false formulae can be proved in Elementary Number Theory, it follows that the Godelian formula is both true and unprovable from Peano's axioms. The mechanist is not putting forward actual machines which actually represent some human being's intellectual output, but is claiming instead that there could in principle be such a machine. No doubt, we cannot prove to a hide-bound mechanist that we can. Although we sometimes contradict ourselves and change our minds, some parts of our conceptual structure are very stable, and immune to revision.
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S) Hao Wanp, From Mathematics to Philosophy, London, 1974, pp 324-326. Only if we also had a proof 400 word essay about japan in Elementary Number Theory yielding!-Cons(ENT)- G would we be able to infer. One can allow the Cartesian possibility of conceptual revision without being guilty, as Hutton supposes, of inconsistency in claiming knowledge of his own consistency.11 To claim to know something is not to claim infallibility but only to have adequate backing for what is asserted. So even if the mind were supposed to take on all challenges even from inconsistent machines, it would often be able to discriminate between those that were to be ploughed for inconsistency and those that were to be failed for not being able to assert. Indeed, I would at once concede that I am very likely not to be entirely right, and that others will be able to articulate the arguments more clearly, and thus more cogently, than I did. I must have touched a raw nerve. We have adequate, more than adequate, reason for affirming our own consistency and the truth, and hence also the consistency, of informal arithmetic, and so can properly say that we know, and that any machine representation of the mind must manifest an output expressed. I cannot prove to the mechanist that anything can be done other than what a machine can do, because he has restricted what he will accept as a proof to such an extent that only "machine-doable" deeds will be accounted doable at all.
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