In this article, I explore the compatibility of inference to the best explanation (IBE) with several influential models and accounts of scientific explanation. First, I explore the different conceptions of IBE and limit my discussion to two: the heuristic conception and the objective Bayesian conception. Next, I discuss five models of scientific explanation with regard to each model’s compatibility with IBE. I argue that Kitcher’s unificationist account supports IBE; Railton’s deductive–nomological–probabilistic model, Salmon’s statistical-relevance model, and van Fraassen’s erotetic account are (...) incompatible with IBE; and Salmon’s causal–mechanical model is merely consistent with IBE. In short, many influential models of scientific explanation do not support IBE. I end by outlining three possible conclusions to draw: (1) either philosophers of science or defenders of IBE have seriously misconstrued the concept of explanation, (2) philosophers of science and defenders of IBE do not use the term ‘explanation’ univocally, and (3) the ampliative conception of IBE, which is compatible with any model of scientific explanation, deserves a closer look. (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)

Rational credence should be coherent in the sense that your attitudes should not leave you open to a sure loss. Rational credence should be such that you can learn when confronted with relevant evidence. Rational credence should not be sensitive to irrelevant differences in the presentation of the epistemic situation. We explore the extent to which orthodox probabilistic approaches to rational credence can satisfy these three desiderata and find them wanting. We demonstrate that an imprecise probability approach does better. Along (...) the way we shall demonstrate that the problem of “belief inertia” is not an issue for a large class of IP credences, and provide a solution to van Fraassen’s box factory puzzle. (shrink)

Bayesian epistemologists support the norms of probabilism and conditionalization using Dutch book and accuracy arguments. These arguments assume that rationality requires agents to maximize practical or epistemic value in every doxastic state, which is evaluated from a subjective point of view (e.g., the agent’s expectancy of value). The accuracy arguments also presuppose that agents are opinionated. The goal of this paper is to discuss the assumptions of these arguments, including the measure of epistemic value. I have designed AI agents based (...) on the Bayesian model and a nonmonotonic framework and tested how they achieve practical and epistemic value in conditions in which an alternative set of assumptions holds. In one of the tested conditions, the nonmonotonic agent, which is not opinionated and fulfills neither probabilism nor conditionalization, outperforms the Bayesian in the measure of epistemic value that I argue for in the paper (α-value). I discuss the consequences of these results for the epistemology of rationality. (shrink)

Epistemic Utility Theory is often identified with the project of *axiology-first epistemology*—the project of vindicating norms of epistemic rationality purely in terms of epistemic value. One of the central goals of axiology-first epistemology is to provide a justification of the central norm of Bayesian epistemology, Probabilism. The first part of this paper presents a new challenge to axiology first epistemology: I argue that in order to justify Probabilism in purely axiological terms, proponents of axiology first epistemology need to justify a (...) claim about epistemic value—what I label ‘Downwards Propriety’—much stronger than any they have offered justification. The second part of this paper offers an argument that this challenge cannot be met: that there is no hope for providing a purely axiological justification of Downwards Propriety, at least given widely accepted assumptions about epistemic value. (shrink)

Imprecise probabilities are an increasingly popular way of reasoning about rational credence. However they are subject to an apparent failure to display convincing inductive learning. This paper demonstrates that a small modification to the update rule for IP allows us to overcome this problem, albeit at the cost of satisfying only a weaker concept of coherence.

How ought you to evaluate your options if you're uncertain about what's fundamentally valuable? A prominent response is Expected Value Maximisation (EVM)—the view that under axiological uncertainty, an option is better than another if and only if it has the greater expected value across axiologies. But the expected value of an option depends on quantitative probability and value facts, and in particular on value comparisons across axiologies. We need to explain what it is for such facts to hold. Also, EVM (...) is by no means self-evident. We need an argument to defend that it’s true. This book introduces an axiomatic approach to answer these worries. It provides an explication of what EVM means by use of representation theorems: intertheoretic comparisons can be understood in terms of facts about which options are better than which, and mutatis mutandis for intratheoretic comparisons and axiological probabilities. And it provides a systematic argument to the effect that EVM is true: the theory can be vindicated through simple axioms. The result is a formally cogent and philosophically compelling extension of standard decision theory, and original take on the problem of axiological or normative uncertainty. (shrink)

