Single Idea 8970

[catalogued under 9. Objects / F. Identity among Objects / 1. Concept of Identity]

Full Idea

Our conceptual grip on the notion of a set is founded on the axiom of extensionality: a set x is the same as a set y iff x and y have the same members. But this axiom deploys the notion of absolute identity ('same members').

Gist of Idea

Our notion of identical sets involves identical members, which needs absolute identity

Source

John Hawthorne (Identity [2003], 3.1)

Book Reference

'The Oxford Handbook of Metaphysics', ed/tr. Loux,M /Zimmerman,D [OUP 2005], p.112


A Reaction

Identity seems to be a primitive, useful and crucial concept, so don't ask what it is. I suspect that numbers can't get off the ground without it (especially, in view of the above, if you define numbers in terms of sets).