Full Idea
Husserl saw that abstracted units, though featureless, must in some way retain their distinctness, some shadowy remnant of their objects. So he wanted to correlate like-numbered sets, not just register their identity, but then abstractionism fails.
Gist of Idea
Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them
Source
comment on Edmund Husserl (Philosophy of Arithmetic [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.12
Book Reference
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.146
A Reaction
Abstractionism is held to be between the devil and the deep blue sea, of depending on units which are identifiable, when they are defined as devoid of all individuality. We seem forced to say that the only distinction between them is countability.