Rational Belief: Rational Acceptance or Rational Action?
Patrick Maher in his book Betting on Theories (1993, chapter 6) notes two common assumptions about belief:
(1) An agent A believes in H just in case A is willing to act as if H
(2) Sincere intentional assertion of H by A expresses A's belief in H
Maher interprets (1) as meaning that A is willing to bet on H at any odds. Unfortunately, certainty is rare, and it does not seem sensible to deem irrational every belief about an uncertain thing. Clearly belief in H cannot be equated with a person's "willingness to act as if H were true under all circumstances" and so (1) needs revision.
(1a) An agent A believes in H just in case A assesses the probability p of H and p is greater than some threshold t.
In (1a) a agent A is willing to bet on H given that H is probable enough, according to person P and that agent's threshold of belief. This is reasonable, but when combined with (2) proves problematic.
Maher argues (1) and (1a) are incompatible with (2), that belief is expressed by sincere intentional assertions, what he calls acceptance. The problem for Maher is that rational acceptance cannot depend (only) on probability, because any arbitrarily high probability (even that of unity) of a hypothesis H is neither necessary nor sufficient for a person's rational acceptance of that hypothesis, and arbitrarily low probabilities are also neither necessary nor sufficient for not accepting H. Instead, rational acceptance depends also on the informativeness and closeness of H to the truth. For example, one might accept a scientific hypothesis because it is close to the truth, even if one believes that the hypothesis has a probability of zero of being exactly true (if only because scientific hypotheses tend to be revised over time). But it would be rational to bet against H in the long run because it has a low probability of being exactly true! Maher concludes that, "the folk concept of belief appears to regard belief in H as a single mental state that is expressed both by a willingness to act as if H were true and also by sincere intentional assertion of H; and these are in fact two distinct states."
In sum, willingness to act as if H were true can reasonably be said to depend on the probability of H, but a person's acceptance of H depends also on the informativeness or closeness of H to the truth. Hence these two so-called folk notions of belief actually correspond to two different but related mental states about H. Incidentally, Maher also rejects another possibility, that belief is not a discrete qualitative state. Instead of saying that one either believes or does not believe something, one may talk about degrees of belief in H. But that will have to wait discussion for another day.
A final note on Maher's argument. Plausibly one could design an artificial agent such that (1a) and (2) are treated in the same way; in fact, based on my readings in artificial intelligence, I would argue that we already do. In such cases willingness to act as if H were true and acceptance of H as true might correspond to the same "mental" state in the agent. If one accepts Maher's arguments, these agents are not entirely rational agents. If they were, (1/1a) and (2) would not correspond to the same states, as Maher says. Hence it may be an uncharitable reading of Maher to suggest that he regards these as necessarily being distinct mental states in human beings, given that we are not purely rational agents!
A conundrum of rational action
Maher points out another of those conundrums of rationality: performing the calculations necessary to decide the rational thing to do in a given situation is frequently too costly to be rational. Indeed, frequently it is too costly to calculate whether calculating the most rational action in a given situation is the rational thing to do. Hence, the only rational thing to do in such situations is to do something, perhaps based on rules of thumb, or by just guessing. Maher argues that if one is fortunate to have accidentally chosen to do the right thing, one has acted rationally. But in general, in such situations one must be resigned to choosing the irrational course of action, even if one arrived at choosing that action by acting rationally and avoiding the costly calculation.
Maher is obviously concerned with rational agents, or more precisely, with the question of rationality itself, and not with agents per se. His arguments are not based on empirical research of actual animal behavior. There is no real good reason to expect empirical behavior to be always rational; and one might reasonably question why social scientists ought to pay attention to the issues Maher raises. Yet I think that there are some good reasons that they should be of general interest, if one first acknowledges that it is not a descriptive theory of action, but a prescriptive one, with particular applicability to how we think about science.
(Originally posted December 5th 2009, at the OAC)