Full Idea
The uncompromising abstractionist rejects set theory, seeing the theory of abstractions as an alternative, rather than as a supplement, to the standard theory of sets.
Gist of Idea
Abstractionism can be regarded as an alternative to set theory
Source
Kit Fine (The Limits of Abstraction [2002], I.1)
Book Reference
Fine,Kit: 'The Limits of Abstraction' [OUP 2008], p.10
A Reaction
There is also a 'compromising' version. Presumably you still have equivalence classes to categorise the objects, which are defined by their origin rather than by what they are members of... Cf. Idea 10145.
Related Idea
Idea 10145 Abstracts cannot be identified with sets [Fine,K]