 be a set", i.e. there really are 
&gt;proper classes, and the paradoxes arise when they are mistaken for sets. 

When it comes to sets, I'm an agnostic.  I'm not happy with
the fact that all of the hierarchies of uncountable sets depend
on a single proof by contradiction:  Cantor's diagonalization
method.  I don't go as far as the intuitionists in ruling out
all proofs by contradiction, but I agree with Whitehead that
it is very dangerous to try to establish a positive result
by such arguments.

Whitehead'