Many of you are probably familiar with Richard Taylor's famous illustration in support of the PSR. He reasons that if you were walking in a forest and came across a glowing translucent ball, you would immediately ask, "why is that translucent ball here?" You would find the response that it has no explanation quite unsatisfying, if intelligible at all. Rather, you would surely conclude that it has some explanation, even if you have no idea what the explanation is. Now imagine the ball were the size of a continent: it would still need an explanation. What about the size of a planet? Same problem. What if it were the size of the entire universe? Same problem. Merely increasing the size of the ball, or anything for that matter, doesn't at all do away with its need for an explanation. It seems quite plausible then to say:
1. Every existing thing has an explanation of its existence, either in the necessity of its own nature or in an external cause. (Premise, PSR)
A thing can be explained in one of two ways. A) It is the type of thing that exists because it cannot not-exist. Something necessary exists because it is self-sufficient. B) It is the type of thing that exists because it is dependent on another. This type of entity is not-self-sufficient. Both (A) and (B) are explanations, but they are different types of explanations.
Now, in order to make the LCA an argument for God's existence, our next premise must be justified:
2. If the universe has an explanation of its existence, that explanation is God. (Premise)
Think of what the universe is for a moment: the totality of all physical space, time, matter and energy. Whatever explains the universe, then, must transcend the universe and be timeless, changeless, and immaterial, in addition to being enormously powerful. This is very close, at any rate, to being a God-concept.
Notice that it doesn't do any good to say that the universe has existed eternally. For, a translucent ball resting on the ground of a forest would still need an explanation even if it existed for all eternity. Just as we can't get around the need for an explanation by increasing the size of something, neither can we get around the need for an explanation by increasing its age.
Another objection might be that everything in the universe has an explanation, but that this isn't true of the universe itself. Every part of a mountain may be small, but this isn't necessarily true of the mountain itself. This objection may be disposed of by sticking with the same analogy. If every part of the mountain has an explanation, then the mountain itself must also have an explanation. (In fact, we know this to be true, anyway.) Likewise, it is special pleading to say that the universe itself has no explanation.
A final objection to premise (2) is that the universe exists by a necessity of its own nature. In order to successfully respond to this objection, all we need to do is show that the universe does not possess one or more attributes that something necessary would have to have. This is fairly easy to show. Take some changing entity X. X if becomes Y, then it is no longer the case that X. This implies that X doesn't exist necessarily. Now, the universe is constantly changing in that every part of the universe is at least capable of a change in location. This implies that the universe does not have necessary existence. The universe could be something other than what it is.
Our final premise:
3. The universe exists. (Premise)
Now, what follows from these three premises?
4. The universe has an explanation of its existence. (From 1 and 3)
5. Therefore, the explanation of the universe is God. (From 2 and 4)