The topic of the PSR has cropped up several times in my discussions with theists. It has generally been seen by them as an inviolable law of nature that provides justification for belief in God as the ultimate reason for everything. The thinking goes something like this:
1. Everything has an explanation. (PSR)Why should we accept the PSR? It seems that through much of history, there was not universal agreement among philosophers that it must be true. Many of the Greeks, as well as early Christians, thought that the universe had no beginning, and as such, it simply existed as a brute fact. It wasn't until the development of philosophically sophisticated theism that the PSR began to catch on as a key principle in philosophy. Only then did it become fashionable to reject the notion of things that exist as a brute fact.
2. The world exists.
3. Therefore, the world has an explanation for its existence.
4. Whatever is the explanation for the world, must itself have an explanation or reason.
5. Contingent things (including the world) are explained as being caused by something else.
6. The causal chain of contingent things must either be infinite, or must begin with something that exists necessarily or exists as a brute fact.
7. Both an infinite chain of contingent things and a brute fact are rejected as violations of the PSR.
8. Therefore, the ultimate explanation for the existence of the world is something that exists necessarily.
9. God is the thing that exists necessarily, and necessity is the explanation for God's existence.
10. Therefore, God's existence is consistent with the PSR.
One thing that I note in reading the SEP article on PSR is that there is a distinction made between cause and explanation or reason. God is said to be uncaused, but God has an explanation in the necessity of its being. An explanation or reason is said to be something intelligible, as noted in the SEP article. A cause is an explanation, but an explanation is not a cause. That brings up an interesting point. The reason for something, according to the PSR is not necessarily a cause, but an intelligible explanation. However, in the absence of minds with the ability to reason, there is no intelligible explanation for anything. Before humans existed, there were no explanations, there were no reasoning minds. There was only reality. So there was no reason for anything to abide by the PSR. The existence of the world and everything else was independent of the PSR (which didn't exist until it was invented by mankind). I point this out because reality is separate from man's ability to rationalize and explain things. It doesn't matter whether we have an explanation for things. Reality doesn't need an explanation. Reality is what it is, and that's a brute fact. It is only people who insist that everything must have an explanation. Reality doesn't care.
One major factor in the justification of the PSR is the observation that there is a cause for all contingent things, as was noted by Aquinas. However, in the modern era of highly sophisticated detection devices, we may no longer be justified in saying that the observation holds true for all things. We are able to observe things that come into existence (such as the spontaneous creation of particles) and events that happen (such as atomic decay) without any apparent cause. Adherents of the PSR will argue that there really is a cause for these things, even if we can't see it. In fact that could very well be the case. From a materialist perspective, there could be aspects of reality that are hidden from our perception. There could be more dimensions than we are able to perceive, and there could be things that exist in that extra-dimensional space that are the cause of things that we can observe. From a theistic perspective, God is the cause of everything we observe, and God is the go-to answer whenever we need an explanation for something. But in either of these situations, materialistic or theistic, we don't really know. The things we postulate as explanations for our world and everything we observe may or may not be true. It might be the case that there is simply no explanation for some things.
Of course, the theist will still insist that God is the ultimate explanation for everything we observe, and that's based on the reasoning of people like Aquinas. The second way makes this explicit. But the third way attempts to prove that God exists necessarily. Aquinas' argument from necessity is as follows:
1. Since objects in the universe come into being and pass away, it is possible for those objects to exist or for those objects not to exist at any given time.So according to this argument, the necessity of God follows logically from the existence of contingent things. In other words, God's necessary existence is explained by the fact of contingent things. So contingent things have an explanation for their existence, according to the PSR, and a necessary being, or God, is the ultimate explanation for them. At the same time, the existence of contingent things is the explanation for the necessity of God, according to Aquinas' third way. By his reasoning, a necessary being is the explanation for the world, and the world is the explanation for a necessary being. This sounds dangerously close to circular reasoning.
2. Since objects are countable, the objects in the universe are finite in number.
3. If, for all existent objects, they do not exist at some time, then, given infinite time, there would be nothing in existence. (Nothing can come from nothing—there is no creation ex nihilo) for individual existent objects.
4. But, in fact, many objects exist in the universe.
5. Therefore, a Necessary Being (i.e., a Being of which it is impossible that it should not exist) exists.
Even if we accept that everything in the observable world has a cause, we need not accept that all things have an explanation. There may be something that exists as a brute fact. By rejecting the PSR, we can postulate that something is the cause of the observable world, but that thing need not have an explanation. This avoids the circularity of reasoning that leads to postulation of a necessary being. We already observe that nature apparently doesn't care about what happens in the world. It's no great stretch to think that nature doesn't care whether we have an explanation for it.