David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophy 36 (April-July):112-127 (1961)
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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John R. Searle (1980). Minds, Brains and Programs. Behavioral and Brain Sciences 3 (3):417-57.
Darren Abramson (2011). Philosophy of Mind Is (in Part) Philosophy of Computer Science. Minds and Machines 21 (2):203-219.
Samuel A. Alexander (2014). A Machine That Knows Its Own Code. Studia Logica 102 (3):567-576.
Amir Horowitz (2009). Turning the Zombie on its Head. Synthese 170 (1):191 - 210.
Gualtiero Piccinini & Sonya Bahar (2013). Neural Computation and the Computational Theory of Cognition. Cognitive Science 37 (3):453-488.
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