The epistemic force of beauty in laws of nature does not reduce to simplicity

Some people think that simplicity of laws of nature is a guide to truth, and some think beauty of laws of nature is. One might ask: Is the beauty of laws of nature a guide that goes beyond simplicity? Are there times when one could make epistemic decisions about the laws of nature on the basis of beauty where simplicity wouldn’t do the job?

I think so. Here is one case. Suppose we live in a Newtonian universe, and we are discovering fundamental forces. The first one has an inverse cube law. The second has an inverse cube law. These two laws account for most phenomena, but a few don’t fit. Scientists think there is a third fundamental force. For the third force law, we have two proposals that fit the data: an inverse square law and a slightly more complicated inverse cube law. It is, I think, quite reasonable to go for an inverse cube law by induction over the laws.

There is something indeed beautiful about the idea that the same power law applies to all the forces of nature. But if we just go with simplicity, we will go for an inverse square law. However, going for the inverse cube law seems clearly reasonable, and it is what beauty suggests—but not simplicity.

Here is another thought. Sometimes a fundamental law has some particularly lovely mathematical implications. For instance, a conservative force law is connected in a lovely way with a potential. But it need not be the case that a conservative force law is simpler than a non-conservative alternative. (It is true that a conservative force is the gradient of a potential. If the potential can be particularly simply expressed, this makes it easier to express the conservative force law. But we can have a case where the potential is harder to express than the force itself.)