'Unless' is 'Or', Unless '¬A Unless A' is Invalid

Abstract

The proper translation of "unless" into intuitionistic formalisms is examined. After a brief examination of intuitionistic writings on "unless", and on translation in general, and a close examination of Dummett's use of "unless" in Elements of Intuitionism (1975b), I argue that the correct intuitionistic translation of "A unless B" is no stronger than "-B -> A". In particular, "unless" is demonstrably weaker than disjunction. I conclude with some observations regarding how this shows that one's choice of logic is methodologically prior to translation from informal natural language to formal systems.