13 ideas
| 10528 | Definitions concern how we should speak, not how things are [Fine,K] |
| 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] |
| 10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
| 10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
| 10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |