XPost: comp.theory, sci.math, sci.lang.semantics   
   XPost: comp.ai.nat-lang   
   From: polcott333@gmail.com   
      
   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.   
      
   >   
   >>   
   >> ∀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.   
      
   >>   
   >>>>   
   >>>> 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   
      
      
   --   
   Copyright 2026 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)