6 ideas
17833 | The first-order ZF axiomatisation is highly non-categorical [Hallett,M] |
17834 | Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M] |
17837 | Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M] |
17836 | The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M] |
18284 | Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper] |
4001 | The meaning of a word contains all its possible uses as well as its actual ones [Nagel] |