This is a note I wrote on Salmon and Kitcher’s criticisms of van Fraassen’s view of explanation in the Scientific Image. It is a little flawed in that the defense I gave in the last third doesn’t mesh with what van Fraassen says in the book. I didn’t realize this when I wrote it though. Alas. Up until then I think it is not bad though.

In their article ”Van Fraassen on Explanation,” Salmon and Kitcher charge van Fraassen with presenting a theory of the pragmatics of explanation that fails to be a pragmatic theory of explanation. This is a hefty charge because van Fraassen denies that there is any sui generis explanatory virtue and defends this claim by providing a theory of explanation that purports to show how explanation is merely pragmatic. In this paper I will present two of Salmon and Kitcher’s objections to van Fraassen’s theory of explanation. I will then present replies on behalf of van Fraassen and argue that the criticisms do not undermine his project. I will close by presenting what seems correct in Salmon and Kitcher’s.

Briefly, van Fraassen sees explanations as answers to questions of the form ”Why is Pk the case?” A question Q in a given context can be identified with the triple (Pk, X,R), where Pk is the topic of the question, X is the contextually determined contrast class for Pk, and R is the contextually determined relevance relation. An explanation is an answer A to some ‘why’ question such that the A stands in R to (Pk, X). This makes van Fraassen’s theories of explanation and ‘why’ questions heavily dependent on context. This is explicit at the end of the chapter on explanation in the Scientific Image, where van Fraassen says, ”The discussion of explanation went wrong at the very beginning when explanation was conceived of as a relationship like description: a relation between theory and fact. Really it is a three-term relation, between theory, fact, and context.” Finally, for evaluating answers we need the background theory K and the part K(Q) that is salient to the question, both contextually dependent. With this background in mind, we will move to the objections to van Fraassen’s account.

I will focus on two of Salmon and Kitcher’s arguments against van Fraassen which deal with the relevance relations. One is that without any restrictions on what counts as a relevance relation, van Fraassen’s account of explanation reduces to triviality. The other is that without any restrictions on relevance relations, van Fraassen’s theory of explanation cannot rule out bad explanations without incorporating elements that undermine the claim that explanation is merely pragmatic.

According to Salmon and Kitcher, to reduce van Fraassen’s account to triviality, let Pk be a true proposition and X a set of propositions containing Pk and whose other elements are all false. Let R be {( A, ( Pk, X))}U S where S is any set of pairs of the form ( B, ( Y , Z)) where B and Y are propositions and Z is a set of propositions containing Y. Further, S cannot contain any pairs ( B, ( Y , Z)) such that B is true and ( Y , Z)=( Pk, X). Thus, for any true propositions A and Pk, there is a question Q such that A answers Q and Pk is the topic of Q. The conclusion is then: ”If explanations are answers to why-questions, then it follows that, for any pair of true propositions, there is a context in which the first is the (core of the) only explanation of the second.” Salmon and Kitcher think this is a reductio of van Fraassen’s position. They later go on to say that ”if van Fraassen’s account does not contain context-independent principles that preclude assigning [trivializing propositions] to K(Q)” then the above problems will arise. However, a closer examination of their argument will not support the reductio conclusion.

Salmon and Kitcher’s argument is not a reductio. Assuming that for each triple of topic, contrast class and relevance relation, there is a context that generates it, then all they have shown is that for each topic and explanation there is a context in which the latter explains the former. What they need for reductio is that for any topic and explanation, the relevance relation for a given context will be the one constructed above. If van Fraassen’s account said that any true proposition were an explanation for any question topic in a context, then it would be trivial. However, this is not the case. Some propositions will not explain some question topics in a given context although they could explain the topic in other contexts as the relevance relation of the context would be different. Thus, their reductio fails.

To see why their argument fails, it is helpful to note that the construction above does not invoke context. The contrast class X, the relevance relation R, and the background theory K are all determined by the context, not by the theorist. Formally van Fraassen leaves open the possibility that there are contexts such that for any true proposition they provide contrast classes and relevance relations such that the proposition explains the topic at hand, but this is, prima facie, not different than other theories of formal pragmatics. For example, David Kaplan’s theory of indexicals allows contexts in which the speaker is not at the location of the context or at the time or even in the world. These are in a way deviant contexts, but they are formally allowed. Kaplan suggests a natural way of restricting attention to non-deviant contexts. Turning back to van Fraassen’s theory, the possibility of unusual contexts is not a reductio of his position. The claim that there is no context in which a certain proposition would explain a given topic is quite strong, and various science fiction examples should provide inductive counterevidence to this claim.

One of Salmon and Kitcher’s criticisms of van Fraassen’s theory, and a possible reason why they do not mention context in formulating this objection, is that van Fraassen does not indicate any way in which the contrast class or the relevance relation are to be read off of the context. Looking again to Kaplan’s theory of indexicals, the formal contexts are quadruples ( cA,cT,cL,cW) of a speaker, a time, a location, and a world. It is fairly straightforward to figure out which formal context corresponds to which concrete context. The speaker cA will be the person talking and cT will be the time that person is talking. There are some complicating details, such as the extent of the location region. Ignoring these for the moment, the formal contexts are comprised of features that are easily read off of a concrete context. Returning to van Fraassen’s theory, a difference emerges. The contrast class and relevance relation are less straightforwardly read off the concrete situations. We will return to this point in the conclusion.

