46 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] |
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] |
23647 | Objects have an essential constitution, producing its qualities, which we are too ignorant to define [Reid] |
11958 | Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar] |
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] |
10349 | To be considered 'an individual' is performed by a society [Kusch] |
10344 | Our experience may be conceptual, but surely not the world itself? [Kusch] |
23646 | Reference is by name, or a term-plus-circumstance, or ostensively, or by description [Reid] |
23645 | A word's meaning is the thing conceived, as fixed by linguistic experts [Reid] |
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] |