display all the ideas for this combination of texts
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 |
| 4533 | Logic and maths refer to fictitious entities which we have created [Nietzsche] |
| Full Idea: Logic (like geometry and arithmetic) applies only to fictitious entities that we have created. | |
| From: Friedrich Nietzsche (The Will to Power (notebooks) [1888], §516) | |
| A reaction: This finds Nietzsche on the relativist wing of logical empiricism. The thing is, fictitious entities can have a close relationship with truth, as in a great novel. I believe in necessary logical truth, but there are many ways of slicing it. |