more from E.J. Lowe

Single Idea 4241

[catalogued under 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism]

Full Idea

The Peano postulates imply an infinity of numbers, but there are probably not infinitely many concrete objects in existence, so natural numbers must be abstract objects.

Gist of Idea

If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects


E.J. Lowe (A Survey of Metaphysics [2002], p.375)

Book Reference

Lowe,E.J.: 'A Survey of Metaphysics' [OUP 2002], p.375

A Reaction

Presumably they are abstract objects even if they aren't universals. 'Abstract' is an essential term in our ontological vocabulary to cover such cases. Perhaps possible concrete objects are infinite.