39 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] |
| 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] |
| 15127 | A categorical basis could hardly explain a disposition if it had no powers of its own [Hawthorne] |
| 15123 | Is the causal profile of a property its essence? [Hawthorne] |
| 15124 | If properties are more than their powers, we could have two properties with the same power [Hawthorne] |
| 15122 | Could two different properties have the same causal profile? [Hawthorne] |
| 14590 | If we accept scattered objects such as archipelagos, why not think of cars that way? [Hawthorne] |
| 15128 | We can treat the structure/form of the world differently from the nodes/matter of the world [Hawthorne] |
| 15121 | An individual essence is a necessary and sufficient profile for a thing [Hawthorne] |
| 14591 | Four-dimensionalists say instantaneous objects are more fundamental than long-lived ones [Hawthorne] |
| 8970 | Our notion of identical sets involves identical members, which needs absolute identity [Hawthorne] |
| 14589 | A modal can reverse meaning if the context is seen differently, so maybe context is all? [Hawthorne] |
| 19553 | Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne] |
| 19551 | How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne] |
| 19552 | We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne] |
| 19554 | Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne] |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| 15126 | Maybe scientific causation is just generalisation about the patterns [Hawthorne] |
| 15125 | We only know the mathematical laws, but not much else [Hawthorne] |
| 14588 | Modern metaphysicians tend to think space-time points are more fundamental than space-time regions [Hawthorne] |