### Single Idea 15443

#### [catalogued under 18. Thought / E. Abstraction / 7. Abstracta by Equivalence]

Full Idea

When mathematicians abstract one thing from others, they take an equivalence class. ....But it is only superficially a one; underneath, a class are still many.

Gist of Idea

Mathematicians abstract by equivalence classes, but that doesn't turn a many into one

Source

David Lewis (Against Structural Universals [1986], 'The pictorial')

Book Reference

Lewis,David: 'Papers in Metaphysics and Epistemology' [CUP 1999], p.93

A Reaction

This is Frege's approach to abstraction, and it is helpful to have it spelled out that this is a mathematical technique, even when applied by Frege to obtaining 'direction' from classes of parallels. Too much philosophy borrows inappropriate techniques.