Theoretical parsimony

As is usual, distinguish ontological parsimony, namely positing fewer beings, from ideological parsimony, namely positing fewer fundamental undefined concepts.

The principle that we should assign higher probabilities to more ontologically parsimonious theories is wacky. It violates the Principal Principle. If you are flipping a coin and planning to have children if and only if you get heads, then you should assign a slightly higher probability to tails. (Granted, this argument fails if eternalism is false. But you can tweak it by supposing that a hundred years ago Alice flipped a fair coin with that intention, and now you should again assign a slightly higher probability to tails.)

What about ideological parsimony? It initially sounds a lot better to assign higher probabilities to more ideologically parsimonious theories. Indeed, I think there has to be something right about such a principle of simplicity. But I don’t at present fully know how to formulate it in a way that escapes objection.

For suppose that we are non-reductionists about biological species, so we think that species are fundamental undefined concepts. You are working with a bacterium in the lab, and on a whim plan to flip a coin. On heads, you will irradiate the bacterium, and on tails you will do no such thing. Irradiated, the bacterium is more likely to produce a new species when it reproduces. So on ideological parsimony it seems we should assign a slightly higher probability to tails, as then it is more likely that the true theory of the world posits fewer species, and hence fewer fundamental undefined concepts.

Objection 1: Reductionism is the right theory about biological species.

Response: Maybe it is. But it’s not the case that it certainly is. And as long as there is a non-zero probability that non-reductionism about species is right, we should assign a slightly higher probability to tails—for conditionally on reductionism, the probabilities are equal, while conditionally on non-reductionism, we should assign a higher probability on tails.

Objection 2: There are so many species that the difference from positing one more is negligible.

Response: Maybe it is. But now parsimony cannot do the work it’s designed to do, and hence it is largely unmotivated. Here’s an example of the kind of work it’s designed for. You observe the world’s koalas and see no significant differences in behavior or appearance. You could suppose there are two species of koalas and you just haven’t been able to tell them apart. But that’s not parsimonious. So you suppose one species. But given how large the number of species on earth is, positing one more makes little difference—assuming the objection is correct.

Objection 3: A full story of the world will include the causal powers in the world. If the radiation has the causal power C_S to produce a new species S of bacteria, then a full description of the world will contain a description of C_S, and hence of S, even if S has no members. Thus it makes no difference to the ideological complexity of the world whether the radiation is applied or not.

Response: This seems the most powerful objection. But it might undercut the applications of parsimony. Plausibly, the world has a first cause behind everything else. Now either the first cause’s causal powers are such that their complete description includes all possible kinds or not (this may depend on questions involving the first cause’s simplicity). If it has such causal powers, then ideological parsimony does rather less work than we thought, since the total description of reality already includes the concepts of the two species of koalas as per my previous response. Suppose now the first cause’s causal powers are not such that their complete description includes all possible kinds. Imagine that you make the following plan. You will flip a fair coin. On heads you will pray that the first cause produce a new kind of thing. Now, the first cause might not fulfill your prayer—indeed, perhaps you are not even confident the first cause is a person. But it is at least slightly more likely that the first cause will make a new kind of thing if you pray than if you don’t. And that’s enough to change the epistemic probabilities for your coin flip, in an implausible way.