The preface paradox dissolved

T h e preface paradox strikes us as puzzling because we feel that if a person holds a set of inconsistent beliefs, i.e. beliefs such that at least one of them must be incorrect, then he should give at least one of them up. Equally, if a person’s belief is rational, then he has a right to hold it. Yet the preface example is prima facie a case in which a person holds an inconsistent set of beliefs each of which is rational, and thus a case in which that person has a duty to relinquish what he has a right to keep. I shall argue that counterintuitive appearances are not always deceptive; the preface case demonstrates the possibility of rational inconsistent belief. Attempts to deny the inconsistency of the case by giving it a probabilistic treatment misrepresent it. On the other hand, attempts to deny the rationality of the case by insisting upon the dependence of the available sets of evidence, stem from a crucial failure to recognise that the relevant beliefs are inconsistent rather than contradictory. It might be thought that this distinction is trivial, but it has important consequences for rational belief. One reason for ignoring it is a misguided ‘conjunction principle’, namely that belief or rational belief in various propositions entails a belief or rational belief in their conjunction. It is this principle that gives the example its air of paradox. Once we make explicit and abandon the conjunction principle, the example can be seen as a possible and perhaps natural kind of situation.