Why Is There Everything Rather Than Nothing?

Sometimes when answering the question "Why is there something rather than nothing?" the atheist will say:

“Science now suggests that there is in fact a multiverse containing an infinitude of universes, and the laws can be different in each universe. Thus, there it is no mystery why there is this universe: all universes exist, because anything that can happen does happen.”

Some theists have misunderstood the multiverse answer as just an atheist's way of evading the question. In fact, there are unrelated, principled scientific reasons to suppose that the multiverse is true, though its truth has not been demonstrated definitively.

Still, it does not answer the question adequately. Here's why. 

If we suppose that the "world" can contain contain multiple worlds or universes, each of which instantiates one possibility among many, and if we further argue that the multiverse is a world that in fact instantiates all such possible worlds, then it is a world of all worlds. This is where, I suppose, we get the line "anything that can happen does happen." Logically, though, the set of all possible worlds that could exist is a set of sets (each set being a possible configuration of existing worlds) such that it must contain not only a set with a single element for every possible world existing alone (e.g. {A}, {B}, {C}), but also all sets containing some combination of those worlds, including the set containing all possible worlds (e.g. {A, B, C}, {A, B}, {B, C}, {A, C}), but also the empty set containing no worlds (e.g. {}).

The all-possible-universes answer offers only a single of these sets as really existing: the set of all universes (e.g. {A, B, C}), while excluding the other combinations. But these other configurations ("no world" and all variations on "some worlds but not all worlds") are logically possible.

Further, it is metaphysically impossible that all logically possible sets are instantiated, because the sets are mutually exclusive. If set {A, B, C} defines the contents of reality, then set {A} or {A, B} or {} cannot also define the contents of reality. While the atheist may think that what he is saying is that the multiverse means that "anything that can happen does happen", he is mistaken: the instantiation of the multiverse that contains all possible worlds excludes the instantiation of the other sets which are also realities that "can happen". 

So we still require a reason why it is that the multiverse set is instantiated rather than the empty set or any of the infinitude of alternate sets. 

In short: If the answer to the question "Why is there something rather than nothing?" is "The Multiverse, because its everything", then the further question is "Why is there everything, rather than nothing?"