In this article, the model of an inconsistent mind according to suggestions of Hilary Putnam and Alan Turing is presented from the perspective of the cognitive sciences and the evolutionary psychology. An attempt to reconcile the two versions of the modular model of mind by Jerry Fodor and Steven Pinker is undertaken followed by the discussion of the problem of evolutionary origin of mind. Next, the problem of the central module (interface) is considered which is supposed to integrate the individual and specialized modules of mind. The main thesis of this article states that the ‘global’ inconsistency of mind may result from the inconsistencies among ‘local’ computational modules of mind. Mind may be modeled as an inconsistent formal system which remains non-trivial. Consequently, it seems rational to postulate that the operation of mind is not based on the classical Aristotelian logic and is better described the systems of a paraconsistent logic. Best examples of such logical systems include the discussive logic by Stanisław Jaśkowski, the logic of formal inconsistency (LFI) by Newton da Costa and the many-valued logic by Jan Łukasiewicz and Graham Priest.