10 ideas
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
22329 | Logic is highly general truths abstracted from reality [Russell, by Glock] |
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] |
21570 | Numbers are just verbal conveniences, which can be analysed away [Russell] |
21569 | It is good to generalise truths as much as possible [Russell] |