The Second Part of the Third Way

​As in Maimonides’ case, Aquinas adds a second stage to the argument. He wants to establish not only the existence of a necessary being, but of a necessary being that has existence “in and of itself”, that doesn’t derive its necessary existence from something else.  Here again Aquinas has recourse to his no-infinite-regress assumption: the chain of causation explaining why derivatively necessary beings are necessary must terminate in a thing that is non-derivatively necessary, and this being will be God (a being whose essence is its existence).
 
Here’s a way of thinking about this second stage. Let’s suppose for contradiction that there is an infinite regress of necessary beings, each of which derives its necessity from its predecessor. So, N1 is caused to be necessary by N2, N2 is caused to be necessary by N3, and so on. And let’s assume that all necessary beings belong to such a regress: nothing is necessary in and of itself (unconditionally). Now, a world in which none of N1, N2, N3, etc. exist is an impossible world, since each of these beings exists necessarily and so exists in every possible world. So, the scenario in which none of the N’s exist is an “impossible world”, if you’ll allow me to talk of it that way. Let’s call this impossible world w!.
 
Let’s assume that if a scenario S is impossible, and this scenario S can be derived from some possible world w simply by deleting entities that exist in w, then there must be some ground or explanation of S's impossibility. Let's stipulate that the impossible world w! comes from the actual world (which is possible) by deleting all of the conditionally necessary beings in the actual world. Then the impossibility of w! must be explained in one of two ways: it fails to include something that is unconditionally necessary, or it violates some constraint of conditional necessity, i.e., it contains A but not B, even though A would (if it existed) necessitate B’s existence (which it could do by necessitating B’s necessary existence). But w! is not impossible in either of these ways. There is (by hypothesis) no unconditionally necessary being, so it isn’t impossible for that reason. And it satisfies all of the conditional constraints by never including any of the N’s. Its non-inclusion of Ni is permissible, because it also fails to include N(i+1), and Ni is necessary only conditional on N(i+1)’s existence. So, w! is possible, after all, which means that none of the N’s is necessary.
 
Therefore, it is impossible for anything to be necessary unless something is necessary unconditionally. And to be necessary unconditionally is to be necessary in and of oneself.