Luc Bovens

The coherentist theory of justification provides a response to the sceptical challenge: even though the independent processes by which we gather information about the world may be of dubious quality, the internal coherence of the information provides the justification for our empirical beliefs. This central canon of the coherence theory of justification is tested within the framework of Bayesian networks, which is a theory of probabilistic reasoning in artificial intelligence. We interpret the independence of the information gathering processes (IGPs) in terms of conditional independences, construct a minimal sufficient condition for a coherence ranking of information sets and assess whether the confidence boost that results from receiving information through independent IGPs is indeed a positive function of the coherence of the information set. There are multiple interpretations of what constitute IGPs of dubious quality. Do we know our IGPs to be no better than randomization processes? Or, do we know them to be better than randomization processes but not quite fully reliable, and if so, what is the nature of this lack of full reliability? Or, do we not know whether they are fully reliable or not? Within the latter interpretation, does learning something about the quality of some IGPs teach us anything about the quality of the other IGPs? The Bayesian-network models demonstrate that the success of the coherentist canon is contingent on what interpretation one endorses of the claim that our IGPs are of dubious quality.

Why do we find it upsetting when the victim of our wrongdoing refuses to accept our apologies? Why do we find it upsetting when the victim is unwilling to grant us the forgiveness that we are asking for? Let us introduce some terminology to address these questions. The offender initiates a redemption practice by apologizing or asking forgiveness. If the victim accepts the apologies or grants forgiveness, then the practice succeeds. If the victim does not accept the apologies or refuses to forgive, then the practice fails. Offender' s distress is the distress that an offender typically experiences when a redemption practice fails. As a matter of convention, the masculine pronoun refers to the offender, the feminine to the victim. So, suppose that we have two offenders who initiate a redemption practice and they are counterparts in all respects except for the fact that for the former the practice fails, whereas for the latter the practice succeeds. I will try to provide a normative account of the fact that the former typically experiences a kind of distress that is absent for the latter. That is, I will try to provide an account of offender's distress that makes the emotion into an apt emotion. I start with three unsuccessful attempts that are implicit in the literature on forgiveness, then construct my own account, and conclude by showing how my account provides error theories for the unsuccessful accounts.

The Distribution View provides a model that integrates four distributional concerns in the evaluation of risky prospects. Starting from these concerns, we can generate an ordering over a set of risky prospects, or, starting from an ordering, we can extract a characterization of the underlying distributional concerns. Separability of States and/or Persons for multiple-person risky prospects, for single-person risky prospects and for multiple-person certain prospects are discussed within the model. The Distribution View sheds light on public health policies and provides a framework for the discussion of Parfit's Priority View for risky prospects.

This paper addresses a problem for theories of epistemic democracy. In a decision on a complex issue which can be decomposed into several parts, a collective can use different voting procedures: Either its members vote on each sub-question and the answers that gain majority support are used as premises for the conclusion on the main issue (premise based-procedure, pbp), or the vote is conducted on the main issue itself (conclusion-based procedure, cbp). The two procedures can lead to different results. We investigate which of these procedures is better as a truth-tracker, assuming that there exists a true answer to be reached. On the basis of the Condorcet jury theorem, we show that the pbp is universally superior if the objective is to reach truth for the right reasons. If one instead is after truth for whatever reasons, right or wrong, there will be cases in which the cbp is more reliable, even though, for the most part, the pbp still is to be preferred.

John Locke proposed a straightforward relationship between qualitative and quantitative doxastic notions: belief corresponds to a sufficiently high degree of confidence. Richard Foley has further developed this Lockean thesis and applied it to an analysis of the preface and lottery paradoxes. Following Foley's lead, we exploit various versions of these paradoxes to chart a precise relationship between belief and probabilistic degrees of confidence. The resolutions of these paradoxes emphasize distinct but complementary features of coherent belief. These features suggest principles that tie together qualitative and quantitative doxastic notions. We show how these principles may be employed to construct a quantitative model - in terms of degrees of confidence - of an agent's qualitative doxastic state. This analysis fleshes out the Lockean thesis and provides the foundation for a logic of belief that is responsive to the logic of degrees of confidence.

Bovens (2010) points out that there is a structural analogy between the Judy Benjamin problem (JB) and the Sleeping Beauty problem (SB). On grounds of this structural analogy, he argues that both should receive the same solution, viz. the posterior probability of the eastern region of the matrix in Table 1 should equal 1/3. Hence, P*(Red) = 1/3 in the JB and P*(Heads) = 1/3 in the SB. Bovens’s argument rests on a standard error in implementing Bayesian updating, which is spelled out in Shafer 1985. When we are informed of some proposition, we do not only learn the proposition in question, but also that we have learned the proposition as one of the many propositions that we might have learned. The information is generated by a protocol, which determines the various propositions that we might learn. We should then update not on the proposition in question, but rather on the fact that we learned this proposition as one of the many propositions that we might have learned. A well-known application of this insight is the Monty Hall problem (MH) as Speed (1985: 276) points out in a discussion of Shafer 1985. As an illustration, let us apply Shafer’s insight to the MH. In the MH, the contestant in a game show learns that there is a goat behind two of three doors X, Y and Z and a car behind one door. She is asked to pick one of the three doors. The contestant picks door X. Monty will then open one of the remaining doors, which he knows to have a goat behind it. Suppose Monty opens door Y. The contestant is then asked whether she wants to …

