Timeline for Intuitive and/or philosophical explanation for set theory paradoxes
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 19, 2010 at 10:45 | comment | added | Harry Altman | @Ewan: If ZFC minus foundation is consistent, then the well-founded sets form a model of ZFC. | |
| Jun 19, 2010 at 5:05 | comment | added | Ewan Delanoy | @ Timothy : how do we know that "ZFC is consistent if and only if ZFC minus foundation is" ? | |
| Jun 18, 2010 at 21:53 | comment | added | Timothy Chow | @Harry: You mean that foundation is never used in "ordinary mathematics"? The point is that the question being asked here is whether ZFC is consistent, not whether ZFC faithfully mimics every aspect of mathematical practice. And ZFC is consistent if and only if ZFC minus foundation is, so as far as consistency is concerned, it does no harm to throw in foundation if it helps you see more clearly that inconsistencies will not arise. | |
| Jun 18, 2010 at 20:52 | comment | added | Harry Altman | The "cumulative hierarchy" justification seems a bit strange when you consider that axiom of foundation is pretty much never used. | |
| Jun 18, 2010 at 20:46 | history | answered | Timothy Chow | CC BY-SA 2.5 |