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| From | Richard Damon <news.x.richarddamon@xoxy.net> |
|---|---|
| Newsgroups | comp.theory, sci.logic, sci.math, sci.lang.semantics, comp.ai.nat-lang |
| Subject | Re: Back in 2020 I proved that Wittgenstein was correct all along |
| Date | 2026-01-22 19:13 -0500 |
| Organization | A noiseless patient Spider |
| Message-ID | <10kueei$306qt$2@dont-email.me> (permalink) |
| References | (4 earlier) <10kplsj$1r5sj$1@dont-email.me> <10kqhcd$23pt6$2@dont-email.me> <10kqqh4$274n4$1@dont-email.me> <2XocR.342073$ZkQ4.213724@fx47.iad> <10ktk3c$35tto$2@dont-email.me> |
Cross-posted to 5 groups.
On 1/22/26 11:43 AM, olcott wrote: > On 1/22/2026 6:42 AM, Richard Damon wrote: >> On 1/21/26 10:14 AM, olcott wrote: >>> On 1/21/2026 6:38 AM, Richard Damon wrote: >>>> On 1/20/26 11:49 PM, olcott wrote: >>>>> On 1/20/2026 10:00 PM, Richard Damon wrote: >>>>>> On 1/20/26 1:13 PM, olcott wrote: >>>>>>> On 1/19/2026 11:29 PM, Richard Damon wrote: >>>>>>>> On 1/19/26 12:56 PM, olcott wrote: >>>>>>>>> Back in 2020 I proved that Wittgenstein was correct >>>>>>>>> all along. His key essence of grounding truth in >>>>>>>>> well-founded proof theoretic semantics did not exist >>>>>>>>> at the time that he made these remarks. Because of >>>>>>>>> this his remarks were misunderstood to be based >>>>>>>>> on ignorance instead of the profound insight that >>>>>>>>> they really were. >>>>>>>>> >>>>>>>> >>>>>>>> Nope. >>>>>>>> >>>>>>>>> According to Wittgenstein: >>>>>>>>> 'True in Russell's system' means, as was said: proved >>>>>>>>> in Russell's system; and 'false in Russell's system' >>>>>>>>> means: the opposite has been proved in Russell's system. >>>>>>>>> (Wittgenstein 1983,118-119) >>>>>>>> >>>>>>>> Which is only ONE interpretation, (and not a correct one). >>>>>>>> >>>>>>> >>>>>>> All we need to do to make PA complete >>>>>>> is replace model theoretic semantics >>>>>>> with wellfounded proof theoretic sematics >>>>>>> and ground true in OA the way Haskell >>>>>>> Curry defines it entirely on the basis >>>>>>> of the axioms of PA, >>>>>> >>>>>> Nope, doesn't work. >>>>>> >>>>>> THe system breaks as it can't consistantly determine the truth >>>>>> value of some statements. >>>>> >>>>> Just to make it simpler for you to understand think >>>>> of it as a truth and falsity recognizer that gets >>>>> stuck in an infinite loop on anything else. >>>>> So PA is complete for its domain. >>>> >>>> Nope, as your idea to make it complete breaks everything. >>>> >>> >>> You keep asserting that it “breaks everything,” >>> but you haven’t identified a single axiom of >>> PA, rule of inference, or valid derivation that fails. >> >> What fails, is your definition of truth. >> >>> >>> The recognizer does exactly what it’s supposed to: >>> – returns true when PA proves ϕ >>> – returns false when PA proves ¬ϕ >>> – diverges on anything PA cannot settle >> >> But your "not-well-founded" isn't a REcOGNIZER, it is a PREDICATE, >> which ALWAYS needs to return a value. >> >>> >>> That’s not breaking anything. >>> That’s the definition of a recognizer. >>> >>> So what, specifically, do you think is broken? >> >> You definition of "Truth", which can't have a value by your logic. >> >>> >>>>> >>>>>> >>>>>>> >>>>>>> ∀x ∈ PA ((True(PA, x) ≡ (PA ⊢ x)) >>>>>>> ∀x ∈ PA ((False(PA, x) ≡ (PA ⊢ ~x)) >>>>>>> ∀x ∈ PA (~WellFounded(PA, x) ≡ (~True(PA, x) ∧ (~False(PA, x)) >>>>>>> Then PA becomes complete. >>>>>> >>>>>> And, in proof-theoretic semantics, this is just