Single Idea 8297

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers]

Full Idea

My view is that numbers are universals, beings kinds of sets (that is, kinds whose particular instances are individual sets of appropriate cardinality).

Gist of Idea

Numbers are universals, being sets whose instances are sets of appropriate cardinality

Source

E.J. Lowe (The Possibility of Metaphysics [1998], 10)

Book Reference

Lowe,E.J.: 'The Possibility of Metaphysics' [OUP 2001], p.210


A Reaction

[That is, 12 is the set of all sets which have 12 members] This would mean, I take it, that if the number of objects in existence was reduced to 11, 12 would cease to exist, which sounds wrong. Or are we allowed imagined instances?