XPost: sci.logic, sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 1/15/2026 4:02 AM, Mikko wrote:   
   > On 15/01/2026 07:30, olcott wrote:   
   >> On 1/14/2026 9:44 PM, Richard Damon wrote:   
   >>> On 1/14/26 4:36 PM, olcott wrote:   
   >>>> Interpreting incompleteness as a gap between mathematical truth and   
   >>>> proof depends on truth-conditional semantics; once this is replaced   
   >>>> by proof-theoretic semantics a framework not yet sufficiently   
   >>>> developed at the time of Gödel’s proof the notion of such a gap   
   >>>> becomes unfounded.   
   >>>>   
   >>>   
   >>> But that isn't what Incompleteness is about, so you are just showing   
   >>> your ignorance of the meaning of words.   
   >>>   
   >>> You can't just "change" the meaning of truth in a system.   
   >>>   
   >>   
   >> Yet that is what happens when you replace the foundational basis   
   >> from truth-conditional semantics to proof-theoretic semantics.   
   >   
   > Gödel constructed a sentence that is correct by the rules of first   
   > order Peano arithmetic   
      
   within truth conditional semantics and non-well-founded   
   in proof theoretic semantics. All of PA can be fully   
   expressed in proof theoretic semantics. Even G can be   
   expressed, yet rejected as semantically non-well-founded.   
      
   > but neither a theorem nor the negaition of   
   > a theorem of Peano artihmetic. Being a theorem does not depend on   
   > semantics, only on the existence of a syntatically valid proof.   
      
   That incorrectly assumes syntax always carries coherent   
   semantics.   
      
   > Gödel's sentence can be interpreted as a perfiectly valid game.   
      
   Where one of the players cheats.   
      
   > That at the start of the game neither player can choose a strategy   
   > that ensures the winning does not invalidate the game.   
   >   
      
   Proof theoretic semantics is the actual way that   
   "true on the basis of meaning expressed in language"   
   has always worked.   
      
   --   
   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)