12 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] |
| 20416 | By 1790 aestheticians were mainly trying to explain individual artistic genius [Kemp] |
| 20417 | Expression can be either necessary for art, or sufficient for art (or even both) [Kemp] |
| 20419 | We don't already know what to express, and then seek means of expressing it [Kemp] |
| 20418 | The horror expressed in some works of art could equallly be expressed by other means [Kemp] |
| 1451 | Design is seen in the way ideas match the world, in the mechanisms of evolution, and in values [Tennant,FR, by PG] |