabilities. But as I mentioned earlier, the case for those postulates does not rest upon that intuition alone, for there are at least three other grounds of support. First, reductionist accounts of the direction of causation are open to decisive objections - objections that an account based on postulates (Cd through (C4) totally avoids. Second, those postulates - or, rather, the strengthened versions of them that I shall be setting out shortly - generate the desired formal properties for causal relations. Third, the above postulates also serve to explain how justified beliefs concerning causal relations are possible.
Michael Tooley
It will not be possible here to discuss these considerations in a detailed way. I shall, however, touch upon the second and third points in later sections. 27 I mentioned earlier that, although the postulates just set out appear to provide a perfectly sound basis for an account of causal relations, a strengthening of those postulates makes possible an analysis that is in a certain respect more satisfying. In addition, the strengthened postulates will help to make it clearer precisely how the theory that I am setting out would need to be modified if one decided that, contrary to what I am assuming, causal relations need not be asymmetrical. So let me indicate, very briefly, how the postulates can be strengthened. The basic idea is simply this. Postulates (C 1) through (C4 ) all refer to laws expressed by statements of the following form:
- associated with the ancestral of the causal relation in question. The idea then is that there should be postulates that are comparable to (Cd through (C4) except that they concern laws expressed by statements of the following form:
D(x)(Px =:J C*[Px][Qx]). Here, as before, it will make the postulates more perspicuous if we have an abbreviated way of expressing the law-statements in question. I shall use the expression 'P ->*Q' to do so. The required postulates can then be formulated as follows: (C~):
Prob(Px,P ->*Q & L)
It seems clear that postulates that are comparable to (C 1 ) through (C4 ) should hold when references to laws of the former sort are replaced by references to laws of the latter sort. For after all, in a world where causal processes exhibit continuity, the connection between x's having property P and x's having the relational property Q will involve causally intermediate states of affairs. But if the existence of causal intermediaries does not, in the case of laws of the simpler sort, block the transmission of probabilities, then it would seem that law-statements of the slightly more complex sort, where there is an explicit reference to a two-step causal chain, should also enter into corresponding postulates dealing with the relation between posterior probabilities and prior probabilities. Granted this, the next point is that there is, of course, nothing special about two-step causal processes. If the appeal to continuity in the case of the simplest laws justifies the conclusion that there must be corresponding postulates for law-statements that involve explicit reference to a two-link causal chain, then it must equally justify the corresponding conclusion for law-statements that involve explicit reference to causal chains containing an indefinite number of links. The natural way of representing laws of the latter sort is by introducing a predicate - say, 'C*'
Prob(Px,L)
(C;): Prob(Qx,P ->*Q & L) =
Prob(Px, L)
+ Prob( ~ Px, L)
x Prob(Qx, ~ Px & P ->*Q & L)
o (x)(Px =:J C[Px][Qx]). Suppose, however, that one considers, instead, laws expressed by statements ofthe following form:
=
(C;): Prob(Qx, ~ Px & P ->*Q & L) = Prob(Qx, ~ Px & L) (C~): Prob(Qx,P ->*Q & L) = Prob(Px,L) + Prob(~ Px,L) x Prob(Qx, ~ Px & L) Though (Cj) through (C~) are stronger than (Cd through (C 4 ), it seems to me that the case for accepting them, if one accepts (Cd through (C4), is very strong indeed. For expressed very briefly, it is simply this. If all causal relations must satisfy (C 1) through (C 4 ), then the ancestral of a given causal relation could fail to satisfy (Cd through (C 4 ) only if the ancestral was not itself a causal relation. But if the ancestral of a given causal relation satisfies (Cd through (C4 ), then (Cj) through (C~) must be true of the relation in question. Therefore, if all causal relations must satisfy (Cd through (C 4), the only way that any of them can fail to satisfy (Cj) through (C~) as well is if there are causal relations whose ancestrals are not causal relations.
or
the concept of causation It is now a straightforward matter to set out an analysis of the concept of causation. For by combining statements concerning the formal properties of causal relations with, for example, the first set of postulates for causal laws set out above, one has a theory of causation that consists entirely of analytically true statements, and, given such a theory, one need merely appeal to whatever one takes to be the correct method of defining theoretical terms in
An analysis
The Nature of Causation
order to generate an analytical account of what it is to be a causal relation. The method of analysing theoretical terms that seems to me correct is that suggested by F. P. Ramsey's approach to theories, and later developed in detail by David Lewis. 28 Let me briefly indicate, therefore, how things proceed if one adopts a Ramsey/Lewis approach.29 The basic idea is to define causal relations as those relations that satisfy a certain open sentence. We need, therefore, to transform the above theory of causation into a single sentence, containing occurrences of an appropriate variable. Doing so involves three steps. First, the individual sentences of the theory are all conjoined, so that one has a single sentence. Second, wherever the theory involves an expression of the form 'Cst' - which says that a certain causal relation holds between state of affairs s and state of affairs t - one replaces the expression by an onto logically more explicit one that contains some term - say, 'c' - that denotes the causal relation in question. The new expression will thus say that the causal relation in question obtains between sand t. This shift to terms that refer to the causal relation then makes possible the third and final step, which involves replacing all the occurrences of' c' by occurrences of some variable - say, 'v'. With that replacement, one has arrived at the open formula that one needs, and one can then define a causal relation as any relation that satisfies that open formula. The open formula depends, of course, on precisely what one incorporates into the theory of causation. One possibility is to include statements expressing all of the formal properties that are common to all causal relations, together with the first set of postulates for causal laws. In that case, if we let Tbe the open sentence that results when the above procedure is applied only to the relevant postulates for causal laws - that is, to statements (Cd through (C4 ) - we would have the following account of what it is to be a causal relation: A causal relation is any relation between states of affairs which is irreflexive and asymmetric, which excludes loops, and which satisfies the open sentence, T. But this account can obviously be simplified, since if a relation cannot enter into loops, then it must be asymmetric and irreflexive. So the above analysis can be expressed more succinctly as follows:
A causal relation is any relation between states of affairs which cannot enter into loops, and which satisfies the open sentence, T. Can the analysis be condensed even more? The answer is that it can be, provided that one shifts to the second, and stronger set of postulates, (Cj) through (C:). For, then, if T* is the open sentence that results when the above procedure is applied to postulates (Cj) through (C';), all reference to the formal properties that are shared by all causal relations can be dropped, and the following analysis can be offered: A causal relation is any relation between states of affairs which satisfies the open sentence, T*. How does the shift to postulates (CD through (C';) make possible this simplified formulation? The answer lies in an argument whose structure is as follows. First, it can be argued that any genuine relation is necesarily 'directly irreflexive'. Second, assume that there is some causal relation that is not asymmetric. Since any relation is directly irreflexive, it follows that there is some causal relation that is not anti-symmetric - where a relation R is antisymmetric just in case one cannot have both xRy and yRx unless x is identical with y. But third, if there is some causal relation that is not anti-symmetric, then it must be possible for there to be causal laws that are not anti-symmetric. However, it can be shown, fourth, that any laws that satisfy postulates (Cj) through (C:) must be anti-symmetric. So the assumption that there is some causal relation that is not asymmetric leads to a contradiction, and hence must be rejected. Fifth, a precisely parallel argument can be used to show that no causal relation can enter into loops. That is to say, the assumption that some causal relation can enter into loops leads to the conclusion that causal laws can enter into loops - something which is also ruled out by postulates (Cj) through (C:). In short, it follows from the above account of what it is to be a causal relation that causal relations must be asymmetric, and that they cannot enter into causal loops. I shall not attempt to develop this argument in a detailed way, but let me comment briefly on some of the steps involved. The first one involves the claim that any genuine relation is necessarily directly irreflexive. What does this claim come to, and what reason is there for accepting it? As regards the content, I need to explain what is meant by a genuine relation, and what it is for
Michael Tooley
a relation to be directly irreflexive. First, then, the concept of a genuine relation. This is tied up with a distinction between concepts and universals where the latter, rather than being mind-dependent entities, are features of the world which are the basis of objective, qualitative identity. Given this distinction, one can ask whether it need be the case that, corresponding to any given concept, there is a single universal. The answer, surely, is that this need not be so: a given concept may be applicable to something in virtue of any number of distinct properties. But if this is so, then, in some of the cases where one speaks of a relation, there will be a relational concept, but no single universal corresponding to that concept. When I refer to a genuine relation, I am referring to something which is a universal, and not to a relational concept. Now it is sometimes claimed that all genuine relations are necessarily irreflexive 30 - a contention that might be supported by an argument along the following lines. Consider a relational concept that is reflexive, such as that of simultaneity. If E and F are distinct events, and if E is simultaneous with F, then the latter state of affairs may well involve a dyadic universal. By contrast, the state of affairs that consists of E's being simultaneous with itself surely does not involve the instantiation of any dyadic universal: the mere existence of E itself is sufficient to guarantee that it is simultaneous with itself. But this argument, tempting though it is, is flawed, as can be shown by a simple example. Consider the relation - call it spatial accessibility - that obtains between two locations, A and B, when there is a path along which one can move from A to B. Now every location, of course, is trivially accessible from itself, in virtue of the path of zero length consisting of the location in question. But a location may also be spatially accessible from itself in virtue of a path leading to some other point, together with a path - possibly the same one, possibly a different one - leading back to the original point. So a point may be accessible from itself in a way that is not trivial, and which might well involve the instantiation of a dyadic universal. In general, the objection to the thesis that all genuine relations are necessarily irreflexive is that it would seem that there could well be genuine relations that are transitive but not asymmetric, and in such cases something could well stand in a genuine relation to itself. But while this refutes the original thesis, it also points towards a revision that avoids the objection.
What one needs to do is to draw a distinction between a relation's being irreflexive and its being directly irreflexive, where to say that a relation R is directly irreflexive is to say that it can be the case that xRx only if xRx holds in virtue of the fact that R is transitive, together with the fact that there is somey such that both xRy andyRx. It can then be claimed - plausibly, I believe - that genuine relations are, necessarily, directly irreflexive. The second step in the argument involves assuming that there can be a causal relation that is not necessarily asymmetric - the intention being to show that that assumption leads to a contradiction. Given this assumption, it immediately follows, in view of the thesis that all genuine relations are directly irreflexive, that there can be a causal relation that is not necessarily anti-symmetric. For if state of affairs S causes state of affairs U, and vice versa, it will follow, unless S is identical with U, that the relation is not anti-symmetric. But if S is identical with U, then in virtue of the property of direct irreflexivity, there must be a state of affairs T that is distinct from S, such that S causes Tand T causes S. So regardless of whether S is identical with U or not, the causal relation in question will be anti-symmetric. To assume that some causal relation is not necessarily asymmetric forces one to assume, therefore, that there can be distinct properties, P and Q, and an individual, a, such that the state of affairs EPa] causes the state of affairs [Qa], and vice versa. But if there can be such a world, then it would seem that there could be a world where, first, there were a large number of things with property P, and second, every state of affairs of the form [Px] caused a state of affairs [Qx], and vice versa. If one is a realist about laws, of course, the truth of a generalization, even one involving a very large number of instances, does not ensure the existence of a corresponding law. However, if laws are relations among universals, then it would seem that if there can be worlds where certain generalizations are all true, and where none of the generalizations involve essential reference to individuals, or 'gruesome' predicates, etc., then there can also be worlds where the same generalizations are not only true, but true in virtue of underlying relations among universals, and so express laws. If this is right, then the possibility of a world where there are a large number of things with property P, and where every state of affairs of the form [Px] causes [Qx], and vice versa, entails the possibility of a world where it is a causal law that,
The Nature of Causation
for all x, x's having property P causes x to have property Q, and also a causal law that for all x, x's having property Q causes x to have property P. What has been shown, therefore, is that the assumption that there can be a causal relation that is not asymmetric leads to the conclusion that causal laws need not be characterized by antisymmetry. But - and this brings me to the fourth step in the argument - the above theory of causation asserts that all causal laws must satisfy postulates (Cn through (C:). The question then becomes whether those postulates are compatible with anti-symmetry's not holding for laws. The answer is that they are not. For I have shown elsewhere, for a set of postulates that are weaker than postulates (C~) through (C:) in all respects that are relevant to the proof, that any laws satisfying the postulates in question must be anti-symmetric. 31 The assumption that some causal relation might not be asymmetric leads, therefore, to a contradiction. Any causal relation that satisfies postulates (Cn through (C~) must be asymmetric. A parallel argument can be offered with respect to the possibility of causal loops. That is to say, if one assumes that there is some causal relation that can enter into causal loops, one can argue that it follows that it must be possible for there to be a world where there are causal laws that exhibit a loop structure. It can be shown, however, that postulates (Cj) through (C:) entail that such loops, involving causal laws, are impossible. 32 It therefore follows that no causal relation which satisfies postulates (Cj) through (C4) can enter into causal loops. Finally, the fact that causal loops are impossible, together with the fact that all genuine relations are directly irreflexive, entails that all causal relations are irreflexive. The conclusion, accordingly, is that if causal relations are defined as above, namely, A causal relation is any relation between states of affairs which satisfies the open sentence, T*, then, although all explicit references to the formal properties of causal relations have been eliminated from the analysis, it can be shown that causal relations must possess certain formal properties: they must be irreflexive and asymmetric, and they cannot enter into causal loops. In short, the formal properties shared by all causal relations follow from the analytical con-
straints upon causal laws, together with the fact that what distinguishes causal laws from non-causal laws is that the former involve causal relations. This is, I think, an appealing result. For if there could be other relations which satisfied the postulates for causal laws, but whose formal properties differed from those that are common to causal relations, one would be left with the somewhat puzzling question of what those other relations were. Earlier, in the first part of section 3, A, I considered the question of whether all causal relations are reducible to a single, basic, causal relation, and I argued that one must allow for the possibility of at least two distinct, basic causal relations - namely, the relation of direct, quantized causation and that of non-discrete causation. I then went on to discuss what properties serve to distinguish those two relations, and settled, in the end, upon the properties of intrinsic transitivity and intrinsic denseness. If those conclusions are sound, one can offer the following accounts of those specific, basic causal relations: C is the relation of non-discrete causation if and only if C is a causal relation that is intrinsically dense and intrinsically transitive. D is the relation of direct, quantized causation if and only if D is a causal relation that is neither intrinsically dense nor intrinsically transitive.
Finally, the above analyses have all been predicated on the assumption that causal relations are necessarily irreflexive and asymmetric, and such as cannot enter into loops. How would the above approach need to be reformulated if it turned out, as some have contended, that that assumption is mistaken? Given that any relation that satisfies the open sentence, T*, corresponding to postulates (Cj) through (C4), must, for example, be irreflexive, those postulates would have to be abandoned. The basic idea would then be to reformulate the account in terms of the open sentence, T, that corresponds to the weaker postulates, (Cj) through (C 4). That in itself will not be sufficient, however, since, as I indicated earlier, if all causal relations satisfy T, they must also satisfy T*, provided that the ancestral of any causal relation is also a causal relation. But this difficulty can be avoided if one holds that only basic causal relations need satisfy T. Given those two modifications, the proofs that causal relations are irreflexive, asymmetric, and
Michael Tooley
such as cannot enter into loops will no longer go through. But on the other hand, the contrast between postulates (C 1) and (C4) will still capture the crucial idea of the direction of causation. The general approach would therefore seem to be compatible with different views concerning the formal properties of causal relations.
C.
