13 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] |
| 10993 | Ramsey's Test: believe the consequent if you believe the antecedent [Ramsey, by Read] |
| 14279 | Asking 'If p, will q?' when p is uncertain, then first add p hypothetically to your knowledge [Ramsey] |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| 6894 | Mental terms can be replaced in a sentence by a variable and an existential quantifier [Ramsey] |
| 9418 | All knowledge needs systematizing, and the axioms would be the laws of nature [Ramsey] |
| 9420 | Causal laws result from the simplest axioms of a complete deductive system [Ramsey] |