A special case of a counterfactual conditional with the property that the antecedent is not merely false, but necessarily so. Frequently, violations of some mathematical truth or other are used to give examples of counterpossible conditionals:

• • If all magnitudes were rational, then the philosophy of Pythagoreanism would be vindicated.

While semantics for conditional logics frequently evaluate counterfactual conditionals by appealing to possible worlds at which the contrary-to-fact antecedent is true, counterpossibles constitute a challenge to this approach. The very notion that an antecedent $\phi$ is contrary to what is possible presupposes that there are no possible worlds at which $\phi$ is true.