I know philosophers like David Lewis, have covered the idea of “modal realism”, the idea that there are other possible worlds are just as real as our actual world that we inhabit. It seems the implication is that there is an indefinite infinite set of worlds, but that they are limited in spatio-temporality. A metaphor might be that a physical library building cannot contain every possible physical book without bursting its own walls. Similarly, in his view, a single continuous spacetime cannot hold the limitless physical contents of every possible universe.
The objection would be that why should universes have this limit? But I think a more interesting paradox that comes out of this is the idea that a true multiverse would have to have simultaneously a world where there is only one universe (or none, or two, or three, etc.), all the way to there are an indefinitely infinite amount of universes at the same time. How can this simultaneous case hold?
I think a common objection might be that no universes exist that can have a logical contradiction (a square circle, or something like that), but I don’t know that this isn’t just an ad hoc limiting factor to the many worlds/possible worlds realist position.
Is the assumption that continuous space time is finite warranted? The objection seems to be that this finite space cannot contain infinite objects within it such as universes. The way to resolve this is to make the initial condition of finitude infinite, then we can accommodate infinite universes within it.
Or to use your analogy why can’t the library itself be infinite to contain infinite books ?
Just reread your OP and the paradox seems to have become apparent in my mind. And that is an infinite container cannot contain an infinite object, if we’re to assume that universes are infinite … that is multiple object’s mass would mingle/interfere with the next universe and you would be unable to tell where one universe is in relation to the next if they’re infinite.
If you take worlds to be sets/collections, then every world is completely defined by its contents (axiom of extensionality in set theory). So it would be redundant or maybe even contradictory to add to the definition of a world whether this world is the only one in existence or whether there are two, three or whatever number of other worlds.
Logical consistency is not an ad hoc limiting factor; it is one of the three classical laws of thought. And many worlds/possible worlds realism need not be inconsistent.
Realistically the whole multiverse thing is extremely speculative. For all intents and purposes, attributes assigned to it are only limited by imagination. Not unlike God and other supernatural entities. That said, the evidence and reasoning for multiverse is much more sound than any of the supernatural entities which have absolutely nothing.
Just to be clear, there are two very different ways of talking about multiple universes.
The one is physical, being a response to Schrödinger’s equations that rejects the notion of quantum collapse that is part of the Copenhagen interpretation; it says that instead of collapsing within one universe, the various possibilities diverge into other parallel universes.
The other is an artefact of logic applied to modal statements such as contain “perhaps” and “necessarily”, and comes from the work of Kripke and others on a semantics for modal logic. So the analysis of “I might not have written this post” is formalised - and it is a very good formalisation - by talking about those possible worlds in which I did not write this post.
These are two very different games. Possible worlds have nothing to do with quantum mechanics.
Lewis’s modal realism comes from treating the existential statements in possible world semantics very seriously; as if “I might have not written this post” brings into being worlds that are for all intents and purposes as real as the world in which I did write this. It’s not a majority view amongst logicians, but considering it does bring out some very interesting aspects of the logic.
Back to the OP; it appears that the proposed paradox comes about by treating these two very different accounts as if they were the same.
In modal logic the availability of a world is set by the accessibility relation, which sets out where one can go from where one is; so for example, now that I have written this post, those worlds in which I did not write this post are no longer accessible.
There are logics that deal with worlds that contain logical contradictions. They are the impossible worlds. More fun.