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#1




Mathematicians are in deep trouble for 2 reasons
The australian philosopher colin leslie dean points out Mathematicians are
in deep shit for 2 reasons 1) skolem discovered a paradox which makes set theory inconsistent of which freankel and most mathematicians at the time saw http://www.math.ucla.edu/~asl/bsl/0602/0602001.ps. Quote:
mathematicians just ignored it and used set theory for all sorts of proofs Now mathematicians are in deep shit for there is now so much invested in set theory that the skolem paradox threatens the very foundations of mathematics so some mathematician now try to argue away the paradox by saying it is not a contradiction but skolems paradox want go away it is at present unable to be disproved and modern maths is buried so much in shit for useing set theory they cant get out 2) mathematician have so much invested in godels incompleteness theorem much maths is reliant on it but at the time godel wrote his theorem he had no idea of what truth was as peter smith the Cambridge expert on Godel admitts Quote:
as peter smith kindly tellls us http://assets.cambridge.org/97805218...40_excerpt.pdf Quote:
and godels theorem is http://en.wikipedia.org/wiki/G%C3%B6...s_theorems#Fir... Quote:
but Gödel didn't rely on the notion of truth now because Gödel didn't rely on the notion of truth he cant tell us what true statements are thus his theorem is meaningless this puts mathematicians in deep shit because all the modern idea derived from godels theorem have no epistemological or mathematical worth for we dont know what true statement are without a notion of truth we dont know what makes those statements true thus the theorem is meaningless and modern mathematics is in deep shit for useing a meaningless theorem 
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#2




EXTENTION TO SKOLEMS PARADOX
1) skolem discovered a paradox which makes set theory inconsistent http://en.wikipedia.org/wiki/Skolem's_paradox THE PARADOX IS Quote:
http://www.math.ucla.edu/~asl/bsl/0602/0602001.ps. Quote:
http://www.math.ucla.edu/~asl/bsl/0602/0602001.ps Quote:
http://www.earlham.edu/~peters/cours...skol.htm#amb3] Quote:
mathematicians just ignored it and used set theory for all sorts of proofs Now mathematicians are in deep shit for there is now so much invested in set theory that the skolem paradox threatens the very foundations of mathematics so some mathematician now try to argue away the paradox by saying it is not a contradiction but skolems paradox want go away it is at present unable to be disproved and modern maths is buried so much in shit for useing set theory they cant get out so we have either the paradox means set theory ZFC is inconsistent or set theory is destroyed 
#3




I don't know the specfics of your articles above but I knew long ago from Morris Kline Mathematics The Loss of Certainty and other sources the socalled crises in mathematics. They are ignored as you say and not only that but progress in mathematics has accelerated in the last century  more was done in the last century than the previous century (Professor Steven Goldman Science in the Twentieth Century lecture series for The Teaching Company lectures 12 and 13. The concensus seems to be the problem will go away on its own with new developments and as a practical matter, the socalled crises in mathematics are not crises in science because scientific truth is not the same as mathematical truth.
I will save your post for reference the next time I get around that way on Set Theory and Godel. Mike Dubbeld 
#4




How can you say they're in deep shit, using Wikipedia as a reference for your post, and not include this tidbit from the same page?
Quote:
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If you're frightened of dying, then you're holding on. You'll see devils tearing your life away. If you've made your peace, then the devils are really angels, freeing you from the earth. Forsaken, VNV Nation "War is god's way of teaching Americans geography." Ambrose Bierce 
#5




Mathematicians are in deep trouble for 2 reasons
1) they are boring! 2) they need to get laid! but i hope they don't give up the good work, i have no doubt's they benifit my life in some way, so way to go Mathematicians, just explain again, what the fuck is algibra for, and how do you spell it again?
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History is a great teacher, but a very poor master. 
#6




Quote:
most mathematician at the time saw it as a contradiction paradox read suber skolem and von neumann etc same wiki article even they say it is a paradox most logivian only say it is not a paradox based on skolems attempted solution but even skolem said his solution destroyed set theorythats why many say his attempt is not accepted, 
#7




I did read the whole article.
Quote:
__________________
If you're frightened of dying, then you're holding on. You'll see devils tearing your life away. If you've made your peace, then the devils are really angels, freeing you from the earth. Forsaken, VNV Nation "War is god's way of teaching Americans geography." Ambrose Bierce 
#8




Quote:
it says also Quote:
they say it is not a contradiction but cannot resolve the contradiction Quote:
but could not resolve according to many Quote:
Last edited by nightdreamer; 05122008 at 04:50 AM. 
#9




There are a number of contradictions that result from the skolem paradox as pointed out by suber
Quote:

#10




I still don't see how mathematicians are in deep trouble because of this.. there are countless unsolvable problems in science, but that doesn't make it inaccurate, just incomplete.
__________________
If you're frightened of dying, then you're holding on. You'll see devils tearing your life away. If you've made your peace, then the devils are really angels, freeing you from the earth. Forsaken, VNV Nation "War is god's way of teaching Americans geography." Ambrose Bierce 
#11




It is a bit different though. Maths is (largely) a closed system of logic which doesn't rely on empirical evidence and must be selfconsistent. If an inconsistency (paradox) can be shown to exist in set theory (which is what we are talking about here) then it calls into question the whole notion.

