Re: universe set?

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Sujet : Re: universe set?
De : ross.a.finlayson (at) *nospam* gmail.com (Ross Finlayson)
Groupes : sci.math
Date : 19. Jun 2024, 21:23:10
Autres entêtes
Message-ID : <4zedndW53Ymto-77nZ2dnZfqnPWdnZ2d@giganews.com>
References : 1 2 3 4 5 6
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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, ....

Date Sujet#  Auteur
18 Jun 24 * universe set?10David Chmelik
18 Jun 24 `* Re: universe set?9David Chmelik
18 Jun 24  `* Re: universe set?8FromTheRafters
18 Jun 24   +* Re: universe set?6Ross Finlayson
18 Jun 24   i`* Re: universe set?5Ross Finlayson
19 Jun 24   i +- Re: universe set?1Ross Finlayson
19 Jun 24   i +* Re: universe set?2David Chmelik
19 Jun 24   i i`- Re: universe set?1Ross Finlayson
26 Dec 24   i `- Re: universe set?1Ross Finlayson
19 Jun 24   `- Re: universe set?1David Chmelik

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