XPost: sci.logic, sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 1/24/2026 2:23 AM, Mikko wrote:   
   > On 22/01/2026 18:47, olcott wrote:   
   >> On 1/22/2026 2:21 AM, Mikko wrote:   
   >   
   >>> Anyway, what can be provven that way is true aboout PA. You can deny   
   >>> the proof but you cannot perform what is meta-provably impossible.   
   >   
   >> The meta-proof does not exist in the axioms of PA   
   >> and that is the reason why an external truth in   
   >> an external model cannot be proved internally in PA.   
   >> All of these years it was only a mere conflation   
   >> error.   
   >   
   > It is perfectly clear which is which.   
   > But every proof in PA is also   
   > a proof in Gödel's metatheory.   
   >   
      
   ∀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)))   
      
      
   --   
   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)