The epistemological question
A crucial question for any account of causation, and especially for one that treats causation as a theoretical relation, is whether it is compatible with our everyday views concerning the possibility of causal knowledge, and concerning the sorts of evidence that serve to confirm causal claims. The analysis just offered fares very well, I believe, in those respects. For, so far as I can see, any evidence that we normally take to be relevant to causal claims turns out to be relevant on the present account. The grounds for this view are as follows. First, I have argued elsewhere that in the case of both intermediate and supervenience approaches to causation which are based upon the idea of relating causation to the transmission of probabilities, all of the things that we normally take to be evidence for causal claims can be shown to be evidence given the analyses in question. 33 Thus it can be shown, for example, that such things as the direction of irreversible processes, both entropic and non-en tropic, the direction of open forks, especially those of high complexity, and the direction of apparent control, all provide good evidence for claims about causal relations. Second, this situation is not altered when one jettisons the intermediate and supervenience accounts in favour of a singularist conception based upon the same idea of the transmission of probabilities. For it can be shown - though I have not attempted to do so here - that even if one adopts a singularist conception of causation, one is never justified in believing that two events are causally connected unless one is also justified in believing that there is some causal law of which the relation in question is an instance. 34
4
Summing Up
In this paper I have tried to show that there is a singularist account of the nature of causation
that is not only coherent, but plausible. My argument in support of this contention involved the following steps. First, I argued that, other things being equal, a singularist account is preferable to both intermediate accounts and supervenience accounts. For intermediate accounts suffer from greater complexity, while supervenience accounts are exposed to decisive counterexamples. Second, I argued that it is only if causation is treated as a theoretical relation that there is any hope of finding a successful singularist account. For in the first place, the relation of causation cannot be given in immediate experience. And in the second place, a Humean-style argument, especially when supplemented with the idea of possible worlds where causation is gappy, appears to make it very unlikely that a reductionist analysis can be given for causation if causal relations do not presuppose causal laws. But in addition, there appear to be very strong reasons for thinking that causation must be treated as a theoretical relation, regardless of whether a singularist account is correct. I then went on to develop a theory which enables one to provide an account of the nature of causal relations. That theory involved two central ideas. The first was that the fact that a theory of causation involves the concept of a law of nature does not mean that it cannot provide an account of causal relations according to which events can be causally related even in worlds where there are no causal laws. The second was that the correct account of causal laws is one that captures, in a precise way, the idea of the transmission of probabilities. For, among other things, such an account both escapes the objections to which competing accounts of causal laws are exposed, and it has, in addition, a very plausible intuitive basis. The outcome was a characterization of causal relations as those relations which satisfy the appropriate open sentence corresponding to the analytical theory of causation set out above. Given that definition, it then follows that causal relations have the formal properties they are normally taken to have, that they are epistemologically accessible relations between events, and that events can be causally related even in worlds where there are no causal laws. 35
The Nature of Causation
Notes
2 3
4
6
7
8
9
10 11
12
13
14 15 16 17
Michael Tooley, 'Laws and causal relations', in P. A. French, T. E. Uehling and H. K. Wettstein (eds), Midwest studies in Philosophy, vol. 9 (Minneapolis: University of Minnesota Press, 1984), pp. 93-112, and idem, Causation - A Realist Approach (Oxford: Oxford University Press, 1988), ch. 6. Tooley, Causation, ch. 8. Fred I. Dretske, 'Laws of nature', Philosophy of Science 44 (1977), pp. 248-68; David M. Armstrong, What L, a Law of Nature? (Cambridge: Cambridge University Press, 1983), esp. chs 1-5; and my own discussions in 'The nature of Laws', (Canadian Journal of Philosophy 7/4 (1977), pp. 667-98, and in Causation, sect. 2.1.1. For a more detailed discussion, see Tooley, Causation, pp.268-74. The only restriction upon properties here is that they must not involve particulars. Tooley, 'Laws and causal relations', pp. 99-107. Some axiomatic formulations of Newtonian spacetime involve the postulate of a generalized betweenness relation that, rather than being restricted to locations at a given time, can hold between spacetime points belonging to different temporal slices. See, e.g., Hartry Field's Science without Numbers (Princeton: Princeton University Press, 1980), pp. 52-3. But the idea that such a spatio-temporal relation can be basic is, I believe, very dubious. G. E. M. Anscombe, 'Causality and determination', in E. Sosa (ed.), Causation and Conditionals (Oxford: Oxford University Press, 1975), pp. 63-81, at p.81. David Hume, A Treatise of Human Nature, pt 2, sect. 14, and An Inquiry Concerning Human Understanding, sect. 7. Anscombe, 'Causality and determination', pp. 67-9. c.]. Ducasse, 'The nature and the observability ofthe causal relation', Journal of Phllosophy 23 (1926), pp. 57-67, repro in Sosa (ed.), Causation and Conditionals, pp. 114-25; see p. 116. Ibid., p. 122. Ducasse thought he could get around this difficulty, but as Ernest Sosa and others have shown, Ducasse's response is unsatisfactory. See, e.g., Sosa's discussion in the introduction to Causation and Conditionals, pp. 8-10. Wesley Salmon, 'Theoretical explanation', in S. Korner (ed.), Explanation (Oxford: Oxford University Press, 1975), pp. 118-43, at pp. 128ff. A more extended discussion can be found in Tooley, Causation, pp. 235-6. Ibid., esp. pp. 247-50. I am indebted to David Armstrong for pointing out the possibility of quantized causal relations. Compare David Lewis's 'The paradoxes of time travel', American Philosophical Quarterly 13 (1976), pp. 145-52.
18 Adolf Grunbaum, 'Carnap's views on the foundations of geometry', in Paul A. Schilpp (ed.), The Philosophy ofRudolfCarnap (La Salle, Ill: Open Court, 1963), pp. 599-684; see pp. 614-15. 19 See, e.g., Antony Flew, 'Can an effect precede its cause?', Proceedings of the Aristotelian Society, suppl. vol. 28 (1954), pp. 45-62; Max Black, 'Why cannot an effect precede its cause?', Analysis 16 (1955--6), pp. 49-58; David Pears, 'The priority of causes,' Analysis 17 (1956-7), pp. 54-63; Richard Swinburne, Space and Time (London: Macmillan, 1968), p. 109; D. H. Mellor, Real Time (Cambridge: Cambridge University Press, 1981), ch. 9. 20 See, e.g., my discussion in Causation, pp. 234-5. 21 The relevant proofs are set out in ibid., pp. 277-80 and 325-35. 22 The postulate in question is the second of the six postulates set out in ibid., p. 262. 23 Ibid., ch. 7. 24 The intuitive idea set out in the previous section applies to both probabilistic and non-probabilistic causal laws. For my purposes here, however, it will suffice to consider only the case of non-probabilistic causal laws. The extension to the case of probabilistic laws is straightforward, and is discussed in ibid., pp.291-6. 25 Compare the slightly different notation proposed by Jaegwon Kim in his article 'Causes and events: Mackie on causation,' Journal of Philosophy 68 (1971), pp. 426-41, repro in Sosa (ed.), Causation and Conditionals, pp. 48-62: 'we shall use the notation "[x, P, t]" to refer to the event of x's exemplifying property P at time t' (p. 60). 26 Tooley, Causation, pp. 256-62. 27 The problems that confront reductionist accounts of the direction of causation are discussed at length in ibid., esp. ch. 7 and the first section of ch. 8. 28 F. P. Ramsey, Theories', in R. B. Braithwaite (ed.), The Foundations ofMathematics (Paterson, NJ: Littlefield, Adams & Co., 1960), pp. 212-36; David Lewis, 'How to define theoretical terms', Journal of Philosophy 67 (1970), pp. 427-46. 29 For a fuller discussion of this method, see Tooley, Causation, pp. 13-25. 30 See, e.g., David Armstrong's Universals and Scientific Realism, vol. 2 (Cambridge: Cambridge University Press, 1978), pp. 91-3. 31 For the proof, see Tooley, Causation, pp. 278-9. 32 For a proof of a stronger theorem, from comparable postulates, see ibid., pp. 328-35. 33 Ibid., pp. 296-303. 34 This thesis needs to be qualified slightly, since it assumes that there are no 'confirmation machines', and if this were false, it would be possible to have reason to believe that there were causally related events that did not fall under any law. For the relevant
Michael Tooley argument, see Edward Erwin, 'The confirmation machine', in Boston Studies in the Philosophy of Science, vol. 8 (Dordrecht: D. Reidel, 1971), pp. 306--21. 35 I am indebted to David Armstrong, to Evan Fales, to Ernest Sosa, and to two anonymous referees of the Canadian Journal of Philosophy for detailed written
comments on an earlier draft, and to John Burgess, Lloyd Humberstone, Peter Menzies, Robert Pargetter, Philip Pettit, Michael Smith, Neil Tennant and Aubrey Townsend for their comments on earlier versions which I read at Monash University and at the Australian National University.
Introduction
Introduction Causation perhaps is not the only "cement of the universe." There may well be other relations that generate structure for events, facts, properties, and things of this world. Consider, for example, the part-whole ("mereological") relation: the properties of a whole seem entirely determined by the properties and relations that characterize its parts - in that if you build, say, two tables from parts that are exactly identical and configure them in an exactly identical structure, you would have two tables that are indistinguishable - the same shape, the same weight, the same functionality, and even the same aesthetic qualities. Modern science encourages a metaphysical picture of the world in which the basic building blocks of all things are unobservable microscopic particles (atoms, elementary particles, quarks, or whatever), with everything else - tables and chairs, trees and animals, the planets and stars - being wholly composed of them. Given that a macro-object is decomposable into micro-parts without remainder, what is the relationship between its (the whole's) properties and the properties and relations holding for its parts? C. D. Broad, in his "Mechanism and Emergentism" (chapter 37) discusses two major alternatives: mechanism, according to which the properties of a whole can be deduced or predicted from the properties of its parts, and emergentism, which affirms that some properties of a whole are "emergent" in the sense that they cannot be so deduced or predicted. According to Broad, there are emergent properties in this sense, and this is a position that has been, and still is, quite popular with philosophers and with scientists in many fields. It is a widely shared view that complex systems often exhibit characteristics that are irreducible to, and not deducible from, those of their simpler constituent systems. What Broad calls "mechanism" is now standardly called "reductionism" or "micro-reductionism."
Note In "The nature of mental states," in Philosophical Papers, vol. 2 (Cambridge: Cambridge University Press, 1975; first pub. 1967).
Although the main topic of Quine's "Ontological Reduction and the World of Numbers" (chapter 38) is the reduction in the abstract domain of numbers and other mathematical objects, what he has to say is directly relevant to broader metaphysical issues of ontological reduction - that is, reduction of ontological domains. Jerry Fodor's "Special Sciences" (chapter 39) deploys the so-called 'multiple realizability' of higher-level kinds and properties, first explicitly discussed by Hilary Putnam, 1 as a powerful and influential argument against their reducibility to lower-level properties. The Putnam/Fodor argument has been primarily responsible for the decline of various reductionisms in philosophy. In "Multiple Realization and the Metaphysics of Reduction", (chapter 40) Jaegwon Kim subjects the phenomenon of multiple realization to close scrutiny, and reaches conclusions at variance with those of Putnam and Fodor - in particular, concerning reductionism and the scientific/nomic status of multiply realizable properties. In "Physicalism: Ontology, and Determination, and Reduction" (chapter 41), Geoffrey Hellman and Frank Thompson attempt to develop a position that is physicalist in its ontology, but which makes sense of the priority and basicness of physics without, however, embracing reductionism. They develop their ideas by the use of formal model theory, but these ideas turn out to be closely related to the idea of "supervenience." Many nonreductive physicalists look upon supervenience as a relation that enables a perspicuous formulation of physicalism that is nonreductive: all the facts supervene on the physical facts in the sense that physical facts determine all the facts, but this does not imply that all facts are reducible to physical facts. Kim's "Supervenience as a Philosophical Concept" (chapter 42) surveys the main results in this area and discusses the controversial and complicated relationship between supervenience and reduction.
Part VIII Further reading Bonevac, Daniel A., Reduction in the Abstract Sciences (Indianapolis: Hackett, 1982). Causey, Robert L., Unity oj Science (Dordrecht: Reidel, 1977). Churchland, Patricia, Neurophilosophy (Cambridge, Mass.: MIT Press, 1986), ch. 7. Dupre, John, The Disorder oJ Things (Cambridge, Mass.: Harvard University Press, 1993). Humphreys, Paul W., "How properties emerge," Philosophy oJScience 64 (1997), pp. 1-17. Kim, Jaegwon, "Concepts of supervenience," in Supervenience and Mind (Cambridge: Cambridge University Press, 1993). - - "Making sense of emergence," Philosophical Studies, forthcoming. McLaughlin, Brian, "The rise and fall of British emergentism," in Ansgar Beckermann, Hans Flohr, and Jaegwon Kim (eds), Emergence or Reduction (Berlin: De Gruyter, 1992). --"Varieties of supervenience", in Savellos and Yalcin, Supervenience: New Essays.
Morgan, Lloyd c., Emergent Evolution (London: William & Norgate, 1923). Nagel, Ernest, The Structure oj Science (New York: Harcourt, Brace & World, 1961), ch. II. Oppenheim, Paul, and Putnam, Hilary "Unity of science as a working hypothesis," in H. Feigl, M. Scriven, and G. Maxwell (eds), Minnesota Studies in the Philosophy oj Science, vol. 2 (Minneapolis: University of Minnesota Press, 1958), pp. 3-36. Paull, Cranston, and Sider, Theodore, "In defense of global supervenience," Philosophy and Phenomenological Research 32 (1992), pp. 830-45. Post, John F., The Faces ojExistence (Ithaca, NY: Cornell University Press, 1987). Rosenberg, Alexander, Instrumental Biology, or the Disuni~y oJScience (Chicago: U ni versity of Chicago Press, 1994). Savellos, Elias, and Yaicin, Umit (eds), Supervenience: New Essays (Cambridge: Cambridge University Press, 1995). Stalnaker, Robert, "Varieties of supervenience," Philosophical Perspectives 10 (1996), pp. 221-41.
37
c. D. Broad I want to consider some of the characteristic differences which there seem to be among material objects, and to enquire how far these differences are ultimate and irreducible. On the face of it, the world of material objects is divided pretty sharply into those which are alive and those which are not. And the latter seem to be of many different kinds, such as oxygen, silver, etc. The question which is of the greatest importance for our purpose is the nature of living organisms, since the only minds that we know of are bound up with them. But the famous controversy between Mechanists and Vitalists about living organisms is merely a particular case of the general question: Are the apparently different kinds of material objects irreducibly different? It is this general question which I want to discuss at present. I do not expect to be able to give a definite answer to it; and I am not certain that the question can ever be settled conclusively. But we can at least try to analyse the various alternatives, to state them clearly, and to see the implications of each. Once this has been done, it is at least possible that people with an adequate knowledge of the relevant facts may be able to answer the question with a definite Yes or No; and, until it has been done, all controversy on the subject is very much in the air. I think one feels that the disputes between Mechanists and Vitalists are unsatisfactory for two reasons. (i) One is never quite sure what is meant From The Mind and its Place in Nature, published by Routledge and Kegan Paul, London, 1925.
by 'Mechanism' and by 'Vitalism'; and one suspects that both names cover a multitude of theories which the protagonists have never distinguished and put clearly before themselves. And (ii) one wonders whether the question ought not to have been raised long before the level of life. Certainly living beings behave in a very different way from non-living ones; but it is also true that substances which interact chemically behave in a very different way from those which merely hit each other, like two billiard-balls. The question: Is chemical behaviour ultimately different from dynamical behaviour? seems just as reasonable as the question: Is vital behaviour ultimately different from nonvital behaviour? And we are much more likely to answer the latter question rightly if we see it in relation to similar questions which might be raised about other apparent differences of kind in the material realm.
The Ideal of Pure Mechanism Let us first ask ourselves what would be the ideal of a mechanical view of the material realm. I think, in the first place, that it would suppose that there is only one fundamental kind of stuff out of which every material object is made. Next, it would suppose that this stuff has only one intrinsic quality, over and above its purely spatio-temporal and causal characteristics. The property ascribed to it might, e.g., be inertial mass or electric charge. Thirdly, it would suppose that there is only one
c. D. Broad fundamental kind of change, viz., change in the relative positions of the particles of this stuff. Lastly, it would suppose that there is one fundamental law according to which one particle of this stuff affects the changes of another particle. It would suppose that this law connects particles by pairs, and that the action of any two aggregates of particles as wholes on each other is compounded in a simple and uniform way from the actions which the constituent particles taken by pairs would have on each other. Thus the essence of Pure Mechanism is (a) a single kind of stuff, all of whose parts are exactly alike except for differences of position and motion; (b) a single fundamental kind of change, viz., change of position. Imposed on this there may of course be changes of a higher order, e.g., changes of velocity, of acceleration, and so on; (c) a single elementary causal law, according to which particles influence each other by pairs; and (d) a single and simple principle of composition, according to which the behaviour of any aggregate of particles, or the influence of anyone aggregate on any other, follows in a uniform way from the mutual influences of the constituent particles taken by pairs. A set of gravitating particles, on the classical theory of gravitation, is an almost perfect example of the ideal of Pure Mechanism. The single elementary law is the inverse-square law for any pair of particles. The single and simple principle of composition is the rule that the influence of any set of particles on a single particle is the vector-sum of the influences that each would exert taken by itself. An electronic theory of matter departs to some extent from this ideal. In the first place, it has to assume at present that there are two ultimately different kinds of particle, viz., protons and electrons. Secondly, the laws of electromagnetics cannot, so far as we know, be reduced to central forces. Thirdly, gravitational phenomena do not at present fall within the scheme; and so it is necessary to ascribe masses as well as charges to the ultimate particles, and to introduce other elementary forces beside those of electromagnetics. On a purely mechanical theory, all the apparently different kinds of matter would be made of the same stuff. They would differ only in the number, arrangement and movements of their constituent particles. And their apparently different kinds of behaviour would not be ultimately different. For they would all be deducible by a single simple principle of composition from the mutual influences of the particles taken by pairs; and these mutual influences would all obey a single law which
is quite independent of the configurations and surroundings in which the particles happen to find themselves. The ideal which we have been describing and illustrating may be called 'Pure Mechanism' . When a biologist calls himself a 'Mechanist', it may fairly be doubted whether he means to assert anything so rigid as this. Probably all that he wishes to assert is that a living body is composed only of constituents which do or might occur in non-living bodies, and that its characteristic behaviour is wholly deducible from its structure and components and from the chemical, physical and dynamical laws which these materials would obey if they were isolated or were in non-living combinations. Whether the apparently different kinds of chemical substance are really just so many different configurations of a single kind of particles, and whether the chemical and physical laws are just the compounded results of the action of a number of similar particles obeying a single elementary law and a single principle of composition, he is not compelled as a biologist to decide. I shall later on discuss this milder form of 'Mechanism', which is all that is presupposed in the controversies between mechanistic and vitalistic biologists. In the meanwhile I want to consider how far the ideal of Pure Mechanism could possibly be an adequate account of the world as we know it.
