more from E Reck / M Price

### Single Idea 10166

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets]

Full Idea

In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements.

Clarification

The prefix 'ur' means 'basic'

Gist of Idea

ZFC set theory has only 'pure' sets, without 'urelements'

Source

E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)

A Reaction

The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do?