LAUSR

How does logic relate to rational belief? Is logic normative for belief, as some say? What, if anything, do facts about logical consequence tell us about norms of doxastic rationality? In this paper, we consider a range of putative logic-rationality bridge principles. These purport to relate facts about logical consequence to norms that govern the rationality of our beliefs and credences. To investigate these principles, we deploy a novel approach, namely, epistemic utility theory. That is, we assume that doxastic attitudes have different epistemic value depending on how accurately they represent the world. We then use the principles of decision theory to determine which of the putative logicrationality bridge principles we can derive from considerations of epistemic utility. How does logic relate to rational belief? Is logic normative for belief, as some say? What, if anything, do facts about logical consequence tell us about norms of doxastic rationality? Here are some putative norms that seek to connect logic and rational belief: (BP1) If Priest’s Logic of Paradox governs propositions A and B, and B is strictly stronger than A in that logic, then, if you believe A, then you ought to believe B. (BP2) If classical logic governs A1, . . . , An, B, and A1, . . . , An entails B in that logic, then you ought not to believe each of A1, . . . , An while disbelieving B. (BP3) If you know that strong Kleene logic governs A and B, and you know that A entails B in that logic, then you have reason to see to it that your credence in A is at most your credence in B. These illustrate something of the variety of claims that we might make in this area. Following MacFarlane (ms), we call such claims bridge principles — in particular, they are logic-rationality bridge principles. Below, I will extend MacFarlane’s taxonomy of such bridge principles to bring some order to this variety. Having done that, I wish to explore a novel way of adjudicating between them. In the existing literature, the following sorts of reasons are used to justify rejecting a given proposal of this sort: Conflicts with intuition. For instance, we might reject (BP2) by appealing to our intuitive reaction to cases like the Preface Paradox (Makinson, 1965). Suppose A1, . . . , An enumerate all of my beliefs about British birdlife. So, for each Ai, I believe it. But I also realise that I am fallible on this topic. And thus, I disbelieve B, the proposition that all of my beliefs are true — that is, I disbelieve B = A1 & . . . & An. Nonetheless, A1, . . . , An entail B. So I violate (BP2). Yet intuitively, we judge that I am perfectly rational. For this reason, some argue, we should reject (BP2).