Degrees of Belief

In this paper it will be attempted to dissolve the lottery problem based on fallibilism, probabilism and the introduction of a so far widely neglected second context of knowledge. First, it will be argued that the lottery problem is actually an exemplification of the much wider Humean "future knowledge problem" (ch. 1). Two types of inferences and arguments will be examined, compared and evaluated in respect to their ability to fittingly describe the thought processes behind lottery/future knowledge propositions (ch. 2). (...) A second context of knowledge that underlines the importance of fallibilism and probabilism in a somewhat different manner will be introduced (ch. 3) and, based on that "two-context probabilism," the lottery/future knowledge problem will be dissolved (ch. 4). Lastly, it will be hinted at the necessity of adopting not just fallibilism including and two context minding probabilism, but, beyond that, also the even more encompassing position of both ontological and epistemological "gradualism" (ch. 5). (shrink)

There is a well-known equivalence between avoiding accuracy dominance and having probabilistically coherent credences (see, e.g., de Finetti 1974, Joyce 2009, Predd et al. 2009, Schervish et al. 2009, Pettigrew 2016). However, this equivalence has been established only when the set of propositions on which credence functions are defined is finite. In this paper, we establish connections between accuracy dominance and coherence when credence functions are defined on an infinite set of propositions. In particular, we establish the necessary results to (...) extend the classic accuracy argument for probabilism originally due to Joyce (1998) to certain classes of infinite sets of propositions including countably infinite partitions. (shrink)

Doxasticism is the thesis that intention is or involves belief in the forthcoming action (Velleman, Harman). Supporters claim that it is only by accepting that thesis that we can explain a wide array of important phenomena, including the special knowledge we have of intentional action, the roles intention plays in facilitating coordination, and the norms of rationality for intention. Others argue that the thesis is subject to counterexample (Davidson, Bratman). Yet some others contend that the thesis can be reformulated in (...) a way that avoids such counterexamples and preserves its explanatory significance (Pears, Setiya). Their suggestion is that we view intention as involving partial –rather than full—belief. I argue that while the move from full to partial doxasticism helps to accommodate such counterexamples, it does so in a way that undermines the ability of the resulting view to explain the coordinating roles of and rationality norms for intention. (shrink)

According to the so-called Lockean thesis, a rational agent believes a proposition just in case its probability is sufficiently high, i.e., greater than some suitably fixed threshold. The Preface paradox is usually taken to show that the Lockean thesis is untenable, if one also assumes that rational agents should believe the conjunction of their own beliefs: high probability and rational belief are in a sense incompatible. In this paper, we show that this is not the case in general. More precisely, (...) we consider two methods of computing how probable must each of a series of propositions be in order to rationally believe their conjunction under the Lockean thesis. The price one has to pay for the proposed solutions to the paradox is what we call "quasi-dogmatism": the view that a rational agent should believe only those propositions which are "nearly certain" in a suitably defined sense. (shrink)

One very popular framework in contemporary epistemology is Bayesian. The central epistemic state is subjective confidence, or credence. Traditional epistemic states like belief and knowledge tend to be sidelined, or even dispensed with entirely. Credences are often introduced as familiar mental states, merely in need of a special label for the purposes of epistemology. But whether they are implicitly recognized by the folk or posits of a sophisticated scientific psychology, they do not appear to fit well with perception, as is (...) often noted. -/- This paper investigates the tension between probabilistic cognition and non-probabilistic perception. The tension is real, and the solution—to adapt a phrase from Quine and Goodman—is to renounce credences altogether. (shrink)

Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed that this problem (...) generalizes: there exists no local function from degrees of belief to binary beliefs that satisfies some minimal conditions of rationality and non-triviality. “Locality” means that the binary belief in each proposition depends only on the degree of belief in that proposition, not on the degrees of belief in others. One might think that the impossibility can be avoided by dropping the assumption that binary beliefs are a function of degrees of belief. We prove that, even if we drop the “functionality” restriction, there still exists no local relation between degrees of belief and binary beliefs that satisfies some minimal conditions. Thus functionality is not the source of the impossibility; its source is the condition of locality. If there is any non-trivial relation between degrees of belief and binary beliefs at all, it must be a “holistic” one. We explore several concrete forms this “holistic” relation could take. (shrink)

