Abstract

In its traditional Priorean form, tense logic involves four sentence-modifying operators (P, F (it was/will be the case) and H, G (it has always/will always be the case)) that act in an analogous way traditional alethic modal operators do and indicate the temporal properties of the state of affairs in question. It has traditionally been deemed that the addition of the present-tense operator to tense logic would be superfluous as the basic propositions modified by the Priorean temporal operators have been claimed to automatically be in the present tense. The aim of this lecture will be to show that such a view, while being harmless in the propositional tense logic, leads to the very counterintuitive metaphysical consequences in the first-order tense logic. In such logics, where the rules of temporal operators are combined with the classical theory of quantification, some of the weakest systems contain the so-called Barcan and the Converse Barcan Formulas as theorems. These formulas directly entail the permanentist metaphysical picture of the world according to which beings neither start nor cease to exist in the flow of time. By treating the quantifier ∃x as existentially unloaded and granting the function of expressing (present) existence to the present-tense operator, Barcan and the Converse Barcan Formulas become metaphysically innocuous.