Negating Conditionals

A recurring narrative in the literature is that the empirical facts about negated conditionals 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 an innovative conditional analysis in a bilateral semantic setting that takes inspiration from the Ramsey test for conditionals but distinguishes the classical Ramseyan question of what it takes to accept a conditional from the one of what it takes to reject a conditional. The resulting framework disentangles the empirical facts about negated conditionals from the validity of Conditional Excluded Middle but also shows how the principle can live happily in a strict analysis of conditionals, and how it can co-exist with other non-classical principles such as Simplification of Disjunctive Antecedents without negative side-effects.