10 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] |
8417 | Direct realism is false, because defeasibility questions are essential to perceptual knowledge [Galloway] |
7458 | The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking] |
3441 | If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace] |