Abstract Entities by Roger Teichmann (auth.)

By Roger Teichmann (auth.)

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We may choose either of these to be the result of substituting '--Socrates' for 'Socrates', but we cannot have both. But whichever sentence we choose, the other contains the expression' --Socrates' in a position where we cannot substitute 'Socrates' for it. For if we could, the result could only be '(3x)(Socrates died before x)' again, but by hypothesis the reverse substitution from that does not lead back to the sentence we began with. ) It may be added that in the very course of establishing scope distinctions we typically make use of scopeless bound variables.

And won't the negation of' --a' be the same expression as 'a' itself? In fact, however, we must recognise that even if there is such an expression as the negation of' --a' - we might write it: '(a-)' - it is not the same expression as 'a'. For a simple argument shows that'-a' is of a different logical type from 'a', since it and 'a' are not properly intersubstitutable in all contexts: that is, there is (on occasion) more than one way of substituting' --a' for 'a', and this indicates difference of level.

Involving modus ponens) in which these two sentences have exactly parallel roles. And to the extent that sentences logically related to 'p' are grammatically more similar to it than to its equivalent 'q', it is the grammatical form of 'p' which may be said to be more closely associated with the logical form of both 'p' and 'q'. The issue is complicated by the fact that, rather than speaking of the logical form of a sentence, one should really speak of the logical form which needs to be apprehended in a sentence as it occurs in a given context or argument; Quine is fond of stressing this point.

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