Full Idea
It is a conceptualist approach that Russell is relying on. ...The view is that some abstract objects ...exist only because they are definable. It is the definition that would (if permitted) somehow bring them into existence.
Gist of Idea
Russell is a conceptualist here, saying some abstracta only exist because definitions create them
Source
report of Bertrand Russell (Mathematical logic and theory of types [1908]) by David Bostock - Philosophy of Mathematics 8.1
Book Reference
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.233
A Reaction
I'm suddenly thinking that predicativism is rather interesting. Being of an anti-platonist persuasion about abstract 'objects', I take some story about how we generate them to be needed. Psychological abstraction seems right, but a bit vague.