14 ideas
| 9944 | We understand some statements about all sets [Putnam] |
| 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] |
| 9937 | I do not believe mathematics either has or needs 'foundations' [Putnam] |
| 9939 | It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 9940 | Maybe mathematics is empirical in that we could try to change it [Putnam] |
| 9941 | Science requires more than consistency of mathematics [Putnam] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 9943 | You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam] |
| 12742 | A whole is just its parts, but there are no smallest parts, so only minds and perceptions exist [Leibniz] |