XPost: comp.theory, sci.math, comp.prolog   
   From: mikko.levanto@iki.fi   
      
   olcott kirjoitti 10.12.2025 klo 18.29:   
   > On 12/10/2025 4:10 AM, Mikko wrote:   
   >> olcott kirjoitti 8.12.2025 klo 21.12:   
   >>> On 12/5/2025 4:49 AM, Tristan Wibberley wrote:   
   >>>> 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.   
   >>   
   >>> Semantics tautologies that define finite strings in   
   >>> terms of other finite strings to give the LHS its   
   >>> semantic meaning on the basis of the RHS.   
   >>   
   >> You havn't given a single example of a smenatic tautology that can be   
   >> interpreted as a definition nor a single example of defintion that is   
   >> a semantic tautology. Perhaps it is possible if you define "semantic   
   >> taultology" so that it needn't be anything like a tautology.   
   >   
   >  From my signature line:   
   > "true on the basis of meaning expressed in language"   
   >   
   > Here is an example: "cats"  "animals"   
      
   Yes, that is an example of your inability mentioned above.   
      
   Your example not define anything and therefore is neither an exmaple   
   of a semantic tautology that can be interpreted as a defintion nor an   
   axample of a defintion that is a semantic tautology.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)