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Re: Back in 2020 I proved that Wittgenstein was correct all along

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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]

-- 
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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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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