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] |
| 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] |
| 10486 | If we are rebuilding our ship at sea, we should jettison some cargo [Boolos on Neurath] |
| 8485 | We must always rebuild our ship on the open sea; we can't reconstruct it properly in dry-dock [Neurath] |
| 14802 | Physical and psychical laws of mind are either independent, or derived in one or other direction [Peirce] |
| 14800 | The world is full of variety, but laws seem to produce uniformity [Peirce] |
| 14801 | Darwinian evolution is chance, with the destruction of bad results [Peirce] |