JUSTIFICATION, PROBABILITY, AND CONSISTENCY

Professor Kyburg’s paper is refreshing. Indeed, I am pleased to see this latest defense of the probabilistic approach, because I believe there are many applications where this approach yields results much superior to the general “default” approach. This is especially so in cases where a series of uncertain conclusions are chained together to yield a still more uncertain conclusion. Unless the loss of certainty involved in each inference is recorded and propagated in a sound fashion, disastrous results may ensue. Of course, there are applications where the default approach can be safely employed, but I know of no class of problems where the default approach is more likely to yield correct results than the probabilistic approach. To be sure, various criticisms of the probabilistic approach have been advanced by members of the “default” camp, but apart from the lottery paradox, I believe these criticisms have been rendered innocuous by Cheeseman (1985). As for the lottery paradox, we have Kyburg’s response. It is certainly true that most humans manage surprisingly well, despite the fact that their total belief sets are usually inconsistent. Moreover, there are other solutions to the paradox that preserve the consistency of one’s relevant beliefs. One of these is discussed in what follows. However, let us first examine Kyburg’s position on the acceptance and justification of an agent’s most fundamental beliefs, that is, beliefs that comprise the background knowledge that renders probabilistic reasoning possible. In Section 3 (REGRESS AND PROGRESS), Kyburg raises the question, “Where does background knowledge and evidence come from?” His remarks throughout most of this section seem directed at the justification of observational evidence rather than at physical laws and mathematical principles. Although he does briefly allude to “mathematical and logical generalizations,” I am somewhat unclear whetheir Kyburg intends his remarks regarding justification of evidence to apply to the most basic empirical laws found in an agent’s background knowledge. Possibly, Kyburg sees the justification and acceptance of particular pieces of evidence as different in kind (with respect to the regress issue) from the justification of fundamental physical laws. In any case, in Section 3 Kyburg clearly maintains that observation statements and other kinds of evidence should be accepted when their probability surpasses some threshold of “practical certainty.” However, this threshold cannot be taken as equal to 1 , for the jusrificution of evidence (in Kyburg’s view) presupposes the ever present potential of gathering supporting evidence having a higher probability than the evidence to be justified. Now, it is somewhat difficult to reconcile these views with Kyburg’s remarks in Section 8, where he seems to be saying that physical laws anid obseivation statements should be accepted only when we (provisionally) assign them a subjective probability of 1. There he says