Groups | Search | Server Info | Login | Register
Groups > comp.theory > #109436
| From | Richard Damon <richard@damon-family.org> |
|---|---|
| Newsgroups | comp.theory, sci.logic |
| Subject | Re: Tarski / Gödel and redefining the Foundation of Logic |
| Date | 2024-07-22 20:12 -0400 |
| Organization | i2pn2 (i2pn.org) |
| Message-ID | <c2eb6a8d264dd2ab6079abef07def1e440301615@i2pn2.org> (permalink) |
| References | (26 earlier) <v7gdmn$3hlc2$3@dont-email.me> <v7ikah$1hri$1@dont-email.me> <v7j1u4$3o7r$2@dont-email.me> <v7l4c9$ijpn$1@dont-email.me> <v7lr19$luh0$3@dont-email.me> |
Cross-posted to 2 groups.
On 7/22/24 10:40 AM, olcott wrote: > On 7/22/2024 3:14 AM, Mikko wrote: >> On 2024-07-21 13:20:04 +0000, olcott said: >> >>> On 7/21/2024 4:27 AM, Mikko wrote: >>>> On 2024-07-20 13:22:31 +0000, olcott said: >>>> >>>>> On 7/20/2024 3:42 AM, Mikko wrote: >>>>>> On 2024-07-19 13:48:49 +0000, olcott said: >>>>>> >>>>>>> >>>>>>> Some undecidable expressions are only undecidable because >>>>>>> they are self contradictory. In other words they are undecidable >>>>>>> because there is something wrong with them. >>>>>> >>>>>> Being self-contradictory is a semantic property. Being >>>>>> uncdecidable is >>>>>> independent of any semantics. >>>>> >>>>> Not it is not. When an expression is neither true nor false >>>>> that makes it neither provable nor refutable. >>>> >>>> There is no aithmetic sentence that is neither true or false. If the >>>> sentnece >>>> contains both existentia and universal quantifiers it may be hard to >>>> find out >>>> whether it is true or false but there is no sentence that is neither. >>>> >>>>> As Richard >>>>> Montague so aptly showed Semantics can be specified syntactically. >>>>> >>>>>> An arithmetic sentence is always about >>>>>> numbers, not about sentences. >>>>> >>>>> So when Gödel tried to show it could be about provability >>>>> he was wrong before he even started? >>>> >>>> Gödel did not try to show that an arithmetic sentence is about >>>> provability. >>>> He constructed a sentence about numbers that is either true and >>>> provable >>>> or false and unprovable in the theory that is an extension of Peano >>>> arithmetics. >>>> >>> >>> You just directly contradicted yourself. >> >> I don't, and you cant show any contradiction. >> > > Gödel's proof had nothing what-so-ever to do with provability > except that he proved that g is unprovable in PA. Right, which since G was TRUE in PA, makes PA incomplete. So, you argee that Godel was correct, but then argue he isn;t YOU are just showing your logic is inconsistent, and thus unusable. > >>>>>> A proof is about sentences, not about >>>>>> numbers. >>>>>> >>>>>>> The Liar Paradox: "This sentence is not true" >>>>>> >>>>>> cannot be said in the language of Peano arithmetic. >>>>> >>>>> Since Tarski anchored his whole undefinability theorem in a >>>>> self-contradictory sentence he only really showed that sentences that >>>>> are neither true nor false cannot be proven true. >>>> >>>> By Gödel's completeness theorem every consistent incomplete first order >>>> theory has a model where at least one unprovable sentence is true. >>>> >>>>> https://liarparadox.org/Tarski_247_248.pdf // Tarski Liar Paradox >>>>> basis >>>>> https://liarparadox.org/Tarski_275_276.pdf // Tarski proof >>> >>> It is very simple to redefine the foundation of logic to eliminate >>> incompleteness. >> >> Yes, as long as you don't care whether the resulting system is useful. >> Classical logic has passed practical tests for thousands of years, so >> it is hard to find a sysem with better empirical support. >> > > When we show how incompleteness is eliminated then this also shows > how undefinability is eliminated and this would have resulted in a > chatbot that eviscerated Fascist lies about election fraud long > before they could have taken hold in the minds of 45% of the electorate. HOW did you "eliminate" incompleteness. YOo ADMITTED that statements could be true by just an infinte chain of steps, which is not a proof. You just are proving you don't unstand what you are talking about, it seems, because you just don't understand what "Formal Systems" are, perhaps because they are just too abstract for you. > > Because people have been arguing against my correct system of reasoning > we will probably see the rise of the fourth Reich. No, you have proved that your system of reasoning can't be correct, because it denies things you admit are true., > >>> Any expression x of language L that cannot be shown >>> to be true by some (possibly infinite) sequence of truth preserving >>> operations in L is simply untrue in L: True(L, x). >> >> That does not help much if you cannot determine whether a particular >> string can be shown to be true. >> > > Every element of the set of human knowledge can be proven true > by a finite sequence of truth preserving operations. Also every > line can be proved to be false by this same basis. So? You confuse KNOWLEDGE wth TRUTH. > > The Heritage Foundation is the author of Project > 2025 and a staunch Trump ally could only find 1546 > cases of voter fraud in the last ten years. And you ar just validating theeir method of logic by using t your self. You ignore the truth presented to you, bacause you "know" it can't be true. YOU USE THE METHOD OF THE BIG LIE. > > #ElectionFraudLies > Even the Heritage Foundation agrees > Never any evidence of election fraud > that could possibly change the results: > > Only 1,546 total cases of voter fraud > https://www.heritage.org/voterfraud > Trump is just copying Hitler's "big lie" > >>> Tarski showed that True(Tarski_Theory, Liar_Paradox) cannot be defined >>> never understanding that Liar_Paradox is not a truth bearer. >> >> However, every arithmetic sentence is either true or false. >> > > The same diagonalization proof that Gödel used works on > the arithmetization of the Tarski proof. Diagonalization > never shows why g is unprovable in PA, it only shows that > g is unprovable in PA. So? The fact that it IS unprovable is enough. > > The Tarski proof shows why x is unprovable in the Tarski Theory > (because x is self-contradictory in the Tarski Theory) No, he shows that the assumption of a universal truth primative leads to contradictions, and thus can not exist. > > Tarski's Liar Paradox from page 248 > It would then be possible to reconstruct the antinomy of the liar > in the metalanguage, by forming in the language itself a sentence > x such that the sentence of the metalanguage which is correlated > with x asserts that x is not a true sentence. > https://liarparadox.org/Tarski_247_248.pdf Right, he PROVES that, given the existance of the truth primative, you can build as a sentence in the logic, a sentence of that form. > > Formalized as: > x ∉ True if and only if p > where the symbol 'p' represents the whole sentence x Which you don't understand where that comes from. You seem to think it is jus something he made uo, he PROVES that you can form that statement given that a Truth Primative exists. > > https://www.researchgate.net/publication/315367846_Minimal_Type_Theory_MTT > > In my own Minimal Type Theory the self contradiction > is much easier to see: LP := ~True(LP) > Because you don't actually understand what Tarski is doing.
Back to comp.theory | Previous | Next — Previous in thread | Next in thread | Find similar
Re: DDD correctly emulated by HHH is correctly rejected as non-halting. Mikko <mikko.levanto@iki.fi> - 2024-07-15 10:57 +0300
Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention olcott <polcott333@gmail.com> - 2024-07-15 08:32 -0500
Re: DDD incorrectly emulated by HHH is incorrectly rejected as non-halting. --- You are not paying attention Richard Damon <richard@damon-family.org> - 2024-07-15 22:19 -0400
Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention Mikko <mikko.levanto@iki.fi> - 2024-07-16 10:18 +0300
Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention olcott <polcott333@gmail.com> - 2024-07-16 09:46 -0500
Re: DDD INcorrectly emulated by HHH is INcorrectly rejected as non-halting. --- You are not paying attention Richard Damon <richard@damon-family.org> - 2024-07-16 21:12 -0400
Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention Mikko <mikko.levanto@iki.fi> - 2024-07-17 10:08 +0300
Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention olcott <polcott333@gmail.com> - 2024-07-17 08:14 -0500
Re: DDD emulated by HHH is incorrectly rejected as non-halting. joes <noreply@example.org> - 2024-07-17 17:08 +0000
Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention Mikko <mikko.levanto@iki.fi> - 2024-07-18 10:55 +0300
Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention olcott <polcott333@gmail.com> - 2024-07-18 08:36 -0500
Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention Mikko <mikko.levanto@iki.fi> - 2024-07-19 10:30 +0300
Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention olcott <polcott333@gmail.com> - 2024-07-19 08:48 -0500
Re: DDD incorrectly emulated by HHH is incorrectly rejected as non-halting. --- You are not paying attention Richard Damon <richard@damon-family.org> - 2024-07-19 11:28 -0400
Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention Mikko <mikko.levanto@iki.fi> - 2024-07-20 11:42 +0300
Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention olcott <polcott333@gmail.com> - 2024-07-20 08:22 -0500
Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention Mikko <mikko.levanto@iki.fi> - 2024-07-21 12:27 +0300
Tarski / Gödel and redefining the Foundation of Logic olcott <polcott333@gmail.com> - 2024-07-21 08:20 -0500
Re: Tarski / Gödel and redefining the Foundation of Logic Richard Damon <richard@damon-family.org> - 2024-07-21 13:53 -0400
Re: Tarski / Gödel and redefining the Foundation of Logic Mikko <mikko.levanto@iki.fi> - 2024-07-22 11:14 +0300
Re: Tarski / Gödel and redefining the Foundation of Logic olcott <polcott333@gmail.com> - 2024-07-22 09:40 -0500
Re: Tarski / Gödel and redefining the Foundation of Logic Richard Damon <richard@damon-family.org> - 2024-07-22 20:12 -0400
Re: Tarski / Gödel and redefining the Foundation of Logic Mikko <mikko.levanto@iki.fi> - 2024-07-23 11:07 +0300
Re: Tarski / Gödel and redefining the Foundation of Logic olcott <polcott333@gmail.com> - 2024-07-23 09:53 -0500
Re: Tarski / Gödel and redefining the Foundation of Logic Richard Damon <richard@damon-family.org> - 2024-07-23 22:16 -0400
Re: Tarski / Gödel and redefining the Foundation of Logic Mikko <mikko.levanto@iki.fi> - 2024-07-25 11:55 +0300
Re: Tarski / Gödel and redefining the Foundation of Logic olcott <polcott333@gmail.com> - 2024-07-25 10:51 -0500
csiph-web