The New Theory of Reference Entails Absolute Time and Space

Page 411 of Smith, Quentin, 1991, “The New Theory of Reference Entails Absolute Time and Space”, Philosophy of Science, vol. 58, no. 3, pp. 411-416.

Department of Philosophy Antioch College

If uses of "now" and "here" refer directly and rigidly to times and places, as proponents[1] of the New Theory of Reference (NTR) hold, then the absolutist theories of time and space must be true. Since no proponent of the NTR has acknowledged this, this entailment is worth demonstrating. This will be shown explicitly for the case of time, which has the following relationalist and absolutist definitions:

By "is logically independent of an event E" I mean "exists in some possible world in which E does not". Definitions (Dl) and (D2) are familiar in the literature and do not need to be made more exact (e.g. , by defining "events") for the limited purposes of my argument. If the special theory of relativity is to be introduced, append "relative to some reference frame

Page 412 of Smith, Quentin, 1991, “The New Theory of Reference Entails Absolute Time and Space”, Philosophy of Science, vol. 58, no. 3, pp. 411-416.

Before I proceed, I will introduce some textual support for the claim that (Dl) is the familiar relational definition of a time, since several phi- losophers have responded to the argument in this paper by claiming that my argument, although valid, is unsound since the relational theory does not define a time as a set of simultaneous events. That (Dl) or something relevantly similar is the standard relational definition can be shown from several sources. For instance, W. H. Newton-Smith calls the relational theory the "reductionist theory":

...we can form the collection of all events simultaneous with any particular event used in identifying the moment. This collection, the reductionist claims, just is the moment. To say that such and such an event occurred at such and such a moment is just to say that the event in question is a member of the set of events constituting the moment. (1980, 6-7)

G. J. Whitrow defends what he calls "the relational theory of time" and he defines a time as "the class of events simultaneous with a given event" (1980, 36). Mario Bunge also claims to be espousing the relational theory of time when he defines a time as "a class of simultaneous events" (1968, 365). John A. Winnie writes, in a similar spirit, that "a set of events no two of which causally interact. ..[is] an instant of time" (1977, 136) and Bertrand Russell introduces the relational definition:

An "instant" is a collection of events belonging to one biography, and having the two properties that (a) any two events in the collection overlap, (b) no event outside the collection overlaps with all the members of the collection. (1948, 275)

theory of time who has denied that a time is a set of simultaneous events (or something relevantly similar, such as Russell's construction).

Given that (Dl) corresponds to the relational theory, my argument is that if we assume that uses of "now" refer directly and rigidly to times as conceived by the relational theory , then we must assume, contrary to fact, that all temporally counterfactual sentence-utterances of a relevant i sort are necessarily false. Suppose that at noon, 14 April 1989, there ii occurs an utterance U that is a token of the sentence-type

Since John Doe is asleep then but is not compelled to be, the proposition (PI) expressed by this utterance is true. But if both NTR and the relational theory of time are true, (PI) is logically equivalent to the proposition (P2) expressed by

Page 413 of Smith, Quentin, 1991, “The New Theory of Reference Entails Absolute Time and Space”, Philosophy of Science, vol. 58, no. 3, pp. 411-416.

where "t" refers to the set of all and only those events that actually occur at noon, 14 April 1989. Since (P2) entails that the set t accidentally contains John's sleeping, it violates the principle that sets contain their members essentially and therefore is necessarily false. Since this implies that (PI), which is in fact true, is necessarily false, one of our premises must be rejected. If we retain the NTR, we must assume that the absolutist theory of time is true, for the conjunction of the NTR and the premise that (PI) is true entails that "t" in (2) refers to a time that is logically independent of the events that occupy it. But if we retain the relational theory of time, we must assume the NTR is false, for the conjunction of the relational theory and the premise that (PI) is true entails that the use of "now" in U and "t" in (2) are nonrigid designators, designating different sets of events in different worlds. The use of "now" and "t" are nonrigid if (but not only if) they express the sense that is also expressible by an attributive use of the definite description, "whatever set of simultaneous events contains the events that are 1,988 years, 3 months, 13 days and 12 hours later than Christ's birth", for in different worlds different sets of events possess the property of containing the events that are 1,988 years, 3 months, 13 days and 12 hours later than Christ's birth. For example, in world W the set that contains all the events that are actually 1,988 years, 3 months, 13 days and 12 hours later than Christ's birth but for John's sleeping exemplifies this property; W, consequently, is one of the worlds that satisfies the counterfactuals U and (2) on their nonrigid interpretation.

