29 ideas
| 20768 | Like spiderswebs, dialectical arguments are clever but useless [Ariston, by Diog. Laertius] |
| 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] |
| 23805 | Some explanations offer to explain a mystery by a greater mystery [Schulte] |
| 23806 | Naturalist accounts of representation must match the views of cognitive science [Schulte] |
| 23793 | On the whole, referential content is seen as broad, and sense content as narrow [Schulte] |
| 23796 | Naturalists must explain both representation, and what is represented [Schulte] |
| 23792 | Phenomenal and representational character may have links, or even be united [Schulte] |
| 23795 | Naturalistic accounts of content cannot rely on primitive mental or normative notions [Schulte] |
| 23804 | Maybe we can explain mental content in terms of phenomenal properties [Schulte] |
| 23802 | Conceptual role semantics says content is determined by cognitive role [Schulte] |
| 23797 | Cause won't explain content, because one cause can produce several contents [Schulte] |
| 23799 | Teleosemantics explains content in terms of successful and unsuccessful functioning [Schulte] |
| 23800 | Teleosemantic explanations say content is the causal result of naturally selected functions [Schulte] |
| 23798 | Information theories say content is information, such as smoke making fire probable [Schulte] |
| 3049 | The chief good is indifference to what lies midway between virtue and vice [Ariston, by Diog. Laertius] |
| 3549 | Ariston says rules are useless for the virtuous and the non-virtuous [Ariston, by Annas] |