Timeline for Do mathematical objects disappear?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 27, 2015 at 3:34 | comment | added | N. Virgo | @AsafKaragila I would rather say that classes are a different way in which the inconsistent notion of a naïve set can be "patched up" to make it consistent. That they are not the same can be seen from the fact that you can consider the class of sets that don't contain themselves, but you can't consider the class of classes that don't contain themselves, because a class cannot be a member of a class. | |
| Dec 26, 2015 at 18:43 | comment | added | Asaf Karagila♦ | Naive sets are now often called "classes". | |
| Dec 26, 2015 at 18:36 | history | edited | Pete L. Clark | CC BY-SA 3.0 |
added 63 characters in body
|
| Dec 24, 2015 at 6:29 | comment | added | Noah Schweber | That's fair - I still don't really think this counts as a "disappearance," especially because even in logic we still consider naive sets (e.g. in paraconsistent set theories, or when talking about possible choices of axioms for set theory). (Btw I was not the downvoter.) | |
| Dec 24, 2015 at 6:13 | comment | added | N. Virgo | That's covered in my second paragraph. "An inconsistent theory can often be 'patched up' and made consistent in such a way that the core results are preserved ... in mathematics [the disappearance of a theory is] more likely to take the form of a small change, and be of interest only to a small group of researchers." Naive sets disappeared as an object of study for formal logicians, but the change was so small it barely affected anyone else on a day to day basis. | |
| Dec 24, 2015 at 6:02 | comment | added | Noah Schweber | I think naive sets are very much still in play in mathematics - most mathematicians work most of the time without a specific background set theory, under the (almost always correct) assumption that nothing bad will happen. | |
| S Dec 24, 2015 at 4:51 | history | answered | N. Virgo | CC BY-SA 3.0 | |
| S Dec 24, 2015 at 4:51 | history | made wiki | Post Made Community Wiki by N. Virgo |