XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   On 1/2/2026 2:15 AM, Tristan Wibberley wrote:   
   > On 02/01/2026 03:26, olcott wrote:   
   >> On 1/1/2026 8:38 PM, olcott wrote:   
   >>> On 1/1/2026 8:25 PM, Richard Damon wrote:   
   >>>> On 1/1/26 9:07 PM, olcott wrote:   
   >>>>> On 1/1/2026 4:12 PM, Tristan Wibberley wrote:   
   >>>>>> On 31/12/2025 23:27, Richard Damon wrote:   
   >>>>>>   
   >>>>>>> So, how do you think you can prove it in F?   
   >>>>>>   
   >>>>>> What does "F" refer to?   
   >>>>>>   
   >>>>>   
   >>>>> F ⊢ G_F ↔ ¬Prov_F(⌜G_F⌝)   
   >>>>> F proves that: G_F is equivalent to G_F is not provable in F   
   >>>>> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom   
   >>>>>   
   >>>>> ∃G ∈ WFF(F) (G ↔ (F ⊬ G))   
   >>>>> There exists a G in F that is logically   
   >>>>> equivalent to its own unprovability in F   
   >>>>>   
   >>>>> ∃G ∈ WFF(F) (G := (F ⊬ G))   
   >>>>> There exists a G in F that asserts its own unprovability in F   
   >>>>>   
   >>>>> The proof of G in F would seem to require a sequence   
   >>>>> of inference steps in F that prove that they themselves   
   >>>>> do not exist.   
   >>>>>   
   >>>>>   
   >>>>   
   >>>> But that isn't what G is in the proof, so you are just using a bad   
   >>>> reference.   
   >>>>   
   >>>   
   >>> That you do not know exactly how semantics works in   
   >>> linguistics (making sure to ignore all context) is   
   >>> not my mistake. The reason that Ludwig Wittgenstein   
   >>> was never understood is that none of his detractors   
   >>> understood how language itself really works. Not   
   >>> knowing how language really works results in   
   >>> undetected muddled thinking.   
   >>>   
   >>> ...We are therefore confronted with a proposition which   
   >>> asserts its own unprovability. 15 … (Gödel 1931:40-41)   
   >>>   
   >>> G asserts its own unprovability.   
   >>> Is what the above means semantically.   
   >>>   
   >>> The proof of G does semantically entail a sequence   
   >>> of inference steps that prove that they themselves   
   >>> do not exist.   
   >>>   
   >>   
   >> Ludwig Wittgenstein   
   >>   
   >> 8. I imagine someone asking my advice; he says:   
   >> "I have constructed a proposition (1 will use   
   >> 'P' to designate it) in Russell's symbolism,   
   >> and by means of certain definitions and   
   >> transformations it can be so interpreted that   
   >> it says: 'P is not provable in Russell's system'.   
   >   
   > False. He did not do that; he tried to do so then hallucinated that he   
   > succeeded. A contradiction follows from the negation of my   
   > characterisation of his actions and so from the truth of the proposition   
   > that he defined P so. That definitional proposition follows from the   
   > axioms of inconsistent systems and not from those of useful consistent   
   > ones. Typically it /is/ an axiom of inconsistent systems and not of   
   > consistent ones.   
   >   
   >   
      
   His paper is a convoluted mess hiding this simple fact   
   ...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   
      
   When we combine that with this:   
      
       Let {T} be such a theory. Then the elementary   
       statements which belong to {T} we shall call the   
       elementary theorems of {T}; we also say that   
       these elementary statements are true for {T}.   
       Thus, given {T}, an elementary theorem is an   
       elementary statement which is true.   
       https://www.liarparadox.org/Haskell_Curry_45.pdf   
   Foundations of Mathematical Logic 1977   
      
   Then Gödel simply made a very convoluted analog   
   to the Liar Paradox.   
      
   --   
   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   
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