Full Idea
Although (in Cantor and Dedekind) abstraction does not (as has often been observed) play any role in their proofs, but it does play a role, in that it fixes the grammar, the domain of meaningful propositions, and so determining the objects in the proofs.
Gist of Idea
Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs
Source
William W. Tait (Frege versus Cantor and Dedekind [1996], V)
Book Reference
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.47
A Reaction
[compressed] This is part of a defence of abstractionism in Cantor and Dedekind (see K.Fine also on the subject). To know the members of a set, or size of a domain, you need to know the process or function which created the set.