Path: utzoo!utgpu!news-server.csri.toronto.edu!bonnie.concordia.ca!thunder.mcrcim.mcgill.edu!snorkelwacker.mit.edu!mit-eddie!media-lab!minsky From: minsky@media-lab.MEDIA.MIT.EDU (VA) Newsgroups: comp.ai.philosophy Subject: Re: Minds, machines, and Godel Message-ID: <4914@media-lab.MEDIA.MIT.EDU> Date: 17 Jan 91 18:55:42 GMT References: <91Jan16.135532edt.1132@neuron.ai.toronto.edu> <1991Jan17.040803.8205@bronze.ucs.indiana.edu> <1991Jan17.170401.8536@bronze.ucs.indiana.edu> Reply-To: minsky@media-lab.media.mit.edu (Marvin Minsky) Organization: MIT Media Lab, Cambridge MA Lines: 23 In article <1991Jan17.170401.8536@bronze.ucs.indiana.edu> chalmers@bronze.ucs.indiana.edu (David Chalmers) writes: >In article jmc@DEC-Lite.Stanford.EDU (John McCarthy) writes: >> One mistaken intuition behind the widespread belief that >>a program can't do mathematics on a human level is the assumption >>that a machine must necessarily do mathematics within a single >>axiomatic system with a predefined interpretation. >... Of course humans >are inconsistent in practice, but I'm not sure that I'd want a refutation >of Lucas/Penrose to be based solely on this fact. At the very least you'd >have to hold that's it's a *deep* and important fact about human competence >(as opposed to some kind of noise in the system, a performance/competence >distinction). Important, but scarcely deep. Can't you paraphrase Godel as showing that any system that is consistent is also limited in expressive ability. Humans have no problem in making deductions about 'sets than do not have themselves as members', and so on. The observation that humans are inconsistent seems obvious, shallow, and categorically incontrovertible. When you say, "at the very least", I can't fugure out the intended effect of that clause.