According to an increasingly popular view in epistemology and philosophy of mind, beliefs are sensitive to contextual factors such as practical factors and salient error possibilities. A prominent version of this view, called credal sensitivism, holds that the context-sensitivity of belief is due to the context-sensitivity of degrees of belief or credence. Credal sensitivism comes in two variants: while credence-one sensitivism (COS) holds that maximal confidence (credence one) is necessary for belief, threshold credal (...) class='Hi'>sensitivism (TCS) holds that belief consists in having credence above some threshold, where this threshold doesn’t require maximal confidence. In this paper, I argue that COS has difficulties in accounting for three important features about belief: i) the compatibility between believing p and assigning non-zero credence to certain error possibilities that one takes to entail not-p, ii) the fact that outright beliefs can occur in different strengths, and iii) beliefs held by unconscious subjects. I also argue that TCS can easily avoid these problems. Finally, I consider an alleged advantage of COS over TCS in terms of explaining beliefs about lotteries. I argue that lottery cases are rather more problematic for COS than TCS. In conclusion, TCS is the most plausible version of credal sensitivitism. (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)

Recently many have argued that agents must sometimes have credences that are imprecise, represented by a set of probability measures. But opponents claim that fans of imprecise credences cannot provide a decision theory that protects agents who follow it from foregoing sure money. In particular, agents with imprecise credences appear doomed to act irrationally in diachronic cases, where they are called to make decisions at earlier and later times. I respond to this claim on behalf of imprecise credence fans. Once (...) we appreciate the complexity of our intuitions about rational decision making, we can see that diachronic cases are in fact evidence for the essential claims motivating imprecise credence models. I argue that our decision theory for imprecise agents should mirror our decision theory for agents in moral dilemmas, and I develop permissive norms that explain our intuitions about both sorts of agents. (shrink)

The last 20 years or so has seen an intense search carried out within Dempster–Shafer theory, with the aim of finding a generalization of the Shannon entropy for belief functions. In that time, there has also been much progress made in credal set theory—another generalization of the traditional Bayesian epistemic representation—albeit not in this particular area. In credal set theory, sets of probability functions are utilized to represent the epistemic state of rational agents instead of the single probability (...) function of traditional Bayesian theory. The Shannon entropy has been shown to uniquely capture certain highly intuitive properties of uncertainty, and can thus be considered a measure of that quantity. This article presents two measures developed with the purpose of generalizing the Shannon entropy for (1) unordered convex credal sets and (2) possibly non-convex credal sets ordered by second order probability, thereby providing uncertainty measures for such epistemic representations. There is also a comparison with the results of the measure AU developed within Dempster–Shafer theory in a few instances where unordered convex credal set theory and Dempster–Shafer theory overlap. (shrink)

The basic Bayesian model of credence states, where each individual’s belief state is represented by a single probability measure, has been criticized as psychologically implausible, unable to represent the intuitive distinction between precise and imprecise probabilities, and normatively unjustifiable due to a need to adopt arbitrary, unmotivated priors. These arguments are often used to motivate a model on which imprecise credal states are represented by sets of probability measures. I connect this debate with recent work in Bayesian cognitive science, (...) where probabilistic models are typically provided with explicit hierarchical structure. Hierarchical Bayesian models are immune to many classic arguments against single-measure models. They represent grades of imprecision in probability assignments automatically, have strong psychological motivation, and can be normatively justified even when certain arbitrary decisions are required. In addition, hierarchical models show much more plausible learning behavior than flat representations in terms of sets of measures, which—on standard assumptions about update—rule out simple cases of learning from a starting point of total ignorance. (shrink)

Traditional epistemologists assumed that the most important doxastic norms were rational requirements on belief. This orthodoxy has recently been challenged by the work of revolutionary epistemologists on the rational requirements on credences. Revolutionary epistemology takes it that such contemporary work is important precisely because traditional epistemologists are mistaken—credal norms are more fundamental than, and determinative of, belief norms. To make sense of their innovative project, many revolutionary epistemologists have also adopted another commitment, that norms on credences are governed by (...) a fundamental accuracy norm. Unfortunately for the revolutionary epistemologist, it has been difficult to define a measure of accuracy while maintaining that credal norms are more basic than belief norms. In this paper, I criticize one such proposal for measuring accuracy, that the accuracy of our credences should be assessed in terms of what we know, arguing that this picture ultimately cannot vindicate the revolutionary approach. (shrink)

This paper is about a tension between two theses. The first is Value of Evidence: roughly, the thesis that it is always rational for an agent to gather and use cost‐free evidence for making decisions. The second is Rationality of Imprecision: the thesis that an agent can be rationally required to adopt doxastic states that are imprecise, i.e., not representable by a single credence function. While others have noticed this tension, I offer a new diagnosis of it. I show that (...) it arises when an agent with an imprecise doxastic state engages in an unreflective inquiry, an inquiry where they revise their beliefs using an updating rule that doesn't satisfy a weak reflection principle. In such an unreflective inquiry, certain synchronic norms of instrumental rationality can make it instrumentally irrational for an agent to gather and use cost‐free evidence. I then go on to propose a diachronic norm of instrumental rationality that preserves Value of Evidence in unreflective inquiries. This, I suggest, may help us reconcile this thesis with Rationality of Imprecision. (shrink)

This paper defends the use of possibility and necessity models based on the Logics of Formal Inconsistency, taking advantage of their expressivity in terms of the notions of consistency and inconsistency. The present proposal directly generalizes the approach of Besnard and Lang, whose main guidelines we borrow here. Some basic properties of possibility and necessity functions over the Logics of Formal Inconsistency are obtained and it is shown, by revisiting a paradigmatic example, how paraconsistent possibility and necessity reasoning can, in (...) general, attain realistic models for artificial judgement. We will call such models credal calculi, emphasizing some of their appealing consequences. (shrink)

Many have claimed that epistemic rationality sometimes requires us to have imprecise credal states (i.e. credal states representable only by sets of credence functions) rather than precise ones (i.e. credal states representable by single credence functions). Some writers have recently argued that this claim conflicts with accuracy-centered epistemology, i.e., the project of justifying epistemic norms by appealing solely to the overall accuracy of the doxastic states they recommend. But these arguments are far from decisive. In this essay, (...) we prove some new results, which show that there is little hope for reconciling the rationality of credal imprecision with accuracy-centered epistemology. (shrink)

It is a prevalent, if not popular, thesis in the metaphysics of belief that facts about an agent’s beliefs depend entirely upon facts about that agent’s underlying credal state. Call this thesis ‘credal reductivism’ and any view that endorses this thesis a ‘credal reductivist view’. An adequate credal reductivist view will accurately predict both when belief occurs and which beliefs are held appropriately, on the basis of credal facts alone. Several well-known—and some lesser known—objections to (...) credal reductivism turn on the inability of standard credal reductivist views to get the latter, normative, results right. This paper presents and defends a novel credal reductivist view according to which belief is a type of “imprecise credence” that escapes these objections by including an extreme credence of 1. (shrink)

A number of Bayesians claim that, if one has no evidence relevant to a proposition P, then one's credence in P should be spread over the interval [0, 1]. Against this, I argue: first, that it is inconsistent with plausible claims about comparative levels of confidence; second, that it precludes inductive learning in certain cases. Two motivations for the view are considered and rejected. A discussion of alternatives leads to the conjecture that there is an in-principle limitation on formal representations (...) of belief: they cannot be both fully accurate and maximally specific. (shrink)

Considerations involving disagreement, as well as related considerations involving correction and retraction, have played an important role in recent debates about epistemic modals. For instance, it has been argued that contextualist views about epistemic modals have problems when it comes to explaining cases of disagreement. In response to these challenges, I explore the idea that the relevant cases of disagreement may involve credal disagreement. In a case of credal disagreement, the parties have different degrees of belief or credences. (...) There does not have to be a difference in outright beliefs in order for the parties to disagree. I argue that the idea of credal disagreement allows us to make sense of otherwise problematic cases of disagreement involving epistemic modals. I also discuss how these ideas can be extended to cases of correction and retraction. (shrink)

Credal reductivism is the view that outright belief is reducible to degrees of confidence or ‘credence’. The most popular versions of credal reductivism all have the consequence that if you are near-maximally confident that p in a low-stakes situation, then you outright believe p. This paper addresses a recent objection to this consequence—the Correctness Objection— introduced by Jeremy Fantl and Matthew McGrath and further developed by Jacob Ross and Mark Schroeder. The objection is that near-maximal confidence cannot entail (...) outright belief because when you believe a false proposition, you are wrong or incorrect, whereas you can be highly confident of a false proposition in a low-stakes situation without being incorrect. Both Fantl and McGrath’s and Ross and Schoeder’s versions of the Correctness Objection admit of multiple interpretations. But it is argued that even on the most charitable interpretations the objection fails. (shrink)

