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| From | olcott <polcott333@gmail.com> |
|---|---|
| Newsgroups | sci.math, sci.logic, comp.theory, "]" |
| Subject | Re: Gödel's G has never actually been true in arithmetic |
| Date | 2026-01-21 23:18 -0600 |
| Organization | A noiseless patient Spider |
| Message-ID | <10ksbuu$2nled$1@dont-email.me> (permalink) |
| References | (6 earlier) <10kqh7e$23pt6$1@dont-email.me> <10kqsb3$27pfl$1@dont-email.me> <10ks62i$2l2n9$1@dont-email.me> <10ks70p$2m8fa$1@dont-email.me> <-M8w7ApLHAiK9B-bPjcdK_CB6vQ@jntp> |
Cross-posted to 4 groups.
On 1/21/2026 10:59 PM, Python wrote: > Le 22/01/2026 à 04:54, olcott a écrit : >> On 1/21/2026 9:37 PM, Richard Damon wrote: >>> On 1/21/26 10:45 AM, olcott wrote: >>>> On 1/21/2026 6:35 AM, Richard Damon wrote: >>>>> On 1/20/26 11:54 PM, olcott wrote: >>>>>> On 1/20/2026 10:04 PM, Richard Damon wrote: >>>>>>> On 1/20/26 4:23 PM, olcott wrote: >>>>>>>> On 1/19/2026 11:29 PM, Richard Damon wrote: >>>>>>>>>> My system is not supposed to decide in advance whether >>>>>>>>>> Goldbach is well‑founded. A formula becomes a truth‑bearer >>>>>>>>>> only when PA can classify it in finitely many steps. >>>>>>>>>> Goldbach may or may not be classifiable; that’s an open >>>>>>>>>> computational fact, not a semantic requirement. This has >>>>>>>>>> no effect on Gödel, because Gödel’s sentence is structurally >>>>>>>>>> non‑truth‑bearing, not merely unclassified. >>>>>>>>> >>>>>>>>> Which shows that you don't understand what logic systems are. >>>>>>>>> >>>>>>>>> The don't "Decide" on truths, they DETERMINE what is true. >>>>>>>>> >>>>>>>>> Your problem is that either there is, or there isn't a finite >>>>>>>>> length proof of the statement. >>>>>>>>> >>>>>>>>> Semantics can't change in a formal system, or they aren't >>>>>>>>> really semantics. >>>>>>>>> >>>>>>>>> Your problem is you don't understand Godel statement, as it >>>>>>>>> *IS* truth bearing as it is a simple statement with no middle >>>>>>>>> ground, does a number exist that satisfies a given >>>>>>>>> relationship. Either there is, or there isn't. No other >>>>>>>>> possiblity. >>>>>>>>> >>>>>>>>> You confuse yourself by forgetting that words have actual >>>>>>>>> meaning, and that meaning can depend on using the right context. >>>>>>>>> >>>>>>>>> Godel's G is a statement in the system PA. >>>>>>>>> >>>>>>>>> It is a statement about the non-existance of a natural number >>>>>>>>> that satisfies a particular computable realtionship. >>>>>>>>> >>>>>>>>> It is a statement defined purely by mathematics and thus >>>>>>>>> doesn't "depend" on other meaning. >>>>>>>>> >>>>>>>>> It is a mathematical FACT, that for this relationship, no >>>>>>>>> matter what natural number we test, none will satisfy it, so >>>>>>>>> its assertation that no number satisfies it makes it true. >>>>>>>> >>>>>>>> PA augmented with its own True(PA,x) and False(PA,x) >>>>>>>> is a decider for Domain of every expression grounded >>>>>>>> in the axioms of PA. >>>>>>> >>>>>>> No, it becomes inconsistant. >>>>>>> >>>>>>>> >>>>>>>> A system at a higher level of inference than PA can >>>>>>>> reject any expressions that define a cycle in the >>>>>>>> directed graph of the evaluation sequence of PA >>>>>>>> expressions. Then PA could test back chained inference >>>>>>>> from expression x and ~x to the axioms of PA. >>>>>>>> >>>>>>> >>>>>>> But there is no "cycle" in the statement of G. It is PURELY a >>>>>>> statement of the non-existance of a number that satisfies a >>>>>>> purely mathematic relationship (which has no meaning by itself in >>>>>>> PA). >>>>>>> >>>>>> >>>>>> Even the relationship cannot exist <in> PA. >>>>>> Instead it is about PA in outside model theory >>>>> >>>>> No, it doesn't mention PA, it is about the numbers that are IN PA. >>>>> >>>>> Your problem is you forget to actually know what Godel's G is, a >>>>> you only read the Reader's Digest version of the proof, as that is >>>>> all you can understand. >>>>> >>>>> That, or you are saying that mathematics itself isn't in PA, and >>>>> that you proof-theoretic stuff isn't in PA either, >>>>> >>>>> Sorry, you are just showing how ignorant you are. >>>>> >>>> >>>> G_F ↔ ¬Prove_F(Gödel_Number(G_F)) contains a semantic >>>> dependency loop, because evaluating G_F requires >>>> evaluating Prove_F on the Gödel number of G_F, which >>>> in turn requires evaluating G_F again; >>> >>> But that isn't G_F >>> >>> G_F is a statement that a particular relationship (lets call it >>> R(x) ) will not be satisfied for any natural number x. >>> >> >> That relationship has never existed inside actual >> arithmetic > > It actually IS a relationship in the domain of PA. PUNTO. > > It is what it is. Denial is hopeless. When PA is actually given its own truth predicate anchored only in its own axioms then for the first time one see that meta-math truth in the standard model of arithmetic never was actually true in PA itself at all. -- Copyright 2026 Olcott<br><br> My 28 year goal has been to make <br> "true on the basis of meaning expressed in language"<br> reliably computable.<br><br> This required establishing a new foundation<br>
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Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-17 15:08 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-17 16:54 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-17 16:50 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-17 19:14 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-17 18:49 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-17 20:20 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-17 19:30 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-17 20:46 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-17 19:59 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-17 22:20 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-17 21:59 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-17 23:13 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-17 22:38 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-18 12:37 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-18 12:38 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-18 15:55 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-18 15:49 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-18 18:28 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-18 17:41 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-18 19:28 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-18 21:17 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 00:29 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-20 10:50 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 23:00 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-18 21:19 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-18 22:56 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-18 22:28 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-19 06:49 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-19 08:43 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 00:29 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-20 15:23 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 23:04 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-20 22:54 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-21 07:35 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-21 09:45 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-21 22:37 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-21 21:53 -0600
Re: Gödel's G has never actually been true in arithmetic Python <python@cccp.invalid> - 2026-01-22 04:59 +0000
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-21 23:18 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-22 19:17 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-22 18:33 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-22 21:51 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-22 22:18 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-23 20:33 -0500
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-22 19:15 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-19 13:20 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 00:29 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-20 14:00 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 23:12 -0500
Re: Gödel's G has never actually been true in arithmetic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-20 23:08 +0000
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-20 17:33 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-22 19:23 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-22 18:49 -0600
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-22 19:05 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-22 21:48 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-22 19:30 -0600
Re: Gödel's G has never actually been true in arithmetic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-23 00:23 +0000
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-22 18:29 -0600
Re: Gödel's G has never actually been true in arithmetic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-23 01:15 +0000
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-22 19:38 -0600
Re: Gödel's G has never actually been true in arithmetic Mikko <mikko.levanto@iki.fi> - 2026-01-18 12:09 +0200
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-19 20:39 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 00:29 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-20 15:39 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 23:21 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-28 12:17 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <news.x.richarddamon@xoxy.net> - 2026-02-01 07:33 -0500
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-28 12:08 -0600
Re: Gödel's G has never actually been true in arithmetic Richard Damon <news.x.richarddamon@xoxy.net> - 2026-02-01 07:33 -0500
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