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Ideas for 'On the Heavens', 'Review of Bob Hale's 'Abstract Objects'' and 'The Nature of Mathematics'

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2 ideas

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

9183	Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist [Williamson]
	Full Idea: The Fregean argument for platonism is that some true assertions contain singular terms which denote abstract objects if they denote anything; since the assertions are true, the singular terms denote.
	From: Timothy Williamson (Review of Bob Hale's 'Abstract Objects' [1988])
	A reaction: I am perplexed that anyone would rest their view of reality on such an argument. The obvious comparison would be with true remarks about blatantly fictional characters, or blatantly invented concepts such as 'checkmate'.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

14788	Mathematics is close to logic, but is even more abstract [Peirce]
	Full Idea: The whole of the theory of numbers belongs to logic; or rather, it would do so, were it not, as pure mathematics, pre-logical, that is, even more abstract than logic.
	From: Charles Sanders Peirce (The Nature of Mathematics [1898], IV)
	A reaction: Peirce seems to flirt with logicism, but rejects in favour of some subtler relationship. I just don't believe that numbers are purely logical entities.