10 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] |
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] |
579 | Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle] |
578 | Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle] |
7388 | McGinn invites surrender, by saying it is hopeless trying to imagine conscious machines [Dennett on McGinn] |
3185 | Multiple realisability rules out hidden essences and experts as the source of water- and gold-concepts [McGinn] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |