Positive versus Negative Undermining in Belief Revision

Abstract

I am going to compare two competing theories of reasoned belief revision. I will call the theories I am concerned with the theory of belief and the theory of belief revision, respectively, since there are similarities between these theories and certain philosophical theories of sometimes called foundation and theories [Sosa 1980, Pollock 1980]. But the theories I am concerned with are not precisely the same as the corresponding philosophical theories of justification, which are not normally presented as theories of belief revision. So, although I will be using the term justification in what follows, as well as the terms and foundations, I do not claim that my use of any of these terms is the same as its use in these theories of justification. I mean to be raising a new issue, not discussing an old one. The key point in what I am calling the foundations theory is that some of one's beliefs others for their justification; these other beliefs may depend on still others, until one gets to foundational beliefs that do not depend on any further beliefs for their justification. In this theory, reasoning or belief revision should consist, first, in subtracting any of one's beliefs that do not now have a satisfactory and, second, in adding new beliefs that either need no or are justified on the basis of other justified beliefs one has. On the other hand, according to what I am calling the coherence theory, it is not true that one's beliefs have, or ought to have, the sort of justificational structure required by the foundations theory. In this view beliefs do not usually require any sort of at all. Justification is taken to be required only if one has a special reason to doubt a particular belief. Such a reason might consist in a conflicting belief or in the observation that one's beliefs could