Limitations ofpure mechanism No one of course pretends that a satisfactory account even of purely physical processes in terms of Pure Mechanism has ever been given; but the question for us is: How far, and in what sense, could such a theory be adequate to all the known facts? On the face of it, external objects have plenty of other characteristics beside mass or electric charge, e.g., colour, temperature, etc. And, on the face of it, many changes take place in the external world beside changes of position, velocity, etc. Now of course many different views have been held about the nature and status of such characteristics as colour; but the one thing which no adequate theory of the external world can do is to ignore them altogether. I will state here very roughly the alternative types of theory, and show that none of them is compatible with Pure Mechanism as a complete account of the facts. (I) There is the naive view that we are III immediate cognitive contact with parts of the sur-
Mechanism and Emergentism
faces of external objects, and that the colours and temperatures which we perceive quite literally inhere in those surfaces independently of our minds and of our bodies. On this view, Pure Mechanism breaks down at the first move, for certain parts of the external world would have various properties different from and irreducible to the one fundamental property which Pure Mechanism assumes. This would not mean that what scientists have discovered about the connection between heat and molecular motion, or light and periodic motion of electrons, would be wrong. It might be perfectly true, so far as it went; but it would certainly not be the whole truth about the external world. We should have to begin by distinguishing between 'macroscopic' and 'microscopic' properties, to use two very convenient terms adopted by Lorentz. Colours, temperatures, etc. would be macroscopic properties; i.e., they would need a certain minimum area or volume (and perhaps, as Dr Whitehead has suggested, a certain minimum duration) to inhere in. Other properties, such as mass or electric charge, might be able to inhere in volumes smaller than these minima and even in volumes and durations of any degree of smallness. Molecular and electronic theories of heat and light would then assert that a certain volume is pervaded by such and such a temperature or such and such a colour if and only if it contains certain arrangements of particles moving in certain ways. What we should have would be laws connecting the macroscopic qualities which inhere in a volume with the number, arrangement and motion of the microscopic particles which are contained in this volume. On such a view, how much would be left of Pure Mechanism? (i) It would of course not be true of macroscopic properties. (ii) It might still be true of the microscopic particles in their interactions with each other. It might be that there is ultimately only one kind of particle, that it has only one non-spatiotemporal quality, that these particles affect each other by pairs according to a single law, and that their effects are compounded according to a single law. (iii) But, even if this were true of the microscopic particles in their relations with each other, it plainly could not be the whole truth about them. For there will also be laws connecting the presence of such and such a configuration of particles, moving in such and such ways, in a certain region, with the pervasion of this region by such and such a determinate value of a certain macroscopic quality, e.g., a certain shade of red or a temperature of 57° C. These will be just as much laws of the external
world as are the laws which connect the motions of one particle with those of another. And it is perfectly clear that the one kind oflaw cannot possibly be reduced to the other, since colour and temperature are irreducibly different characteristics from figure and motion, however close may be the causal connection between the occurrence of the one kind of characteristic and that of the other. Moreover, there will have to be a number of different and irreducible laws connecting microscopic with macroscopic characteristics; for there are many different and irreducible determinable macroscopic characteristics, e.g., colour, temperature, sound, etc. And each will need its own peculiar law. (2) A second conceivable view would be that in perception we are in direct cognitive contact with parts of the surfaces of external objects, and that, so long as we are looking at them or feeling them, they do have the colours or temperatures which they then seem to us to have; but that the inherence of colours and temperatures in external bodies is dependent upon the presence of a suitable bodily organism, or a suitable mind, or of both, in a suitable relation to the external object. On such a view it is plain that Pure Mechanism cannot be an adequate theory of the external world of matter. For colours and temperatures would belong to external objects on this view, though they would characterize an external object only when very special conditions are fulfilled. And evidently the laws according to which, e.g., a certain shade of colour inheres in a certain external region when a suitable organism or mind is in suitable relations to that region cannot be of the mechanical type. (3) A third conceivable view is that physical objects can seem to have qualities which do not really belong to any physical object; e.g., that a pillar-box can seem to have a certain shade of red, although really no physical object has any colour at all. This type of theory divides into two forms. (a) It might be held that, when a physical object seems to have a certain shade of red, there really is something in the world which has this shade of red, although this something cannot be a physical object or literally a part of one. Some would say that there is a red mental state - a 'sensation'; others that the red colour belongs to something which is neither mental nor physical. (b) It might be held that nothing in the world really has colour, though certain things seem to have certain colours. The
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relation of 'seeming to have' is taken as ultimate. On either of these alternatives it would be conceivable that Pure Mechanism was the whole truth about matter considered in its relations with matter. But it would be certain that it is not the whole truth about matter when this limitation is removed. Granted that bits of matter only seem to be red or to be hot, we still claim to know a good deal about the conditions under which one bit of matter will seem to be red and another to be blue and about the conditions under which one bit of matter will seem to be hot and another to be cold. This knowledge belongs partly to physics and partly to the physiology and anatomy of the brain and nervous system. We know little or nothing about the mental conditions which have to be fulfilled if an external object is to seem red or hot to a percipient; but we can say that this depends on an unknown mental factor x and on certain physical conditions a, b, c, etc., partly within and partly outside the percipient's body, about which we know a good deal. It is plain then that, on the present theory, physical events and objects do not merely interact mechanically with each other; they also play their part, along with a mental factor, in causing such and such an external object to seem to such and such an observer to have a certain quality which really no physical object has. In fact, for the present purpose, the difference between theories (2) and (3) is simply the following. On theory (2) certain events in the external object, in the observer's body, and possibly in his mind, cause a certain quality to inhere in the external object so long as they are going on. On theory (3) they cause the same quality to seem to inhere in the same object, so long as they are going on, though actually it does not inhere in any physical object. Theory (1), for the present purpose, differs from theory (2) only in taking the naive view that the body and mind of the observer are irrelevant to the occurrence of the sensible quality in the external object, though of course it would admit that these factors are relevant to the perception of this quality by the observer. This last point is presumably common to all three theories. I will now sum up the argument. The plain fact is that the external world, as perceived by us, seems not to have the homogeneity demanded by Pure Mechanism. If it really has the various irreducibly different sensible qualities which it seems to have, Pure Mechanism cannot be true of the whole of the external world and cannot be the whole truth about any part of it. The best that we can do for Pure
Mechanism on this theory is to divide up the external world first on a macroscopic and then on a microscopic scale; to suppose that the macroscopic qualities which pervade any region are causally determined by the microscopic events and objects which exist within it; and to hope that the latter, in their interactions with each other at any rate, fulfil the conditions of Pure Mechanism. We must remember, moreover, that there is no a priori reason why microscopic events and objects should answer the demands of Pure Mechanism even in their interactions with each other; that, so far as science can tell us at present, they do not; and that, in any case, the laws connecting them with the occurrence of macroscopic qualities cannot be mechanical in the sense defined. If, on the other hand, we deny that physical objects have the various sensible qualities which they seem to us to have, we are still left with the fact that some things seem to be red, others to be blue, others to be hot, and so on. And a complete account of the world must include some explanation of such events as 'seeming red to me', 'seeming blue to you', etc. We can admit that the ultimate physical objects may all be exactly alike, may all have only one non-spatio-temporal and non-causal property, and may interact with each other in the way which Pure Mechanism requires. But we must admit that they are also cause-factors in determining the appearance, if not the occurrence, of the various sensible qualities at such and such places and times. And, in these transactions, the laws which they obey cannot be mechanical. We may put the whole matter in a nutshell by saying that the appearance of a plurality of irreducible sensible qualities forces us, no matter what theory we adopt about their status, to distinguish two different kinds of law. One may be called 'intra-physical' and the other 'trans-physical'. The intra-physical laws may be, though there seems no positive reason to suppose that they are, of the kind required by Pure Mechanism. If so, there is just one ultimate elementary intra-physical law and one ultimate principle of composition for intra-physical transactions. But the trans-physical laws cannot satisfy the demands of Pure Mechanism; and, so far as I can see, there must be at least as many irreducible trans-physical laws as there are irreducible determinable sense-qualities. The nature of the trans-physical laws will of course depend on the view that we take about the status of sensible qualities. It will be somewhat different for each of the three alternative types of theory which I have
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mentioned, and it will differ according to which form of the third theory we adopt. But it is not necessary for our present purpose to go into further detail on this point.
The Three Possible Ways of Accounting for Characteristic Differences of Behaviour So far, we have confined our attention to pure qualities, such as red, hot, etc. By calling these 'pure qualities' I mean that, when we say 'This is red', 'This is hot', and so on, it is no part of the meaning of our predicate that 'this' stands in such and such a relation to something else. It is logically possible that this should be red even though 'this' were the only thing in the world; though it is probably not physically possible. I have argued so far that the fact that external objects seem to have a number of irreducibly different pure qualities makes it certain that Pure Mechanism cannot be an adequate account of the external world. I want now to consider differences of behaviour among external objects. These are not differences of pure quality. When I say 'This combines with that', 'This eats and digests', and so on, I am making statements which would have no meaning if 'this' were the only thing in the world. Now there are apparently extremely different kinds of behaviour to be found among external objects. A bit of gold and a bit of silver behave quite differently when put into nitric acid. A cat and an oyster behave quite differently when put near a mouse. Again, all bodies which would be said to be 'alive', behave differently in many ways from all bodies which would be said not to be 'alive'. And, among nonliving bodies, what we call their 'chemical behaviour' is very different from what we call their 'merely physical behaviour'. The question that we have now to discuss is this: 'Are the differences between merely physical, chemical and vital behaviour ultimate and irreducible or not? And are the differences in chemical behaviour between oxygen and hydrogen, or the differences in vital behaviour between trees and oysters and cats, ultimate and irreducible or not?' I do not expect to be able to give a conclusive answer to this question, as I do claim to have done to the question about differences of pure quality. But I hope at least to state the possible alternatives clearly, so that people with an adequate knowledge of the relevant empirical facts may know exactly what we want them to discuss,
and may not beat the air in the regrettable way in which they too often have done. We must first notice a difference between vital behaviour, on the one hand, and chemical behaviour, on the other. On the macroscopic scale, i.e., within the limits of what we can perceive with our unaided senses or by the help of optical instruments, all matter seems to behave chemically from time to time, though there may be long stretches throughout which a given bit of matter has no chance to exhibit any marked chemical behaviour. But only a comparatively few bits of matter ever exhibit vital behaviour. These are always very complex chemically; they are always composed of the same comparatively small selection of chemical elements; and they generally have a characteristic external form and internal structure. All of them after a longer or shorter time cease to show vital behaviour, and soon after this they visibly lose their characteristic external form and internal structure. We do not know how to make a living body out of non-living materials; and we do not know how to make a once living body, which has ceased to behave vitally, live again. But we know that plants, so long as they are alive, do take up inorganic materials from their surroundings and build them up into their own substance; that all living bodies maintain themselves for a time through constant change of material; and that they all have the power of restoring themselves when not too severely injured, and of producing new living bodies like themselves. Let us now consider what general types of view are possible about the fact that certain things behave in characteristically different ways. (l) Certain characteristically different ways of behaving may be regarded as absolutely unanalysable facts which do not depend in any way on differences of structure or components. This would be an absurd view to take about vital behaviour, for we know that all living bodies have a complex structure even on the macroscopic scale, and that their characteristic behaviour depends in part at least on their structure and components. It would also be a foolish view to take about the chemical behaviour of non-living substances which are known to be compounds and can be split up and re-synthesized by us from their elements. But it was for many years the orthodox view about the chemical elements. It was held that the characteristic differences between the behaviour of oxygen and hydrogen are due in no way to
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differences of structure or components, but must simply be accepted as ultimate facts. This first alternative can hardly be counted as one way of explaining differences of behaviour , since it consists in holding that there are certain differences which cannot be explained, even in part, but must simply be swallowed whole with that philosophic jam which Professor Alexander calls 'natural piety'. It is worthwhile to remark that we could never be logically compelled to hold this view, since it is always open to us to suppose that what is macroscopically homogeneous has a complex microscopic structure which wholly or partly determines its characteristic macroscropic behaviour. Nevertheless, it is perfectly possible that this hypothesis is not true in certain cases, and that there are certain ultimate differences in the material world which must just be accepted as brute facts. (2) We come now to types of theory which profess to explain, wholly or partly, differences of behaviour in terms of structure or components or both. These of course all presuppose that the objects that we are dealing with are at any rate microscopically complex; a hypothesis, as I have said, which can never be conclusively refuted. We may divide up these theories as follows. (a) Those which hold that the characteristic behaviour of a certain object or class of objects is in part dependent on the presence of a peculiar component which does not occur in anything that does not behave in this way. This is of course the usual view to take about the characteristic chemical behaviour of compounds. We say that silver chloride behaves differently from common salt because one contains silver and the other sodium. It is always held that differences of microscopic structure are also relevant to explaining differences of macroscopic chemical behaviour. For example, the very marked differences between the chemical behaviour of acetone and prop ion aldehyde, which both consist of carbon, hydrogen and oxygen in exactly the same proportions, are ascribed to the fact that the former has the structure symbolized by
and that the latter has the structure symbolized by
-::?'O CH 3 · CHz· C
.
