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Ideas for 'A Puzzle about Belief', 'Introduction to the Philosophy of Mind' and 'works'

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2 ideas

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem

10232	Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro]
	Full Idea: Cantor's theorem entails that there are more property extensions than objects. So there are not enough objects in any domain to serve as extensions for that domain. So Frege's view that numbers are objects led to the Caesar problem.
	From: report of George Cantor (works [1880]) by Stewart Shapiro - Philosophy of Mathematics 4.6
	A reaction: So the possibility that Caesar might have to be a number arises because otherwise we are threatening to run out of numbers? Is that really the problem?

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

18176	Pure mathematics is pure set theory [Cantor]
	Full Idea: Pure mathematics ...according to my conception is nothing other than pure set theory.
	From: George Cantor (works [1880], I.1), quoted by Penelope Maddy - Naturalism in Mathematics I.1
	A reaction: [an unpublished paper of 1884] So right at the beginning of set theory this claim was being made, before it was axiomatised, and so on. Zermelo endorsed the view, and it flourished unchallenged until Benacerraf (1965).