[igiveup]

Thanks, clear.

Though, I think my example was misunderstood. I meant, why is it a problem that there is no set meeting Russell's definition, but not a problem that there is no number meeting my definition. The example would violate an axiom if there was an axiom like:

  To every definition of a certain kind about natural numbers, there is a number which satisfies it.

Which of course would be rather useless, while the unrestricted comprehension axiom is necessary for the rest of the theory.