15 ideas
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 5637 | Nowadays logic is seen as the science of extensions, not intensions [Scruton] |
| 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] |
| 16730 | If matter is entirely atoms, anything else we notice in it can only be modes [Gassendi] |
| 16619 | We observe qualities, and use 'induction' to refer to the substances lying under them [Gassendi] |
| 5636 | Cartesian 'ideas' confuse concepts and propositions [Scruton] |
| 5660 | Allegiance is prior to the recognition of individual rights [Scruton] |
| 5653 | A right is a power which is enforced in the name of justice [Scruton] |
| 16593 | Atoms are not points, but hard indivisible things, which no force in nature can divide [Gassendi] |
| 16729 | How do mere atoms produce qualities like colour, flavour and odour? [Gassendi] |