XPost: sci.math, comp.theory   
   From: acm@muc.de   
      
   [ Followup-To: set ]   
      
   In comp.theory Tristan Wibberley   
    wrote:   
   > On 15/02/2026 01:41, Richard Damon wrote:   
   >> On 2/14/26 3:59 PM, polcott wrote:   
      
   [ .... ]   
      
   >>> So it looks like you are saying that no one can count   
   >>> until after they first count to infinity?   
      
   >> No, he is pointing out that if you claim to encode ALL the knowledge   
   >> that is expressible in language, you can't stop until you finish, and   
   >> since there are an infinite number of those in Peano Arithmetic, you   
   >> can't stop at any finite number.   
      
   > You're talking about decompressing the encoding of knowledge. Stating   
   > the axioms (and full detail of inference rules) symbolically is   
   > sufficient to /encode/ the knowledge if you have lambda calculus or   
   > illative combinatory logic.   
      
   Olcott's system, by his own admission, is insufficiently powerful to   
   express a true proposition it can't prove.  Thus Peano arithmetic is   
   outside of its scope.  You can't count in Olcott's system.   
      
   > --   
   > Tristan Wibberley   
      
   --   
   Alan Mackenzie (Nuremberg, Germany).   
      
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