16 ideas
| 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] |
| 13795 | Properties only have identity in the context of their contraries [Elder] |
| 13798 | Maybe we should give up the statue [Elder] |
| 13797 | The loss of an essential property means the end of an existence [Elder] |
| 13794 | Essential properties by nature occur in clusters or packages [Elder] |
| 13796 | Essential properties are bound together, and would be lost together [Elder] |
| 1554 | Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind] |
| 1555 | People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus] |
| 535 | The gods are just personified human benefits [Prodicus] |
| 1543 | He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus] |