It is truism that accuracy is valued. Some deem accuracy to be among the most fundamental values, perhaps the preeminent value, of inquiry. Because of this, accuracy has been the focus of two different, important programs in epistemology. The truthlikeness program pursued the notion of propositional accuracy—an ordering of propositions by closeness to the objective truth of some matter. The epistemic utility program pursued the notion of credal state accuracy—an ordering of credal states by closeness to the ideal (...) credal state. It may be tempting to think that each question that informs an inquiry must be  determinate of necessity. That is to say, there must be one correct, precise answer to it. That precise, correct answer is not only the maximally accurate answer to the question, but it also singles out the ideal credal state that is the epistemic target of the inquiry. An enormous amount of the effort has been focused on accuracy with respect to necessarily determinate questions. But often the focus of an inquiry is a question that is not necessarily determinate. Those who deem accuracy to be cognitively valuable, and fundamentally so, need an account of accuracy for indeterminate questions. Ideally such an account would cover both propositional accuracy and credal state accuracy. This is a tall order, and it is not clear that the order can be filled. (shrink)

Traditionally epistemologists have taken doxastic states to come in three varieties—belief, disbelief, and suspension. Recently many epistemologists have taken our doxastic condition to be usefully represented by credences—quantified degrees of belief. Moreover, some have thought that this new credal picture is sufficient to account for everything we want to explain with the old traditional picture. Therefore, belief, disbelief, and suspension must map onto the new picture somehow. In this paper I challenge that possibility. Approaching the question from the angle (...) of suspension, I argue that all possible credal accounts face serious challenges. They either (i) falsify central claims that uphold the credal picture itself or (ii) do not permit suspension in cases where it is permissible or (iii) rule out the possibility of plainly possible confidence comparisons. (shrink)

According to the probabilistic relevance account of confirmation, E confirms H relative to background knowledge K just in case P(H/K&E) > P(H/K). This requires an inequality between the rational degree of belief in H determined relative to two bodies of total knowledge which are such that one (K&E) includes the other (K) as a proper part. In this paper, I argue that it is quite plausible that there are no two possible bodies of total knowledge for ideally rational agents meeting (...) this requirement. Hence, the positive relevance account may have to be rejected. (shrink)

The knowledge extraction from data with noise or outliers is a complex problem in the data mining area. Normally, it is not easy to eliminate those problematic instances. To obtain information from this type of data, robust classifiers are the best option to use. One of them is the application of bagging scheme on weak single classifiers. The Credal C4.5 model is a new classification tree procedure based on the classical C4.5 algorithm and imprecise probabilities. It represents a type (...) of the so-calledcredal trees. It has been proven that CC4.5 is more robust to noise than C4.5 method and even than other previous credal tree models. In this paper, the performance of the CC4.5 model in bagging schemes on noisy domains is shown. An experimental study on data sets with added noise is carried out in order to compare results where bagging schemes are applied on credal trees and C4.5 procedure. As a benchmark point, the known Random Forest classification method is also used. It will be shown that the bagging ensemble using pruned credal trees outperforms the successful bagging C4.5 and RF when data sets with medium-to-high noise level are classified. (shrink)

This major work challenges some widely held positions in epistemology - those of Peirce and Popper on the one hand and those of Quine and Kuhn on the other.

In the original publication of the article, Table 1 was incorrectly published. The corrected table is give below.

In this paper, I offer reasons to conclude that either belief impermissivism or credal impermissivism is false. That is to say, I argue against the conjunction of belief impermissivism and credal impermissivism. I defend this conclusion in three ways. First, I show what I take to be an implausible consequence of holding that for any rational credence in p, there is only one correlating rational belief-attitude toward p, given a body of evidence. Second, I provide thought experiments designed (...) to support the intuition that there are at least a few credences in some cases for which more than one belief-attitude is rationally permissible. Third, I provide one possible theoretical grounding for my position by appeal to Jamesian values. (shrink)

This paper offers a noncognitivist characterization of moral attitudes, according to which moral attitudes count as such because of their inclusion of moral concepts. Moral concepts are distinguished by their contribution to the functional roles of some of the attitudes in which they can occur. They have no particular functional role in other attitudes, and should instead be viewed as evolutionary spandrels. In order to make the counter-intuitive implications of the view more palatable, the paper ends with an account of (...) the evolution of normative judgments as exaptations of the cognitive structures that underlie beliefs. (shrink)

