13 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] |
| 17423 | The essence of natural numbers must reflect all the functions they perform [Sicha] |
| 17425 | To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha] |
| 17424 | Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha] |
| 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] |
| 3597 | Foundations need not precede other beliefs [Wittgenstein] |
| 3596 | Total doubt can't even get started [Wittgenstein, by Williams,M] |
| 4721 | If you are not certain of any fact, you cannot be certain of the meaning of your words either [Wittgenstein] |