22 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] |
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] |
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] |
9224 | Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K] |
9222 | The objects and truths of mathematics are imperative procedures for their construction [Fine,K] |
9223 | My Proceduralism has one simple rule, and four complex rules [Fine,K] |
6613 | The natural kinds are objects, processes and properties/relations [Ellis] |
6616 | Least action is not a causal law, but a 'global law', describing a global essence [Ellis] |
6615 | A species requires a genus, and its essence includes the essence of the genus [Ellis] |
6614 | A hierarchy of natural kinds is elaborate ontology, but needed to explain natural laws [Ellis] |
6612 | Without general principles, we couldn't predict the behaviour of dispositional properties [Ellis] |