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Ideas for 'Sweet Dreams', 'Lectures 1930-32 (student notes)' and 'Realistic Rationalism'

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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 / b. Against mathematical platonism

2521	'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz]
	Full Idea: Three objections to realism in philosophy of mathematics: mathematical objects have no space/time location, and so no causal role; that such objects are determinate, but reference to numbers aren't; and that there is no abstract/concrete distinction.
	From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxix)