Aristotle’s modal syllogistic and first-order modal logic

In Prior Analytics 1.1–22, Aristotle develops his proof system of non-modal and modal propositions. This system is given in the language of propositions, and Aristotle is concerned with establishing some properties and relations that the expressions of this language enjoy. However, modern scholarship has found some of his results inconsistent with positions defended elsewhere. The set of rules of inference of this system has also caused perplexity: there does not seem to be a single interpretation that validates all the rules which Aristotle is explicitly committed to using in his proofs. Some commentators have argued that these and other problems cannot be successfully addressed from the viewpoint of the traditional, ‘first-order’ interpretation of Aristotle’s syllogistic, whereby propositions are taken to involve quantification over individuals only. Accordingly, this interpretation not only is inadequate for formal analysis, but also stems from a misunderstanding of Aristotle’s ideas about quantification. On the contrary, in this study I purport to vindicate the adequacy and plausibility of the first-order interpretation. Together with some assumptions about the language of propositions and an appropriate regimentation, the first-order interpretation yields promising solutions to many of the problems raised by the modal syllogistic. Thus, I present a reconstruction of the language of propositions and a formal interpretation thereof which will prove respectful and responsive to most of the views endorsed by Aristotle in the ‘modal’ chapters of the Analytics.