A Modal Logic with Temporal Variables

Abstract

There appear thus far to have been five general methods suggested in the literature for formalizing indeterministic tense-modal logics. The first consists in the introduction of a third truth-value, but this has the absurb consequence that the law of non-contradiction must be denied since the conjunction of any two propositions having the indeterminate truth-value must be indeterminate rather than false. (The absurdity is apparent from the fact that in this context “having an indeterminate truth- value” means the same as, “possibly being true”). A second alternative called by Prior a “Peircean tense logic” has the very awkward result that true, contingent propositions about the future cannot be -tated at all. The third method which Prior calls “Ockhamist” is the one considered below. (Cahn’s and Thomason’s systems I have tried to investigate elsewhere.)¹