XPost: comp.theory, sci.logic, sci.math   
   XPost: sci.lang   
   From: mikko.levanto@iki.fi   
      
   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 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.   
   Gödel's sentence can be interpreted as a perfiectly valid game.   
   That at the start of the game neither player can choose a strategy   
   that ensures the winning does not invalidate the game.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)