#12




In the early part of the 20'th century (1929) Hilbert formulated 23 (famous) outstanding problems in mathematics and challenged mathematicians to solve them. One of them was attempting to show mathematics was a complete and consistent system on all accounts. Godel showed not even something as simple as arithmetic can be proven to be both complete and consistent. Thats an example of a problem in mathematics. Another example is that it was taken for granted for 2000 years that Euclidean geometry was the beallendall geometry but that was flushed down the tubes in the 19'th century leading to having to deal with just what is the ultimate set of axioms/selfevident truths that require no proofs? Then along came chaos.....
The bottom line is if you do not have certainty in mathematics? Where do you get certainty. In the universe NOTHING whatsoever is certain except to x number of decimal places as agreed on by population x at time t. The ONLY reality there is for anything whatsoever for things in the universe (as opposed to abstract ideas like mathematics where 1 + 1 = 2 was true before the universe came into being and will still be true when it is gone). So much for the so called 'ad populum' fallacy which is not a fallacy at all. Apart from agreement (popularity) of minds on something being what it is to x number of decimal places nothing in the universe has any reality at all. Agreement by minds for things in the universe to x number of decimals as empirical truth is the ONLY reality available. But 1 + 1 = 2 is true regardless of a beholder of it but this (abstract/metaphysical) mathematical truth is arithmetic and as I already said, Godel showed that even something as simple as arithmetic is not certain in the sense it cannot be proven to be certain as a complete closed consistent system. On the other hand, almost EVERYTHING YOU KNOW cannot be proven to be true another consequence of what Godel showed. Nightdreamer thinks he has shown Godel to be wrong but so do about 20,000 other AI nuts. I went through Godels work as well as Alan Turing (who basically did the same thing algorithmically) and I agree with Godel as does Stephen Hawking and Roger Penrose. Other 'problems' in mathematics are interpretations of what mathematics means. There is a Philosophy of Mathematics just like there is a Philosophy of Science. Formalism, Logical Positivism, Intuitionism. I don't really care about pure mathematics. If you can't apply mathematics to things in the universe it is basically useless to me so I don't really think much of these socalled problems. For instance only a mathematician goes into existential despair over things like infinity. To me as long as set theory is useful it serves as a tool. (In a town whose barber shaves all heads that don't shaves themselves, who shaves the barber? Mother/set of all setsFrege/Russell/Whitehead/Principia Mathematicia/ etc yippee dippee) I don't know about Nightdreamer's skolems paradox though. Below is one of the best web pages on Godel (first 2 paragraphs below) http://users.ox.ac.uk/~jrlucas/mmg.html Minds, Machines and Gödel First published in Philosophy, XXXVI, 1961, pp.(112)(127); reprinted in The Modeling of Mind, Kenneth M.Sayre and Frederick J.Crosson, eds., Notre Dame Press, 1963, pp.[269][270]; and Minds and Machines, ed. Alan Ross Anderson, PrenticeHall, 1954, pp.{43}{59}. "Gödel's theorem seems to me to prove that Mechanism is false, that is, that minds cannot be explained as machines. So also has it seemed to many other people: almost every mathematical logician I have put the matter to has confessed to similar thoughts, but has felt reluctant to commit himself definitely until he could see the whole argument set out, with all objections fully stated and properly met.1 This I attempt to do. Gödel's theorem states that in any consistent system which is strong enough to produce simple arithmetic there are formulae which cannot {44} be provedinthesystem, but which we can see to be true. Essentially, we consider the formula which says, in effect, "This formula is unprovableinthesystem". If this formula were provableinthesystem, we should have a contradiction: for if it were provableinthesystem, then it would not be unprovableinthesystem, so that "This formula is unprovableinthesystem" would be false: equally, if it were provableinthesystem, then it would not be false, but would be true, since in any consistent system nothing false can be provedinthesystem, but only truths. So the formula "This formula is unprovableinthesystem" is not provableinthesystem, but unprovableinthesystem. Further, if the formula "This formula is unprovablein thesystem" is unprovableinthesystem, then it is true that that [256] formula is unprovableinthesystem, that is, "This formula is unprovableinthesystem" is true." The best books on Godel I have ever seen is Godel a Life of Logic by John L. Casti and Werner DePauli and Roger Penrose books The Emperor's New Mind and Shadows of the Mind which in their own way trashes AI nuts. We are not what we are conscious of/we are not minds any more than we are our toaster or our cars. Consciousness is one thing and the mind or brain something entirely different. Mike Dubbeld 
#13




Whilst I agree with some of this, I find the assertion that consciousness is 'apart from' mind/brain to be insupportable.
What Penrose (and others) have deduced from Godel is that (human?) consciousness is not entirely algorithmic. He deduces from this that AI will not, in its present formulation, be able to mimic the abilities of the conscious mind. It's an interesting hypothesis but it is certainly not a done deal. Neither is he saying that consciousness is not a product of the mind/brain  in fact he is saying quite the opposite. His hypothesis is that quantum effects are a necessary part of consciousness. He thinks that certain 'microtubules' in the brain are small enough to display quantum effects  decoherence/superposition etc  and that these effects are necessary for what we regard as human consciousness. http://findarticles.com/p/articles/m..._15447461/pg_1 
#14




PS  there is an interesting treatment of the Penrose hypothesis here
http://www.valdostamuseum.org/hamsmith/QuanCon.html And here are some critiques of Penrose's hypothesis http://psyche.cs.monash.edu.au/v2/ps...mcdermott.html http://www.1729.com/consciousness/godel.html Critique of Godel's theorem http://gamahucherpress.yellowgum.com...phy/GODEL5.pdf Last edited by Bikerman; 05122008 at 09:02 PM. 
#15




Mile Dubbled can wax poetic with mathematics and science, but when it comes to beating David Blaine's underwater stunt, his yoga let's him down. Tut tut.

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