XPost: comp.theory   
   From: polcott333@gmail.com   
      
   On 11/16/2025 7:45 PM, Tristan Wibberley wrote:   
   > On 17/11/2025 00:52, olcott wrote:   
   >> On 11/16/2025 1:11 PM, Tristan Wibberley wrote:   
   >>> On 16/11/2025 01:29, olcott wrote:   
   >>>> G ↔ ¬Prov(⌜G⌝)   
   >>>> Directed Graph of evaluation sequence   
   >>>> 00 ↔               01 02   
   >>>> 01 G   
   >>>> 02 ¬               03   
   >>>> 03 Prov            04   
   >>>> 04 Gödel_Number_of 01  // cycle   
   >>>   
   >>>   
   >>> I would argue that ⊢ G := ¬Prov(⌜G⌝) is not a theorem. Before you   
   find   
   >>> that a value of G exists (so that you may evaluate G) you must first   
   >>> find that the statement defining G is a theorem.   
   >>>   
   >>   
   >> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom   
   >> It is the G sentence of the first incompleteness theorem.   
   >>   
   >> ?- G = not(provable(F, G)).   
   >> G = not(provable(F, G)).   
   >>   
   >> ?- unify_with_occurs_check(G, not(provable(F, G))).   
   >> false.   
   >>   
   >> It has a cycle proving that it cannot be resolved   
   >> because it remains stuck in an infinite loop.   
   >   
   >   
   > A proposition that claims G so defined is not a theorem, therefore G is   
   > not so defined. It is not a theorem based on proof by contradiction:   
   >   
   >   
   > Suppose a proposition   
   > derive absurdity from it   
   > conclude the proposition is not a theorem   
   >   
   >   
   > Suppose G := not(provable(F, G))   
   > derive absurdity (G contradicts itself)   
   > conclude G :≠ not(provable(F,G))   
   >   
      
   https://en.wikipedia.org/wiki/List_of_logic_symbols   
   G := (F ⊬ G)   
      
   Means G "is defined as" (F ⊬ G)   
      
   >   
   > We're not about to say that proof by contradiction is invalid.   
   >   
   >   
      
   It turns out that absurdity is the basis of the   
   1931 incompleteness theorem.   
      
   *You simply erased my proof of this*   
   https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom   
   It is the G sentence of the first incompleteness theorem.   
      
   > --   
   > Tristan Wibberley   
   >   
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   >   
      
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning" computable.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)