# Contrastive probabilistic explanation

I want to propose something I’m not totally convinced is correct, but that I think is worth considering. In general we have the question about contrastive indeterministic explanation: an antecedent A can give rise to two different consequences B and C, it actually gives rise to B, and we want to know why it gave rise to B rather than C.

There are two cases that encode this, each prima facie in different ways (though they may be ultima facie reducible to the same case, more on this later): libertarian free choice and quantum indeterminism. Let’s take them in turn.

In a free choice we are impressed by reasons R for choosing between B and C. In the event we choose B, we want to know what explains why we chose B rather than C. The answer comes in being more precise about the content of R: it includes reasons R1 for choosing B over C and R2 for choosing C over B, and it’s in virtue of this that we are choosing between B and C in the first place (see section 4 in Divine Creative Freedom by Alexander Pruss). When we choose B then R1 explains why we chose it over C, and when we choose C then R2 explains why we chose it over B. Thus, the explanation is contrastive in virtue of the reasons themselves being contrastive. We’ll return to this shortly.

In an event of quantum indeterminism we have some quantum event — radioactive decay, say — that happens with a certain probability. Let A be the circumstance involving an atom at t1 which will decay with some probability, B be the circumstance involving it having decayed at t2, and C the circumstance involving it not having decayed at t2. In B, how would we explain why it had decayed rather than not?

The first Aristotelian step is to give an account of probabilistic causation, and the second is to elucidate the explanation this affords us. With regards to the first, something like what Feser has proposed here seems plausible, namely that the probabilistic behaviour the atom exhibits is grounded in its substantial form. This explains why the atom in the same antecedent state can result in two different consequent states, in a similar way to how the form of a material thing explains its inertia (see Nature and Inertia by Thomas McLaughlin for a fantastic discussion of this). It also plausibly explains why B is realised when it is realised. But it does not seem to explain why B was realised rather than C.

And here comes my proposal: there is no contrastive fact over and above the plain fact that B occurred and C did not. The difference between the two cases is a relation, and a relation is wholly grounded in the relata themselves (see Aquinas on the Ontological Status of Relations by Mark Henninger). Thus to explain why I am taller than you, it is sufficient to explain why I am my height, why you are your height, and note that the former is greater than the latter. There is no additional fact to explain. Similarly to explain B, and note that B excludes C, is sufficient to explain why B rather than C. If the situation were slightly different such that we had two identical atoms at t1 that at t2 realised B and C respectively, then to explain B for the first and to explain C for the second just is is to explain the outcome of the difference, since this consists precisely in the two outcomes being realised.

But wait! Why was there some irreducible contrastive fact to explain in the free choice case? Because in this case the content of the choice itself was contrastive. It was not that the relation between the choices had to be explained contrastively, but rather that in order to explain every aspect of the choice we also had to explain the contrastive aspects.