28 ideas
19259 | If 2-D conceivability can a priori show possibilities, this is a defence of conceptual analysis [Vaidya] |
6859 | Analytic philosophy has much higher standards of thinking than continental philosophy [Williamson] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
6862 | Fuzzy logic uses a continuum of truth, but it implies contradictions [Williamson] |
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] |
6858 | Formal logic struck me as exactly the language I wanted to think in [Williamson] |
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] |
6863 | Close to conceptual boundaries judgement is too unreliable to give knowledge [Williamson] |
6861 | What sort of logic is needed for vague concepts, and what sort of concept of truth? [Williamson] |
19262 | Essential properties are necessary, but necessary properties may not be essential [Vaidya] |
19267 | Define conceivable; how reliable is it; does inconceivability help; and what type of possibility results? [Vaidya] |
19268 | Inconceivability (implying impossibility) may be failure to conceive, or incoherence [Vaidya] |
19265 | Can you possess objective understanding without realising it? [Vaidya] |
6860 | How can one discriminate yellow from red, but not the colours in between? [Williamson] |
19260 | Gettier deductive justifications split the justification from the truthmaker [Vaidya] |
19266 | In a disjunctive case, the justification comes from one side, and the truth from the other [Vaidya] |
19264 | Aboutness is always intended, and cannot be accidental [Vaidya] |