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Ideas for 'fragments/reports', 'Contemporary theories of Knowledge (2nd)' and 'Remarks on axiomatised set theory'

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6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics

17880	Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]
	Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind.
	From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299)
	A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers.

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

17881	Mathematician want performable operations, not propositions about objects [Skolem]
	Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that.
	From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300)