XPost: comp.theory, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 02/01/2026 00:21, Richard Damon wrote:   
      
   > It started as a statement, and then was proven true in the system (but   
   > not by the system).   
   >   
   > What else do you need to make it a Theorem?   
      
      
   You have to derive the statement from the axioms of the system using the   
   deduction rules of the system. It's the actual definition of "Theorem of   
   a Formal System".   
      
   Deriving it or other demonstration in your choice of alternative system   
   does not make it a theorem of the base-system.   
      
   --   
   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.   
      
   --- SoupGate-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)