The common sense conviction that rationality is based on the classical logic requires major revision since the essential assumption of many standpoints in the cognitive science, concerning the non-contradictory character of mind, seems to be no longer tenable. Firstly, the non-algorithmic models of mind proposed by John Lucas and Roger Penrose are presented. In the context of these models, the importance of the Gödel incompleteness theorems for the philosophy of mind and artificial intelligence is debated. Secondly, several
specific difficulties in applying the ‘Gödelian arguments’ in the modeling of mind are pointed out. As the main thesis of the article, it is stipulated that mind operates according to a wrong algorithm that is functionally equivalent to a contradictory formal system. The examples of the contradictory contents of mental states, evidenced in the phenomenon of self-deception and the mediaeval double truth theory in science, are discussed. Some consequences of the model of an inconsistentmind, based on the revision of the classical logic, are surveyed.