19 ideas
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
| 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] |
| 13672 | All the axioms for mathematics presuppose set theory [Neumann] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 2705 | How can intuitionists distinguish universal convictions from local cultural ones? [Hare] |
| 2712 | You can't use intuitions to decide which intuitions you should cultivate [Hare] |
| 2706 | Emotivists mistakenly think all disagreements are about facts, and so there are no moral reasons [Hare] |
| 2708 | An 'ought' statement implies universal application [Hare] |
| 2704 | If morality is just a natural or intuitive description, that leads to relativism [Hare] |
| 2703 | Descriptivism say ethical meaning is just truth-conditions; prescriptivism adds an evaluation [Hare] |
| 2707 | If there can be contradictory prescriptions, then reasoning must be involved [Hare] |
| 2711 | Prescriptivism implies a commitment, but descriptivism doesn't [Hare] |
| 2709 | Prescriptivism sees 'ought' statements as imperatives which are universalisable [Hare] |
| 2710 | Moral judgements must invoke some sort of principle [Hare] |