According to comparativism, degrees of belief are reducible to a system of purely ordinal comparisons of relative confidence. (For example, being more confident that P than that Q, or being equally confident that P and that Q.) In this paper, I raise several general challenges for comparativism, relating to (i) its capacity to illuminate apparently meaningful claims regarding intervals and ratios of strengths of belief, (ii) its capacity to draw enough intuitively meaningful and theoretically relevant distinctions between doxastic states, and (...) (iii) its capacity to handle common instances of irrationality. (shrink)

According to comparativism, comparative confidence is more fundamental than absolute confidence. In a pair of recent papers, Stefánsson has argued that comparativism is capable of explaining interpersonal confidence comparisons. In this paper, I will argue that Stefansson’s proposed explanation is inadequate; that we have good reasons to think that comparativism cannot handle interpersonal comparisons; and that the best explanation of interpersonal comparisons requires thinking about confidence in a fundamentally different way than that which comparativists propose—specifically, we should think of confidence (...) as a dimensionless quantity. (shrink)

Much of the literature on the relationship between belief and credence has focused on the reduction question: that is, whether either belief or credence reduces to the other. This debate, while important, only scratches the surface of the belief-credence connection. Even on the anti-reductive dualist view, belief and credence could still be very tightly connected. Here, I explore questions about the belief-credence connection that go beyond reduction. This paper is dedicated to what I call the independence question: just how independent (...) are belief and credence? I look at this question from two angles: a descriptive one (as a psychological matter, how much can belief and credence come apart?) and a normative one (for a rational agent, how closely connected are belief and credence?) Ultimately, I suggest that the two attitudes are more independent than one might think. (shrink)

In Unsettled Thoughts, Julia Staffel argues that non-ideal thinkers should seek to approximate ideal Bayesian rationality. She argues that the more rational you are, the more benefits of rationality you will enjoy. After summarizing Staffel’s main results, this paper looks more closely at two issues that arise later in the book: the relationship between Bayesian rationality and other kinds of rationality, and the role that outright belief plays in addition to credence. Ultimately, I argue that there are several roles that (...) outright belief might play, and I explore different ways that these roles for belief might fit together. (shrink)

This paper introduces and motivates a solution to a dilemma from peer disagreement. Following Buchak (forthcoming), I argue that peer disagreement puts us in an epistemic dilemma: there is reason to think that our opinions should both change and not change when we encounter disagreement with our epistemic peers. I argue that we can solve this dilemma by changing our credences, but not our beliefs in response to disagreement. I explain how my view solves the dilemma in question, and then (...) offer two additional arguments for it: one related to contents and attitudes, and another related to epistemic peerhood. (shrink)

A question of recent interest in epistemology and philosophy of mind is how belief and credence relate to each other. A number of philosophers argue for a belief-first view of the relationship between belief and credence. On the belief-first view, what it is to have a credence just is to have a particular kind of belief, that is, a belief whose content involves probabilities or epistemic modals. Here, I argue against the belief-first view: specifically, I argue that it cannot account (...) for agents who have credences in propositions they barely comprehend. I conclude that, however credences differ from beliefs, they do not differ in virtue of adding additional content to the believed proposition. (shrink)

What is faith? How is faith different than belief and hope? Is faith irrational? If not, how can faith go beyond the evidence? This chapter introduces the reader to philosophical questions involving faith and reason. First, we explore a four-part definition of faith. Then, we consider the question of how faith could be rational yet go beyond the evidence.

Radical moral encroachment is the view that belief itself is morally evaluable, and that some moral properties of belief itself make a difference to epistemic rationality. To date, almost all proponents of radical moral encroachment hold to an asymmetry thesis: the moral encroaches on rational belief, but not on rational credence. In this paper, we argue against the asymmetry thesis; we show that, insofar as one accepts the most prominent arguments for radical moral encroachment on belief, one should likewise accept (...) radical moral encroachment on credence. We outline and reject potential attempts to establish a basis for asymmetry between the attitude types. Then, we explore the merits and demerits of the two available responses to our symmetry claim: (i) embracing moral encroachment on credence and (ii) denying moral encroachment on belief. (shrink)

We call attention to certain cases of epistemic akrasia, arguing that they support belief-credence dualism. Belief-credence dualism is the view that belief and credence are irreducible, equally fundamental attitudes. Consider the case of an agent who believes p, has low credence in p, and thus believes that they shouldn’t believe p. We argue that dualists, as opposed to belief-firsters (who say credence reduces to belief) and credence-firsters (who say belief reduces to credence) can best explain features of akratic cases, including (...) the observation that akratic beliefs seem to be held despite possessing a defeater for those beliefs, and that, in akratic cases, one can simultaneously believe and have low confidence in the very same proposition. (shrink)

Disagreement is a ubiquitous feature of human life, and philosophers have dutifully attended to it. One important question related to disagreement is epistemological: How does a rational person change her beliefs (if at all) in light of disagreement from others? The typical methodology for answering this question is to endorse a steadfast or conciliatory disagreement norm (and not both) on a priori grounds and selected intuitive cases. In this paper, I argue that this methodology is misguided. Instead, a thoroughgoingly Bayesian (...) strategy is what's needed. Such a strategy provides conciliatory norms in appropriate cases and steadfast norms in appropriate cases. I argue, further, that the few extant efforts to address disagreement in the Bayesian spirit are laudable but uncompelling. A modelling, rather than a functional, approach gets us the right norms and is highly general, allowing the epistemologist to deal with (1) multiple epistemic interlocutors, (2) epistemic superiors and inferiors (i.e. not just epistemic peers), and (3) dependence between interlocutors. (shrink)

Epistemic decision theory produces arguments with both normative and mathematical premises. I begin by arguing that philosophers should care about whether the mathematical premises (1) are true, (2) are strong, and (3) admit simple proofs. I then discuss a theorem that Briggs and Pettigrew (2020) use as a premise in a novel accuracy-dominance argument for conditionalization. I argue that the theorem and its proof can be improved in a number of ways. First, I present a counterexample that shows that one (...) of the theorem’s claims is false. As a result of this, Briggs and Pettigrew’s argument for conditionalization is unsound. I go on to explore how a sound accuracy-dominance argument for conditionalization might be recovered. In the course of doing this, I prove two new theorems that correct and strengthen the result reported by Briggs and Pettigrew. I show how my results can be combined with various normative premises to produce sound arguments for conditionalization. I also show that my results can be used to support normative conclusions that are stronger than the one that Briggs and Pettigrew’s argument supports. Finally, I show that Briggs and Pettigrew’s proofs can be simplified considerably. (shrink)

James Joyce’s article “A Nonpragmatic Vindication of Probabilism” introduced an approach to arguing for credal norms by appealing to the epistemic value of accuracy. The central thought was that credences ought to accurately represent the world, a guiding thought that has gone on to generate an entire research paradigm on the rationality of credences. Recently, a number of epistemologists have begun to apply this same thought to full beliefs, attempting to explain and argue for norms of belief in terms of (...) epistemic value. This paper examines these recent attempts, showing how they interact with work on the accuracy of credences. It then examines how differing judgments about epistemic value give rise to distinct rational requirements for belief, concluding by considering some of the fundamental questions and issues yet to be fully explored. (shrink)

In this paper, I investigate the betting behavior of a decision-maker who can influence the likelihood of the events upon which she is betting. In decision theory, this is best known as a situation of moral hazard. Focusing on a particularly simple case, I sketch the first systematic analysis of moral hazard in the canonical Savage framework. From the results of this analysis, I draw two philosophical conclusions. First, from an observational and a descriptive point of view, there need to (...) be no incompatibility between moral hazard and the Savage framework. This qualifies the incompatibility view, that is ubiquitous in decision theory. Second, in general, moral hazard is not sufficient to overcome the challenges posed by state-dependent utility to the behavioral identification of beliefs. This qualifies the sufficiency view, that is influential in decision theory. These two philosophical conclusions are the main contributions of my paper. (shrink)

State-dependent utility is a problem for the behavioural branch of decision theory under uncertainty. It questions the very possibility that beliefs be revealed by choice data. According to the current literature, all models of beliefs are equally exposed to the problem. Moreover, the problem is solvable only when the decision-maker can influence the resolution of uncertainty. This article gives grounds to reject these two views. The various models of beliefs can be shown to be unequally exposed to the problem of (...) state-dependent utility. The problem can be argued to be solved even when the decision-maker has no influence over the resolution of uncertainty. The implications of such reappraisal for a philosophical appreciation of the revealed preference methodology are discussed. 1Introduction 2The Problem of State-Dependent Utility: An Exposition 3The Current State of the State-Dependent Utility Literature 4On State-Dependent Utility and Moral Hazard 5The Problem of State-Dependent Utility: A Reappraisal 6Implications for the Revealed Preference Methodology 7Conclusion Appendix. (shrink)

In the peer disagreement debate, three intuitively attractive claims seem to conflict: there is disagreement among peers on many important matters; peer disagreement is a serious challenge to one’s own opinion; and yet one should be able to maintain one’s opinion on important matters. I show that contrary to initial appearances, we can accept all three of these claims. Disagreement significantly shifts the balance of the evidence; but with respect to certain kinds of claims, one should nonetheless retain one’s beliefs. (...) And one should retain them even though these beliefs would not be supported by the new total evidence if one didn’t already hold them. (shrink)

The Dutch Book Argument for Probabilism assumes Ramsey's Thesis (RT), which purports to determine the prices an agent is rationally required to pay for a bet. Recently, a new objection to Ramsey's Thesis has emerged (Hedden 2013, Wronski & Godziszewski 2017, Wronski 2018)--I call this the Expected Utility Objection. According to this objection, it is Maximise Subjective Expected Utility (MSEU) that determines the prices an agent is required to pay for a bet, and this often disagrees with Ramsey's Thesis. I (...) suggest two responses to Hedden's objection. First, we might be permissive: agents are permitted to pay any price that is required or permitted by RT, and they are permitted to pay any price that is required or permitted by MSEU. This allows us to give a revised version of the Dutch Book Argument for Probabilism, which I call the Permissive Dutch Book Argument. Second, I suggest that even the proponent of the Expected Utility Objection should admit that RT gives the correct answer in certain very limited cases, and I show that, together with MSEU, this very restricted version of RT gives a new pragmatic argument for Probabilism, which I call the Bookless Pragmatic Argument. (shrink)

Our evidence can be about different subject matters. In fact, necessarily equivalent pieces of evidence can be about different subject matters. Does the hyperintensionality of ‘aboutness’ engender any hyperintensionality at the level of rational credence? In this paper, I present a case which seems to suggest that the answer is ‘yes’. In particular, I argue that our intuitive notions of independent evidence and inadmissible evidence are sensitive to aboutness in a hyperintensional way. We are thus left with a paradox. While (...) there is strong reason to think that rational credence cannot make such hyperintensional distinctions, our intuitive judgements about certain cases seem to demand that it does. (shrink)

Religious people are expected to believe in their religious creeds faithfully and firmly. How can one acquire such belief? In order to answer that question, I propose a model for all belief-like propositional attitudes. The model differentiates, firstly, between voluntary and involuntary, and, secondly, between categorical and quantitative belief-like attitudes. The whole variety of belief-like attitudes is then reduced into two main groups. The first group combines all voluntary and categorical attitudes, and the second group combines all involuntary and quantitative (...) attitudes. The resultant first-group attitude is called “judgment,” and the second-group attitude—“confidence.” Thus, judgment is the generic voluntary categorical propositional attitude, which can have only two values: “true” or “false.” Confidence is the generic involuntary quantitative attitude, which can have any value between “certainly false” and “certainly true.” A religious person can form the creedal judgment simply by her act of will, while her confidence depends upon the actual content of her doxastic system. However, a person can indirectly increase her confidence in the creedal statement via relevant factors that control her doxastic system. Such factors include corroboration, desirability, and ethicality of the proposition, and also its centrality and entrenchment in the doxastic system. I suggest several practical guidelines for increasing the relevant factors. I claim that the suggested model and the practical guidelines for acquiring the “faithful and firm belief” can be used not only within the religious context, but can also be applied to any propositional beliefs. (shrink)

Comparativism is the view that comparative confidences (e.g., being more confident that P than that Q) are more fundamental than degrees of belief (e.g., believing that P with some strength x). In this paper, I outline the basis for a new, non-probabilistic version of comparativism inspired by a suggestion made by Frank Ramsey in `Probability and Partial Belief'. I show how, and to what extent, `Ramseyan comparativism' might be used to weaken the (unrealistically strong) probabilistic coherence conditions that comparativism traditionally (...) relies on. (shrink)

The logic of indicative conditionals remains the topic of deep and intractable philosophical disagreement. I show that two influential epistemic norms—the Lockean theory of belief and the Ramsey test for conditional belief—are jointly sufficient to ground a powerful new argument for a particular conception of the logic of indicative conditionals. Specifically, the argument demonstrates, contrary to the received historical narrative, that there is a real sense in which Stalnaker’s semantics for the indicative did succeed in capturing the logic of the (...) Ramseyan indicative conditional. (shrink)

According to the Rational Threshold View, a rational agent believes p if and only if her credence in p is equal to or greater than a certain threshold. One of the most serious challenges for this view is the problem of statistical evidence: statistical evidence is often not sufficient to make an outright belief rational, no matter how probable the target proposition is given such evidence. This indicates that rational belief is not as sensitive to statistical evidence as rational credence. (...) The aim of this paper is twofold. First, we argue that, in addition to playing a decisive role in rationalizing outright belief, non-statistical evidence also plays a preponderant role in rationalizing credence. More precisely, when both types of evidence are present in a context, non-statistical evidence should receive a heavier weight than statistical evidence in determining rational credence. Second, based on this result, we argue that a modified version of the Rational Threshold View can avoid the problem of statistical evidence. We conclude by suggesting a possible explanation of the varying sensitivity to different types of evidence for belief and credence based on the respective aims of these attitudes. (shrink)

I explore how rational belief and rational credence relate to evidence. I begin by looking at three cases where rational belief and credence seem to respond differently to evidence: cases of naked statistical evidence, lotteries, and hedged assertions. I consider an explanation for these cases, namely, that one ought not form beliefs on the basis of statistical evidence alone, and raise worries for this view. Then, I suggest another view that explains how belief and credence relate to evidence. My view (...) focuses on the possibilities that the evidence makes salient. I argue that this makes better sense of the difference between rational credence and rational belief than other accounts. (shrink)

This guide accompanies the following article(s): Jackson, E., Philosophy Compass 15/6 (2020) pp. 1-13 10.1111/phc3.12668.x.

Sometimes epistemologists theorize about belief, a tripartite attitude on which one can believe, withhold belief, or disbelieve a proposition. In other cases, epistemologists theorize about credence, a fine-grained attitude that represents one’s subjective probability or confidence level toward a proposition. How do these two attitudes relate to each other? This article explores the relationship between belief and credence in two categories: descriptive and normative. It then explains the broader significance of the belief-credence connection and concludes with general lessons from the (...) debate thus far. (shrink)

This paper elaborates a new solution to the lottery paradox, according to which the paradox arises only when we lump together two distinct states of being confident that p under one general label of ‘belief that p’. The two-state conjecture is defended on the basis of some recent work on gradable adjectives. The conjecture is supported by independent considerations from the impossibility of constructing the lottery paradox both for risk-tolerating states such as being afraid, hoping or hypothesizing, and for risk-averse, (...) certainty-like states. The new proposal is compared to views within the increasingly popular debate opposing dualists to reductionists with respect to the relation between belief and degrees of belief. (shrink)

This paper explains and defends a belief-first view of the relationship between belief and credence. On this view, credences are a species of beliefs, and the degree of credence is determined by the content of what is believed. We begin by developing what we take to be the most plausible belief-first view. Then, we offer several arguments for it. Finally, we show how it can resist objections that have been raised to belief-first views. We conclude that the belief-first view is (...) more plausible than many have previously supposed. (shrink)

In this paper I take up the question of the nature of the doxastic attitudes we entertain while inquiring into some matter. Relying on a distinction between two stages of open inquiry, I urge to acknowledge the existence of a distinctive attitude of cognitive inclination towards a proposition qua answer to the question one is inquiring into. I call this attitude “hypothesis”. Hypothesis, I argue, is a sui generis doxastic attitude which differs, both functionally and normatively, from suspended judgement, full (...) belief, credences, and acceptance. In closing, I point to the epistemological significance of hypothesis. More specifically, I contend that holding an attitude of hypothesis enables us to respond rationally to peer disagreement, and I suggest that such an attitude offers a suitable articulation of the view, originally put forward by Philip Kitcher, that cognitive diversity in inquiry has epistemic benefits. (shrink)

Can perceptual experiences be states of uncertainty? We might expect them to be, if the perceptual processes from which they're generated, as well as the behaviors they help produce, take account of probabilistic information. Yet it has long been presumed that perceptual experiences purport to tell us about our environment, without hedging or qualifying. Against this long-standing view, I argue that perceptual experiences may well occasionally be states of uncertainty, but that they are never probabilistically structured. I criticize a powerful (...) line of reasoning that we should expect perceptual experience to be probabilistic, given their interfaces with unconscious probabilistic information, with behavior responsive to it, and with credences. (shrink)

In his new book "The Importance of Being Rational", Errol Lord aims to give a real definition of the property of rationality in terms of normative reasons. If he can do so, his work is an important step towards a defense of ‘reasons fundamentalism’ – the thesis that all complex normative properties can be analyzed in terms of normative reasons. I focus on his analysis of epistemic rationality, which says that your doxastic attitudes are rational just in case they are (...) correct responses to the objective normative reasons you possess. For some fact to be an objective normative reason to do something that you possess, you have to be in a position to know this fact and be able to competently use it as a reason to do that thing. Lord’s view is thus a knowledge-first view about possessing normative reasons. Throughout the book, Lord conceptualizes belief in the traditional tripartite way – if you take any attitude at all towards a proposition, then you either believe it, or disbelieve it, or you suspend judgment about it. Lord doesn’t discuss cases in which we’re uncertain. Yet, those cases are ubiquitous. I explore how his view can be extended to them. I first discuss whether his strategy for vindicating coherence requirements in terms of normative reasons can be applied to credences. I then ask how Lord can conceive of the doxastic attitudes that encode uncertainty . (shrink)

The article proceeds upon the assumption that the beliefs and degrees of belief of rational agents satisfy a number of constraints, including: consistency and deductive closure for belief sets, conformity to the axioms of probability for degrees of belief, and the Lockean Thesis concerning the relationship between belief and degree of belief. Assuming that the beliefs and degrees of belief of both individuals and collectives satisfy the preceding three constraints, I discuss what further constraints may be imposed on the aggregation (...) of beliefs and degrees of belief. Some possibility and impossibility results are presented. The possibility results suggest that the three proposed rationality constraints are compatible with reasonable aggregation procedures for belief and degree of belief. (shrink)

To what extent do our beliefs, and how strongly we hold them, depend upon how they matter to us, on what we take to be at stake on them? The idea that beliefs are sometimes stake-sensitive (Armendt 2008, 2013) is further explored here, with a focus on whether beliefs may be stake-sensitive and rational. In contexts of extended deliberation about what to do, beliefs and assessments of options interact. In some deliberations, a belief about what you will do may rationally (...) influence your estimate of the value of doing it; deliberation dynamics provides a framework for modeling such interactions. A distinction is drawn between sensitivity to the magnitude of the stakes, and sensitivity to the shape of the stakes. Contexts of extended deliberation are settings in which some beliefs that p rationally depend on the shape of the stakes on p. The dependence is either rational stake-sensitivity or an outcome of rational learning; empirical evidence concerning contexts of deliberation may lead us to model rational beliefs in one way or the other. (shrink)

In this contribution we will present a generalization of de Finetti's betting game in which a gambler is allowed to buy and sell unknown events' betting odds from more than one bookmaker. In such a framework, the sole coherence of the books the gambler can play with is not sucient, as in the original de Finetti's frame, to bar the gambler from a sure-win opportunity. The notion of joint coherence which we will introduce in this paper characterizes those coherent books (...) on which sure- win is impossible. Our main results provide geometric characterizations of the space of all books which are jointly coherent with a xed one. As a consequence we will also show that joint coherence is decidable. (shrink)

