Chrysippus' Modal Logic and Its Relation to Philo and Diodorus

In K. Doering & Th Ebert (eds.), Dialektiker und Stoiker. Franz Steiner. 63--84 (1993)
Abstract
ABSTRACT: The modal systems of the Stoic logician Chrysippus and the two Hellenistic logicians Philo and Diodorus Cronus have survived in a fragmentary state in several sources. From these it is clear that Chrysippus was acquainted with Philo’s and Diodorus’ modal notions, and also that he developed his own in contrast of Diodorus’ and in some way incorporated Philo’s. The goal of this paper is to reconstruct the three modal systems, including their modal definitions and modal theorems, and to make clear the exact relations between them; moreover, to elucidate the philosophical reasons that may have led Chrysippus to modify his predessors’ modal concept in the way he did. It becomes apparent that Chrysippus skillfully combined Philo’s and Diodorus’ modal notions, with making only a minimal change to Diodorus’ concept of possibility; and that he thus obtained a modal system of modalities (logical and physical) which fit perfectly fit into Stoic philosophy.
Keywords modal logic  necessity  temporal truth  Stoics  Diodorus Cronus  Chrysippus  Stoic logic  contingency  master argument  propositions
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