more from James Robert Brown

Single Idea 9610

[catalogued under 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism]

Full Idea

Numbers are not 'abstract' (in the old sense, of universals abstracted from particulars), since each of the integers is a unique individual, a particular, not a universal.

Gist of Idea

Numbers are not abstracted from particulars, because each number is a particular


James Robert Brown (Philosophy of Mathematics [1999], Ch. 2)

Book Reference

Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.12

A Reaction

An interesting observation which I have not seen directly stated before. Compare Idea 645. I suspect that numbers should be thought of as higher-order abstractions, which don't behave like normal universals (i.e. they're not distributed).

Related Ideas

Idea 645 If two is part of three then numbers aren't Forms, because they would all be intermingled [Aristotle]

Idea 8311 If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2 [Lowe]