The thoughts that I’ve presented over the last few posts – about possibility and necessity, and their grounding in the causal powers of the things that exist – lead nicely into another discussion: one about what I believe to be a fundamental metaphysical principle, second only to the laws of logic in its significance for the nature of reality. It has usually been referred to, since the time of polymath Gottfried Leibniz, as the Principle of Sufficient Reason.
Roughly speaking, the principle says that everything has an explanation. But different forms of it have had an influence on philosophical thought since ancient times. We can see an echo of it in this saying (which is Latin, but it is attributed to an ancient Greek philosopher):
“Ex nihilo nihil fit.” – Parmenides
That is, out of nothing, nothing comes. Everything has to have a cause.
To be more precise, I believe the Principle of Sufficient Reason (the PSR, for short) is best stated this way: every contingent true proposition has an explanation for its truth. Or, we could say: every contingent state of affairs that occurs in reality has an explanation for its occurrence.
The PSR is restricted to contingent truths – that is, propositions that are true, but could be false – because it isn’t really clear how necessary truths can be explained in many cases, beyond explaining their truth by their necessity. For example, how could we explain why 1 + 1 = 2 is true? It seems like we just have to say something to the effect that it must be true.
However, when it comes to contingent truths, we are very familiar with how to explain them. And it seems to me that explanations for contingent truths are always ultimately causal explanations.
- We can give conceptual explanations: the metal is hot because its atoms have high kinetic energy.
- We can give scientific explanations: the atoms have high kinetic energy because energy transferred to them from the electric current passing through the metal, according to the laws of physics.
- But ultimately, to explain this state of affairs, we need to cite a cause: the energy transferred from the electric current to the atoms because of the causal powers and liabilities of those electrons and atoms (mediated in this case by the electromagnetic field).
And this coheres well with the causal account of modality that I gave in my last post. If contingent states of affairs are made possible by the fact that something has or had the causal power to bring them about, then it is natural to believe that every contingent state of affairs has a causal explanation.
I think we have ample reason to believe that the PSR is not only true, but necessarily true. Here are three reasons why I think so.
Validity of Abductive and Inductive Reasoning
The first argument is that the validity of abductive and inductive inferences – the kind of inferences that we need in order to do science – depends on the necessary truth of the PSR. In inference to the best explanation, we assume that the best explanation for some phenomenon is the one that is most likely to be correct. Or, if we have eliminated all but one explanation, we assume the remaining explanation is correct. Does that remind you of a certain fictional detective?
“When you have eliminated the impossible, whatever remains, however improbable, must be the truth.” – Sherlock Holmes
Holmes’ famous saying, and inference to the best explanation in general, would not work without the Principle of Sufficient Reason. If it is possible that the PSR is false, then when we compare and evaluate different hypotheses for some fact, we have to include the possibility that the fact just has no explanation at all. And when we do that, we lose the ability to say that the best explanation is most likely to be true.
If we try to compare the no-explanation hypothesis (the NEH) to other hypotheses, we are forced to a halt:
- The NEH postulates nothing at all, so it is simpler than any other hypothesis, and therefore cannot be ruled out by Occam’s razor.
- The NEH completely lacks explanatory power, of course, but we can only rule it out for that reason if we presume that things must have explanations, which is now in question.
- The NEH does not conflict with what we already believe unless we already believe that the PSR is true.
- In fact, without the PSR, we can’t even say that the no-explanation hypothesis is unlikely, so neither can we rule it out for being less probable than other hypotheses.
If some phenomenon has an objective probability of occurring, it is because the scientific laws governing that phenomenon assign some probability to it, or more generally, its probability comes from the properties of things that could cause that phenomenon in an indeterministic way. For example, an electron in a Stern-Gerlach experiment has a certain probability of being deflected up, and a certain probability of being deflected down, because of the laws of physics.
But if a phenomenon has no explanation at all, it cannot be said to be governed by any laws, or caused by anything – otherwise it would have an explanation. But that means that a phenomenon without any explanation has no probability – its probability is not 0, 1, or anything in between. We cannot say that the NEH is probable or improbable, and no amount of evidence for other hypotheses is able to change this fact – that evidence could just have no explanation as well.
So, the possibility of the no-explanation hypothesis ruins any attempted inference to the best explanation. No matter what we do, we cannot get rid of it once it is an available alternative.
Things are similar with inductive inferences (which I think are just a subset of abductive inferences, anyways). The validity of inductive reasoning depends, essentially, on the fact that reality operates in regular, predictable ways. But if the PSR is false, or even just possibly false, we have no reason to expect reality to operate in regular, predictable ways – all kinds of things could be happening for no explanation, so any apparent regularities could just be unexplainable facts, with no guarantee that they will continue to hold.
