# Set theory and number of universes

If a set is just a collection of objects, then a universe could be called a set, right? Assuming the answer to this question is yes, then is it even possible to have a universe containing all universes (assuming multiple universes)? I don't think it's possible because according to set theory, there can be no set that contains all sets (Russell's paradox). Then, what does this imply about the number of universes that there could possibly be?

Note by Hobart Pao
4 years, 5 months ago

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- 3 years, 3 months ago

There is no contradiction. The "thing" containing all universe is NOT a universe. It's true tutoriage.

- 3 years, 4 months ago

With regards to set theory, it depends on the variant of set theory. If you're using the idea that a set is literally any collection of things, then that's in the realm of naive set theories, and as you rightly point out, naive set theory does lead to all sorts of paradoxes and contradictions (like Russel's Paradox).

That's why mathematicians created more restricted versions of set theory. I believe the most commonly used one is called ZFC, and in ZFC, not every collection of objects can count as a set. For instance, a collection that contained every possible set, wouldn't be considered a set. With that in mind, I wouldn't say that set theory proves that there's no set of all sets. Rather, I'd say that it's been designed so as to make sure that the issue doesn't come up.

Also: I believe that in ZFC, the only things that a set can contain, are other sets. So under these rules, a physical universe wouldn't be called a set. (If you meant a metaphorical universe, like the Von Neuman Universe, then that doesn't exist as a set in ZFC either. It's a collection that isn't considered to be a set.)

Or perhaps it can help you: you could choose to follow the example set by ZFC - and not worry about it. :)

- 3 years, 6 months ago

Well then that universe has to Contain itself

- 3 years, 7 months ago

Only a one dimensional string of infinite length/energy is sufficient to incorporate all possible universes. Cheers

- 3 years, 10 months ago

There is no contradiction. The "thing" containing all universe is NOT a universe. (Call it 'multiverse' if you want). Hence, a multiverse need not contain itself. Eg : A plane can be set as the collection of all lines. But, it is still one plane and does not 'contain' any planes.

On the other hand, if you define universe as 'set of everything', there cannot be a second universe. Hence, there is only one set here.

- 4 years, 1 month ago

Nice solution

- 4 years, 4 months ago

Darkmind, once you have a totality of everything, you cannot have something outside of it. Just because you find a separate universe somewhere doesn't mean it wasn't already in the set. If the set is defined as the "totality of everything" than nothing can be outside of it; the idea that it was outside is one of subjective perception, not of the function of the set. Right?

(Of course, I'm not as smart as most of you, so I could be wrong.)

- 4 years, 4 months ago

Remember also that "Uni Verse or one turning" is a misnomer referring to the heliocentric view that the sun was the center of EVERYTHING (see Newman's Idea of a University) Soooo, if one uses the word KOSMOS meaning the totality of everything, I agree with DarkMind that "more than one totality" is a contradiction in terminology and perhaps also in reality. Jim Farley Santa Fe, New Mexico The question of odd or even is perhaps a bit metaphysical even for cosmology!!

- 4 years, 5 months ago

Nothing. The question is incoherent. A universe is not ""something"". It is the Totality of Everything. And the Totality of Everything is only one. More than One Totality is a contradiction.

- 4 years, 5 months ago

What do you mean by "totality"? What about having multiple universes?

- 4 years, 5 months ago