A Prolegomenon to Meinongian Semantics Terence Parsons The Journal of Philosophy, Vol. 71, No. 16. (Sep. 19, 1974), pp. 561-580. Stable URL: http://links.jstor.org/sici?sici=0022-362X%2819740919%2971%3A16%3C561%3AAPTMS%3E2.0.CO%3B2-T The Journal of Philosophy is currently published by Journal of Philosophy, Inc..
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A PROLEGOMENON TO ILIEINONGIAN SEMANTICS
561
cause such names (etc.) are intended to belong to things (etc.) whose identity is determined by these rules. If this is correct, then these de re modalities need not in themselves offend empiricists. But, as I have indicated, there may be metaphysical assumptions that underlie our ways of handling identity, and these, 01 course, may be open to dispute. J. L. MACKIE
University College, Oxford
A PROLEGOMENON T O MEINONGIAN SEMANTICS " I t is strange . . . t h a t Meinong's object-theory should have been regarded by some as a bewildering a n d tangled 'jungle', i t resembles r a t h e r a n old formal garden containing some beautiful a n d difficult mazes. . . . Meinong's round square could be stitched, with complete seamlessness, i n t o t h e fabric of Carnap's Meaning and Necessity. J . N . Findlay
I
N section
I of this paper I will describe Meinong's jungle. In section 11 I will attempt to reconstruct it as a formal garden. And in section 111 I will try to place i t within the tradition of semantics to which Carnap's Meaning and Necessity belongs. I make the following claim to historical accuracy: although I don't know what Meinong meant, if I had said what I know him to have said, I would have meant the following. I. THE JUNGLE
Ideally I would begin with a good exposition of Meinong, but that would take too long. Instead I'll give a rough sketch, which may be a caricature.? NIeinong's theory of objects is about objects. What are objects? This much is clear: anything that could be an object of thought is an
* I am indebted to R. Chisholm, G. Fitch, E. Gettier, K. Parsons, R. Routley J. Farrell Smith, J. Vickers, K. Wilson, and (especially) to K. Lambert. Two papers which bear some similarity to this one are H. Castafieda, "Thinking and the Structure of the World," and R. Routley, Exploring Meinong's Jungle, both unpublished manuscripts. t This is based principally on the accounts in A. Meinong, "The Theory of Objects," in R. Chisholm, ed., Realism and the Background of Phenomenology (New York: Free Press, 1960), hereafter abbreviated "M," followed by arabic numerals for section numbers; and in J. N. Findlay, Meinong's Theory of Objects and Values (New York: Oxford, 1963), chs. 11 and VI, hereafter abbreviated "F," followed by arabic numerals for pages or roman numerals for chapters. The quotations from Findlay, above, come from this book, pp. xi and 327, respectively.
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object. This includes all objects which have been conceived, plus objects that could have been, but just weren't lucky enough to attract anyone's attention. You and I are objects. So is the gold mountain. This bothers some people-they think there isn't any gold mountain, so how could it be an object? Of course, if all you mean by saying, "The gold mountain is an object," is "Someone could think about the gold mountain," and if this paraphrase has a funny kind of logical form which doesn't really require reference to an object a t all, then there's no problem. But that isn't Meinong's theory. The gold mountain is a genuine object, and the phrase 'the gold mountain' refers to it. Well, then how come we've never seen the gold mountain? Simple: it doesn't exist. It's a nonexistent possible objectwhich doesn't mean "Possibly it's an object," but rather "It is an object, and i t has the property of being possible." Period. The round square, on the other hand, is also an object, but an impossible one. Unlike the gold mountain, which might have existed, the round square couldn't exist; still that doesn't stop it from being an object. What are these nonexistent objects like, in addition to some being possible and others being impossible? We know a t least this much: the gold mountain is a mountain, and it's made of gold ; the round square is round, and it's also square (M 2). This doesn't tell us much, but it told Bertrand Russell enough to formulate a couple of very tough objections to the the0ry.l First, if the gold mountain is both gold and a mountain, then the existent gold mountain ought to be gold and a mountain and exist. But we've already explained that the gold mountain doesn't exist.2 Second, it's impossible for anything to be both round and square; that would violate the law of noncontradiction. But the round square is both round and square. So, if Meinong is right, the law of noncontradiction is violated. Tough objections! What did Meinong reply? Well, about the existent gold mountain he said, yes, it's existent all right, but it doesn't exist. And about the round square he said, sure it violates the law of noncontradiction-what else would you expect an impossible object to do? Besides, everybody knows that the laws of logic hold only in
* "On Denoting," Mind, XIV, 56 (October 1905): 479-493; "Critical Notice: 'Untersuchungen zur Gegenstandstheorie und Psychologie'," Mind, XIV (1905) ; "Critical Notice: 'Uber die Stellung der Gegenstandstheorie im System der Wissenschaften'," Mind, XVI (1907). For a capsule exposition, see Chisholm, op. cit., pp. 10-11. 2 Actually Russell's original objection concerned the "existent round square" ; Meinong changed this to the "existent gold mountain" (cf. Russell, "Critical Notice: 'Uber die Stellung . . .' " o p cit.). I've maintained the latter form so as not to confuse this with Russell's other objection concerning the round square; see below in text.