All this means that our ability to understand reality is heavily dependent on the Principle of Sufficient Reason. In fact, if the PSR is possibly false, it is arguable that we have no knowledge at all – our experiences could all be happening with absolutely no explanation and no connection to reality, and we can’t even say this scenario would be improbable. But since we can know and understand reality through these non-deductive forms of reasoning, we should believe that the PSR is necessarily true.
No Observed Violations
The second argument is an inference to the best explanation (rather than being an argument about inference to the best explanation). The necessary truth of the Principle of Sufficient Reason is the best explanation of the fact that we do not see violations of it all the time – random phenomenon happening with no explanation or cause.
We never observe bicycles coming into existence from thin air, or planets inexplicably altering their courses. Why don’t we see things like this? (Someone might object that we do see events with no explanation, such as in the spontaneous decay of an unstable particles – but I would maintain that those events do have explanations, in the quantum state of the particle and its indeterministic causal powers.)
Can we get away with explaining the absence of these events with some kind of local causal principle that only applies to the ordinary states of affairs that we observe around us, without using the full PSR? It doesn’t look like it. There are problems with local causal principles that suggest that the full PSR is required to explain why we do not observe states of affairs that have no explanation:
- The laws of physics seem to be valid across the whole physical universe, so if the causal principle is spatially localized, it does not seem like it could rule out the laws of physics changing everywhere for no reason at all.
- If it is temporally localized, it does not rule out the possibility that the laws of physics have always had, for no reason at all, the disposition to suddenly change at a random point in time.
- If it is restricted to finite sets of events, it does not seem to rule out infinite chains of events that ultimately have no explanation: for example, event1 that occurred a half second ago, which was caused by event2 a quarter second earlier than that, caused by event3 an eighth second earlier, and so on, but with no explanation for why the whole chain began just shy of one second ago.
- If it is restricted to states of affairs within the physical universe, it does not rule out the possibility of supernatural immaterial beings coming into existence for no reason, and then proceeding to wreak havoc with the laws of physics.
A quick note on that last point: acts of interference in nature from the supernatural – in other words, miracles – are logically possible as long as it is possible that something supernatural exists. I’ll probably belabour this point again in a later post, but I’ll go over it quickly here.
Scientific laws do not rule out the possibility of miracles. They tell us what happens when only natural causes are operating, and are silent on what might happen when a supernatural cause is operating. I don’t see any good justification for claiming that scientific laws have the built-in implication that nature is impervious to every possible supernatural influence.
Further to that, I don’t see how you can rule out the possibility of the existence of a supernatural cause unless you suppose that no supernatural beings exist, and that the PSR is true to ensure it stays that way. So the last bullet above is indeed a valid problem for a restricted causal principle.
Adding all this up, a merely local causal principle is insufficient to accord with the fact that we do not see inexplicable events happening. We need something with universal applicability.
The philosopher Alexander Pruss has a more in-depth argument along the same lines. He contends that the intuitions supporting a local causal principle (so that we could rule out the possibility of bricks coming into being without a cause, for example) are able to justify a non-local causal principle just as well. Then he goes further, showing that a plausible non-local causal principle actually entails the PSR. (See Section 3 of his paper here. Be warned, it gets pretty technical.)
So, I believe that the Principle of Sufficient Reason is the best, if not only, explanation for why we never observe things like bricks or bicycles popping into existence, or planets randomly changing their orbits: without a cause, such events simply cannot occur, and the entities that do exist are not able or not disposed to cause them.
Wait, you might say, can I really use inference to the best explanation to argue for the PSR now, when my first argument was that inference to the best explanation depends on the PSR? The answer is yes, actually, I can.
The first argument reasons that if the PSR is false, than abductive reasoning is invalid. Then it directly invokes our rational intuitions that say abductive reasoning is valid, therefore it can’t be the case that the PSR is false. We are justifying the PSR by our rational intuitions, not the other way around.
The second argument, on the other hand, indirectly invokes our rational intuitions about abductive reasoning, the same way we do whenever we use inference to the best explanation. Then it reasons to the truth of the PSR from the fact that we never see any apparent violations of it. So, both arguments rely on our rational intuitions, but they use them in different ways, making them neither circular nor redundant.
Impossibility of Exceptions
Rather than being a separate argument, this is more of an extension of the first and second arguments to drive the point home. (So I am not counting it, but it’s an important enough point to have its own section.) There is good reason to believe that there simply cannot be any exceptions to the PSR – either all contingent states of affairs have explanations, or none of them do.
As I stated earlier, it seems to me, very strongly, that all contingent states of affairs are ultimately explained by causes, if they are explained at all. If you haven’t given a cause, you haven’t really finished explaining the phenomenon.
Now, the range of possible effects of some cause are constrained by that cause’s properties, or the situation that the cause is in. For example, I am able to walk from my house to the park, but I cannot fly there. A forest fire can burn trees, but it cannot assemble them into log cabins. The effects that a given cause can produce are constrained by the cause’s nature.
