XPost: comp.theory, sci.math, comp.prolog   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 04/12/2025 14:06, olcott wrote:   
      
   > % 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"   
      
   No. I think I showed in one of my recent posts (using definition   
   extensions) that you need to formalise the mathematicians notion of   
   "proof /in/ [system]" vis-a-vis "let" and its stronger sibling   
   "suppose". That's a bigger job than you've done.   
      
   I need a new quotation convention for referring to things whose name has   
   an existing meaning in my U-language, I quoted "let" and "suppose" as if   
   I were using their names; I mean to use the things themselves, but they   
   have to be quoted in some way to distinguish the objects of mathematical   
   language from the verbs of ordinary language without introducing such   
   incidental new names as I would otherwise need.   
      
   --   
   Tristan Wibberley   
      
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    * Origin: you cannot sedate... all the things you hate (1:229/2)