Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site jhunix.UUCP Path: utzoo!linus!philabs!cmcl2!seismo!umcp-cs!aplcen!jhunix!ins_apmj From: ins_apmj@jhunix.UUCP (Patrick M Juola) Newsgroups: net.philosophy Subject: Re: Sc--nce Attack (self-awareness) Message-ID: <1074@jhunix.UUCP> Date: Thu, 31-Oct-85 00:11:31 EST Article-I.D.: jhunix.1074 Posted: Thu Oct 31 00:11:31 1985 Date-Received: Sun, 3-Nov-85 10:34:46 EST References: <45200016@hpfcms.UUCP> <1605@pyuxd.UUCP> Reply-To: ins_apmj@jhunix.ARPA (Patrick M Juola) Organization: Johns Hopkins Univ. Computing Ctr. Lines: 53 In article <10642@ucbvax.ARPA> tedrick@ucbernie.UUCP (Tom Tedrick) writes: >>Ie. maybe a Turing machine can simulate the brain, but ... > >OK, here is a question. > >My understanding is that Godel's incompleteness theorems prove >(assuming the consistency of Arithmetic) that no Turing machine >can possibly simulate the human mind. > >This is because for any particular Turing machine there are certain >statements that the human mind can recognize as true (again with >the consistency assumption), that the machine cannot recognize >as true. > >Does anyone dispute this? > > -Tom > tedrick@ucbernie.ARPA Gack!!! Tom, leave the mathematics to the mathematicians! :-) Your second paragraph is true but does not imply the first. Godel's Incompleteness Theorem states that for any formal system powerful enough to contain arith- metic, either it is incomplete OR inconsistent. So, first of all, there may be a Turing machine that will (correctly) recognize any true statement; in fact, I will design one right now -- writeln ('this is a true statement.') (send royalty checks to ins_apmj@jhunix :-) The problem, of course, is that this machine will say that ANY statement is true, but Godel's theorem doesn't prevent this. Secondly, human minds (assuming they are powerful enough to do arithmetic, which is a big assumption in a few cases :-) are equally subject to Godel's theorem. In other words, if there is a statement that the Turing machine will not recognize as true but a human can, there is also one that a T. machine WILL recognize and a human cannot. Case in point : "Tom cannot consistently assert this statement." I think you will have no trouble recognizing this as a true statement, but to state that this statement is true puts you in the same position as saying "Lawyers never tell the truth; I am a lawyer." I believe the philospher Lucas espoused this argument, and Doug Hofstadter trashed it quite thouroughly in _Godel, Escher, Bach_, which I recommend if you can get through it. Pat Juola JHU Math Dept. -- Note : I am schizophrenic, and this was written by my other personality; I assume no responsibility for its content.