Epistemic inconsistency and categorical coherence: a study of probabilistic measures of coherence

Is logical consistency required for a set of beliefs or propositions to be categorically coherent? An affirmative answer is often assumed by mainstream epistemologists, and yet it is unclear why. Cases like the lottery and the preface call into question the assumption that beliefs must be consistent in order to be epistemically rational. And thus it is natural to wonder why all inconsistent sets of propositions are incoherent. On the other hand, Easwaran and Fitelson (2015) have shown that particular kinds of inconsistency entail the epistemically 'irrationality' of holding certain sets of beliefs. In cases of the latter kind of inconsistency, it seems more reasonable to insist that such sets of beliefs or propositions are categorically incoherent. What the precise relationship is between coherence and consistency depends on the nature of the coherence relation. We shall examine recent attempts to explicate the coherence relation in terms of probabilistic measures of confirmation or agreement to see what they can teach us about the relationship between coherence and consistency. We shall show that some probabilistic measures of coherence allow for inconsistent sets to be categorically coherent, while satisfying plausible epistemic rationality constraints. Other probabilistic measures of coherence impose very strong logical consistency requirements, and some measures are tolerant of most forms of inconsistency. As we try to understand what distinguishes coherence measures in this respect, we will also draw some important lessons about Bayesian confirmation measures and differences in the way that they treat contradictory propositions.