A PROLEGOMENON TO MEINONGIAN SEMANTICS
s63
reality, and nonexistent objects like the round square are unreal (cf. F IV). Perhaps one can sympathize with Western philosophy for giving up on Meinong. Nevertheless, I think it was a mistake. T o substantiate this I want to develop a coherent Meinongian theory, a theory that preserves the main points outlined above. Further, it's to be a theory in which persuasive replies can be made to Russell's objections, and in which the replies are in fact exactly those which Meinong made. I'm not going to argue for the truth of the theory I'll sketch. I think that a first step in Meinongian scholarship is to get a version of his theory that is clearly consistent and to find some interesting uses for it. Only then can one begin to question its truth. Before proceeding to my reconstruction, one more aspect of Meinong's philosophy needs to be mentioned: incomplete objects (cf. F VI). Suppose I'm giving you a geometrical proof, and I begin as follows: "Consider a triangle, ABC." Now ask yourself: is the triangle that you're considering equilateral? Or is i t isosceles? Or is i t scalene? There's no answer to these questions. Or maybe in some sense the answer is "no" to all of them. You see, I was about to do a proof about all triangles, and I didn't want to begin by considering an equilateral triangle, for then the proof would just be about eguilateral triangle^.^ And similarly for scalene and isosceles. Well, maybe that's a bad argument; really I want to appeal t o the phenomenological data. I think it's clear that you can "consider a triangle" and that you can do so in such a manner that the object that is then before your mind is neither scalene nor nonscalene. And if so, that's an example of what Meinong calls an incomplete or indeterminate object. It's determinate with respect to being a triangle, but it's indeterminate with respect to scaleneness, color, size, and so on. Incomplete objects will play an important role in the theory I will sketch. 11. THE FORMAL GARDEN
Ideally I would define the notion of being an object in more familiar terms. But I don't know how. Instead I'm going to represent Meinong's theory within a set-theoretic reconstruction of the theory. What I have in mind is the kind of thing that logicists do in the foundations of arithmetic. Instead of talking about numbers, they talk about certain sets. These sets aren't numbers, but they play the role of numbers in the given theory. Maybe you let the empty set Of course you could have considered an equilateral triangle, but you neednt' have.
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represent zero, and then the unit set of the empty set represents one, and so on. Properties of numbers get represented by properties of the sets that represent the numbers. Similarly with relations. And wheri you get done, you have a kind of picture of arithmetic within set theory. This is what I want to do for the theory of objects. I want to use some familiar metaphysical notions plus some set theory to form a reconstruction of the theory of objects. If I succeed 1'11 a t least have communicated the structure of the theory of objects, and maybe that will give us some insight into what objects really are. If successful it would also show the (relative) consistency of the theory of objects, but what I'll do is too sketchy to accomplish that in any very complete sense. The "familiar" metaphysical notions that I'll use include that of being an individual and that of being a property. Since both notions are somewhat obscure, I'll say a little bit about each before beginning with the theory. First, individuals. I include among individuals people, physical objects, shadows, numbers, etc. That leaves the borderline pretty hazy, but for my purposes that's not really important-different decisions about what individuals are will give you different versions of the theory I'm about to sketch, and since I have no idea which version is best, just draw the lines as you like and see what you get. Except: please don't try to include any nonexistent individuals among your individuals. I have nothing against nonexistent individuals, but one of the main points of this theory is to try to analyze the notion of nonexistent objects, so there's no point in beginning with it. 1'11 use '9' to stand for the set of individuals, and i, it,i", . . . to range over them. As for properties, these are all to be "ordinary" properties of individuals. I mean something special by 'ordinary' here, but I'll come back to that later. Examples of ordinary properties are: being blue, being clever, being 6 feet tall, etc. I'll use ' 6' for the set of these properties, and p, p', p", . . . to range over them. I make certain assumptions about properties in order to be sure I have enough of them. One is, if you have an ordinary relation among individuals and if you plug up one end of that relation with a particular individual, then you get a property. Thus, being taller than Socrates is a property, as is being such that Socrates is taller than you. I'll indicate the property got by plugging up relation r with individual i by ir (if it's the left-hand place) or r , (if it's the right-hand pla~e).~ 4
See the Appendix for a partial account of "plugging u p one end of a relation."
A PROLEGOMENON TO MEINONGIAN SEMANTICS
565
1'11 also assume that the negation of a property is itself a property, and 1'11 write that 6. I'll also assume that double negation amounts to identity, i.e., that p = 3. There are a lot of theories about what properties are, and I don't much care which you prefer. If you want to identify properties of individuals with sets of individuals then you get a nice simple version of the theory I am sketching, but with certain drawbacks. Or you might define properties in terms of functions on possible worlds-that's better, but only if you feel comfortable with possible worlds. I sketch both options in the Appendix of this paper. But it's better, I think, just to use the notion of property here with no particular analysis in mind. Individuals are not sets of properties. However, corresponding to each individual is a unique set of properties-the set of properties that the individual has. I call this set the "correlate" of the individunl16and use this notation :
iC
=
{ ~ has : ip]
Likewise, Meinongian objects are not sets of properties either, but I'll talk as if they were. More literally, sets of properties (i.e., subsets of @) will "represent" objects in this theory, much as certain sets of sets represent numbers for logicists.6 I'll use '0' for the set of "objects" (i.e., for the set of things which represent objects), and I'll use o, o', off, . . . as variables which range over 8. Then we define 0 as: O = t h e s e t of all nonempty subsets of 6
i.e., any nonempty set of properties (from 6) will represent an obj e ~ t Now . ~ for every individual there will be an analogous Meinongian object, namely the correlate of that individual ; for the correlate will be a set of properties. For example, if i = Madame Curie, then ic = the set of properties possessed by Madame Curie, and this will -
-
David Lewis calls in the "character" of i ; cf. his "General Semantics," in Donald Davidson and Gilbert Harman, eds., Semantics of Natural Language (Dordrecht: Reidel, 1972). I assume for purposes of exposition that, for every individua! i and every property p, either i has p or i has p. For example, I assume that stones have the property of nonredheadedness, rather than that such a predication makes no sense. Strictly, this is a condition on the meaning of predicate negation: the negation of p is supposed to be a property that is had by all individuals that don't have p. This assumption is strictly for simplicity; a more complete exploration of object theory would investigate the results of relaxing this requirement in various ways. Compare Castaiieda, op. cit., where sets of properties are mapped onto objects by a function, c. 'Strictly speaking, I have defined not 'object', but rather 'objectum'; my "objects" exclude "objectives" ; cf. M 2-4 and F III.
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THE JOURNAL OF PHILOSOPHY
be an object. But Meinongian objects outrun correlates of individuals in a t least three ways: 1. There are incomplete objects. For example, the gold mountain is not determinate with respect to any properties except for its goldness and its mountainhood. I t will be represented by the set (goldness, mountainhood ]. Its incompleteness is represented by the fact that nothing else occurs in the set. For example neither highness nor nonhighness is there, indicating that it is indeterminate with respect to height. No individual correlates are incomplete in this sense.* 2. There are supposed to be objects that don't exist.9 These will simply be sets of properties that aren't the correlates of any individuals. These can be either complete or incomplete. The gold mountain is incomplete, and doesn't exist. Alternatively, if a character in a novel were completely described and if no such person existed, then the complete description would specify a complete object, but one that doesn't exist.lO 3. There are impossible objects, for example, the round square. This object may be represented by (roundness, squareness J . The round square happens to be incomplete, but there are complete impossible objects too; just add enough properties to (roundness, squareness] and you'll have an example. I've been using technical terms without defining them; let me do that now. First : o i s complete = dt ($) ( $ 6 o v fi 6 0 )
So, if you attempt to completely describe an individual, and if you succeed in being complete, then you've specified a complete objectalthough there may be no individual corresponding to it. o i s incomplete = df o is not complete o exists = d f (3 i ) (ic = 0 )
That is, to say that an object exists is to say that there is an jndividual corresponding to it, in the obvious way. [Meinong distinguished two sorts of being: existence and subsistence (M 2). This is a disThis is a consequence of the assumption of fn 5. Some people insist on equating "there are" with "there exist"; such an equation would make nonsense of this account. Even Meinong tends in this direction sometimes; cf. M , end of section 3. But I intend 'there are' in the broadest sensethe sense of 'some'. In particular, my quantifiers are to range over all objects; cf. K. Lambert, "Review Discussion: The Theory of Objects," Inquiry, XVI, 2 (Summer 1973) : 221-230, p. 229. It is clear from M 4 that Meinong would not regard such a quantifier as existentially loaded. lo F 166. To describe such a character directly, property by property, would presumably require a n infinite novel. The point is for illustration only. 9
A PROLEGOMENON TO MEINONGIAN SEMANTICS
567
tinction which I think is not important for my present purposes. Strictly, I have defined 'has being' ; I'm departing from Meinongian terminology in using 'exists' to mean "has being" in the general sense, instead of limiting it to the special sort of being that he uses 'exists' for. I think that this is only a terminological departure from Meinong.] o i s possible = df
0(3 i ) (o E i c )
This means that an object is possible if and only if it is a set of compossible properties. The definition isn't really circular, since I've defined a one-place property of objects in terms of a statement operator. In any event, my purpose is not to analyze the notion of possibility, but rather to communicate to you what it means to ascribe it to an object. (If you like possible worlds, this definition has a neat analysis in terms of them: see the Appendix, Account 11). o is impossible = df o is not possible
Another Meinongian notion" that will be of use later is: o i s embedded i n o' = dr o
C o'
111. A MEINONGIAN SEMANTICS
In discussing an unusual ontology, great care must be taken not to presuppose semantical theories based on other ontologies. One can easily misconstrue Meinong, for example, by reading him as if he were speaking in a Russellian canonical notation. This is one reason for developing a peculiarly Meinongian semantics. Another reason is that an object theory might provide the basis for a natural semantical treatment of ordinary language; some illustration of this will be given below. I t would be nice to give a Meinongian semantics for English, but that's too big a job to do here. So instead I'll use object theory to give a semantics for an artificial language much like the first-order predicate calculus. Anyone who's studied logic has acquired some skill a t "translating" English into the predicate calculus; 1'11 presuppose such skills in informally associating what I do here with English. The artificial language will be called !Dl. Its syntax is roughly that of the predicate calculus. I t has : Names: a , b, c, . . . Variables: x, y, z, . . . Connectives : O , (and others defined in terms of these) Quantifiers : (x) , (3 x) l1
This idea is based on the discussion in F 168.
