What Gödel’s theorem tells us, in a nutshell, is the following (which is not controversial). Suppose that we are given some computational procedure P for establishing mathematical assertions (let us say, assertions of a particularly well-defined type, such as the famous ‘Fermat’s last theorem’ (cf. pp. 76–7)). Then if we are prepared to accept that the rules of P are trustworthy—in the sense that we accept that the successful derivation of some mathematical assertion by use of the rules of P provides us with an unassailable demonstration of the truth of that assertion—then we must also accept
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