37 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] |
| 13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [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] |
| 13258 | The 'aggregative' objections says mereology gets existence and location of objects wrong [Koslicki] |
| 13288 | Consequence is truth-preserving, either despite substitutions, or in all interpretations [Koslicki] |
| 14506 | 'Roses are red; therefore, roses are colored' seems truth-preserving, but not valid in a system [Koslicki] |
| 13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
| 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] |
| 14505 | Some questions concern mathematical entities, rather than whole structures [Koslicki] |
| 13289 | Structures have positions, constituent types and number, and some invariable parts [Koslicki] |
| 14501 | 'Categorical' properties exist in the actual world, and 'hypothetical' properties in other worlds [Koslicki] |
| 14495 | I aim to put the notion of structure or form back into the concepts of part, whole and object [Koslicki] |
| 13264 | If a whole is just a structure, a dinner party wouldn't need the guests to turn up [Koslicki] |
| 14497 | The clay is just a part of the statue (its matter); the rest consists of its form or structure [Koslicki] |
| 13280 | Statue and clay differ in modal and temporal properties, and in constitution [Koslicki] |
| 14496 | Structure or form are right at the centre of modern rigorous modes of enquiry [Koslicki] |
| 13279 | There are at least six versions of constitution being identity [Koslicki] |
| 14498 | For three-dimensionalist parthood must be a three-place relation, including times [Koslicki] |
| 13283 | The parts may be the same type as the whole, like a building made of buildings [Koslicki] |
| 13266 | Wholes in modern mereology are intended to replace sets, so they closely resemble them [Koslicki] |
| 14500 | Wholes are entities distinct from their parts, and have different properties [Koslicki] |
| 13281 | Wholes are not just their parts; a whole is an entity distinct from the proper parts [Koslicki] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 14504 | The Kripke/Putnam approach to natural kind terms seems to give them excessive stability [Koslicki] |
| 13285 | Natural kinds support inductive inferences, from previous samples to the next one [Koslicki] |
| 13287 | Concepts for species are either intrinsic structure, or relations like breeding or ancestry [Koslicki] |
| 13284 | Should vernacular classifications ever be counted as natural kind terms? [Koslicki] |
| 13286 | There are apparently no scientific laws concerning biological species [Koslicki] |