A Modal Logic with Temporal Variables

  • T. Chapman
Part of the Synthese Library book series (SYLI, volume 159)


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


Modal Logic Contingent Proposition Definite Description Propositional Variable Atomic Proposition 
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  1. 1.
    T. Chapman, “On a New Escape from Logical Determinism”, Mind, Vol. LXXXI, N.S., No. 324, Oct. 1972, pp. 597–599. Cahn has replied to my criticism but he appears to agree with my point that an indeterminist logic must be non-truth-functional, which is all that is relevant for our purposes here. Thomason’s system can be found in his “Indeterminist Time and Truth-Value Gaps”, Theoria, Vol. 36 (1970) pp. 264–281.Google Scholar

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© D. Reidel Publishing Company, Dordrecht, Holland 1982

Authors and Affiliations

  • T. Chapman
    • 1
  1. 1.Department of PhilosophyUniversity of GuelphCanada

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