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Ideas for 'fragments/reports', 'The Nature of Mathematics' and 'Word and Object'

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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics

9556	Nearly all of mathematics has to quantify over abstract objects [Quine]
	Full Idea: Mathematics, except for very trivial portions such as very elementary arithmetic, is irredeemably committed to quantification over abstract objects.
	From: Willard Quine (Word and Object [1960], §55)
	A reaction: Personally I would say that we are no more committed to such things than actors in 'The Tempest' are committed to the existence of Prospero and Caliban (which is quite a strong commitment, actually).

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.