11 ideas
| 22820 | Early Romantics sought a plurality of systems, in a quest for freedom [Hösle] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 22329 | Logic is highly general truths abstracted from reality [Russell, by Glock] |
| 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] |
| 21569 | It is good to generalise truths as much as possible [Russell] |
| 22819 | In the 18th century history came to be seen as progressive, rather than cyclical [Hösle] |