dmcanzi@watdcsu.UUCP (David Canzi) (11/05/85)
In article <2004@umcp-cs.UUCP> mangoe@umcp-cs.UUCP (Charley Wingate) writes: >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. > >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. Charley's brief description above is less than clear. Maybe I can make the matter clearer: a statement, S, was constructed which, in effect, stated that "S cannot be recognized as true by the mind of God" (but didn't actually contain such a direct self-reference). If God could recognize S as true, then this would contradict S, thus S would be false and God would be mistaken. Thus it follows that God *can't* recognize S as true, thus S is true. And God doesn't know it. Says Charley: >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!). And what's wrong with semantics? If we don't understand the semantic content of what we're saying, we literally don't know what we're talking about. Let's suppose, as Charley suggests, that God's mind is divided into two parts: one, the "false half", recognizes false statements as true; the other, the "true half", recognizes true statements as true. What can it possibly mean to say that this "bicameral mind of God" recognizes a statement as true? One meaning that Charley uses is for some part of God's mind to recognize that statement as true. The other possible meaning, which Charley also uses, is for God's mind as a whole to recognize this statement as true. This latter meaning is a function that God's mind *must* be able to perform, or else we would have to wonder *which* part of God's mind wrote which parts of the Bible. My argument used the expression "recognize as true" consistently, meaning the same thing by it in all of its occurrences in the argument. Charley changed the meaning of one occurrence of "recognize as true" to evade the contradiction. By doing so, he attempts to invalidate my argument by changing its meaning. This doesn't work. In order to invalidate somebody's argument, you have to invalidate *what* *they* *meant*, not some clever re-interpretation of their words. -- David Canzi "Permission is not freedom."
mangoe@umcp-cs.UUCP (Charley Wingate) (11/07/85)
>>>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. >Charley's brief description above is less than clear. Due largely to an important typo. >[A] statement, S, was constructed which, in effect, >stated that "S cannot be recognized as true by the mind of God" (but >didn't actually contain such a direct self-reference). If God could >recognize S as true, then this would contradict S, thus S would be >false and God would be mistaken. Thus it follows that God *can't* >recognize S as true, thus S is true. And God doesn't know it. One can therefore also extrapolate that, not knowing anything false, He cannot be aware of this argument either; if He knew this argument, and since he (presumably) could not recognize the statement as true, he would then be in a position to recognize that the statement WAS true. ["paradox alert" light begins flashing at this point] Now, wait a minute! Let's take God out of there a minute, and put in Charley Wingate. *I* do know this argument. *I* recognize this statement (correctly) as paradoxical. I can't recognize it as true, because then the statement itself indicates it to be false. But if I can't recognize it as true, then the argument tells me that the statement is true, and therefore I recognize it as being true! Paradox! So I recognize it as being paradoxical. NOW what happens? The statement then becomes true, and therefore the argument tells me that the statement is true, and therefore there is a contradiction, and therefore a paradox. See? It really IS paradoxical. So much for that argument. Obviously one can put God back in there and achieve the same results. P.S.: It doesn't help to argue that I am not a formal system. No one ever said that God was one, after all. P.P.S.: We can go ahead and throw my original argument out the window. Charley Wingate