Minds, Machines, and Gödel: A Retrospect
J. R. LUCAS
I must start with an apologia. My original paper, 'Minds, Machines and Gödel', was written in the wake of Turing's 1950 paper in Mind, and was intended to show that minds were not Turing machines. Why, then, didn't I couch the argument in terms of Turing's theorem, which is easyish to prove and applies directly to Turing machines, instead of Gödel's theorem, which is horrendously difficult to prove, and doesn't so naturally or obviously apply to machines? The reason was that Gödel's theorem gave me something more: it raises questions of truth which evidently bear on the nature of mind, whereas Turing's theorem does not; it shows not only that the Gödelian well-formed formula is unprovable-in-the-system, but that it is true. It shows something about reasoning, that it is not completely rule-bound, so that we, who are rational, can transcend the rules of any particular logistic system, and construe the Gödelian well-formed formula not just as a string of symbols but as a proposition which is true. Turing's theorem might well be applied to a computer which someone claimed to represent a human mind, but it is not so obvious that what the computer could not do, the mind could. But it is very obvious that we have a concept of truth. Even if it is not the summum bonum, it is a bonum, and one it is characteristic of minds to value. A representation of the human mind which could take no account of truth would be inherently implausible. Turing's theorem, though making the same negative point as Gödel's theorem, that some things cannot be done by even idealized computers, does not make the further positive point that we, inasmuch as we are rational agents, can do that very thing that the computer cannot. I have,
Questia, a part of Gale, Cengage Learning. www.questia.com
Publication information: Book title: The Legacy of Alan Turing. Volume: 1. Contributors: P. J. R. Millican - Author, A. F. Clark - Editor, Alan Mathison Turing - Author. Publisher: Clarendon Press. Place of publication: Oxford. Publication year: 1996. Page number: 103.
This material is protected by copyright and, with the exception of fair use, may not be further copied, distributed or transmitted in any form or by any means.