Timeline for Is there a metamathematical $V$?
Current License: CC BY-SA 4.0
23 events
when toggle format | what | by | license | comment | |
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Mar 11, 2023 at 3:50 | answer | added | C7X | timeline score: 1 | |
Mar 24, 2021 at 11:31 | answer | added | Peter Scholze | timeline score: 8 | |
Feb 15, 2021 at 10:42 | answer | added | Vincent R.B. Blazy | timeline score: 0 | |
Feb 12, 2021 at 22:19 | vote | accept | Pace Nielsen | ||
Feb 12, 2021 at 21:42 | comment | added | Akiva Weinberger | @PaceNielsen Easy enough | |
Feb 12, 2021 at 21:40 | answer | added | Akiva Weinberger | timeline score: 10 | |
Feb 12, 2021 at 21:38 | comment | added | Pace Nielsen | @AkivaWeinberger After considering all the comments and answers, I think your comment is actually the best answer to the question as I stated it. There is no meta-V because there cannot be a finished Ord (assuming V satisfies separation). If you want to make your comment into an answer, I'll accept it. | |
Feb 4, 2021 at 6:16 | comment | added | David Roberts♦ | Related: What is the real category of sets? | |
Feb 4, 2021 at 5:49 | answer | added | Timothy Chow | timeline score: 6 | |
Feb 4, 2021 at 3:28 | comment | added | user141903 | No it is not a completed whole yet! Nice question and lots of nice answers. It is a completed whole in any universe from the perspective of any universe, or anywhere you want to study it from. But any universe is not yet really complete because the Multiverse is alive. | |
Feb 4, 2021 at 2:53 | comment | added | Qfwfq | Just a comment to ask a clarification about terminology. I think there are two senses in which the expression "metamathematical question" is used, namely: 1) a non-formalized philosophical question concerning mathematics; and 2) a question in a specific formalized metatheory [in particular, "metamathematical" in sense 2) is a particular case of "mathematical"] E.g. Goedel's incompleteness theorems are (mathematical theorems which are) metamathematical in the sense 2). Do I understand it correctly that you are using "metamathematical" in the sense 1) i.e. as a synonym with "philosophical" etc? | |
Feb 4, 2021 at 2:05 | comment | added | Akiva Weinberger | To me, the idea of ordinals being a completed infinity contradicts the idea of ordinals (I mean the informal idea of ordinals, that is, that after every "completed collection" of ordinals there should be another ordinal). | |
Feb 4, 2021 at 1:52 | answer | added | Julia Williams | timeline score: 21 | |
Feb 4, 2021 at 1:02 | history | edited | Pace Nielsen | CC BY-SA 4.0 |
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Feb 4, 2021 at 0:56 | comment | added | Tim Campion | If we're comparing the completedness of $\mathbb N$ and $V$, why not throw $\mathbb R$ into the mix? I find the question in this case particularly interesting because when $\mathbb R$ is used to model phenomena in the real world, the use of $\mathbb R$ for such modeling is often naively justified in terms of some kind of map taking each distinct real number to a distinct real-world object, but when one steps back it seems very strange to assert that the corresponding real-world objects are actually uncountable in number. | |
Feb 4, 2021 at 0:13 | comment | added | Alec Rhea | I think that Joel's multiverse view is probably relevant to this question and your interests, although I can't see exactly how (besides the obvious) right now. | |
Feb 4, 2021 at 0:05 | comment | added | Asaf Karagila♦ | What should I believe if I'm a mathematical nihilist that believe that all that "believing" stuff cannot be properly justified, mathematically speaking, and that at the end of the day all the approaches have their pros and cons, none is perfect, and that ultimately you should be a utilitarian and choose whichever approach helps you present the clearest argument in a given context? | |
Feb 3, 2021 at 23:27 | comment | added | Tim Campion | I think "isomorphic to" is not intended. It's just that if you ever find yourself needing such a product, it's probably because you're trying to embed something into it or something like that, and for those purposes it suffices to use the skeleton. | |
Feb 3, 2021 at 23:10 | comment | added | Monroe Eskew | Why do you say that the product of all equivalence classes of countable rings (coded as reals) “would have been” isomorphic to the product of all countable rings? Do you not consider products where one term is repeated many times? | |
Feb 3, 2021 at 23:06 | history | edited | Monroe Eskew |
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Feb 3, 2021 at 22:51 | comment | added | Pace Nielsen | @LSpice Perhaps I should have said "pop up". Less "popping" that way. | |
Feb 3, 2021 at 22:49 | comment | added | LSpice | "They occasionally pop their heads" is both totally comprehensible and very disturbing as an idiom. | |
Feb 3, 2021 at 22:36 | history | asked | Pace Nielsen | CC BY-SA 4.0 |