Full Idea
Frege decided that all logical objects, or at least all those needed for mathematics, could be defined by logical abstraction, except the classes needed for such definitions. ..This definition by equivalence classes has been adopted as a standard device.
Gist of Idea
Frege introduced the standard device, of defining logical objects with equivalence classes
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §64-68) by Michael Dummett - Frege philosophy of mathematics
Book Reference
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.233
A Reaction
This means if we are to understand modern abstraction (instead of the psychological method of ignoring selected properties of objects), we must understand the presuppositions needed for a definition by equivalence.