27 ideas
| 18543 | Do aesthetic reasons count as reasons, if they are rejectable without contradiction? [Scruton] |
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 18542 | Defining truth presupposes that there can be a true definition [Scruton] |
| 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] |
| 18546 | The pleasure taken in beauty also aims at understanding and valuing [Scruton] |
| 18550 | Art gives us imaginary worlds which we can view impartially [Scruton] |
| 18544 | Maybe 'beauty' is too loaded, and we should talk of fittingness or harmony [Scruton] |
| 18553 | Beauty shows us what we should want in order to achieve human fulfilment [Scruton] |
| 18556 | Beauty is rationally founded, inviting meaning, comparison and self-reflection [Scruton] |
| 18548 | Natural beauty reassures us that the world is where we belong [Scruton] |
| 18551 | Croce says art makes inarticulate intuitions conscious; rival views say the audience is the main concern [Scruton] |
| 18541 | Beauty (unlike truth and goodness) is questionable as an ultimate value [Scruton] |
| 18554 | Prostitution is wrong because it hardens the soul, since soul and body are one [Scruton] |
| 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] |