XPost: comp.theory, sci.math, comp.prolog   
   From: polcott333@gmail.com   
      
   On 12/11/2025 2:40 AM, Mikko wrote:   
   > 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.   
   >   
      
   Kurt Gödel in his 1944 Russell's mathematical logic gave the following   
   definition of the "theory of simple types" in a footnote:   
      
   By the theory of simple types I mean the doctrine which says that the   
   objects of thought (or, in another interpretation, the symbolic   
   expressions) are divided into types, namely: individuals, properties of   
   individuals, relations between individuals, properties of such   
   relations, etc. (with a similar hierarchy for extensions), and that   
   sentences of the form: " a has the property φ ", " b bears the relation   
   R to c ", etc. are meaningless, if a, b, c, R, φ are not of types   
   fitting together.   
      
   The finite string "cats" is stipulated to have   
   the type_of_relation  to the finite string   
   "animals".   
      
   --   
   Copyright 2025 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)