Timeline for What governs our "perception?" about the platonic realm of sets?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 15 at 15:06 | review | Close votes | |||
| May 20 at 3:06 | |||||
| May 15 at 14:35 | answer | added | Randall Holmes | timeline score: 3 | |
| May 6 at 15:35 | answer | added | Randall Holmes | timeline score: 15 | |
| Apr 23 at 19:18 | vote | accept | Zuhair Al-Johar | ||
| Apr 23 at 13:57 | comment | added | Zuhair Al-Johar | @TimothyChow, Sam Hopkins, well an Ur-element is understood not to be a set since they are discriminated from each other while having the same membership. If a theory is dominated by Ur-elements, like with the usual models of NFU in which you have more Ur-elements than sets, then naturally some people would object to it being a theory about sets. Well at least on the face of it, it is not solely a theory about sets. The presence of Ur-elements enables nice features like choice, it is easy to interpret relative to ZFC, more flexible technically, etc.. That's why many would prefer it. | |
| Apr 23 at 13:00 | comment | added | Timothy Chow | @SamHopkins I suppose so, but I don't really understand those who are philosophically opposed to ur-elements, so I hesitate to speak on their behalf. | |
| Apr 23 at 12:49 | comment | added | Sam Hopkins | @TimothyChow: Thanks for linking to that article, Timothy. I found it very enlightening and convincing (regarding its central thesis that ZFC has no special claim as the only possible foundation of mathematics)! And incidentally, while Holmes himself might not find the consistency of NF relevant to his arguments there, at a minimum it represents a technical upgrade over NFU from the perspective of those who are philosophically opposed to ur-elements, no? | |
| Apr 23 at 6:15 | history | became hot network question | |||
| Apr 23 at 2:38 | comment | added | Timothy Chow | Although your question isn't about NF per se, it's worth pointing out that Randall Holmes himself does not regard the consistency of NF to have any philosophical consequences beyond what we can already get from the consistency of NFU, which was established decades ago. In this article, Holmes addresses some of the objections articulated by Joel David Hamkins, and tries to give an intuitive picture of what NFU is all about. | |
| Apr 22 at 23:47 | review | Close votes | |||
| Apr 28 at 3:06 | |||||
| Apr 22 at 23:25 | answer | added | Joel David Hamkins | timeline score: 19 | |
| Apr 22 at 22:48 | comment | added | Zuhair Al-Johar | @JoelDavidHamkins, It's over. NF is consistent. The remaining part is only expositional for clarity and readability. The proof of existence of a structure for TTT has been verified, and that completes it. Practically this matter is closed!logicmatters.net/2024/04/21/nf-really-is-consistent, also see Randall Holmes home page. | |
| Apr 22 at 22:33 | comment | added | Joel David Hamkins | My understanding is that only part of the proof of Con(NF) has been verified, an important difficult part, but is it overstating matters to say we have a verified proof of Con(NF)? | |
| Apr 22 at 22:10 | history | asked | Zuhair Al-Johar | CC BY-SA 4.0 |