33 ideas
9307 | Modern Western culture suddenly appeared in Jena in the 1790s [Svendsen] |
9297 | You can't understand love in terms of 'if and only if...' [Svendsen] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
9308 | If subjective and objective begin to merge, then so do primary and secondary qualities [Svendsen] |
9309 | Emotions have intentional objects, while a mood is objectless [Svendsen] |
17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
9304 | Death appears to be more frightening the less one has lived [Svendsen] |
9298 | We can be unaware that we are bored [Svendsen] |
9301 | Boredom is so radical that suicide could not overcome it; only never having existed would do it [Svendsen] |
9302 | We are bored because everything comes to us fully encoded, and we want personal meaning [Svendsen] |
9310 | The profoundest boredom is boredom with boredom [Svendsen] |
9311 | We have achieved a sort of utopia, and it is boring, so that is the end of utopias [Svendsen] |
9303 | The concept of 'alienation' seems no longer applicable [Svendsen] |