Elgin on Lewis's Putnam's Paradox

Elgin on Lewis's Putnam's Paradox Bas C. Van Fraassen The Journal of Philosophy, Vol. 94, No. 2. (Feb., 1997), pp. 85-93. Stable URL: http://links.jstor.org/sici?sici=0022-362X%28199702%2994%3A2%3C85%3AEOLPP%3E2.0.CO%3B2-N The Journal of Philosophy is currently published by Journal of Philosophy, Inc..

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COMMENTS AND CRITICISM ELGIN ON LEWIS'S PUTNAM'S PARADOX* n "Unnatural Science," Catherine Z. Elgin1 examines the dilemma that David Lewis sees posed by Hilary Putnam's modeltheoretic argument against realism. One horn of the dilemma commits us to seeing truth as something all too easily come by, a virtue to be attributed to any theory meeting relatively minimal conditions of adequacy. The other horn commits us to "antinominalism," some version of the ancient doctrine that language must "carve nature at the joints": that there are natural kinds or classes that alone quallfy as referents (extensions) for our predicates. Elgin offers a searching critique of Lewis's response (accepting the second horn) and an illuminating defense of its contrary: "we cannot construe (mere) truth as the end of scientific inquiry. Not ...because truth is too hard to come by, but because it is too easy" (301). I have no issue to take with Elgin's arguments, or indeed most of her main conclusions. But she grants Lewis too much. When Putnam's argument was construed as posing that crucial dilemma, it became an entrance into t h e very kind of metaphysics Putnam intended to undercut. First, I shall outline exactly how (as I see it) Elgin follows Putnam and Lewis in their dialectic. I mean to be accurate but not slavish: the outline should bring to light some possibilities of opting out at various points along the way.

I

I

Elgin's statement of Putnam's argument brings out very clearly its initial incredible degree of generality. Assume the world consists of infinitely many things and consider any theory T that says as much.2 Then there is an interpretation of the language (call it L) in which T is stated which assigns, to all its terms, extensions in the world and which satisfies T. Neither Lewis nor Elgin nor I demur from the proof by which Putnam establishes this. Elgin completes the argument: "Under the resulting truth definition, truth (under that interpretation) is truth. ( T ) then is true" (289). A moment's pause: What explication of truth is indicated here? Let us give it a name:

* I want to thank Catherine 2. Elgin for very helpful discussions and correspondence; also Igor Douven, Mary Kate McGowan, and Gideon Rosen for helpful comments. ' This JOURNAL, XCII, 6 ( June 1995): 289-302. However we construe this 'says as much', it implies that Tis consistent and has an infinite model. 0022-362X/97/9402/85-93

O 1997 The Journal of Philosophy, Inc.

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( E Q T is true if a n d only if T is true under a n interpretation that assigns parts of the world as extensions to the terms of L.

The first response will be to reject this as too generous. I1

Putnarn himself had restricted the scope of his conclusion to ideal theories, as Elkin acknowledges: T "answer[s] to all observational evidence, past, present, and future. It is theoretically adequate: consistent, simple, informative, and so on (add any other theoretical virtues you like) " (289).3 These qualifications play absolutely no role in the proof to which, as I said, we offer no demurral. What role do they play, then? In (EQJ we see all possible interpretations admitted on a par, even the most gruesome (even those which interpret 'green' as 'grue') in Elgin's elegant turn of phrase. But if T can be a real theory stated in part of our language, many such interpretations are unintendgd. The restrictions on T may be regarded as means to cull interpretations. This insight of Lewis's shapes much of the ensuing discussion. That all observation reports framed in L and never taken back or formally contradicted, in the history of the speakers of L, must come out true may be taken as a constraint on interpretations. If T is assumed to contain all those statements, that will ensure that, if it is satisfied by any interpretation, it is satisfied by one that meets this constraint. Therefore, the restriction on T may be seen equally as a constraint on the admissible interpretations (candidates for the status of "intended" interpretation). Putnam himself appears to hold that any constraint we may use to cull interpretations can take this form: the form of specifications concerning what an ideal theory is to contain. That is why he says that any constraints we can impose are all "just more theory." If Putnam is right, there is nothing we can do to evade this result. For whatever we d o is just more theory. I think h e is right. So does Lewis

(290).

The reflection that the original proof was insensitive to the content of T is, of course, grist to Putnam's mill. We may replace the explicaV have omitted Elgin's addition of 'empirically adequate'. As I understand it, a theory is empirically adequate if it is true in part, to a certain extent. The virtues that make for an ideal theory must, in this context, all be ones that we can in principle (if only in the ideal long run) tell before facing questions of truth. Otherwise, why not include truth overall in what makes for an ideal theory? I have also, like Elgin, omitted 'complete', which occurs in Putnam's text but seems neither to play much of a role in the argument nor be the sort of desideratum we could humanly demand of our theories, even in principle.

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tion of truth so as to accommodate the intended/unintended distinction, by revising ( E Q to: (EQ*) T is true if and only if T is true under an admissible interpretation that assigns parts of the world as extensions to the terms of L.

Suppose all the culling of interpretations can proceed, in principle, by insisting that (on any intended interpretation) certain classes of statements in L are to come out true. Require ideal theories to contain all those favored statements. Then the original proof still works, and we conclude: If an ideal theory is true on ( E Q then it is also true on (EQ*).

This defeats any possible critique based on Putnam's mistakenly granting equal rights for the linguistically disadvantaged, in such matters as these. 111

Enter Lewis's dilemma. The first horn: every ideal theory is true (on some admissible interpretation-hence, by EQ* or similarly strong principle, true). Second horn: to be admissible, an interpretation must have virtues beyond that of meeting our intentions. The latter is possible, on the face of it. As Elgin phrases Lewis's second insight, "even if we cannot disqualify motley collections from serving as extensions of our terms and truth makers of our theories,...the world may disqualify them for us" (290). There may be privileged or "natural" classes that alone may be assigned as extensions; any interpretation that fails to do so is inadmissible. Elgin's main agreements and disagreements with Lewis are concisely stated at exactly this point. Using 'Putnam's result' to denote the conclusion that every ideal theory is true (see what I called the first horn of the dilemma), she writes: Lewis contends that unless the world privileges certain schemes of organization, and precludes reference to sufficiently gruesome properties, Putnam's result is inevitable. I agree. Lewis concludes that the world confers such privilege. I conclude that Putnam's result holds (290-91).

This is also the very point where, I shall argue, Elgin has gone too far to meet Lewis's terms for the dialectic. IV

The insertion of 'admissible' into the truth conditions for a theory certainly did something. It provides the form of a solution to the problem posed by the initial argument. Form is not enough. The putative result that all (ideal) theories are true can be avoided by a solution of this form, but only if it has something to be said for it in its

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own right. Thus, Lewis faces two tasks. The first is to give real content to the distinction between natural and arbitrary classes (how the world can "privilege" certain classes or properties). 'Admissible' cannot stand for something like 'whatever it takes to avoid the unwanted result'; it needs real content. The second task is to provide support for the claim that natural classes are the sole candidates for reference. I oversimplify: natural classes are the prime candidates, and anything defined from them is also a candidate, to a degree that varies directly with the complexity of definition (however that is to be spelled out). The simplification does not affect the challenge very much; both the distinction between natural classes and the character or nature of reference need to be spelled out satisfactorily. That means: in such a way that there will (or at the very least, can) be evident support for the claim that reference in our language, by means of our terms, is restricted in such fashion. Elgin's main arguments are to the effect that this second task cannot be carried out successfully, regardless of how the first is performed. To me, these arguments seem very telling, but I shall leave their examination to Lewis; I am anyway not a disinterested party in this matter.* Nor d o I mean to examine the possibilities of success for the first task. Rather, I mean to examine the grounds on which these two tasks could become imperative in the first place.

v In the initial argument, when Elgin completes Putnam's argument by drawing a devastating conclusion from his proof (the conclusion Lewis called Putnam's "bomb"), I construed her as relying on an explication of truth conditions for theories: (EQ T is true if a n d only if T is true under a n interpretation that assigns parts of the world as extensions to the terms of L.

Apart from cardinality constraints due to the world's size,5 this equates truth with consistency-which is absurd. Not only absurd: that equation allocates truth to distinct theories that stand in formal contradiction to each other, thus engendering inconsistency in the strict formal sense. Thus, if we like, we can take the initial argument simply as reductio ad absurdurn of this simplistic attempt to relate the notions of truth, on the one hand, and truth in a model or under an interpretation, on the other. See my Laws and Symmtty (New York: Oxford, 1989), ch. 3, sect. 5. So to speak. What matters is the finite/infinite distinction; and that the context of discussion is classical rather than intuitionistic. j