In mainstream Anglo-American philosophy, the relation between cognition and community has been defined primarily in terms of the generalization of the mathematical function, especially as a model for the nature of rules, which thus come to be under-stood as algorithms. This leads to the elimination of both the reflexive, synthesizing subject, and the intrinsic communal-historical nature of argumentation and belief-formation. Against this approach, I follow R.G. Collingwood’s hitherto unrecognized strategy in his Essay on Metaphysics and argue that the relation of (...) cognition and community is better understood by way of the ancient and forgotten model of creedal rules of faith or trust. These will be shown to have the logical form of first person performative rules of faith or trust that generate third person declaratives or proposi-tions, and so constitute the possibility conditions for an argumentational logic of question and answer. They restore the synthetic subject, for they are not algorithms but reflexive and interpretive formulae; they are communally constituted and so historically saturated; and they reinstate an ontological theory of truth as disclosure, with coherence and comprehensiveness as its criteria. In these respects, as Collingwood saw, the creedal model provides a fresh interpretation of the historicality of argumentation and redefines the relation of cognition and community in terms of the interdependence of faith and reason. (shrink)

Credal Conservatism says that an agent’s credal states should be conserved as far as possible when she undergoes a learning experience. Uniqueness says that for any given total evidence, there is a unique credal state that any agent with that total evidence should have. Epistemic Impartiality is the idea that there are no significant differences between intrapersonal and interpersonal rationality requirements when determining what credal states one ought to have for purposes of epistemic evaluation. I construe (...) Epistemic Impartiality as a meta-principle governing epistemic norms, and argue that it is compatible with Conservatism. Then I show that on the assumption of Epistemic Impartiality, Credal Conservatism is equivalent to Uniqueness. (shrink)

I present a puzzle about belief and credence, which takes the form of three independently supported views that are mutually inconsistent. The first is the view that S has a modal belief that p (e.g., S believes that probably-p) if and only if S has a corresponding credence that p. The second is the view that S believes that p only if S has some credence that p. The third is the view that, possibly, S believes that p without a (...) modal belief that p. [Word Count: 85]. (shrink)

This paper compares two alternative explanations of pragmatic encroachment on knowledge (i.e., the claim that whether an agent knows that p can depend on pragmatic factors). After reviewing the evidence for such pragmatic encroachment, we ask how it is best explained, assuming it obtains. Several authors have recently argued that the best explanation is provided by a particular account of belief, which we call pragmatic credal reductivism. On this view, what it is for an agent to believe a proposition (...) is for her credence in this proposition to be above a certain threshold, a threshold that varies depending on pragmatic factors. We show that while this account of belief can provide an elegant explanation of pragmatic encroachment on knowledge, it is not alone in doing so, for an alternative account of belief, which we call the reasoning disposition account, can do so as well. And the latter account, we argue, is far more plausible than pragmatic credal reductivism, since it accords far better with a number of claims about belief that are very hard to deny. (shrink)

I develop a conception of expressivism according to which it is chiefly a pragmatic thesis about some fragment of discourse, one imposing certain constraints on semantics. The first half of the paper uses credal expressivism about the language of probability as a stalking-horse for this purpose. The second half turns to the question of how one might frame an analogous form of expressivism about the language of deontic modality. Here I offer a preliminary comparison of two expressivist lines. The (...) first, expectation expressivism, looks again to Bayesian modelling for inspiration: it glosses deontically modal language as characteristically serving to express decision-theoretic expectation (expected utility). The second, plan expressivism, develops the idea (due to Gibbard 2003) that this language serves to express 'plan-laden' states of belief. In the process of comparing the views, I show how to incorporate Gibbard's modelling ideas into a compositional semantics for attitudes and modals, filling a lacuna in the account. I close with the question whether and how plan expressivism might be developed with expectation-like structure. (shrink)

Quasi-realists face the challenge of providing a plausible analysis of acknowledgments of moral fallibility. This paper devel...

This paper develops a compositional, type-driven constraint semantic theory for a fragment of the language of subjective uncertainty. In the particular application explored here, the interpretation function of constraint semantics yields not propositions but constraints on credal states as the semantic values of declarative sentences. Constraints are richer than propositions in that constraints can straightforwardly represent assessments of the probability that the world is one way rather than another. The richness of constraints helps us model communicative acts in essentially (...) the same way that we model agents’ credences. Moreover, supplementing familiar truth-conditional theories of epistemic modals with constraint semantics helps capture contrasts between strong necessity and possibility modals, on the one hand, and weak necessity modals, on the other. (shrink)

Traditional Bayesianism requires that an agent’s degrees of belief be represented by a real-valued, probabilistic credence function. However, in many cases it seems that our evidence is not rich enough to warrant such precision. In light of this, some have proposed that we instead represent an agent’s degrees of belief as a set of credence functions. This way, we can respect the evidence by requiring that the set, often called the agent’s credal state, includes all credence functions that are (...) in some sense compatible with the evidence. One known problem for this evidentially motivated imprecise view is that in certain cases, our imprecise credence in a particular proposition will remain the same no matter how much evidence we receive. In this article I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid it without compromising the initial evidentialist motivation. _1_ Introduction _2_ Precision and Its Problems _3_ Imprecise Bayesianism and Respecting Ambiguous Evidence _4_ Local Belief Inertia _5_ From Local to Global Belief Inertia _6_ Responding to Global Belief Inertia _7_ Conclusion. (shrink)

