Re: universe set?

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.