display all the ideas for this combination of texts
2 ideas
| 8203 | All the arithmetical entities can be reduced to classes of integers, and hence to sets [Quine] |
| Full Idea: The arithmetic of ratios and irrational and imaginary numbers can all be reduced by definition to the theory of classes of positive integers, and this can in turn be reduced to pure set theory. | |
| From: Willard Quine (Vagaries of Definition [1972], p.53) | |
| A reaction: This summarises Quine's ontology of mathematics, which tries to eliminate virtually everything, but has to affirm the existence of sets. Can you count sets and their members, if the sets are used to define the numbers? |
| 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. |