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

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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.

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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 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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