The University of Edinburgh -
Division of Informatics
Forrest Hill & 80 South Bridge

Research Paper #498

Title:On the Nature of Mathematical Judgement: Reply to Penrose
Date: 1990
Presented:Submitted to Artificial Intelligence Journal
Abstract:In his book, "The Emperor's New Mind," Roger Penrose argues that Goedel's incompleteness theorem implies limitations on the abilities of artificial intelligence, which are not shared by human intelligence. I analyse this argument, which is different from, but similar to, the well-known, Lucas argument. This analysis reveals a systematic ambiguity over the central concept in the argument: the procedure for forming mathematical judgements. When this ambiguity is resolved the Penrose argument collapses. The Penrose argument metamorphoses into an exposure of the inadequacies of formal representations of methods of mathematical proof. This suggests that those of us building artificial reasoning systems should also build what I have called extended theorem provers that evolve and compare their methods of reasoning.

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