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The predicates of %! are restricted t o one- and two-place predicates, and they all have superscripts 'n' or 'e' : One place predicates : P n , Qn, Rn, . . . Pe,Qe, Re, . . . Two-place predicates : "Q", "Rn, . . . npe n e n , Re,.. . Q l
, eQn , eR n , . .. epe e e e , Q, Re,... epn
The language also has one extra connective which represents predicate negation; it combines only with one-place predicates that have a superscript of 'n', and it is written: pa. For most of this paper I will ignore two-place predicates, so for now it's just the monadic part I'm discussing. The wffs are defined in the usual manner. But the semantics is nonstandard, 1'11 have to tell you about that. An interpretation of the language consists of a domain of objects plus an assignment, g, which assigns appropriate semantical items to the basic symbols of the language. I'm going t o be interested only in applications in which the domain is equal to 0 : the entire set of objects; in other words, our quantifiers will always range over all objects. T h a t leaves g t o discuss. Names are t o name objects, which means that me require that g(a) E 8 for each name a . For example we might let 'a' name the object which is the correlate of Agatha Christie: g(a) =
( p :A g a t h a Christie has p }
Then 'a' would play the role in this language that the name 'Agatha Christie' plays in English. Similarly, we might have: g(b) =
(p:p is
ascribed t o God b y such a n d such a religion)
Then 'b' might play the role of 'God'.12 g(c) = ( $ : i t is clear from t h e Conan Doyle stories t h a t Sherlock Holmes has pJ
Thus Holmes would live a t 22 Baker Street, be a detective, solve crimes, etc., but would be indeterminate with respect t o having a mole on his left leg. lP Typically, religions are silent about certain characteristics of God; if so our definition would make God be an incomplete (and thus nonexistent) object. I t might be more conducive to the spirit of some religions to let 'b' name some complete superset of the set described in the text. If God exists, then this superset could be specified as: "the correlate of the unique individual that has all the properties in the set specified in the text." If God does not exist, then there is some difficulty in specifying an appropriate complete set.
A PROLEGOMENON TO MEINONGIAN SEMANTICS
$9
Now for the predicates. But first I have t o tell you about their superscripts. 'n' stands for "nuclear", and 'e' stands for "extranuclear." These are Meinongian notions, and they distinguish kinds of properties. A property is nuclear if it's part of the nature of any object that has i t ; otherwise it is extranuclear ( F VI, sec. VIII). Now I suppose you want to know what that means. Well I don't really know how to say; but I find that I have a sort of feel for it that I'll try to communicate to you. First some examples: First, all the properties in @-that is, all the ordinary properties that we started with-are nuclear properties. Second, all the properties that I've defined are extranuclear: being an object, being possible, being complete, . . . These are not members of 6. However this explanation of the distinction is a cheat, since I never really told you what went into set 6 t o begin with. Within the reconstructed theory, the distinction between nuclear and extranuclear properties is artificially precise : nuclear properties are those things which are members of 6 , and thus are members of the sets that represent objects; whereas extranucl&r properties are not members of 6 ;they are represented by properties of these sets. T h a t helps a little. Also, we can generalize somewhat on earlier examples. For example, if philosophers of the past have argued that a certain notion is not a property (as with existence and possibility) then it will be extranuclear. I suspect also that supervenience may also be evidence of extranuclearity. In addition, if having or lacking a given property would affect the identity of a given object, then the property is nuclear, otherwise extranuclear.13 Wnat we really want, however, is some criterion that would sort antecedently identified properties into nuclear and extranuclear. And I have no such criterion. The best I can do, then, is to tell you how the theory is supposed to work, and leave a good explication of these notions for later.14 l3 This is vague; it's a rewording of the idea that nuclear properties, unlike extranuclear ones, constitute part of the natures of objects that have them. Occasionally this has a clear application. For example, "thought about by Russell" cannot be nuclear, for then the round square (i.e., {roundness, squareness))could not have been thought about by Russell without being the round square thought about by Russell (i.e., (roundness, squareness, thought-about-by-Russell-ness)). (This point is due to G. Fitch). This will be discussed more fully in another paper. I might mention here that the disjointness of nuclear and extranuclear properties is assumed in order to give my reconstruction of Meinong's theory a constructive character. Castaiieda, op. cit., does not assume this; however, he does invoke two different manners of analyzing predicates, one manner for the predicates that I have called "nuclear", and another manner for those I call "extranuclear". I do not assume that every English predicate has a unique classification into "nuclear" or "extranuclear"; see discussion of 'exists' below in the text.
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Back to the predicates. Those with superscript n's-the nuclear predicates-stand for nuclear properties. T h a t is, we require that g(Pn) E (P. But this isn't the whole story. We also want to know what objects such a predicate is true of and which it's false of. I'll call the former the "truth set" for the predicate, and the latter its "falsity set." Certainly the correlates of individuals that have g(Pn) should be in the truth set of P n , and the correlates of individuals that lack g(Pn) should be in its falsity set. The rest of the story is the treatment of objects that are not correlates of individuals. Here are the definitions : t ( P U ) = {o: f(PU)= (0:
-
g(Pn)€o} (g(PU)€ 0) & g(pn)
0)
Take the predicate 'blue' for example. Its truth set includes all objects that have blueness as a member. This includes all actual blue things (or their correlates, anyway) plus all the nonactual objects (even incomplete objects) which have blueness as part of their natures. Its falsity set includes all actual objects that aren't blue-because they're all nonblue-plus all the nonactual ones that are nonblue without also being blue. Notice that there are objects that aren't in either the truth set or the falsity set of 'blue'. The round square, for example, is indeterminate with respect to whether or not it's blue: blueness is in neither of its truth-value sets. Now how about extranuclear predicates? They stand for extranuclear properties-properties of objects. Thus we require that g(Pe) = some property appropriate to members of @.I5The truth set for Pe will be specified by this property. For example, t (exists) = ( 0 : (3 i) (ic = o)}, and this can be generalized to cover all the definitions given earlier. It's not completely clear what the falsity sets for extranuclear predicates should be. The simplest line would be to make them the complements of their truth sets: i.e., f(Pe) = 8 t(Pe). Or we could make them smaller in some cases, so that some predications of extranuclear predicates would be indeterminate.16 In this paper I'll focus on the first suggestion, for simplicity. Predicate negation: nuclear predicates can be negated, and the negation of such a predicate is to designate the negation of what the predicate designates ; i.e., g(P") = g p ) . -
-
See the Appendix for a partial account of extranuclear properties. "For example, hleinong would prefer this policy for our "exists" (his "has being") ; he would treat "exists" as: t(exists) = (0: ( 3 4 (io = 0)) f (exists) = (0: o is impossible or (o is complete & (3i)(io = 0))) so that "the triangle exists" would be indeterminate. Cf. F 167. l6
-
A PROLEGOMENON TO MEINONGIAN SEMANTICS
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Now we can define truth relative to an interpretation. I'll start with the atomic cases. If P is a predicate, either nuclear or extranuclear, and if a is a name, then: P a is true iff g(a) e t ( P )
P a is false iff g(a) e f ( P )
Notice that some sentences can lack truth value; this will happen whenever a names an object that is indeterminate with respect t o the property that P stands for. For the general case it is convenient t o talk about objects satisfying wffs. T h e atomic clause here is: o satisfies P x iff o e t (P) o dissatisfies P x iff o E f ( P )
This should be generalized in the usual way t o talk of infinite sequences of objects satisfying or dissatisfying wffs. Then the nonatomic cases go as follows : A sequence s of objects
) - A iff s{dissatisfies)g
satisfies dissatisfies
satisfies
satisfies ) {and) s{satisfies ) iff '{dissatisfies A or dissatisfies satisfies ) (x)A fi{",:): sequence s' just like s except for w h a t dissatisfies satisfies dissatisfies
i t assigns t o x
) (3x)A i f f Pevery ome)
satisfies dissatisfies
{EZzfiesP
sequences' just likes except for what i t assigns to x
{EZf:,es>~
Note: s (dis)satisfies (x)A iff s (dis)satisfies -- (3 x) - - A . Now here are some uses of the language. Symbolize English sentences in the simplest and most obvious ways. Then you get the usual logic-text results, except :I7 Pegasus is a winged horse: Wnp G1 Hnp TRUE Pegasus is left-footed : Lnp INDETERMINATE Pegasus exists : EeP FALSE l 7 I suppose a definition of 'Pegasus' similar to that of 'Sherlock Holmes' given above. There are special difficulties with fictional objects, which I discuss in "A Meinongian Analysis of Fictional Objects," presently in draft.
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(This example, unlike the first two, employs an extranuclear predicate.) There are winged horses :
AMBIGUOUS
The last sentence has two nonequivalent representations. One corresponds to the true thing that people mean when they say things like "There are winged horses-Pegasus, for example." This is symbolized : (3 X ) ( W Xb Hnx)
TRUE
The other corresponds t o the true thing that people say when they deny that there are winged horses; they are denying that there are any real winged horses; this is represented as: (3 X ) (Eex 6' Wnx b Hnx)
FALSE
What about sentences concerning the gold mountain and the round square? Well, these sentences contain definite descriptions, and we haven't yet said how t o treat them in the language. I suggest that these be treated in two ways. First, for ordinary talk about existent objects it's convenient to have a variant of a RussellianStrawsonian definite description. This would go as follows : If A is a wff of one free variable, x, then ( i x ) A is a singular term, and g ( ( i x ) A ) = the one and only object that satisfies A , if there is one : otherwise g ( ( i x ) A ) is undefined. 'Typically, an English expression of the form 'the so and so' would be symbolized ' ( i x ) ( x exists & x is so and so)'. The reason for the addition of 'exists' is that without it the uniqueness clause is rarely satisfied. For example, when Quine asks about "the [merely] possible fat man in the doorway," he uses a definite description which, on this account, fails t o refer-for there are many possible fat men in the do~nvay.'~ However it is clear that, when Meinong talked about the gold mountain, for example, he was not using a definite description that fails t o refer, simply because many objects are both golden and mountains. Some other account is needed; one that will also let Quine ask about the possible man in the doorway without failure of reference. What is needed is the proper generalization of the hypothesis adopted earlier, that when Meinong said "the gold mountain" he was talking about the object: (goldenness, mountainhood]. l8 W. V. Quine, From a Logical Point of View (Cambridge, Mass.: Haward, 1953), p. 4.
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The proposal is : If PI,. . . , P k a r e nuclear predicates of m, t h e n '(mx) (Pi,. . . , Pk)' is a singular t e r m , a n d g ((mx)(PI, . . . , Pk)) = ( g (PI), .. . , g (Pt)1.I9 Notice that the restriction t o nuclear predicates is essential here, since objects are composed of the references of nuclear predicates only. I t is now clear how to answer Russell's obiections about the round square. T h e phrase 'the round square', when construed as a Meinongian description, refers to a certain incomplete object. T h a t object does satisfy the formula 'x is round & x is square', because it satisfies each conjunct singly. Clearly no actual object could satisfy that formula, and we might call this fact a "law" ; stretching things a bit, we might even call it a "law of But, as Meinong points out, laws of this'sort apply only to actual objects, and one need not be surprised t o find that certain nonactual impossible objects "violate" them. I t is unfortunate however, that Meinong and Russell agreed in referring to this state of affairs as a violation of "the law of noncontradiction" ; for the real law of noncontradiction-that no object can satisfy Ax & (AX), for any A (nuclear or extranuclear)is not violated by any object a t all, even the round square.21 The "existent gold mountain" objection is slightly more complicated. Part of the issue has to do with whether or not 'is existent' and 'exists' mean the same; let me avoid begging that question by schematizing the problem sentence ('The existent gold mountain exists') as 'the E l G M Ez'sl, leaving it open that E l and Ez might mean the same. Since it's the Meinongian description that is a t issue,
-
l9 The 'x' in ' ( m x ) 'is superfluous; I include i t out of habit. The reader may find it interesting to compare our two kinds of definite descriptions with >leinongls notions of "auxiliary" and "ultimate" objects; cf. F VI, sec. VIII. Russell says that the laws of logic apply to propositions, not to objects ("Critical Notice: 'Uber die Stellung . . .' " op. cit.). But the notion of satisfaction gives a clear sense in which they can also be said to apply to objects. 21 I t is important t o keep track here of the distinction between pedicate negation and sentence negation (emphasized in this connection by Routley, op. cit.). The "real" law of noncontradiction involves sentence negation ; nothing can satisfy ' A x & N A X ' . This does not mean, however, t h a t nothing can satisfy ' A x & A x ' ; indeed, the nonsquare square satisfies 'square x & nonsquare x'. Excluded middle (and bivalence) is violated even with sentence negation, given our treatment of sentence negation (though it holds for a "wider" sense of negation; cf. F 166-167). For example, the answer to the question, "Is the possible fat man in the doorway bald?" is t h a t there is no answer, and this should not disconcert anyone. B u t many of Quine's "embarrassing" questions about possible objects d o have answers. For example, no t.&~ possible fat men are alike, if 'alike' means "both have and lack exactly the same properties." As for "How many possible fat men are there?", the answer depends on how many properties there are (typically the answer will be, "An infinite number of them, of course"). For Quineans, this may be enough t o refute the theory; for others it may count as a n answer.
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this is symbolized as : Now we must ask whether El ("is existent") is nuclear or extranuclear. And I think we have to admit that neither choice is automatically ruled out for us a t the start. That is, there is an extranuclear sense of existence-the one defined above-and for all we know, that might have been what Russell meant by "existent." On the other hand one might also insist that there is also a nuclear sense of existence. For example, we could define a property of individuals as follows : i is existent = dr (3i') (i' = i)
This would be a nuclear property, the universal property among individuals, and its definition has the form of definitions of existence that have occasionally been proposed.22So I think we must leave it open that Russell might also have meant something like this. So let's proceed on the assumption that we have two options open to us. Now, if El is extranuclear, then Meinong is not committed to the proposed s e n t e n c e f o r he is committed only to the view that any set of nuclear properties yield an object; in terms of the symbolism, if El is extranuclear, then the sentence contains a nonreferring singular term, and the semantics does not make it true. So let's suppose that El is nuclear. Then again we have two options for Ez. If Ez is also nuclear, then our Meinongian semantics does make the sentence true, but this is innocuous. For it's being true does not require that the object referred to correspond to any actual individual. The troublesome version of the sentence is that in which Ez is extranuclear. But in this case the semantics makes the sentence false. These last two points can be put in the following way: Suppose we use 'is existent' for the nuclear sense of existence, and 'exists' for the extranuclear sense. Then our conclusion is: Although t h e existent gold mountain is existent, t h e existent gold mountain does n o t exist.
We're told that it was words like these that Meinong used in reply to Russell. I don't know whether he meant by them what I've attributed to him, but if he did it was the right reply.23 22 Cf. J. Hintikka, "Studies in the Logic of Existence and Necessity; I : Existence," The Monist, L, 1 (January 1966): 55-76. aa Meinong also talked about something he called the "modal moment," and about 'is existent' being a "watered-down version" of 'exists' (cf. F rv). That
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Before moving on to relations I should mention another use of this theory. Professor Findlay has pointed out that incomplete objects resemble Platonic Forms (F 59, 164-166). Now Plato generates puzzles by seeming to hold that the Forms participate in themselves ; e.g., the ideal Bed is itself a bed. On Meinong's theory the sentence "The bed is a bed" is true, and its subject refers to Ibednessl-a good condidate for Plato's ideal Bed.24 Plato's notion of participation can be defined as follows: o
participates in
of = dr of
is embedded in
o
One remaining trick in assimilating Plato to Meinong is a "realityreversal" move; for Plato the things that are really real, the Forms, are things which, in Meinong's terms, don't exist a t all (because they are incomplete). But I think that this is in part just a shift in word meanings. There isn't even this shift between Aristotle and M e i n ~ n g . ~ ~ Finally, if the theory is to be any good, it must provide an acceptable treatment of relational predicates. Syntactically, all relational predicates work in the language by first being converted into complex monadic predicates by having one end plugged up with a singular term. Either end may be plugged up first, and sometimes the order makes a difference: i.e., sometimes [aR]b will differ in significance from ~ [ R b l The . ~ ~syntactical formation rules are these: if a is a singular term, then : [akPj] is a monadic predicate that is nuclear (extranuclear) iff j = n ( j = e). CkPja] is a monadic predicate that is nuclear (extranuclear) iff k = n (k = e).
If we form a monadic predicate by first plugging up its right-hand suggests something like the following: Suppose p is nuclear and P is extranuclear. We say that p is a watered-down version of P if and only if necessarily p applies to exactly those individuals whose correlates P applies to. In the terminology of llccount I1 of the Appendix this is:
(i)(w)[i e p(w) if and only if ic, e P(w)] Then, given our definitions of 'exists' and of 'is existent' in the text, it turns out that 'is existent' is a watered-down version of 'exists'. I discuss this more fully in another paper (presently in draft). 24 Cf. R. Chisholm, "Homeless Objects," Revue Internationale de Philosophie, 104/5 (Fall 1973) : 207-223. 26 That is, for Aristotle, the reality of the forms is parasitic on the reality of particulars; if we count embeddedness as a parasitic kind of reality, we get this result. 26 I am indebted here t o R. Chisholm, especially as regards the problem mentioned in fn 27 below.
