36 ideas
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 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] |
| 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] |
| 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] |
| 14064 | If a statue is identical with the clay of which it is made, that identity is contingent [Gibbard] |
| 14066 | A 'piece' of clay begins when its parts stick together, separately from other clay [Gibbard] |
| 14067 | Clay and statue are two objects, which can be named and reasoned about [Gibbard] |
| 14069 | We can only investigate the identity once we have designated it as 'statue' or as 'clay' [Gibbard] |
| 14076 | Essentialism is the existence of a definite answer as to whether an entity fulfils a condition [Gibbard] |
| 14077 | Essentialism for concreta is false, since they can come apart under two concepts [Gibbard] |
| 14070 | A particular statue has sortal persistence conditions, so its origin defines it [Gibbard] |
| 14073 | Claims on contingent identity seem to violate Leibniz's Law [Gibbard] |
| 14065 | Two identical things must share properties - including creation and destruction times [Gibbard] |
| 14074 | Leibniz's Law isn't just about substitutivity, because it must involve properties and relations [Gibbard] |
| 14072 | Possible worlds identity needs a sortal [Gibbard] |
| 14078 | Only concepts, not individuals, can be the same across possible worlds [Gibbard] |
| 14079 | Kripke's semantics needs lots of intuitions about which properties are essential [Gibbard] |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| 14071 | Naming a thing in the actual world also invokes some persistence criteria [Gibbard] |
| 21788 | The moral will is self-determining, but the ethical will is met in society [Houlgate] |