dmcanzi@watdcsu.UUCP (David Canzi) (10/25/85)
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. (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. -- David Canzi "Permission is not freedom."
pmd@cbsck.UUCP (Paul M. Dubuc) (10/29/85)
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
dmcanzi@watdcsu.UUCP (David Canzi) (11/02/85)
In article <1436@cbsck.UUCP> pmd@cbsck.UUCP (Paul M. Dubuc) 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. ...the proof is too long, so I'm leaving it out... >>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. [David Canzi] > >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. Actually, I *have* met people who believe logic doesn't apply to God. One of my high school teachers, in a discussion of the existence of God (he was pro, I was con), responded to a logical point I made by saying "God is not bounded by puny human logic." One of my friends was a fan of an ancient Greek philosopher, Plotinus. Plotinus began his magnum opus with the statement "The One [ie. God] is, and yet, is not." Last year somebody said, in an article in net.religion, that if God wanted 2+2 to equal 5, it would. I can think of a logically consistent way that an omnipotent being *could* manage this stunt, but I'm pretty sure it's not what the fellow had in mind. > 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. "God must obey the law of non-contradiction." I have a different way of looking at the working of the laws of logic. Let me illustrate by rephrasing that quoted statement: "Our descriptions of God must obey the law of non-contradiction." I think of logic as not constraining God or reality in any way, but rather constraining the ways in which we can describe reality. In a way, I'm sneakily agreeing with my old high-school geography teacher that "God is not bounded by puny human logic", without agreeing with him that a logical contradiction can be true when it happens to be about God. (Hmmm. I posted that article as a lark. Strange to see me get this serious about it.) I probably haven't succeeded in understanding your friend's proof that God can't identify himself, but I'll take a stab at it anyway. It seems to rest on an assumption that things can't be identified in terms of each other. If you're sitting in front of your stereo system, how do you identify the left speaker? It's the one to the left of the right speaker. How do you identify the right speaker? It's the one to the right of the left speaker, of course. If there are only two speakers in the room, we can now identify them relative to each other. (I hope this paragraph is not too disgustingly naive by the standards of net.philosophy people.) -- David Canzi "Permission is not freedom."
mangoe@umcp-cs.UUCP (Charley Wingate) (11/21/85)
In article <27500154@ISM780B.UUCP> jim@ISM780B.UUCP writes: [BTW, jim, your system isn't handling references properly] >>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. >The problem is analogous to asking whether God can create a stone so heavy >that he cannot lift it, yet I could have readily predicted that you would >reject any argument which limits the capabilities of God, a word the meaning >of which I am unable to determine other than that some people appear to >believe that to it refers to an actual entity without limits, regardless of >the lack of evidence of such an entity or the lack of credibility of a >notion such as omniscience. Actually, I will argue that the answer is YES. The reason is that omnipotence implies the ability to change oneself so as to cease to be omnipotent. So the arguments aren't really related. The rest of jim's article is a reply to an obsolete argument of mine, so I will not reply to it. Charley Wingate