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

Source

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]**