Modality and Time (I). The Principle of Plenitude

Abstract

At first sight, all there is to Aristotle’s modal logic in the strict sense appears to have been set out in our general scheme of absolute and relative modalities. Although the issue of the necessity of the past, introduced in the last section of the preceding chapter, might prove to be essential to other aspects of Aristotle’s philosophy, it does not, so it may seem, drastically upset our account of his logic of modalities. If one were to label past and present events as absolutely necessary, the general scheme can easily be adapted by replacing the original base of definitions and axioms S by a new one, S’, being the union of S. and the set of all true assertoric sentences about past and present. If desired, the whole scheme could then be reformulated to fit a temporalized version of modal logic.