According to evidentialist views, credence in a proposition p should be proportional to the degree of evidential support that one has in favor of p. However, empirical evidence suggests that our credences are systematically sensitive to practical factors. In this article, I provide a cost–benefit analysis of credences' practical sensitivity. The upshot of this analysis is that credences sensitive to practical factors fare better than practically insensitive ones along several dimensions. All things considered, our credences should be sensitive to practical (...) factors. (shrink)

We defend a set of acceptance rules that avoids the lottery paradox, that is closed under classical entailment, and that accepts uncertain propositions without ad hoc restrictions. We show that the rules we recommend provide a semantics that validates exactly Adams’ conditional logic and are exactly the rules that preserve a natural, logical structure over probabilistic credal states that we call probalogic. To motivate probalogic, we first expand classical logic to geo-logic, which fills the entire unit cube, and then (...) we project the upper surfaces of the geo-logical cube onto the plane of probabilistic credal states by means of standard, linear perspective, which may be interpreted as an extension of the classical principle of indifference. Finally, we apply the geometrical/logical methods developed in the paper to prove a series of trivialization theorems against question-invariance as a constraint on acceptance rules and against rational monotonicity as an axiom of conditional logic in situations of uncertainty. (shrink)

Two different programmes are in the business of explicating accuracy—the truthlikeness programme and the epistemic utility programme. Both assume that truth is the goal of inquiry, and that among inquiries that fall short of realizing the goal some get closer to it than others. Truthlikeness theorists have been searching for an account of the accuracy of propositions. Epistemic utility theorists have been searching for an account of the accuracy of credal states. Both assume we can make cognitive progress in (...) an inquiry even while falling short of the target. I show that the prospects for combining these two programmes are bleak. A core accuracy principle, proximity, that is universally embraced within the truthlikeness programme turns out to be incompatible with a central principle within the epistemic utility programme, namely propriety. 1Truthlikeness and Epistemic Utility 2Inquiries 3Accuracy for Propositions 4Proximity 5Accuracy for Credal States 6Propriety 7Proximity for Credal States 8Extensionality 9Admissible Weightings 10Propriety Violates Proximity 11Possible Responses 11.1Retreat to convexity 11.2Reject boundedness 11.3Reject additivity 12The Upshot. (shrink)

The preface paradox does not show that it can be rational to have inconsistent beliefs, because preface writers do not have inconsistent beliefs. I argue, first, that a fully satisfactory solution to the preface paradox would have it that the preface writer's beliefs are consistent. The case here is on basic intuitive grounds, not the consequence of a theory of rationality or of belief. Second, I point out that there is an independently motivated theory of belief – sensitivism – (...) which allows such a solution. I sketch a sensitivist account of the preface writer's doxastic state. (shrink)

Two compelling principles, the Reasonable Range Principle and the Preservation of Irrelevant Evidence Principle, are necessary conditions that any response to peer disagreements ought to abide by. The Reasonable Range Principle maintains that a resolution to a peer disagreement should not fall outside the range of views expressed by the peers in their dispute, whereas the Preservation of Irrelevant Evidence Principle maintains that a resolution strategy should be able to preserve unanimous judgments of evidential irrelevance among the peers. No standard (...) Bayesian resolution strategy satisfies the PIE Principle, however, and we give a loss aversion argument in support of PIE and against Bayes. The theory of imprecise probability allows one to satisfy both principles, and we introduce the notion of a set-based credal judgment to frame and address a range of subtle issues that arise in peer disagreements. (shrink)

Belief and credal commitment sometimes seem to make less and less sense in the West. A kind of 'cultural amnesia' has taken hold, where formal religious adherence begins to seem almost unthinkable. This is especially so for the idea of divine revelation. Robyn Horner argues this means we need to re-evaluate how theology proceeds, focusing not so much on beliefs but on experience. Exploring ways in which the experiential might open human beings up to divine possibility, the author turns (...) to phenomenology because it seeks to examine unrestrictedly what is given through involved encounter. Bringing phenomenology and poststructuralism together, Horner develops the idea of revelation as an 'event' wherein God interrupts and exceeds human experience, affecting and transforming it. This striking concept, named but largely unexplored by theology, articulates a notion of supernatural revelation which now starts to appear both coherent and plausible. (shrink)