Single Idea 8322

[catalogued under 4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set]

Full Idea

It is not clear to me that the empty set has well-defined identity-conditions. A set has these only to the extent that its members do - but the empty set has none.

Gist of Idea

I don't believe in the empty set, because (lacking members) it lacks identity-conditions

Source

E.J. Lowe (The Possibility of Metaphysics [1998], 12.3 n8)

Book Reference

Lowe,E.J.: 'The Possibility of Metaphysics' [OUP 2001], p.254


A Reaction

The empty set is widely used by those who base their metaphysics of maths on sets. It defines zero, and hence is the starting poing for Peano's Postulates (Idea 5897). It might not have identity in itself, but you know where you have arrived after 2 - 2.

Related Idea

Idea 5897 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew]