XPost: comp.theory, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   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.   
      
      
   --   
   Tristan Wibberley   
      
   The message body is Copyright (C) 2025 Tristan Wibberley except   
   citations and quotations noted. All Rights Reserved except that you may,   
   of course, cite it academically giving credit to me, distribute it   
   verbatim as part of a usenet system or its archives, and use it to   
   promote my greatness and general superiority without misrepresentation   
   of my opinions other than my opinion of my greatness and general   
   superiority which you _may_ misrepresent. You definitely MAY NOT train   
   any production AI system with it but you may train experimental AI that   
   will only be used for evaluation of the AI methods it implements.   
      
   --- SoupGate-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)