In order for Humeanism about laws to be guilty of an explanatory circle, the explanations appealed to must be of the same kind. If we use A to explain B and then use B to explain A in the same kind of way, then, intuitively, there is something wrong with the explanation being offered. But if B is used to explain A in a different kind of way from the first case, then intuition may not tell against this. To put it another way, we might be prepared to grant that the transitivity principle in (P4) of the formalised argument holds for one kind of explanation, but resist the claim that transitivity will hold across different kinds of explanation. That is exactly the approach that I will describe in this section.
Here is a quick and dirty way of motivating the idea that we do treat explanations in this way. I am currently drinking a cup of tea, which a rather common event. Someone – presumably a person unfamiliar with British customs – might wonder why it is that I am so often found drinking tea. One kind of explanation available would be to identify certain kinds of distributions of fundamental particles as being tea drinking events (in a way analogous to how particles distributed table-wise might well constitute a table or a catty distribution of particles might be identified with a cat). We might then point out that if you were able to know the distribution of fundamental particles across my lifetime, you would find many such events. Another kind of explanation makes no reference to particles and instead appeals to my desires, local customs and, perhaps, mild addiction. While these two kinds of explanation are very different to one another, both of them deserve to be called explanations of my tea drinking habits.
Moreover, the two explanations do not merely explain the tea drinking, but they also explain each other to a certain extent. The first kind of explanation provides a physical ground for the mental states and cultural tendencies that the second appeals to. The second kind of explanation tells us why we should expect there to be the physical patterns that the first is built upon. But this interdependency of the two explanations introduces no problematic circles. The distinctness of the explanations is not diminished by acknowledgement of this connection. It would be very odd to
dismiss either of these explanations on the grounds that having both makes each one guilty of self-explanation.
So much for the everyday case. For this to work when applied to laws, of course, we will need to see some details as to exactly what the different kinds of explanation appealed to by Humeans are supposed to be. Barry Loewer has suggested that there is such a distinction between metaphysical and scientific explanations.66
Metaphysical explanations are concerned with constitution in some way. To say that A metaphysically explains B is to say that B is grounded in A, or that B holds in virtue of A or that B is constituted by B.67 An explanation of this sort does not need to cite
laws. If explanans and explanandum are both temporal entities, then they must be co-temporal. This last captures the following idea: if we want to say that A is the underlying stuff out of which we get B then they clearly must both exist at the same time. It would make little sense to claim that B is constituted by something no longer around.
Scientific explanations do not need to mention grounds in that way. Rather, Loewer suggests that the core of scientific explanation of some event is showing why that event occurred through appeal to other events and certain laws. If B scientifically explains A, then events mentioned in B will typically be temporally prior to events in A. That said, this is not a strict requirement since there is no requirement that the explanans or the explanandum be temporally located entities. Another difference between the two kinds of explanation is probability: scientific explanations may be probabilistic while metaphysical ones cannot.
For example, the quantum mechanical explanation of why a lump of radium emits alpha particles goes by way of showing how the laws and the quantum state of the radium atoms make the emission likely. But of course, this doesn’t show what the emission of alpha particles consists in.68
66 Loewer (2012) p. 131. See also his (2007).
67 More details about the contemporary notion of grounding can be found in Fine (2012)
and Rosen (2010). The link between grounding and explanation specifically is considered in Jansson (2016).
This is far from a full account of scientific explanation. That said, it is not intended to be one. Loewer is simply trying to give some characterisation of what the kind of scientific explanation he has in mind is. The most important point is that it be clearly distinct from metaphysical explanation; this at least seems successful. Suppose that your window was shattered and you came to me for an explanation. Setting aside claims of ignorance, there are multiple different reasons that I might offer for why your window is in its current state. I might point out that the various component pieces of your window are disconnected from one another. It is in virtue of this disconnectedness that your window is shattered. In ordinary conversations it is implicit that this is unlikely to be the sort of explanation that you are looking for, but it is a reason nonetheless. This sort of explanation is a metaphysical one: I am claiming that your window’s current state is grounded in how its parts are distributed (widely, we can assume). Another kind of explanation I might offer is by way of telling you a story about Suzy kicking a ball through the window. I could talk about the fragility of the window, the hardness of the ball and the momentum with which it travelled through the air. If pressed, I might make appeal to Newton’s laws of motion. This is an explanation of a different sort to the first. It seems likely that Loewer would be inclined to count this causal story as the basis of a scientific explanation. A further alternative exists. I might instead point out that every other house on your street has had a broken window this week and yours is no different. Here I am identifying some sort of pattern in recent events and portraying the incident with your window as another instance of that pattern.
