What makes true universal statements true?

Bob Hale (University of Sheffield)

Abstract:

In discussing this question, I shall be especially interested in how it is to be answered within the framework of what Kit Fine calls exact truth-maker semantics. On the version of exact truth-making which Fine presents in recent papers, a true universally quantified statement, ∀xB(x), is made true a state composed of the states which verify its instances. This might reasonably be viewed as the standard account. Its widespead acceptance is hardly surprising, since it can appear both very natural and even inevitable, given that ∀xB(x) is true iff B(x) is true of every object which is an admissible value of its free variable. But whilst I think there is a subclass of universal statements for which the standard account is correct, I do not think it gives the right account of truth-making for universal statements in general.

My main aim here is promote an alternative – generic – account of the truth-makers for quantified propositions. I shall also give some attention to two closely related questions: first, when, and why, we should favour an alternative to the standard account, and second, whether the alternative account I favour can be accommodated within the framework of exact truth-maker semantics, in Fine’s sense. If time permits, I shall also discuss the bearing of my alternative account on some questions about classical and intuitionist logics and truth-making discussed by Fine and by Øystein Linnebo is recent work.