Path: utzoo!utgpu!news-server.csri.toronto.edu!bonnie.concordia.ca!thunder.mcrcim.mcgill.edu!snorkelwacker.mit.edu!apple!julius.cs.uiuc.edu!zaphod.mps.ohio-state.edu!sol.ctr.columbia.edu!bronze!chalmers From: chalmers@bronze.ucs.indiana.edu (David Chalmers) Newsgroups: comp.ai.philosophy Subject: Re: Minds, machines, and Godel Message-ID: <1991Jan18.001524.23027@bronze.ucs.indiana.edu> Date: 18 Jan 91 00:15:24 GMT References: <1991Jan16.035058.7465@bronze.ucs.indiana.edu> Organization: Indiana University, Bloomington Lines: 25 In article mikeb@wdl31.wdl.loral.com (Michael H Bender) writes: >I am not an expert in these areas, but I do have a question: isn't the word >"prove" being used in two different ways? I.e., when you say: > "there would be a mathematical sentence G (the "Godel sentence" > of T) that I could not prove" >you are referring to proof in the mathematical/formal context. However, >when you say: > "But in fact I can see that G must be true. Therefore I cannot be T" >you are referring to a completely different concept -- what we believe >or we "know" about the world. I probably shouldn't have used the word "prove" in the first sentence quoted, due to the connotations of derivation in a particular formal system. All that is required is mathematical judgment. I assume that mathematicians are able to judge certain statements to be "certainly true", irrespective of how they do this (formal proof is a common method, but not the only method: e.g. it doesn't apply to axioms, and applies in a subtly different way to Godel sentences). If mathematicians are computationally simulable, then we can make a TM perform this process, and the Lucas argument applies. -- Dave Chalmers (dave@cogsci.indiana.edu) Center for Research on Concepts and Cognition, Indiana University. "It is not the least charm of a theory that it is refutable."