Polarity and Inseparability: The Foundation of the Apodictic Portion of Aristotle's Modal Logic

TLDR: In this paper, a system based on Aristotle's tests for things that can never combine (polarity) and things that cannot separate (inseparability) is presented. But it does not make full use of tests found throughout Aristotle's corpus and ancient Greek philosophy.

Abstract: Modern logicians have sought to unlock the modal secrets of Aristotle's Syllogistic by assuming a version of essentialism and treating it as a primitive within the semantics. These attempts ultimately distort Aristotle's ontology. None of these approaches make full use of tests found throughout Aristotle's corpus and ancient Greek philosophy. I base a system on Aristotle's tests for things that can never combine (polarity) and things that can never separate (inseparability). The resulting system not only reproduces Aristotle's recorded results for the apodictic syllogistic in the Prior Analytics but it also generates rather than assumes Aristotle's distinctions among ‘necessary’, ‘essential’ and ‘accidental’. By developing a system around tests that are in Aristotle and basic to ancient Greek philosophy, the system is linked to a history of practices, providing a platform for future work on the origins of logic.