more from Michèle Friend

Single Idea 8677

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

Full Idea

As a realist choice of what is basic in mathematics, set theory is rather clever, because it only makes a very simple ontological claim: that, independent of us, there exists the empty set. The whole hierarchy of finite and infinite sets then follows.

Gist of Idea

Set theory makes a minimum ontological claim, that the empty set exists


Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.3)

Book Reference

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.32

A Reaction

Even so, for non-logicians the existence of the empty set is rather counterintuitive. "There was nobody on the road, so I overtook him". See Ideas 7035 and 8322. You might work back to the empty set, but how do you start from it?

Related Ideas

Idea 7035 God does not create the world, and then add the classes [Heil]

Idea 8322 I don't believe in the empty set, because (lacking members) it lacks identity-conditions [Lowe]