10 ideas
| 19404 | Necessities rest on contradiction, and contingencies on sufficient reason [Leibniz] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 14665 | We can call the quality of Plato 'Platonity', and say it is a quality which only he possesses [Boethius] |
| 19403 | Each of the infinite possible worlds has its own laws, and the individuals contain those laws [Leibniz] |