Timeline for Why should we believe in the axiom of regularity?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 2, 2016 at 21:22 | comment | added | Todd Trimble | It sounds to me that Flash is rejecting the premise of the question: that one actually should believe it. As an answer though it's rather skeletal. | |
| Mar 2, 2016 at 19:51 | review | Low quality posts | |||
| Mar 2, 2016 at 23:08 | |||||
| Oct 5, 2015 at 5:13 | comment | added | Flash Sheridan | I fail to see a useful parallel between disbelief in the axiom of foundation and belief in the inconsistency of arithmetic. And of course a universal set is inconsistent with the Axiom of Separation; the justification for Separation from the iterative concept of set (which others here have discussed) obviously doesn’t apply to ill-founded sets. More on this in Forster’s Oxford Logic Guide pp. 141–2, or §1 of my forthcoming Logique et Analyse article, preprint at logic-center.be/Publications/Bibliotheque. | |
| Oct 1, 2015 at 16:36 | comment | added | Wojowu | This also doesn't answer my question, because I have asked for reasons why people should believe this axiom. Of course you don't have to believe in it, just like you don't have to believe in consistency of arithmetic. | |
| Oct 1, 2015 at 16:35 | comment | added | Wojowu | Existence of the universal set gives a contradiction even if we don't assume axiom of foundation - it follows from other axioms of ZF that the universal set doesn't exist. | |
| Oct 1, 2015 at 16:33 | history | answered | Flash Sheridan | CC BY-SA 3.0 |