Montague’s Intensional Logic

Abstract

Up to this point we have treated tense and other modal operators syncategorematically, i.e., we have not defined a denotation for the symbol F directly, but only a denotation of the whole expression Fø in terms of the interpretation of the expression ø. Now let us consider the question whether we can assign a denotation separately to F in such a way that the denotation of Fø can be determined entirely on the basis of the denotation of F and the denotation of ø. (This would parallel the way in which we gave a denotation for it-is-not-the-case-that in L_0E in such a way that the denotation of it-is-not-the-case-that ø was the result of applying the function denoted by it-is-not-the-case-that to the denotation of ø.) However, this simply cannot be done for F because the denotation of ø is a truth value, yet the truth value of Fø is independent of the truth value of ø. Fø may be true at a given time whether or not ø is true at that time; the same is true of formulas of the form Pø. To bring the point home for natural languages, consider (6–1) and (6–2) versus (6–3) and (6–4) (examples cited by Thomason 1974a, to establish the same point):

• (6–1) Iceland is covered with a glacier.

• (6–2) Africa is covered with a glacier.

• (6–3) Iceland was (once) covered with a glacier.

• (6–4) Africa was (once) covered with a glacier.