¹ See for example Goodman's “On Likeness of Meaning”, Analysis, Vol. 10, pp. 1–7, White's “The Analytic and the Synthetic: An Untenable Dualism” in John Dewey: Philosopher of Science and Freedom, ed. S. Hook, Dial, 1950, and Quine's From A Logical Point of View, Harvard, 1953.

² In a different connection, some aspects of such a consideration are discussed in the writer's “An Inscriptional Approach to Indirect Quotation”, Analysis, Vol. 14, pp. 83–90.

³ In Carnap, R. Meaning and Necessity, Univ. of Chicago Press, 1947.

⁴ See his remark, Ibid., P. 58, “The present definition makes no claim to exactness; an exact definition would have to refer to one or two semantical systems whose rules are stated completely.”

⁵ See his statement, Ibid., P. 53, “Although sentences of this kind … are, indeed, used and understood in everyday life without any difficulty, they have proved very puzzling to logicians who have tried to analyze them. Let us see whether we can throw some light upon them with the help of our semantical concepts.”

⁶ See Goodman's argument in “On a Pseudo-Test of Translation”, Phil. Studies, Vol. III, pp. 81–82, that knowing of a specified kind can be only a pseudo-test of translational equivalence. Perhaps one motivation for offering this pseudo-test is precisely the notion disputed in the present paper, that synonymy must be explicated so as to apply to indirect discourse, e.g., “John knows that ———”, so that if interchangeability fails here, synonymy is precluded.

See also White's suggestion in “Ontological Clarity and Semantic Obscurity”, Jour. Phil., Vol. 48, P. 379, of the need for a psychological analysis of even synonymy. For our limited consideration of indirect discourse directly referring to reactions like stating, believing, etc., the point seems even clearer, in favor of some pragmatic requirement.

⁷ This criticism of (iv) seems more general than Mates’ point in “Synonymity”, Univ. of Calif. Pub. in Phil., Vol. 25, 1950, “that, for any pair of intensionally isomorphic sentences—let them be abbreviated by ‘D’ and ‘D”,—if anybody even doubts that whoever believes that D believes that D′, then Carnap's explication is incorrect.” His argument assumes that the sentences:

(1) Whoever believes that D believes that D.

(2) Whoever believes that D believes that D′.

are intensionally isomorphic, and since nobody doubts (1), if anybody doubts (2), Carnap's analysis is faulty. Putnam, in “Synonymity and the Analysis of Belief Sentences”, Analysis, Vol. 14, pp. 114–122, has tried to meet this argument by revising the notion “intensional isomorphism” to include identical logical structure, and hence to render (1) and (2) non-synonymous. But, since Putnam's criterion does allow some different sentences to be intensionally isomorphic in his revised sense, (say ‘D’ and ‘T’ in our treatment above), his proposal, even if it meets Mates’ objection, fails to upset our criticism of (iv) above, which does not depend on Carnap's omission of logical structure from his explanation of intensional isomorphism. Further, as Chomsky suggests, this point can be used to formulate an example analogous to that of Mates which seems difficult even for Putnam's revision: Suppose ‘A’, ‘B’, and ‘C’ all intensionally isomorphic. Then the sentences:

(3) Whoever believes that A believes that B.

(4) Whoever believes that A believes that C.

are intensionally isomorphic even for Putnam's revision. Yet how is the factual possibility ruled out that nobody doubts that (3) but someone doubts that (4), or that John believes that (3) but not that (4)?

⁸ This example was suggested to me by Dr. Goodman, in conversation.

⁹ For a general, inscriptional treatment of indicators, see Ch. XI of Goodman's The Structure of Appearance, Harvard, 1951.

¹⁰ The point made here seems applicable generally to theories of indirect discourse depending on senses or rules of terms. Frege, e.g., in “Ueber Sinn und Bedeutung”, translated in Feigl and Sellars Readings in Philosophical Analysis, says that in such discourse, “words have their indirect nominata which coincide with what are ordinarily their senses.” What is the ordinary sense of an indicator term?

¹¹ In “An Inscriptional Approach to Indirect Quotation” (see Note 2. above), concerned with the structure rather than the basic terms for analyzing indirect discourse, I used the term “rephrasal” rather than “intensional isomorphism” for the relation between the that-content of a true Q and its appropriate N. There, the issue of structure is independent of choice of term. Here, in criticizing Carnap's term, I make no claim to be able to define any alternative like “rephrasal”. But if my arguments in the present paper are well-taken, any alternative will need to be conceived as graded and contextually variable with purpose, perhaps with the particular verb introducing the indirect mode, etc., such variable relation being at times tighter than synonymy or translation, at times considerably weaker. To suggest these characteristics which appear to me necessary, I use the term “rephrasal”.

¹² The present paper was accepted for publication prior to the appearance of Professor A. Church's “Intensional Isomorphism and Identity of Belief” (Phil. Stud., V, 5, October 1954, pp. 65–73), but the editors have been kind enough to allow me space for the following comments:

(A) Church proposes to replace intensional isomorphism by synonymous isomorphism as a “criterion of identity of belief,” illustrating his rejection of the former by appeal to the historical difficulty of finding a proof of Format's Last Theorem (and hence the possibility of believing its denial while disbelieving an obviously false counterpart which, assuming Fermat's claim correct, is intensionally isomorphic to this denial).

But if the history of belief-responses to sentences is held relevant in controlling proposals for identity-criteria, must we not reject synonymous isomorphism too? If someone (apparently confused by the terms “optician,” “oculist,” “optometrist,” and “ophthalmologist”) says “I believe that eye-doctors are eye-doctors but not that eye-doctors are oculists,” ought we not, in a perfectly good sense of “belief,” take him literally at his word, especially in view of the patent history of confusion of these terms in the popular mind?

(B) Church seeks to rebut Mates’ conclusion with respect to synonymous isomorphism by denying that one of the latter's illustrative sentences (see fn. 7 above) is really doubted while the other is not. Instead, Church construes the purported doubt as applying to an equivalent (but not synonymously isomorphic) metalinguistic sentence.

But this strategy can (with slight modification) be applied equally to save intensional isomorphism as well, i.e. to reconstrue ostensible divergence in belief-response to intensionally isomorphic pairs as holding actually of equivalent but not intensionally isomorphic sentences. Thus, e.g. suppose ‘A’ and ‘B’ to be intensionally isomorphic. Then “‘B’ is true” is intensionally isomorphic to neither, and can be taken to be the real object of doubt in every case where it is claimed that ‘A’ is believed and ‘B’ doubted. Why, in sum, does Church draw the line just between intensional and synonymous isomorphism, when his argument from history can be applied against the latter and his reconstruction of doubt can be used for the former?

(C) As support for his rebuttal of Mates, Church cites a case where translation of Mates’ pair results in identical sentences in a different language, while translation of the associated metalinguistic sentence preserves its distinctness. Now if intensionally as well as synonymously isomorphic sentences may ever be said to translate each other, then analogous support could be found for a resolution to save intensional isomorphism. If translation is, however, synonymous isomorphism, then Church's argument restates simply the original case of divergent beliefs about synonymous sentences, which Mates began with. To one who is willing to accept such a case, the translation argument offers no new deterrent. If, finally, Church's point concerns not the differing truth-values of “Mates doubts that (15) but not that (14)” and its German translation, but depends rather on the assumption that both represent the same reasoning while only the second is self-contradictory, then is not the assumption that translatability implies identity of reasoning itself a (partial) criterion of identity of belief, which is precisely what is at issue?