System AX’

Abstract

The last class of modal syllogisms in Aristotle’s system are those that contain unqualified assertoric forms. In this Chapter we propose a semantics, based on Angelelli’s analysis of unqualifieds as ampliated assertorics, which distinguishes these forms both from ordinary assertorics and from apodeictics. Angelelli’s analysis is shown to be superior to the analyses of Ockham and Buridan which treat unqualifieds as assertorics that are always or necessarily true; and it is shown to be superior to Pseudo-Scotus’s analysis of unqualifieds as ampliated problematics. Our semantics has the consequence that Barbara and Darii XQM (with ordinary assertoric major) are valid despite Aristotle’s argument to the contrary. Our semantics also shows that Aristotle’s procedure of modal reductio, though unsound as a general principle, is sound for the particular case in which he applies it.