14 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] |
| 17064 | 1: Coherence is a symmetrical relation between two propositions [Thagard, by Smart] |
| 17065 | 2: An explanation must wholly cohere internally, and with the new fact [Thagard, by Smart] |
| 17066 | 3: If an analogous pair explain another analogous pair, then they all cohere [Thagard, by Smart] |
| 17067 | 4: For coherence, observation reports have a degree of intrinsic acceptability [Thagard, by Smart] |
| 17068 | 5: Contradictory propositions incohere [Thagard, by Smart] |
| 17069 | 6: A proposition's acceptability depends on its coherence with a system [Thagard, by Smart] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |