50 ideas
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 10354 | Correspondence could be with other beliefs, rather than external facts [Kusch] |
| 10353 | Tarskians distinguish truth from falsehood by relations between members of sets [Kusch] |
| 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] |
| 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] |
| 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] |
| 10337 | We can have knowledge without belief, if others credit us with knowledge [Kusch] |
| 10357 | Methodological Solipsism assumes all ideas could be derived from one mind [Kusch] |
| 10339 | Foundations seem utterly private, even from oneself at a later time [Kusch] |
| 10331 | Testimony is reliable if it coheres with evidence for a belief, and with other beliefs [Kusch] |
| 10338 | The coherentist restricts the space of reasons to the realm of beliefs [Kusch] |
| 10340 | Individualistic coherentism lacks access to all of my beliefs, or critical judgement of my assessment [Kusch] |
| 10345 | Individual coherentism cannot generate the necessary normativity [Kusch] |
| 10350 | Cultures decide causal routes, and they can be critically assessed [Kusch] |
| 10343 | Process reliabilism has been called 'virtue epistemology', resting on perception, memory, reason [Kusch] |
| 10341 | Justification depends on the audience and one's social role [Kusch] |
| 10334 | Testimony is an area in which epistemology meets ethics [Kusch] |
| 10336 | Powerless people are assumed to be unreliable, even about their own lives [Kusch] |
| 10324 | Testimony does not just transmit knowledge between individuals - it actually generates knowledge [Kusch] |
| 10327 | Some want to reduce testimony to foundations of perceptions, memories and inferences [Kusch] |
| 10329 | Testimony won't reduce to perception, if perception depends on social concepts and categories [Kusch] |
| 10330 | A foundation is what is intelligible, hence from a rational source, and tending towards truth [Kusch] |
| 10325 | Vindicating testimony is an expression of individualism [Kusch] |
| 10335 | Myths about lonely genius are based on epistemological individualism [Kusch] |
| 10323 | Communitarian Epistemology says 'knowledge' is a social status granted to groups of people [Kusch] |
| 10348 | Private justification is justification to imagined other people [Kusch] |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| 10349 | To be considered 'an individual' is performed by a society [Kusch] |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| 10344 | Our experience may be conceptual, but surely not the world itself? [Kusch] |
| 10358 | Often socialising people is the only way to persuade them [Kusch] |
| 10333 | Communitarianism in epistemology sees the community as the primary knower [Kusch] |
| 10351 | Natural kinds are social institutions [Kusch] |
| 10332 | Omniscience is incoherent, since knowledge is a social concept [Kusch] |