FOM: Goedel: truth and misinterpretations

Torkel Franzen torkel at
Wed Nov 1 02:07:48 EST 2000

  V.Kanovei says. with reference to

   (1)  Even if Goldbach's conjecture is true, it is not necessarily
        provable in ZFC
   >To be scientifically considerable, "thesis" (1) has to be 
   >preceded by at least explanation, if not a rigorous definition, 
   >what is the intended meaning of "true". That has not been made 
   >clear in the course of the discussion.

  I'm a bit surprised by this comment, since I have explicitly stated
that "Goldbach's conjecture is true" in (1) is equivalent to
Goldbach's conjecture itself. That is, (1) says exactly the same thing

   (2) Even if every even number greater than 2 is the sum of two
       primes, this is not necessarily provable in ZFC.

   You have a difficulty, then, with the use of Goldbach's conjecture
in a context such as (2). Can you explain the nature of this
difficulty?  It is insufficient to merely *claim* that we cannot
meaningfully say such things as "every even number greater than 2 is
the sum of two primes" except in certain restricted types of context,
such as "it has been mathematically proved that ...".


  Torkel Franzen

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