We consider a special set of risky prospects in which the outcomes are either life or death (or, more generally, binary utilities). There are various alternatives to the utilitarian objective of minimizing the expected loss of lives in such prospects. We start off with the two-person case with independent risks and construct taxonomies of ex ante and ex post evaluations for such prospects. We examine the relationship between the ex ante and the ex post in this restrictive framework: There are more possibilities to respect ex ante and ex post objectives simultaneously than in the general framework, i.e. without the restriction to binary utilities (cf. Harsanyi's aggregation theorem). We extend our results to n persons and to dependent risks. We study optimal strategies for allocating risk reductions given different objectives. We place our results against the backdrop of various pro-poorly off (or prioritarian) value functions (Diamond 1967; Rabinowicz 2002; Fleurbaey 2010) for the evaluation of risky prospects.

We appeal to the theory of Bayesian Networks to model different strategies for obtaining confirmation for a hypothesis from experimental test results provided by less than fully reliable instruments. In particular, we consider (i) repeated measurements of a single test consequence of the hypothesis, (ii) measurements of multiple test consequences of the hypothesis, (iii) theoretical support for the reliability of the instrument, and (iv) calibration procedures. We evaluate these strategies on their relative merits under idealized conditions and show some surprising repercussions on the variety-of-evidence thesis and the Duhem-Quine thesis.

In decision-theory, the notion of regret enters into the minimax decision-rule and has a determinate usage in this context. However, there are many alternative ways of conceiving of regret. The chapter constructs the _einmal-ist-nicht-keinmal_ (‘once is not never’) game, in which a single sampling radically changes the expected value of the game in a way that is quite counterintuitive, as the basis for studying regret after a loss following the choice of an uncertain action. Crucially, the very loss affects the posterior expectation of the game and the posterior credence about the objective chances of a win. Our taxonomy of regret contains regret over the action chosen and regret over the outcome obtained as its main categories, and is mirrored by a taxonomy of joy after a win following the choice of an uncertain action, and is used to critique of Krähmer and Stone’s analysis of risk aversion for uncertain actions.

Probabilistic models have much to offer to epistemology and philosophy of science. Arguably, the coherence theory of justification claims that the more coherent a set of propositions is, the more confident one ought to be in its content, ceteris paribus. An impossibility result shows that there cannot exist a coherence ordering. A coherence quasi-ordering can be constructed that respects this claim and is relevant to scientific-theory choice. Bayesian-Network models of the reliability of information sources are made applicable to Condorcet-style jury voting, Tversky and Kahneman’s Linda puzzle, the variety-of-evidence thesis, the Duhem–Quine thesis, and the informational value of testimony.

A committee has to address a complex question, the answer to which requires answering several sub-questions. Two different voting procedures can be used. On one procedure, the committee members vote on each sub-question and the voting results then are used as premises for the committee’s conclusion on the main issue. This premise-based procedure can be contrasted with the conclusion-based procedure. On that procedure, the members directly vote on the conclusion, with the vote of each member being guided by her views on the relevant sub-questions. These procedures are by no means equivalent, which has been pointed out in legal theory in connection with jury votes. There may be a majority of voters supporting each premise, but if these majorities do not significantly overlap, there will be a majority against the conclusion. Pettit connects the choice between the two procedures with general political theory, in particular, with the discussion of deliberative democracy. However, the problem we want to examine concerns the relative advantages and disadvantages of the two procedures from the epistemic point of view. In some cases one can assume that the question before the committee has the right answer. In cases like this, is one of the two procedures better when it comes to tracking the truth? As it turns out, the answer to this query is not univocal. On the basis of Condorcet’s jury theorem, we show that the premise-based procedure is clearly superior if the objective is reach truth for the right reasons, i.e. without making any mistakes on the way. However, if the goal instead is to reach truth for whatever reasons, right or wrong, there will be cases in which using the conclusion-based procedure turns out to be more reliable, even though, for the most part, the premise-based procedure will retain its superiority. Our results partly confirm and partly disconfirm the tentative conjectures that have been put forward in Pettit and Rabinowicz.

"The Personal is Political": This was an often-heard slogan of feminist groups in the late sixties and early seventies. The slogan is no doubt open to many interpretations. There is one interpretation which touches on the epistemology of social facts, viz. the slogan claims that in assessing the features of a political system, personal experiences have privileged evidentiary value. For instancte, in the face of third person reports about political corruption, I may remain unmoved in my belief that the political powers are morally upstanding, and it is only when I myself am adversely affected, that I come to change my views. There are two standard patterns of explanation of this type of belief formation: (i) We know that third-person reports may be lessreliable than first-person experiences; (ii) If the third-person reports are no less reliable than first-person experiences, we may just be dealing with a standard pattern of epistemic irrationality. However, we argue that there is also a much more surprising pattern of explanation: under certain conditions, a Bayesian argument can be proffered to the effect that it is rational to change one's beliefs in the face of personal experiences and not in the face of third-person reports, even if these experiences and reports are equally reliable. Hence, the feminist slogan (at least on one particular interpretation of it) receives unexpected support from Bayesian comers. We also show that this pattern of explanation has surprising repercussions on the question of the evidentiary value of miracles in philosophy of religion.

