Single Idea 9149

[catalogued under 18. Thought / E. Abstraction / 2. Abstracta by Selection]

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]