"H
The doctrine which I will call 'Substantial Vitalism' is logically a theory of this type about vital behaviour. It assumes that a necessary factor in explaining the characteristic behaviour of living bodies is the presence in them of a peculiar component, often called an 'Entelechy', which does not occur in inorganic matter or in bodies which were formerly alive but have now died. I will try to bring out the analogies and differences between this type of theory as applied to vital behaviour and as applied to the behaviour of chemical compounds. (i) It is not supposed that the presence of an entelechy is sujJicient to explain vital behaviour; as in chemistry, the structure of the complex is admitted to be also an essential factor. (ii) It is admitted that entelechies cannot be isolated, and that perhaps they cannot exist apart from the complex which is a living organism. But there is plenty of analogy to this in chemistry. In the first place, elements have been recognized, and the characteristic behaviour of certain compounds has been ascribed to their presence, long before they were isolated. Secondly, there are certain groups, like CH 3 and C6HS in organic chemistry, which cannot exist in isolation, but which nevertheless play an essential part in determining the characteristic behaviour of certain compounds. (iii) The entelechy is supposed to exert some kind of directive influence over matter which enters the organism from outside. There is a faint analogy to this in certain parts of organic chemistry. The presence of certain groups in certain positions in a benzene nucleus makes it very easy to put certain other groups and very hard to put others into certain positions in the nucleus. There are well-known empirical rules on this point. Why then do most of us feel pretty confident of the truth of the chemical explanation and very doubtful of the formally analogous explanation of vital behaviour in terms of entelechies? I think that our main reasons are the following, and that they are fairly sound ones. (i) It is true that some elements were recognized and used for chemical explanations long before they were isolated. But a great many other elements had been isolated, and it was known that the process presented various degrees of difficulty. No entelechy, or anything like one, has ever been isolated; hence an entelechy is a purely hypothetical entity in a sense in which an as yet unisolated but suspected chemical element is not. If it be said that an isolated entelechy is from the nature of the case something which could not be perceived, and that this objection is therefore
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unreasonable, I can only answer (as I should to the similar assertion that the physical phenomena of mediumship can happen only in darkness and in the presence of sympathetic spectators) that it may well be true but is certainly very unfortunate. (ii) It is true that some groups which cannot exist in isolation play a most important part in chemical explanations. But they are groups of known composition, not mysterious simple entities; and their inability to exist by themselves is not an isolated fact but is part of the more general, though imperfectly understood, fact of valency. Moreover, we can at least pass these groups from one compound to another, and can note how the chemical properties change as one compound loses such a group and another gains it. There is no known analogy to this with entelechies. You cannot pass an entelechy from a living man into a corpse and note that the former ceases and that latter begins to behave vitally. (iii) Entelechies are supposed to differ in kind from material particles; and it is doubtful whether they are literally in space at all. It is thus hard to understand what exactly is meant by saying that a living body is a compound of an entelechy and a material structure; and impossible to say anything in detail about the structure of the total complex thus formed. These objections seem to me to make the doctrine of Substantial Vitalism unsatisfactory, though not impossible. I think that those who have accepted it have done so largely under a misapprehension. They have thought that there was no alternative between Biological Mechanism (which I shall define a little later) and Substantial Vitalism. They found the former unsatisfactory, and so they felt obliged to accept the latter. We shall see in a moment, however, that there is another alternative type of theory, which I will call 'Emergent Vitalism', borrowing the adjective from Professors Samuel Alexander and C. Lloyd Morgan. Of course, positive arguments have been put forward in favour of entelechies, notably by Hans Driesch. I do not propose to consider them in detail. I will merely say that Driesch's arguments do not seem to me to be in the least conclusive, even against Biological Mechanism, because they seem to forget that the smallest fragment which we can make of an organized body by cutting it up may contain an enormous number of similar microscopic structures, each of enormous complexity. And, even if it be held that Driesch has conclusively disproved Biological Mechanism, I cannot see that his arguments have the least tendency to prove Substantial
Vitalism rather than the Emergent form of Vitalism which does not assume entelechies. (b) I come now to the second type of theory which professes to explain, wholly or partly, the differences of behaviour between different things. This kind of theory denies that there need be any peculiar component which is present in all things that behave in a certain way and is absent from all things which do not behave in this way. It says that the components may be exactly alike in both cases, and it tries to explain the difference of behaviour wholly in terms of difference of structure. Now it is most important to notice that this type of theory can take two radically different forms. They differ according to the view that we take about the laws which connect the properties of the components with the characteristic behaviour of the complex wholes which they make up. (i) On the first form of the theory the characteristic behaviour of the whole could not, even in theory, be deduced from the most complete knowledge of the behaviour of its components, taken separately or in other combinations, and of their proportions and arrangements in this whole. This alternative, which I have roughly outlined and shall soon discuss in detail, is what I understand by the 'Theory of Emergence'. I cannot give a conclusive example of it, since it is a matter of controversy whether it actually applies to anything. But there is no doubt, as I hope to show, that it is a logically possible view with a good deal in its favour. I will merely remark that, so far as we know at present, the characteristic behaviour of common salt cannot be deduced from the most complete knowledge of the properties of sodium in isolation, or of chlorine in isolation, or of other compounds of sodium, such as silver chloride. (ii) On the second form of the theory, the characteristic behaviour of the whole is not only completely determined by the nature and arrangement of its components; in addition to this, it is held that the behaviour of the whole could, in theory at least, be deduced from a sufficient knowledge of how the components behave in isolation or in other wholes of a simpler kind. I will call this kind of theory 'Mechanistic'. A theory may be 'mechanistic' in this sense without being an instance of Pure Mechanism, in the sense defined earlier in this chapter. For example, if a biologist held that all the characteristic behaviour ofliving beings could be deduced from an adequate knowledge of the physical and chemical laws which its components would obey in isolation or in nonliving complexes, he would be called a 'Biological Mechanist', even though he believed that the
C. D. Broad different chemical elements are ultimately different kinds of stuff and that the laws of chemical composition are not of the type demanded by Pure Mechanism. The most obvious examples of wholes to which a mechanistic theory applies are artificial machines. A clock behaves in a characteristic way. But no one supposes that the peculiar behaviour of clocks depends on their containing as a component a peculiar entity which is not present in anything but clocks. Nor does anyone suppose that the peculiar behaviour of clocks is simply an emergent quality of that kind of structure and cannot be learnt by studying anything but clocks. We know perfectly well that the behaviour of a clock can be deduced from the particular arrangement of springs, wheels, pendulum, etc. in it, and from general laws of mechanics and physics which apply just as much to material systems which are not clocks. To sum up: We have distinguished three possible types of theory to account wholly or partly for the characteristic differences of behaviour between different kinds of material object: viz., the Theory of a Special Component, the Theory of Emergence, and the Mechanistic Theory. We have illustrated these, so far as possible, with examples which everyone will accept. In the special problem of the peculiar behaviour of living bodies these three types of theory are represented by Substantial Vitalism, Emergent Vitalism and Biological Mechanism. I have argued that Substantial Vitalism, though logically possible, is a very unsatisfactory kind of theory, and that probably many people who have accepted it have done so because they did not recognize the alternative of Emergent Vitalism. I propose now to consider in greater detail the emergent and the mechanistic types of theory.
Emergent theories Put in abstract terms, the emergent theory asserts that there are certain wholes, composed (say) of constituents A, Band C in a relation R to each other; that all wholes composed of constituents of the same kind as A, Band C in relations of the same kind as R have certain characteristic properties; that A, Band C are capable of occurring in other kinds of complex where the relation is not of the same kind as R; and that the characteristic properties of the whole R(A, B, C) cannot, even in theory, be deduced from the most complete knowledge of the properties of A, Band C in isolation or in other
wholes which are not of the form R(A, B, C). The mechanistic theory rejects the last clause of this assertion. Let us now consider the question in detail. If we want to explain the behaviour of any whole in terms of its structure and components, we always need two independent kinds of information. (a) We need to know how the parts would behave separately. And (b) we need to know the law or laws according to which the behaviour of the separate parts is compounded when they are acting together in any proportion and arrangement. Now it is extremely important to notice that these two bits of information are quite independent of each other in every case. Let us consider, e.g., the simplest possible case. We know that a certain tap, when running by itself, will put so many cubic centimetres of water into a tank in a minute. We know that a certain other tap, when running by itself, will put so many cubic centimetres of water into this tank in the same time. It does not follow logically from these two bits of information that, when the two taps are turned on together, the sum of these two numbers of cubic centimetres will be added to the contents of the tank every minute. This might not happen for two reasons. In the first place, it is quite likely that, if the two taps came from the same pipe, less would flow from each when both were turned on together than when each was turned on separately; i.e., the separate factors do not behave together as they would have behaved in isolation. Again, if one tap delivered hot water and the other cold water, the simple assumption about composition would break down although the separate factors continued to obey the same laws as they had followed when acting in isolation. For there would be a change of volume on mixture of the hot and cold water. Next let us consider the case oftwo forces acting on a particle at an angle to each other. We find by experiment that the actual motion of the body is the vector-sum of the motions which it would have had if each had been acting separately. There is not the least possibility of deducing this law of composition from the laws of each force taken separately. There is one other fact worth mentioning here. As Mr Russell pointed out long ago, a vector-sum is not a sum in the ordinary sense of the word. We cannot strictly say that each force is doing what it would have done if it had been alone, and that the result of their joint action is the sum of the results of their separate actions. A velocity of 5 miles an hour in a certain direction does not literally contain as parts a
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velocity of 3 miles an hour in a certain other direction and a velocity of 4 miles an hour in a direction at right angles to this. All that we can say is that the effect of several forces acting together is a fairly simple mathematical function of the purely hypothetical effects which each would have had if it had acted by itself, and that this function reduces to an algebraical sum in the particular case where all the forces are in the same line. We will now pass to the case of chemical composition. Oxygen has certain properties, and hydrogen has certain other properties. They combine to form water, and the proportions in which they do this are fixed. Nothing that we know about oxygen by itself or in its combinations with anything but hydrogen would give us the least reason to suppose that it would combine with hydrogen at all. Nothing that we know about hydrogen by itself or in its combinations with anything but oxygen would give us the least reason to expect that it would combine with oxygen at all. And most of the chemical and physical properties of water have no known connection, either quantitative or qualitative, with those of oxygen and hydrogen. Here we have a clear instance of a case where, so far as we can tell, the properties of a whole composed of two constituents could not have been predicted from a knowledge of the properties of these constituents taken separately, or from this combined with a knowledge of the properties of other wholes which contain these constituents. Let us sum up the conclusions which may be reached from these examples before going further. It is clear that in no case could the behaviour of a whole composed of certain constituents be predicted mereZy from a knowledge of the properties of these constituents, taken separately, and of their proportions and arrangements in the particular complex under consideration. Whenever this seems to be possible, it is because we are using a suppressed premiss which is so familiar that it has escaped our notice. The suppressed premiss is the fact that we have examined other complexes in the past and have noted their behaviour; that we have found a general law connecting the behaviour of these wholes with that which their constituents would show in isolation; and that we are assuming that this law of composition will hold also of the particular complex whole at present under consideration. For purely dynamical transactions this assumption is pretty well justified, because we have found a simple law of composition and have verified it very fully for wholes of very different
composition, complexity and internal structure. It is therefore not particularly rash to expect to predict the dynamical behaviour of any material complex under the action of any set of forces, however much it may differ in the details of its structure and parts from those complexes for which the assumed law of composition has actually been verified. The example of chemical compounds shows us that we have no right to expect that the same simple law of composition will hold for chemical as for dynamical transactions. And it shows us something further. It shows us that, if we want to know the chemical (and many of the physical) properties of a chemical compound, such as silver chloride, it is absolutely necessary to study samples of that particular compound. It would of course (on any view) be useless merely to study silver in isolation and chlorine in isolation; for that would tell us nothing about the law of their conjoint action. This would be equally true even if a mechanistic explanation of the chemical behaviour of compounds were possible. The essential point is that it would also be useless to study chemical compounds in general and to compare their properties with those of their elements in the hope of discovering a general law of composition by which the properties of any chemical compound could be foretold when the properties of its separate elements were known. So far as we know, there is no general law of this kind. It is useless even to study the properties of other compounds of silver and of other compounds of chlorine in the hope of discovering one general law by which the properties of silver compounds could be predicted from those of elementary silver and another general law by which the properties of chlorine compounds could be predicted from those of elementary chlorine. No doubt the properties of silver chloride are completely determined by those of silver and of chlorine, in the sense that whenever you have a whole composed of these two elements in certain proportions and relations, you have something with the characteristic properties of silver chloride, and that nothing has these properties except a whole composed in this way. But the law connecting the properties of silver chloride with those of silver and of chlorine and with the structure of the compound is, so far as we know, a unique and ultimate law. By this I mean (a) that it is not a special case which arises through substituting certain determinate values for determinable variables in a general law which connects the properties of any chemical compound with those of its separate
C. D. Broad
elements and with its structure. And (b) that it is not a special case which arises by combining two more general laws, one of which connects the properties of any silver compound with those of elementary silver, whilst the other connects the properties of any chlorine compound with those of elementary chlorine. So far as we know, there are no such laws. It is (c) a law which could have been discovered only by studying samples of silver chloride itself, and which can be extended inductively only to other samples of the same substance. We may contrast this state of affairs with that which exists where a mechanistic explanation is possible. In order to predict the behaviour of a clock, a man need never have seen a clock in his life. Provided he is told how it is constructed, and that he has learnt from the study of other material systems the general rules about motion and about the mechanical properties of springs and of rigid bodies, he can foretell exactly how a system constructed like a clock must behave. The situation with which we are faced in chemistry, which seems to offer the most plausible example of emergent behaviour, may be described in two alternative ways. These may be theoretically different, but in practice they are equivalent. (i) The first way of putting the case is the following. What we call the 'properties' of the chemical elements are very largely propositions about the compounds which they form with other elements under suitable conditions. For example one of the 'properties' of silver is that it combines under certain conditions with chlorine to give a compound with the properties of silver chloride. Likewise, one of the 'properties' of chlorine is that under certain conditions it combines with silver to give a compound with the properties of silver chloride. These 'properties' cannot be deduced from any selection of the other properties of silver or of chlorine. Thus we may say that we do not know all the properties of chlorine and of silver until they have been put in the presence of each other; and that no amount of knowledge about the properties which they manifest in other circumstances will tell us what property, if any, they will manifest in these circumstances. Put in this way, the position is that we do not know all the properties of any element, and that there is always the possibility of their manifesting unpredictable properties when put into new situations. This happens whenever a chemical compound is prepared or discovered for the first time. (ii) The other way to put the matter is to confine the name 'property' to those charac-
teristics which the elements manifest when they do not act chemically on each other: i.e., the physical characteristics of the isolated elements. In this case we may indeed say, if we like, that we know all the properties of each element; but we shall have to admit that we do not know the laws according to which elements, which have these properties in isolation, together produce compounds having such and such other characteristic properties. The essential point is that the behaviour of an as yet unexamined compound cannot be predicted from a knowledge of the properties of their other compounds; and it matters little whether we ascribe this to the existence of innumerable 'latent' properties in each element, each of which is manifested only in the presence of a certain other element, or to the lack of any general principle of composition, such as the parallelogram law in dynamics, by which the behaviour of any chemical compound could be deduced from its structure and from the behaviour of each of its elements in isolation from the rest. Let us now apply the conceptions, which I have been explaining and illustrating from chemistry, to the case of vital behaviour. We know that the bits of matter which behave vitally are composed of various chemical compounds arranged in certain characteristic ways. We have prepared and experimented with many of these compounds apart from living bodies, and we see no obvious reason why some day they might not all be synthesized and studied in the chemical laboratory. A living body might be regarded as a compound of the second order, i.e., a compound composed of compounds; just as silver chloride is a compound of the first order, i.e., one composed of chemical elements. Now it is obviously possible that, just as the characteristic behaviour of a first-order compound could not be predicted from any amount of knowledge of the properties of its elements in isolation or of the properties of other first-order compounds, so the properties of a second-order compound could not be predicted from any amount of knowledge about the properties of its first-order constituents taken separately or in other surroundings. Just as the only way to find out the properties of silver chloride is to study samples of silver chloride, and no amount of study of silver and of chlorine taken separately or in other combinations will help us; so the only way to find out the characteristic behaviour of living bodies may be to study living bodies as such. And no amount of knowledge about how the constituents of a living body behave in
Mechanism and Emergentism
isolation or in other and non-living wholes might suffice to enable us to predict the characteristic behaviour of a living organism. This possibility is perfectly compatible with the view that the characteristic behaviour of a living body is completely determined by the nature and arrangement of the chemical compounds which compose it, in the sense that any whole which is composed of such compounds in such an arrangement will show vital behaviour and that nothing else will do so. We should merely have to recognize, as we had to do in considering a first-order compound like silver chloride, that we are dealing with a unique and irreducible law, and not with a special case which arises by the substitution of particular values for variables in a more general law, nor with a combination of several more general laws. We could state this possibility about living organisms in two alternative but practically equivalent ways, just as we stated the similar possibility about chemical compounds. (i) The first way would be this. Most of the properties which we ascribe to chemical compounds are statements about what they do in presence of various chemical reagents under certain conditions of temperature, pressure, etc. These various properties are not deducible from each other; and, until we have tried a compound with every other compound and under every possible condition of temperature, pressure, etc., we cannot possibly know that we have exhausted all its properties. It is therefore perfectly possible that, in the very special situation in which a chemical compound is placed in a living body, it may exhibit properties which remain 'latent' under all other conditions. (ii) The other, and practically equivalent, way of putting the case is the following. If we confine the name 'property' to the behaviour which a chemical compound shows in isolation, we may perhaps say that we know all the 'properties' of the chemical constituents of a living body. But we shall not be able to predict the behaviour of the body unless we also know the laws according to which the behaviour which each of these constituents would have shown in isolation is compounded when they are acting together in certain proportions and arrangements. We can discover such laws only by studying complexes containing these constituents in various proportions and arrangements. And we have no right to suppose that the laws which we have discovered by studying non-living complexes can be carried over without modification to the very different case ofliving complexes. It may be that the only way to
discover the laws according to which the behaviour of the separate constituents combines to produce the behaviour of the whole in a living body is to study living bodies as such. For practical purposes it makes little difference whether we say that the chemical compounds which compose a living body have 'latent properties' which are manifested only when they are parts of a whole of this peculiar structure; or whether we say that the properties of the constituents of a living body are the same whether they are in it or out of it, but that the law according to which these separate effects are compounded with each other is different in a living whole from what it is in any non-living whole. This view about living bodies and vital behaviour is what I call 'Emergent Vitalism'; and it is important to notice that it is quite different from what I call 'Substantial Vitalism'. So far as I can understand them, I should say that Driesch is a Substantial Vitalist, and that Dr]. S. Haldane is an Emergent Vitalist. But I may quite well be wrong in classifying these two distinguished men in this way.
