25 ideas
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] |
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] |
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] |
18284 | Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper] |
23865 | Morality would improve if people could pursue private interests [Weil] |
23866 | In oppressive societies the scope of actual control is extended by a religion of power [Weil] |
23871 | No central authority can initiate decentralisation [Weil] |
23867 | After a bloody revolution the group which already had the power comes to the fore [Weil] |
23870 | Decentralisation is only possible by co-operation between strong and weak - which is absurd [Weil] |
23863 | Only individual people of good will can achieve social progress [Weil] |
23869 | In the least evil societies people can think, control community life, and be autonomous [Weil] |
23861 | Marx showed that capitalist oppression, because of competition, is unstoppable [Weil] |
23868 | The pleasure of completing tasks motivates just as well as the whip of slavery [Weil] |
23864 | Inequality could easily be mitigated, if it were not for the struggle for power [Weil] |