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Ideas for 'Parmenides', 'Critical Common-Sensism' and 'The Nature of Mathematics'

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2 ideas

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

16150	One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]
	Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it.
	From: Plato (Parmenides [c.364 BCE], 144a)
	A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed.

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.