By a similar argument, it can be proven that the NTR entails the falsity of the relational theory of space, for otherwise all the relevant counter- factuals about places (e.g. , "He might not have been sleeping here") would be necessarily false.

It might be thought that modal versions of the relational theory of time and space are consistent with the NTR since they define times and spaces in terms of possibilities. For example, Leibniz holds that "Space and Time taken together comprise the order of possibilities of one whole Universe, so that these orders (Space and Time, that is) relate not only to what actually is, but also to whatever could be put in its place" (Arthur 1985, 286).[2] However, modal theories are either consistent with the NTR or

Page 414 of Smith, Quentin, 1991, “The New Theory of Reference Entails Absolute Time and Space”, Philosophy of Science, vol. 58, no. 3, pp. 411-416.

(D3) A time as conceived on a modal theory T =_df. A time is a possibility p of there occurring some simultaneous events, such that p exists as actualized by some events in some worlds, as actualized by other events in other worlds, and as unactualized in still other worlds.

The phrase "p exists as actualized by some events" entails "p exists and is occupied by some events" and "p exists as unactualized" entails "p exists and is unoccupied by events" .(The distinction between the existence and actualization of possibilities is familiar in the literature on the applied semantics of quantified modal logic; see, for example, Plantinga 1974, 44-51 and Chisholm 1981, 129-131.) Modal definition (D3) is consistent with the NTR but is absolutist since it entails that p is logically independent of the simultaneous events, if any, that occupy it. On the other hand, the modal definition

is relationalist but inconsistent with the NTR. Modal definition (D4) entails that a time t is a set of simultaneous events that occur in some possible world Wand thus that t contains all and only these events in each world in which it exists, which prevents "now" from being a rigid designator of t in the relevant counterfactuals.

In talking of the relational theory , I have been talking of the times it posits as "existing" in different possible worlds, which might seem in- consistent with these theories. Relational theorists often obscurely claim that "time does not exist" but this claim, if consistent with their thesis that there are sets of simultaneous events and that these sets are times, must be interpreted in some restricted sense, for example, as meaning that quantification over times is not quantification over concrete existents (sets being abstract existents).

It might also be objected to my account that the criteria of transworld identity involved in temporal counterfactuals show that the absolutist theory reduces to the relational theory .It is plausible to think that we identify an actual time t across different possible worlds as the time that actually includes a certain event E, such as the utterance U, which seems to suggest that t is not logically independent of E. But this objection is based on a modal fallacy. If t is identified as the time that actually includes E, that does not entail t essentially includes E, but merely that t essentially includes E in the actual world. In each world in which t exists, t has the world-indexed property of including-E-in-the-actual-world, but that does

Page 415 of Smith, Quentin, 1991, “The New Theory of Reference Entails Absolute Time and Space”, Philosophy of Science, vol. 58, no. 3, pp. 411-416.

not entail that in each world in which t exists, t has the property of including E .

In this paper, I have made no attempt to decide between the NTR and the relational theory of time and space, but merely to show that, contrary to the received view, each of us must make this choice. But I would add that the fact that we must make this choice does not imply that there is defect in the formulation of the NTR, as if a philosophy of language were defective simply by virtue of carrying some metaphysical commitments. No philosophy of language is devoid of metaphysical entailments, if only because the philosophy of language includes semantics, that is, the study of the relation of language to reality .The point of this paper is in part to show that, in assessing the semantics of NTR, one of the factors we must take into account is its commitment to absolute time and space. Hitherto, discussions of the metaphysical commitments of the NTR have focused on its alleged entailment of essentialism about natural kinds (see, for example, Salmon 1981, Shapere 1984, Nersessian 1984, and Leplin 1988), but whether there is such an entailment,[3] there certainly is an entailment of absolutism, and this must be considered. The converse side of this point is that the assessment of the relational and absolute theories of space and time cannot proceed in independence of the philosophy of language, but must take into account the uses of spatial and temporal expressions in counterfactuals. Even if the philosophy of space and time is "based strictly on the sciences" and not on "ordinary language", it must take into account, and be consistent with, the uses of temporal and spatial expressions in the counterfactuals that implicitly or explicitly occur in scientific treatises. If the NTR is metaphysically committed to absolutism, the relational theory of space and time is semantically committed to nonrigid designation, and that must be taken into account in assessing it.

It might be thought that a partial version of the NTR can be maintained by the relationalist, inasmuch as no logical contradiction exists in the conjunction of the two theses that (a) personal indexicals, proper names and natural kinds terms are rigid designators and (b) temporal and spatial indexicals are nonrigid. But a theory based on this conjunction would seem to be an ad hoc construction rather than a viable philosophy of language, for it is counterintuitive (for example) that it is a rule of use that "now" and "here" refer nonrigidly but "I" rigidly. It is plausible to think that if some indexicals are nonrigid, all are, and that if "I" is non- rigid, then so are proper names of persons, as reflections on the coreferentially of personal indexicals and proper names of persons in some modal contexts would suggest. Furthermore, if proper names of persons

Page 416 of Smith, Quentin, 1991, “The New Theory of Reference Entails Absolute Time and Space”, Philosophy of Science, vol. 58, no. 3, pp. 411-416.

are nonrigid, it is natural to think all proper names are nonrigid. Perhaps a connected line of reasoning would lead to the conclusion that natural kind terms are also nonrigid, although this is less clear. In any case, these are issues that must be faced by each of us as we decide between relationalism and the account of temporal and spatial indexicals in the NTR.

Almog, J. (1981), "Dthis and Dthat: Indexicality Goes Beyond That", Philosophical Studies 39; 347-381.

Arthur, R. (1985), "Leibniz's Theory of Time", in K. Okruhlik and J. R. Brown (eds.), The Natural Philosophy of Leibniz. Dordrecht: Reidel, pp. 263-313.

Bunge, M. (1968), "Physical Time: The Objective and Relational Theory", Philosophy of Science 35; 355-388.

Chisholm, R. M. (1981), The First Person, an Essay on Reference and Intensionality. Minneapolis: University of Minnesota Press.

Coppock, P. ( 1984), "Review of Nathan U. Salmon's Reference and Essence" , The Journal of Philosophy 81; 261-270.

Kaplan, D. (1977), Demonstratives. Mimeograph. Los Angeles: University of California in Los Angeles.

Kripke, S. A. (1980), Naming and Necessity. Cambridge, MA: Harvard University Press. Leplin, J. (1988), "Is Essentialism Unscientific?", Philosophy of Science 55; 493-510. Marcus, R. B. (1961), "Modalities and Intensional Languages", Synthese 130 303-322. Nersessian, N. J. (1984), Faraday to Einstein; Constructing Meaning in Scientific Theo-

Newton-Smith, W. H. (1980), The Structure of Time. London: Routledge & Kegan Paul. Perry, J. (1977), "Frege on Demonstratives", The Philosophical Review 86; 474-497. Plantinga, A. (1974), The Nature of Necessity. Oxford: Clarendon Press.

Putnam, H. (1975), Philosophical Papers. Cambridge: Cambridge University Press. Russell, B. (1948), Human Knowledge; its Scope and Limits. New York: Simon & Schuster.

Salmon, N. (1981), Reference and Essence. Princeton: Princeton University Press- -.(1986), Frege's Puzzle. Cambridge, MA: MIT Press.

Shapere, D. (1984), Reason and the Search for Knowledge; Investigations in the Philos- ophy of Science. Dordrecht: Reidel.

Wettstein, H. K. (1979), "Indexical Reference and Propositonal Content", Philosophical Studies 36; 91-100.

Whitrow, G. J. (1980), The Natural Philosophy of Time. 2d ed. Oxford: Clarendon Press. Winnie, J. A. (1977), "The Causal Theory of Space-Time", in J. Earman, C. Glymour

and J. Stachel (eds.), Minnesota Studies in the Philosophy of Science. Vol. 8, Foun- dations of Space-Time Theories. Minneapolis: University of Minnesota Press, pp. 134-205.

* Received April 1989; revised August 1989.

** I am grateful to a referee for helpful comments on an earlier version of this paper.

*** Send reprint requests to the author, Department of Philosophy, Antioch College, Yellow Springs, OH 45387.

[1] Proponents of the New Theory of Reference include, among others, Joseph Almog (1981), David Kaplan (1977), Saul Kripke (1980), Ruth Barcan Marcus (1961), Hilary Putnam (1975, vol. 2, chap. 12), John Perry (1977), Nathan Salmon (1981, 1986), and Howard Wettstein (1979).

[2] Arthur suggests that this passage expresses Leibniz's conception of ideal time, which is an "abstraction in the minds of men" (1985, 288). Real times are defined in terms of events in a way that might be expressed (in contemporary set-theoretic terms) by saying that a time is a "class of simultaneous [events]" (ibid. , 270). On this interpretation, Leibniz is an absolutist about ideal time and a relationalist about real time, which is to say he is a relationalist, since time is just real time.

[3] It seems to me that Paul Coppock (1984) has correctly explained the respect in which the NTR entails essentialism about natural kinds.