The syllogism

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The book provides a formal analysis of Aristotle's non-modal syllogistic, exploring the relationships between various syllogistic systems, sub-systems, and extensions, while addressing the fundamental nature of the syllogism. It synthesizes recent logical and philological work on the non-modal sections of the Analytics within a new formal system that merges Lukasiewicz's axiomatic approach with Corcoran and Smiley's natural deduction. This system is contextualized within the broader development of categorical syllogistic from Aristotle's time to the present, including systems with negative or singular terms and those with axiomatic structures for rejected formulae. The author demonstrates that Aristotle's syllogistic can be grounded in singular syllogisms using Aristotelian rules of ecthesis and offers a new explanation for Aristotle's incomplete logic of singular terms. An auxiliary theory is identified for systems based on propositional logic. The nature of the syllogism is examined syntactically, generalizing traditional rules to elucidate Aristotle's syntactic metatheory in Prior Analytics Book B. Additionally, a property defined by Smiley is employed to interpret semantic metatheorems by Aristotle. The semantic understanding of the syllogism is linked to a theory of fallacies, connecting to epistemic logic through the concept of petitio principii. This account of the syllogism is epistemological but not psychologistic, ap