As this is something of a toy example, let’s consider a more detailed case. The following example, of Arbuthnot’s regularity, will hopefully bring out the distinction that Loewer has in mind.69 The regularity which forms our explanandum is simple:
over an 82 year span from 1623 onwards, more boys than girls were born in London. Calling this mere coincidence is hardly credible given how unlikely this is to have come about by chance. But there are two kinds of explanation on offer for this regularity. Call the first the fundamental physics explanation. We may not have such
69 A discussion of Arbuthnot’s regularity and explanation can be found in Kitcher (2001) p.
71. See Frisch (2011) for further discussion. The relevance of this example to Loewer’s distinction was first brought to my attention in a talk by John Roberts.
an explanation presently available, but we can sketch out the form it might take. Take the fundamental laws of physics and assume that they are deterministic. Now take the exact state of all of the fundamental physical particles at some point prior to 1623. (Given deterministic laws it doesn’t matter when; the initial conditions of the universe would suffice. We might also appeal to the position of the particles at some future time, but the sense in which that would explain why this past regularity occurred is very slim indeed.) As the laws are deterministic, we can now in principle derive the positions of the particles for any later time, and for the relevant 82 year period in particular. Associate some distributions of particles with the birth of a boy and some other distributions with the birth of a girl. Count the number of boy-birth distributions and compare it to the number of girl-birth distributions. We can clearly see that more boys than girls were born in London each year!
There is a sense in which this constitutes a good explanation of the Arbuthnot regularity. We have given the details (or, at least, the form such details might take) of what the regularity might fundamentally consist in. The regularity obtains in virtue of such-and-such fundamental physical facts (despite my having just called it a fundamental physics explanation, this is a metaphysical explanation in the sense of giving information regarding what grounds what). But it is also easy to see what this explanation misses. Most obviously, it is an ‘in principle’ explanation: we do not have epistemic access to the world’s fundamental state prior to 1623, we do not believe we have discovered what the fundamental laws actually are and we cannot even decide whether such laws will turn out to be deterministic. But even if we had all of this information available to us, the explanation would still be missing out on something. The fundamental physics explanation does nothing to help us understand why the regularity is not some big coincidence. It might not be a coincidence in the sense of having come about by a random process since deterministic laws rule out any of that kind of coincidence. But there is still the unanswered question: why this particular fundamental distribution that generates the Arbuthnot regularity when so many others are compatible with the laws? Furthermore, the explanation explains too much. For the fundamental physics explanation not only explains the Arbuthnot regularity but also every other event and regularity that occurs after the time associated with the given state of the
particles. So the very same explanans will explain my tea drinking, the first moon landing, and the rise and fall of alien empires in other galaxies. The sense in which this is an explanation of the Arbuthnot regularity is perhaps a rather slim one. So there is plenty of room for an alternative to the metaphysical explanation just given. Contrast this with Fisher’s neo-Darwinian explanation of the regularity. In any population which differs from a 1:1 ratio at sexual maturity, there is a selection pressure in favouring of producing more offspring of the sex that is not as well represented. If one sex in a population is more vulnerable than the other, and so less likely to reach sexual maturity, natural selection will favour a birth ratio skewed towards the more vulnerable sex. In humans, males are more vulnerable than females: boys are more likely to die before puberty than girls. Any large human population which fails to birth more boys will experience a selection pressure towards having more boys. This is why Arbuthnot observed this regularity; because of natural selection, every year is likely to be a year in which more boys are born than girls.
This scientific explanation does not generate the same sense of mystery as the metaphysical one given previously. The regularity in the London births no longer appears to be a coincidence, but rather something we should expect to hold. This is a virtue of the second explanation in that it grants a greater understanding of the explanandum than the first does.70 We might also note that this explanation is more
specific than the first. It does explain more than just a regularity in seventeenth- century London – it explains similar birth trends across different places and times – but it explains far less than the first does. By appealing to the entire Humean mosaic, the metaphysical explanation explains every regularity that holds (assuming the fundamental state of the world was given at an early enough point; even if it were given at the beginning of 1623, it would still cover a wide range of regularities). So the explanations differ in how widely applicable they are.71
70 See de Regt and Dieks (2005) for an emphatic defence of the importance of understanding
in explanation.
71 A third difference between the two explanations is that the first appeals to fundamental