Timeline for When is something too big to be a set?
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 20, 2010 at 23:39 | answer | added | T.. | timeline score: 0 | |
| Jul 20, 2010 at 22:50 | answer | added | Theo Johnson-Freyd | timeline score: 2 | |
| Jul 20, 2010 at 21:52 | comment | added | Charles Staats | When Frege first tried to axiomatize arithmetic, one of his axioms was (something like) for every property P, there exists a set of all things that satisfy P. He then defined n, in essence, as the set of all sets having n elements (only his version was not circular). Then Russell wrote him a letter pointing out that this axiom allows us to form the set of all sets that are not elements of themselves, leading to a contradiction. When you say something like "the set of all___," rather than "the set of all ___ contained in the set Y," you are implicitly using Frege's faulty axiom. | |
| Jul 20, 2010 at 21:01 | answer | added | Sebastian Reichelt | timeline score: 3 | |
| Jul 20, 2010 at 20:16 | vote | accept | Dedalus | ||
| Jul 20, 2010 at 19:40 | answer | added | Paul Siegel | timeline score: 30 | |
| Jul 20, 2010 at 19:31 | answer | added | Charles Stewart | timeline score: 5 | |
| Jul 20, 2010 at 18:46 | answer | added | Simon Thomas | timeline score: 17 | |
| Jul 20, 2010 at 18:44 | answer | added | Greg Kuperberg | timeline score: 5 | |
| Jul 20, 2010 at 18:26 | answer | added | Andrew Stacey | timeline score: 25 | |
| Jul 20, 2010 at 18:10 | comment | added | The Mathemagician | This is really a question for the set-theorists and logicians in here. I think they're really the ones that can give more then a hand waving response invoking classes. | |
| Jul 20, 2010 at 18:07 | comment | added | Chao Xu | Is this something related to things like "the class of all ordinals"? It lead to a paradox if it's defined as a set. | |
| Jul 20, 2010 at 18:06 | comment | added | Robin Chapman | These large collections are called proper classes. There is an axiomatization of set theory (NBG: von Neumann, Bernays, Goedel) which allows proper classes as well as sets. But these have to be distinuguished from sets somehow to avoid Russell's paradox. | |
| Jul 20, 2010 at 18:02 | history | asked | Dedalus | CC BY-SA 2.5 |