Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site cbsck.UUCP Path: utzoo!linus!decvax!bellcore!petrus!sabre!zeta!epsilon!gamma!ulysses!mhuxr!mhuxn!ihnp4!cbosgd!cbsck!pmd From: pmd@cbsck.UUCP (Paul M. Dubuc) Newsgroups: net.philosophy Subject: Re: God knows. Message-ID: <1436@cbsck.UUCP> Date: Mon, 28-Oct-85 16:16:57 EST Article-I.D.: cbsck.1436 Posted: Mon Oct 28 16:16:57 1985 Date-Received: Thu, 31-Oct-85 23:42:03 EST References: <1790@watdcsu.UUCP> Organization: AT&T Bell Laboratories, Columbus Lines: 95 From David Canzi: >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. (rn exhibited unpleasantly surprising behaviour when >I tried to follow up that article.) Feel free to skip over it to my >comments at the end, on your first reading. > >> 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 "'". So if T is >> >> "Two times two equals for", >> >> Q(T) is >> >> "`Two times two equals for'". >> >> Let SQ(T), or T *self*quoted, mean: Q(T) followed by T. >> >> So if T is >> >> " contains no digits" >> >> then T, selfquoted, is >> >> "` contains no digits' contains no digits" >> >> (which is a true statement). >> >> 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. > >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. While the proof is rather convoluted, if I follow it right it seems only to set up a logical contradiction. It posits the same sort of dilemma for God as the question, "Can God make a rock so big that he can't lift it?" thus apparently disposing with omnipotence in the same manner as the above proof claims to dispose of omniscience. But who ever defined omniscience or omnipotence to include things that are *actually* impossible to know or do (as in direct contradiction)? Only those who wish to "prove" that God can't have these qualities. The fact that God must obey the law of non-contradiction does not take away from the qualities of omniscience or omnipotence attributed to him. The definition of those qualities never included things that are hypothetically outside non-contradictory boundaries. On another level, this proof seems to parallel one once offered to me by a friend of mine. That was that is is not possible for God to identify himself (i.e. be consistent with the law of identity) since to do so requires using a reference that makes God relative to something else. This seems to be a contradiction to his omniscience, since the terms by which he is identified cannot also have their identity in him. (Think of the descriptive terms by which we identify ourselves, for example. ("Me", "myself", and "I" are not descriptive, just redundant)). Maybe I am not reconstructing this very well. It's not clear in my memory. If someone recognizes it and has a better construction, maybe they could explain it. I'm not sure if it fails by the same criterion as the above or not. The God of the Bible is called by many names, but the one most hallowed is that revealed to Moses when he is commissioned to go to Egypt (Exodus 3:14). When Moses asks, "Who shall I say sent me?", God, in effect, responds, "Just tell them 'I AM' sent you". I thought this particular name was curious in light of the proposed contradiction. Here God seems to be making a deliberate attempt at identifying himself without reference to anything in space or time. I'm not sure if it resolves the contradiction (if there is one), but it does make it seem that God is aware of the problem. Maybe he's working on it? :-) -- Paul Dubuc cbsck!pmd