Objection 1: Explanation without Explanatory Power?

I have already considered, in Section 2.7, objections to my explication of explanatory power that exploit cases where we have a positive degree of statistical relevance between some h and e, and so E (e, h) > 0, in spite of the fact that h clearly does not provide a potential explanation of e. Such objections fail to appreciate the distinction between explications of explanatory power and analyses of explanation. It is up to the latter type of account, and not to the former, to rule out such cases. A measure of the strength of a potential explanation, like E , presumes that the h and e in question do sit in the proper relation – whatever that might be – in order for h to be a potential explanation of e. However, one might also criticize our explication by referring to cases in which a hypothesis does seem to provide a potential

explanation of the evidence (and so it seems to have some positive degree of explanatory power over the evidence) but where E takes a non-positive value.

In such cases, h is supposed to offer a potential explanation of e in spite of the fact that it does not increase the expectedness of e (i.e., it does not decrease the degree to which e is surprising). In developing his own statistical relevance theory of the nature of explanation, Salmon(1970, pp. 63) puts forward some cases which are meant to exemplify this situation, including the following:

Suppose [...] that a game of heads and tails is being played with two crooked pennies, and that these pennies are brought in and out of play in some irregular manner. Let one penny [penny A] be biased for heads to the extent that 90 percent of the tosses with it yield heads; let the other [penny B] be similarly biased for tails. Furthermore, let the two pennies be used with equal frequency in this game, so that the overall probability of heads is one-half. [...] Suppose a play of this game results in a head; the prior [probability] of this event is one-half. [Now suppose] that the toss were made with the penny biased for tails [penny B]; [the probability of the explanandum] is decreased from 0.5 to 0.1.

Despite the fact that the hypothesis that penny B was flipped lowers the probability of getting a heads from 0.5 to 0.1, Salmon asserts that this hypothesis does provide a genuine explanation; as he writes, “No further explanation can be required or can be given” (ibid.). As soon as we have stated the probabilistic facts of the matter pertaining to the stochastic process that resulted in our explanandum event, according to Salmon, we have given the entire statistical explanation of that event.

Such cases seem to pose a problem for E as an explication of explanatory power because it seems that, insofar as h provides all of the explanatory details about e, it should be rendered as positively explanatory by a satisfactory measure of explanatory power. But since h actually decreases the probability of e, E (e, h) < 0.

The first thing to say about Salmon’s example – and the other examples given in this vein – is this: if one grants that there is a sense in which the hypothesis that penny B was flipped (along with the corresponding probabilistic details) has explanatory power over the result of this flip, it is manifestly not the sense of explanatory power that we commonly refer to when reasoning. In order to motivate the intuitions that Salmon calls upon, he must set up this and other examples in such a way that we know for certain which hypothesis is true – in this case, it is stipulated that coin B was the one flipped. But note that this is never

the situation when we are interested in reasoning explanatorily. Such reasoning seeks reason in favor of some hypothesis on account of its explanatory power over the evidence. Thus, if we are already in the know regarding which hypothesis is true, then we will find no use for explanatory reasoning. The scenario where we know that penny B was the one flipped thus does not represent a typical scenario in which we would be inclined to reason explanatorily in real life.

Furthermore, we can consider the situation where we are not already clued in to the truth of a hypothesis, and where we are inclined to reason explanatorily (i.e., where we are interested in developing a rational preference for one hypothesis over the other based on their relative explanatory powers over the evidence). And, in this scenario, explanatory intuitions would seem to favor the hypothesis that penny A was chosen over the hypothesis that penny B was chosen, contrary to stipulated fact. Given the stochastic facts of the scenario, the former hypothesis just seems to be a far better explanation of the observed flip of a heads than the the latter hypothesis. And this intuitive judgment falls right in line with the sense of explanatory power explicated in this dissertation rather than the sense proposed by Salmon. This is because the hypothesis that penny A was chosen would increase the expectedness of flipping heads to a far greater extent than the hypothesis that penny B was chosen. So, in our variation of Salmon’s example in which one is reasoning explanatorily without already knowing what hypothesis is true, it is the sense of explanatory power explicated in this dissertation – rather than that which Salmon has in mind – that seems to be at work. Examples such as Salmon’s thus do not show that E fails to capture the notion of explanatory power that we have in mind when reasoning explanatorily.

Still, it is an interesting question whether examples like Salmon’s point to a sense of explanatory power distinct from that which E claims to capture. In all such examples, as Salmon (1971a, p. 9) says, we put forward a “statistical explanation of an event [which] exhibits that event as the result of a stochastic process from which such events arise with some probability whose degree may be high, middling, or even very low.” In effect, we respond to a why query by reciting the chances of the explanandum’s occurrence. Another past proponent of the statistical relevance theory along with Salmon, Richard Jeffrey(1969, p. 24) puts this point very clearly: “The knowledge that the process was random answers

the question, ‘Why?’ – the answer is, ‘By chance’. Knowledge of the probabilistic law governing the process answers the question ‘How’ – the answer is, ‘Improbably, as a product of such-and-such a stochastic process’.”

The key question here is whether the hypotheses in these examples offer explanations that do not fall in line with our notion of explanatory power, or whether instead they just do not really offer explanations at all. With regards to this question, it seems to me that these are cases where the hypotheses do not offer an explanation – in fact, where we are denying that there is any explanation to be had. As such, they are cases that we would not want our measure of explanatory power to accommodate. As noted above, in these examples, “there’s no reason for the fact: it came about by chance” (Jeffrey 1969, p. 24). But when we can only appeal to the stochastic facts of a scenario, we are effectively throwing our hands up and saying, “the explanandum just happened, and there is nothing further to say about it other than how likely its chance occurrence was.” If we gain no “reason” for the explanandum, as Jeffrey puts it, or any other information about the explanandum other than knowledge of its likeliness, then it is unclear at best why we would think we have gained an explanation. Any psychological relief that such a move may give us in a particular instance is not, I suggest, due to the fact that we now have a deeper understanding of the explanandum but rather to the fact that we are no longer unsettled in our search for one; we have decidedly given up on our search for understanding in this case.

Another way to think about this is that when we are faced with a ‘why?’ question, we may respond either by giving an explanation or by saying that there is none available. In the former case, we – at least typically – will cite causes, reasons, laws, or the like that go some way to showing that the explanandum was actually not so unexpected as previously thought. In the latter case, on the other hand, we can effectively say that there is no such explanation simply by saying that the explanandum event just happened by chance; we can give a more informative response of this sort by saying that the explanandum event just happened by chance, and by citing the probability of its occurrence – if we know it. It is the latter sort of move that Salmon and Jeffrey exploit, and so it seems that they are pointing to a case where one denies the possibility of an explanation.1