more from E.J. Lowe

Single Idea 8266

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle]

Full Idea

That one-to-one correlated sets of objects are equinumerous is a more sophisticated achievement than the simple ability to count sets of objects.

Gist of Idea

Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous


E.J. Lowe (The Possibility of Metaphysics [1998], 2.9)

Book Reference

Lowe,E.J.: 'The Possibility of Metaphysics' [OUP 2001], p.49

A Reaction

This is an objection to Frege's way of defining numbers, in terms of equinumerous sets. I take pattern-recognition to be the foundation of number, and so spotting a pattern would have to precede spotting that two patterns were identical.