11 ideas
| 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] |
| 13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
| 13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
| 13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
| 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] |
| 13415 | An adequate account of a number must relate it to its series [Benacerraf] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |