15 ideas
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| 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] |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| 13857 | Truth-functional possibilities include the irrelevant, which is a mistake [Edgington] |
| 13853 | It is a mistake to think that conditionals are statements about how the world is [Edgington] |
| 13855 | A conditional does not have truth conditions [Edgington] |
| 13859 | X believes 'if A, B' to the extent that A & B is more likely than A & ¬B [Edgington] |
| 13854 | Conditionals express what would be the outcome, given some supposition [Edgington] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |