Dale Jacquette CONUNDRUMS OF CONDITIONALS IN CONTRAPOSITION

A previously unnoticed metalogical paradox about contraposition is formulated in the informal metalanguage of propositional logic, where it exploits a reflexive self-non-application of the truth table definition of the material conditional to achieve semantic diagonalization. Three versions of the paradox are considered. The main modal formulation takes as its assumption a conditional that articulates the truth table conditions of conditional propositions in stating that if the antecedent of a true conditional is false, then it is possible for its consequent to be true. When this true conditional is contraposed in the conclusion of the inference, it produces the false conditional conclusion that if it is not the case that the consequent of a true conditional can be true, then it is not the case that the antecedent of the conditional is false.