It's no surprise to some of you that the Modal Third Way (MTW) is my favorite contemporary argument for God's existence. What has occurred to me in discussing the argument with those of a skeptical persuasion is that many people are often willing to accept the premises individually, but not in conjunction with one another. Let me explain.
1. Necessarily, if something exists right now, then there was never a past time at which nothing existed. (Premise)
2. Something exists. (Premise)
3. Possibly, there was a past time at which nothing contingent existed. (Premise)
From these three premises alone, along with some definitions, we can begin an argument for the existence of a necessary entity. Assume that a necessary entity does not exist. This implies: Possibly, there was a past time at which nothing existed. However, this contradicts the implication of (1) and (2) - namely, that there was never a past time at which nothing existed.
One way to avoid this conclusion is to deny that (1) and (2) are compossible with (3). In this case, it is contended that while there was never a past time at which nothing existed, it is still possible that there was such a past time. It just so happens that the actual world includes presently existing entities. However, if it had ever been the case in the past that everything contingent failed to exist, then nothing would exist at present.
On the face of it, this objection appears consistent, although perhaps a bit contrived. Nevertheless, the objection does help us to better formulate the argument in such a way that it avoids this conclusion. Let's simply add an additional premise:
4. The states of affairs entailing 1, 2 and 3 are compossible. (Premise)
From this we can infer:
5. Possibly, a necessary entity exists. (Implied by 4)
Then, of course, our modal buddy S5 comes along:
6. Therefore, a necessary entity exists. (From 5 and S5)
Obviously, (4) cannot simply be asserted without support. The skeptic may just dismiss it as impossible. The problem is that there is a good rule of thumb to follow when gauging whether or not a set of states of affairs is compossible, which is that conjunctions of individually possible states of affairs yield a possible conjunction, unless a contradiction is derivable.
For example, p1: "the Boston Red Sox won the 2004 World Series," and p2: "the Chicago White Sox won the 2005 World Series." These propositions are compossible (in fact, we know they're actual). So now, let's take p3: "the Boston Red Sox did not win the 2004 World Series." Both p1 and p3 are possible, but they are not compossible. We know this because their mutual instantiation entails a contradiction.
I suggest that apart from the skeptic's ability to derive a contradiction from the conjunction of (1) through (3), he should admit their compossibility and therefore conclude that a necessary entity exists.