XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 12/29/2025 10:04 AM, Tristan Wibberley wrote:   
   > On 28/12/2025 13:49, olcott wrote:   
   >   
   >> ...We are therefore confronted with a proposition which   
   >> asserts its own unprovability. 15 … (Gödel 1931:40-41)   
   >>   
   >> According to Gödel this last line sums up his whole proof.   
   >> Thus the essence of his G is correctly encoded below:   
   >>   
   >> ?- G = not(provable(F, G)).   
   >> G = not(provable(F, G)).   
   >   
   > You mean "therefore the essence ..." or else "... G is, by his   
   > standards, correctly encoded..."   
   >   
   >   
   >> Gödel, Kurt 1931.   
   >> On Formally Undecidable Propositions of Principia   
   >> Mathematica And Related Systems   
   >   
   > He uses = as a shorthand for an asymmetric relation that he credits to   
   > PM. I have a copy of PM 1st edition here; it does /not/ define equality   
   > that way.   
   >   
   > His system also has a number ("individual") available in universal   
   > quantification over individuals that is indefinite *and* that indefinite   
   > number supposedly maps to a unique formula along with the other   
   > individuals (despite all formulas being finite! O.o). I'm deeply   
   > suspicious but the paper is so unreasonably difficult that I'm minded   
   > not to bother going on studying it.   
   >   
   >   
      
   Yet the essence of what he is saying is boiled down   
   to something much simpler as he says in his own words:   
      
   ...there is also a close relationship with the “liar” antinomy,14 ...   
   ...14 Every epistemological antinomy can likewise be used for a similar   
   undecidability proof...   
   ...We are therefore confronted with a proposition which asserts its own   
   unprovability. 15 … (Gödel 1931:40-41)   
      
   Gödel, Kurt 1931.   
   On Formally Undecidable Propositions of Principia Mathematica And   
   Related Systems   
      
   The Liar Paradox is an epistemological antinomy.   
      
   This sentence is not true.   
   It is not true about what?   
   It is not true about being not true.   
   It is not true about being not true about what?   
   It is not true about being not true about being not true.   
   Oh I see you are stuck in a loop!   
      
   The simple English shows that the Liar Paradox never   
   gets to the point. It is ungrounded in a truth value.   
      
   This is formalized in the Prolog programming language   
   ?- LP = not(true(LP)).   
   LP = not(true(LP)).   
   ?- unify_with_occurs_check(LP, not(true(LP))).   
   False.   
      
   Expands to: not(true(not(true(not(true(not(true(...))))))))   
      
   --   
   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-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)