Abstract

This paper discusses the question of whether all counterfactuals with necessarily false antecedents (counterpossibles) are vacuously true. The orthodox view of counterpossibles (vacuism) answers that question in the affirmative. This paper explains vacuism before turning to examples from science that seem to require us to reason non-trivially using counterpossibles, and it seems that the counterpossibles used in such cases can be true or false. This is a threat to vacuism. It is then argued that the same kind of reasoning which produces non-trivial counterpossibles in scientific cases can be extended to the case of counterpossibles in mathematics. Ordinary counterfactual reasoning relies on rejecting background assumptions in order to assume the truth of the antecedent. A failure to perform this process in the counterpossible case is what leads one to vacuism and it is explained how this process produces non-vacuous; counterfactuals, scientific counterpossibles, and mathematical counterpossibles.