18 ideas
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 9358 | There are several logics, none of which will ever derive falsehoods from truth [Lewis,CI] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 9357 | Excluded middle is just our preference for a simplified dichotomy in experience [Lewis,CI] |
| 9364 | Names represent a uniformity in experience, or they name nothing [Lewis,CI] |
| 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] |
| 9362 | Necessary truths are those we will maintain no matter what [Lewis,CI] |
| 9365 | We can maintain a priori principles come what may, but we can also change them [Lewis,CI] |
| 9361 | We have to separate the mathematical from physical phenomena by abstraction [Lewis,CI] |
| 8108 | Aesthetics presupposes a distinctive sort of experience, and a unified essence for art [Gardner] |
| 8112 | Art works originate in the artist's mind, and appreciation is re-creating this mental object [Gardner] |
| 8111 | Aesthetic objectivists must explain pleasure being essential, but not in the object [Gardner] |
| 8109 | Aesthetic judgements necessarily require first-hand experience, unlike moral judgements [Gardner] |
| 9363 | Science seeks classification which will discover laws, essences, and predictions [Lewis,CI] |