# What is the Principle of Sufficient Reason?

The following two principles, both of which might be attempts to formalise a Principle of Sufficient Reason, seem distinct to me.

(1) Every truth has an explanation.
(2) Every truth is explicable.

To see how they may come apart, consider (3), (4) and, especially, (5)

(3) It’s raining in Seattle.
(4) I’m wearing green socks.
(5) It’s raining in Seattle and I’m wearing green socks.

Assume, as shouldn’t be too hard, that the world really does make (3) and (4) true. (I can see that (4) is true, and my computer tells me (3) is true, at least as I write this sentence. Perhaps by the time I finish the post it will have cleared up!) I assume each of these facts has some explanation or other. The explanation for (3) will be in terms of meteorological facts about the Pacific Northwest, and the explanation for (4) will be in terms of the state of my sock drawer and my sock preferences. Call these explanations E3 and E4 respectively.

Will (5) have an explanation? I don’t see any reason to think that it will. The concatenation of E3 and E4 is not, I think, an explanation. It looks, to me at least, like two explanations. Since the best we’re likely to do by way of explaining (5) is to offer E3 and E4, and offering those two explanations does not, I say, amount to offering an explanation, I suspect that (5) does not have an explanation.

That’s not to say that (5) is inexplicable. Indeed it is perfectly explicable. Once we’ve offered E3 and E4, we’ve explained it. If we thought that anything explicable had an explanation, we would conclude that (5) must have an explanation. But that seems too quick. Offering several explanations, the conclusions of which collectively entail (5), renders (5) perfectly explicable, even if there’s no one explanation which has those explanations as parts. More generally, any logical consequence of some explicable facts is, in virtue of being that way, explicable. But not all such consequences have single explanations; (5) doesn’t.

The argument here makes heavy use of the idea that E3 and E4 don’t combine to form an explanation. That seems intuitively correct to me, but you might want a more substantive argument here. So note that this conclusion falls out naturally from the best theory of explanations on the market right now, namely Michael Strevens’ causal inference account.

Roughly speaking, Strevens’ idea is that an explanation is an entailment from general principles (as Hempel said). As is well known, Hempel’s account overgenerates by allowing effects to ‘explain’ their causes. Strevens’ innovation was a clever idea about how to resist that conclusion. He says that only entailments where there is a proof of the conclusion from the premises such that each inferential step corresponds (in some intuitive sense) a causal connection between the steps. So an inference from the flagpole’s height to the length of its shadow is causal, in the relevant sense, while an inference from the length of its shadow to its height is not.

The notion of corresponding to a causal process is rough, to say the least. But it does seem to track something important in the notion of explanation. And note that it rules out any simple way of putting E3 and E4 together. If E3 and E4 are arguments, with (3) and (4) respectively as their conclusions, then there will be a valid argument that has the premises of E3 and E4 as premises, and (5) as a conclusion. But the last step of that argument will be a step of and-introduction, to get from (3) and (4) to (5). And that doesn’t seem to correspond to any causal process at all. So on Strevens’ account, there isn’t any way, or at least isn’t any simple way, to put E3 and E4 together into a simple explanation. That seems like useful supporting evidence to the intuitive claim that there is no way to put E3 and E4 together into a simple explanation.

The distinction between (1) and (2) is important because it matters for the prospects of any cosmological argument for the existence of God from a plausible Principle of Sufficient Reasons. The best version of such an argument is in Alexander Pruss’ The Principle of Sufficient Reason, and he makes quite heavy use of (1). Consider, for instance, the following possibility. We have some propositions, p1, p2, …, such that pn is explained by pn+1 for each n. Pruss claims this won’t do, because the conjunction of all the pn, call it P, would be self-explanatory, and it is the wrong kind of proposition to be self-explanatory.

I deny the inference here. P wouldn’t be self-explanatory, because P would be neither the right kind of thing to be an explanation, nor to have an explanation. P is explicable. It is explained in virtue of the explanation of each of its conjuncts. If P had an explanation, that explanation would be P itself. (Or perhaps it would be P minus p1.) And that’s absurd. But since there’s no reason to assume that P has an explanation, there’s no reason to assume that it must be self-explanatory.

