From: borkent@cs.utwente.nl   
      
   > Can someone give an example of something in world, that can't be easily   
   > described by predicate logic, or something which is computationally hard   
   to   
   > handle?   
      
   I think predicate logic is not strong enough to do higher order abstraction   
   like:   
      
   You can say this in predicate logic (proof by induction to n):   
      
   P(n) <-> "some fact has been proven for n"   
   P(0). Induction hypothesis.   
   For all n: P(n) -> P(n+1)   
      
   This demonstrates the idea of proving by induction.   
      
   But now we want to abstract from all predicates and say something like:   
      
   for all predicates P:   
   P(n) <-> "some fact has been proven" etc etc   
      
   We can't quantify over the Predicate symbols, only over variables, this is   
   the weakness I think.   
      
   Another problem arises with self-reference. We can't put something like this   
   in logic: "This sentence is not true".   
      
   Please correct my thoughts if I have said anything that is not quite   
   applicable here (I am not a master student in logic or smth).   
      
   Greetings,   
   Michiel Borkent   
      
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