XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 20/01/2026 23:08, Tristan Wibberley wrote:   
   > On 18/01/2026 23:41, olcott wrote:   
   >   
   >> I already just said that the proof and refutation of   
   >> Goldbach are outside the scope of PA axioms.   
   >   
   > So Richard is right that you need a truth value for not being covered:   
   >   
   > True(S, Goldbach) = OutOfScope   
      
      
   Oh ho! but is Goldbach definable as a shortcode for a statement of the   
   goldbach conjecture in PA? If there's no such statement then it's out of   
   scope without a truth value for that.   
      
   In addition to equality, it requires negation, either forall or exists,   
   either conjunction or disjunction... but my memory says not all of those   
   are available in PA in sufficient generality! Oh if only my brain worked   
   as well as it once did I could work this through in a sitting, instead I   
   get mentally disorganised.   
      
   --   
   Tristan Wibberley   
      
   The message body is Copyright (C) 2026 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-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)