Minds, machines and Godel

Philosophy 36 (April-July):112-127 (1961)
Abstract
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
Keywords Machine  Mechanism  Minds  Philosophical Anthropology  Goedel
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DOI 10.1017/S0031819100057983
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Minds, Brains and Programs.John R. Searle - 1980 - Behavioral and Brain Sciences 3 (3):417-57.
Intrinsic Intentionality.John Searle - 1980 - Behavioral and Brain Sciences 3 (3):450.
The ‘Causal Power’ of Machines.Zenon W. Pylyshyn - 1980 - Behavioral and Brain Sciences 3 (3):442.

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