XPost: comp.theory, sci.logic, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   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.   
      
      
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   Tristan Wibberley   
      
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