Human and Machine Interpretation of Expressions in Formal Systems

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’