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!decvax!ucbvax!ucdavis!lll-crg!gymble!umcp-cs!aplcen!jhunix!ins_apmj From: ins_apmj@jhunix.UUCP (Patrick M Juola) Newsgroups: net.philosophy Subject: Re: Yet Another Spurious Proof Message-ID: <1116@jhunix.UUCP> Date: Thu, 7-Nov-85 00:16:37 EST Article-I.D.: jhunix.1116 Posted: Thu Nov 7 00:16:37 1985 Date-Received: Mon, 11-Nov-85 23:14:33 EST References: <2004@umcp-cs.UUCP> <2030@pyuxd.UUCP> <2118@umcp-cs.UUCP> Reply-To: ins_apmj@jhunix.ARPA (Patrick M Juola) Distribution: na Organization: Johns Hopkins Univ. Computing Ctr. Lines: 56 Summary: Let's not play semantics games here, folks In article <2118@umcp-cs.UUCP> mangoe@umcp-cs.UUCP (Charley Wingate) writes: >In article <2030@pyuxd.UUCP> rlr@pyuxd.UUCP (Rich Rosen) writes: > >[ A proof was proffered which claimed that there must be at least one true > statement which cannot be recognized as true by God. My contention was > that the proof was flawed because it assumed that God was like a formal > system in a particular way; I then showed how the statement could be > recognized as true (but erroneously) in one facility, and thus correctly > recognized to be false in the main part. Rich's reply: ] > >>I think this just shows to go you that you don't understand the proof. >>A simplification of such an example is the statement "You will say that >>this statement is false." If I ask you if this is true, what will your >>answer be? There can be no answer to this that YOU can give that would be >>correct. > >Au contraire. In analogy to my contradiction to the first problem, I could >claim it is false, and then (quite correctly) claim it to be true. I could >also claim it to be not true because it attempts a paradox. This >is a true statement, and it falsifies the orginal statement. > > I stepped through the formalist crack and made a meta-statement about >the orginal statement. This new statement was true, but it did not say that >the orginal statement was false. Or I could simply make two statements with >the knowledge that one was false. Either way, since I am not a formal >system (as far as I know), the claim is bogus. > >Charley Wingate All right, Charley, no more mister nice guy :-) : You're simply taking advantage of the informality of the original phrasing; to wit, "You will *SAY*, etc." Let's try a bit more formal version : The mind of Charley Wingate will not be able to recognize this as a true statement. In other words, if you decide that the statement is false (by whatever convoluted reasoning) and if you assume that a statement cannot be both true and false simultaneously, you have reached a paradox, since you cannot recognize it as true if you have decided it is false, which means it is a true statement (obvious to everyone except Charley). What you were doing was essentially the same thing Godel did -- reasoning *about* the system, rather than within it. However, if there is a system of reasoning of which God's thought is a proper subset, then God is not omnicient. QED Oh, and by the way, if God is omnicient, then he would *have* to know whether or not any given statement is true or false and all of the implications thereof. Therefore, you can't sidestep around this by making two sentences of which one is true and one false, but God doesn't know which one, nor by making a statement that *implies* the truth or falsity of the Godel sentence without actually deciding directly. Death to Rhetoric! Long Live Pred. Cal! Patrick M. Juola Johns Hopkins Univ. Dept. of Maths