Possibility, necessity, and logical truth

Abstract

N 'The Province of Logic' (ANALYSIS 36.1, pp. 47-8) Charles Sayward criticises certain arguments I have produced against both Quine's definition of logical truth and Quine's criticisms of Strawson's logical theory ('Quine and Strawson on Logical Theory', ANALYSIS 34.6, pp. 207-8). I believe I can answer Sayward's criticisms and also show more clearly just how Quine is mistaken. First, let us recall what Quine says. According to Quine, 'formal validity' and 'logical truth' should be defined in terms of 'statement forms which are logical, in the sense of containing no constants beyond logical vocabulary, and (extensionally) valid, in the sense that all statements exemplifying the form in question are true' (The Ways of Paradox, New York, 1966, pp. 138-9). In response to this I claimed that 'Quine's definition is acceptable only if we construe All statements of the form in question are to mean that all statements of the form in question are true. The fact that all statements of the form are true would not entitle us to infer that any having this form is a logical truth' (op. cit., p. zo8). I then argued that this idea ofpossibility can be used to define 'necessity', and to vindicate Strawson against Quine's critique. Sayward challenges my claim, and contends that it would be a mistake to construe Quine's definition in the way I suggest. Furthermore, he maintains that it is doubtful whether my construal even makes sense. He says that 'Insofar as possible sentence makes any sense at all, it is coextensive with actual sentence.' Sayward also says that 'Quine did not intend statement to refer to occurrences of sentences. ... In this respect, a statement, in Quine's sense, is like a formula of a logical system. A string of symbols of the system, whether actually produced [my emphasis] or not, is a formula just in case the string satisfies certain rules' (op. cit., p. 47). Apparently, Sayward is implying that what I mistakenly call 'possible statements' are in fact statements, on Quine's usage. I believe Sayward's description of how Quine intends us to understand 'statement' is correct. And I concede that on this usage no distinction between and statements exists. However, even on Quine's usage a distinction exists between sentences which have actually been produced and those which it is merely to produce. This is revealed by Sayward when he says, 'A string of symbols of the system, whether actually produced or not.. .'. In recognizing this distinction Sayward is pointing to the very distinction which I was marking with the terms 'actual sentence' and 'possible sentence'. My usage of these terms seems quite natural, especially when we consider