Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site umcp-cs.UUCP Path: utzoo!decvax!ucbvax!ucdavis!lll-crg!gymble!umcp-cs!mangoe From: mangoe@umcp-cs.UUCP (Charley Wingate) Newsgroups: net.philosophy Subject: Re: Yet Another Spurious Proof Message-ID: <2143@umcp-cs.UUCP> Date: Thu, 7-Nov-85 10:07:51 EST Article-I.D.: umcp-cs.2143 Posted: Thu Nov 7 10:07:51 1985 Date-Received: Tue, 12-Nov-85 00:35:10 EST References: <1116@jhunix.UUCP> Distribution: na Organization: U of Maryland, Computer Science Dept., College Park, MD Lines: 39 Summary: Still Spurious In article <1116@jhunix.UUCP> ins_apmj@jhunix.ARPA (Patrick M Juola) writes: >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). But then, I would know by your argument that it IS true: so I would recognize it to be true, and thus it's STILL paradoxical. Thanks to David Canzi, who kicked at my original argument once too often, for bringing this to my attention. Since I can evaluate the argument this way, either the argument is malformed, or the statement is in fact paradoxical. THis looks like a permanent problem with any logical argument which claims that a certain statement is unknowable by X but is true: the argument itself should be sufficient evidence that it is true, and there is knowable to be true, and is therefore false. It certainly relies on X not being in the formal system (as far as his/her reasoning is concerned), but the fact that such an argument can be made *indicates* that this is so. >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. Wouldn't he immediately fail to be omnicient anyway, not knowing the whole system? What this amounts to is an argument that God's mind is NOT a formal system. Charley Wingate