15 ideas
| 15527 | Defining terms either enables elimination, or shows that they don't require elimination [Lewis] |
| 17807 | To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry] |
| 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] |
| 17806 | It is untenable that mathematics is general physical truths, because it needs infinity [Curry] |
| 17808 | Saying mathematics is logic is merely replacing one undefined term by another [Curry] |
| 15530 | A logically determinate name names the same thing in every possible world [Lewis] |
| 15531 | The Ramsey sentence of a theory says that it has at least one realisation [Lewis] |
| 15528 | A Ramsey sentence just asserts that a theory can be realised, without saying by what [Lewis] |
| 15526 | There is a method for defining new scientific terms just using the terms we already understand [Lewis] |
| 15529 | It is better to have one realisation of a theory than many - but it may not always be possible [Lewis] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |