Rips, in The Psychology of Proof, argues that, through the processes of evolution, logic (e.g., modus ponens) has become established in the human mind as the basis for thinking, and that production systems rest on this foundation. In this paper we defend the converse argument that, through evolution, a production system architecture has become the basis for human thinking, and that formal logics rest on this production system and the accompanying mechanisms for recognition and search. It is through the “automaticity” (...) of the execution of productions that we experience the compellingness of deductive arguments. (shrink)

This paper uses a proof of Gödels theorem, implemented on a computer, to explore how a person or a computer can examine such a proof, understand it, and evaluate its validity. It is argued that, in order to recognize it (1) as Gödel's theorem, and (2) as a proof that there is an undecidable statement in the language of PM, a person must possess a suitable semantics. As our analysis reveals no differences between the processes required by people and machines (...) to understand Gödel's theorem and manipulate it symbolically, an effective way to characterize this semantics is to model the human cognitive system as a Turing Machine with sensory inputs. La logistique n'est plus stérile: elle engendre la contradicion! – Henri Poincaré ‘Les mathematiques et la logique’. (shrink)