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The revised condition (EQ*), which results from inserting the placeholder 'admissible', is not subject to that quick reductio. But that is, initially, only because of our ignorance about what is and is not admissible. What must supplant the placeholder 'admissible' to put a genuine halt to Putnam's argument? If the language has two genuinely differing interpretations, there must exist two distinct complete theories (possibly framable only in extensions of language L) which are satisfied by those two interpretations. Given (EQ*), they are both true. But being distinct and complete, they stand in formal contradiction to each other. Although their conjunction may not be expressible in the language in which they are stated (namely, if they are not finitely axiomatizable), it remains that the law of noncontradiction is definitively violated. That is an absurd consequence. Thus, (EQ*) is reduced to absurdity in exactly the same way, unless there is only one single unique admissible interpretation of the language. I am by no means protesting vagueness of reference or the idea that candidacy for reference is a matter of degree. On the contrary! I would assume these to be features of any realistically conceived language. But if they are present, or if even the least bit of leeway of any other sort is allowed, then the language will have more than one admissible interpretation. If that is so, the acceptance of (EQ*) throws us immediately into inc~nsistency.~ Escaping the import of Putnam's argument by the insertion of 'admissible' looked easy. The insight that we can circumvent Putnam's own very limiting strictures, on how intended interpretations are to be demarcated, may have increased its appearance of feasibility. But the ease is deceptive. The reductio is avoided only if correct interpretation is unique-that which there may be very little, in the entire history of philosophy, more difficult to defend. And this on pain not of skepticism or metaphysical discomfort but outright logical inconsistency. It may not be amiss, at this point, to remember Donald Davidson's longstanding cautions about simplistic links between truth and relativized truth. We cannot equate ' 'Snow is white' is true' with 'there TO postulate or require that real language cut nature at the joints gives us a solution that (we granted) does indeed have the form of possibly tenable solution. But look at how much weight the postulate must bear. Suppose that the only constraints we can put on interpretation is that certain sentences about cats, accepted during the history of the human race, must come out m e . Suppose in addition that the only further constraint upon interpretation is that 'cat' must have as extension a natural kind or class. Between the two of them, can they really select a single candidate for that extension?

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is a model of type X in which 'snow is white' is true', unless we can clearly show that the latter is the case if and only if snow is white. VI

When interpretation is our aim, a method of translation deals with the wrong topic, a relation between two languages, where what is wanted is an interpretation of one (in another, of course, but that goes without saying since any theory is in some language) .'

Why should something like (EQ) be so appealing, when it leads so quickly and almost unavoidably to inconsistency? Well, if T is stated in a foreign language, an artificially created language, or a part of our own language that we place under study (during which we describe but do not use it), something like (EQ) is clearly correct. That is, in such a case we are allowed to regard T as true if we can find an interpretation which answers to all our constraints on interpretative engagement, and under which T is satisfied. But note what is allowed, even then: to take T to be true as construed. To go beyond what I have just delimited (either by not restricting the theory under discussion to one stated in described rather than used language, or by allocating truth simpliciter under such conditions) is to bring us at once into those semantic paradoxes to which Alfred Tarski himself alerted us. The point is easily obscured, for it is only right that, for example, English should be studied by English speaking linguists, natural language by those with natural linguistic competence, brains by those who have brains, intelligence by the intelligent. However crudely I have managed to state it now, the point is not only easily obscured but in some of its aspects exceedingly subtle. Consider the question asked by a Dutch speaker: Is het Engels woord 'green' een woord voor groene dingen?

and its putative English translation: Is the English word 'green' a word for green things?

Despite the extreme care I took in translation, recalling even how Alonzo Church famously rapped Rudolf Carnap's knuckles, the two questions are not the same, at least not for native speakers of those two languages. The first question is an empirical question, which the Dutch speaker must settle by empirical research, field work, and can settle to the extent that scientific research can settle any empirical question. But the second question, posed or heard by an English speaker, calls for no

' Donald Davidson, Truth and Infqpetation

(New York: Oxford, 1984), p. 129.

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empirical research. For the English speaker to contemplate a negative answer thereto is to lose coherence. This despite the obvious consideration that the English language might and indeed could have evolved so as to make 'green' a word for red things-and might yet evolve into that condition. But though easily obscured, and in some of its aspects exceedingly subtle, the point is not to be missed. VII

Suppose I do want to explicate the formal conditions of truth for an actual scientific theory-say, QED or psychoanalysis-stated in English. To see whether it is true under some admissible interpretation I must be able to describe the domain of those interpretations (that is, the part of English in which that theory is stated) and their range (that is, the subject matter of those theories). I shall do both in my own language. Indeed, I cannot otherwise. But now, on this assumption that the theory is stated in the language I am using, I shall court contradiction, unless I insist that the admissible interpretations are those which assign the set of photons as extension to the predicate 'is a photon', the set of green things to 'green', and so forth. Thus, we have not only an immediately accessible way to disqmlzljl aU unintended intqbretutions, but one which is imperative, which we must use and may say nothing to contravene, on pain of inconsistency in our own mouths. Am I willfully and unphilosophically dismissing skeptical doubts when I say this? Do I fail to feel the force of those qualms about relying on a language whose reference we have not demonstrably "fixed" firmly in the world? (Do we understand this metaphor?) Just what doubt am I supposed to harbor? The doubt that some green things are not in the extension of my predicate 'is green'? Or the doubt that some things that are not green are accidentally included? Either doubt would make me say things contrary to: The extension of 'is green' is the set of green things.

