Reflection

Consider the following two sentences: These two sentences are both examples of counterfactual conditionals with impossible antecedents (henceforth ‘counterpossible conditionals’). According to the orthodox semantics for counterfactuals due to Lewis and Stalnaker,1 among others, what is required for a sentence like (1) to be true is for the most similar possible worlds to the actual world in which the antecedent is true (in this case, worlds in which Sally squared the circle), to be worlds in which the consequent is true (in this case, worlds in which we are surprised). According to these theories, because the antecedents of (1) and (2) are impossible, and thus true at no possible worlds, sentences (1) and (2) both come out vacuously true, as in all the possible worlds in which their antecedent is true (i.e., none of them), their consequent is also true. These are vacuist theories of counterpossible conditionals—theories according to which all counterpossibles are vacuously true.