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side, then we will usually write its argument before rather than after it; i.e., we'll write a[Rb] instead of [Rbla. The semantics of relational predicates depends on what kind of predicates they are. We'll begin with nuclear-nuclear predicates. These stand for "ordinary" relations among individuals, e.g., kicks, climbs, is taller than, . . . The semantical rule is: g("Pn) = an ordinary two-place relation between individuals. Adding a singular term to either end of such a predicate yields a monadic nuclear predicate, and we need to say which nuclear property it stands for. Suppose we have assigned g(P) = r. Then if g(a) = i" for some individual i, then : g([aP])=
ir
and
g([Pa]) =
ri
That is, if a refers to a real object, then [Pa] refers to the property of bearing r to the individual corresponding to that object; similarly for [UP].But what if a does not refer to a real object [i.e., if g(a) z i", for every i]?Then there appears to be no natural way to define g ([UP]). But then how do we define t ([UP]) and f ([UP]) ? The natural response is to make t([aP]) = A, i.e., [UP]isn't true of anything. With regard to f ([UP]) I see a t least three options: ( 1 ) f ( [ U P ] )= A. Then [aP]b will always be indeterminate. (2) f ( [ a P ] ) = 0. Then [aP]b will always be false. (3) f ( [ a P ] )= the set o f complete objects. Then [aP]b would be false i f g(b) is complete, and indeterminate otherwise.
I suspect that any of these choices will be somewhat arbitrary. The above needs some illustration. First note that if g (a) and g (b) both exist, then a[Rb] is always equivalent to [aR]b, which seems desirable. In other cases, the equivalence breaks down. Here's an example. Let b stand for Billy Graham, let d stand for God, and suppose also that God doesn't exist. We make the additional assumption that creating is a nuclear relation, and that it's part of our conception of God that he created Billy Graham [so the property of creating Billy Graham will be a member of g(d)]. Now, did God create Billy Graham? Well, on the theory given here, that's ambiguous. First, did God have the property of creating Billy Graham? That is, d[Cb] ? The answer is "yes" ; because g ([Cb]) e g (d). But does Billy Graham have the property of being created by God? That is, [dC]b ? And the answer to that is not "yes"; it's either "no" or "no truth value," depending on which choice we made above among (1)-(3). So, you see, we can nicely sever all connection between our theology and our more mundane matters-retaining theological truth with no problematic conflict with worldly truths-sort of a reification of hy-
A PROLEGOMENON TO MEINONGIAN SEMANTICS
577
pocrisy. The two can be brought back together again, of course; all you have to do is to accomplish one of the central goals of natural theology: prove that God exists.27 Let's move on now to nuclear-extranuclear predicates. I suppose that these designate relations between individuals and objects in general, and that paradigm examples are the relations: worships, conceives of, is a picture of, . . Suppose that g(nFe) = a.Then if the nuclear end of this relation gets plugged up first, the result is just as before :
.
If
g(a) = iCfor some i, then : g([anP])
=
ia.
Otherwise it's undefined, and we are faced with choices (1) and (2) above. If it's the extranuclear end that's plugged up first, then: If g(a) = o, t h e n g ( p P a ] ) =
a,.
A nice result of this treatment is that we need no special logical form to account for intentional verbs and related idioms. For example "Jones worships God" is symbolized as either j[Wg] or [jW]g (if j refers to a real individual then the two symbolizations are equivalent). This is either true or false, depending on whether or not Jones does worship God.28 The theory validates the inference: Jones worships a god/
.'.T h e r e i s a god t h a t Jones worships
when 'there is' is read in its widest sense (for both premise and conclusion are symbolized (] x) (Gx & [jW]x)'), but it does not validate : Jones worships a god/.'. T h e r e exists a god t h a t Jones worships (3 X)(Gx G1 CjWlx) / (3 x) (Eex 6.Gx 6CjWlx)
.'.
The theory can also handle cross reference between objects of propositional attitudes, as in : Certain gods were worshipped by both t h e Greeks a n d t h e Romans. 27 This treatment was prompted in part by the following objection to Meinong by K. Wilson: "On Meinong's theory we should have: the giraffe in the corner that is seen by me is seen by me. But I don't see any such giraffe, so how can that be true?" The solution lies in separating (i) the giraffe's having the property of being seen by me, from (ii) my having the property of seeing the giraffe. 28 The standard objection to the symbolization given in the text is that it entails that God exists; but in our system it does not. A related objection has to do with specificity. Supposedly, if I say, "This is a picture of a cow," I may have a particular cow in mind, or I may not. If the latter, then there is supposed to be a difficulty, because it is just a cow-picture, and not about any particular cow. But then why not say that it is about an indeterminate cow? This suggestion will be discussed in a later paper.
