45 ideas
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
3593 | The only way to specify the corresponding fact is asserting the sentence [Williams,M] |
3585 | Coherence needs positive links, not just absence of conflict [Williams,M] |
3584 | Justification needs coherence, while truth might be ideal coherence [Williams,M] |
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] |
3599 | Deduction shows entailments, not what to believe [Williams,M] |
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] |
3591 | We could never pin down how many beliefs we have [Williams,M] |
3582 | Propositions make error possible, so basic experiential knowledge is impossible [Williams,M] |
3592 | Phenomenalism is a form of idealism [Williams,M] |
3579 | Sense data avoid the danger of misrepresenting the world [Williams,M] |
3581 | Sense data can't give us knowledge if they are non-propositional [Williams,M] |
3564 | Is it people who are justified, or propositions? [Williams,M] |
3595 | What works always takes precedence over theories [Williams,M] |
3580 | Experience must be meaningful to act as foundations [Williams,M] |
3578 | Are empirical foundations judgements or experiences? [Williams,M] |
3576 | Foundationalists are torn between adequacy and security [Williams,M] |
3577 | Strong justification eliminates error, but also reduces our true beliefs [Williams,M] |
3589 | Why should diverse parts of our knowledge be connected? [Williams,M] |
3590 | Coherence theory must give a foundational status to coherence itself [Williams,M] |
3571 | Externalism does not require knowing that you know [Williams,M] |
3574 | Externalism ignores the social aspect of knowledge [Williams,M] |
3569 | In the causal theory of knowledge the facts must cause the belief [Williams,M] |
3567 | How could there be causal relations to mathematical facts? [Williams,M] |
3586 | Only a belief can justify a belief [Williams,M] |
3573 | Externalist reliability refers to a range of conventional conditions [Williams,M] |
3565 | Sometimes I ought to distrust sources which are actually reliable [Williams,M] |
3566 | We control our beliefs by virtue of how we enquire [Williams,M] |
3594 | Scepticism just reveals our limited ability to explain things [Williams,M] |
3575 | Scepticism can involve discrepancy, relativity, infinity, assumption and circularity [Williams,M] |
3587 | Seeing electrons in a cloud chamber requires theory [Williams,M] |
3588 | Foundationalists base meaning in words, coherentists base it in sentences [Williams,M] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |