31 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] |
| 1635 | Mathematics reduces to set theory (which is a bit vague and unobvious), but not to logic proper [Quine] |
| 7627 | You can't reduce epistemology to psychology, because that presupposes epistemology [Maund on Quine] |
| 8871 | We should abandon a search for justification or foundations, and focus on how knowledge is acquired [Quine, by Davidson] |
| 8826 | If we abandon justification and normativity in epistemology, we must also abandon knowledge [Kim on Quine] |
| 8827 | Without normativity, naturalized epistemology isn't even about beliefs [Kim on Quine] |
| 8899 | Epistemology is a part of psychology, studying how our theories relate to our evidence [Quine] |
| 8898 | Inculcations of meanings of words rests ultimately on sensory evidence [Quine] |
| 8900 | In observation sentences, we could substitute community acceptance for analyticity [Quine] |
| 23262 | Experience, sympathy and history are sensible grounds for laying claim to rights [Grayling] |
| 23263 | Politics is driven by power cliques [Grayling] |
| 23255 | It is essential for democracy that voting is free and well informed [Grayling] |
| 23254 | Democracies should require a supermajority for major questions [Grayling] |
| 23260 | A cap on time of service would restrict party control and career ambitions [Grayling] |
| 23253 | Majority decisions are only acceptable if the minority interests are not vital [Grayling] |
| 23256 | Liberty and equality cannot be reconciled [Grayling] |
| 23258 | The very concept of democracy entails a need for justice [Grayling] |
| 23259 | There should be separate legislative, executive and judicial institutions [Grayling] |