An interpretation of Aristotle's modal syllogistic is proposed which is intuitively graspable, if only formally correst. The individuals to which a term applies, and possibly-applies, are supposed to be determined in a uniform way by the set of individuals to which the term necessarily-applies.

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. (shrink)

Ever since ?ukasiewicz, it has been opinio communis that Aristotle's modal syllogistic is incomprehensible due to its many faults and inconsistencies, and that there is no hope of finding a single consistent formal model for it. The aim of this paper is to disprove these claims by giving such a model. My main points shall be, first, that Aristotle's syllogistic is a pure term logic that does not recognize an extra syntactic category of individual symbols besides syllogistic terms and, second, (...) that Aristotelian modalities are to be understood as certain relations between terms as described in the theory of the predicables developed in the Topics. Semantics for modal syllogistic is to be based on Aristotelian genus-species trees. The reason that attempts at consistently reconstructing modal syllogistic have failed up to now lies not in the modal syllogistic itself, but in the inappropriate application of modern modal logic and extensional set theory to the modal syllogistic. After formalizing the underlying predicable-based semantics (Section 1) and having defined the syllogistic propositions by means of its term logical relations (Section 2), this paper will set out to demonstrate in detail that this reconstruction yields all claims on validity, invalidity and inconclusiveness that Aristotle maintains in the modal syllogistic (Section 3 and 4). (shrink)