Dit is een quote van JR Lucas over Gödel.Rogier schreef:Verder ben ik bekend met Gödel, maar dit argument begrijp ik niet:
Waar komt deze conclusie vandaan? Waarom zou voor de mind niet net zo goed gelden dat er bepaalde waarheden zijn die niet als zodanig kunnen worden geproduceerd?
volledige artikel (minds, machines and Gödel)
http://users.ox.ac.uk/~jrlucas/mmg.html
The conclusions it is possible for the machine to produce as being true will therefore correspond to the theorems that can be proved in the corresponding formal system. We now construct a Gödelian formula in this formal system. This formula cannot be proved-in-the- system. Therefore the machine cannot produce the corresponding formula as being true. But we can see that the Gödelian formula is true: any rational being could follow Gödel's argument, and convince himself that the Gödelian formula, although unprovable-in-the-system, was nonetheless----in fact, for that very reason---true. Now any mechanical model of the mind must include a mechanism which can enunciate truths of arithmetic, because this is something which minds can do: in fact, it is easy to produce mechanical models which will in many respects produce truths of arithmetic far [259] better than human beings can. But in this one respect they cannot do so well: in that for every machine there is a truth which it cannot produce as being true, but which a mind can. This shows that a machine cannot be a complete and adequate model of the mind. It cannot do everything that a mind can do, since however much it can do, there is always something which it cannot do, and a mind can. This is not to say that we cannot build a machine to simulate any desired piece of mind-like behaviour: it is only that we cannot build a machine to simulate every piece of mind-like behaviour. We can (or shall be able to one day) build machines capable of reproducing bits of mind-like behaviour, and indeed of outdoing the performances of human minds: but however good the machine is, and however much better (116) it can do in nearly all respects than a human mind can, it always has this one weakness, this one thing which it cannot do, whereas a mind can. The Gödelian formula is the Achilles' heel of the cybernetical machine. And therefore we cannot hope ever to produce a machine that will be able to do all that a mind can do: we can never not even in principle, have a mechanical model of the mind.