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3 ideas
| 18079 | Newton developed a kinematic approach to geometry [Newton, by Kitcher] |
| Full Idea: The reduction of the problems of tangents, normals, curvature, maxima and minima were effected by Newton's kinematic approach to geometry. | |
| From: report of Isaac Newton (Principia Mathematica [1687]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.1 | |
| A reaction: This approach apparently contrasts with that of Leibniz. |
| 18082 | Quantities and ratios which continually converge will eventually become equal [Newton] |
| Full Idea: Quantities and the ratios of quantities, which in any finite time converge continually to equality, and, before the end of that time approach nearer to one another by any given difference become ultimately equal. | |
| From: Isaac Newton (Principia Mathematica [1687], Lemma 1), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.2 | |
| A reaction: Kitcher observes that, although Newton relies on infinitesimals, this quotation expresses something close to the later idea of a 'limit'. |
| 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. |