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Ideas for 'Parmenides', 'Lectures 1930-32 (student notes)' and 'Grundrisse'

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3 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

18738	We don't get 'nearer' to something by adding decimals to 1.1412... (root-2) [Wittgenstein]
	Full Idea: We say we get nearer to root-2 by adding further figures after the decimal point: 1.1412.... This suggests there is something we can get nearer to, but the analogy is a false one.
	From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], Notes)

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite

18708	Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein]
	Full Idea: 'Infinite' is not an answer to the question 'How many?', since the infinite is not a number. ...Infinity is the property of a law, not of an extension.
	From: Ludwig Wittgenstein (Lectures 1930-32 (student notes) [1931], A VII.2)

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.