While the idea of a generic multiverse is certainly one that might be true, there is one particular idea of the multiverse that can only be false, given the nature of what follows from it. A multiverse is a collection of separate universes, each having their own beginnings, events, and potential endings. The laws of physics that govern each could vary drastically; the one universal constant would be the necessary laws of logic. The existence of a multiverse would not necessitate that all possible universes exist, as even two coexisting universes would validate concept of a multiverse. In fact, all possible universes cannot exist.
If all possible universes exist (an alogical realm cannot exist, since such a thing contradicts necessary truths), then there is a universe in which some natural or artificial event destroyed that universe and all other universes, rendering all matter nonexistent. Only immaterial things like logic and space would be left. But what follows, by necessity, is that there could be no universe in the present moment, since all universes were destroyed in this catastrophe! The conclusion inescapably follows, as there is a possible universe in which a calamity annihilates all matter.
However, there is a universe. As long as I experience physical sensations, matter of some form exists. Thus, the notion of a multiverse that contains every possible world is itself impossible. A key fact about this conception of the multiverse is that it does not reflect how a multiverse would necessarily be: a multiverse does not have to contain all possible worlds, because it only needs to contain more than universe to be a multiverse. There could be a multiverse--and, if there is, it does not include all possible universes, because then there would be no universe at all.
The existence of a multiverse is only logically possible if that multiverse does not contain all possible worlds. However, the fact that this kind of multiverse could exist does not grant anyone the ability to verify if it does. Setting out to prove the existence of a multiverse is setting out to prove an unverifiable thing, for spatial and sensory limitations will necessitate that one will not advance very far in such a quest. If there is a vast multiverse, I am in no position to discover it, because I can be present in merely one spatial location at a time and because my senses allow me to perceive a very small amount of the external world at most.
The multiverse remains an unverifiable and unfalsifiable concept, but that does not mean that no conceptual knowledge about a multiverse can be obtained. At the very least, one can know that a multiverse is possible, but only if it does not contain every possible universe. The idea of a multiverse encompassing all possible universes is a self-defeating one--it carries within itself the facts that dissolve it from the inside out.
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