I maintain, pace the common narrative in the existing literature, that negated ifs fail to provide good evidence for Conditional Excluded Middle. The full story, entitled “Negating Conditionals,” is now forthcoming in Oxford Studies in Philosophy of Language, Volume 2. The abstract is below and you can find the final draft in the Research section.
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. I do so 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 in fact how it can co-exist with other non-classical principles such as Simplification of Disjunctive Antecedents without negative side effects