The Logic and Metaphysics Workshop will meet on October 7th from 4:15-6:15 in-person at the Graduate Center (Room 4419) for a talk by Cian Dorr (NYU) and Matt Mandelkern (NYU).

Title: The logic of sequences

Abstract: In the course of proving a tenability result about the probabilities of conditionals, van Fraassen (1976) introduced a semantics for conditionals based on ω-sequences of worlds, which amounts to a particularly simple special case of ordering semantics for conditionals. On that semantics, ‘If p, then q’ is true at an ω-sequence just in case q is true at the first tail of the sequence where p is true (if such a tail exists). This approach has become increasingly popular in recent years. However, its logic has never been explored. We axiomatize the logic of ω-sequence semantics, showing that it is the result of adding two new axioms to Stalnaker’s logic C2: one, Flattening, which is prima facie attractive, and a second, Sequentiality, which is complex and difficult to assess. We also show that when sequence semantics is generalized to arbitrary (transfinite) ordinal sequences, the result is the logic that adds only Flattening to C2. We also explore the logics of a few other interesting restrictions of ordinal sequence semantics, and explore whether sequence semantics is motivated by probabilistic considerations, answering, pace van Fraassen, in the negative.