Logic Language

Deductive Logic by Warren Goldfarb

By Warren Goldfarb

This article presents an easy, energetic yet rigorous, creation to truth-functional and predicate common sense, whole with lucid examples and incisive workouts, for which Warren Goldfarb is popular.

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AN AMBIGUITY IN ORDINARY LANGUAGE Moreover, in addition to justifying the falsity of the consequent, Quine's assumption perhaps also helps to remove a residual awkwardness about the truth of the antecedent of (1). I am not denying that such ordinarylanguage statements as (6) 'the next president of the United States is necessarily the next president of the United States' can occasionally be understood so as to be false. In general, my basic semantical idea of 'possible worlds' shows that almost any ordinary-language statement in which a singular term occurs within a modal context is in principle potentially ambiguous.

Because bound variables range over actual individuals, the latter (8) can be formalized by (8*) '(Ex)(x = a & N(x = a))' or perhaps rather by (8**) '(x) (x = a:::l N(x = a)'. Unlike (7), (8)-(8**) can certainly be false - and in fact seem to be so. If you felt uncomfortable about my bland initial assertion that the antecedent of (1) is true, you had some right to do so, for the best translation of the antecedent into ordinary language admits of an interpretation which makes it false. This does not belie my point, however, that under the intended interpretation (1) is in fact false.

In order for the terms 'a' and 'b' to be interchangeable at such an occurrence, they must refer to the same individual in each of these possible worlds. That this is the case is precisely what 'N"i(a=b)' expresses. N =) is very plausible even without the possibility of reducing it to the simpler condition (C. = ). N =) are the form which the principle of the substitutivity of identity takes in modal contexts. N =) EXISTENTIAL AND UNIQUENESS PRESUPPOSITIONS 25 follows from the other conditions (in the sense that it does not affect the notion of satisfiability), and hence does not embody any assumptions not already made in ordinary non-modal first-order logic.

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