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Ideas for 'Structures and Structuralism in Phil of Maths', 'Some Judgements of Perception' and 'Which Logic is the Right Logic?'

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2 ideas

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?

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

10775	The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp]
	Full Idea: The main objection to the axiom of choice was that it had to be given by some law or definition, but since sets are arbitrary this seems irrelevant. Formalists consider it meaningless, but set-theorists consider it as true, and practically obvious.
	From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3)