XPost: comp.theory, sci.logic, sci.math   
   XPost: sci.lang   
   From: polcott333@gmail.com   
      
   On 1/14/2026 3:36 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.   
   >   
      
   Gödel and Turing incompleteness results expose the limits of   
   denotational and truth-conditional semantics, not limits of proof or   
   computation per se. When meaning is grounded operationally or   
   proof-theoretically, the problematic self-referential constructions are   
   rejected as semantically unfounded rather than treated as determinate   
   but unknowable facts.   
      
   --   
   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)