display all the ideas for this combination of texts
3 ideas
| 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. |
| 14648 | Could I name all of the real numbers in one fell swoop? Call them all 'Charley'? [Plantinga] |
| Full Idea: Can't I name all the real numbers in the interval (0,1) at once? Couldn't I name them all 'Charley', for example? | |
| From: Alvin Plantinga (De Re and De Dicto [1969], p.40) | |
| A reaction: Plantinga is nervous about such a sweeping move, but can't think of an objection. This addresses a big problem, I think - that you are supposed to accept the real numbers when we cannot possibly name them all. |
| 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. |