Mechanistic theories The mechanistic type of theory is much more familiar than the emergent type, and it will therefore be needless to consider it in great detail. I will just consider the mechanistic alternative about chemical and vital behaviour, so as to make the emergent theory still clearer by contrast. Suppose it were certain, as it is very probable, that all the different chemical atoms are composed of positive and negative electrified particles in different numbers and arrangements; and that these differences of number and arrangement are the only ultimate difference between them. Suppose that all these particles obey the same elementary laws, and that their separate actions are compounded with each other according to a single law which is the same no matter how complicated may be the whole of which they are constituents. Then it would be theoretically possible to deduce the characteristic behaviour of any element from an adequate knowledge of the number and arrangement of the particles in its atom, without needing to observe a sample of the substance. We could, in theory, deduce what other elements it would combine with and in what proportions; which of these compounds would be stable to heat, etc.; and how the various compounds would react in the presence of each other under given conditions of temperature, pressure, etc. And
C. D. Broad all this should be theoretically possible without needing to observe samples of these compounds. I want now to explain exactly what I mean by the qualification 'theoretically'. (l) In the first place the mathematical difficulties might be overwhelming in practice, even if we knew the structure and the laws. This is a trivial qualification for our present purpose, which is to bring out the logical distinction between mechanism and emergence. Let us replace Sir Ernest Rutherford by a mathematical archangel, and pass on. (2) Secondly, we cannot directly perceive the microscopic structure of atoms, but can only infer it from the macroscopic behaviour of matter in bulk. Thus, in practice, even if the mechanistic hypothesis were true and the mathematical difficulties were overcome, we should have to start by observing enough of the macroscopic behaviour of samples of each element to infer the probable structure of its atom. But, once this was done, it should be possible to deduce its behaviour in macroscopic conditions under which it has never yet been observed. That is, if we could infer its microscopic structure from a selection of its observed macroscopic properties, we could henceforth deduce all its other macroscopic properties from its microscopic structure without further appeal to observation. The difference from the emergent theory is thus profound, even when we allow for our mathematical and perceptual limitations. If the emergent theory of chemical compounds be true, a mathematical archangel, gifted with the further power of perceiving the microscopic structure of atoms as easily as we can perceive hay stacks, could no more predict the behaviour of silver or of chlorine or the properties of silver chloride without having observed samples of those substances than we can at present. And he could no more deduce the rest of the properties of a chemical element or compound from a selection of its properties than we can. Would there be any theoretical limit to the deduction of the properties of chemical elements
and compounds if a mechanistic theory of chemistry were true? Yes. Take any ordinary statement, such as we find in chemistry books: e.g., 'Nitrogen and hydrogen combine when an electric discharge is passed through a mixture of the two. The resulting compound contains three atoms of hydrogen to one of nitrogen; it is a gas readily soluble in water, and possessed of a pungent and characteristic smell.' If the mechanistic theory be true, the archangel could deduce from his knowledge of the microscopic structure of atoms all these facts but the last. He would know exactly what the microscopic structure of ammonia must be; but he would be totally unable to predict that a substance with this structure must smell as ammonia does when it gets into the human nose. The utmost that he could predict on this subject would be that certain changes would take place in the mucous membrane, the olfactory nerves and so on. But he could not possibly know that these changes would be accompanied by the appearance of a smell in general or of the peculiar smell of ammonia in particular, unless someone told him so or he had smelled it for himself. If the existence of the socalled secondary qualities, or the fact of their appearance, depends on the microscopic movements and arrangements of material particles which do not have these qualities themselves, then the laws of this dependence are certainly of the emergent type. The mechanistic theory about vital behaviour should now need little explanation. A man can hold it without being a mechanist about chemistry. The minimum that a Biological Mechanist need believe is that, in theory, everything that is characteristic of the behaviour of a living body could be deduced from an adequate knowledge of its structure, the chemical compounds which make it up, and the properties which these show in isolation or in non-living wholes.
38
w. V. Quine One conspicuous concern of analytical or scientific philosophy has been to reduce some notions to others, preferably to less putative ones. A familiar case of such reduction is Frege's definition of number. Each natural number n became, if I may speak in circles, the class of all n-member classes. As is also well known, Frege's was not the only good way. Another was von Neumann's. Under it, if! may again speak in circles, each natural number n became the class of all numbers less than n. In my judgment we have satisfactorily reduced one predicate to others, certainly, if in terms of these others we have fashioned an open sentence that is coextensive with the predicate in question as originally interpreted; i.e., that is satisfied by the same values of the variables. But this standard does not suit the Frege and von Neumann reductions of number; for these reductions are both good, yet not coextensive with each other. Again, consider Carnap's clarification of measure, or impure number, where he construes 'the temperature of x is n°C' in the fashion 'the temperature-in-degrees-Centigrade of x is n' and so dispenses with the impure numbers nOC in favor of the pure numbers n. l There had been, we might say, a two-place predicate 'H' of temperature such Originally published in Journal of Philosophy 61 (1964), pp. 209-16; the substantially revised version reprinted here is from my The Ways of Paradox (New York: Random House, 1966). I am grateful to Kenneth F. Schaffner for a letter of inquiry that sparked the revision. Copyright © byW. V. Quine. Reprinted by permission of Columbia University.
that 'H(x, a)' meant that the temperature of x was a. We end up with a new two-place predicate 'Ho' of temperature in degrees Centigrade. 'H (x, n° C)' is explained away as 'H,(x, n)'. But 'H' is not coextensive with 'Hc', or indeed with any surviving open sentence at all; 'H' had applied to putative things a, impure numbers, which come to be banished from the universe. Their banishment was Carnap's very purpose. Such reduction is in part ontological, as we may say, and coextensiveness here is clearly not the point. The definitions of numbers by Frege and von Neumann are best seen as ontological reductions too. Carnap, in the last example, showed how to skip the impure numbers and get by with pure ones. Just so, we might say, Frege and von Neumann showed how to skip the natural numbers and get by with what we may for the moment call Frege classes and von Neumann classes. There is only this -difference of detail: Frege classes and von Neumann classes simulate the behavior of the natural numbers to the point where it is convenient to call them natural numbers, instead of saying that we have contrived to dispense with the natural numbers as Carnap dispensed with impure numbers. Where reduction is in part ontological, we see, coextensiveness is not the issue. What then is? Consider again Frege's way and von Neumann's of construing natural number. And there is yet a third well-known way, Zermelo's. Why are these all good? What have they in common? Each is a structure-preserving model of the natural numbers. Each preserves arithmetic, and that is
W. V. Quine enough. It has been urged that we need more: we need also to provide for translating mixed contexts in which the arithmetical idioms occur in company with expressions concerning physical objects and the like. Specifically, we need to be able to say what it means for a class to have n members. But in fact this is no added requirement. We can say what it means for a class to have n members no matter how we construe the numbers, as long as we have them in order. For to say that a class has n members is simply to say that the members of the class can be correlated with the natural numbers up to n, whatever they are. The real numbers, like the natural numbers, can be taken in a variety of ways. The Dedekind cut is the central idea, but you can use it to explain real numbers either as certain classes of ratios, or as certain relations of natural numbers, or as certain classes of natural numbers. Under the first method, if I may again speak in circles, each real number x becomes the class of all ratios less than x. Under the second method, x becomes this relation of natural numbers: m bears the relation to n if m stands to n in a ratio less than x. For the third version, we change this relation of natural numbers to a class of natural numbers by mapping the ordered pairs of natural numbers into the natural numbers. All three alternatives are admissible, and what all three conspicuously have in common is, again, just the relevant structure: each is a structure-preserving model of the real numbers. Again it seems that no more is needed to assure satisfactory translation also of any mixed contexts. When real numbers are applied to magnitudes in the physical world, any model of the real numbers could be applied as well. The same proves true when we come to the imaginary numbers and the infinite numbers, cardinal and ordinal: the problem of construing comes to no more, again, than modeling. Once we find a model that reproduces the formal structure, there seems to be no difficulty in translating any mixed contexts as well. These cases suggest that what justifies the reduction of one system of objects to another is preservation of relevant structure. Since, according to the Liiwenheim-Skolem theorem, any theory that admits of a true interpretation at all admits of a model in the natural numbers, G. D. W. Berry concluded that only common sense stands in the way of adopting an all-purpose Pythagorean ontology: natural numbers exclusively. There is an interesting reversal here. Our first examples of ontological reduction were Frege's and von Neumann's reductions of natural number to
set theory. These and other examples encouraged the thought that what matters in such reduction is the discovery of a model. And so we end up saying, in view of the Liiwenheim-Skolem theorem, that theories about objects of any sort can, when true, be reduced to theories of natural numbers. Instead of reducing talk of numbers to talk of sets, we may reduce talk of sets - and of all else - to talk of natural numbers. And here there is an evident again, since the natural numbers are relatively clear and, as infinite sets go, economical. But is it true that all that matters is a model? Any interpretable theory can, in view of the Liiwenheim -Skolem theorem, be modeled in the natural numbers, yes; but does this entitle us to say that it is once and for all reducible to that domain, in a sense that would allow us thenceforward to repudiate the old objects for all purposes and recognize just the new ones, the natural numbers? Examples encouraged in us the impression that modelling assured such reducibility, but we should be able to confirm or remove the impression with a little analysis. What do we require of a reduction of one theory to another? Here is a complaisant answer: any effective mapping of closed sentences on closed sentences will serve if it preserves truth. If we settle for this, then what of the thesis that every true theory B can be reduced to a theory about natural numbers? It can be proved, even without the Liiwenheim-Skolem theorem. For we can translate each closed sentence S of B as 'Tx' with x as the Giidel number of S and with 'T' as the truth predicate for B, a predicate satisfied by all and only the Giidel numbers of true sentences of B. Of this trivial way of reducing an ontology to natural numbers, it must be said that whatever it saves in ontology it pays for in ideology: we have to strengthen the primitive predicates. For we know from Giidel and Tarski that the truth predicate ofB is expressible only in terms that are stronger in essential ways than any originally available in B itself. 2 Nor is this a price that can in general be saved by invoking the Liiwenheim-Skolem theorem. I shall explain why not. When, in conformity with the proof of the Liiwenheim - Skolem theorem, we reinterpret the primitive predicates of a theory B so as to make them predicates of natural numbers, we do not in general make them arithmetical predicates. That is, they do not in general go over into predicates that can be expressed in terms of sum, product, equality and logic. If we are modeling merely the theorems of a deductive system - the
Ontological Reduction and the World of Numbers
implicates of an effective if not finite set of axioms - then certainly we can get arithmetical reinterpretations of the predicates ..1 But that is not what we are about. We are concerned rather to accommodate all the truths of (j - all the sentences, regardless ofaxiomatizability, that were true under the original interpretation of the predicates of (j. There is, under the Liiwenheim-Skolem theorem, a reinterpretation that carries all these truth into truths about natural numbers; but there may be no such interpretation in arithmetical terms. There will be if (j admits of complete axiomatization, of course, and there will be under some other circumstances, but not under all. In the general case the most that can be said is, again, that the numerical reinterpretations are expressible in the notation of arithmetic plus the truth predicate for (j.4 So on the whole the reduction to a Pythagorean ontology exacts a price in ideology whether we invoke the truth predicate directly or let ourselves be guided by the argument of the LiiwenheimSkolem theorem. Still there is a reason for preferring the latter, longer line. When I suggested simply translating S as 'Tx' with x as Giidel number of S, I was taking advantage of the liberal standard: reduction was just any effective and truth-preserving mapping of closed sentences on closed sentences. Now the virtue of the longer line is that it works also for a less liberal standard of reduction. Instead of accepting just any and every mapping of closed sentences on closed sentences so long as it is effective and truth-preserving, we can insist rather that it preserve predicate structure. That is, instead of mapping just whole sentences of (j on sentences, we can require that each of the erstwhile primitive predicates of (j carryover into a predicate or open sentence about the new objects (the natural numbers). Whatever its proof and whatever its semantics, a doctrine of blanket reducibility of ontologies to natural numbers surely trivializes most further ontological endeavor. If the universe of discourse of every theory can as a matter of course be standardized as the Pythagorean universe, then apparently the only special ontological reduction to aspire to in any particular theory is reduction to a finite universe. Once the size is both finite and specified, of course, ontological considerations lose all force; for we can then reduce all quantifications to conjunctions and alternations and so retain no recognizably referential apparatus. Some further scope for ontological endeavor does still remain, I suppose, in the relativity to
ideology. One can try to reduce a given theory to the Pythagorean ontology without stepping up its ideology. This endeavor has little bearing on completely axiomatized theories, however, since they reduce to pure arithmetic, or elementary number theory. 5 Anyway we seem to have trivialized most ontological contrasts. Perhaps the trouble is that our standard of ontological reduction is still too liberal. We narrowed it appreciably when we required that the predicates be construed severally. But we still did not make it very narrow. We continued to allow the several predicates of a theory (j to go over into any predicates or open sentences concerning natural numbers, so long merely as the truth-values of closed sentences were preserved. Let us return to the Carnap case of impure number for a closer look. We are initially confronted with a theory whose objects include place-times x and impure numbers a and whose primitive predicates include 'If'. We reduce the theory to a new one whose objects include placetimes and pure numbers, and whose predicates include 'He'. The crucial step consists of explaining 'H(x, nOC)' as 'Hc(x, n)'. Now this is successful, if it is, because three conditions are met. One is, of course, that 'Hc(x, n)' under the intended interpretation agrees in truth-value with 'H(x, nO)C', under its originally intended interpretation, for all values of x and n. A second condition is that, in the original theory, all mention of impure numbers a was confined or confinable to the specific form of context 'H(x, a)'. Otherwise the switch to 'Hc(x, n)' would not eliminate such mention. But if this condition were to fail, through there being further predicates (say a predicate oflength or of density) and further units (say meters) along with 'If' and degrees, we could still win through by just treating them similarly. A third condition, finally, is that an impure number a can always be referred to in terms of a pure number and a unit: thus nOC, n meters. Otherwise explaining 'H(x, nOC)' as 'Hc(x, n)' would not take care of 'H(x,oo)'. This third condition is that we be able to specify what I shall call a proxy function: a function which assigns one of the new things, in this example a pure number, to each of the old things - each of the impure numbers of temperature. In this example the proxy function is the function 'how many degrees centigrade' - the function f such that f(n°C) = n. It is not required that such a function be expressible in the original theory (j to which 'H'
W. V. Quine belonged, much less that it be available in the final theory (j' to which 'He' belongs. It is required rather of us, out in the metatheory where we are explaining and justifying the discontinuance of (j in favor of (j', that we have some means of expressing a proxy function. Only upon us, who explain 'H(x, a)' away by 'Hr(x, n)', does it devolve to show how every a that was intended in the old (j determines an n of the new (j'. In these three conditions we have a further narrowing of what had been too liberal a standard of what to count as a reduction of one theory or ontology to another. We have in fact narrowed it to where, as it seems to me, the things we should like to count as reduction do so count and the rest do not. Carnap's elimination of impure number so counts; likewise Frege's and von Neumann's reduction of natural arithmetic to set theory; likewise the various essentially Dedekindian reductions of the theory of real numbers. Yet the general trivialization of ontology fails; there ceases to be any evident way of arguing, from the Liiwenheim-Skolem theorem, that ontologies are generally reducible to the natural numbers. The three conditions came to us in an example. If we restate them more generally, they lose their tripartite character. The standard of reduction of a theory (j to a theory (j' can now be put as follows. We specify a function, not necessarily in the notation of (j or (j', which admits as arguments all objects in the universe of (j' and takes values in the universe of (j'. This is the proxy function. Then to each n-place primitive predicate of (j, for each n, we effectively associate an open sentence of (j' in n free variables, in such a way that the predicate is fulfilled by an n-tuple of arguments of the proxy function always and only when the open sentence is fulfilled by the corresponding n-tuple of values. For brevity I am supposing that (j has only predicates, variables, quantifiers, and truth functions. The exclusion of singular terms, function signs, abstraction operators, and the like is no real restriction, for these accessories are reducible to the narrower basis in familiar ways. Let us try applying the above standard of reduction to the Frege case: Frege's reduction of number to set theory. Here the proxy function I is the function which, applied, e.g., to the 'genuine' number 5, gives as value the class of all five-member classes (Frege's so-called 5). In general, Ix is describable as the class of all x-member classes.
When the real numbers are reduced (by what I called the first method) to classes of ratios, jx is the class of all ratios less than the 'genuine' real number x. I must admit that my formulation suffers from a conspicuous element of make-believe. Thus, in the Carnap case I had to talk as if there were such things as xOC, much though I applaud Carnap's repudiation of them. In the Frege case I had to talk as if the 'genuine' number 5 were really something over and above Frege's, much though I applaud his reduction. My formulation belongs, by its nature, in an inclusive theory that admits the objects of (j, as unreduced, and the objects of (j' on an equal footing. But the formulation seems, if we overlook this imperfection, to mark the boundary we want. Ontological reductions that were felt to be serious do conform. Another that conforms, besides those thus far mentioned, is the reduction of an ontology of place-times to an ontology of number quadruples by means of Cartesian coordinates. And at the same time any sweeping Pythagoreanization on the strength of the Liiwenheim-Skolem theorem is obstructed. The proof of the Liiwenheim-Skolem theorem is such as to enable us to give the predicates of the numerical model; but the standard of ontological reduction that we have now reached requires more than that. Reduction of a theory (j to natural numbers - true reduction by our new standard, and not mere modeling - means determining a proxy function that actually assigns numbers to all the objects of (j and maps the predicates of (j into open sentences of the numerical model. Where this can be done, with preservation of truthvalues of closed sentences, we may well speak of reduction to natural numbers. But the Liiwenheim-Skolem argument determines, in the general case, no proxy function. It does not determine which numbers are to go proxy for the respective objects of (j. Therein it falls short of our standard of ontological reduction. It emerged early in this paper that what justifies an ontological reduction is, vaguely speaking, preservation of relevant structure. What we now perceive is that this relevant structure runs deep; the objects of the one system must be assigned severally to objects of the other. Goodman argued along other lines to this conclusion and more;6 he called for isomorphism, thereby requiring one-to-one correspondence between the old objects and their proxies. I prefer to let different things have the same proxy. For
Ontological Reduction and the World of Numbers
instance, n is wanted as proxy for both nOC and n 7 meters. Or again, consider hidden inflation. Relieving such inflation is a respectable brand of
ontological reduction, and it consists precisely in taking one thing as proxy for all the things that were indiscriminable from it. R
Notes 1 Rudolf Carnap, Physikalische BegrijJsbildung (Karlsruhe: G. Brawn, 1926). 2 See A. Tarski, Logic, Semantics, Metamathematics, (Oxford: Clarendon Press, 1956), p. 273. There are exceptions where () is especially weak; see J. R. Myhill, 'A complete theory of natural, rational, and real numbers',lournal "f"Symbolic LogIc 15 (1950), pp. 185-96, at p. 194. 3 See Hao Wang, 'Arithmetic models for formal systems', Methodos 3 (I951), pp. 217-32; also S. C. Kleene, IntroductIon to Metamathematics (New York: Van Nostrand, 1952), pp. 389-98 and more particularly p. 431. For exposition see also my 'Interpretations of sets of conditions', Journal (if" Symbolic Logic 19 (I954), pp. 97-102. 4 This can be seen by examining the general construction in sect.1 of my 'Interpretations of sets of conditions'.
Thus far in this paper I have been recording things that I said in the Shearman Lectures at University College, London, February 1954. Not so from here on. 6 Nelson Goodman, The Structure ofAppearance (Cambridge, Mass.: Harvard University Press, 1951), pp. 5-19. 7 For details see W. V. Quine, 'Necessary truth', in The Ways (if" Paradox (New York: Random Hause, 1966). 8 I am indebted for this observation to Paul Benacerraf. On such deflation see further my discussion of identification of indiscernibles in Word and Object (Cambridge, Mass.: MIT Press, 1960), p. 230; in From a LogIcal Point of" View (Cambridge, Mass.: Harvard University Press, 1953), pp. 71f; and in 'Reply to Professor Marcus', in Quine, Ways of Paradox.
39
Jerry A. Fodor
A typical thesis of positivistic philosophy of science is that all true theories in the special sciences should reduce to physical theories in the 'long run'. This is intended to be an empirical thesis, and part of the evidence which supports it is provided by such scientific successes as the molecular theory of heat and the physical explanation of the chemical bond. But the philosophical popularity of the reductionist program cannot be explained by reference to these achievements alone. The development of science has witnessed the proliferation of specialized disciplines at least as often as it has witnessed their elimination, so the widespread enthusiasm for the view that there will eventually be only physics can hardly be a mere induction over past reductionist successes. I think that many philosophers who accept reductionism do so primarily because they wish to endorse the generality of physics vis-a-vis the special sciences: roughly, the view that all events which fall under the laws of any science are physical events and hence fall under the laws of physics. 1 For such philosophers, saying that physics is basic science and saying that theories in the special sciences must reduce to physical theories have seemed to be two ways of saying the same thing, so that the latter doctrine has come to be a standard construal of the former. Originally published in Synthese 28 (1974), pp. 77115, appearing under the title 'Special sciences, or The disunity of science as a working hypothesis: Copyright © by Kluwer Academic Publishers. Reprinted by permission of the author and the publisher.
In what follows, I shall argue that this is a considerable confusion. What has traditionally been called 'the unity of science' is a much stronger, and much less plausible, thesis than the generality of physics. If this is true, it is important. Though reductionism is an empirical doctrine, it is intended to playa regulative role in scientific practice. Reducibility to physics is taken to be a constraint upon the acceptability of theories in the special science, with the curious consequence that the more the special sciences succeed, the more they ought to disappear. Methodological problems about psychology, in particular, arise in just this way: The assumption that the subject matter of psychology is part of the subject matter of physics is taken to imply that psychological theories must reduce to physical theories, and it is this latter principle that makes the trouble. I want to avoid the trouble by challenging the inference. Reductionism is the view that all the special sciences reduce to physics. The sense of 'reduce to' is, however, proprietary. It can be characterized as follows. 2 Let formula (1) be a law of the special science S.
Formula (1) is intended to be read as something like 'all events which consist of x's being SI bring about events which consist of .v's being S2" I assume that a science is individuated largely by reference to its typical predicates (see n. 2), hence that if S is a special science, 'SI' and 'Sz' are not predicates of basic physics. (I also assume that the
Special Sciences
'all' which quantifies laws of the special sciences needs to be taken with a grain of salt. Such laws are typically not exceptionless. This is a point to which I shall return at length.) A necessary and sufficient condition for the reduction of formula (1) to a law of physics is that the formulae (2) and (3) should be laws, and a necessary and sufficient condition for the reduction (2a)
SIX ..... PIX
(2b)
SLy ..... PLY
(3)
PjJ-.' --+ PLY
of S to physics is that all its laws should be so reduced. 3 'PI' and 'PI' are supposed to be predicates of physics, and formula (3) is supposed to be a physicallaw. Formulae like (2) are often called 'bridge' laws. Their characteristic feature is that they contain predicates of both the reduced and the reducing science. Bridge laws like formula (2) are thus contrasted with 'proper' laws like formulae (1) and (3). The upshot of the remarks so far is that the reduction of a science requires that any formula which appears as the antecedent or consequent of one of its proper laws must appear as the reduced formula in some bridge law or other. 4 Several points about the connective '--+' are now in order. First, whatever properties that connective may have, it is universally agreed that it must be transitive. This is important, because it is usually assumed that the reduction of some of the special sciences proceeds via bridge laws which connect their predicates with those of intermediate reducing theories. Thus, psychology is presumed to reduce to physics via, say, neurology, biochemistry, and other local stops. The present point is that this makes no difference to the logic of the situation so long as the transitivity of'--+' is assumed. Bridge laws which connect the predicates of S to those of S* will satisfy the constraints upon the reduction of S to physics so long as there are other bridge laws which, directly or indirectly, connect the predicates of S* to physical predicates. There are, however, quite serious open questions about the interpretation of '--t' in bridge laws. What turns on these questions is the extent to which reductionism is taken to be a physicalist thesis. To begin with, if we read '--t' as 'brings about' or 'causes' in proper laws, we will have to have some other connective for bridge laws, since bring-
ing about and causing are presumably asymmetric, while bridge laws express symmetric relations. Moreover, unless bridge laws hold by virtue of the identity of the events which satisfy their antecedents with those that satisfy their consequents, reductionism will guarantee only a weak version of physicalism, and this would fail to express the underlying ontological bias of the reductionist program. If bridge laws are not-identity statements, then formulae like (2) claim at most that, by law, x's satisfaction of a P predicate and x's satisfaction of an S predicate are causally correlated. It follows from this that it is nomologically necessary that S and P predicates apply to the same things (i.e., that S predicates apply to a subset of the things that P predicates apply to). But, of course, this is compatible with a non physicalist ontology, since it is compatible with the possibility that x's satisfying S should not itself be a physical event. On this interpretation, the truth of reductionism does not guarantee the generality of physics vis-a-vis the special sciences, since there are some events (satisfactions of S predicates) which fall in the domain of a special science (S) but not in the domain of physics. (One could imagine, for example, a doctrine according to which physical and psychological predicates are both held to apply to organisms, but where it is denied that the event which consists of an organism's satisfying a psychological predicate is, in any sense, a physical event. The upshot would be a kind of psychophysical dualism of a nonCartesian variety, a dualism of events and/ or properties rather than substances.) Given these sorts of considerations, many philosophers have held that bridge laws like formula (2) ought to be taken to express contingent event identities, so that one would read formula (2a) in some such fashion as 'every event which consists of an x's satisfying S I is identical to some event which consists of that x's satisfying PI and vice versa'. On this reading, the truth of reductionism would entail that every event that falls under any scientific law is a physical event, thereby simultaneously expressing the ontological bias of reductionism and guaranteeing the generality of physics vis-a-vis the special sciences. If the bridge laws express event identities, and if every event that falls under the proper laws of a special science falls under a bridge law, we get classical reductionism, a doctrine that entails the truth of what I shall call 'token physicalism'. Token physicalism is simply the claim that all the events
Jerry A. Fodor that the sciences talk about are physical events. There are three things to notice about token physicalism. First, it is weaker than what is usually called 'materialism'. Materialism claims both that token physicalism is true and that every event falls under the laws of some science or other. One could therefore be a token physicalist without being a materialist, though I don't see why anyone would bother. Second, token physicalism is weaker than what might be called 'type physicalism', the doctrine, roughly, that every property mentioned in the laws of any science is a physical property. Token physicalism does not entail type physicalism, if only because the contingent identity of a pair of events presumably does not guarantee the identity of the properties whose instantiation constitutes the events; not even when the event identity is nomologically necessary. On the other hand, if an event is simply the instantiation of a property, then type physicalism does entail token physicalism; two events will be identical when they consist of the instantiation of the same property by the same individual at the same time. Third, token physicalism is weaker than reductionism. Since this point is, in a certain sense, the burden of the argument to follow, I shan't labor it here. But, as a first approximation, reductionism is the conjunction of token physicalism with the assumption that there are natural kind predicates in an ideally completed physics which correspond to each natural kind predicate in any ideally completed special science. It will be one of my morals that reductionism cannot be inferred from the assumption that token physicalism is true. Reductionism is a sufficient, but not a necessary, condition for token physicalism. To summarize: I shall be reading reductionism as entailing token physicalism, since, if bridge laws state nomologically necessary contingent event identities, a reduction of psychology to neurology would require that any event which consists of the instantiation of a psychological property is identical with some event which consists of the instantiation of a neurological property. Both reductionism and token physicalism entail the generality of physics, since both hold that any event which falls within the universe of discourse of a special science will also fall within the universe of discourse of physics. Moreover, it is a consequence of both doctrines that any prediction which follows from the laws of a special science (and a statement of initial con-
ditions) will follow equally from a theory which consists only of physics and the bridge laws (together with the statement of initial conditions). Finally, it is assumed by both reductionism and token physicalism that physics is the only basic science; viz., that it is the only science that is general in the sense just specified. I now want to argue that reductionism is too strong a constraint upon the unity of science, but that, for any reasonable purposes, the weaker doctrine will do. Every science implies a taxonomy of the events in its universe of discourse. In particular, every science employs a descriptive vocabulary of theoretical and observation predicates, such that events fall under the laws of the science by virtue of satisfying those predicates. Patently, not every true description of an event is a description in such a vocabulary. For example, there are a large number of events which consist of things having been transported to a distance of less than three miles from the Eiffel Tower. I take it, however, that there is no science which contains 'is transported to a distance of less than three miles from the Eiffel Tower' as part of its descriptive vocabulary. Equivalently, I take it that there is no natural law which applies to events in virtue of their instantiating the property is transported to a distance of less than three miles from the Eiffel Tower (though I suppose it is just conceivable that there is some law that applies to events in virtue of their instantiating some distinct but coextensive property). By way of abbreviating these facts, I shall say that the property is transported ... does not determine a (natural) kind, and that predicates which express that property are not (natural) kind predicates. If! knew what a law is, and if! believed that scientific theories consist just of bodies of laws, then I could say that 'P' is a kind predicate relative to S if S contains proper laws of the form 'Pr --> .. . y' or ' . .. y --> P/: roughly, the kind predicates of a science are the ones whose terms are the bound variables in its proper laws. I am inclined to say this even in my present state of ignorance, accepting the consequence that it makes the murky notion of a kind viciously dependent on the equally murky notions of law and theo~y. There is no firm footing here. If we disagree about what a kind is, we will probably also disagree about what a law is, and for the same reasons. I don't know how to break out of this circle, but I think that there are some interesting things to say about which circle we are in.
Special Sciences
For example, we can now characterize the respect in which reductionism is too strong a construal of the doctrine of the unity of science. If reductionism is true, then every kind is, or is coextensive with, a physical kind. (Every kind is a physical kind if bridge statements express nomologically necessary property identities, and every kind is coextensive with a physical kind if bridge statements express nomologically necessary event identities.) This follows immediately from the reductionist premise that every predicate which appears as the antecedent or consequent of a law of a special science must appear as one of the reduced predicates in some bridge law, together with the assumption that the kind predicates are the ones whose terms are the bound variables in proper laws. If, in short, some physical law is related to each law of a special science in the way that formula (3) is related to formula (I), then every kind predicate of a special science is related to a kind predicate of physics in the way that formula (2) relates 'S1 ' and 'S2' to 'PI' and 'PI' respectively. I now want to suggest some reasons for believing that this consequence is intolerable. These are not supposed to be knock-down reasons; they couldn't be, given that the question of whether reductionism is too strong is finally an empirical question. (The world could turn out to be such that every kind corresponds to a physical kind, just as it could turn out to be such that the property is transported to a distance of less than three miles from the EifJel Tower determines a kind in, say, hydrodynamics.
