display all the ideas for this combination of philosophers
3 ideas
| 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 |
| 9974 | Ten sheep and ten dogs are the same numerically, but it is not the same ten [Aristotle] |
| Full Idea: If there are ten sheep and ten dogs, the number is the same (because it does not differ by a numerical difference), but it is not the same ten (because the objects it is predicated of are different - dogs in one instance, horses in the other). | |
| From: Aristotle (Physics [c.337 BCE], 224a2-14) | |
| A reaction: Mega! Abstract objects are unique, and can't be 'added' to themselves. I think we need 'units' here, because 2+2 adds four units, so each 2 refers to something different. '2' must refer to something other than itself. |