35 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] |
| 12132 | Indiscernibility is a necessary and sufficient condition for identity [Brody] |
| 15834 | Brody bases sortal essentialism on properties required throughout something's existence [Brody, by Mackie,P] |
| 12140 | Modern emphasis is on properties had essentially; traditional emphasis is on sort-defining properties [Brody] |
| 11895 | A sortal essence is a property which once possessed always possessed [Brody, by Mackie,P] |
| 12141 | Maybe essential properties are those which determine a natural kind? [Brody] |
| 12137 | De re essentialism standardly says all possible objects identical with a have a's essential properties [Brody] |
| 12142 | Essentially, a has P, always had P, must have had P, and has never had a future without P [Brody] |
| 12143 | An object having a property essentially is equivalent to its having it necessarily [Brody] |
| 12144 | Essentialism is justified if the essential properties of things explain their other properties [Brody] |
| 12139 | Mereological essentialism says that every part that ensures the existence is essential [Brody] |
| 12135 | Interrupted objects have two first moments of existence, which could be two beginnings [Brody] |
| 12130 | a and b share all properties; so they share being-identical-with-a; so a = b [Brody] |
| 12138 | Identity across possible worlds is prior to rigid designation [Brody] |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |