Online research in philosophy

Mechanism is the thesis that men can be considered as machines, that there is no essential difference between minds and machines.John Lucas has argued that it is a consequence of Gödel's theorem that mechanism is false. Men cannot be considered as machines, because the intellectual capacities of men are superior to that of any machine. Lucas claims that we can do something that no machine can do-namely to produce as true the Gödel-formula of any given machine. But no machine can prove its own Gödel-formula.

Goedel's theorem states that in any consistent system which is strong enough to produce simple arithmetic there are formulae which cannot be proved-in-the-system, but which we can see to be true. Essentially, we consider the formula which says, in effect, "This formula is unprovable-in-the-system". If this formula were provable-in-the-system, we should have a contradiction: for if it were provablein-the-system, then it would not be unprovable-in-the-system, so that "This formula is unprovable-in-the-system" would be false: equally, if it were provable-in-the-system, then it would not be false, but would be true, since in any consistent system nothing false can be provedin-the-system, but only truths. So the formula "This formula is unprovable-in-the-system" is not provable-in-the-system, but unprovablein-the-system. Further, if the formula "This formula is unprovablein- the-system" is unprovable-in-the-system, then it is true that that formula is unprovable-in-the-system, that is, "This formula is unprovable-in-the-system" is true. Goedel's theorem must apply to cybernetical machines, because it is of the essence of being a machine, that it should be a concrete instantiation of a formal system. It follows that given any machine which is consistent and capable of doing simple arithmetic, there is a formula which it is incapable of producing as being true---i.e., the formula is unprovable-in-the-system-but which we can see to be true. It follows that no machine can be a complete or adequate model of the mind, that minds are essentially different from machines.