Constructible falsity

Abstract

The present note introduces a constructible interpretation for the logical connectives of number theory which is divergent from that of the intuitionists. Under the intuitionistic interpretation, the principle of excluded middle and certain other classically acceptable principles of logic must be rejected. Under the present interpretation, while some classical principles may be reinstated, other principles, acceptable both classically and intuitionistically, may be shown to be invalid. Among these is the principle of contradiction.