27 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] |
| 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] |
| 22190 | If a theory is more informative it is less probable [Gorham] |
| 22189 | Why abandon a theory if you don't have a better one? [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] |
| 22197 | Theories aren't just for organising present experience if they concern the past or future [Gorham] |
| 22196 | For most scientists their concepts are not just useful, but are meant to be true and accurate [Gorham] |
| 22193 | Consilience makes the component sciences more likely [Gorham] |
| 7260 | If there are intuited moral facts, why should we care about them? [Dancy,J] |
| 7261 | Internalists say that moral intuitions are motivating; externalist say a desire is also needed [Dancy,J] |
| 7262 | Obviously judging an action as wrong gives us a reason not to do it [Dancy,J] |
| 7265 | Moral facts are not perceived facts, but perceived reasons for judgements [Dancy,J] |
| 22198 | Aristotelian physics has circular celestial motion and linear earthly motion [Gorham] |