I just realized I’ve said more on the subject already here, but in this short essay I’ll take a different (and more trivial) approach.
Astrophyicists seem to say that it’s unknown whether the universe is finite or infinite, such as in this answer: https://www.quora.com/Infinity/Is-the-universe-finite-or-infinite-1/answer/Frank-Heile. But if infinity is not a number and not the same type of value as any finite amount, and no amount of counting or addition can get from a finite amount to infinity, then isn’t it impossible for the universe to be infinite? If the universe is infinite, then infinity is the quantity of mass-energy or information in the universe, yet we are able to measure and observe finite parts of the physical universe, and these two types of quantities are incompatible—they can’t exist on the same scalarity.
In order for the universe to be infinite, it needs to be at least theoretically possible to observe an infinite amount of it, because by the very epistemic nature of existence it makes no sense to say that something exists if we can’t even in principle be affected by it (I explain why this is the case in my essay linked to above). But, since infinity and the finite cannot exist on the same scalarity, it’s impossible to start at a viewpoint of some finite part of the world and keep expanding its breadth until finally you reach a viewpoint where you can observe an infinite slice of the universe.
Also—and I think this is actually closely related to the above points—the axiom of choice has to be metaphysically assumed in order to be able to find yourself observing any particular limited part of the universe if the universe is infinite, and the axiom of choice is problematic in constructivist mathematics, and I’ve shown that mathematical Platonism, which is basically everything that’s not constructivism, is silly here.
However, if there is a multiverse, the universes contained therein don’t necessarily have a spatial (or temporal?) relationship to each other, so its infinitude wouldn’t have to exist on the same scale as our finitude, so it’s entirely possible that the multiverse is infinite. (Except that I contradict myself because if we can’t ever observe an infinite multiverse infinitely then it can’t exist by my definition of “exists.” Oh well.)
Similarly if there is a spiritual reality beyond the physical universe, it could be infinite because measurement on such a plane is subjective and malleable by mind anyway, so the concept of consistency across all scales of measurement breaks down.
Or something. Idk. Nevermind.