XPost: comp.theory, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 03/01/2026 18:51, Richard Damon wrote:   
   > On 1/3/26 12:35 PM, Tristan Wibberley wrote:   
   >> On 02/01/2026 16:06, Richard Damon wrote:   
   >>>> You have to derive the statement from the axioms of the system using   
   >>>> the   
   >>>> deduction rules of the system. It's the actual definition of   
   >>>> "Theorem of   
   >>>> a Formal System".   
   >>>   
   >>> And the statement G was.   
   >>   
   >> Then a system can be complete.   
   >>   
   >>   
   >   
   > No, because the derivation isn't finite, so isn't a proof.   
   >   
   > It seems you are stuck in a finite world, in a logic that is infinite.   
      
   You mean its a fixed point that terminates at G but doesn't start?   
   Non-constructive? It's reverse derivation (computation of its valuation)   
   doesn't halt? (cue Olcott re. occurs check).   
      
   I'm certain Gödel thought he hadn't produced an inconsistent system. It   
   is supposed to be /consistent/ and in-completable, not /inconsistent/ so   
   who cares.   
      
      
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   Tristan Wibberley   
      
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