Torkel Franzen on truth
in [Logic]
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From: Nam D. Nguyen on 27 Dec 2007 11:33 tchow(a)lsa.umich.edu wrote: > In article <G4Ecj.18314$DP1.3340(a)pd7urf2no>, > Nam D. Nguyen <namducnguyen(a)shaw.ca> wrote: >> What I've asserted from the beginning and through out is *religious belief* is >> supposed to be absolute and is not the relative kind of beliefs we employ in >> mathematical reasoning. That's all I've meant to say! > > Perhaps that's all you *meant* to say, but what you *actually* said was: > > Unfortunately mathematical reasoning isn't religion where "beliefs" > would be much relevant. > > in response to Daryl McCullough's comment: > > So, for example, a proof in PA + the negation of Goldbach's conjecture > would not be very convincing, because we have no reason to believe that > the negation of Goldbach's conjecture is true. > > The "belief" in question, understood as a relative belief in a relative truth > relative to blah blah blah, is entirely relevant. At this point in time, when there's no proof, the belief that the negation of Goldbach's conjecture is not true is of the nature of religion belief, which is quite irrelevant to reasoning: reasoning requires proof not belief. Wouldn't you think so?
From: Nam D. Nguyen on 27 Dec 2007 12:53 Nam D. Nguyen wrote: > tchow(a)lsa.umich.edu wrote: >> In article <G4Ecj.18314$DP1.3340(a)pd7urf2no>, >> Nam D. Nguyen <namducnguyen(a)shaw.ca> wrote: >>> What I've asserted from the beginning and through out is *religious >>> belief* is >>> supposed to be absolute and is not the relative kind of beliefs we >>> employ in >>> mathematical reasoning. That's all I've meant to say! >> >> Perhaps that's all you *meant* to say, but what you *actually* said was: >> >> Unfortunately mathematical reasoning isn't religion where "beliefs" >> would be much relevant. >> in response to Daryl McCullough's comment: >> >> So, for example, a proof in PA + the negation of Goldbach's conjecture >> would not be very convincing, because we have no reason to believe that >> the negation of Goldbach's conjecture is true. >> >> The "belief" in question, understood as a relative belief in a >> relative truth >> relative to blah blah blah, is entirely relevant. > > At this point in time, when there's no proof, the belief that the > negation of Goldbach's conjecture is not true is of the nature of > religion belief, which is quite irrelevant to reasoning: reasoning > requires proof not belief. Wouldn't you think so? In fact, DMC's whole statement above is a religion statement, dressed in formalism! A proof is supposed to be the only reason for belief. One could disprove a proof by proving the negation and proving the theory is consistent. But one should *not* dismiss a proof simply because one already has the opposite belief, *without* a proof!
From: tchow on 27 Dec 2007 16:00 In article <qERcj.21015$DP1.9137(a)pd7urf2no>, Nam D. Nguyen <namducnguyen(a)shaw.ca> wrote: >Nam D. Nguyen wrote: >> tchow(a)lsa.umich.edu wrote: >>> in response to Daryl McCullough's comment: >>> >>> So, for example, a proof in PA + the negation of Goldbach's conjecture >>> would not be very convincing, because we have no reason to believe that >>> the negation of Goldbach's conjecture is true. [...] >> At this point in time, when there's no proof, the belief that the >> negation of Goldbach's conjecture is not true is of the nature of >> religion belief, which is quite irrelevant to reasoning: reasoning > > requires proof not belief. Wouldn't you think so? > >In fact, DMC's whole statement above is a religion statement, dressed in >formalism! A proof is supposed to be the only reason for belief. >One could disprove a proof by proving the negation and proving the >theory is consistent. But one should *not* dismiss a proof simply because >one already has the opposite belief, *without* a proof! Your remarks here are even more absurd than your remark that belief is not relevant. Daryl McCullough is not asserting that the negation of Goldbach's conjecture is not true He asserts only that we have no reason to believe that the negation of Goldbach's conjecture is true That is, he is withholding belief in the negation of Goldbach's conjecture, because there is no proof of that statement. In other words, he is behaving in exactly the way that you say he should. So what are you complaining about? Obviously you're just not reading what he wrote very carefully. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
From: Nam D. Nguyen on 27 Dec 2007 20:22 tchow(a)lsa.umich.edu wrote: > In article <qERcj.21015$DP1.9137(a)pd7urf2no>, > Nam D. Nguyen <namducnguyen(a)shaw.ca> wrote: >> Nam D. Nguyen wrote: >>> tchow(a)lsa.umich.edu wrote: >>>> in response to Daryl McCullough's comment: >>>> >>>> So, for example, a proof in PA + the negation of Goldbach's conjecture >>>> would not be very convincing, because we have no reason to believe that >>>> the negation of Goldbach's conjecture is true. > [...] >>> At this point in time, when there's no proof, the belief that the >>> negation of Goldbach's conjecture is not true is of the nature of >>> religion belief, which is quite irrelevant to reasoning: reasoning >>> requires proof not belief. Wouldn't you think so? >> In fact, DMC's whole statement above is a religion statement, dressed in >> formalism! A proof is supposed to be the only reason for belief. >> One could disprove a proof by proving the negation and proving the >> theory is consistent. But one should *not* dismiss a proof simply because >> one already has the opposite belief, *without* a proof! > > Your remarks here are even more absurd than your remark that belief is not > relevant. Daryl McCullough is not asserting that > > the negation of Goldbach's conjecture is not true > > He asserts only that > > we have no reason to believe that the negation of Goldbach's conjecture > is true I'm giving you one clue: had he only said exactly no more than that sentence, then what you've said would have been true; and in fact I would have not involved in this conversation at all! He did use the words "_for example_", "_because_" didn't he? The point being is he was making an (meta level) *assertion*/*argument* with a hypothesis that would lead to a conclusion, however informal his whole statement may have sounded. And since his " we have no reason to believe... is true" is a *supporting hypothesis*, one would have no choice but interpreting it as the assertion "the negation of Goldbach's conjecture is not true". > > That is, he is withholding belief in the negation of Goldbach's conjecture, > because there is no proof of that statement. In other words, he is behaving > in exactly the way that you say he should. So what are you complaining about? One of the things I'd complain about his whole statement is the absurdity that *any* proof of ~GC in PA would be not convincing, without seeing that proof! As I mentioned, proof is very fundamental to what we should or should not believe. So how could one possibly say that as far as reasoning is concerned? And you're defending this "absurdity"? (It'd be quite a surprise to me!) > Obviously you're just not reading what he wrote very carefully. I think it's you, not I, who didn't read what he asserted or what has been being argued carefully.
From: tchow on 27 Dec 2007 23:07
In article <BdYcj.22608$DP1.12527(a)pd7urf2no>, Nam D. Nguyen <namducnguyen(a)shaw.ca> wrote: >And since his " we have no reason to believe... >is true" is a *supporting hypothesis*, one would have no choice but >interpreting it as the assertion "the negation of Goldbach's conjecture >is not true". Well, if you refuse to take what he said at face value, but insist on twisting his words into some totally different statement, then there's no arguing with you. I'm satisfied that you admit that you were totally wrong, *provided* we assume that Daryl meant what he said, and that you are correct only if we forcibly misinterpret Daryl as saying something completely different from what he actually said. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences |