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| Message-ID | <-M8w7ApLHAiK9B-bPjcdK_CB6vQ@jntp> (permalink) |
|---|---|
| Subject | Re: Gödel's G has never actually been true in arithmetic |
| References | (5 earlier) <10kpm74$1r90m$1@dont-email.me> <10kqh7e$23pt6$1@dont-email.me> <10kqsb3$27pfl$1@dont-email.me> <10ks62i$2l2n9$1@dont-email.me> <10ks70p$2m8fa$1@dont-email.me> |
| Newsgroups | sci.logic, sci.math, comp.theory, comp.ai.philosophy |
| Followup-To | sci.math |
| Date | 2026-01-22 04:59 +0000 |
| Organization | Nemoweb |
| From | Python <python@cccp.invalid> |
Cross-posted to 4 groups.
Followups directed to: sci.math
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.
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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 Python <python@cccp.invalid> - 2026-01-18 21:59 +0000
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 Python <python@cccp.invalid> - 2026-01-19 01:24 +0000
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 Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-19 13:58 +0000
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 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 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 Moebius <invalid@example.invalid> - 2026-01-22 02:23 +0100
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 Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-18 12:44 +0000
Re: Gödel's G has never actually been true in arithmetic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-18 12:38 +0000
Re: Gödel's G has never actually been true in arithmetic Mikko <mikko.levanto@iki.fi> - 2026-01-18 12:09 +0200
Glossary building (Was: Re: Gödel's G has never actually been true in arithmetic) Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-18 11:53 +0000
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 Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-28 16:34 +0000
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 Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-28 16:21 +0000
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 Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-28 23:59 +0000
Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-28 20:10 -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 Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-02-01 20:04 +0000
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