XPost: comp.theory, sci.math   
   From: polcott333@gmail.com   
      
   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'.   
      
      
   Must I not say that this proposition on the one   
   hand is true, and on the other hand is unprovable?   
   For suppose it were false; then it is true that   
   it is provable. And that surely cannot be And   
   if it is proved, then it is proved that it is   
   not provable. Thus it can only be true, but   
   unprovable. " Just as we ask: " 'provable'   
   in what system?", so we must also ask:"   
   'true' in what system?" 'True in Russell's system'   
   means, as was said: proved in Russell's system;   
   and 'false in Russell's system' means: the   
   opposite has been proved in Russell's system   
      
   --   
   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)