Combining Texts

Ideas for 'Letters to Bentley', 'A Study of Concepts' and 'Beyond Individualism'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers

13152	We can talk of 'innumerable number', about the infinite points on a line [Newton]
	Full Idea: If any man shall take the words number and sum in a larger sense, to understand things which are numberless and sumless (such as the infinite points on a line), I could allow him the contradictious phrase 'innumerable number' without absurdity.
	From: Isaac Newton (Letters to Bentley [1692], 1693.02.25)
	A reaction: [compressed] I take the key point here to be the phrase of taking number 'in a larger sense'. Like the word 'atom' in physics, the word 'number' retains its traditional reference, but has considerably shifted its scope. Amateurs must live with this.

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

13151	Not all infinites are equal [Newton]
	Full Idea: It is an error that all infinites are equal.
	From: Isaac Newton (Letters to Bentley [1692], 1693.01.17)
	A reaction: There follows a discussion of the mathematicians' view of infinity. Cantor was not the first to notice that there is more than one sort of of infinity.