Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned. Each argument concludes that rationality requires your credences to be probabilities. I contend that each argument is invalid as formulated. In each case there is a mirror-image theorem and (...) a corresponding argument of exactly equal strength that concludes that rationality requires your credences not to be probabilities. Some further consideration is needed to break this symmetry in favour of probabilism. (shrink)

I develop a general framework with a rationality constraint that shows how coherently to represent and deal with second-order information about one's own judgmental reliability. It is a rejection of and generalization away from the typical Bayesian requirements of unconditional judgmental self-respect and perfect knowledge of one's own beliefs, and is defended by appeal to the Principal Principle. This yields consequences about maintaining unity of the self, about symmetries and asymmetries between the first- and third-person, and a principled way of (...) knowing when to stop second-guessing oneself. Peer disagreement is treated as a special case where one doubts oneself because of news that an intellectual equal disagrees. This framework, and variants of it, imply that the typically stated belief that an equally reliably peer disagrees is incoherent, and thus that pure rationality constraints without further substantive information cannot give an answer as to what to do. The framework also shows that treating both ourselves and others as thermometers in the disagreement situation does not imply the Equal Weight view. (shrink)

My conclusion will be that, more often than we might have thought, suspension of judgment is the epistemically proper attitude. It follows that in such cases we lack reasonable belief and so, at least on standard conceptions, knowledge. This is a kind of contingent real-world skepticism that has not received the attention it deserves. I hope that this paper will help to bring this issue to life.

Knowledge and its Limits presents a systematic new conception of knowledge as a kind of mental stage sensitive to the knower's environment. It makes a major contribution to the debate between externalist and internalist philosophies of mind, and breaks radically with the epistemological tradition of analyzing knowledge in terms of true belief. The theory casts new light on such philosophical problems as scepticism, evidence, probability and assertion, realism and anti-realism, and the limits of what can be known. The arguments are (...) illustrated by rigorous models based on epistemic logic and probability theory. The result is a new way of doing epistemology and a notable contribution to the philosophy of mind. (shrink)

My aim in this paper is to develop and defend a novel answer to a question that has recently generated a considerable amount of controversy. The question concerns the normative significance of peer disagreement. Suppose that you and I have been exposed to the same evidence and arguments that bear on some proposition: there is no relevant consideration which is available to you but not to me, or vice versa. For the sake of concreteness, we might picture.

Looking back on it, it seems almost incredible that so many equally educated, equally sincere compatriots and contemporaries, all drawing from the same limited stock of evidence, should have reached so many totally different conclusions---and always with complete certainty.

The pragmatic character of the Dutch book argument makes it unsuitable as an "epistemic" justification for the fundamental probabilist dogma that rational partial beliefs must conform to the axioms of probability. To secure an appropriately epistemic justification for this conclusion, one must explain what it means for a system of partial beliefs to accurately represent the state of the world, and then show that partial beliefs that violate the laws of probability are invariably less accurate than they could be otherwise. (...) The first task can be accomplished once we realize that the accuracy of systems of partial beliefs can be measured on a gradational scale that satisfies a small set of formal constraints, each of which has a sound epistemic motivation. When accuracy is measured in this way it can be shown that any system of degrees of belief that violates the axioms of probability can be replaced by an alternative system that obeys the axioms and yet is more accurate in every possible world. Since epistemically rational agents must strive to hold accurate beliefs, this establishes conformity with the axioms of probability as a norm of epistemic rationality whatever its prudential merits or defects might be. (shrink)

How should you take into account the opinions of an advisor? When you completely defer to the advisor's judgment, then you should treat the advisor as a guru. Roughly, that means you should believe what you expect she would believe, if supplied with your extra evidence. When the advisor is your own future self, the resulting principle amounts to a version of the Reflection Principle---a version amended to handle cases of information loss. When you count an advisor as an epistemic (...) peer, you should give her conclusions the same weight as your own. Denying that view---call it the ``equal weight view''---leads to absurdity: the absurdity that you could reasonably come to believe yourself to be an epistemic superior to an advisor simply by noting cases of disagreement with her, and taking it that she made most of the mistakes. Accepting the view seems to lead to another absurdity: that one should suspend judgment about everything that one's smart and well-informed friends disagree on, which means suspending judgment about almost everything interesting. But despite appearances, the equal weight view does not have this absurd consequence. Furthermore, the view can be generalized to handle cases involving not just epistemic peers, but also epistemic superiors and inferiors. (shrink)

How should one react when one has a belief, but knows that other people—who have roughly the same evidence as one has, and seem roughly as likely to react to it correctly—disagree? This paper argues that the disagreement of other competent inquirers often requires one to be much less confident in one’s opinions than one would otherwise be.

Looking back on it, it seems almost incredible that so many equally educated, equally sincere compatriots and contemporaries, all drawing from the same limited stock of evidence, should have reached so many totally different conclusions---and always with complete certainty.

In this paper, we investigate various possible (Bayesian) precisifications of the (somewhat vague) statements of “the equal weight view” (EWV) that have appeared in the recent literature on disagreement. We will show that the renditions of (EWV) that immediately suggest themselves are untenable from a Bayesian point of view. In the end, we will propose some tenable (but not necessarily desirable) interpretations of (EWV). Our aim here will not be to defend any particular Bayesian precisification of (EWV), but rather to (...) raise awareness about some of the difficulties inherent in formulating such precisifications. (shrink)

Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned.Each argument concludes that rationality requires your credences to be probabilities.I contend that each argument is invalid as formulated. In each case there is a mirror-image theorem and a corresponding (...) argument of exactly equal strength that concludes that rationality requires your credences not to be probabilities. Some further consideration is needed to break this symmetry in favour of probabilism. I discuss the extent to which the original arguments can be buttressed.1. Introduction2. The Dutch Book Argument2.1. Saving the Dutch Book argument2.2. ‘The Dutch Book argument merely dramatizes an inconsistency in the attitudes of an agent whose credences violate probability theory’3. Representation Theorem-based Arguments4. The Calibration Argument5. The Gradational Accuracy Argument6. Conclusion. (shrink)

James Joyce's 'Nonpragmatic Vindication of Probabilism' gives a new argument for the conclusion that a person's credences ought to satisfy the laws of probability. The premises of Joyce's argument include six axioms about what counts as an adequate measure of the distance of a credence function from the truth. This paper shows that (a) Joyce's argument for one of these axioms is invalid, (b) his argument for another axiom has a false premise, (c) neither axiom is plausible, and (d) without (...) these implausible axioms Joyce's vindication of probabilism fails. (shrink)

This paper assesses the comparative reliability of two belief-revision rules relevant to the epistemology of disagreement, the Equal Weight and Stay the Course rules. I use two measures of reliability for probabilistic belief-revision rules, calibration and Brier Scoring, to give a precise account of epistemic peerhood and epistemic reliability. On the calibration measure of reliability, epistemic peerhood is easy to come by, and employing the Equal Weight rule generally renders you less reliable than Staying the Course. On the Brier-Score measure (...) of reliability, epistemic peerhood is much more difficult to come by, but employing the Equal Weight rule always renders you more reliable than Staying the Course. I conclude with some normative lessons we can draw from these formal results. (shrink)