24 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] |
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] |
20660 | At one level maths and nature are very similar, suggesting some deeper origin [Wolfram] |
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] |
7590 | Consequentialism emphasises value rather than obligation in morality [Scruton] |
7589 | Altruism is either emotional (where your interests are mine) or moral (where they are reasons for me) [Scruton] |
7595 | The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton] |
7588 | Allegiance is fundamental to the conservative view of society [Scruton] |
7594 | Democrats are committed to a belief and to its opposite, if the majority prefer the latter [Scruton] |
7593 | Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG] |
7592 | For positivists law is a matter of form, for naturalists it is a matter of content [Scruton] |
7587 | The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton] |
20659 | Space and its contents seem to be one stuff - so space is the only existing thing [Wolfram] |