I won’t go into the details, but a similar (if more sophisticated) argument is at the core of Pruss’ contention that the only explanation of the conjunction of all (contingent) truths, is a necessarily existing God. Perhaps such a God is the only possible explanation of the conjunction of all truths. It doesn’t matter for any epistemological purposes, because we have no reason to believe this conjunction has a (single) explanation. Whatever intuitive plausibility a rough Principle of Sufficient Reason has only extends as far as (2), but to derive the existence of a necessitarian God, we need (1). This is important, because the primary argument Pruss has for the Principle of Sufficient Reason is that it is intuitive, and that there are no clear counterexamples to it. I think if we interpret the Principle as (1), both claims are false – (5) is a counterexample and shows it isn’t intuitive. What is intuitively plausible is (2), but that doesn’t ground any result of philosophical or theological significance.

In two recent books, Graham Oppy has objected to cosmological arguments on the grounds that they are based on an excessively strong Principle of Sufficient Reason. I think his main philosophical conclusions are correct, but they’re stated in a needlessly counterintuitive way. Oppy argues as follows, where T is the conjunction of all contingent truths about the world. (I’m bracketing here an interesting argument from Kevin Davey and Rob Clifton that there is no such conjunction. If that’s true, the cosmological argument fails for independent reasons.)

(6) If T is explained by a contingent fact, then it is explained by something it entails
(7) If T is explained by a necessary fact, then some necessary fact explains a contingent fact
(8) Nothing is explained by what it entails
(9) No necessary fact explains a contingent fact
(10) So, T does not have an explanation

That argument looks sound to me, assuming T exists. But I think Oppy is a little misleading when he then describes T as being a “brute fact”. If we want that phrase to mean, by stipulation, that the truth in question has no single explanation, then I suppose it is true that T is brute. But there’s a much more natural interpretation for the claim that something is a brute fact, namely that it is inexplicable. And there’s nothing in this argument that implies T is inexplicable. Indeed, it may well be that all the different conjuncts in T explain all the conjuncts in T collectively, without anything explaining itself. As long as T is infinite, that will be a possibility. So we don’t have yet a reason to regard T as a brute fact, in the most natural sense of that expression. None of this undermines the conclusions Oppy draws about infinite regresses, or the cosmological argument, but it is I think worth getting clear on what denying (1) does and doesn’t imply.

The way I’m suggesting we regiment our terminology allows for a nice distinction. Assume that a, b, c and d are all F; that a, b, c and d are all the Gs; that there are perfectly good explanations of each fact Fa, Fb, Fc and Fd; but that there is no way to simply combine these explantions into a single explanation. Assume in fact that there is no single explanation of either the fact that Fa & Fb & Fc & Fd, or of the fact that All Fs are Gs. Then I want to say that this is a coincidence, but not a brute fact. Coincidences are generalisations (perhaps over somewhat gruesome classes) that don’t have an explanation, even if they are explicable. If one of the coincidents were inexplicable, then the coincidence would (perhaps) be a brute fact. But most coincidences are explicable, it’s the lack of a single explanation that makes them coincidences. It’s part of folk wisdom that there are coincidences, which is to say that it’s part of folk wisdom that whether or not (2) is true, (1) is false.

## 9 Replies to “What is the Principle of Sufficient Reason?”

1. arpruss says:

I think ungrounded infinite regresses are not only unexplained, but inexplicable. Suppose that we look at the infinite regress of states strictly after noon of a cannonball shot out exactly at noon. That regress is explicable only in light of the shooting of the cannonball. If time began strictly after noon (e.g., if time was an open interval (noon, infinity)), the regress would neither be explained nor explicable. But this regress is just like the infinite regress of causes of the universe (the difference between (-infinity,infinity) and (noon,infinity) does not appear significant to me in light of the order isomorphism between the two intervals).

2. I don’t really see why the flight of the cannonball would be inexplicable. Every part of it is explicable! This is really just an intuition clash, I guess, but once I’ve realised that every part of the cannonball’s flight is explicable, the flight seems explicable to me.

It’s true that there isn’t, as far as I can tell, an explanation for the flight. But I think that’s a very different question.

3. jlamont says:

I’m inclined to agree with the criticism of the principle of sufficient reason but the cannonball? Isn’t there a surfeit of explanation on Brian’s view? If an actual cannonball is shot out in the circumstances described, Brian holds that the flight of the cannonball explains itself (since every state in the flight is explained by a previous state), and there is hence no need for further explanation of the cannonball’s flight. But then the explanation of the cannonball’s flight as due to being shot out of the cannon is surplus to requirements.
The idea that one state in the flight of a cannonball can be causally explained by a previous state might of course be called into question (you could say that only things, not states of things, can be causes) – which would explain an irresolvable clash of intuitions here.

