The origins of conditional logic: Theophrastus on hypothetical syllogisms (Marko Malink and Anubav Vasudevan)

The Logic and Metaphysics Workshop will meet on November 21st from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 7314) for a talk by Marko Malink (NYU) and Anubav Vasudevan (University of Chicago).

Title: The origins of conditional logic: Theophrastus on hypothetical syllogisms

Abstract: Łukasiewicz maintained that “the first system of propositional logic was invented about half a century after Aristotle: it was the logic of the Stoics”. In this talk, we argue that the first system of propositional logic was, in fact, developed by Aristotle’s pupil Theophrastus. Theophrastus sought to establish the priority of categorical over propositional logic by reducing various modes of propositional reasoning to categorical form. To this end, he interpreted the conditional “If φ then ψ” as a categorical proposition “A holds of all B”, in which B corresponds to the antecedent φ, and A to the consequent ψ. Under this interpretation, Aristotle’s law of subalternation (A holds of all B, therefore A holds of some B) corresponds to a version of Boethius’ Thesis (If φ then ψ, therefore not: If φ then not-ψ). Jonathan Barnes has argued that this consequence renders Theophrastus’ program of reducing propositional to categorical logic inconsistent. In this paper, we show that Barnes’s objection is inconclusive. We argue that the system developed by Theophrastus is both non-trivial and consistent, and that the propositional logic generated by Theophrastus’ system is exactly the connexive variant of the first-degree fragment of intensional linear logic.

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