XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 12/29/2025 12:24 PM, Richard Damon wrote:   
   > On 12/29/25 11:27 AM, olcott wrote:   
   >> 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 ...   
   >   
   > Yes, but "close relationship" doesn't mean is the same as.   
   >   
   >> ...14 Every epistemological antinomy can likewise be used for a   
   >> similar undecidability proof...   
   >   
   > Right, but that doesn't mean he derives directly from the liar.   
   >   
   >> ...We are therefore confronted with a proposition which asserts its   
   >> own unprovability. 15 … (Gödel 1931:40-41)   
   >   
   > Right, in the meta-system that understands the encoded meaning that the   
   > PRR understands.   
   >   
   > But that meaning is NOT in the base system.   
   >   
   >>   
   >> 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(...))))))))   
   >>   
   >   
   > Which proves nothing about Godel and his G, as he doesn't "derive" from   
   > the liars paradox, but uses its general form but with a transformation   
   > that breaks the actual contraditction in the epistemological antinomy,   
   > because there IS a resolution, the statement is True but Unprovable.   
      
      
   ...14 Every epistemological antinomy can likewise be   
   used for a similar undecidability proof...   
      
   The Liar Paradox is an epistemological antinomy.   
   Your inability to pay 100% complete attention to the   
   exact meaning of words never has been my mistake.   
      
      
   --   
   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)