How, if at all, is knowing how to do something defeasible? Some, the “intellectualists”, treat the defeasibility of knowledge-how as in some way derivative on the defeasibility of knowledge-that. According to a recent proposal by Carter and Navarro (Philos Phenomenol Res 3:662–685, 2017), knowledge-how defeat cannot be explained in terms of knowledge-that defeat; instead, knowledge-how defeat merits and entirely separate treatment. The thought behind “separatism” is easy to articulate. Assuming that knowledge of any kind is defeasible, since knowledge-that and knowledge-how (...) are fundamentally different beasts, the best accounts of their defeasibility must reflect the underlying differences between them. I reject a separatist treatment of the defeasibility of knowledge-that and knowledge-how. One can acknowledge certain important differences between knowledge-that and knowledge-how without thereby needing two theories of defeasibility. Ultimately, though, I’ll argue that the defeasibility of basic knowledge-how, unlike non-basic knowledge-how, is a much more difficult issue than has been acknowledged. (shrink)

A distinctive feature of Juan Comesaña's epistemological account is the possibility of an agent possessing a false proposition as evidence. Comesaña argues that there are a number of theoretical virtues of his account once we accept this possibility, however, one might expect that there are particular vices of his account as well. Littlejohn and Dutant (2021) claim that a reflective agent who accepts Comesaña's view is rationally compelled to update their credences differently than unreflective agents, or else they will be (...) guilty of a problematic kind of doublethink: evidence in general can be false, but my evidence is never false. I argue that parallel reasoning applies to any epistemological view that says that it is possible for a rational agent to be wrong about what their evidence is. When a rational agent reflectively accepts that they could be wrong about their evidence they are rationally compelled to update their credences differently than unreflective agents, or else they will be guilty of a problematic kind of doublethink: even though rational agents in general are wrong about their evidence, I'm never wrong about my evidence. Reflecting on a particular challenge to Comesaña's view ultimately reveals a general challenge to fallibilism. (shrink)

Bayesianism can be characterized as the following twofold position: (i) rational credences obey the probability calculus; (ii) rational learning, i.e., the updating of credences, is regulated by some form of conditionalization. While the formal aspect of various forms of conditionalization has been explored in detail, the philosophical application to learning from experience is still deeply problematic. Some philosophers have proposed to revise the epistemology of perception; others have provided new formal accounts of conditionalization that are more in line with how (...) we learn from perceptual experience. The current investigation argues that Bayesian epistemology is still incomplete; the epistemology of perception and the epistemology of rational reasoning have not been reconciled. (shrink)

Reasoning from inconclusive evidence, or ‘induction’, is central to science and any applications we make of it. For that reason alone it demands the attention of philosophers of science. This Element explores the prospects of using probability theory to provide an inductive logic, a framework for representing evidential support. Constraints on the ideal evaluation of hypotheses suggest that overall support for a hypothesis is represented by its probability in light of the total evidence, and incremental support, or confirmation, indicated by (...) an increased probability given the evidence than otherwise. This proposal is shown to have the capacity to reconstruct many canons of the scientific method and inductive inference. Along the way, significant objections are discussed, such as the challenge from inductive scepticism and the objection that the probabilistic approach makes evidential support arbitrary. (shrink)

Philosophical Issues, Volume 31, Issue 1, Page 41-65, October 2021.

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

We explore the question of whether cost-free uncertain evidence is worth waiting for in advance of making a decision. A classical result in Bayesian decision theory, known as the value of evidence theorem, says that, under certain conditions, when you update your credences by conditionalizing on some cost-free and certain evidence, the subjective expected utility of obtaining this evidence is never less than the subjective expected utility of not obtaining it. We extend this result to a type of update method, (...) a variant of Judea Pearl’s virtual conditionalization, where uncertain evidence is represented as a set of likelihood ratios. Moreover, we argue that focusing on this method rather than on the widely accepted Jeffrey conditionalization enables us to show that, under a fairly plausible assumption, gathering uncertain evidence not only maximizes expected pragmatic utility, but also minimizes expected epistemic disutility. (shrink)