not-well-founded >>>>>> as there are statements that you can not determine if any of these >>>>>> are applicable or not. >>>>>>> >>>>>>> This is very similar to my work 8 years ago >>>>>>> where the axioms are construed as BaseFacts. >>>>>>> It was pure proof theoretic even way back then. >>>>>>> >>>>>>> The ultimate foundation of [a priori] Truth >>>>>>> Olcott Feb 17, 2018, 12:42:55 AM >>>>>>> https://groups.google.com/g/sci.logic/c/dbk5vsDzZbQ/m/4ajW9R08CQAJ >>>>>> >>>>>> At least that accepted that there were statement that it couldn't >>>>>> handle as they were neiteher true or false. >>>>>> >>>>>> With your addition, we get that there are statements that can be >>>>>> none of True, False, or ~WellFounded. >>>>>> >>>>> >>>>> This was the earliest documented work that >>>>> can be classified as well-founded proof theoretic semantics. >>>>> My actual work is documented to go back to 1998. >>>> >>> >>> An BaseFact is an expression X of (natural or formal) >>> language L that has been assigned the semantic property >>> of True. (Similar to a math Axiom). >>> >>> A Collection T of BaseFacts of language L forms the >>> ultimate foundation of the notion of Truth in language L. >>> >>> To verify that an expression X of language L is True or >>> False only requires a syntactic logical consequence >>> inference chain (formal proof) from one or more elements >>> of T to X or ~X. >>> >>> True(L, X) ↔ ∃Γ ⊆ BaseFact(L) Provable(Γ, X) >>> False(L, X) ↔ ∃Γ ⊆ BaseFact(L) Provable(Γ, ~X) >> >> And what it the provable truth value of Godel's G statement? >> >> It can't be True, since it turns out to not be provable. >> >> It can't be False, as no number exists to make it false. >> >> It can't be Proven Not-Well-Founded, as proving that it can't be >> false, establishes that no such number exists, which makes it true in >> the system. >> >> Thus, your definition of "Truth" as being True/False/Not-Well-Founded >> is just self-contradictory. >> >> All you are doing is your normal back-pedeling and dupliciously >> changing you claim that actually negates your other position. >> >>> >>>> But it isn't well-founded, as it isn't actualy based on proof. >>>> >>> >>> True(L, X) means: there exists a proof of X from the base facts >>> >>> False(L, X) means: there exists a proof of ¬X from the base facts >>> >>> Everything else → the recognizer diverges (no proof either way) >> >> In other words, your "Proff-Theoretic" system is actually Truth- >> Conditional, and thus you can't use it. >> >>> >>> That is proof‑theoretic semantics. >> > > It is literally the definition of truth in a proof‑theoretic >> framework. >> >> Which means proof-theoretic needs truth-conditional to be accepted by >> your logic. >> >> Proof-Theoretic can work if it says that it just can't handle some >> statements like G. >> >> Which is an admission of its own limitations. >> >> Proof-Theoretic ADMITS it is incomplete in PA, as there are statements >> it can not determine if they are true, false, or neither in the >> system, because a "proof" on not being true or false actually >> establishes the statement as true (or for other statments, that they >> are false). >> >> >>> >>>>> >>>>>>> >>>>>>>>> >>>>>>>>> Formalized by Olcott as: >>>>>>>>> >>>>>>>>> ∀F ∈ Formal_Systems ∀𝒞 ∈ WFF(F) (((F⊢𝒞)) ↔ True(F, 𝒞)) >>>>>>>>> ∀F ∈ Formal_Systems ∀𝒞 ∈ WFF(F) (((F⊬𝒞)) ↔ ¬True(F, 𝒞)) >>>>>>>>> ∀F ∈ Formal_Systems ∀𝒞 ∈ WFF(F) (((F⊢¬𝒞)) ↔ False(F, 𝒞)) >>>>>>>> >>>>>>>> Which can be not-well-founded, as determining *IF* a statement >>>>>>>> is proveable or not provable might not be provable, or even >>>>>>>> knowable. >>>>>>>> >>>>>>>> So, therefore you can't actually evaluate your statement. >>>>>>>> >>>>>>> >>>>>>> All meta-math is defined to be outside the scope of PA. >>>>>> >>>>>> But we don't need "meta-math" to establish the answer. >>>>>> >>>>>> It is a FACT that no number will satisfy the Relationship, >>>>> >>>>> That relationship does not even exist outside of meta-math >>>>> >>>>> >>>> >>>> So, numbers don't exsist? >>>> OR is it the "for all" part that doesn't exist, and thus your proof- >>>> theoretic logic can't exist either? >>>> >>>> Sorry, you are just stuck trying to outlaw that which you need. >>> >>> PA contains arithmetic relations about numbers. >>> It does not contain meta‑mathematical relations about PA itself. >>> Gödel’s construction uses the latter, not the former. >>> >> >> But G doesn't dp that. It just asserts that a given relationship is >> never satisfied. >> >> Or, is your claim that you can't do qualification over statements in >> PA, and thus your definition of truth doesn't actually exist in PA, so >> your truth is still external to PA. >> >> Your problem is you don't understand what the relationship in G >> actually is, because you don't understand how context works, so you >> don't actually understand how semantics work. > > See my reply to Mikko > [The Halting Problem asks for too much] > Which as I remember just says, in essence, that if we don't know we can answer a question, we can't ask it. Since the actual question of the field is CAN we answer, you are just showing you don't understand the actual question.
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Back in 2020 I proved that Wittgenstein was correct all along olcott <NoOne@NoWhere.com> - 2026-01-19 11:56 -0600
Re: Back in 2020 I proved that Wittgenstein was correct all along Richard Damon <Richard@Damon-Family.org> - 2026-01-20 00:29 -0500
Re: Back in 2020 I proved that Wittgenstein was correct all along olcott <polcott333@gmail.com> - 2026-01-20 12:13 -0600
Re: Back in 2020 I proved that Wittgenstein was correct all along Richard Damon <Richard@Damon-Family.org> - 2026-01-20 23:00 -0500
Re: Back in 2020 I proved that Wittgenstein was correct all along olcott <polcott333@gmail.com> - 2026-01-20 22:49 -0600
Re: Back in 2020 I proved that Wittgenstein was correct all along Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-21 07:38 -0500
Re: Back in 2020 I proved that Wittgenstein was correct all along olcott <polcott333@gmail.com> - 2026-01-21 09:14 -0600
Re: Back in 2020 I proved that Wittgenstein was correct all along Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-21 19:02 +0000
Re: Back in 2020 I proved that Wittgenstein was correct all along olcott <polcott333@gmail.com> - 2026-01-21 14:14 -0600
Re: Back in 2020 I proved that Wittgenstein was correct all along olcott <polcott333@gmail.com> - 2026-01-21 21:24 -0600
Re: Back in 2020 I proved that Wittgenstein was correct all along Richard Damon <Richard@Damon-Family.org> - 2026-01-22 07:42 -0500
Re: Back in 2020 I proved that Wittgenstein was correct all along olcott <polcott333@gmail.com> - 2026-01-22 10:43 -0600
Re: Back in 2020 I proved that Wittgenstein was correct all along Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-22 19:13 -0500
Re: Back in 2020 I proved that Wittgenstein was correct all along Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-21 18:55 +0000
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