Ancient Logic, Language, and Metaphysics by Andrea Falcon

Author:Andrea Falcon
Language: eng
Format: epub
Publisher: Taylor and Francis
Published: 2020-06-15T00:00:00+00:00

Its formal counterpart may be represented as follows

(8) ∀t P(t).

It seems natural to claim that (8) is true if and only if it rains at every instant; that is, if and only if…, P(ti), P(tj),…, P(tm),…. Suppose that (8) is true. If the domain over which the variable t ranges is infinite, then at whatever time we evaluate (8) we cannot say that (8) is true. For instance, at tm we cannot conclude that (8) is true. Of course, if it happens that ¬P(tm+1), we can infer at this stage that (8) is false. But if P(m+1), we have still to postpone an assignment of a truth value to (8) and so there is no time at which we can say that it is true.

Because we cannot state that (8) is true, we cannot assert that a particular indefinite proposition such as

(9) ∃t P(t)

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