FOM: Goedel: truth and misinterpretations

Torkel Franzen torkel at
Tue Oct 24 03:31:04 EDT 2000

 V.Kanovei says:

  >Now, how can it be claimed that any given mathematical 
  >statement is either true or false? 
  >Not, and exactly by a very 
  >elementary reason: the Structure is not fully determined.

  Sure, but that's no obstacle to statements that refer only to a
determinate part of that indeterminate structure being determinately
true or false.

  >Any further reference to "true but not provable" is a misconception, 
  >whose philosophical nature is the misidentification of the 
  >Human and ZFC-dweller as Observers.

  That's a very odd statement, since after all it is mathematically
provable that if ZFC is consistent then there is a true arithmetical
sentence A such that the canonical translation A* of A into the
language of ZFC is not a theorem of ZFC. Apparently you don't regard
this particular result as even meaningful. Why not?

  >Since Euclid, "we *know*" well that a mathematical statement is true  
  >if there is a (mathematically sound) PROOF of the statement -- this 
  >is by the way why Mathematics has been called EXACT science.

  Right, but what is your view of the axioms used in this proof?


  Torkel Franzen, University of Luleå

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