Recently[1] I’ve been doing some reading on (amoung other things) Leibnizian Cosmological Arguments and the Principle of Sufficient Reason. One thing that’s involved in these arguments is the idea of an “explanation”. We generally have a firm grasp or intuition of whether something is an explanation for some fact or not. Consider the following statements involving explanations:

  1. John sent his children to school A rather than school B because school A has good sports facilities
  2. The kettle is boiling because John turned it on and it was working properly
  3. The kettle is boiling because the heat of the flame is being conducted via the copper bottom of the kettle to the water, increasing the kinetic energy of the water molecules, such that they vibrate so violently that they break the surface tension of the water and are thrown off in the form of steam[2]
  4. We die because the process of natural selection has selected organisms that die over the course of the earth’s evolutionary history

In each of the above cases, the explanation is italicised and the explanandum (the fact to be explained) comes before the “because”. Cases (1) and (2) involve personal or libertarian explanations, case (3) involves a scientific explanation and case (4) an evolutionary explanation (we’ll see later why such evolutionary explanations, including case (4), often fail to explain their explanandum).

Now, as far as I can tell, no-one has been able to give a complete reductive analysis[3] of explanations. Nonetheless, we know a number of things about explanations; two of which I wish to share here.

1. Explanations can be non-entailing

An explanation entails its explanadum if it is impossible for the facts in the explanation to be true and not the facts in the explanadum. Consider example (2) above: it is not possible for the facts John has turned the kettle on and the kettle is working properly to be true without the kettle is boiling following. Simply put, the facts in the explanation entail the facts in the explanadum. We can see another example of this in (3).

But what about (1)? This doesn’t seem to be an entailing explanation. After all, the facts in the explanation there could be true and the following could still hold:

1′. John sent his children to school B rather than school A because school B has a good maths department

Notice how the facts in the two explanations could be true at the same time, and yet they explain two different (non-compatible) outcomes. This would be what I mean by a non-entailing explanation: one that doesn’t entail its explanadum. Now, to some, these non-entailing explanations might seem weird and unintuitive, and so they might object to my example. After all, they might say, we haven’t actually explained the explanadum here. What we’ve explained in (1) is why John chose school A, not why he chose school A rather than school B. In order to explain the rather than bit we need to make reference to John’s preferences (or something like that) and in that case we’d have incompatible facts in our explanations.

Now while I agree that we haven’t properly explained the explanadum, I don’t think a non-entailing explanation is out of reach. The following two facts, after all, are possibly both true at the same time:

1.1. John is impressed by reasons for choosing school A over school B

1.1′. John is impressed by reasons for choosing school B over school A

This is usually the case when we choose between two alternatives. In fact, if one of these weren’t true, then I don’t think we could even say that John chose one school rather than the other. But since both of these are compossible[4], it follows that (at least libertarian) explanations can be non-entailing. For, certainly, (1.1) explains (1) and (1.1′) explains (1′).

Another, more trivial, example of a non-entailing explanation is a statistical explanation. Consider some stochastic process, P, which will either light up the blue light or the red light. Then we have the following plausible explanations of those outcomes:

5. The blue light lit up rather than the red light because there was a 24% chance of P lighting up the blue light rather than the red light

5′. The red light lit up rather than the blue light because there was a 76% chance of P lighting up the red light rather than the blue light

Again, we have compossible facts in our explanation (in fact, they’re pretty much the same fact in different words) and different outcomes in our explanadum. Thus, we have another example of a non-entailing explanation.

2. There can be multiple explanations for a single explanandum

I suppose this is obvious just from the initial four examples we gave. After all, both (2) and (3) explain their explanadum sufficiently. The difference comes in the way we explain it: (2) makes reference to the choices and actions of a free agent, while (3) makes reference to the scientific laws working off of initial conditions. Beyond these, we can also talk about conceptual or constitutive explanations. To quote philosopher Alexander Pruss[5], 

[Conceptual explanations] explain a state of affairs by saying what the state of affairs is constituted by or consists in.  For instance, in Metaphysics Z, Aristotle suggests explaining an eclipse of the sun by noting that an eclipse of the sun is identical with the earth’s entry into the moon’s shadow.  Likewise, one might explain a knife’s being hot by noting that its being hot consists in, or maybe is constituted by, its molecules having high kinetic energy.

