Full Idea
In abstracting from the elements of a doubleton to obtain 2, we do not wish to abstract away from all features of the objects. We wish to take account of the fact that the two objects are distinct; this alone should be preserved under abstraction.
Clarification
A 'doubleton' is a set with two members
Gist of Idea
To obtain the number 2 by abstraction, we only want to abstract the distinctness of a pair of objects
Source
Kit Fine (Cantorian Abstraction: Recon. and Defence [1998], §3)
Book Reference
-: 'Journal of Philosophy' [-], p.10
A Reaction
This is Fine's strategy for meeting Frege's objection to abstraction, summarised in Idea 9146. It seems to use the common sense idea that abstraction is not all-or-nothing. Abstraction has degrees (and levels).
Related Idea
Idea 9146 After abstraction all numbers seem identical, so only 0 and 1 will exist! [Fine,K]