Igor Douven

We talk and think about our beliefs both in a categorical and in a graded way. How do the two kinds of belief hang together? The most straightforward answer is that we believe something categorically if we believe it to a high enough degree. But this seemingly obvious, near-platitudinous claim is known to give rise to a paradox commonly known as the 'lottery paradox' – at least when it is coupled with some further seeming near-platitudes about belief. How to resolve that paradox has been a matter of intense philosophical debate for over fifty years. This volume offers a collection of newly commissioned essays on the subject, all of which provide compelling reasons for rethinking many of the fundamentals of the debate.

As part of an exceptionally lucid analysis of the Lottery Paradox, Dana Nelkin castigates the solutions to that paradox put forward by Laurence Bonjour and Sharon Ryan. According to her, these are “so finely tailored to lottery-like cases that they are limited in their ability to explain [what seem the intuitively right responses to such cases]”. She then offers a solution to the Lottery Paradox that allegedly has the virtue of being independently motivated by our intuitions regarding certain non-lottery-like cases. This note argues that Nelkin fails to show that her solution applies to other than lottery-like cases or in any event that it is more general than Bonjour’s and Ryan’s solutions.

Over recent decades, computer simulations have become a common tool among practitioners of the social sciences. They have been utilized to study such diverse phenomena as the integration and segregation of different racial groups, the emergence and evolution of friendship networks, the spread of gossip, fluctuations of housing prices in an area, the transmission of social norms, and many more. Philosophers of science and others interested in the methodological status of these studies have identified a number of distinctive virtues of the use of computer simulations. For instance, it has been generally appreciated that as simulations require the formulation of an explicit algorithm, they foster precision and clarity about whatever conceptual issues are involved in the study. The value of computer simulations as a heuristic tool for developing hypotheses, models, and theories has also been recognized, as has been the fact that they can serve as a substitute for real experiments. This is especially useful in the social domain, given that human beings cannot be freely manipulated at the discretion of the experimenter. However, the main virtue of computer simulations is generally believed to be that they are able to deal with the complexities that arise when many elements interact in a highly dynamic system and which often evade an exact formal analysis.

A recent argument by Hawthorne and Lasonen-Aarnio purports to show that we can uphold the principle that competently forming conjunctions is a knowledge-preserving operation only at the cost of a rampant skepticism about the future. A key premise of their argument is that, in light of quantum-mechanical considerations, future contingents never quite have chance 1 of being true. We argue, by drawing attention to the order of magnitude of the relevant quantum probabilities, that the skeptical threat of Hawthorne and Lasonen-Aarnio’s argument is illusory.

It has been claimed that epistemic peers, upon discovering that they disagree on some issue, should give up their opposing views and ‘split the difference’. The present paper challenges this claim by showing, with the help of computer simulations, that what the rational response to the discovery of peer disagreement is—whether it is sticking to one’s belief or splitting the difference—depends on factors that are contingent and highly context-sensitive.Keywords: Peer disagreement; Computer simulations; Opinion dynamics; Hegselmann–Krause model; Social epistemology.

It has seemed natural to model phenomena related to vagueness in terms of graded membership. However, so far no satisfactory answer has been given to the question of what graded membership is nor has any attempt been made to describe in detail a procedure for determining degrees of membership. We seek to remedy these lacunae by building on recent work on typicality and graded membership in cognitive science and combining some of the results obtained there with a version of the conceptual spaces framework.

A common objection against deflationist theories of truth is that they cannot do justice to the correspondence intuition, i.e. the intuition that there is an explanatory relationship between, for instance, the truth of ‘Snow is white’ and snow's being white. We scrutinize two attempts to meet this objection and argue that both fail. We then propose a new response to the objection which, first, sheds doubt on the correctness of the correspondence intuition and, second, seeks to explain how we may nonetheless have come to have that intuition.

According to van Fraassen, constructive empiricism yields a better account of science than does scientific realism. One particularly important advantage van Fraassen claims his position to have over scientific realism is that the former can make sense of science without invoking (what he calls) pre-Kantian metaphysics. In the present paper the consistency of van Fraassen's position is put in doubt. Specifically, it will be argued that van Fraassen faces the paradox that he cannot do with nor without the pre-Kantian metaphysics he abhors.

External world skeptics are typically opposed to admitting as evidence anything that goes beyond the purely phenomenal, and equally typically, they disown the use of rules of inference that might enable one to move from premises about the phenomenal alone to a conclusion about the external world. This seems to bar any a posteriori resolution of the skepticism debate. This paper argues that the situation is not quite so hopeless, and that an a posteriori resolution of the debate becomes possible once it is recognized that the skeptic holds overly defensive and ill-motivated positions vis-à-vis both evidence and inference, and that more reasonable ones are available. In stating these more reasonable positions, as well as in showing how they make possible an a posteriori resolution of the skepticism debate, the paper draws on the machinery of Bayesian epistemology.

The two-envelope paradox is a paradox in game theory. This paper offers a solution to it in three steps. The first step is to recognize that the paradox is dependent on how one represents the game-theoretic situation that gives rise to it. In the second step, we note that the representation used in the paradox violates a familiar symmetry requirement. And in the third, we derive the solution from the symmetry requirement plus the given that we are dealing with a zero-sum game. © 2012 Elsevier B.V., All rights reserved.

According to Stalnaker’s Hypothesis, the probability of an indicative conditional, $\Pr(\varphi \rightarrow \psi),$ equals the probability of the consequent conditional on its antecedent, $\Pr(\psi | \varphi)$. While the hypothesis is generally taken to have been conclusively refuted by Lewis’ and others’ triviality arguments, its descriptive adequacy has been confirmed in many experimental studies. In this paper, we consider some possible ways of resolving the apparent tension between the analytical and the empirical results relating to Stalnaker’s Hypothesis and we argue that none offer a satisfactory resolution.

According to the deontological view on justification, being justified in believing some proposition is a matter of having done one's epistemic duty with respect to that proposition. The present paper argues that, given a proper articulation of the deontological view, it is defensible that knowledge is justified true belief, pace virtually all epistemologists since Gettier. One important claim to be argued for is that once it is appreciated that it depends on contextual factors whether a person has done her epistemic duty with respect to a given proposition, many so-called Gettier cases, which are supposed to be cases of justified true belief that are not cases of knowledge, will be seen to be not really cases of justified belief after all. A second important claim is that the remaining alleged Gettier cases can be qualified as cases of knowledge. This requires that we countenance a notion of epistemic luck, but the requisite kind of luck is of a quite benign nature.