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Standard accuracy-based approaches to imprecise credences have the consequence that it is rational to move between precise and imprecise credences arbitrarily, without gaining any new evidence. Building on the Educated Guessing Framework of Horowitz (2019), we develop an alternative accuracy-based approach to imprecise credences that does not have this shortcoming. We argue that it is always irrational to move from a precise state to an imprecise state arbitrarily, however it can be rational to move from an imprecise state to a precise state arbitrarily.

It seems like we care about at least two features of our credence function: gradational-accuracy and verisimilitude. Accuracy-first epistemology requires that we care about one feature of our credence function: gradational-accuracy. So if you want to be a verisimilitude-valuing accuracy-firster, you must be able to think of the value of verisimilitude as somehow built into the value of gradational-accuracy. Can this be done? In a recent article, Oddie has argued that it cannot, at least if we want the accuracy measure to be proper. I argue that it can. 1Introduction2Some Nuts and Bolts3First Attempts4Oddie’s Constraint5The Good5.1Proximity over the disagreement metric 5.2Proximity over the magnitude metric 6The Bad and the Ugly 7Some More Good: The Role of Evenness of Distribution 8Some More Bad: Which Propositions to Privilege? 9Concluding Thoughts: Accuracy and Practical Value

In recent years, permissivism—the claim that a body of evidence can rationalize more than one response—has enjoyed somewhat of a revival. But it is once again being threatened, this time by a host of new and interesting arguments that, at their core, are challenging the permissivist to explain why rationality matters. A version of the challenge that I am especially interested in is this: if permissivism is true, why should we expect the rational credences to be more accurate than the irrational ones? My aim is to turn this challenge on its head and argue that, actually, those who deny permissivism will have a harder time responding to such a challenge than those who accept it.

The aim of this paper is to apply the accuracy based approach to epistemology to the case of higher order evidence: evidence that bears on the rationality of one's beliefs. I proceed in two stages. First, I show that the accuracy based framework that is standardly used to motivate rational requirements supports steadfastness—a position according to which higher order evidence should have no impact on one's doxastic attitudes towards first order propositions. The argument for this will require a generalization of an important result by Greaves and Wallace for the claim that conditionalization maximizes expected accuracy. The generalization I provide will, among other things, allow us to apply the result to cases of self-locating evidence. In the second stage, I develop an alternative framework. Very roughly, what distinguishes the traditional approach from the alternative one is that, on the traditional picture, we're interested in evaluating the expected accuracy of conforming to an update procedure. On the alternative picture that I develop, instead of considering how good an update procedure is as a plan to conform to, we consider how good it is as a plan to make. I show how, given the use of strictly proper scoring rules, the alternative picture vindicates calibrationism: a view according to which higher order evidence should have a significant impact on our beliefs. I conclude with some thoughts about why higher order evidence poses a serious challenge for standard ways of thinking about rationality.

It has been claimed that, in response to certain kinds of evidence, agents ought to adopt imprecise credences: doxastic states that are represented by sets of credence functions rather than single ones. In this paper I argue that, given some plausible constraints on accuracy measures, accuracy-centered epistemologists must reject the requirement to adopt imprecise credences. I then show that even the claim that imprecise credences are permitted is problematic for accuracy-centered epistemology. It follows that if imprecise credal states are permitted or required in the cases that their defenders appeal to, then the requirements of rationality can outstrip what would be warranted by an interest in accuracy.

Abstract: This paper defends a constraint that any satisfactory decision theory must satisfy. I show how this constraint is violated by all of the decision theories that have been endorsed in the literature that are designed to deal with cases in which opinions or values are represented by a set of functions rather than a single one. Such a decision theory is necessary to account for the existence of what Ruth Chang has called “parity” (as well as for cases in which agents have incomplete preferences or imprecise credences). The problem with the all of the decision theories that have been defended to account for parity is that they are committed to a claim I call unanimity: when all of the functions in the set agree that an agent ought to do A, then an agent ought to do A. A decision theory committed to unanimity violates the constraint I defend in this paper. Thus, if parity exists, a new approach to decision theory is necessary.

Greaves and Wallace argue that conditionalization maximizes expected accuracy. In this paper I show that their result only applies to a restricted range of cases. I then show that the update procedure that maximizes expected accuracy in general is one in which, upon learning P, we conditionalize, not on P, but on the proposition that we learned P. After proving this result, I provide further generalizations and show that much of the accuracy-first epistemology program is committed to KK-like iteration principles and to the existence of a class of propositions that rational agents will be certain of if and only if they are true.

Internalists face the following challenge: what is it about an agent's internal states that explains why only these states can play whatever role the internalist thinks these states are playing? Internalists have frequently appealed to a special kind of epistemic access that we have to these states. But such claims have been challenged on both empirical and philosophical grounds. I will argue that internalists needn't appeal to any kind of privileged access claims. Rather, internalist conditions are important because of the way in which we expect them to act as causal mediators between states of the world, on the one hand, and our beliefs and actions on the other.

The aim of this paper is to describe a problem for calibrationism: a view about higher order evidence according to which one's credences should be calibrated to one's expected degree of reliability. Calibrationism is attractive, in part, because it explains our intuitive judgments, and provides a strong motivation for certain theories about higher order evidence and peer disagreement. However, I will argue that calibrationism faces a dilemma: There are two versions of the view one might adopt. The first version, I argue, has the implausible consequence that, in a wide range of cases, calibrationism is the only constraint on rational belief. The second version, in addition to having some puzzling consequences, is unmotivated. At the end of the paper I sketch a possible solution