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
Source
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.