Negating Conditionals in Bilateral Semantics

Abstract

A recurring narrative in the literature on conditionals is that the empirical facts about negated ifs provide compelling evidence for the principle of Conditional Excluded Middle and sit uncomfortably with a large family of analyses of conditionals as universal quantifiers over possible worlds. I show that both parts of the narrative are in need of a rewrite by articulating a bilateral update semantics for conditionals that distinguishes itself from previous frameworks by giving separate acceptance and rejection conditions for conditionals. The resulting framework shows that CEM is inessential for explaining the empirical facts about negated ifs but also how the principle can live happily in a strict analysis of conditionals.