What are we asking when we ask why?

“Why? WHY?” If, like me, you have small children, you spend all day trying to answer this question. It’s not easy: sometimes there is no answer (a recent exchange: “Sharing is when you let someone else use your things.” “Why?”); sometimes you don’t know the answer; even when you do, your child isn’t satisfied, he just goes on to ask “why?” about the answer.

This follow-up why-question is worth pausing over. Suppose you were asked why the lights came on and you answered that the lights came on because you flipped the switch. When your child immediately follows-up with a “why?” his question is ambiguous. Is he asking: why did you flip the switch? Or is he asking: why is it that the lights went on because you flipped the switch? The second interpretation is a meta-question, equivalent to: why is what you said the answer to the original question? Now we’re in philosophical territory. Philosophy is concerned, not just with answering this or that why-question, but also with answering a meta-question about why-questions: what does it take for a proposition to be an answer to a why-question?

If we start with a small diet of examples there appears to be a clear pattern. Why did the bomb explode? Because someone lit the fuse. Why did the balloon pop? Because it hit a sharp branch. In these cases we have asked, of something that happened, why it happened; and in all of these cases the answer mentions a cause of that thing. This observed regularity suggests a hypothesis: you can answer a question of the form “why did such-and-such happen?” with “such-and-such happened because X” when, and only when, X describes a cause of that thing.

To test this hypothesis we need more data. One place to look is science. But science appears to casts doubt on it, for scientific answers to why-questions often seem to go beyond describing causes.

Do they really go beyond causes? Let’s look at a particular example. The spruce budworm lives in the forests of eastern Canada and eats the leaves of the balsam fir tree. Usually the budworm population is held in check, but occasionally the population explodes; when this happens the budworms can eat all the leaves and thus kill all the forest’s fir trees in about four years. Suppose the budworm population explodes; our question is: why did the population explode?

One response uses a mathematical model of the growth of the budworm population. The equation for the model, which describes how the budworm population X changes over time, is

dX/dt = rX(1-X/k)-X²/(1+X²).

There are two influences on number of budworms: reproduction, which increases the population — that is the term rX(1-X/k) in the equation; and predation by birds, which decreases it — that is the term -X²/(1+X²). The term r is the budworm’s “natural growth rate,” and k is the forest’s “carrying capacity” (the maximum number of budworms that the forest can sustain).

We can depict the information contained in this model on a line. The points on the line represent possible sizes of the budworm population. The points toward the left represent small sizes, the points toward the right, larger sizes. The solid circles are stable equilibrium points: the population quickly moves toward and stays near a stable point. The open circle is an unstable equilibrium point; the population moves away from it. So if the budworm population is smaller than point B, it will move toward (a); if the population is larger than (b), it will move toward (c) Before the population explosion, when the budworm population is relatively low, it is at (a). After the population explodes it is at (c). The question is, why did it jump to the higher point?

To answer we need to see how the positions of (a), (b), and (c) change as r, the natural growth rate, changes. The value of r goes up as the forest grows. And as r goes up (a) and (b) move toward each other, as in figure 2, until, at a certain value for r, they vanish. When that happens (c) becomes the only stable equilibrium, and the population it quickly increases to it — and the population explodes.

I’ve answered the question of why the budworm population exploded. Now if everything I said is part of the answer, then the hypothesis I’ve been investigating, that “such-and-such happened because X” is true when and only when X describes a cause, is false. For the only relevant cause of the explosion is: the forest grew above a critical size. But I didn’t just say that this happened. I also wrote down a law governing the budworm population’s evolution. That law didn’t (couldn’t!) cause the budworm population to explode. If the law is part of the answer to the question of why the population exploded, then answers can do more than describe causes.

I, however, do not think that the law is part of the answer to the question of why the population exploded. I think that the answer consisted just in the fact that the forest grew big enough.

But how can this be? Doesn’t this mean that those paragraphs I wrote contain a bunch of information that is not part of the answer to the question of why the population exploded? Surely that can’t be. If you ask a question, and someone gives you a bunch of information that is not part of the answer, you will notice that they are changing the subject. But when I described the model of the budworm population it didn’t feel like I was changing the subject.

Responding to a question by providing information that is not part of the answer does not always feel like changing the subject. If I ask who came to the party and you respond “Jones did, I saw him there myself” you’re providing information that goes beyond the answer (which is just “Jones did”). But the extra information is relevant: in this case, it is your evidence for why your answer is correct.

That’s what I think is going on in the budworm example. If I just say that the budworm population exploded because the forest reached a certain size, you might well be skeptical: forests grow slowly, how can a small change in the forest size trigger such a huge change in the budworm population? The model shows how: when the forest grows above a certain size the low-population equilibrium state vanishes.

I’ve been defending a simple theory of answers to why-questions: the complete answer to “why did such-and-such happen?” lists the causes of that thing, and nothing else. But please don’t take this theory to say that scientists are wasting their time developing mathematical models, or searching for laws governing the phenomena they are interested in. The laws and models, while not parts of answers to questions about why things happened, are essential for coming to know that those answers are correct. In fact I think their role is even more exalted: they are essential for coming to know why those answers are correct. But that is a story for another time.

Featured image: Light Bulb by jniittymaa0. Public domain via Pixabay.