A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non-public or even private information (learnt by not all or (...) just one individual), or to non-representable information (not representable by any event in the domain where credences are held). I pro- pose a taxonomy of six types of ‘group Bayesianism’. They differ in the information for which Bayesian revision of group credences is required: public representable information, private representable information, public non-representable information, etc. Six corre- sponding theorems establish how individual credences must (not) be aggregated to ensure group Bayesianism of any type, respectively. Aggregating through standard averaging is never permitted; instead, different forms of geometric averaging must be used. One theorem—that for public representable information—is essentially Russell et al.’s central result (with minor corrections). Another theorem—that for public non-representable information—fills a gap in the theory of externally Bayesian opinion pooling. (shrink)

One response to the problem of logical omniscience in standard possible worlds models of belief is to extend the space of worlds so as to include impossible worlds. It is natural to think that essentially the same strategy can be applied to probabilistic models of partial belief, for which parallel problems also arise. In this paper, I note a difficulty with the inclusion of impossible worlds into probabilistic models. Under weak assumptions about the space of worlds, most of the propositions (...) which can be constructed from possible and impossible worlds are in an important sense inexpressible; leaving the probabilistic model committed to saying that agents in general have at least as many attitudes towards inexpressible propositions as they do towards expressible propositions. If it is reasonable to think that our attitudes are generally expressible, then a model with such commitments looks problematic. (shrink)

According to the preference-centric approach to understanding partial belief, the connection between partial beliefs and preferences is key to understanding what partial beliefs are and how they’re measured. As Ramsey put it, the ‘degree of a belief is a causal property of it, which we can express vaguely as the extent to which we are prepared to act on it’ The Foundations of Mathematics and Other Logical Essays, Routledge, Oxon, pp 156–198, 1931). But this idea is not as popular as (...) it once was. Nowadays, the preference-centric approach is frequently dismissed out-of-hand as behaviouristic, unpalatably anti-realist, and/or prone to devastating counterexamples. Cases like Eriksson and Hájek’s :183–213, 2007) preferenceless Zen monk and Christensen’s :356–376, 2001) other roles argument have suggested to many that any account of partial belief that ties them too closely to preferences is irretrievably flawed. In this paper I provide a defence of preference-centric accounts of partial belief. (shrink)

According to doxastic pragmatism, certain perceived practical factors, such as high stakes and urgency, have systematic effects on normal subjects’ outright beliefs. Upholders of doxastic pragmatism have so far endorsed a particular version of this view, which we may call threshold pragmatism. This view holds that the sensitivity of belief to the relevant practical factors is due to a corresponding sensitivity of the threshold on the degree of credence necessary for outright belief. According to an alternative but yet unrecognised version (...) of doxastic pragmatism, practical factors affect credence rather than the threshold on credence. Let’s call this alternative view credal pragmatism. In this paper, I argue that credal pragmatism is more plausible than threshold pragmatism. I show that the former view better accommodates a cluster of intuitive and empirical data. I conclude by considering the issue of whether our doxastic attitudes’ sensitivity to practical factors can be considered rational, and if yes, in what sense. (shrink)

We generalize, by a progressive procedure, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. In our coherence-based approach, conjunctions and disjunctions are suitable conditional random quantities. We define the notion of negation, by verifying De Morgan’s Laws. We also show that conjunction and disjunction satisfy the associative and commutative properties, and a monotonicity property. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals; in particular (...) we examine the Fréchet-Hoeffding bounds. Moreover, we study the reverse probabilistic inference from the conjunction Cn+1 of n + 1 conditional events to the family {Cn,En+1|Hn+1}. We consider the relation with the notion of quasi-conjunction and we examine in detail the coherence of the prevision assessments related with the conjunction of three conditional events. Based on conjunction, we also give a characterization of p-consistency and of p-entailment, with applications to several inference rules in probabilistic nonmonotonic reasoning. Finally, we examine some non p-valid inference rules; then, we illustrate by an example two methods which allow to suitably modify non p-valid inference rules in order to get inferences which are p-valid. (shrink)

