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Lucas Champollion (New York University): Antecedents of counterfactuals violate de Morgan's law

Antecedents of counterfactuals violate de Morgan's law

(Joint work with Ivano Ciardelli and Linmin Zhang.) I present the results of a web survey suggesting that (1) can be true in situations where (2) is false.

(1) If switch A was down or switch B was down, the light would be off.
(2) If switch A and switch B were not both up, the light would be off.

Assuming that the antecedents of these sentences are correctly analyzed as "(NOT A) OR (NOT B)" and "NOT (A AND B)", this creates a problem for any compositional account of counterfactuals that interprets the two antecedents in classical propositional logic: by de Morgan's law, their denotations are identical. I argue that we can distinguish between (1) and (2) on a principled basis by interpreting their antecedents in propositional inquisitive logic. I also tentatively discuss distinguishing them via alternative-based implicature computations.