Time and Indexicality in Buridan's Concept of Logical Consequence. Issue 4 (2nd October 2021) - Dahlquist, Manuel A.
Abstract : Jean Buridan developed his theory of consequence within a semantical framework compatible with what we now call token-based semantics. In his Treatise on Consequences and Sophismata, Buridan showed that the notion of consequence accepted by the logicians of his time (that the antecedent cannot be true without the consequent being true) fails when we consider inferences such as: (1) 'No proposition is negative, therefore, no ass is running'; and (2) 'Every proposition is affirmative, therefore, no proposition is negative'. Our analysis of Buridan's semantic and logical theory shows that: (a) for Buridan, time was a fundamental needed concept to adequately define the notion of consequence; (b) sentences like 'No proposition is negative' — appearing in (1) and (2) — are temporal indexicals; (c) these indexicals appealed to Buridan because they suggest a new type of validity, that has been called contextual validity by Blackburn and Jørgensen, and which was originally discussed by Kamp and Kaplan in the twentieth century. Finally, we offer a reconstruction of Buridan's theory of consequence in terms of a contextual hybrid logic, a logical-symbolic apparatus that allows us to assess Buridan's logical and philosophical contributions in contemporary terms and contribute to the current discussion on the topic.