mangoe@umcp-cs.UUCP (Charley Wingate) (10/28/85)
In article <1790@watdcsu.UUCP> dmcanzi@watdcsu.UUCP (David Canzi) writes: >The following constitutes a proof that for some random arbitrary person, >"Tom", there is at least one true statement that Tom doesn't know -- >in fact *can't* know. I've borrowed it from an article posted by >lambert@boring. I've removed the argument to the end, and heavily edited it to shorten it. The gist of it is that one sets up a statement about whether a function of that statement can be recognized as true by a person X. The statement is constructed so that supposedly the person can erroneously recognize it as true, or if it is true, he can recognize it as true (since to do so would contradict the statement. David Canzi then makes the following claim: >Now, this proof that there is at least one true statement that Tom doesn't >know still works if we substitute the word "God" for "Tom". So much for >omniscience. Unfortunately, this argument is totally bogus when applied to God, possibly for multiple reasons. Let us postulate that God has some sort of facility which erroneously recognizes false statements as true (a function which has some obvious utility). We therefore have God's mind recognizing the statement as true. Another part, presumably dealing only with true statements, realizes that the statement is in fact false (since He is recognizing it somewhere else). So there is no paradox, and God is still omnicient (and without resort to semantics!). What's the hole? There's an implicit assumption that minds are like formal systems, and can't maintain contradictions in any useful way. I think this assumption is unwarranted; it's not even clear that it's true for humans, much less gods. So I don't believe this argument at all. Charley Wingate umcp-cs!mangoe ------------------------------------------------------------- The original argument: >> Consider texts (some of which represent statements, such as: "Two times two >> equals four" and "`Two times two equals four' is a true statement about >> natural numbers", and some of which do not, like "Who? Me?" and "Don't >> `Aw, mom' me".). Some of these texts contain *internal* quoted texts. If >> T is a text, then let Q(T), or, in words, T *quoted*, stand for another >> text, consisting of T put between the quotes "`" and "'". >> Let SQ(T), or T *self*quoted, mean: Q(T) followed by T. >> Now consider the text S = >> "`, selfquoted, is not recognizable as true by the mind of Tom', >> selfquoted, is not recognizable as true by the mind of Tom". >> S is a statement, and states that some text T, selfquoted, is not >> recognizable as true by the mind of Tom. >> So can Tom (or his mind) recognize SQ(T) as true, and is SQ(T) true in the >> first place? If Tom can recognize SQ(T) as true, then S is apparently >> false. But note that T is the text >> ", selfquoted, is not recognizable as true by the mind of Tom", >> so SQ(T) = S. So Tom would have recognized a false statement as true. If >> we collectively assume that Tom would never do such a thing, then all of us >> non-Toms can now recognize S as true, something Tom can not.
rlr@pyuxd.UUCP (Rich Rosen) (11/04/85)
>>The following constitutes a proof that for some random arbitrary person, >>"Tom", there is at least one true statement that Tom doesn't know -- >>in fact *can't* know. I've borrowed it from an article posted by >>lambert@boring. > I've removed the argument to the end, and heavily edited it to shorten it. > The gist of it is that one sets up a statement about whether a function of > that statement can be recognized as true by a person X. The statement is > constructed so that supposedly the person can erroneously recognize it as > true, or if it is true, he can recognize it as true (since to do so would > contradict the statement. David Canzi then makes the following claim: > >>Now, this proof that there is at least one true statement that Tom doesn't >>know still works if we substitute the word "God" for "Tom". So much for >>omniscience. > > Unfortunately, this argument is totally bogus when applied to God, possibly > for multiple reasons. Let us postulate that God has some sort of facility > which erroneously recognizes false statements as true (a function which has > some obvious utility). We therefore have God's mind recognizing the > statement as true. [WINGATE] 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. The same thing applies to god. But note that this "some sort of facility" exists in a sense, and is nothing unique to god. After all, you just figured out that you couldn't give a correct answer to that question put to you. Didn't you? -- "to be nobody but yourself in a world which is doing its best night and day to make you like everybody else means to fight the hardest battle any human being can fight and never stop fighting." - e. e. cummings Rich Rosen ihnp4!pyuxd!rlr
js2j@mhuxt.UUCP (sonntag) (11/04/85)
> >Now, this proof that there is at least one true statement that Tom doesn't > >know still works if we substitute the word "God" for "Tom". So much for > >omniscience. > > Unfortunately, this argument is totally bogus when applied to God, possibly > for multiple reasons. Let us postulate that God has some sort of facility > which erroneously recognizes false statements as true (a function which has > some obvious utility). We therefore have God's mind recognizing the > statement as true. Another part, presumably dealing only with true > statements, realizes that the statement is in fact false (since He is > recognizing it somewhere else). So there is no paradox, and God is still > omnicient (and without resort to semantics!). There never *was* a paradox, Charley. Just as Goedel showed that any *complete* formal system must be inconsistant, you've showed that an omnoscient being is no paradox as long as it is inconsistant. Inconsistancy is considered a bad feature of formal systems. I guess the specs for gods are more relaxed. > > Charley Wingate umcp-cs!mangoe -- Jeff Sonntag ihnp4!mhuxt!js2j "What would Captain Kirk say?"
