XPost: comp.theory, sci.math, sci.math.symbolic   
   From: polcott333@gmail.com   
      
   On 1/24/2026 1:23 PM, Richard Damon wrote:   
   > On 1/24/26 1:20 PM, olcott wrote:   
   >> On 1/22/2026 11:25 AM, olcott wrote:   
   >>> Well-founded proof theoretic semantics where   
   >>> True(L, x) is anchored in provability from   
   >>> the axioms of formal system L seems to   
   >>> eliminate the undecidability that model   
   >>> theoretic semantics encounters when truth is   
   >>> measured from outside of the formal system in   
   >>> a separate model.   
   >>>   
   >>   
   >> Gödel’s incompleteness theorem only “works” if   
   >> one smuggles in an external notion of truth   
   >> (truth in ℕ) and then pretends it is an   
   >> internal notion of truth (truth in PA).   
   >> If we refuse to make that identification,   
   >> incompleteness evaporates.   
   >>   
   >   
   > Nope.   
   >   
   > The existance of non-existance of a number is the same inside and outside.   
   >   
      
   So model theory  the axioms of PA   
   itself and nothing else not even the model.   
      
      
   --   
   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)