It's just that, as things stand, it seems very unlikely that the world will turn out to be either of these ways.) The reason it is unlikely that every kind corresponds to a physical kind is just that (a) interesting generalizations (e.g., counterfactual supporting generalizations) can often be made about events whose physical descriptions have nothing in common; (b) it is often the case that whether the physical descriptions of the events subsumed by such generalizations have anything in common is, in an obvious sense, entirely irrelevant to the truth of the generalizations, or to their interestingness, or to their degree of confirmation, or, indeed, to any of their epistemologically important properties; and (c) the special sciences are very much in the business of formulating generalizations of this kind. I take it that these remarks are obvious to the point of self-certification; they leap to the eye as soon as one makes the (apparently radical) move of taking the existence of the special sciences at all
seriously. Suppose, for example, that Gresham's 'law' really is true. (If one doesn't like Gresham's law, then any true and counterfactual supporting generalization of any conceivable future economics will probably do as well.) Gresham's law says something about what will happen in monetary exchanges under certain conditions. I am willing to believe that physics is general in the sense that it implies that any event which consists of a monetary exchange (hence any event which falls under Gresham's law) has a true description in the vocabulary of physics and in virtue of which it falls under the laws of physics. But banal considerations suggest that a
physical description which covers all such events must be wildly disjunctive. Some monetary exchanges involve strings of wampum. Some involve dollar bills. And some involve signing one's name to a check. What are the chances that a disjunction of physical predicates which covers all these events (i.e., a disjunctive predicate which can form the right-hand side of a bridge law of the form 'x is a monetary exchange ... ') expresses a physical kind? In particular, what are the chances that such a predicate forms the antecedent or consequent of some proper law of physics? The point is that monetary exchanges have interesting things in common; Gresham's law, if true, says what one of these interesting things is. But what is interesting about monetary exchanges is surely not their commonalities under physical description. A kind like a monetary exchange could turn out to be coextensive with a physical kind; but if it did, that would be an accident on a cosmic scale. In fact, the situation for reductionism is still worse than the discussion thus far suggests. For reductionism claims not only that all kinds are coextensive with physical kinds, but that the coextensions are nomologically necessary: bridge laws are laws. So, if Gresham's law is true, it follows that there is a (bridge) law of nature such that 'x is a monetary exchange x is P' is true for every value of x, and such that P is a term for a physical kind. But, surely, there is no such law. If there were, then P would have to cover not only all the systems of monetary exchange that there are, but also all the systems of monetary exchange that there could be; a law must succeed with the counterfactuals. What physical predicate is a candidate for P in 'x is a nomologically possible monetary exchange iff Px'? To summarize: An immortal econophysicist might, when the whole show is over, find a predicate in physics that was, in brute fact, coextensive with 'is a monetary exchange'. If physics is
Jerry A. Fodor general - if the ontological biases of reductionism are true - then there must be such a predicate. But (a) to paraphrase a remark Professor Donald Davidson made in a slightly different context, nothing but brute enumeration could convince us of this brute coextensivity, and (b) there would seem to be no chance at all that the physical predicate employed in stating the coextensivity would be a physical kind term, and (c) there is still less chance that the coextension would be lawful (i.e., that it would hold not only for the nomologically possible world that turned out to be real, but for any nomologically possible world at all). 5 I take it that the preceding discussion strongly suggests that economics is not reducible to physics in the special sense of reduction involved in claims for the unity of science. There is, I suspect, nothing peculiar about economics in this respect; the reasons why economics is unlikely to reduce to physics are paralleled by those which suggest that psychology is unlikely to reduce to neurology. If psychology is reducible to neurology, then for every psychological kind predicate there is a coextensive neurological kind predicate, and the generalization which states this coextension is a law. Clearly, many psychologists believe something of the sort. There are departments of psychobiology or psychology and brain science in universities throughout the world whose very existence is an institutionalized gamble that such lawful coextensions can be found. Yet, as has been frequently remarked in recent discussions of materialism, there are good grounds for hedging these bets. There are no firm data for any but the grossest correspondence between types of psychological states and types of neurological states, and it is entirely possible that the nervous system of higher organisms characteristically achieves a given psychological end by a wide variety of neurological means. It is also possible that given neurological structures subserve many different psychological functions at different times, depending upon the character of the activities in which the organism is engaged. 6 In either event, the attempt to pair neurological structures with psychological functions could expect only limited success. Physiological psychologists of the stature of Karl Lashley have held this sort of view. The present point is that the reductionist program in psychology is clearly not to be defended on ontological grounds. Even if (token) psychological events are (token) neurological events, it does not follow that the kind predicates of psychology are
coextensive with the kind predicates of any other discipline (including physics). That is, the assumption that every psychological event is a physical event does not guarantee that physics (or, afortiori, any other discipline more general than psychology) can provide an appropriate vocabulary for psychological theories. I emphasize this point because I am convinced that the make-or-break commitment of many physiological psychologists to the reductionist program stems precisely from having confused that program with (token) physicalism. What I have been doubting is that there are neurological kinds coextensive with psychological kinds. What seems increasingly clear is that, even if there are such coextensions, they cannot be lawful. For it seems increasingly likely that there are nomologically possible systems other than organisms (viz., automata) which satisfy the kind predicates of psychology but which satisfy no neurological predicates at all. Now, as Putnam has emphasized,7 if there are any such systems, then there must be vast numbers, since equivalent automata can, in principle, be made out of practically anything. If this observation is correct, then there can be no serious hope that the class of automata whose psychology is effectively identical to that of some organism can be described by physical kind predicates (though, of course, if token physicalism is true, that class can be picked out by some physical predicate or other). The upshot is that the classical formulation of the unity of science is at the mercy of progress in the field of computer simulation. This is, of course, simply to say that that formulation was too strong. The unity of science was intended to be an empirical hypothesis, defeasible by possible scientific findings. But no one had it in mind that it should be defeated by Newell, Shaw, and Simon. I have thus far argued that psychological reductionism (the doctrine that every psychological natural kind is, or is coextensive with, a neurological natural kind) is not equivalent to, and cannot be inferred from, token physicalism (the doctrine that every psychological event is a neurological event). It may, however, be argued that one might as well take the doctrines to be equivalent, since the only possible evidence one could have for token physicalism would also be evidence for reductionism: viz., that such evidence would have to consist in the discovery of type-to-type psychophysical correlations. A moment's consideration shows, however, that this argument is not well taken. If type-to-type
Special Sciences
psychophysical correlations would be evidence for token physicalism, so would correlations of other specifiable kinds. We have type-to-type correlations where, for every n-tuple of events that are of the same psychological kind, there is a correlated n-tuple of events that are of the same neurological kind. 8 Imagine a world in which such correlations are not forthcoming. What is found, instead, is that for every n-tuple of type-identical psychological events, there is a spatiotemporally correlated ntuple of type-distinct neurological events. That is, every psychological event is paired with some neurological event or other, but psychological events of the same kind are sometimes paired with some neurological events of different kinds. My present point is that such pairings would provide as much support for token physicalism as type-to-type pairings do so long as we are able to show that the typedistinct neurological events paired with a given kind of are identical in respect of whatever properties are relevant to type identification in psychology. Suppose, for purposes of explication, that
It is only that such correlations might give us as much reason to be token physicalists as typeto-type correlations would. If this is correct, then epistemological arguments from token physicalism to reductionism must be wrong. It seems to me (to put the point quite generally) that the classical construal of the unity of science has really badly misconstrued the goal of scientific reduction. The point of reduction is not primarily to find some natural kind predicate of physics coextensive with each kind predicate of a special science. It is, rather, to explicate the physical mechanisms whereby events conform to the laws of the special sciences. I have been arguing that there is no logical or epistemological reason why success in the second of these projects should require success in the first, and that the two are likely to come apart in fact wherever the physical mechanisms whereby events conform to a law of the special sciences are heterogeneous.
p~ychological event
psychological events are type-identified by reference to their behavioral consequences. 9 Then what is required of all the neurological events paired with a class of type-homogeneous psychological events is only that they be identical in respect of their behavioral consequences. To put it briefly, type-identical events do not, of course, have all their properties in common, and type-distinct events must nevertheless be identical in some of their properties. The empirical confirmation of token physicalism does not depend on showing that the neurological counterparts of type-identical psychological events are themselves type-identical. What needs to be shown is just that they are identical in respect of those properties which determine what kind of p~y(hological event a given event is. Could we have evidence that an otherwise heterogeneous set of neurological events have those kinds of properties in common? Of course we could. The neurological theory might itself explain why an n-tuple of neurologically type-distinct events are identical in their behavioral consequences, or, indeed, in respect of any of indefinitely many other such relational properties. And, if the neurological theory failed to do so, some science more basic than neurology might succeed. My point in all this is, once again, not that correlations between type-homogeneous psychological states and type-heterogeneous neurological states would prove that token physicalism is true.
I take it that the discussion thus far shows that reductionism is probably too strong a construal of the unity of science; on the one hand, it is incompatible with probable results in the special sciences, and, on the other, it is more than we need to assume if what we primarily want, from an ontological point of view, is just to be good token physicalists. In what follows, I shall try to sketch a liberalized version of the relation between physics and the special sciences which seems to me to be just strong enough in these respects. I shall then give a couple of independent reasons for supposing that the revised doctrine may be the right one. The problem all along has been that there is an open empirical possibility that what corresponds to the kind predicates of a reduced science may be a heterogeneous and unsystematic disjunction of predicates in the reducing science. We do not want the unity of science to be prejudiced by this possibility. Suppose, then, that we allow that bridge statements may be of this form, (4)
Sx
P~y V PiyV ... V
P;y
The point would be that the schema in figure 39.1 implies PIX -> Piy, Pzx -> P~y, etc., and the argument from a premise of the form (P::) R) and (Q::) 5) to a conclusion of the form (P V Q) ::) (R V 5) is valid. What I am inclined to say about this is that it just shows that 'it's a law that - ' defines a non-truthfunctional context (or, equivalently for these purposes, that not all truth functions ofkind predicates are themselves kind predicates); in particular, that one may not argue from: 'it's a law that P brings about R' and 'it's a law that Q brings about 5' to 'it's a law that P or Q brings about R or S'. Though, of course, the argument from those premises to 'P or Q brings about R or 5' simpliciter is fine.) I think, for example, that it is a law that the irradiation of green plants by sunlight causes carbohydrate synthesis, and I think that it is a law that friction causes heat, but I do not think that it is a law that (either the irradiation of green plants by sunlight or friction) causes (either carbohydrate synthesis or heat). Correspondingly, I doubt that 'is either
science:
Disjunctive predicate reducing science:
of PiX V
I Laws
each disjunct of PI V Pz V ... V Pn is a kind predicate, as is each disjunct of PI V Pi V ... V P~. This, however, is where push comes to shove. For it might be argued that if each disjunct of the P disjunction is lawfully connected to some disjunct of the P* disjunction, then it follows that formula (5) is itself a law.
of redUCing science:
P2 x
v . . . Pnx,
•
P'x
P*iY v . . ,P*2Y v . .. P*m Y
•
~
I
•
Figure 39.1 Schematic representation of the proposed relation between the reduced and the reducing science on a revised account of the unity of science. If any SI events are of the type pI, they will be exceptions to the law Sp' -> S2Y.
Special Sciences
carbohydrate synthesis or heat' is plausibly taken to be a kind predicate. It is not strictly mandatory that one should agree with all this, but one denies it at a price. In particular, if one allows the full range of truth-functional arguments inside the context 'it's a law that ~', then one gives up the possibility of identifying the kind predicates of a science with the ones which constitute the antecedents or consequents of its proper laws. (Thus formula (5) would be a proper law of physics which fails to satisfy that condition.) One thus inherits the need for an alternative construal of the notion of a kind, and I don't know what that alternative would be like. The upshot seems to be this. If we do not require that bridge statements must be laws, then either some of the generalizations to which the laws of special sciences reduce are not themselves lawlike, or some laws are not formulable in terms of kinds. Whichever way one takes formula (5), the important point is that the relation between sciences proposed by figure 39.1 is weaker than what standard reductionism requires. In particular, it does not imply a correspondence between the kind predicates of the reduced and the reducing science. Yet it does imply physicalism given the same assumption that makes standard reductionism physicalistic: viz., that bridge statements express token event identities. But these are precisely the properties that we wanted a revised account of the unity of science to exhibit. I now want to give two further reasons for thinking that this construal of the unity of science is right. First, it allows us to see how the laws of the special sciences could reasonably have exceptions, and, second, it allows us to see why there are special sciences at all. These points in turn. Consider, again, the model of reduction implicit in formulae (2) and (3). I assume that the laws of basic science are strictly exception less, and I assume that it is common knowledge that the laws of the special sciences are not. But now we have a dilemma to face. Since '--+' expresses a relation (or relations) which must be transitive, formula (1) can have exceptions only if the bridge laws do. But if the bridge laws have exceptions, reductionism loses its ontological bite, since we can no longer say that every event which consists of the satisfaction of an S predicate consists of the satisfaction of a P predicate. In short, given the reductionist model, we cannot consistently assume that the bridge laws and the basic laws are exceptionless while assuming that the special laws are not. But we cannot accept
the violation of the bridge laws unless we are willing to vitiate the ontological claim that is the main point of the reductionist program. We can get out of this (salve the reductionist model) in one of two ways. We can give up the claim that the special laws have exceptions, or we can give up the claim that the basic laws are exceptionless. I suggest that both alternatives are undesirable - the first because it flies in the face of fact. There is just no chance at all that the true, counterfactual supporting generalizations of, say, psychology, will turn out to hold in strictly each and every condition where their antecedents are satisfied. Even when the spirit is willing, the flesh is often weak. There are always going to be behavioral lapses which are physiologically explicable but which are uninteresting from the point of view of psychological theory. But the second alternative is not much better. It may, after all, turn out that the laws of basic science have exceptions. But the question arises whether one wants the unity of science to depend on the assumption that they do. On the account summarized figure 39.1, however, everything works out satisfactorily. A nomologically sufficient condition for an exception to SIX --+ S2.Y is that the bridge statements should identify some occurrence of the satisfaction of Sl with an occurrence of the satisfaction of any P* predicate which is not itself lawfully connected to the satisfaction of any P* predicate (i.e., suppose Sl is connected to pi such that there is no law which connects pi to any predicate which bridge statements associate with Sz. Then any instantiation of S I which is contingently identical to an instantiation of pi will be an event which constitutes an exception to SIX --+ S2.Y). Notice that, in this case, we need assume no exceptions to the laws of the reducing science, since, by hypothesis, formula (5) is not a law. In fact, strictly speaking formula (5) has no status in the reduction at all. It is simply what one gets when one universally quantifies a formula whose antecedent is the physical disjunction corresponding to Sl and whose consequent is the physical disjunction corresponding to Sz. As such, it will be true when SIX --+ S2.Y is exceptionless and false otherwise. What does the work of expressing the physical mechanisms whereby n-tuples of events conform, or fail to conform, to SIX --+ S2.Y is not formula (5) but the laws which severally relate elements of the disjunction PI V P z V ... V Pn to elements of the disjunction P; V Pi V ... V P~ Where there is a law which relates an event that
Jerry A. Fodor satisfies one of the P disjuncts to an event which satisfies one of the P* disjuncts, the pair of events so related conforms to SIX --t SzY. When an event which satisfies a P predicate is not related by law to an event which satisfies a P* predicate, that event will constitute an exception to SIX --t Szy. The point is that none of the laws which effect these several connections need themselves have exceptions in order that SIX --t Szy should do so. To put this discussion less technically: We could, if we liked, require the taxonomies of the special sciences to correspond to the taxonomy of physics by insisting upon distinctions between the kinds postulated by the former whenever they turn out to correspond to distinct kinds in the latter. This would make the laws of the special sciences exceptionless if the laws of basic science are. But it would also likely lose us precisely the generalizations which we want the special sciences to express. (If economics were to posit as many kinds of monetary systems as there are physical realizations of monetary systems, then the generalizations of economics would be exceptionless - but, presumably, only vacuously so, since there would be no generalizations left for economists to state. Gresham's law, for example, would have to be formulated as a vast, open disjunction about what happens in monetary system I or monetary system. under conditions which would themselves defy uniform characterization. We would not be able to say what happens in monetary systems tout court since, by hypothesis, 'is a monetary system' corresponds to no kind of predicate of physics.) In fact, what we do is precisely the reverse. We allow the generalizations of the special sciences to have exceptions, thus preserving the kinds to which the generalizations apply. But since we know that the physical descriptions of the members of these kinds may be quite heterogeneous, and since we know that the physical mechanisms which connect the satisfaction of the antecedents of such generalizations to the satisfaction of their consequents may be equally diverse, we expect both that there will be exceptions to the generalizations and that these will be 'explained away' at the level of the reducing science. This is one of the respects in which physics really is assumed to be bedrock science; exceptions to its generalizations (if there are any) had better be random, because there is nowhere 'further down' to go in explaining the mechanism whereby the exceptions occur. This brings us to why there are special sciences at all. Reductionism, as we remarked at the outset,
flies in the face of the facts about the scientific institution: the existence of a vast and interleaved conglomerate of special scientific disciplines which often appear to proceed with only the most casual acknowledgment of the constraint that their theories must turn out to be physics 'in the long run'. I mean that the acceptance of this constraint often plays little or no role in the practical validation of theories. Why is this so? Presumably, the reductionist answer must be entire~v epistemological. If only physical particles weren't so small (if only brains were on the outside, where one can get a look at them), then we would do physics instead of paleontology (neurology instead of psychology, psychology instead of economics, and so on down). There is an epistemological reply: viz., that even if brains were out where they could be looked at, we wouldn't, as things now stand, know what to look for. We lack the appropriate theoretical apparatus for the psychological taxonomy of neurological events. ffit turns out that the functional decomposition of the nervous system corresponds precisely to its neurological (anatomical, biochemical, physical) decomposition, then there are only epistemological reasons for studying the former instead of the latter. But suppose that there is no such correspondence? Suppose the functional organization of the nervous system cross-cuts its neurological organization. Then the existence of psychology depends not on the fact that neurons are so depressingly small, but rather on the fact that neurology does not posit the kinds that psychology requires. I am suggesting, roughly, that there are special sciences not because of the nature of our epistemic relation to the world, but because of the way the world is put together: not all the kinds (not all the classes of things and events about which there are important, counter factual supporting generalizations to make) are, or correspond to, physical kinds. A way of stating the classical reductionist view is that things which belong to different physical kinds ipso facto can have none of their projectable descriptions in common: 10 that if X and y differ in those descriptions by virtue of which they fall under the proper laws of physics, they must differ in those descriptions by virtue of which they fall under any laws at all. But why should we believe that this is so? Any pair of entities, however different their physical structure, must nevertheless converge in indefinitely many of their properties. Why should there not be, among those convergent properties, some whose lawful interrelations support
Special SCiences the generalizations of the special sciences? Why, in short, should not the kind predicates of the special sciences cross-classify the physical natural kinds? Physics develops the taxonomy of its subject matter which best suits its purposes: the formulation of exceptionless laws which are basic in the several senses discussed above. But this is not the only taxonomy which may be required if the purposes of science in general are to be served: e.g., if we are to state such true, counterfactual supporting
generalizations as there are to state. So there are special sciences, with their specialized taxonomies, in the business of stating some of these generalizations. If science is to be unified, then all such taxonomies must apply to the same things. If physics is to be basic science, then each of these things had better be a physical thing. But it is not further required that the taxonomies which the special sciences employ must themselves reduce to the taxonomy of physics. It is not required, and it is probably not true.
Notes For expository convenience, I shall usually assume that sciences are about events in at least the sense that it is the occurrence of events that makes the laws of a science true. Nothing, however, hangs on this assumption. 2 The version of reductionism I shall be concerned with is a stronger one than many philosophers of science hold, a point worth emphasizing, since my argument will be precisely that it is too strong to get away with. Still, I think that what I shall be attacking is what many people have in mind when they refer to the unity of science, and I suspect (though I shan't try to prove it) that many of the liberalized versions of reductionism sutTer from the same basic defect as what I shall take to be the classical form of the doctrine. 3 There is an implicit assumption that a science simply is a formulation of a set of laws. I think that this assumption is implausible, but it is usually made when the unity of science is discussed, and it is neutral so far as the main argument of this chapter is concerned. 4 I shall sometimes refer to 'the predicate which constitutes the antecedent or consequent of a law'. This is shorthand for 'the predicate such that the antecedent or consequent of a law consists of that predicate, together with its bound variables and the quantifiers which bind them' .. P. Oppenheim and H. Putnam, "Unity of science as a working hypothesis," in H. Feigl, M. Scriven, and G. Maxwell (cds), Minnesota Studies in the Philosophy oj Science, vol. 2 (Minneapolis: University of Minnesota Press, 1958), pp. 3-36, argue that the social sciences probably can be reduced to physics assuming that the reduction proceeds via (individual) psychology. Thus, they remark, "in economics, if very weak assumptions are satisfied, it is possible to represent the way in which an individual orders his choices by means of an individual preference function. In terms of these functions, the economist attempts to explain group phenomena, such as the market, to account for
collective consumer behavior, to solve the problems of welfare economics, etc." (p. 17). They seem not to have noticed, however, that even if such explanations can be carried through, they would not yield the kind of predicate-by-predicate reduction of economics to psychology that Oppenheim and Putnam's own account of the unity of science requires. Suppose that the laws of economics hold because people have the attitudes, motives, goals, needs, strategies, etc., that they do. Then the fact that economics is the way it is can be explained by reference to the fact that people are the way that they are. But it doesn't begin to follow that the typical predicates of economics can be reduced to the typical predicates of psychology. Since bridge laws entail biconditionals, PI reduces to Pz only if PI and Pz are at least coextensive. But while the typical predicates of economics subsume (e.g.) monetary systems, cash flows, commodities, labor pools, amounts of capital invested, etc., the typical predicates of psychology subsume stimuli, responses, and mental states. Given the proprietary sense of 'reduction' at issue, to reduce economics to psychology would therefore involve a very great deal more than showing that the economic behavior of groups is determined by the psychology of the individuals that constitute them. In particular, it would involve showing that such notions as commodity, labor pool, etc., can be reconstructed in the vocabulary of stimuli, responses, and mental states, and that, moreover, the predicates which affect the reconstruction express psychological kinds (viz., occur in the proper laws of psychology). I think it's fair to say that there is no reason at all to suppose that such reconstructions can be provided: prima facie there is every reason to think that they cannot. 6 This would be the case if higher organisms really are interestingly analogous to general-purpose computers. Such machines exhibit no detailed structureto-function correspondence over time: rather, the function subserved by a given structure may change from instant to instant depending upon the
Jerry A. Fodor character of the program and of the computation being performed. 7 H. Putnam, "Minds and machines," in S. Hook (ed.), Dimensions ojMind (New York, New York University Press, (1960), pp. 138-64. 8 To rule out degenerate cases, we assume that n is large enough to yield correlations that are significant in the statistical sense.
9 I don't think there is any chance at all that this is true. What is more likely is that type identification for psychological states can be carried out in terms of the 'total states' of an abstract automation which models the organism whose states they are. 10 For the notion of projectability, see N. Goodman, Fact, Fiction and Forecast (Indianapolis: BobbsMerrill, 1965).
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Jaegwon Kim
Introduction It is part of today's conventional wisdom in philosophy of mind that psychological states are "multiply realizable," and are in fact so realized, in a variety of structures and organisms. We are constantly reminded that any mental state, say pain, is capable of "realization," "instantiation," or "implementation" in widely diverse neural-biological structures in humans, felines, reptiles, molluscs, and perhaps other organisms further removed from us. Sometimes we are asked to contemplate the possibility that extraterrestrial creatures with a biochemistry radically different from the earthlings', or even electromechanical devices, can "realize the same psychology" that characterizes humans. This claim, to be called hereafter "the Multiple Realization Thesis" ("MR,"] for short), is widely accepted by philosophers, especially those who are inclined to favor the functionalist line on mentality. I will not here dispute the truth of MR, although what I will say may prompt a reassessment of the considerations that have led to its nearly universal acceptance. And there is an influential and virtually uncontested view about the philosophical significance of MR. This is the belief that MR refutes psychophysical reductionism once and for all. In particu-
Originally published in Philosophy and Phenomenological Research 52 (1992), pp. 309-35. Reprinted by permission of Brown University, Providence, 1992.
lar, the classic psychoneural identity theory of Feigl and Smart, the so-called type physicalism, is standardly thought to have been definitively dispatched by MR to the heap of obsolete philosophical theories of mind. At any rate, it is this claim, that MR proves the physical irreducibility of the mental, that will be the starting point of my discussIOn. Evidently, the current popularity of anti-reductionist physicalism is owed, for the most part, to the influence of the MR-based anti-reductionist argument originally developed by Hilary Putnam and elaborated further by Jerry Fodor 2 - rather more so than to the "anomalist" argument associated with Donald Davidson. 3 For example, in their elegant paper on nonreductive physicalism,4 Geoffrey Hellman and Frank Thompson motivate their project in the following way: Traditionally, physicalism has taken the form of reductionism - roughly, that all scientific terms can be given explicit definitions in physical terms. Of late there has been growing awareness, however, that reductionism is an unreasonably strong claim. But why is reductionism "unreasonably strong"? In a footnote Hellman and Thompson explain, citing Fodor's "Special Sciences": Doubts have arisen especially in connection with functional explanation in the higher-level sciences (psychology, linguistics, social theory,
Jaegwon Kim
etc.). Functional predicates may be physically realizable in heterogeneous ways, so as to elude physical definition. And Ernest Lepore and Barry Loewer tell us this: It is practically received wisdom among philosophers of mind that psychological properties (including content properties) are not identical to neurophysiological or other physical properties. The relationship between psychological and neurophysiological properties is that the latter realize the former. Furthermore, a single psychological property might (in the sense of conceptual possibility) be realized by a large number, perhaps infinitely many, of different physical properties and even by non-physical properties. 5
They then go on to sketch the reason why MR, on their view, leads to the rejection of mind-body reduction: If there are infinitely many physical (and perhaps nonphysical) properties which can realize F, then F will not be reducible to a basic physical property. Even if F can only be realized by finitely many basic physical properties, it might not be reducible to a basic physical property since the disjunction of these properties might not itself be a basic physical property (i.e., occur in a fundamental physical law). We will understand "multiple realizability" as involving such irreducibility.6 This anti-reductionist reading of MR continues to this day; in a recent paper, Ned Block writes: Whatever the merits of physiological reductionism, it is not available to the cognitive science point of view assumed here. According to cognitive science, the essence of the mental is computational, and any computational state is "multiply realizable" by physiological or electronic states that are not identical with one another, and so content cannot be identified with anyone ofthem. 7 Considerations of these sorts have succeeded in persuading a large majority of philosophers of minds to reject reductionism and type physicalism. The upshot of all this has been impressive: MR has not only ushered in "nonreductive physicalism" as
the new orthodoxy on the mind-body problem, but in the process has put the very word "reductionism" in disrepute, making reductionisms of all stripes an easy target of disdain and curt dismissals. I believe a reappraisal of MR is overdue. There is something right and instructive in the antireductionist claim based on MR and the basic argument in its support, but I believe that we have failed to follow out the implications of MR far enough, and have as a result failed to appreciate its full significance. One specific point that I will argue is this: the popular view that psychology constitutes an autonomous special science, a doctrine heavily promoted in the wake of the MR-inspired anti-reductionist dialectic, may in fact be inconsistent with the real implications of MR. Our discussion will show that MR, when combined with certain plausible metaphysical and methodological assumptions, leads to some surprising conclusions about the status of the mental and the nature of psychology as a science. I hope it will become clear that the fate of type physicalism is not among the more interesting consequences of MR.
2 Multiple Realization It was Putnam, in a paper published in 1967,9 who first injected MR into debates on the mind-body problem. According to him, the classic reductive theories of mind presupposed the following naive picture of how psychological kinds (properties, event and state types, etc.) are correlated with physical kinds: For each psychological kind M there is a unique physical (presumably, neurobiological) kind P that is nomologically coextensive with it (i.e., as a matter oflaw, any system instantiates M at tiff that system instantiates Pat t). (We may call this "the Correlation Thesis.") So take pain: the Correlation Thesis has it that pain as an event kind has a neural substrate, perhaps as yet not fully and precisely identified, that, as a matter oflaw, always co-occurs with it in all pain-capable organisms and structures. Here there is no mention of species or types of organisms or structures: the neural correlate of pain is invariant across biological species and structure types. In his 1967 paper, Putnam pointed out something that, in retrospect, seems all too obvious:
Multiple Realization and Reduction
Consider what the brain-state theorist has to do to make good his claims. He has to specify a physical-chemical state such that any organism (not just a mammal) is in pain if and only if(a) it possesses a brain of a suitable physical-chemical structure; and (b) its brain is in that physicalchemical state. This means that the physicalchemical state in question must be a possible state of a mammalian brain, a reptilian brain, a mollusc's brain (octopuses are mollusca, and certainly feel pain), etc. At the same time, it must not be a possible brain of any physically possible creature that cannot feel pain. 10 Putnam went on to argue that the Correlation Thesis was empirically false. Later writers, however, have stressed the multiple realizability of the mental as a conceptual point: it is an a priori, conceptual fact about psychological properties that they are "second-order" physical properties, and that their specification does not include constraints on the manner of their physical implementation. I I Many proponents of the functionalist account of psychological terms and properties hold such a vIew. Thus, on the new, improved picture, the relationship between psychological and physical kinds is something like this: there is no single neural kind N that "realizes" pain across all types of organisms or physical systems; rather, there is a multiplicity of neural-physical kinds, N h , N" N m , . .. such that Nh realizes pain in humans, NT realizes pain in reptiles, N m realizes pain in Martians, etc. Perhaps, biological species as standardly understood are too broad to yield unique physical-biological realization bases; the neural basis of pain could perhaps change even in a single organism over time. But the main point is clear: any system capable of psychological states (that is, any system that "has a psychology") falls under some structure type T such that systems with structure T share the same physical base for each mental state-kind that they are capable of instantiating (we should regard this as relativized with respect to time to allow for the possibility that an individual may fall under different structure types at different times). Thus physical realization bases for mental states must be relativized to species or, better, physical structure types. We thus have the following thesis: If anything has mental property M at time t, there is some physical structure type T and physical property P such that it is a system of
type Tat t and has P at t, and it holds as a matter of law that all systems of type T have M at a time just in case they have P at the same time. We may call this "the Structure-Restricted Correlation Thesis" (or "the Restricted Correlation Thesis" for short). It may have been noticed that neither this nor the correlation thesis speaks of "realization." 12 The talk of "realization" is not metaphysically neutral: the idea that mental properties are "realized" or "implemented" by physical properties carries with it a certain ontological picture of mental properties as derivative and dependent. There is the suggestion that when we look at concrete reality, there is nothing over and beyond instantiations of physical properties and relations, and that the instantiation on a given occasion of an appropriate physical property in the right contextual (often causal) setting simply counts as, or constitutes, an instantiation of a mental property on that occasion. An idea like this is evident in the functionalist conception of a mental property as extrinsically characterized in terms of its "causal role," where what fills this role is a physical (or, at any rate, nonmental) property (the latter property will then be said to "realize" the mental property in question). The same idea can be seen in the related functionalist proposal to construe a mental property as a "second-order property" consisting in the having of a physical property satisfying certain extrinsic specifications. We will recur to this topic later; however, we should note that someone who accepts either of the two correlation theses need not espouse the "realization" idiom. That is, it is prima facie a coherent position to think of mental properties as "first-order properties" in their own right, characterized by their intrinsic natures (e.g., phenomenal feel), which, as it happens, turn out to have nomological correlates in neural properties. (In fact, anyone interested in defending a serious dualist position on the mental should eschew the realization talk altogether and consider mental properties as first-order properties on a par with physical properties.) The main point of MR that is relevant to the anti-reductionist argument it has generated is just this: mental properties do not have nomically coextensive physical properties, when the latter are appropriately individuated. It may be that properties that are candidates for reduction must be thought of as being realized, or implemented, by properties in the prospective reduction base;13 that is, if we think of certain properties as having their own
Jaegwon Kim
intrinsic characterizations that are entirely independent of another set of properties, there is no hope of reducing the former to the latter. But this point needs to be argued, and will, in any case, not playa role in what follows. Assume that property M is realized by property P. How are M and P related to each other and, in particular, how do they covary with each other? Lepore and Loewer say this: The usual conception is that e's being P realizes e's being F iff e is P and there is a strong connection of some sort between P and F. We propose to understand this connection as a necessary connection which is explanatory. The existence of an explanatory connection between two properties is stronger than the claim that P --> F is physically necessary since not every physically necessary connection is explanatory. 14 Thus, Lepore and Loewer require only that the realization base of M be sufficient for M, not both necessary and sufficient. This presumably is in response to MR: if pain is multiply realized in three ways as above, each of N h, N" and N m will be sufficient for pain, and none necessary for it. This I believe is not a correct response, however; the correct response is not to weaken the joint necessity and sufficiency of the physical base, but rather to relativize it, as in the Restricted Correlation Thesis, with respect to species or structure types. For suppose we are designing a physical system that will instantiate a certain psychology, and let MI .... ,Mn be the psychological properties required by this psychology. The design process must involve the specification of an n-tuple of physical properties, PI . ... ,Pn , all of them instantiable by the system, such that for each i, Pi constitutes a necessary and sufficient condition in this system (and others of relevantly similar physical structure), not merely a sufficient one, for the occurrence of Mi. (Each such n-tuple of physical properties can be called a "physical realization" of the psychology in question. IS) That is, for each psychological state we must design into the system a nomologically coextensive physical state. We must do this if we are to control both the occurrence and nonoccurrence ofthe psychological states involved, and control of this kind is necessary if we are to ensure that the physical device will properly instantiate the psychology. (This is especially clear if we think of building a computer; computer
analogies loom large in our thoughts about "realization.") But isn't it possible for multiple realization to occur "locally" as well? That is, we may want to avail ourselves of the flexibility of allowing a psychological state, or function, to be instantiated by alternative mechanisms within a single system. This means that Pi can be a disjunction of physical properties; thus, Mi is instantiated in the system in question at a time if and only if at least one of the disjuncts of Pi is instantiated at that time. The upshot of all this is that Lepore and Loewer's condition that P --> M holds as a matter oflaw needs to be upgraded to the condition that, relative to the species or structure type in question (and allowing P to be disjunctive), P
