XPost: comp.theory, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 02/01/2026 03:09, Richard Damon wrote:   
      
   > I guess it depends on your definition of a "Theorem".   
   >   
   > I am using the one that goes:   
   >   
   > "A Theorem is a statement that has been proven."   
   >   
   > note, no restriction that the proof was in the system the Theorem is   
   > stated in, as long as the proof shows that it is actually True in that   
   > system.   
   >   
   > Do you have a source that limits the proof to the system in question?   
   >   
   > Perhaps this is just a diffence of schools of logic.   
      
      
   See Curry and Feys Combinatory Logic 1, Chapters 0-2. The term is well   
   defined as it applies to formal systems. It's out of copyright and   
   available online.   
      
   Informal logic is another matter, where "theorem" /may/ be taken to mean   
   what you thought and where mistakes are commonplace, and pretty-much   
   inevitable.   
      
   "Truth" is not part of formal systems except in AI where personal   
   intuitive philosophy is computationally modelled. "Truth" is personal as   
   any spiritualist can attest.   
      
      
   --   
   Tristan Wibberley   
      
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