Complex sentential operators refute unrestricted Simplification of Disjunctive Antecedents

Abstract

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 > χ) ∧ (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 are promising pragmatic explanations for the currently known counter-examples, which have led several authors to argue in recent work that SDA is unrestrictedly valid 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 valid tout court. While SDA-supporting interpretations do exist and require an explanation, every theory of counterfactuals also requires an explanation of examples that can only be read in a way that does not support SDA.

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