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2 ideas
| 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. |
| 5399 | Maths is not known by induction, because further instances are not needed to support it [Russell] |
| Full Idea: If induction was the source of our mathematical knowledge, we should proceed differently. In fact, a certain number of instances make us think of two abstractly, and we then see the general principle, and further instances become unnecessary. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: In practice, of course, we stop checking whether the sun has come up yet again this morning. Russell's point is better expressed as: if contradictory evidence were observed, we would believe the arithmetic and doubt the experience. |