more from David M. Armstrong

Single Idea 18392

[catalogued under 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units]

Full Idea

Classes, because they have a particular cardinality, are essentially a certain number of ones, things that, within the particular class, are each taken as a unit.

Gist of Idea

Classes have cardinalities, so their members must all be treated as units


David M. Armstrong (Truth and Truthmakers [2004], 09.1)

Book Reference

Armstrong,D.M.: 'Truth and Truthmakers' [CUP 2004], p.114

A Reaction

[Singletons are exceptions] So units are basic to set theory, which is the foundations of technical analytic philosophy (as well as, for many, of mathematics). If you can't treat something as a unit, it won't go into set theory. Vagueness...

Related Idea

Idea 18396 The set theory brackets { } assert that the member is a unit [Armstrong]