The Role of Chance in Explanation

Abstract

‘Those ice cubes melted because by melting total entropy increased and entropy increase has a very high objective chance.’ What role does the chance in this explanation play? I argue that it contributes to the explanation by entailing that the melting was almost necessary, and defend the claim that the fact that some event was almost necessary can, in the right circumstances, constitute a causal explanation of that event.

Keywords:

• explanation
• causation
• chance.

Notes

¹ One way to explain a fact F is to show how F is grounded in deeper facts. This is a ‘grounding’ explanation. None of my examples are grounding explanations and I will ignore grounding explanations in this paper.

² Not all cases are straightforward. If Billy hangs back because he sees Suzy throw her rock then it is Suzy's throw that causes the window to break. This is so even if Suzy has worse aim and her throwing actually lowered the chance of the window's breaking. So just how do facts about chance ground facts about causes? To answer this question is to give an analysis of causation partly in terms of chances. The guiding idea behind this kind of analysis is the idea that, typically, causes increase the chance of their effects. But this is not the place to get into the nitty-gritty details of what these analyses look like, for which see Hitchcock [2010].

³ This view resembles the Statistical Relevance model of explanation [Salmon 1989: 62–7], though that model incorporates a specific analysis of causation in terms of probability-raising. It is also similar to Humphreys’ theory of chancy explanation [Humphreys 1989].

⁴ This is a controversial claim about the interpretation of quantum mechanics. But even if it is false, what matters is that this example would be an example of an explanation if the claims it makes were true. Throughout the paper I will assume that those claims are true.

⁵ A grounding explanation of F shows F to be necessary in the light of some deeper facts. And grounding explanations are not causal. But, again, I am ignoring grounding explanations, and stipulate that ‘necessity explanation’ as I use it does not apply to grounding explanations.

⁶ Much of Woodward's book is about what features are to be ‘held fixed’ in these counterfactuals. The theory needs a way to solve the problem of pre-emption: cases where if the cause had not occurred, a backup cause would still have produced the effect. This is an important problem but throughout this paper I will ignore it.

⁷ Lurking in the background here is a counterfactual analysis of event causation: C is a cause of E iff C and E are distinct and had C not occurred, and certain facts been just as they actually are, then E would not have occurred. But Woodward treats causation as a relation between variables rather than events. (A variable is a kind of ‘generalized event’. While events must either occur or fail to occur, a variable may in principle have more than two values. The current atmospheric pressure is an example of a variable: when measured in atmospheres it can take any smallish real number as a value.) Taking causation to be a relation between variables makes the distance between ‘C is a cause of E’ and ‘if C* had occurred instead of C then E* would have occurred instead of E’ smaller. It is also smaller on David Lewis's [2000] analysis of causation as influence, and the view that causation is contrastive [Schaffer 2005].

⁸ Lewis [1986] uses the idea that an event can be causally explained by saying it was uncaused to respond to some alleged examples of non-causal explanations.

⁹ Marc Lange [forthcoming] argues that ‘distinctively mathematical explanations’ of physical phenomena are non-causal. His description of these explanations makes them look a lot like necessity explanations. (He would regard The Hiking Habit as distinctively mathematical.) If he is right then I am wrong to say that necessity explanations are causal. Now I am not sure that he and I are using the same criteria to classify explanations as causal. Setting that aside, the most his argument shows is that The Supernova and The Hiking Habit should not be classified together. But what matters for my argument is that there are some explanations that fit my definition of necessity explanations as a kind of causal explanation. And there are. The Supernova is one. It does not matter if there are other explanations that do not.

¹⁰ I am here assuming the Boltzmannian way of thinking about the relationship between the second law of thermodynamics and statistical mechanics, as defended in, for example, Albert [2000].

¹¹ Another theory might not identify chances with relative sizes. But since probability functions are special cases of measure functions, a theory like that in effect has two ways of measuring sizes of sets of states or possible worlds (only one of which is identified with chances). That means that a proposition could be almost necessary relative to one of the measures but not relative to the other. Which kind of almost necessary is explanatorily relevant? I say that only the chance measure is; the other is not. I do not have space here to give an extended defence of this idea. But, briefly, I think it is only the chance measure that has real physical meaning.

¹² For the record, I do not agree (and doubt many others would) that we remain completely in the dark. We have learned something about the causes of the weather. But maybe Railton's point is just that there is still a lot of explanatory information we do not have.

¹³ Actually Batterman would say that he focuses more on explanations of regularities than explanations of single events. He would say that the kind of example he is interested in is an explanation of the fact that every time anyone has put ice in a glass in a warm room the ice has melted. But (as Strevens notes in a different context) this explanation of a regularity can still be regarded as an explanation of a single event: it is just a large and spatiotemporally scattered event.

¹⁴ Hempel attempted to reconcile his view with Paresis. An excellent discussion of what is wrong with that attempt may be found in chapter 4 of Woodward [2003].

¹⁵ What follows summarizes material from in and around chapter 10 of Strevens [2008].

¹⁶ For a mathematically rigorous statement and proof of this claim see Strevens [1998, 2003].