Lucas, J.R.
(1961)
*Minds, Machines and Goedel.*
[Journal (Paginated)]

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## 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.

Item Type: | Journal (Paginated) |
---|---|

Keywords: | goedel's theorem, computation, computability, symbolsystems, computationalism, cognitivism, machines, mind, provability, mental models, Penrose, Searle |

Subjects: | Psychology > Cognitive Psychology Computer Science > Artificial Intelligence Philosophy > Logic Philosophy > Philosophy of Mind Philosophy > Philosophy of Science |

ID Code: | 356 |

Deposited By: | Harnad, Stevan |

Deposited On: | 24 Jul 1998 |

Last Modified: | 11 Mar 2011 08:53 |

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