XPost: comp.theory   
   From: polcott333@gmail.com   
      
   On 11/16/2025 1:11 PM, Tristan Wibberley wrote:   
   > On 16/11/2025 01:29, olcott wrote:   
   >> G ↔ ¬Prov(⌜G⌝)   
   >> Directed Graph of evaluation sequence   
   >> 00 ↔               01 02   
   >> 01 G   
   >> 02 ¬               03   
   >> 03 Prov            04   
   >> 04 Gödel_Number_of 01  // cycle   
   >   
   >   
   > I would argue that ⊢ G := ¬Prov(⌜G⌝) is not a theorem. Before you find   
   > that a value of G exists (so that you may evaluate G) you must first   
   > find that the statement defining G is a theorem.   
   >   
      
   https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom   
   It is the G sentence of the first incompleteness theorem.   
      
   ?- G = not(provable(F, G)).   
   G = not(provable(F, G)).   
      
   ?- unify_with_occurs_check(G, not(provable(F, G))).   
   false.   
      
   It has a cycle proving that it cannot be resolved   
   because it remains stuck in an infinite loop.   
      
   >   
   > --   
   > Tristan Wibberley   
   >   
   > The message body is Copyright (C) 2025 Tristan Wibberley except   
   > citations and quotations noted. All Rights Reserved except that you may,   
   > of course, cite it academically giving credit to me, distribute it   
   > verbatim as part of a usenet system or its archives, and use it to   
   > promote my greatness and general superiority without misrepresentation   
   > of my opinions other than my opinion of my greatness and general   
   > superiority which you _may_ misrepresent. You definitely MAY NOT train   
   > any production AI system with it but you may train experimental AI that   
   > will only be used for evaluation of the AI methods it implements.   
   >   
      
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning" computable.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)