The main aims in this article are to discuss and criticize the core thesis of a position that has become known as phenomenal conservatism. According to this thesis, its seeming to one that p provides enough justification for a belief in p to be prima facie justified. This thesis captures the special kind of epistemic import that seemings are claimed to have. To get clearer on this thesis, the article embeds it, first, in a probabilistic framework in which updating on (...) new evidence happens by Bayesian conditionalization, and second, a framework in which updating happens by Jeffrey conditionalization. The article spells out problems for both views, and then generalizes some of these to nonprobabilistic frameworks. The main theme of the discussion is that the epistemic import of a seeming should depend on its content in a plethora of ways that phenomenal conservatism is insensitive to. (shrink)

Philosophical Issues, Volume 30, Issue 1, Page 54-70, October 2020.

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)

According to the recent Perceptual Confidence view, perceptual experiences possess not only a representational content, but also a degree of confidence in that content. The motivations for this view are partly phenomenological and partly epistemic. We discuss both the phenomenological and epistemic motivations for the view, and the resulting account of the interface between perceptual experiences and degrees of belief. We conclude that, in their present state of development, orthodox accounts of perceptual experience are still to be favoured over the (...) perceptual confidence view. (shrink)

Our main aims in this paper is to discuss and criticise the core thesis of a position that has become known as phenomenal conservatism. According to this thesis, its seeming to one that p provides enough justification for a belief in p to be prima facie justified (a thesis we label Standard Phenomenal Conservatism). This thesis captures the special kind of epistemic import that seemings are claimed to have. To get clearer on this thesis, we embed it, first, in a (...) probabilistic framework in which updating on new evidence happens by Bayesian conditionalization, and second, a framework in which updating happens by Jeffrey conditionalization. We spell out problems for both views, and then generalize some of these to non-probabilistic frameworks. The main theme of our discussion is that the epistemic import of a seeming (or experience) should depend on its content in a plethora of ways that phenomenal conservatism is insensitive to. (shrink)

This paper considers a problem for Bayesian epistemology and proposes a solution to it. On the traditional Bayesian framework, an agent updates her beliefs by Bayesian conditioning, a rule that tells her how to revise her beliefs whenever she gets evidence that she holds with certainty. In order to extend the framework to a wider range of cases, Jeffrey (1965) proposed a more liberal version of this rule that has Bayesian conditioning as a special case. Jeffrey conditioning is a rule (...) that tells the agent how to revise her beliefs whenever she gets evidence that she holds with any degree of confidence. The problem? While Bayesian conditioning has a foundationalist structure, this foundationalism disappears once we move to Jeffrey conditioning. If Bayesian conditioning is a special case of Jeffrey conditioning, then they should have the same normative structure. The solution? To reinterpret Bayesian updating as a form of diachronic coherentism. (shrink)

As a general rule, whenever a hearer is justified in forming the belief that p on the basis of a speaker’s testimony, she will also be justified in assuming that the speaker has formed her belief appropriately in light of a relevantly large and representative sample of the evidence that bears on p. In simpler terms, a justification for taking someone’s testimony entails a justification for trusting her assessment of the evidence. This introduces the possibility of what I will call (...) “evidential preemption.” Evidential preemption occurs when a speaker, in addition to offering testimony that p, also warns the hearer of the likelihood that she will subsequently be confronted with apparently contrary evidence: this is done, however, not so as to encourage the hearer to temper her confidence in p in anticipation of that evidence, but rather to suggest that the (apparently) contrary evidence is in fact misleading evidence or evidence that has already been taken into account. Either way, the speaker is signalling to the hearer that the subsequent disclosure of this evidence will not require her to significantly revise her belief that p. Such preemption can effectively inoculate an audience against future contrary evidence, and thereby creates an opening for a form of exploitative manipulation that I will call “epistemic grooming.” Nonetheless, I argue, not all uses of evidential preemption are nefarious; it can also serve as an important tool for guiding epistemically limited agents though complex evidential scenarios. (shrink)

According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that govern a logically ignorant individual at any given time; (...) an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence; and an account of when logical ignorance is irrational and when it isn’t. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations. (shrink)

Much work in the philosophy of action in the last few decades has focused on the elucidation and justification of a series of purported norms of practical rationality that concern the presence or absence of intention in light of belief, and that demand a kind of structural coherence in the psychology of an agent. Examples of such norms include: Intention Detachment, which proscribes intending to do something in case some condition obtains, believing that such condition obtains, and not intending to (...) do that thing; Intention-Belief Consistency, which proscribes intending to do what you believe you will not do; Intention Consistency, which proscribes intending each of two ends you believe to be inconsistent; and Means-End Coherence, which proscribes intending an end and not intending the means you believe to be implied by your end. In this paper, I present a series of examples that show that these requirements are not genuine requirements of rationality. The reason for this is simple: these requirements concern the presence or absence of intention in light of all-out belief. Rational agents like us, however, do not, and in fact should not, always form or revise their intentions in light of what they all-out believe. When such agents do not form or revise their intentions in light of what they all-out believe, they need not be irrational if they do not conform to these requirements. (shrink)

Our senses provide us with information about the world, but what exactly do they tell us? I argue that in order to optimally respond to sensory stimulations, an agent’s doxastic space may have an extra, “imaginary” dimension of possibility; perceptual experiences confer certainty on propositions in this dimension. To some extent, the resulting picture vindicates the old-fashioned empiricist idea that all empirical knowledge is based on a solid foundation of sense-datum propositions, but it avoids most of the problems traditionally associated (...) with that idea. The proposal might also explain why experiences appear to have a non-physical phenomenal character, even if the world is entirely physical. (shrink)

Seeing a red hat can (i) increase my credence in the hat is red, and (ii) introduce a negative dependence between that proposition and po- tential undermining defeaters such as the light is red. The rigidity of Jeffrey Conditionalization makes this awkward, as rigidity preserves inde- pendence. The picture is less awkward given ‘Holistic Conditionalization’, or so it is claimed. I defend Jeffrey Conditionalization’s consistency with underminable perceptual learning and its superiority to Holistic Conditionalization, arguing that the latter is merely (...) a special case of the former, is itself rigid, and is committed to implausible accounts of perceptual con- firmation and of undermining defeat. (shrink)

There are three well-known models of how to account for perceptual belief within a probabilistic framework: (a) a Cartesian model; (b) a model advocated by Timothy Williamson; and (c) a model advocated by Richard Jeffrey. Each of these models faces a problem—in effect, the problem of accounting for the defeasibility of perceptual justification and perceptual knowledge. It is argued here that the best way of responding to this the best way of responding to this problem effectively vindicates the Cartesian model. (...) Finally, it is argued that, given the best interpretation of the probabilistic framework, that the Cartesian model is not vulnerable to the main criticisms that have been raised against it. (shrink)

The externalist says that your evidence could fail to tell you what evidence you do or not do have. In that case, it could be rational for you to be uncertain about what your evidence is. This is a kind of uncertainty which orthodox Bayesian epistemology has difficulty modeling. For, if externalism is correct, then the orthodox Bayesian learning norms of conditionalization and reflection are inconsistent with each other. I recommend that an externalist Bayesian reject conditionalization. In its stead, I (...) provide a new theory of rational learning for the externalist. I defend this theory by arguing that its advice will be followed by anyone whose learning dispositions maximize expected accuracy. I then explore some of this theory’s consequences for the rationality of epistemic akrasia, peer disagreement, undercutting defeat, and uncertain evidence. (shrink)

Famous results by David Lewis show that plausible-sounding constraints on the probabilities of conditionals or evaluative claims lead to unacceptable results, by standard probabilistic reasoning. Existing presentations of these results rely on stronger assumptions than they really need. When we strip these arguments down to a minimal core, we can see both how certain replies miss the mark, and also how to devise parallel arguments for other domains, including epistemic “might,” probability claims, claims about comparative value, and so on. A (...) popular reply to Lewis's results is to claim that conditional claims, or claims about subjective value, lack truth conditions. For this strategy to have a chance of success, it needs to give up basic structural principles about how epistemic states can be updated—in a way that is strikingly parallel to the commitments of the project of dynamic semantics. (shrink)

As I head home from work, I’m not sure whether my daughter’s new bike is green, and I’m also not sure whether I’m on drugs that distort my color perception. One thing that I am sure about is that my attitudes towards those possibilities are evidentially independent of one another, in the sense that changing my confidence in one shouldn’t affect my confidence in the other. When I get home and see the bike it looks green, so I increase my (...) confidence that it is green. But something else has changed: now an increase in my confidence that I’m on color-drugs would undermine my confidence that the bike is green. Jonathan Weisberg and Jim Pryor argue that the preceding story is problematic for standard Bayesian accounts of perceptual learning. Due to the ‘rigidity’ of Conditionalization, a negative probabilistic correlation between two propositions cannot be introduced by updating on one of them. Hence if my beliefs about my own color-sobriety start out independent of my beliefs about the color of the bike, then they must remain independent after I have my perceptual experience and update accordingly. Weisberg takes this to be a reason to reject Conditionalization. I argue that this conclusion is too pessimistic: Conditionalization is only part of the Bayesian story of perceptual learning, and the other part needn’t preserve independence. Hence Bayesian accounts of perceptual learning are perfectly consistent with potential underminers for perceptual beliefs. (shrink)

ABSTRACTRational agents have consistent beliefs. Bayesianism is a theory of consistency for partial belief states. Rational agents also respond appropriately to experience. Dogmatism is a theory of how to respond appropriately to experience. Hence, Dogmatism and Bayesianism are theories of two very different aspects of rationality. It's surprising, then, that in recent years it has become common to claim that Dogmatism and Bayesianism are jointly inconsistent: how can two independently consistent theories with distinct subject matter be jointly inconsistent? In this (...) essay I argue that Bayesianism and Dogmatism are inconsistent only with the addition of a specific hypothesis about how the appropriate responses to perceptual experience are to be incorporated into the formal models of the Bayesian. That hypothesis isn't essential either to Bayesianism or to Dogmatism, and so Bayesianism and Dogmatism are jointly consistent. That leaves the matter of how experiences and credences are related, a... (shrink)

Weisberg introduces a phenomenon he terms perceptual undermining. He argues that it poses a problem for Jeffrey conditionalization, and Bayesian epistemology in general. This is Weisberg’s paradox. Weisberg argues that perceptual undermining also poses a problem for ranking theory and for Dempster-Shafer theory. In this note I argue that perceptual undermining does not pose a problem for any of these theories: for true conditionalizers Weisberg’s paradox is a false alarm.

The foundations of probability are viewed through the lens of the subjectivist interpretation. This article surveys conditional probability, arguments for probabilism, probability dynamics, and the evidential and subjective interpretations of probability.

While recent discussions of contextualism have mostly focused on other issues, some influential early statements of the view emphasized the possibility of its providing an alternative to both coherentism and traditional versions of foundationalism. In this essay, I will pick up on this strand of contextualist thought, and argue that contextualist versions of foundationalism promise to solve some problems that their non-contextualist cousins cannot. In particular, I will argue that adopting contextualist versions of foundationalism can let us reconcile Bayesian accounts (...) of belief updating with a version of the holist claim that all beliefs are defeasible. (shrink)

Consider: -/- The Evidence Question: When, and under what conditions does an agent have proposition E as evidence (at t)? -/- Timothy Williamson's (2000) answer to this question is the well-known E = K thesis: -/- E = K: E is a member of S's evidence set at t iff S knows E at t. -/- I will argue that this answer is inconsistent with the version of Bayesianism that Williamson advocates. This is because E = K allows an agent (...) to garner evidence via inductive inference whereas standard Bayesian views disallow such a thing. Since Williamson's version of Bayesianism shares the key features with the standard Bayesian view, there is an inconsistency. (shrink)

We often evaluate belief-forming processes, agents, or entire belief states for reliability. This is normally done with the assumption that beliefs are all-or-nothing. How does such evaluation go when we’re considering beliefs that come in degrees? I consider a natural answer to this question that focuses on the degree of truth-possession had by a set of beliefs. I argue that this natural proposal is inadequate, but for an interesting reason. When we are dealing with all-or-nothing belief, high reliability leads to (...) high levels of truth-possession. However, when it comes to degrees of belief, reliability and truth-possession part ways. The natural answer thus fails to be a good way to evaluate degrees of belief for reliability. I propose and develop an alternative method based on the notion of calibration, suggested by Frank Ramsey, which does not have this problem and consider why we should care about such assessments of reliability even if they are not tied directly to truth-possession. (shrink)

How do agents with limited cognitive capacities flourish in informationally impoverished or unexpected circumstances? Aristotle argued that human flourishing emerged from knowing about the world and our place within it. If he is right, then the virtuous processes that produce knowledge, best explain flourishing. Influenced by Aristotle, virtue epistemology defends an analysis of knowledge where beliefs are evaluated for their truth and the intellectual virtue or competences relied on in their creation. However, human flourishing may emerge from how degrees of (...) ignorance are managed in an uncertain world. Perhaps decision-making in the shadow of knowledge best explains human wellbeing—a Bayesian approach? In this dissertation I argue that a hybrid of virtue and Bayesian epistemologies explains human flourishing—what I term homeostatic epistemology. Homeostatic epistemology supposes that an agent has a rational credence p when p is the product of reliable processes aligned with the norms of probability theory; whereas an agent knows that p when a rational credence p is the product of reliable processes such that: 1) p meets some relevant threshold for belief, 2) p coheres with a satisficing set of relevant beliefs and, 3) the relevant set of beliefs is coordinated appropriately to meet the integrated aims of the agent. Homeostatic epistemology recognizes that justificatory relationships between beliefs are constantly changing to combat uncertainties and to take advantage of predictable circumstances. Contrary to holism, justification is built up and broken down across limited sets like the anabolic and catabolic processes that maintain homeostasis in the cells, organs and systems of the body. It is the coordination of choristic sets of reliably produced beliefs that create the greatest flourishing given the limitations inherent in the situated agent. (shrink)

Belief revision theory studies how an ideal doxastic agent should revise her beliefs when she receives new information. In part I, I have first presented the AGM theory of belief revision. Then I have focused on the problem of iterated belief revisions. In part II, I will first present ranking theory (Spohn 1988). Then I will show how it solves the problem of iterated belief revisions. I will conclude by sketching two areas of future research.

Weisberg ([2009]) provides an argument that neither conditionalization nor Jeffrey conditionalization is capable of accommodating the holist’s claim that beliefs acquired directly from experience can suffer undercutting defeat. I diagnose this failure as stemming from the fact that neither conditionalization nor Jeffrey conditionalization give any advice about how to rationally respond to theory-dependent evidence, and I propose a novel updating procedure that does tell us how to respond to evidence like this. This holistic updating rule yields conditionalization as a special (...) case in which our evidence is entirely theory independent. 1 Introduction2 Conditionalization3 Holism and Conditionalization4 A Holistic Update5 HCondi and Dutch Books6 Commutativity and Learning about Background Theories6.1 Commutativity6.2 Learning about background theories7 In Summation. (shrink)

It is natural to think that many of our beliefs are rational because they are based on seemings, or on the way things seem. This is especially clear in the case of perception. Many of our mathematical, moral, and memory beliefs also appear to be based on seemings. In each of these cases, it is natural to think that our beliefs are not only based on a seeming, but also that they are rationally based on these seemings—at least assuming there (...) is no relevant counterevidence. This piece is an introduction to a volume dedicated to the question of what the connection is between seemings and justified belief: under what conditions, if any, can a seeming justify its content? (shrink)

Bayesian Epistemology is a general framework for thinking about agents who have beliefs that come in degrees. Theories in this framework give accounts of rational belief and rational belief change, which share two key features: (i) rational belief states are represented with probability functions, and (ii) rational belief change results from the acquisition of evidence. This dissertation focuses specifically on the second feature. I pose the Evidence Question: What is it to have evidence? Before addressing this question we must have (...) an understanding of Bayesian Epistemology. The first chapter argues that we should understand Bayesian Epistemology as giving us theories that are evaluative and not action-guiding. I reach this verdict after considering the popular ‘ought’-implies-‘can’ objection to Bayesian Epistemology. The second chapter argues that it is important for theories in Bayesian Epistemology to answer the Evidence Question, and distinguishes between internalist and externalist answers. The third and fourth chapters present and defend a specific answer to the Evidence Question. The account is inspired by reliabilist accounts of justification, and attempts to understand what it is to have evidence by appealing solely to considerations of reliability. Chapter 3 explains how to understand reliability, and how the account fits with Bayesian Epistemology, in particular, the requirement that an agent’s evidence receive probability 1. Chapter 4 responds to objections, which maintain that the account gives the wrong verdict in a variety of situations including skeptical scenarios, lottery cases, scientific cases, and cases involving inference. After slight modifications, I argue that my account has the resources to answer the objections. The fifth chapter considers the possibility of losing evidence. I show how my account can model these cases. To do so, however, we require a modification to Conditionalization, the orthodox principle governing belief change. I present such a modification. The sixth and seventh chapters propose a new understanding of Dutch Book Arguments, historically important arguments for Bayesian principles. The proposal shows that the Dutch Book Arguments for implausible principles are defective, while the ones for plausible principles are not. The final chapter is a conclusion. (shrink)

Sometimes appearances provide epistemic support that gets undercut later. In an earlier paper I argued that standard Bayesian update rules are at odds with this phenomenon because they are ‘rigid’. Here I generalize and bolster that argument. I first show that the update rules of Dempster–Shafer theory and ranking theory are rigid too, hence also at odds with the defeasibility of appearances. I then rebut three Bayesian attempts to solve the problem. I conclude that defeasible appearances pose a more difficult (...) and pervasive challenge for formal epistemology than is currently thought. 1 The Challenge for Bayesianism1.1 Updating and experience1.2 The problem1.3 Objections2 The Challenge for Dempster–Shafer Theory2.1 Background on Dempster–Shafer theory2.2 The problem for Dempster–Shafer theory3 The Challenge for Ranking Theory4 The Appeal to Metacognition5 The Appeal to Richer Inputs6 The Appeal to a Generic Underminer7 Conclusion. (shrink)

‘Bayesian epistemology’ became an epistemological movement in the 20th century, though its two main features can be traced back to the eponymous Reverend Thomas Bayes (c. 1701-61). Those two features are: (1) the introduction of a formal apparatus for inductive logic; (2) the introduction of a pragmatic self-defeat test (as illustrated by Dutch Book Arguments) for epistemic rationality as a way of extending the justification of the laws of deductive logic to include a justification for the laws of inductive logic. (...) The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of conditionalization. (shrink)

Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...) that is, by employing tools from logic and mathematics. The goal of this entry is to give the reader an overview of the formal tools available to epistemologists for the representation of belief. A particular focus will be the relation between formal representations of qualitative belief and formal representations of quantitative degrees of belief. (shrink)

It has frequently been argued recently that Jeffrey Conditionalization (JC) does not permit undermining. For JC to be inapplicable in cases where the evidence could be undermined would severely compromise JC’s range. However, this paper contends that the argument fails to show that JC cannot accommodate undermining. This response turns on using the proper partition to capture the direct impact of our evidence in redistributing our credences.

Rédei and Gyenis recently displayed strong constraints of Bayesian learning. However, they also presented a positive result for Bayesianism. Despite the limited significance of this positive result, I find it useful to discuss its two possible strengthenings to present new results and open new questions about the limits of Bayesianism. First, I will show that one cannot strengthen the positive result by restricting the evidence to so-called “certain evidence”. Secondly, strengthening the result by restricting the partitions—as parts of one’s evidence—to (...) Jeffrey-independent partitions requires additional constraints on one’s evidence to preserve its commutativity. So, my results provide additional grounds for caution and support for the limitations of Bayesian learning. (shrink)

The coherence of independent reports provides a strong reason to believe that the reports are true. This plausible claim has come under attack from recent work in Bayesian epistemology. This work shows that, under certain probabilistic conditions, coherence cannot increase the probability of the target claim. These theorems are taken to demonstrate that epistemic coherentism is untenable. To date no one has investigated how these results bear on different conceptions of coherence. I investigate this situation using Thagard’s ECHO model of (...) explanatory coherence. Thagard’s ECHO model provides a natural representation of the evidential significance of multiple independent reports. (shrink)