The other objection of Salmon and Kitcher to be discussed is that without any formal requirements on relevance relations, van Fraassen’s account allows bad explanations and the only way to rectify this makes explanation cease to be merely pragmatic. Their examples follow a pattern, so we will focus on their example of the astrological explanation of the date JFK was assassinated. The setup is that the contrast class is the set of propositions saying that JFK died each day in 1963 together with one saying that he survived 1963. The topic Pk is that he died on 11/22/63. Salmon and Kitcher stipulate that R is the relation of astrological relevance in which the answer stands to the contrast class and the topic. The answer consists of the conjunction of a true description D of the positions of the heavenly bodies, the proposition that if D then Pk, and the denial of everything in the contrast class except Pk. Salmon and Kitcher claim that van Fraassen’s theory says this is an explanation. Further, they think that van Fraassen cannot rule out the answer as being astrological because it invokes only facts that are part of the background theory K, i.e. astronomical facts. The only way out of this predicament, according to Salmon and Kitcher, is for van Fraassen to make it so that the relevance relations are not determined solely by merely subjective factors. They say, ”[van Fraassen] ought to be equally serious about showing that relevance is not completely determined by subjective factors. If we are talking about distributions and redistributions of personal probabilities, they must be subject to some kinds of standards or criteria…. To be scientifically acceptable, the redistribution of probabilities must involve differences in objective probabilities…” However, the move to more objective determinations of relevance and to objective probabilities introduces a non-pragmatic aspect into explanation, undermining van Fraassen’s claim that the explanatory virtue is just pragmatic.

Van Fraassen has two responses available, both rejecting excessive assumptions Salmon and Kitcher need for their arguments but to which van Fraassen is not committed. The first of these is that the background theory K includes only contemporary science, possibly with some additional factual information. Thus, in their example given above, the astronomical information is part of K but the astrological beliefs that the agents have and that make it a good explanation to them are not. This provides space for including suspect relations as relevance relations and getting around van Fraassen’s admonition that explanation shouldn’t rely on old wives’ tales. This allows enough space between K and the agents’ beliefs to allow Salmon and Kitcher’s problems to enter.

Van Fraassen should reject this construal of the background theory. Van Fraassen says, ”[K] is a factor in the context, since it depends on who the questioner and audience are.” Since it involves who the questioner and audience are, it would seem that van Fraassen means to include in K at least some of the beliefs of the agents in question. There is nothing to debar them from having mistaken or misguided beliefs, e.g. that astrology is true, which are part of K. Since K is not restricted to just contemporary science, van Fraassen has a response to their argument. He should deny that there are no astrological propositions in K. One of the agents involved in the exchange takes the explanation to be good precisely because they have astrological beliefs, so they should figure in K. If van Fraassen is entitled to claim that explanation should not be based on old wives’ tales then this will provide a way for him to rule the astrological explanation out as an explanation.

Van Fraassen has another response to Salmon and Kitcher’s argument. They assume further that the only solution to the problem is to make the relevance relations more objective and the probabilities involved into objective probabilities. This is a crucial step toward their conclusion that explanatory virtue is not just pragmatic. If the account must involve these objective features then it looks like explanation is not just pragmatic as it latches on to objective features of the world, above and beyond what van Fraassen thinks explanatory virtue involves.

The second response is to deny their crucial premises that the relevance relation and explanation must reflect objective probabilities. Constraints can be put on relevance which do not require tying it and explanation to objective probabilities. Van Fraassen says that ”observable is observable-to-us,” so it is to be expected that relevance would be relevance-to-us. The relevance relation should depend on K, which van Fraassen would allow to include the beliefs of the agents, as well as current science, to give content to van Fraassen’s claim that good explanation should use good science. This ties relevance to subjective factors, in the sense of relying on the subjects involved, possibly including personal probabilities. However, this need not count against it since the subjects and their beliefs are things science investigates, and so, in a sense, objective. Salmon and Kitcher have given no reason to demand more objectivity than that.

Without Salmon and Kitcher’s crucial premises concerning relevance, the pressure on van Fraassen’s theory to give up the claim that explanatory virtue is just pragmatic disappears. Salmon and Kitcher’s argument that van Fraassen’s theory requires explanation to have its own non-pragmatic virtue does not work against van Fraassen’s position. However, part of their criticism still stands.

At the heart of Salmon and Kitcher’s criticism is the charge that van Fraassen does not place any formal constraints on what constitutes a relevance relation while also claiming that not all relations between a proposition and a suitable ordered pair count as genuine relevance relations. This makes the relevance relation an unexplained explainer. It does a lot of the work in van Fraassen’s account of explanation, but there are no constraints on it or indications of what counts as a relevance relation.
As was said above, the relevance relations are less straightforwardly picked out of a concrete context than the speaker. Van Fraassen needs to give an account of how the context determines the relevance relation. Without such an account, van Fraassen has just shifted the focus from problems of explanation to problems of relevance.

While Salmon and Kitcher’s arguments do not work against van Fraassen in the way they claim, they do highlight demands on the relevance relation. The relevance relation should be tightly connected to the background theory. It should involve the beliefs and intentions of the agents involved in the explanation. Salmon and Kitcher supply a promising suggestion: isolating what look like relevance relations for different sciences at different times and generalizing from there. They have not shown that no account of relevance can be given and the pressure is on van Fraassen to supply such an account. If one cannot be given, then Salmon and Kitcher’s arguments will need to be reevaluated.