So perhaps we could say that (3) is a scientific conceptual explanation. Furthermore, we can talk about causal explanations. These involve making reference to some causal power. So for example

7. I exist because my parents successfully reproduced

8. The apple falls to the ground because of the force of gravity

These are extremely simplistic examples (much more could be put in the explanations), but they both illustrate causal explanations. For particular interest, the explanadum in (7) is an example of what we call an existential fact (ie. a fact involving the existence of something). Now it seems to be the case that only causal facts can explain existential facts[6]. In other words, to explain why something exists we need to make reference to causal actions of some other being. Then, finally, there’re evolutionry explanations…

Evolutionary explanations

As the name suggests, evolutionary explanations are explanations that make reference to the workings of biological evolutionary theory. These are technically a subset of scientific explanations, but I want to focus on them because of a recent personal experience. My friend was wondering out loud, why we die. Another one of my friends offered the explanation in (4) and in doing so offered an evolutionary explanation. The only problem is, the explanation in (4) doesn’t explain the explanadum. It doesn’t answer the question. In actual fact, it only explains why those organisms which are currently in existence die. It doesn’t explain why we die. I think the answer to that question would lie in much deeper reasons about how our genetics work.

This illustrates something interesting about evolutionary explanations. Don’t get me wrong here: I’m not saying that they don’t always work. What I’m saying is they may not always explain the explanadum we wish to explain, and their failure to do so is not always obvious.

Principle of Sufficient Reason

I made mention of the “principle of sufficient reason” in my opening paragraph. Simply put, the principle says the following:

PSR. Every contingent fact has an explanation for why it’s true and not false

By “contingent fact” I mean a proposition that is true, but could have been false. So, for example, “I exist” is a contingent fact, since there was a time when I didn’t exist and therefore it’s certainly possible that the proposition “I exist” could have been false. We restrict the PSR to contingent truths because we just don’t know all that much about explaining necessary truths[7]. I suppose, if pressed, we could explain a necessary fact with reference to its necessity: A is true because A could not be false.

I’m not going to give a defence of this principle here (this post is only meant to serve as an introduction to the idea of explanations), but if you think it’s true (and it certainly seems more likely true than not to me) then you have good reason to accept the existence of a necessary being, for:

  1. The PSR is true (Premise)
  2. Therefore, the fact “there exists at least one contingent being” has an explanation
  3. This explanation cannot assume the existence of a contingent being (Premise)
  4. This explanation must involve the causal power a some being (Premise)
  5. Therefore, this fact is explained by the causal power of a necessary being
  6. Therefore, a necessary being exists

(1) is taken as true for the sake of argument, (3) is true because an explanation cannot assume it’s explanadum (otherwise it wouldn’t explain it) and (4) follows from our earlier discussion about explaining existential facts. This isn’t the only way to get from the PSR to a necessary being, but it will do for the current discussion. I haven’t said anything about this necessary being and I don’t plan to here.

Now, perhaps you think the PSR is too strong a claim. I think there are good reasons for accepting it in this form (which I’ll discuss in future posts), but for now, perhaps you’d find one of the following weaker forms more acceptable:

W(eak)PSR. For every fact A, it’s possible that A has an explanation[8]

R(estricted)PSR. If A is a fact and A possibly has an explanation, then A has an explanation[9]

E(xistential)PSR. Everything that exists has an explanation for its existence, either in the necessity of its own nature, or in an external cause[10]

From each of these, a cosmological argument can be run for a necessary being. In future posts we’ll look at these and talk about reasons for accepting them and objections to them, as well as how we could move from the necessary being towards a being closer to the God of classical theism. If you’re impatient (given how long I actually take to post these posts, this seems natural) I’d suggest reading the paper I linked in [5].


  1. I say “recently”, but I guess I’ve been reading about these things, on and off, for some time now.
  2. The wording here is taken directly from The Blackwell Companion to Natural Theology (edited by William Lane Craig and J.P. Moreland) p. 192
  3. Put simply, a reductive analysis for explanations would be a set of necessary and sufficient conditions for some fact A to be the explanation of another fact B.
  4. If P and Q are “compossible”, we mean that it is possibl for them to be true at the same time. In other words, one of them doesn’t entail the negation of the other.
  5. “Leibnizian Cosmological Arguments” in The Blackwell Companion to Natural Theology (edited by William Lane Craig and J.P. Moreland) p. 52. This essay is a fantastic exposition of these sorts of arguments, and (of particular relevance to this post) for it’s discussion of explanation. An online copy of it is available here.
  6. To be more specific I should say contingent existential facts, since the explanation in “A exists because A necessarily exists” seems to be noncausal. But since I’m not really talking about necessary and contingent facts, the reader will just have to forgive me.
  7. Necessary facts are those facts for which it is impossible for them to be false. Often, we minimally take conceptual truths to be necessary, as well as mathematical and logical truths. Classical theists hold that God’s existence is a necessary fact.
  8. A New Cosmological Argument
  9. A Restricted Principle of Sufficient Reason and the Cosmological Argument
  10. This EPSR comes from William Lane Craig, who got something like it from Stephen T. Davis

One thought on “Explanations

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s