The Impossibility of Token-Reflexive Analyses

Published in: Dialogue: Canadian Philosophical Review, Vol. 25, No. 4, Winter 1986, pp. 757-760.

It is logically impossible for any token-refIexive expression to analyze another token-refIexive or non-token-refIexive expression. If the expression being analyzed is token-refIexive, it refers to itself and thereby has a different reference than the allegedly analyzing token-refIexive expression, which refers to itself, and two expressions with different references cannot be related to each other as analysandum to analysans. But if the expression being analyzed does not refer to itself, it is not a token-refIexive expression and for this reason cannot be analyzed by an expression that is token-refiexive.[1]

If this is true, then the attempts by Hans Reichenbach,[2] J. J, C, Smart,[3] Marc Temin,[4] John Searle[5] and others to provide token-refIexive analyses of indexicals like "I", "now", and "here" are doomed to failure. Reichenbach, for example, believes that "1" has the same extensional meaning as "the person who utters this token", and Smart believes that "now" means the same as “is simultaneous with this utterance” (where the italicization of the "is" indicates it is tenseless). But if a tokeri T₁ of' 'I' , refers to itself, it has a different reference than a token T₂ of' “the person who utters this token” which refers to itself, and therefore cannot have the same extensional meaning as the latter. And if, on the other hand, the token T₁ of "I" does not refer to itself, it is not token-reflexive; hence it will be false to say that the implicit token-reflexivity of tokens of "I" is made explicit in their token-reflexive analysantia.[6]

There appears to be a way out of this dilemma, a way first suggested and endorsed by George Schlesinger in his critique of Paul Fitzgerald's criticism of the token-reflexive analysis of "now". Fitzgerald makes a point related to one of the claims made in §1 of this paper:

contains five words. If it is implicitly self-referring, as the suggested analysis implies, then it refers to a five-worded token. But the analysans, namely

refers to a seven-worded token. Since the token to which the analysans refers is different from the token to which the analysandum refers, and since neither of these tokens is a logical construction, the analysans and the analysandum are not logically equivalent. The idea here is that the truth of one token demands the existence of an entity (that token itself), whose existence is not demanded by the truth of the other token. And either token could exist without the other.[7]

Some of the implications of Fitzgerald' s reflections can be brought into sharper focus if we formulate them as the thesis that the theory of the token-reflexive analyses of temporal (and other) indexicals is self-contradictory. If this theory were true, then it would be true both that

(2) The tensed token is analyzed by, and thus has the same extensional meaning as, a tenseless token-reflexive token, and thus does not refer to a tensed token.

Schlesinger believes that the theory of token-reflexive analyses can be rescued from this threat of self-contradiction. He claims that "Fitzgerald misses the point of the analysis, which is to instruct us that the term 'now' is to be treated as an abbreviation and is itself to be taken, to stand for 'simultaneously with this token'. Thus 'this token' refers to the original five-worded token.[8] Since both the tensed token and the tense- less token refer to the tensed token, the analysandum and the analysans have the same extensional meaning, and the contradiction is resolved.

But Schlesinger's claim cannot be correct. If "now" is an abbreviation of "simultaneously with this token", such that tokens of the latter expression refer not to the sentence-tokens of which they are parts but to the sentence-tokens of which tokens of "now" are parts, then "now" and “simultaneously with this token” must obey the principle of the extensional interchangeability of complete expressions and their abbreviations. This principle, stated below, is a necessary but insufficient condition for any expression a to be an abbreviation for some expression b:

P: For any abbreviation a, and for any expression b of which a is an abbreviation, if a token of a is uttered in some extensional context, then a token of b might have been uttered in place of the token of a such that either the token of b would possess the same truth-value in fact possessed by the token of a or (if the tokens of a and b are not sentence-tokens but parts of sentence-tokens) the sentence-token of which the token of b is a part would possess the same truth-value in fact possessed by the sentence-token of which the token of a is a part.

For example, suppose in a certain circumstance I utter a token of "Einstein's STR was first published in 1905". It follows from p that if I had instead uttered in that circumstance a token of "Einstein's Special Theory of Relativity was first published in 1905" the latter utterance would have had the same truth-value as the former utterance.

But now suppose that in a certain circumstance C I utter a true token T₁ of "The hurricane is occurring now". If Schlesinger's theory is correct, then by P I might instead have uttered in C a token T₂ of "The hurricane is occurring simultaneously with this token” and T₂would have the same truth-value as T₁. But if T₂ does not refer to itself but to "the, original five-worded token" (to borrow Schlesinger's phrase) of "The hurricane is occurring now", it is false, since if I had uttered T₂ instead of T₁ in C, then T₁ would not have occurred and thus would not have been simultaneous with the hurricane. Therefore, "now" cannot be an abbreviation for "simultaneously with this token", where tokens or the latter expression are understood to, refer to the sentence-tokens of which tokens of "now" are parts.

The conclusion is inescapable: If it is assumed with Schlesinger that the alleged token-reflexive analysans refers to the analysandum, then it follows that the alleged analysans is not an analysans. But if it is assumed with Fitzgerald that the alleged token-reflexive analysans refers to itself, then it also follows that the alleged analysans is not an analysans. The theory of token-reflexive analyses must be abandoned.[9]

[1] The statement that token-reflexive expressions refer to themselves is elliptical for the statement that each token of a token-reflexive expression refers to itself.

[2] Hans Reichenbach, Elements of Symbolic Logic (New York: Macmillan, 1947), 284ff.

[3] J.J .C. Smart. Philosophy and Scientific Realism (New York: Humanities Press, 1963), 132ff.

[4] Marc Temin, "Relational Sense and Indirect Discourse" , Journal of Philosophy, June 1975. Temin tacitly assumes token-reflexive analyses of indexicals in this article.

[5] John Searle. Intentionality (Cambridge: Cambridge University Press, 1983), 223ff.

[6] John Searle's recent theory of token-reflexivity is somewhat different than Reichen- bach's and Smart's. For Searle, "now" is not synonymous with or analyzed by "is simultaneous with this utterance" because the former but not the latter shows but does not state its token-reflexivity. Searle introduces "at *cotemporal" as a synonym of "now"; "at *cotemporal" refers to the time of its utterance and shows but does not state its self-reference. But this revision of the traditional token-reflexive theory does not avoid the abovementioned problem. If "now" and "at *cotemporal" each refers to itself then they have different extensional meanings and one cannot be synonymous with or analyze the other. And if "now" does not refer to itself it will be false to assert that it has a token-reflexive meaning that is capable of being analyzed or expressed by a synonym.

[7] Paul Fitzgerald, "Nowness and the Understanding of Time", Boston Studies in the Philosophy of Time 20, 267-268.

[8] George Schlesinger, Aspects of Time (Indianapolis, IN: Hackett, 1980), 132.

[9] For further criticism of the token-reflexive theory, see Quentin Smith, ".Sentences About Time", The Philosophical Quarterly 37 (1987),37-53, and ""Problems with the New Tenseless Theory of Time", Philosophical Studies, forthcoming. Also see The Felt Meanings of the World: A Metaphysics of Feeling (West Lafayette, IN: Purdue University Press, 1986), chaps. 4 and 6, and ""The Mind-Independece of Temporal Becoming", Philosophical Studies 47 (1985), 109-119.