Here is a quick modal argument I came up with for the proposition that <something exists> is a necessary truth. Basically, the answer to why there is something rather than nothing is rather straight forward: something had to exist -- it's impossible for there to have been nothing. In any case, here is the argument. I came up with it myself, but I wouldn't be surprised if it were already independently developed by someone like Alexander Pruss or Joshua Rasmussen -- or some medieval theologian who anticipated modern modal logic. In Philosophy, there is not much new under the sun.
Argument:
Assume that possibly, nothing exists. If it is possible that nothing exists, then it is possible that necessarily, nothing exists.
This is because there is
no potentiality in a world w1 at which nothing exists; and what is possible if some w were actual is based on the way w would be. In other words, what grounds the possible existence of entities, events, etc, in the actual world is how the way the world actually is. And what grounds what is possible in another world is how that world would be if it were in fact actual. Possibility is grounded in actuality. And since there is nothing at w1, there is no potentiality for anything to exist at w1. So every world
which w1 has access to will be a world at which nothing exists. So at w1 it is true that <necessarily, nothing exists>. So it is possible that necessarily, nothing exists.
Now, by the S5 modal axiom, ◊◻P entails ◻P. So it follows that <necessarily, nothing exists>. And this entails that nothing exists. But clearly something exists at the actual world. This is a contradiction. Therefore, reject the assumption: it is not possible that nothing exist. So, necessarily, something exists.
Note that the argument's conclusion is not that a necessary being exists, but only that necessarily, something exists. The argument's conclusion is thus consistent with the view that <possibly, only contingent beings exist.> But it seems highly plausible that <if it is possible that only contingent beings exist, then possibly, nothing exists.> After all, for every contingent being x at a world w at which only contingent beings exist, x could have not existed -- this just follows from the definition of what it means to be contingent. So it seems like it could have been the case that none of these contingent beings existed, and hence that nothing exists. But we have already shown that it is impossible for nothing to exist. Therefore, it is not possible that only contingent beings exist. So, there is at least one thing that had to exist -- i.e., there is at least one necessary being.
So from the following three propositions, which strike me as obviously true, it follows in the S5 modal system, pretty much universally accepted among modal logicians and metaphysicians, that there is a necessary being:
1. If it is possible that nothing exists, then it is possible that necessarily, nothing exists.
2. Something exists.
3. If it is possible that only contingent beings exist, then possibly, nothing exists.
