Complex sentential operators refute Simplification of Disjunctive Antecedents

There is a longstanding debate about the status of the principle Simplification of Disjunctive Antecedents (SDA), according to which a counterfactual with a syntactically disjunctive antecedent [(φ ∨ψ) > χ] entails a conjunction of counterfactuals [(φ > ψ)∧(ψ > χ)]. This principle is highly intuitive for most examples that have been considered, but it has also been claimed to be subject to empirical counter-examples. However, there is a promising account of the currently known counter-examples which has led a number of authors to suggest that SDA is empirically accurate principle after all. This short piece introduces new data involving sentential operators that impose both upper and lower bounds on confidence, frequency, etc., such as likely but not certain, there is an exactly n% probability, and usually but not always. These examples show clearly that SDA is not logically valid. I also consider several other arguments for SDA and show that they are empirically invalid or otherwise not decisive. These data are not consider with strict conditional theories of counterfactuals or other accounts that validate SDA. They are consistent with a theory in which a strict Boolean reading of antecedent disjunctions is available, either alongside an SDA-supporting reading (as in Alternative/Inquisitive Semantics) or with SDA derived as a pragmatic inference.