38 ideas
| 14001 | People who use science to make philosophical points don't realise how philosophical science is [Markosian] |
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 13991 | Presentism has the problem that if Socrates ceases to exist, so do propositions about him [Markosian] |
| 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] |
| 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] |
| 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] |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| 14002 | Possible worlds must be abstract, because two qualitatively identical worlds are just one world [Markosian] |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| 14000 | 'Grabby' truth conditions first select their object, unlike 'searchy' truth conditions [Markosian] |
| 13990 | Presentism is the view that only present objects exist [Markosian] |
| 13992 | Presentism says if objects don't exist now, we can't have attitudes to them or relations with them [Markosian] |
| 13994 | Presentism seems to entail that we cannot talk about other times [Markosian] |
| 13995 | Serious Presentism says things must exist to have relations and properties; Unrestricted version denies this [Markosian] |
| 13996 | Maybe Presentists can refer to the haecceity of a thing, after the thing itself disappears [Markosian] |
| 13997 | Maybe Presentists can paraphrase singular propositions about the past [Markosian] |
| 13993 | Special Relativity denies the absolute present which Presentism needs [Markosian] |
| 13998 | Objects in the past, like Socrates, are more like imaginary objects than like remote spatial objects [Markosian] |
| 13999 | People are mistaken when they think 'Socrates was a philosopher' says something [Markosian] |