BELIEVING ON THE BASIS OF QUALITATIVE RULES: COMMENTARY ON KYBURG

Suppose an agent is willing to entertain the possibility of a proposition -A only as a hypothetical. To imagine the world as being such that -A is true is to imagine the world to be something it is not. If this is the case, let’s say A is a “real belief.” This doesn’t mean A is merely very probable; it means it is certain. For the sake of argument, let’s say a certain proposition has probability 1 (at least, subjective probability, relative to that agent). What’s wrong with this, retorts Kyburg’s “cautious philosophical probabilist,” is that stating A is certain means A cannot possibly be false. If an agent claims that P ( A ) = 1, then it can never give up belief in A . Au contraire, responds the pragmatist, agents have been known to be wrong. In fact, this is how we know that people have real beliefs. People often admit that they were wrong, misguided, deluded, or otherwise mistaken. If someone merely thought A to be probable (no matter how probable, short of certainty), how could they ever be wrong? Kyburg, in his article “Believing on the Basis of Evidence,” has quite succinctly summarized some of the issues that must be addressed if we are to adopt the view that agents must (sometimes) accept propositions as “real beliefs.” I agree wholeheartedly with the intent of the article and, for the most part, with the details. Kyburg advocates the use of probabilistic acceptance rules for beliefs. The “evidence for believing” that acceptance is useful comes, oddly enough, in the final section of the paper. There are reasons to think that accepting certain propositions as beliefs will relieve the computational burden of keeping track of many contingencies’ People certainly act and talk as if they believed propositions. Even if it is only a manner of speaking, it is certainly a useful manner of speaking. I agree with Kyburg on these counts; however, I don’t think his proposal goes far enough. The most natural reason for wanting to adopt an acceptance rule is to do away with the numbers altogether; and Kyburg’s notion of acceptance is based on the numbers in an agent’s BIG. If it is useful to represent practical certainties qualitatively, then it is also useful to represent the background information and evidence, the stuff relative to which accepted propositions are deemed acceptable, in a qualitative fashion as well. This is just the purpose for which nonmonotonic logics have been proposed. How might we represent the fact that some body of evidence lends enough support to a proposition to make it believable? Using default rules, of course. In what follows I’ll discuss some of the similarities between recent proposals for nonmonotonic reasoning, in particular, conditional theories, and Kyburg’s notion of acceptance. 1’11 describe what these qualitative theories have to say (or might in the future) about some of the issues Kyburg brings up. The acceptance stance cames with it a commitment to revise beliefs; and conditional theories of revision are rather attractive (semantically at least). I want to argue that counterfactual probabilities offer a way of combining the “accept and revise” viewpoint with the conditioning so beloved by