### Single Idea 14239

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

Full Idea

The empty set is usually derived via Zermelo's axiom of separation. But the axiom of separation is conditional: it requires the existence of a set in order to generate others as subsets of it. The original set has to come from the axiom of infinity.

Gist of Idea

The empty set is usually derived from Separation, but it also seems to need Infinity

Source

Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2)

Book Reference

'Metaphysics (Philosophical Perspectives 20)', ed/tr. Hawthorne,John [Blackwell 2006], p.127

A Reaction

They charge that this leads to circularity, as Infinity depends on the empty set.

Related Ideas

Idea 13486
Not every predicate has an extension, but Separation picks the members that satisfy a predicate **[Zermelo, by Hart,WD]**

Idea 13037
Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) **[Kunen]**