Path: ...!Xl.tags.giganews.com!local-2.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Wed, 19 Jun 2024 20:23:12 +0000 Subject: Re: universe set? Newsgroups: sci.math References: <6wKdncQ4Ibe0YOz7nZ2dnZfqnPSdnZ2d@giganews.com> From: Ross Finlayson Date: Wed, 19 Jun 2024 13:23:10 -0700 User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101 Thunderbird/38.6.0 MIME-Version: 1.0 In-Reply-To: Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 7bit Message-ID: <4zedndW53Ymto-77nZ2dnZfqnPWdnZ2d@giganews.com> Lines: 90 X-Usenet-Provider: http://www.giganews.com X-Trace: sv3-nntilmYOZM6Y7OK7WipaGthJGt7GtaNsQQWkLRZwlUrVGCWtxl0bpsub92wBazVPLlGNy3MiG6W2xxQ!JQUwjBjUT507OaBnSWHc6zqKCbliNHo0awQFMseSXmO3jQhYJMlogwXdPeYQM2p//wJ2V/8P7jAw X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.3.40 Bytes: 5284 On 06/19/2024 02:12 AM, David Chmelik wrote: > On Tue, 18 Jun 2024 14:33:40 -0700, Ross Finlayson wrote: >> On 06/18/2024 02:29 PM, Ross Finlayson wrote: >>> On 06/18/2024 06:18 AM, FromTheRafters wrote: >>>> David Chmelik has brought this to us : >>>>> On Tue, 18 Jun 2024 12:05:45 -0000 (UTC), David Chmelik wrote: >>>>> Is the universe set called universet? >>>> >>>> Domain of Discourse. Usually a blackboard bold (or doublestruck) D is >>>> the symbol. > > I remember that, or 'universe of discourse' but my professors usually just > wrote the specific set such as N, Z, Q, R, C (in blackboard bold). > >>> See for exampler Forster's "Set Theory with a Universal Set". >>> >>> The idea that a universal set exists is called "Domain Principle" >>> or "Domainprinzip". > > I see. I'm not convinced sets exist, or maybe/likely they do, but not > that set theory rather than number theory should be foundation, such as > explained by mathematical philosopher Mike Hockney. Nevertheless, I > always liked the idea of 'universe set', like the greatest infinity (other > than the universe set's power set, haha). > >>> The domain of discourse is a usual term. >>> >>> See for example Finsler and Boffa, Kunen inconsistency, >>> set of all sets, order type of ordinals, group of all groups, >>> infinite-dimensional space, "Continuum", sometimes just "the world". > > Do those authors also call it infinite-dimensional space, or is that your > elaboration? Of course, that exists, but I don't know I'd call that a > set, despite contains everything that exists ideally/mentally/spiritually > (which contains all 'atoms'/'matter'/'physis' as illusion within). > >> https://www.youtube.com/watch?v=aHS0VKOM09U >> >> "Thomas Forster - Recent developments in Set Theory with a Universal >> Set" >> >> I don't vouch for this yet it's part of the study, about things like >> "New Foundations with Ur-Elements" or "New Foundations with Universes" >> and so on. > > There should be new foundations with numbers, whether considered points/ > monads or line segments on the number line, or waves. > >> Here's it's "Null Axiom Theory" or "Universal Axiom Theory", >> for example. > > Axioms are important, but I noticed for some, if it's unclear what they > mean, and they're not geometrically demonstrated (like most/all Euclid's, > and ones from Pythagorean Theorem to Euler's Formula, etc.) then we might > not know if they ever apply to reality, like I don't 100% know what > 'infinite containers' or 'games' mean in relation to reality. Those may > be fun but I prefer ones that describe reality. > The Domain Principle idea that there exists "the domain" is one of the ideas entertained by Georg Cantor, often attributed with the development of uncountability, while du Bois-Reymond at least discovered the diagonal argument and that since time immemorial there was aliquot parts and when sets are countably infinite that there are invertible mappings the bijections between them, while also that there is density that "half of the integers are even integers, according to density", Cantor brought up the domain principle then Cantor's paradox is so named because the powerset result applied to it would result a contradiction, it's still called that even though it contradicts ordinary set theory. The "extra-ordinary" is the key sort of phrase, coined by Mirimanoff, to reflect these things that are Sublime ("greater than themselves"). The "Null Axiom Theory" is "axiomless", a course of "axiomless natural deduction", while "Universal Axiom Theory" is just part of the dually-self-infraconsistent nature of that, "first principles" and "final cause" together. Then I usually call the whole thing "A Theory", what would be foundations for philosophy, logic, mathematics, physics, and science and statistics, physics, .... Physics/Metaphysics, .... All one theory, ....