Humeans laws and constants

On Mill-Ramsey-Lewis accounts of laws of nature, the laws are the propositions that best balance informativeness and brevity (in a language that cuts nature precisely at the joints).

Now, the laws of nature include constants, such as the fine-structure constant whose current best measured value is 1/137.035999206. Now, we might be lucky, and it might turn out that the fine-structure constant will have some neat and elegant precise value. There is a history of speculation that it has such a value—for a while, there was hope it was exactly 1/137, and then other guesses took over. But suppose we don’t get so lucky. Suppose it just is some messy number with no simple expression. That should, after all, be a serious possibility.

In that case, the exact value of the fine-structure constant cannot be a part of the Mill-Ramsey-Lewis “world in a nutshell” system of laws, since the system would then be infinitely long, and we lose our hope of defining laws in terms of brevity.

So we have two options. First, the system of laws might not include any specific information on the value of the fine-structure constant, but might instead be of the form ∃αF(α) where F(α) says nothing about what α is, except maybe that it’s real-valued and positive. If we go for this option, then we have to say that all the things that depend on the actual value of the fine-structure constant—and that apparently includes all of chemistry—are not in fact laws of nature. This will likely fail to yield some counterfactuals that we want, and while the laws will be briefer, they will be far less informative than if they had something to say about the value of α.

So that moves us to the second option, which is that the laws are of the form ∃αF(α) and F(α) includes some constraints on α, such as that it lies between 1/137.04 and 1/137.03. These constraints are sufficiently tight to generate the nomic implications we need for chemistry and biology. But while this result seems a better fit for science, it is metaphysically very strange. For it is very strange to think that the laws allow the fine-structure constant to have any of an infinite number of values, but these values must lie in a narrow range.

Furthermore, the exact narrow range for α would be determined by fine details (I am not sure if the pun is intended) of exactly how informativeness and brevity are balanced in the definition of the laws.

The same issue comes up for other constants in the laws of nature. Either Mill-Ramsey-Lewis laws do not include anything about the values of constants or else they include oddly specific, but not completely specific, ranges.