XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/29/2025 1:23 PM, Richard Damon wrote:   
   > On 12/29/25 1:37 PM, olcott wrote:   
   >> 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.   
   >>   
   >>   
   >   
   > Right, But the FORM of the Liars Paradox, that "X is defined to be X is   
   > not True", can be transformed by a syntactic transformation that changes   
   > its meaning to "X is defined to be X is not Provable".   
   >   
   > Since Provable is NOT the same predicate as True, this changes its   
   > meaning, and makes it only an APPARENT contradiction, as there is a   
   > valid realization of the statement with X actually being True, but also   
   > not being Provable.   
   >   
      
   This has always only been complete ignorance   
   of the deep meaning of: unify_with_occurs_check()   
      
   Ungrounded is a term that computer scientists,   
   mathematicians and logicians never heard of thus   
   they conclude it is complete nonsense on the   
   basis of their own ignorance.   
      
   > By the definitions of the two terms, this means that X logically follows   
   > from the fundamental truth makers of the system, but onlyl with an   
   > infinite number of inferences.   
   >   
   > THe fact that YOU can't understand this, or even comment about where you   
   > think this is wrong, just shows your inability to THINK about the topic.   
   >   
   > Your problem is YOU don't know the meaning for the words, but are   
   > beleiving your own lies about them, and by your refusal to learn the   
   > actual meanings have made yourself a pathological liar.   
      
      
   --   
   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)