9 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] |
8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
17836 | The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M] |
10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
5655 | Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton] |