The Heuristic Approach

The heuristic approach to Bayesian explanationism is put forward as a response to this chal- lenge. This account asserts that Inference to the Best Explanation and Bayesianism are compatible because the former guides us (as a heuristic) to good approximations of sound probabilistic reasoning: “we show that loveliness [i.e., explanatory power] is the inquirer’s

guide to likeliness” (2004, p. 121). According to this approach, Inference to the Best Ex- planation is a heuristically useful mode of inference allowing people to approximate sound probabilistic reasoning without necessarily having to know the relevant probabilities or even the probability calculus. The probability calculus sets the normative standard to which Infer- ence to the Best Explanation attains; Inference to the Best Explanation is a reasonable mode of inference to the extent that it approximates sound probabilistic reasoning. Bayesianism therefore accounts for the normative appeal of Inference to the Best Explanation.

On the other hand, according to the heuristic approach, Inference to the Best Explanation fills in some important psychological details pertaining to Bayesianism. While Bayesianism provides an attractive normative account of uncertain reasoning, it seems to set the standard a bit too high; if it takes reasoning in accord with the probability calculus to be rational, then the vast majority of people might plausibly be thought to be irrational. After all, how many people know how to reason in terms of the probability theory? And even for those that do, how many have access to or knowledge of the precise probabilities involved in typical reasoning contexts? Inference to the Best Explanation goes some way to filling in the details here by providing one example of a way in which our explicit patterns of reasoning allow us to approximate sound probabilistic reasoning even when we are incapable of performing the probabilistic reasoning directly.

Note that, according to the heuristic approach, Inference to the Best Explanation need not be considered a perfect guide to sound probabilistic reasoning in order for the two to be compatible. Lipton writes, “It is glory enough to show that explanatory considerations are an important guide to inference” (2004, p. 121). Unlike what Weisberg assumes, the compatibility of Inference to the Best Explanation and Bayesianism does not come by way of the perfect agreement of their respective conclusions. Rather, it comes by way of their mutually informative but distinct roles in a full theory of human reasoning. Bayesianism provides the logic of such reasoning, including reasoning by Inference to the Best Explana- tion; and Inference to the Best Explanation provides some important details about how we – along with all of our natural, cognitive limitations – are actually able to satisfy this logic approximately when we reason well (i.e., details about the psychological validity of Bayesian- ism). Consistently with this, one might say that both models of inference describe norms of

proper reasoning that are compatible because they are situated on different levels of norma- tive theory. Bayesianism describes the logic that we attain to, but with no regard for our human limitations. Inference to the Best Explanation, on the other hand, has the distinct aim of describing a normative theory that simultaneously respects the bounds set by human capacities; this theory of bounded rationality is normative because of its approximation, in the real world, to Bayesian theory.

The heuristic approach easily avoids all of the serious difficulties encountered by previ- ous attempts to spell out Bayesian explanationism. Unlike the pluralistic position that van Fraassen criticizes, the heuristic approach proposes no change to Bayesian conditionaliza- tion. Rather, this account locates the epistemic utility of explanatory considerations within standard Bayesian reasoning. Consequently, worries about diachronic Dutch books do not arise.

Unlike Weisberg’s principle and van Fraassen’s target, the heuristic approach does at- tempt to shed light on Inference to the Best Explanation. Specifically, the heuristic account aims to clarify the normativity of explanatory inference, and therefore to show why it is that we find instances of this inference form compelling and useful. Depending on how one fills in the details of the heuristic account (see the next two sections), this approach may also specify the sorts of judgments and concepts that people rely on when they judge the explanatory power of a hypothesis relative to some evidence. In this case, the heuristic account may not only clarify the normativity of explanatory inference, but it also might go some way to clarifying the nature of Inference to the Best Explanation.

Finally, the heuristic approach also has the benefit of reserving important and legiti- mate roles both for explanatory considerations and for Bayesianism. Normatively speaking, explanatory inference is defended via Bayesianism; i.e., this strategy maintains that explana- tory reasoning can be given normative backing by being linked to Bayesianism. Thus, in this constrained normative sense, it is indeed true that explanatory reasoning has nothing to offer to the study of human reasoning that isn’t already provided by Bayesianism. How- ever, explanatory considerations have a psychological importance insofar as they are shown to be cognitive heuristics for sound probabilistic reasoning. Inference to the Best Explana- tion describes a logic and epistemology of human reasoning that is mindful of actual human

capabilities and limitations. Explanationists thus have something of great importance to offer the Bayesian in the form of a psychological validity traditionally found wanting in the Bayesian program. Lipton captures this idea nicely when he writes, “Even if Bayesianism gave the mechanics of belief revision, Inference to the Best Explanation might yet illuminate its psychology”(2004, p. 108).