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3 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. |
| 13738 | It is a simple truth that the objects of mathematics have being, of some sort [Aristotle] |
| Full Idea: Since there are not only separable things but also inseparable things (such as, for instance, things which are moving), it is also true to say simpliciter that the objects of mathematic have being and that they are of such a sort as is claimed. | |
| From: Aristotle (Metaphysics [c.324 BCE], 1077b31) | |
| A reaction: This is almost Aristotle's only discussion of whether mathematical entities exist. They seem to have an 'inseparable' existence (the way properties do), but he evidently regards a denial of their existence (Field-style) as daft. |
| 12339 | Aristotle removes ontology from mathematics, and replaces the true with the beautiful [Aristotle, by Badiou] |
| Full Idea: For Aristotle, the de-ontologization of mathematics draws the beautiful into the place of the true. | |
| From: report of Aristotle (Metaphysics [c.324 BCE]) by Alain Badiou - Briefings on Existence 14 |