display all the ideas for this combination of texts
2 ideas
| 10242 | I apply structuralism to concrete and abstract objects indiscriminately [Quine] |
| Full Idea: My own line is a yet more sweeping structuralism (than David Lewis's account of classes), applying to concrete and abstract objects indiscriminately. | |
| From: Willard Quine (Structure and Nature [1992], p.6), quoted by Stewart Shapiro - Philosophy of Mathematics 4.9 | |
| A reaction: Shapiro calls this 'breathtaking', and retreats from it, but it is something like my own view, starting from Mill's pebbles and working up. |
| 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. |