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

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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.

> 
>>
>>>
>>> ∀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.

But it isn't well-founded, as it isn't actualy based on proof.

> 
>>>
>>>>>
>>>>> 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.

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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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