Suppose, contrary to the PSR, that some contingent event or state occurred that did not have any cause or explanation. What, exactly, determined that it was that event in particular that would happen? The answer, of course, is nothing. Because this particular effect was without a cause, there was not anything constraining what this effect could be – no restriction on what things it could affect, how it could affect them, or when or where it could occur. Which means that if there is any exception to the PSR, then no state of affairs is really bound by it.
In a manner of speaking, an effect that has no cause is caused by nothing. If only some kinds of effects can be caused by nothing, then, to quote William Lane Craig, what is it that makes nothing so discriminatory? Nothing has no properties to allow us to make any distinctions in what it can cause; it is literally not anything at all. So either nothing can cause nothing – ex nihilo nihil fit – or there is nothing that nothing cannot cause.
The best rebuttal to this that I can come up with is the proposal that, while it is possible for events to happen with no cause, things that exist only have the capacity to be affected in certain ways, and this is what constrains causeless events. Another way we could say this is that things can only be affected in accordance with their liabilities. (The proposal would go on to say that, in fact, most things do not have liabilities to causeless effects, which is why we do not observe the PSR being violated.)
Liabilities, however, are capacities to be affected by corresponding powers. When an event occurs without any explanation, there is no power in operation, so I don’t really see a good reason to think that a causeless event needs a liability to make it possible. And if it did – would it really be causeless? A liability to be affected by a causeless event looks an awful lot like a passive, indeterministic causal power to affect one’s self.
And do things also need liabilities to causelessly come into existence? If they do, then nothing can come into existence without a cause: existing things are not liable to be brought further into existence, and non-existing things have no liabilities at all. A thing must exist in order to constrain reality in some way. At this point, the rebuttal nearly entails the PSR all by itself.
I suspect the intuition behind this idea, that things can only be affected in accordance with their liabilities, is actually nothing more than a subconscious belief that the only possible effects are ones that are produced by causes. And that intuition, of course, is perfectly suited to the PSR.
The Causal Account of Modality
Finally, the third argument is that the necessary truth of the PSR is logically entailed by the causal account of modality, with one additional assumption: that the accessibility relation between possible worlds is symmetric. I explained in my last post why I think the causal account is correct, and in the post here why the symmetry axiom makes sense. With those assumptions, the proof (which also comes from Pruss’s paper that I linked above) is fairly straightforward:
- Assume that there is a contingent true proposition, P, that does not have an explanation in terms of a cause. Let P* be the following conjunction: P and (P has no causal explanation). Then P* is true by assumption.
- Since P is contingent and therefore possibly false, P* is possibly false: that is, it is false in some possible world accessible from the actual world.
- Since P* is true, it is necessarily possible: that is, it is possible in all possible worlds accessible from the actual world. This is due to the symmetry of the accessibility relation.
- Now we can move to a possible world where P* is false (there is at least one of them, as shown in step 2). In such a world, P* is false, but it is still possible (as shown in step 3).
- According to the causal account of modality, if P* is false but possible, it is because there is something that has the power to originate a chain of causes that would result in P* being made true.
- But that means there is something that could cause P to be true, giving P a causal explanation, and also cause P to not have a causal explanation; a contradiction.
- Moving back to the actual world, this shows that the contradictory state of affairs demonstrated in step 6 is possible.
- But such contradictions are not possible. Therefore, our original assumption, P*, is false. Either P is not contingent, or it is not true, or it has a causal explanation.
- Nothing in steps 1 to 8 depends on the contents of P or on any contingent facts about the actual world: the proof could have been done for any proposition in any possible world. Therefore, necessarily, all contingent true propositions have a causal explanation. As they say, QED.
Since I believe the causal account and the symmetry axiom are both well-justified by our modal intuitions, I believe this is a good argument for the necessary truth of the PSR. (And we can turn this around as well: if the PSR is necessarily true, and explanations must ultimately be causal, it implies that the causal account of modality is correct.)
A Worldview Taking Shape
The Principle of Sufficient Reason ties the concepts of possibility, causation, and explanation into a coherent view of the nature of each, creating a picture of reality with cause-and-effect in its very foundation. In doing so, it explains the validity of abductive and inductive reasoning, giving us further confidence in our ability to understand reality.
Because of its significance for the non-deductive forms of reasoning, the PSR is highly relevant to the project of science, especially if one holds to a realist view of science. If the PSR is false, our rational intuitions are on very shaky ground, and science has no hope of explaining or discovering truth about the natural world.
The catch is that the PSR also has powerful implications for what lies outside the domain of science, particularly when we use it to start asking why the universe exists at all. I will come to that question a little ways down the road. It would appear, though, that in order to have a rational, scientific view of nature, you might have to accept that nature is not all there is.
Because of the powerful implications of the PSR, it would be good to consider the objections to it to make sure we haven’t gone wrong somewhere. I will do that in the next post.