12 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] |
17809 | Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
17810 | The study of mathematical foundations needs new non-mathematical concepts [Kreisel] |
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] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
17811 | The natural conception of points ducks the problem of naming or constructing each point [Kreisel] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |