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] |
| 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] |
| 16078 | Clay is intrinsically and atomically the same as statue (and that lacks 'modal properties') [Rudder Baker] |
| 16077 | The clay is not a statue - it borrows that property from the statue it constitutes [Rudder Baker] |
| 16080 | Is it possible for two things that are identical to become two separate things? [Rudder Baker] |
| 16082 | Statues essentially have relational properties lacked by lumps [Rudder Baker] |
| 16076 | Constitution is not identity, as consideration of essential predicates shows [Rudder Baker] |
| 16081 | The constitution view gives a unified account of the relation of persons/bodies, statues/bronze etc [Rudder Baker] |
| 22189 | Why abandon a theory if you don't have a better one? [Gorham] |
| 22190 | If a theory is more informative it is less probable [Gorham] |
| 22192 | Is Newton simpler with universal simultaneity, or Einstein simpler without absolute time? [Gorham] |
| 22194 | Structural Realism says mathematical structures persist after theory rejection [Gorham] |
| 22195 | Structural Realists must show the mathematics is both crucial and separate [Gorham] |
| 22196 | For most scientists their concepts are not just useful, but are meant to be true and accurate [Gorham] |
| 22197 | Theories aren't just for organising present experience if they concern the past or future [Gorham] |
| 22193 | Consilience makes the component sciences more likely [Gorham] |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| 22198 | Aristotelian physics has circular celestial motion and linear earthly motion [Gorham] |