XPost: sci.logic, comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 12/3/2025 8:32 PM, Tristan Wibberley wrote:   
   > On 30/11/2025 09:58, Mikko wrote:   
   >   
   >> Note that the meanings of   
   >>   ?- G = not(provable(F, G)).   
   >> and   
   >>   ?- unify_with_occurs_check(G, not(provable(F, G))).   
   >> are different. The former assigns a value to G, the latter does not.   
   >>   
   >   
   > For sufficiently informal definitions of "value".   
   > And for sufficiently wrong ones too!   
   >   
      
   % This sentence cannot be proven in F   
   ?- G = not(provable(F, G)).   
   G = not(provable(F, G)).   
   ?- unify_with_occurs_check(G, not(provable(F, G))).   
   false.   
      
   I would say that the above Prolog is the 100%   
   complete formal specification of:   
      
   "This sentence cannot be proven in F"   
      
   that totally and unequivocally rejects it   
   as semantically unsound.   
      
   ...We are therefore confronted with a proposition which   
   asserts its own unprovability. 15 … (Gödel 1931:40-41)   
      
   When we hypothesize that the above sentence does   
   accurately sum up the essence of his theorem (it might not)   
   then within this hypothesis his theorem has been refuted.   
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning" computable.   
      
   This required establishing a new foundation   
   for correct reasoning.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)