KAPLAN RIGIDITY, TIME, AND MODALITY Gilbert PLUMER Some have claimed that though a proper name might denote the same individual with respect to any possible world (or, more generally, possible circumstance) in which he exists, it certainly cannot denote him with respect to a possible world in which he does not exist. With respect to such a world there must be a gap in the name's designation, it designates nothing. This is a mistake. There are worlds in which Quine does not exist. It does not follow that there are worlds with respect to which "Quine" does not denote. What follows is that with respect to such a world "Quine" denotes something which does not exist in that world. Indeed, Aristotle no longer exists, but "Aristotle" continues to denote (him). This is the gist of an argument David Kaplan (1973, p. 503) gives for what has come to be called "Kaplan rigidity", as opposed to "Kripke rigidity" - proponents of which are mistaken, according to the argument. I t is an argument from analogy between time and modality. I t is an argument to which others have subscribed by full rehearsal (Salmon 1981, pp. 37-40) or simple appropriation (Almog 1986, pp. 219-20, 231), yet there is no evaluation of it in recent discussions of the issue of Kaplan versus Kripke rigidity (Steinman 1985; Smith 1987). Although the argument may be initially forceful, I believe it does not withstand scrutiny. Notice, first, that it is cast simply in terms of the name "Aristotle" ("Quine") with respect to different times (worlds). But a name is a word, and a word cannot itself denote anything. Kaplan would appear to agree, for on the preceding page he summarizes his "view of the reference of proper names" in terms of "the proper name used on some particular occasion". This means that in the argument we should understand the temporal case, as we naturally would anyway, to bespeak tokenings of the name "Aristotle" at different times (to token an expression is to think it, and if communication is desired, to utter or write it). Now the problem is that the modal dual to this is tokenings of the name "Quine" 330 G . PLUMER in dif ferent worlds, yet this is irrelevant, f or the issue concerns evaluations with respect to dif ferent worlds of a given tokening of the name "Quine". The issue is over whether such a tokening denotes or designates Quine even in worlds where he doesn't exist. What is probably the right thing to say about the modal dual that is actually present in the argument is unwitt ingly expressed by Kaplan himself as an explanation of why some subscribe to Kripke rigidity : " A s imple confusion between our language and theirs... The inhabitants of a world in which Quine never exists would likely have no name for him. So what H e exists here. We have a name for him, namely, 'Quine'. It is our terms and formulas whose denotation and truth value are being assessed with respect to the possible world in quest ion" (p. 505). Notice from this passage that although Kaplan often speaks simply in terms o f something not existing in a world, what is meant, naturally enough, is never existing in the world. And in a discussion of names from fiction, Kaplan indicates (pp. 507-08) that the real importance of the our language/their language distinction is to restrict the tokenings considered to worlds where the designata exist. I n view of all this, the question in the modal case becomes: (1M) For a tokening (k ) o f a designator in a world where the designatum (d) exists, does k designate d in worlds where d exists at no t ime? I f it were determined that the answer is af f irmat ive f or tokenings of a kind of designator, then that k ind would be Kaplan rigid in what we have found to be the intended sense. Kaplan and his followers believe that proper names and indexicals are Kaplan rigid (Kaplan extends the doctrine to indexicals in his 1977, esp. sec. I V). But perhaps they ought not discriminate against DD's (definite descriptions). W. P. Als ton convincingly argues that while "DD's exhibit type nonrigidity...DD tokens are rigid, when used as designators" (1980, p. 34; cf., e.g., Brody 1979 and Wettstein 1981); and it seems there could be no good grounds for holding that DD's are rigid, but only proper names and indexicals are Kaplan rigid. The exact temporal dual to (1M) is : (IT) Fo r a tokening (k ) o f a designator at a t ime when the designatum (d) exists, does k designate d at t imes when d exists is no world? KAPLAN RIGIDITY, TIME, AND MODALITY 3 3 1 Suppose 1 now token "Quine". The question (IT) poses with respect to that tokening is whether it designates Quine at times when he exists in no possible world - as if Quine could change from and (after a respite) back into a round-square! The problem is that (IT) presupposes that something existing at one time could at an earlier or later time be necessarily non-existent, and this is absurd, and so too the argument from analogy between time and modality for Kaplan rigidity. Or so it appears. There is a relatively painless way of adjusting (1M) to remove the absurdity in its dual : (2M) For a tokening (k) o f a designator in a world where the designatum (d) exists at the time (t) of k, does k designate d in worlds where d doesn't exist at t? The exact temporal dual to (2M) is : (2T) Fo r a tokening (k) o f a designator at a time when the designatum (d) exists in the world (w) of k, does k designate d at times when d doesn't exist in w? (2M) leaves open the question o f whether or not d ever exists in such worlds. Hence, if an affirmative answer to (2T) could be established, and thereby such an answer to (2M) on analogy between time and modality, it seems one could with impunity go on to not require duality and claim an affirmative answer to (1M). The alternative to (1M) and (2M) is a formulation that entirely eliminates the time variable, in which case we have the spectre of treating the (non-) existence of individuals such as Quine as timeless (Quine may be God-like in some respects, but not this one). The reason Kaplan and others hold that the answer to (2T) is affirmative has to do with the problem of negative existentials, the problem being how we are to make sense of their being true. Kaplan writes "suppose 1 say, (3) I do not exist. Under what circumstances would what I said be true? It would be true in circumstances in which 1 did not exist" (1977, p. 15)!' He argues that "we must distinguish possible occasions of use - which I call contexts * Note the language of the correspondence theory of truth. 332 G . PL U M ER - from possible circumstances of evaluation of what was said on a given occasion of use" (p. 12), and regards "the what-is-said in a given context - as propositions" (p. 13). Thus, although the proposition (P) expressed by Kaplan's tokening of (3) is false (e.g.) where the context of the tokening determines the circumstance of evaluation, P is true (e.g.) in the circumstances of the actual world at the turn of the century. This last would not be so unless Kaplan's tokening of " I " designates him at that time. The overall argument for Kaplan rigidity gets off the ground in virtue of an analogy between time and modality which consists of the similar way they are treated in "the formal semantics fo r quantified tensed languages and modal languages" (Salmon, p. 37). What stands out as particularly relevant in this similarity of treatment is the commitment to propositions which are neutral with respect to time on the one hand, and modality on the other. I n contrast to this, i f fo r example (3) were understood as synonymous with " I do not actually exist now", P would be specific as to time and modality, and P's truth-value would change "neither through time nor possibility" (Kaplan, p. 105; cf. 22-23). This does not, incidentally, mean that tense logic treats the (non-) existence of individuals such as Kaplan as timeless; the reason, in terms of Kaplan's semantics, is that every possible circumstance includes a time. This view at least falters over what has been called "the new theory of reference" (Wettstein 1986, p. 185). A number of philosophers, some of whom embrace the argument from analogy for Kaplan rigidity, have given good reasons in support of the theory, which holds that " in the case of a singular term which is directly referential [i.e., it refers "without the mediation of a Fregean Sinn as meaning", and hence in a natural language is supposedly either an indexical or proper name, e.g., "Quine"], the constituent of the proposition is just the object itselP' (Kaplan, pp. 1, 13). It is not "Quine-under-a-guise-F, Quine-under-a-mode-of-presentation, Quine's qualitative essence, not even the nonqualitative property of beingidentical-with-Quine"; rather it is the "flesh-and-blood individual: Quine" (Almog, p. 220). The difficulty is this: One cannot consistently hold both that the object itself is a constituent of a proposition such as P, and that the proposition is true at times when the object doesn't exist, assuming that a proposition would have to exist at a time in order to be true then. Evidentally making this assumption, Almog says concerning "a certain locus where Quine doesn't exist...qua evaluation locus, we take to it propositions involving Quine which we have generated in our generation KAPL AN R I GI D I TY, T I M E, A N D M O D AL I T Y 3 3 3 locus" (p. 240; cf. 219n). I should think that this is either murder, or worse, a self-contradicition. And it seems to me the assumption is true, and here, in brief, is how I'd argue for it. On "the new theory of reference" combined with the only credible theory o f truth, the correspondence theory, it is at best gratuitous to postulate propositions as bearers of truth-values. The correspondence theory says that truth is a matter of fitting the facts. This "fitting" or correspondence is naturally and plausibly understood as a relation of representation, with the relata being sentence tokenings on the one hand, and facts or states of affairs on the other, such that a sentence tokening is true (false) if f it represents (fails to represent) a state of affairs. Something like a tower made of building blocks, a state of affairs is a structured entity with constituents, constituents which include "fleshand-blood" individuals themselves. After all, in postulating propositions you're already committed to sentence tokenings (as the means by which propositions are expressed) and, on a correspondence theory, to facts or states of affairs (as that to which true/false propositions correspond/don't correspond). These middlemen ought to be eliminated, provided, I suppose, that you admit merely possible states of affairs and sentence tokenings (in order to preserve such principles as that every truth-value bearer has a contradictory). Yet in view of common modal locutions such as " I might have (said) ..!', these possibilia are entrenched in a way that propositions are not, provided that propositions are not identified with meanings. And this is an identification which "the new theory of reference" cannot make because, e.g., it would be incompatible with its treatment of indexicals. On pain of fantastic ambiguity, the meaning of an indexical is "the semantical rule which fixes the reference" (Kaplan, p. 43), not the object referred to by a tokening of one. In brief then, "the new theory of reference" should bespeak states of affairs instead of propositions (Wettstein also arrives at this conclusion, p. 198, though he does so from considerations of cognitive significance). In order to deal with temporal questions, sentence tokenings, truth, and states of affairs must all be relativized to times, that is, taken with respect to or as occurring or existing at times. Relativizing the above point that a sentence tokening is true (false) if f it represents (fails to represent) a state of affairs, we get : A sentence tokening at a time t is true (false) at t ' if f it represents (fails to represent) a state of affairs which exists at t ' (t may or may not - t '). Call this principle "R". R is restricted to sentence 334 G P L U M E R tokenings which are neutral with respect to time, which is precisely how we are understanding Kaplan's tokening of (3). For suppose, e.g., I now token "Aristotle was a philosopher". Although this sentence tokening is of course now true, it does not represent a state of affairs which now exists - how could it ? - Aristotle does not now exist. A state of affairs exists at a time only if its constituents do. Rephrasing the above charge of inconsistency in light of what I have argued we get : One cannot consistently hold both that an object itself is a constituent of a state of affairs, and that a sentence tokening which represents the state of affairs is true at times when the object doesn't exist, assuming that a state of affairs would have to exist at a time in order for a sentence tokening representing it to be true then. Needless to say, this assumption is entailed by R. The problem, as applied to Kaplan's tokening of (3), is not that Kaplan himself can't be a constituent of the state of affairs of his not existing. Nothing else could be. Rather, the problem is regarding his tokening as true at a time, hence regarding it as representing a state of affairs which wholly exists at a single time. Kaplan wants to make sense of his tokening of (3) not being eternally false (or true !). This can be done without inconsistency by holding that a negative existential sentence tokening which has a referent (contrast, e.g., now tokening "the king of France doesn't exist") and which changes its truth-value over time so-changes in that it is true at some, but not all, ordered couples of times, i.e., it represents a state of affairs which exists at some, but not all, such ordered couples. To regard it as representing a state of affairs which exists at an ordered couple of times < t, t ' > is to regard it as representing a state of affairs which exists between t and t ' such that the constituents of the state of affairs are the referent itself from t and whatever corresponds to "does not exist" (or a synonymous expression) from t ' . On the other hand, the state of affairs it represents does not exist at every ordered couple of times where t = t ' , the referent does not exist at t, or the referent does exist at t'. Thus, it seems ill-advised and unnecessary to answer (2T) affirmatively in order to semantically represent a particular's finiteness in time. And it could quite well be argued, mutatis mutandis, that it is both ill-advised and unnecessary to answer (1M) affirmatively in order to semantically represent a particular's contingency. The underlying problem seems to be that an affirmative answer to (2T) (or to (1M)) violates the dictum that whatever is referred to must exist. This is why one's immediate reaction KAPLAN RIGIDITY, TIME, AND MODALITY 3 3 5 to the postulation of such temporal (or modal) rigidity is, I believe, incredulity. I t seems that Kaplan's tokening of " I " in his tokening of (3) represents qua designates him only at times when he exists, and likewise that a tokening of "Aristotle", as in "Aristotle is Greek", designates him only with respect to times at which he exists. In fact, it may designate him at only some of the times he exists, as in "Aristotle is a philosopher", since such a sentence tokening presumably is true only at times when Aristotle was an adult. This means that in a sense it is not the case that " 'Aristotle' continues to denote (him)". That is, a (e.g.) present tokening of "Aristotle" does not designate him with respect to the present time. One must be careful to not confuse this with holding that the tokener does not refer to Aristotle at the present time. Of course the tokener's act of reference takes place at the time of tokening. This belongs to the phenomenon of "speaker's reference", as opposed to semantic reference, and of course this paper has been about the latter. Still, it's worth remarking that in the "speaker's reference" sense, it is the case that " 'Aristotle' continues to denote (him)". Law School Admission Services Newtown, Pennsylvania Test Development and Research Div. REFERENCES Gilbert PLUMER Almog, J. (1986), "Naming without Necessity", Journal of Philosophy 83, pp. 210-42. Alston, W.P. (1980), "Rigid Designation", University of Illinois at Urbana-Champaign colloquium mimeograph (unpublished). Brody, B.A. (1979), "Kripke on Proper Names", in French 1979. French, P.A., et al., eds. (1979), Contemporary Perspectives in the Philosophy of Language (2nd edition). Minneapolis, University of Minnesota Press. Kaplan, D. (1973). "Bob and Carol and Ted and Alice", in Approaches to Natural Language (K.J.J. Hintikka, et al., eds.). Dordrecht, D. Reidel. - (1977). Demonstratives (draft * 2). UCLA mimeograph. Forthcoming in Themes from Kaplan (J. Almog, et al., eds.). Oxford University Press. Cf. Kaplan's earlier works, "Dthat" and "On the Logic of Demonstratives", reprinted in French 1979. Salmon, N.U. (1981). Reference and Essence. Princeton University Press. Smith, A.D. (1987). "Semantical Considerations on Rigid Designation", Mind 96, pp. 83-92. Steinman, R. (1985). 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