16 ideas
| 3035 | Dialectic involves conversations with short questions and brief answers [Diog. Laertius] |
| 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] |
| 1816 | Sceptics say demonstration depends on self-demonstrating things, or indemonstrable things [Diog. Laertius] |
| 1819 | Scepticism has two dogmas: that nothing is definable, and every argument has an opposite argument [Diog. Laertius] |
| 3064 | When sceptics say that nothing is definable, or all arguments have an opposite, they are being dogmatic [Diog. Laertius] |
| 22363 | You have only begun to do real science when you can express it in numbers [Kelvin] |
| 3033 | Induction moves from some truths to similar ones, by contraries or consequents [Diog. Laertius] |
| 1838 | Cyrenaic pleasure is a motion, but Epicurean pleasure is a condition [Diog. Laertius] |
| 1769 | Cynics believe that when a man wishes for nothing he is like the gods [Diog. Laertius] |
| 20644 | Energy has progressed from a mere formula, to a principle pervading all nature [Kelvin] |