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Ideas for 'Structures and Structuralism in Phil of Maths', 'The Source of Necessity' and 'Action'

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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

10166	ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
	Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements.
	From: 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?