33 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] |
| 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] |
| 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] |
| 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] |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| 7439 | The qualities involved in sensations are entirely intentional [Anscombe, by Armstrong] |
| 8353 | Freedom involves acting according to an idea [Anscombe] |
| 8352 | To believe in determinism, one must believe in a system which determines events [Anscombe] |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| 20041 | Intentional actions are those which are explained by giving the reason for so acting [Anscombe] |
| 8070 | It would be better to point to failings of character, than to moral wrongness of actions [Anscombe] |
| 8065 | 'Ought' and 'right' are survivals from earlier ethics, and should be jettisoned [Anscombe] |
| 8069 | Between Aristotle and us, a Judaeo-Christian legal conception of ethics was developed [Anscombe] |
| 8351 | With diseases we easily trace a cause from an effect, but we cannot predict effects [Anscombe] |
| 4777 | The word 'cause' is an abstraction from a group of causal terms in a language (scrape, push..) [Anscombe] |
| 10363 | Causation is relative to how we describe the primary relata [Anscombe, by Schaffer,J] |
| 8350 | Since Mill causation has usually been explained by necessary and sufficient conditions [Anscombe] |