XPost: comp.theory, sci.math, sci.lang.semantics   
   XPost: comp.ai.nat-lang   
   From: polcott333@gmail.com   
      
   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,   
      
   ∀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.   
      
   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   
      
   >>   
   >> 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.   
      
   >   
   >>   
   >> The terminology which has just been used implies that   
   >> the elementary statements are not such that their truth   
   >> and falsity are known to us without reference to {T}.   
   >> (Curry 1977:45)   
   >>   
   >> Simply defining Gödel Incompleteness and Tarski Undefinability away V12   
   >> olcott Jun 26, 2020, 4:15:48 PM   
   >> comp.theory,comp.ai.philosophy,comp.ai.nat-lang,sci.lang.semantics   
   >> Message-ID:    
   >> https://groups.google.com/g/comp.ai.nat-lang/c/p_evEnqowPQ/m/0RHg0UjWAAAJ   
   >>   
   >> The Wittgenstein quote above was anchored in what is   
   >> now known as well-founded proof theoretic semantics on   
   >> the basis of what is now known as Curry's basis of   
   >> true in the system. He saw this decades before these   
   >> fields were ever established.   
   >>   
   >> The seed of his idea goes all the way back to his   
   >> Tractatus (1921)   
   >>   
   >> 6.12 The fact that the propositions of logic are   
   >> tautologies shows the formal-logical-properties   
   >> of language, of the world. That its constituent   
   >> parts connected together in this way give a tautology   
   >> characterizes the logic of its constituent parts.   
   >> In order that propositions connected together in a   
   >> definite way may give a tautology they must have   
   >> definite properties of structure. That they give a   
   >> tautology when so connected shows therefore that they   
   >> possess these properties of structure.   
   >>   
   >   
      
      
   --   
   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)