17 ideas
| 8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
| 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] |
| 18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
| 13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 7260 | If there are intuited moral facts, why should we care about them? [Dancy,J] |
| 7261 | Internalists say that moral intuitions are motivating; externalist say a desire is also needed [Dancy,J] |
| 7262 | Obviously judging an action as wrong gives us a reason not to do it [Dancy,J] |
| 7265 | Moral facts are not perceived facts, but perceived reasons for judgements [Dancy,J] |