22 ideas
16000 | Fixed ideas should be tackled aggressively [Kierkegaard] |
23367 | Even pointing a finger should only be done for a reason [Epictetus] |
16012 | Philosophy can't be unbiased if it ignores language, as that is no more independent than individuals are [Kierkegaard] |
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] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
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] |
16003 | If people marry just because they are lonely, that is self-love, not love [Kierkegaard] |
21910 | Our destiny is the highest pitch of world-weariness [Kierkegaard] |
16001 | Life may be understood backwards, but it has to be lived forwards [Kierkegaard] |
16008 | The best way to be a Christian is without 'Christianity' [Kierkegaard] |
20735 | We need to see that Christianity cannot be understood [Kierkegaard] |