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Full Idea
The idea is that the same set may well have different canonical specifications, i.e. there may be different ways of stating its membership conditions, and so long as one of these is predicative all is well. If none are, the supposed set does not exist.
Gist of Idea
A set does not exist unless at least one of its specifications is predicative
Source
report of Bertrand Russell (Mathematical logic and theory of types [1908]) by David Bostock - Philosophy of Mathematics 8.1
Book Ref
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.230