 At this juncture many philosophers join Kyburg in rejecting agglomeration and conclude that it can be rational to have jointly inconsistent beliefs. Kyburg’s solution to the preface paradox raises a methodological question about the nature of paradox. How can paradoxes change our minds if joint inconsistency is permitted? A paradox is commonly defined as a set of propositions that are individually plausible but jointly inconsistent. The inconsistency is the itch that directs us to scratch out a member of the set (or the pain that leads us to withdraw from the stimulus). For instance, much epistemology orbits an ancient riddle posed by the regress of justification, namely, which of the following is false?