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Unveiling the Master: Chrysippus' Logic and Two-Dimensional Semantics

Lucas Champollion
New York University
Wed May 1st 2024, 2:00 - 3:30pm

The ingenious logic of Chrysippus of Soli (c. 279 – c. 206 BC), the third head of the Stoic school, encompasses modality, deixis, conditionals and many more phenomena studied in contemporary formal semantics. This talk explores Chrysippus' response to the Master Argument of Diodorus Cronus, an ancient challenge to unrealized possibilities. In his response, Chrysippus argued that some true conditionals have possible antecedents and impossible consequents, such as "If Dio has died, this one (pointing at Dio) has died". I argue that a proper understanding of this response requires the Kaplanian distinction between character and content, a distinction which is largely absent from modern scholarship on Stoic logic. I develop a model theory for an appropriate fragment of Stoic logic within contemporary branching-time and two-dimensional semantics. The talk adds to the inventory of striking parallels between Stoic logic and modern philosophy of language and bears witness to the sophistication of Stoic logic and its relevance to contemporary thought.