16 ideas
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| 22465 | We see a moral distinction between doing and allowing to happen [Foot] |
| 22466 | We see a moral distinction between our aims and their foreseen consequences [Foot] |
| 22467 | Acts and omissions only matter if they concern doing something versus allowing it [Foot] |
| 22470 | A good moral system benefits its participants, and so demands reciprocity [Foot] |
| 22468 | Virtues can have aims, but good states of affairs are not among them [Foot] |
| 22469 | Some virtues imply rules, and others concern attachment [Foot] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |