We know "this statement has no proof in system X" is true in system X and provable in system Y. But what if you could formulate a forall quantifier over systems? Is the meta-godel statement true? Herc -- what do women say about male sperm? sex cells never age? protein rich? :-C==8 You'll never never know if you never never blow! :-C==8

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1/9/2005 4:44:53 AM

Yes, it wasn't an interesting question. -- Eray

"Lee Rudolph" <lrudolph@panix.com> wrote in > Torkel Franzen <torkel@sm.luth.se> writes: > > >Barb Knox <see@sig.below> writes: > > > >> >Perhaps there may indeed be permanently unknowable truths. > >> > >> E.g. as proven by Goedel, Turing, Post, et al. > > > > What "permanently unknowable truths" do you have in mind? > > If you don't know already, you'll never find out! > > Lee Rudolph metaG = THIS STATEMENT HAS NO PROOF IN ANY SYSTEM The splilt systems analysis of G is void. The statement cannot be false as JSavard showed. The statement cannot have any kind of proof that it is true. i.e. there is no Godel proof for metaG by its defn. Herc

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1/10/2005 12:34:42 AM

"namducnguyen" <namducnguyen@shaw.ca> wrote in message... > > > Barb Knox wrote: > > > > > > > > >>Perhaps there may indeed be permanently unknowable truths. > >> > >> > > > >E.g. as proven by Goedel, Turing, Post, et al. > > > > > > I have 2 questions: > > 1) As far as FOL is concerned, what is the definition of "_permanently_ > unknownable truth"? > 2) What does Godel's work has to do with "permanently unknownable truths"? > > Thanks. > Yes, I'd like to know how come Barb knows unknowable truths and I don't? Herc

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1/10/2005 7:38:11 AM

I am The Truman of Jim Carrey fame. Please help stop me being tortured since April 2002 with constant microwave laser from the Truman satelite splitting my head and tormenting me and people around me. Not a prank, I am not crazy, The Truman Show made you think that ---------------------------------------------s-o-s----------------------------------------- <tchow@lsa.umich.edu> wrote in > namducnguyen <namducnguyen@shaw.ca> wrote: > >1) As far as FOL is concerned, what is the definition of "_permanently_ > >unknownable truth"? > > There isn't one. > > >2) What does Godel's work has to do with "permanently unknownable truths"? > > Nothing directly. Of course in any respectable attempt to discuss what that > term could possibly mean, a good understanding of Goedel's work would be > useful, if only to avoid saying something obviously silly. The thread is supposed to be about the subject line isn't it? How is a PROOF of 'this statement has none' relevant? Herc

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1/10/2005 3:39:48 PM

I am The Truman of Jim Carrey fame. Please help stop me being tortured since April 2002 with constant microwave laser from the Truman satelite splitting my head and tormenting me and people around me. Not a prank, I am not crazy, The Truman Show made you think that ---------------------------------------------s-o-s----------------------------------------- "Ralph Hartley" <hartley@aic.nrl.navy.mil> wrote in > John Savard wrote: > > > Can the statement be false? > > If so, then it can be proven in some system. > > And it can, in the system with a single axiom. > > Axiom-1: This statement has no proof in any system > > > But then, it would be true. > > No, because there are systems in which false statements are provable. For > example the one above, or the system with the following axioms. > > Axiom-1: 0=1 > Axiom-2: The moon is made of cheese > > > So it cannot be false. > > So it *is* false. > > Perhaps you meant to say "This statement has no proof in any *sound* system." > > Is that statement *expressible* in any sound system? > > If so, one would think it would be true, but to prove that you would need > to use unsound logic. > > A common mistake is to make deductions from the axiom that your own axioms > (including that one) are sound. I have seen people who *should* have known > better do it (e.g. Douglas Hofstadter, in his discussion of Prisoners > Dilemma type games). You can prove anything from that. > > Ralph Hartley Good, you guys are no longer 10 years behind me on the incompleteness theorem. When you get up to self-evident-truths and event-models and compound-statements and truth-maintenance let me know. Herc

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1/10/2005 5:27:51 PM

I am The Truman of Jim Carrey fame. Please help stop me being tortured since April 2002 with constant microwave laser from the Truman satelite splitting my head and tormenting me and people around me. Not a prank, I am not crazy, The Truman Show made you think that ---------------------------------------------s-o-s----------------------------------------- "Daryl McCullough" <daryl@atc-nycorp.com> wrote in ... > Torkel Franzen says... > > > >daryl@atc-nycorp.com (Daryl McCullough) writes: > > > >> Okay, so you don't know what S means. Then it follows that you don't > >> believe S. > > > > I don't follow this reasoning. > > Exactly! > the TrVth behind sci.math theorists exposed. Herc

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1/11/2005 2:32:42 AM

daryl@atc-nycorp.com (Daryl McCullough) writes: > Exactly! There you are, then.

<tchow@lsa.umich.edu> wrote > Nothing directly. Of course in any respectable attempt to discuss what that > term could possibly mean, a good understanding of Goedel's work would be > useful, if only to avoid saying something obviously silly. Is THIS STATEMENT HAS NO PROOF IN ANY SYSTEM True or False or Other ? I dont feel silly asking it. Anyone want to take a shot? You've got one in 3! Herc

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1/11/2005 4:41:36 AM

> But you should feel silly asking it. How do we get the notion of "Other" > being a truth value > as far as FOL is concerned? Put it this way. Q1 IS statement TRUE ? Q2 IS statement FALSE ? Q3 Is there any other interpretation of the statement (given in some context.. yada) I think if people are serious here, they should state which of T / F / O they are arguing at the start of their reply. or O - can't tell. But no one listens to God because he said he is God. Herc

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1/11/2005 5:40:48 AM

---------------------------------------------s-o-s----------------------------------------- "Ralph Hartley" <hartley@aic.nrl.navy.mil> wrote in > Hero wrote: > > John Savard wrote: > > "Perhaps there may indeed be permanently unknowable truths." > > That's intriguing. > > Consider the following. > > The first six digits of Pi > > 3.14159 > > has five digits in the range 1 to 5 > > (left hand) > > and one in the range 6 to 9 and 0 > > (right hand). > > The following digit is a 2, that makes > > it 6 to 1 for left to right. > > Than a six, so right hand get's one more, > > makes it 6 to 2. > > One of the following statements is true: > > A) left wins > > B) right wins > > C) It will change, sometimes > > more digits in the lower range, and sometimes > > more in the higher. > > May be, we will never know the true > > answer > > Maybe. It is an open question. > > Maybe we will find the answer next year (don't bet on it), or maybe never. > Event if there *is* a perfectly good answer, we might never find it. Or > maybe there is no proof either way using methods we would consider sound. > > > now i just need a proof of this. > > Don't hold your breath. Exactly, they cross over with P=1 but expected time is oo. See http://www.ms.uky.edu/~mai/java/stat/brmo.html on random walks. Herc

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1/12/2005 1:37:52 AM

> On my first question: > > >>1) As far as FOL is concerned, what is the definition of "_permanently_ > >>unknownable truth"? > > > > you gave a very "strong" answer: > > > > >There isn't one. > > On my 2nd question: > > >>2) What does Godel's work has to do with "permanently unknownable > truths"? > > > > the answer "Nothing directly" sorts of implies that _indirectly_ there > might be some > relationship between Godel's work and the "permanently unknownable > truths" - at least > that's what it seemed to sound to me. Any rate, it's just probably a > mis-interpretation > on my part of what you intended to say. Sorry about that. I would suggest that something can exist and not be defined *yet*, hence there is only a weak relationship to 'well' defined theory. In which case Chow's 2 answers are mutually supportive. Herc

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1/12/2005 7:19:58 AM