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] |
13365 | Russell's Paradox is a stripped-down version of Cantor's Paradox [Priest,G on Russell] |
10711 | Russell's paradox means we cannot assume that every property is collectivizing [Potter on Russell] |
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] |
9127 | Russell refuted Frege's principle that there is a set for each property [Russell, by Sorensen] |
7531 | We don't assert private thoughts; the objects are part of what we assert [Russell] |
6017 | Nomos is king [Pindar] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |