15 ideas
| 9161 | Maybe reasonableness requires circular justifications - that is one coherentist view [Field,H] |
| 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] |
| 10269 | Mathematics eliminates possibility, as being simultaneous actuality in sets [Putnam] |
| 9160 | Lots of propositions are default reasonable, but the a priori ones are empirically indefeasible [Field,H] |
| 9164 | We treat basic rules as if they were indefeasible and a priori, with no interest in counter-evidence [Field,H] |
| 9165 | Reliability only makes a rule reasonable if we place a value on the truth produced by reliable processes [Field,H] |
| 9162 | Believing nothing, or only logical truths, is very reliable, but we want a lot more than that [Field,H] |
| 9166 | People vary in their epistemological standards, and none of them is 'correct' [Field,H] |
| 9163 | If we only use induction to assess induction, it is empirically indefeasible, and hence a priori [Field,H] |