These posts are me “thinking out loud” even more than normal, so if you’re looking for finished philosophical analysis, skip to some other post. (Or, better yet, go pick up the latest AJP.)

I realised my claim that the failure of functionalist explanation in social science is bad news for DN and unificationist theories of explanation had a gap at a crucial step. In particular, I was tacitly assuming that something like the following is a law.

bq. All customs that fulfil useful functions are instantiated.

This is obviously absurd. Some useful functions are unfulfilled. And there’s more than one way to fulfil most functions, so it can’t be that they are *all* instantiated. So there’s no obvious functionalist explanation that fits the DN model, and hence no counterexample to the DN theory. (Or to the unificationist theory, which isn’t that far from the DN theory on these questions, I’d say.)

But … the DN theory allows, as it must, for probabilistic laws. [1] And we can restate the objection that way. For the following is plausibly a law.

bq. The probability of custom C existing is higher given that C plays a useful function than the probability of C existing given that it plays no useful function.

And given that’s a probabilistic law, the facts that (a) C fulfils the F-function, and that (b) the F-function is useful to have filled, should combine with that law to form a good probabilstic explanation. And providing explanations of just those forms is a part of Durkheim and his followers seem to be doing. And since (a large % of?) social scientists eventually rejected this program just because they didn’t think these ‘explanations’ were genuinely explanatory, I think that tells very heavily against the DN model and all its followers.

fn1. Strictly speaking we’re now dealing with Hempel’s IS, or inductive statistical explanations. But the family of Hempel’s views is systematic enough that using the single term DN seems fine. I know it’s odd to call a probabilistic argument _Deductive-Nomological_, but for notes like these I don’t really care.