4. arpruss says:

Professor Weatherson:

First of all, it wouldn’t do justice to our intuitions about the PSR if the flight of cannonball counted as explicable. For then bricks popping into existence ex nihilo and all that would be explicable, as long as they did so on time intervals open at the lower end.

Suppose I first hear of the flight of the cannonball, but don’t hear of the cannon being fired. I then hear of the cannot being fired. It seems that only when I’ve heard of the firing of the cannon that “it makes sense”, that it becomes explicable. (It doesn’t seem to me that this is like the case of a coincidence where when there is no further explanation of the conjunction, we shrug our shoulders and say: “I guess it was just a coincidence”, but when we find a further explanation, we say: “Ah, so it’s not just a coincidence.” Chains of causes aren’t the same sort of thing as coincidences.)

I suppose you’d have the same intuition about circularity? If I learn how to make the time machine from my future self, and then go and make it and tell my past self how to do that, do you have the intuition that this is all explicable?

5. Carrie,

Even if you don’t have the intuition that E3+E4 fails to be an explanation for (5), do you think there’s a theory of explanation that says it is an explanation?

I don’t think E3+E4 unifies, in any interesting way, the relevant facts, so I don’t think it counts as an explanation on a unification approach.

And I think (5) is the wrong kind of thing to be caused, it doesn’t report the occurrence of an event after all, so it can’t have an explanation on a causal account.

And, unsurprisingly, it fails to be an explanation on a prominent hybrid account like Strevens’.

So even if you think intuitively E3+E4 is an explanation for (5), do you think there’s a theory of explanation on which this is true?

6. jlamont and Alexander (if I may),

I wonder if we’re mislocating the clash of intuitions here. I think the cannonball’s flight is explicable because every part of it is explicable. More precisely, I think the following argument is sound.

1) Every part of the cannonball’s flight is explicable.
2) If every part of the cannonball’s flight is explicable, then the flight is explicable.
3) So, the cannonball’s flight is explicable.

I take it the cannonball is an interesting example because it’s meant to be a challenge to (2), which is an instance of a more general principle (the Hume-Edwards principle).

But to the extent I can see any intuitive force here, it’s to reject (3). And, if I try to put myself in the frame of mind to reject (3), what I find is that (2) still seems plausible, but I start to doubt (1). I start to think, that is, that an ‘ungrounded’ explanation, such as the explanation of the cannonball’s later trajectory in terms of its earlier trajectory, is no explanation at all.

That would be independently interesting for debates about regresses. But now I’m interested if there’s any positive reason to think (2) is the culprit in this argument rather than (1)? (Assuming, of course, that there is a culprit. I think on reflection the argument is sound, and the force of the arguments for (1) and (2) is stronger than any intuitive implausibility of (3).)

7. arpruss says:

That’s a nice point. So, now I have two different kinds of intuitions that I can use for purposes of theistic arguments. One is that the ungroundedness of a regress undercuts the explanatory status of the particular steps in the regress. There are indications that something like this intuition is behind claims in Aquinas’ Summa Contra Gentiles. The second is to affirm that there can be genuine explicability grounded din the steps of a regress, but the whole is not thereby explicable.

Myself, I think the intuitions behind (2) come from non-circular finite cases where (2) does in fact hold. (If circular explanation is impossible, then I can drop the “non-circular” in the previous sentence.) I can occasionally get myself into a mood (mainly by reading and thinking about Aquinas) where I find denying (1) plausible. But generally I find (1) fairly plausible, and the conjunction of (1) and (2) very implausible, and so I tend to deny (2).

8. I have a more indirect worry about PSR. I believe Richard Swinburne gives an account of the god of theism as a being who is contingent (exists in some worlds, but not in others), and yet who is a metaphysically indepedent, “free-standing” being at the worlds in which he exists. On this account of God, then, there seems to be no explanation for why God exists.

Now my worry is this: Swinburne’s god seems metaphysically possible, and yet this possibility seems incompatible with PSR. But if so, then why shouldn’t I conclude, “so much the worse for PSR”?