14 ideas
15946 | Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine] |
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] |
15911 | Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine] |
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] |
16129 | Evans argues (falsely!) that a contradiction follows from treating objects as vague [Evans, by Lowe] |
16459 | Is it coherent that reality is vague, identities can be vague, and objects can have fuzzy boundaries? [Evans] |
16460 | Evans assumes there can be vague identity statements, and that his proof cannot be right [Evans, by Lewis] |
16457 | There clearly are vague identity statements, and Evans's argument has a false conclusion [Evans, by Lewis] |
14484 | If a=b is indeterminate, then a=/=b, and so there cannot be indeterminate identity [Evans, by Thomasson] |
16224 | There can't be vague identity; a and b must differ, since a, unlike b, is only vaguely the same as b [Evans, by PG] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |