### Single Idea 8907

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

Full Idea

We can abstract the direction of a line by taking the direction as the equivalence class of that line and all lines parallel to it. There is no subtraction of detail, but a multiplication of it; by swamping it, the specifics of the original line get lost.

Gist of Idea

The abstract direction of a line is the equivalence class of it and all lines parallel to it

Source

David Lewis (On the Plurality of Worlds [1986], 1.7)

Book Reference

Lewis,David: 'On the Plurality of Worlds' [Blackwell 2001], p.85

A Reaction

You can ask how wide a line is, but not how wide a direction is, so a detail IS being subtracted. I don't see how you can define the concept of a banana by just saying it is 'every object which is equivalent to a banana'. 'Parallel' is an abstraction.