Rational agents are supposed to maximize expected utility. But what are the options from which they choose? I outline some constraints on an adequate representation of an agent’s options. The options should, for example, contain no information of which the agent is unsure. But they should be sufficiently rich to distinguish all available acts from one another. These demands often come into conflict, so that there seems to be no adequate representation of the options at all. After reviewing existing proposals (...) for how to construe decision-theoretic options and finding them all wanting, I suggest that our model of rational agents should include a special domain of ‘virtual’ option propositions to serve as formal objects of deliberation and choice. (shrink)

A subject S's belief that Q is well-grounded if and only if it is based on a reason of S that gives S propositional justification for Q. Depending on the nature of S's reason, the process whereby S bases her belief that Q on it can vary. If S's reason is non-doxastic––like an experience that Q or a testimony that Q––S will need to form the belief that Q as a spontaneous and immediate response to that reason. If S's reason (...) is doxastic––like a belief that P––S will need to infer her belief that Q from it. The distinction between these two ways in which S's beliefs can be based on S's reasons is widely presupposed in current epistemology but––we argue in this paper––is not exhaustive. We give examples of quite ordinary situations in which a well-grounded belief of S appears to be based on S's reasons in neither of the ways described above. To accommodate these recalcitrant cases, we introduce the notion of enthymematic inference and defend the thesis that S can base a belief that Q on doxastic reasons P1, P2, …, Pn via inferring enthymematically Q from P1, P2, …, Pn. (shrink)

How should rational beliefs change over time? The standard Bayesian answer is: by conditionalization (a.k.a. Bayes’ Rule). But conditionalization is not an adequate rule for updating beliefs in “centred” propositions whose truth-value may itself change over time. In response, some have suggested that the objects of belief must be uncentred; others have suggested that beliefs in centred propositions are not subject to diachronic norms. Iargue that these views do not offer a satisfactory account of self-locating beliefs and their dynamics. A (...) third response is to replace conditionalization by a new norm that can deal with centred propositions. I critically survey anumber of new norms that have been proposed, and defend one particular approach. (shrink)

I argue that believing that p implies having a credence of 1 in p. This is true because the belief that p involves representing p as being the case, representing p as being the case involves not allowing for the possibility of not-p, while having a credence that’s greater than 0 in not-p involves regarding not-p as a possibility.

Jonathan Weisberg claims that certain probability assessments constructed by Jeffrey conditioning resist subsequent revision by a certain type of after-the-fact defeater of the reasons supporting those assessments, and that such conditioning is thus “inherently anti-holistic.” His analysis founders, however, in applying Jeffrey conditioning to a partition for which an essential rigidity condition clearly fails. Applied to an appropriate partition, Jeffrey conditioning is amenable to revision by the sort of after-the-fact defeaters considered by Weisberg in precisely the way that he demands.

We have several intuitive paradigms of defeating evidence. For example, let E be the fact that Ernie tells me that the notorious pet Precious is a bird. This supports the premise F, that Precious can fly. However, Orna gives me *opposing* evidence. She says that Precious is a dog. Alternatively, defeating evidence might not oppose Ernie's testimony in that direct way. There might be other ways for it to weaken the support that Ernie's testimony gives me for believing F, without (...) the new evidence itself intuitively constituting reasons to believe one way or the other about Precious's flight ability. An example: Ursula tells me that Ernie has no idea what Precious's species is; he's just guessing. She may not herself want to or be in a position to weigh in about Precious's real species or flight ability. I call defeating evidence of this sort *undermining evidence. (shrink)

Traditional procedures for rational updating fail when it comes to self-locating opinions, such as your credences about where you are and what time it is. This paper develops an updating procedure for rational agents with self-locating beliefs. In short, I argue that rational updating can be factored into two steps. The first step uses information you recall from your previous self to form a hypothetical credence distribution, and the second step changes this hypothetical distribution to reflect information you have genuinely (...) learned as time has passed. While the second step resembles traditional procedures of updating by conditionalization, the first is best understood by analogy to traditional models of how agents transmit self-locating opinions through ordinary interpersonal communication. (shrink)