Suppose that we acquire various items of information from various sources and that our degree of confidence in the content of the information set is sufficiently high to believe the information. Now a new item of information is being presented by a new information source. Are we justified to add this new item of information to what we already believe? Consider the following parable: “I go to a lecture about wildlife in Greenland which was supposed to be delivered by an expert in the field. When I arrive I notice that the expert has excused himself and that the biology department has sent a newcomer to fill in for him. I have no beliefs about wildlife in Greenland, but I do have some beliefs about Greenland’s climate and about the kinds of climate conditions that various types of wildlife favor. Suppose that our newcomer proclaims that large colonies of elk roam in a particular valley on the southern tip of Greenland. Then I would certainly be willing to accept this item of information. But suppose that he proclaims that large colonies of armadillos roam in the same valley. Then I would not be willing to accept this item of information. Why do I accept the former but not the latter item of information? Let us suppose that neither item of information is logically inconsistent with what I already believe. Clearly, the former item of information is not inconsistent. But also the latter item is not: after all, there may be small pockets of Greenland with special climatological conditions and some Texan sailors may have set loose a pair of armadillos as a practical joke. But whereas the former item of information is quite plausible given my previous beliefs, the latter item of information is not. And this is what makes for the difference. Now suppose that our newcomer proclaims that large colonies of wild boars roam this valley in Greenland. I am not that sure anymore. Given everything I believe, I find wild boars in Greenland more plausible than armadillos in Greenland, but certainly less plausible than elk in Greenland. Had our expert presented the lecture and provided precisely the 2 same information, then I would have been willing to adopt the belief that there are wild boars in Greenland, but, with our newcomer delivering the lecture, I am not willing to do so. It is not that I would believe anything out of the expert’s mouth: also he could not have convinced me that there are armadillos in Greenland. But when it comes to wild boars, the difference between the expert’s and the newcomer’s credentials simply makes for the difference.” What we learn from this story is that the question of belief expansion has something to do with the reliability of the information source as well as with the plausibility of the new information, given what I already believe. The more reliable the information source is, the less plausible the new information needs to be given what I already believe, for me to be justified to add the belief to our belief set. The more plausible the new information is given what I already believe, the less reliable the information source needs to be given what I already believe, for me to be justified to add the belief to my belief set. The challenge is: can a precise account of this relationship be provided?

The papers in this collection were presented at a workshop on Bayesian Epistemology at the 26th International Wittgenstein Symposium in Kirchberg, Austria (August 4–7, 2003), at a workshop on Philosophy and Probability at the conference GAP5 in Bielefeld, Germany (September 20–22, 2003), at a workshop on Bayesian Epistemology at the Centre for Philosophy of Natural and Social Science, London School of Economics and Political Science in London, UK (June 28, 2004), or at the seminar of the research group Philosophy, Probability and Modeling, Center for Junior Research Fellows, University of Konstanz, Germany. We acknowledge the generous support for these events by the Austrian Ludwig Wittgenstein Society, the Gesellschaft für analytische Philosophie e.V., the Centre for Philosophy of Natural and Social Science, the Alexander von Humboldt Foundation, the Federal Ministry of Education and Research and the Program for the Investment in the Future (ZIP) of the German Government through a Sofja Kovalevskaja Award. We thank the organizers of the conferences in Kirchberg and Bielefeld for their support, the authors and referees of the papers for their work, and John Symons for his interest in dedicating a special issue of this journal to Bayesian Epistemology.

Bovens (2010) points out that there is a structural analogy between the Judy Benjamin problem (JB) and the Sleeping Beauty problem (SB). On grounds of this structural analogy, he argues that both should receive the same solution, viz. the posterior probability of the eastern region of the matrix in Table 1 should equal 1/3. Hence, P*(Red) = 1/3 in the JB and P*(Heads) = 1/3 in the SB. Bovens’s argument rests on a standard error in implementing Bayesian updating, which is spelled out in Shafer 1985. When we are informed of some proposition, we do not only learn the proposition in question, but also that we have learned the proposition as one of the many propositions that we might have learned. The information is generated by a protocol, which determines the various propositions that we might learn. We should then update not on the proposition in question, but rather on the fact that we learned this proposition as one of the many propositions that we might have learned. A well-known application of this insight is the Monty Hall problem (MH) as Speed (1985: 276) points out in a discussion of Shafer 1985. As an illustration, let us apply Shafer’s insight to the MH. In the MH, the contestant in a game show learns that there is a goat behind two of three doors X, Y and Z and a car behind one door. She is asked to pick one of the three doors. The contestant picks door X. Monty will then open one of the remaining doors, which he knows to have a goat behind it. Suppose Monty opens door Y. The contestant is then asked whether she wants to …