and so equally contrary to: 'so and so is green' is true if and only if so and so is green.

thus placing me in formal contradiction with some of my most basic convictions, sure to be reflected in any views I propound elsewhere about truth and reference. VIII

Having listened to Tarski and Davidson, to what shall we liken the "carve nature at the joints" solution to Putnam's paradox? Let us lis ten to a dialectic that could lead to that solution. Imagine someone struck by the point noted above, that the "T-sentences," such as:

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'Snow is white' is true if a n d only if snow is white.

which are to be among the consequences of any adequate theory of truth (for the relevant part of our language), are not logically true and d o not express necessary propositions. The English language could have developed in such a way as to make 'white' a word for black things, and might so evolve yet. Having listened to Tarski, this person is convinced that the T-sentences must all be true; but how to explain that? Worse: if 'white' could have had the set of black things as its extension, how can we be sure that it does not? Since snow is white, if 'white' were a word for black things, then 'Snow is white' would not be true. Is there anything we can do to secure guaranteed truth for all the T-sentences? That would require us to get all the extensions of all the predicates "fixed" in just the right way. There is nothing we can do to make sure of this, with so many classes out there as candidates for the extension of each predicate. But wait: reference is a two-place predicate. If we cannot do it alone, the other relatum can help. Our skeptical doubt, which sees the possible extensions of 'white' ranging over all the classes of things there are, is alleviated if we postulate that nature itself restricts the candidates for its extension. Not removed, perhaps, unless we add the hope or postulate of uniqueness; but certainly alleviated. What is wrong with the reasoning that invited this "solution"? Our imaginary person is in effect trying to play two roles at once. To raise a doubt about whether 'white' is a word for white things, or whether 'Snow is white' is true if and only if snow is white, in these very words, requires two things. To do that, on the one hand, she must use the words 'white' and 'snow' to talk about white things and snow; on the other, she must treat the quoted expressions as if they belonged to a foreign language. To do the latter is to insist that 'white' is part of 'Snow is white' only in the sense, famously, that 'can' is part of 'canary'. The frst role is that of native English speaker. It accounts for the felt need to make the T-sentences come out true at all costs. The second role is really the same as that of the Dutch speaker who asks (in his own language) whether the English word 'white' is a word for white things. When playing this role, there can be no legitimately felt need to make the T-sentences come out true. Both roles are intelligible. But they cannot coherently be played both at once! The putative skeptical doubt is an absurdity in the English speaker's mouth; the Dutchman's doubt is intelligible-not skeptical, however, but empirical. Why are the T-sentences true? They are sentences of our owl language, and undeniable to us, though what they say is not necessary.

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They are "pragmatic tautologies." In uttering them assertively we do no more than acknowledge that the quoted words all belong to our language and are properly put together. The word 'true' is a word of our own making, and we are carried along by its peculiar logic. No truth makers are needed to make the T-sentences true. IX

Truth is not easy to come by. In this matter I disagree with Elgin, and agree-verbally-with Lewis. When I say this, however, I take myself to be paying due respect to the logic of 'true'; no more. Is truth on some interpretation at least easy to come by? Sometimes it is and sometimes not; but that is a different matter.' But my agreement with Elgin runs deeper than any disagreement. Specifically, we share the conviction, expressed at the end of her paper and here in my previous section, that the issues under scrutiny belong to pragmatics, not to its impoverished derivative, pure semantics. Truth on some interpretation-that is prime subject matter for semantics, by definition. But truth is not exhausted there. When I use the word 'true' I am interpreting-hence, automatically and trivially, as Davidson points out, interpreting into my own language, the language I am using-and evaluating the accuracy of the text I am interpreting. This practice cannot be adequately dealt with if equated with a subcase of translation between languages, understood in a sense to which the question whether either or both are foreign or my own is irrelevant. O n e of t h e lessons of contemporary philosophy is that form is not detachable from content. My discussion h e r e suggests that pragmatic considerations are not detachable either (302).

I agree. BAS C. VAN FRAASSEN

Princeton University

T h i n k of the amount of effort that has gone into finding interpretations of scientific theories under which they may or might be true. Even in the case of Newton's mechanics and system of the world, let alone for quantum mechanics, the task has not been completed to everyone's satisfaction. But here I am speaking of genuinely admissible interpretations, by criteria that come to light as we progress. I am not speaking about the existence of functions of a certain type, which preoccupies ontology as done among the analytic philosophers.

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Unnatural Science Catherine Z. Elgin The Journal of Philosophy, Vol. 92, No. 6. (Jun., 1995), pp. 289-302. Stable URL: http://links.jstor.org/sici?sici=0022-362X%28199506%2992%3A6%3C289%3AUS%3E2.0.CO%3B2-9

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