In this paper, I argue that the relationship between belief and credence is a central question in epistemology. This is because the belief-credence relationship has significant implications for a number of current epistemological issues. I focus on five controversies: permissivism, disagreement, pragmatic encroachment, doxastic voluntarism, and the relationship between doxastic attitudes and prudential rationality. I argue that each debate is constrained in particular ways, depending on whether the relevant attitude is belief or credence. This means that epistemologists should pay attention (...) to whether they are framing questions in terms of belief or in terms of credence and the success or failure of a reductionist project in the belief-credence realm has significant implications for epistemology generally. (shrink)

Belief is a familiar attitude: taking something to be the case or regarding it as true. But we are more confident in some of our beliefs than in others. For this reason, many epistemologists appeal to a second attitude, called credence, similar to a degree of confidence. This raises the question: how do belief and credence relate to each other? On a belief-first view, beliefs are more fundamental and credences are a species of beliefs, e.g. beliefs about probabilities. On a (...) credence-first view, credences are more fundamental and beliefs are a species of credence, e.g. credence above some threshold. In this thesis, I develop and defend a third view that I call belief-credence dualism. On this view, belief and credence are independent, equally fundamental attitudes, and neither reduces to the other. I begin by motivating the project: why should we care about the relationship between belief and credence? I argue it has broad implications for many debates in epistemology and beyond. Then, I defend dualism, arguing that it can explain features of our mental lives that a credence-first view and a belief-first view cannot. I also argue that dualism has attractive, interesting implications when applied to the pragmatic encroachment debate. Finally, I explore implications of dualism, both for the nature of evidence and how faith might go beyond the evidence but nonetheless be epistemically rational. I conclude that the human mind is, in some ways, complex, but we should be happy with this conclusion also long as each mental state we posit has a clear role to play. (shrink)

Belief-credence dualism is the view that we have both beliefs and credences and neither attitude is reducible to the other. Pragmatic encroachment is the view that stakes alone can affect the epistemic rationality of states like knowledge or justified belief. In this paper, I argue that dualism offers a unique explanation of pragmatic encroachment cases. First, I explain pragmatic encroachment and what motivates it. Then, I explain dualism and outline a particular argument for dualism. Finally, I show how dualism can (...) explain the intuitions that underlie pragmatic encroachment. My basic proposal is that in high-stake cases, it is not that one cannot rationally believe that p; instead, one ought not to rely on one's belief that p. One should rather rely on one's credence in p. I conclude that we need not commit ourselves to pragmatic encroachment in order to explain the intuitiveness of the cases that motivate it. (shrink)

In this article, I argue that faith’s going beyond the evidence need not compromise faith’s epistemic rationality. First, I explain how some of the recent literature on belief and credence points to a distinction between what I call B-evidence and C-evidence. Then, I apply this distinction to rational faith. I argue that if faith is more sensitive to B-evidence than to C-evidence, faith can go beyond the evidence and still be epistemically rational.

There is a long-standing disagreement in the philosophy of probability and Bayesian decision theory about whether an agent can hold a meaningful credence about an upcoming action, while she deliberates about what to do. Can she believe that it is, say, 70% probable that she will do A, while she chooses whether to do A? No, say some philosophers, for Deliberation Crowds Out Prediction (DCOP), but others disagree. In this paper, we propose a valid core for DCOP, and identify terminological (...) causes for some of the apparent disputes. (shrink)

In a recent article, Krauss (2017) raises some fundamental questions concerning (i) what the desiderata of a definition of lying are, and (ii) how definitions of lying can account for partial beliefs. This paper aims to provide an adequate answer to both questions. Regarding (i), it shows that there can be a tension between two desiderata for a definition of lying: 'descriptive accuracy' (meeting intuitions about our ordinary concept of lying), and 'moral import' (meeting intuitions about what is wrong with (...) lying), vindicating the primacy of the former desideratum. Regarding (ii), it shows that Krauss' proposed 'worse-off requirement' meets neither of these desiderata, whereas the 'comparative insincerity condition' (Marsili 2014) can meet both. The conclusion is that lies are assertions that the speaker takes to be more likely to be false than true, and their distinctive blameworthiness is a function of the extent to which they violate a sincerity norm. (shrink)