mangoe@umcp-cs.UUCP (Charley Wingate) (11/06/85)
In article <1237@mhuxt.UUCP> js2j@mhuxt.UUCP (sonntag) writes: [In reference to an argument against omniscience] >> Unfortunately, this argument is totally bogus when applied to God, possibly >> for multiple reasons. Let us postulate that God has some sort of facility >> which erroneously recognizes false statements as true (a function which has >> some obvious utility). We therefore have God's mind recognizing the >> statement as true. Another part, presumably dealing only with true >> statements, realizes that the statement is in fact false (since He is >> recognizing it somewhere else). So there is no paradox, and God is still >> omnicient (and without resort to semantics!). > There never *was* a paradox, Charley. Just as Goedel showed that >any *complete* formal system must be inconsistant, you've showed that >an omnoscient being is no paradox as long as it is inconsistant. I'll readily admit that paradox was not the right word. I should have said that there's no impediment to God's correctly knowing that the statement is false. > Inconsistancy is considered a bad feature of formal systems. I guess >the specs for gods are more relaxed. Well, of course they are. The thing doesn't represent a *proof*, after all, without the assumption that the Mind of God constitutes a formal system. If I assumed omniscience instead, then this "proof" forces the conclusion that The Mind is *not* a formal system. I have yet to see a good justification for the statement that "God's Mind is a formal system," and certainly no proof of it. So I don't accept this "proof". Charley Wingate
mangoe@umcp-cs.UUCP (Charley Wingate) (11/06/85)
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. (Of course, it's not really a proper 1st order statement either. But that's just the point.) That's the problem with the first "proof"; it only works if God's mind is a formal system. >The same thing applies to god. But note that this "some sort of facility" >exists in a sense, and is nothing unique to god. After all, you just >figured out that you couldn't give a correct answer to that question put to >you. Didn't you? No, 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
ins_apmj@jhunix.UUCP (Patrick M Juola) (11/07/85)
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
mangoe@umcp-cs.UUCP (Charley Wingate) (11/07/85)
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
franka@mmintl.UUCP (Frank Adams) (11/08/85)
In article <2030@pyuxd.UUCP> rlr@pyuxd.UUCP (Rich Rosen) writes: >I think this just shows to go you that you don't understand the proof. [That there is a true statement which God cannot recognize as true.] >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. >The same thing applies to god. But note that this "some sort of facility" >exists in a sense, and is nothing unique to god. After all, you just >figured out that you couldn't give a correct answer to that question put to >you. Didn't you? This kind of sentence, including that used in the orginal "proof", are self- referential. If self-referential statements are allowed, you can prove anything and everything. In general, self-referential sentences cannot be regarded as statements (i.e., as things which are true or false). So the entire "proof" collapses. Frank Adams ihpn4!philabs!pwa-b!mmintl!franka Multimate International 52 Oakland Ave North E. Hartford, CT 06108