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This is symbolized as : (3 x) (Gx & (3 y) (Greek y b (32) (Roman z b
CY W l x
& CzWlx)))
which is either true or false, depending on what the Greeks and Romans did, and does not entail that any gods exist.29 Likewise for witches in one reading of: x believes a witch did
.. .&y
believes s h e also ---
namely, in this reading: (3 z) (witch z & x believes z did
...b y
believes z also - - -)so
Finally, extranuclear-extranuclear predicates: these would refer principally to various abstract relations in the theory of objects: e.g., Plato's "mix" in his questions about which Forms mix with which.31 Here we have the conditions: If g(BP0) = CR and if g ( a ) = o, then : i!([aepB])
=
and
g (CepBa]) =
a,
IV. WHAT ARE OBJECTS?
In section 11 I described a theory in which certain sets represent objects, and in section 111 I sketched a semantics based on that theory. Both enterprises said little about what objects really are-i.e., about what are represented by subsets of 6. In fact, many different interpretations of the representation relation are possible. One might, for example, insist that objects are the sets that we have used to represent them. Or that there really are no objects a t all-nothing is represented; all we have is a pretty metaphysical picture. Or . . But I think the most faithful way to bring Meinong face to face with our modern intuitions is to suppose that objects form a superset of the set of individuals. Specifically, that the objects that correspond to individuals (i.e., the objects represented by correlates of individuals) just are those individuals, and the rest fall outside the class of individuals. In other words, we identify existent objects with individuals, and we suppose that nonexistent objects constitute an expansion of our ontology (insofar as that ontology is originally limited to individuals). Some of the "new" objects look like our old friends, the universals; some (e.g., complete nonexistent objects) are not so familiar.
.
19 This sentence is problematic for Montague's treatment of intentional verbs in his "The Proper Treatment of Quantification in Ordinary English," in J. Hintikka, J. Moravcsik, and P. Suppes, eds., Approaches to Natural Language (Dordrecht: Reidel, 1973). 30 Cf. P. T. Geach, "Intentional Identity." - . this JOURNAL. LXIV.. 20 IOct. . 26, 1967) : 627-632 Cf. any complete edition of Plato, The Sophist.
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E a r l y in this century t h e notion of a nonexistent object fell i n t o disrepute in Anglo-American philosophy. It did s o in p a r t because i t seemed t o b e incoherent. I h a v e tried t o restore some of i t s coherence. I n defending Meinong's theory of objects I h a v e n o t touched o n a n y of his interesting work in epistemology, psychology, o r value theory. Insofar as t h a t work i s dependent o n his notion of a n object, I hope t o h a v e m a d e it more accessible. TERENCE PARSONS
University of Massachusetts at Amherst
APPENDIX
The foregoing theory is parasitic on an understanding of what properties and relations are and of how they're related to one another and to individuals (e.g., how ri is related to r and i ) . I give here two accounts, neither of them particularly good. My intent is simply to give two very specific and explicit characterizations of how to define objects out of properties, so as t o illustrate how i t can be done, and what kinds of assumptions are needed to make i t work. L4ccount I : On this (very inadequate) account we represent properties of individuals by sets of individuals-i.e., we suppose t h a t "properties" are really just the extensio~zsof predicates. 6 = the set of all sets of individuals $, pl, pl', . . . range over sets of individuals The negation of p = fi = g $ = the set of all individuals not in p. On this theory, 'have' means "e"; so ia = df {$:i e p}. Most of the definitions in the body of the paper remain unchanged. But we need an account of relations. A nuclear-nuclear relation r is defined as a set of ordered pairs of individuals. If r is a nuclear-nuclear relation, and i an individual, then : ri = df { i f :(if, i) e r } ;r = df { i1:(i,it) e r } Nuclear-extranuclear relations are sets of ordered pairs of individuals and objects. If (R is a nuclear-extranuclear relation, then : (R, = {i:(i,o) E (R} i(R = ( 0 : (i,o) e (R} Similarly for extranuclear-nuclear relations. Extranuclear-extranuclear relations are sets of pairs of objects. If 8 is one of these, then : %, = (0': (ol,o) e %} o8= {or:(O,ol) E 81
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T h e theory based on this account is hopeless for t h e following reason. Suppose t h a t Adam a n d E v e existed, a n d t h a t it's part of your conception of God t h a t he created Adam, b u t not t h a t he tempted Eve. Also suppose t h a t no real individual either created Adam or tempted Eve. T h e n t h e property of creating Adam = {i:icreated Adam} = A = (i:i tempted E v e ) = t h e property of tempting Eve. B u t since God has t h e property of creating Adam, he also automatically gets t h e property of tempting Eve, which is wrong. Account I1 : W e begin with our set of individuals, 9, and also with a set, W, of possible worlds. A property, p, is defined t o be a function t h a t maps each world w onto a subset of g (i.e., onto t h e "extension" of p in world w). Symbolically, 6' = (the power set of 9)w. T h e negation of p = 3 = t h a t function which maps each world w onto 4 IV p(w) ; i.e., onto t h e complement of t h e extension of p in world w. S o w m a n y of our technical terms m u s t be relativized to worlds. For example, i has p i n w = i $(w). T h e correlate of i in w = ic, = ( p : i r p(w)} = t h e s e t of properties which i has in w. Objects a r e still sets of properties. T h e definitions of 'complete' a n d 'incomplete' s t a y t h e same. Others must be relativized t o worlds: o exists i n w = d l (3 i) (icw = o) Although 'possible' is world-independent, its definition naturally quantifies over worlds : o is possible = (3 w) (3 i) (0 C iCw)
A n extranuclear property is simply a n y function t h a t maps worlds to
sets of objects. For example, t h e extranuclear property of existing will be t h a t function which maps each world, w, t o {o:o exists in w ] , i.e., to {o: (3i)(icw = o)]. Relations are a s follows: Nuclear-nuclear relations a r e functions t h a t m a p worlds t o sets of pairs of individuals. ri = t h a t function which maps each world w to (if:(if,i) e r (w) } ;r = t h a t function which maps each world w to Ii':(i,il) r r(w)} Nuclear-extranuclear relations m a p worlds t o pairs of individuals a n d objects; a n d : a,= t h a t function which maps w t o (i:(i,o) r R ( w ) f i R = t h a t function which maps w t o {o:(i,o) r R(w)} Similarly for extranuclear-extranuclear relations.
.
