Homogenous alternative semantics
The principles of Conditional Excluded Middle (CEM) and Simplification of Disjunctive Antecedents (SDA) have received substantial attention in isolation. Both principles are plausible generalizations about natural language conditionals. But the two principles have not been discussed much in combination. This paper explores the significance of
having both principles constrain the logic of the conditional. Our negative finding is that, together with elementary logical assumptions, CEM and SDA yield a variety of implausible consequences. Despite these incompatibility results, we open up a narrow space to satisfy both.
We show that, by simultaneously appealing to the alternative-introducing analysis of disjunction (Alonso Ovalle 2006) and to the theory of homogeneity presuppositions (von Fintel 1997), we
can satisfy both. Furthermore, the theory that validates both principles resembles a recent proposal that Santorio (2017) defends on independent grounds. The cost of this approach is that
it must give up the transitivity of entailment: we suggest that this is a feature, not a bug, and connect it with with recent developments of intransitive notions of entailment (Ripley 2013, 2015).
coauthored with Fabrizio Cariani
Proceedings of the 2017 Amsterdam Colloquium