If Philosophy

Some Explanations

Sometimes we don’t understand something or other. Every now and then we ask someone to teach us how that something works. If we’re lucky they give us an explanation. Moreover, if we’re capable, we understand the story they tell us. Explanations facilitate understanding, in other words. Is that all there’s to it? At a surface level, it would seem so. Stories are made up of parts, though, and that goes for illuminating ones as well. Let’s have a look at a few of those parts.

When it comes to explanations, there are many kinds, and even more examples of these kinds, to consider. They all consist of at least two parts, however. The first of these we might call the explanandum. It’s a fancy term used to denote the things explained. The second of these can be called the explanans. This is a similarly fabulous little word that denotes the explaining bit in an explanation. Explanations thus consist in something that explains, and something that is being explained.

So, what kinds of explanations are there? Suffice it to say, there are plenty… Why? Maybe that’s because different tasks require different tools, regardless of whether those tasks are practical or intellectual. In either case, let’s begin by assuming that someone asks why the water in a particular canister is boiling. In order to explain this we might feel our understanding is best facilitated by the use of what can be called a causal explanation.

Causal Explanations

These involve laws and initial conditions. These parts might be exemplified like follows.

Law: Water boils when it is heated to 100 degrees Celsius subjected to 1 atmosphere of pressure.

Cause: A container of water is heated to 100 degrees Celsius.

Condition: The container is at sea level, subjected to 1 atmosphere of pressure.

This is what we could call the explanans. It gives a story of why we should expect that…

Explained Event: The water in the canister boils.

… the event that the water in the canister boils. That is, why our explanandum obtains. The law here denotes some generalization where one variable has a productive influence on some other variable. The cause is the instantiation of the first variable. The condition asserts the domain of application for the law; i.e. under which circumstances it holds true. Water boils at 100 degrees Celsius, but not everywhere. It depends on how much pressure it’s under, for instance. We arrive at the second variable (the effect) given this causal variable and condition. Causal explanations thus consist in stories that connect a cause to an effect through some law and set of initial conditions. If we’re lucky, we find the story illuminating enough that we can curiously move on to other questions, such as whether or not the law alluded to is true. That should settle this matter, probably…

Probabilistic Explanations

Let’s say we’re interested in something slightly different now that we have the structure at hand. Perhaps we’re wondering why so-and-so has fallen ill. One kind of explanation we could give is a causal explanation: “you see, all individuals who satisfy these descriptions end up ill, and ol’ Kim happens to have all the relevant traits”. However, we don’t always have such clear-cut universal laws. Sometimes we have to make do with probabilities. So, rather than arriving at our explanandum through deductive means, we use an inductive process. In short, we give a probabilistic explanation.

Probabilistic explanations roughly follow the same form as causal explanations do, but use probabilistic rather than deterministic laws. So, we might have a story like follows.

Probabilistic Law: Approximately 58 per cent of humans develop illness X by the age of 80, unless they have been vaccinated against it.

Cause: Kim is a person at the age of 80.

Condition: Kim has not been vaccinated against illness X.

The law in action here does not make it inevitable that Kim has the disease. It does, however, give us an account of why she has gotten this disease. It turns out (as per the argument) that she was more likely to get it than to not get it. (Tough break, Kim, we’re all rooting for you, I’m sure.) Like in the causal explanation, we have a similar structure. We have a law, cause and condition that constitute the explanans and an explained event constituting our explanandum. Now, I wonder if Kim asks herself what she did to deserve such an outcome. Maybe there isn’t such a thing, but if there is, we would like to know why she did it.

Intentional Explanations

Regardless of why Kim got this illness, she might recover. Illness X is a transitory thing, let’s say. Now Kim goes on to celebrate her newfound good level of health. Now we might ask why is she celebrating? Duh. She just got better, that’s just what you do. Sure, but let me put it this way. If she didn’t celebrate why would that be the case? Here, causal and probabilistic explanations don’t seem to do the trick, and neither does common sense as easily. When it comes to actions, we have a component of intentionality that isn’t so easily captured by these law-like generalisations or probabilistic accounts. Instead, what we’re after is an intentional explanation.

Again, the notions of explanandum and explanans come in handy. Here what we’re trying to explain is some action. So what’s doing the job of actually explaining such an action (i.e. the explanandum)? Well, we’re generally looking for a way of rationalising actions. We want them to make sense from the point of view of the agent (i.e. the person acting). If Kim doesn’t celebrate, this might be due to any number of reasons. But they all have something in common, namely that they would consist in a combination of a belief and a desire. Perhaps she believed that celebrating good health is a way to jinx herself, whereas not celebrating is the best way not to jinx herself. Let’s furthermore assume that she desires to remain in her newfound, and hopefully not transitory, good health. Therefore she refrains from celebrating. Not even with a little jig on the lonesome. Such belief-desire pairs make up the explanans of intentional explanations, and they make the actions “make sense” to us. Even if we are not so easily swayed by notions of being jinxed ourselves, we can understand that if someone does hold that belief, and has the desire not to jinx herself, she would refrain from acting in the way that would jinx her.

There are doubtless other stories to tell here, but these have been a few to get started with. While I might be dim, I hope the stories given here are less so.


Explanations are stories that facilitate understanding. Some are causal, some are probabilistic, and some are intentional. Causal explanations use causal laws, probabilistic explanations relates variables through probabilistic means, and intentional explanations consist in references to belief-desire pairs. Common for them all is that they consist of a thing being explained and a thing doing the explanation. We call these the explanandum and explanans, respectively.

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