15 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] |
| 5163 | Basic propositions refer to a single experience, are incorrigible, and conclusively verifiable [Ayer] |
| 5167 | The argument from analogy fails, so the best account of other minds is behaviouristic [Ayer] |
| 5164 | A statement is meaningful if observation statements can be deduced from it [Ayer] |
| 5165 | Directly verifiable statements must entail at least one new observation statement [Ayer] |
| 5166 | The principle of verification is not an empirical hypothesis, but a definition [Ayer] |
| 5162 | Sentences only express propositions if they are meaningful; otherwise they are 'statements' [Ayer] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 5168 | Moral approval and disapproval concerns classes of actions, rather than particular actions [Ayer] |