My husband described to me a version of the cosmological argument based on explanations. Everything in the world requires an explanation. Since the chain of explanations can’t go on forever, there must be an ultimate Explanation for it all. And that Explanation wants us to stop being gay. At least, that’s how I assume the rest of the argument goes. I don’t actually care.

We were joking about this, because the argument imagines that there is a cosmic pointer from each object to its explanation. But the very idea of an explanation is really quite squishy. What even is an explanation? It depends on social context.

So I dug up an old abandoned blog draft on the subject of explanations.

When you get a degree in physics, there’s a funny change you can see between introductory physics and advanced physics. Specifically, in the way you’re supposed to solve homework problems.

In introductory physics homework, you’re provided with equations of motion (e.g. velocity, acceleration), and the solution is to describe how objects move over time. In advanced physics homework, you’re given a system (e.g. a pendulum on a spring), and the solution is merely to write down the equations of motion. Often, you do not actually solve the equations of motion, and you may not know how to solve them. Or the only way to solve them is to take a separate class in computational simulations.  So you just write down the equations and call it a day.

On the one hand, equations of motion are the solution; on the other hand, they’re a statement of the problem. So there’s a certain amount of social construction that goes into the notion of a “solution”. Likewise for the notions of “explanation” or “proof”.

An explanation is something that conveys an understanding of “why”. But to whom is it conveying understanding, and in what context? Some people may have great difficulty understanding, and require more of an explanation. In other cases, the person already understands, but you still need to explain it to them because that’s the homework assignment.

Also, what even is “why”? Why does it happen? Why do we believe it? What chain of events led to this?

The notion of “explanation” is so squishy, we’re left grasping for any hard truths, any at all. Here’s a proposal: in order for something to count as an explanation, the thing it explains must be true. If you explain something, but that thing is not true, then we can say that the explanation has objectively failed.

Now suppose that an attempted explanation explains something that is true. But you could also take that same explanation word for word, and apply it elsewhere to explain something that is false. Is it really an explanation?

For example, suppose I make the observation that people who lack a skill tend to overestimate their own skill. We ask why that happens, and then we propose that there is a psychological effect that we dub the “Dunning-Kruger” effect. As an explanation, this is already dubious. But supposing this explanation is correct, then we would conclude that it applies to other people with psychology, such as East Asians. It does not. If our explanation did not reference race or culture, then the same explanation also explains something that is false. Objectively, it is not an explanation.

Follow this line of reasoning, and we might end up thinking that an “objective” explanation would look something like a proof. Most fields do not deal in proofs. But at least mathematicians deal in proofs, so let’s follow that thread and hope we get somewhere.

In fact, mathematicians will tell you that even proofs are based on social agreement.

Consider the Four Color Theorem. This mathematical theorem states that if you divide a map into regions, it is possible to assign one of four colors to each region, such that no adjacent regions share a color. The Four Color theorem was proven in 1976 by Appel and Haken, using computer assistance. While there are an infinite number of distinct maps to be checked, the authors managed to reduce it to a mere 1,834 configurations. Each configuration was checked by a computer over a thousand hours of computation. The proof contained 400 pages of microfiche.

A mathematical proof is often considered undeniable, and perhaps only more so when it’s checked by computation. In reality, the original proof contained multiple errors, later corrected. But mathematicians still give credit for the proof to the original authors, rather than the last person to have spotted an error in the proof because c’mon, they basically had it.

Setting aside whether the original 400 pages of microfiche constituted a proof, we can say that this is well and far away from any conventional notion of explanation. I just don’t think the typical person would gain any understanding of the proof by sitting down to read it. In fact, I don’t think anything could convey an understanding of the proof. I can imagine writing a popular explanation of the general outline, but if the explanation does not contain the full proof of the theorem, then does it really qualify as an explanation? There is a sense in which no explanation exists.