Let us recall the arguments given in Chapter 4 establishing Gödel’s theorem and its relation to computability. It was shown there that whatever (sufficiently extensive) algorithm a mathematician might use to establish mathematical truth – or, what amounts to the same thing,1 whatever formal system he* might adopt as providing his criterion of truth – there will always be mathematical propositions, such as the explicit Gödel proposition Pk (k) of the system (cf. p. 140), that his algorithm cannot provide an answer for. If the workings of the mathematician’s mind are entirely algorithmic, then
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