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2 ideas
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? |
18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
Full Idea: For Boolos, the Replacement Axioms go beyond the iterative conception. | |
From: report of George Boolos (The iterative conception of Set [1971]) by Penelope Maddy - Naturalism in Mathematics I.3 |