Sextus Empiricus' Fourth Conditional and Containment Logic

Abstract

In his Outlines of Pyrrhonism 2.110–113, Sextus Empiricus presents four different accounts of the conditional, presumably all from the Hellenistic period, in increasing logical strength. While the interpretation and provenance of the first three accounts is relatively secure, the fourth account has perplexed and frustrated interpreters for decades or longer. Most interpreters have ultimately taken a dismissive attitude towards the fourth account and discounted it as being of both little historical and logical interest. We argue that this attitude is unwarranted and demonstrate that the conditional expressed in the fourth account can profitably be understood as a precursor of analytic entailment, familiar from containment logics such as those developed by Parry and Angell. Exploiting recent work by Fine, we present a formal truthmaker semantics for this conditional and show how it sheds light on a number of longstanding issues in the interpretation of this passage.