We argue that there is a tension between two monistic claims that are the core of recent work in epistemic consequentialism. The first is a form of monism about epistemic value, commonly known as veritism: accuracy is the sole final objective to be promoted in the epistemic domain. The other is a form of monism about a class of epistemic scoring rules: that is, strictly proper scoring rules are the only legitimate measures of inaccuracy. These two monisms, we argue, are (...) in tension with each other. If only accuracy has final epistemic value, then there are legitimate alternatives to strictly proper scoring rules. Our argument relies on the way scoring rules are used in contexts where accuracy is rewarded, such as education. (shrink)

How much does rationality constrain what we should believe on the basis of our evidence? According to this book, not very much. For most people and most bodies of evidence, there is a wide range of beliefs that rationality permits them to have in response to that evidence. The argument, which takes inspiration from William James' ideas in 'The Will to Believe', proceeds from two premises. The first is a theory about the basis of epistemic rationality. It's called epistemic utility (...) theory, and it says that what it is epistemically rational for you to believe is what it would be rational for you to choose if you were given the chance to pick your beliefs and, when picking them, you were to care only about their epistemic value. So, to say which beliefs are permitted, we must say how to measure epistemic value, and which decision rule to use when picking your beliefs. The second premise is a claim about attitudes to epistemic risk, and it says that rationality permits many different such attitudes. These attitudes can show up in epistemic utility theory in two ways: in the way you measure epistemic value; and in the decision rule you use to pick beliefs. This book explores the latter. The result is permissivism about epistemic rationality: different attitudes to epistemic risk lead to different choices of prior beliefs; given most bodies of evidence, different priors lead to different posteriors; and even once we fix your attitudes to epistemic risk, if they are at all risk-inclined, there is a range of different priors and therefore different posteriors they permit. (shrink)

Epistemic injustice is injustice to a person qua knower. In one form of this phenomenon a speaker’s testimony is denied credence in a way that wrongs them. I argue that the received definition of this testimonial injustice relies too heavily on epistemic criteria that cannot explain why the moral concept of injustice should be invoked. I give an account of the nature of the wrong of epistemic injustice that has it depend not on the accuracy of judgments that are used (...) or made in the process of deciding whether to listen to or trust a speaker, but on whether the basis of the decision about a speaker is their reliability or their identity, and the account explains why the latter is a moral wrong. A key difference between the two accounts is how they classify the use of true statistical generalizations connecting identity and reliability. The received view implies that this cannot be an injustice, while the view proposed here implies that it can. As such the new view appears to imply a conflict between moral and epistemic obligations: it is morally wrong to use true statistical generalizations in certain contexts, yet they are part of our evidence, and we are epistemically obligated to take all of our evidence into account. I reconcile these two thoughts without adopting the currently popular view that a belief’s being morally wrong makes it epistemically unjustified, and I argue that following the principle of total evidence encourages epistemic justice rather than thwarting it. (shrink)

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)

The topic of this thesis is axiological uncertainty – the question of how you should evaluate your options if you are uncertain about which axiology is true. As an answer, I defend Expected Value Maximisation (EVM), the view that one option is better than another if and only if it has the greater expected value across axiologies. More precisely, I explore the axiomatic foundations of this view. I employ results from state-dependent utility theory, extend them in various ways and interpret (...) them accordingly, and thus provide axiomatisations of EVM as a theory of axiological uncertainty. (shrink)

Normative ethical theories owe us an account of how to evaluate decisions under risk and uncertainty. Deontologists seem at a disadvantage here: our best decision theories seem tailor-made for consequentialism. For example, decision theory enjoins us to always perform our best option; deontology is more permissive. In this paper, we discuss and defend the idea that, when some pro-tanto wrongful act is all-things considered permissible, because it is a ‘lesser evil’, it is often merely permissible, by the lights of deontology. (...) We show that this raises new problems for deontological decision theory, and we show that to resolve them, we need to take a more innovative approach to morally evaluating decision-making under risk and uncertainty. (shrink)

Resource rationality may explain suboptimal patterns of reasoning; but what of “anti-Bayesian” effects where the mind updates in a direction opposite the one it should? We present two phenomena — belief polarization and the size-weight illusion — that are not obviously explained by performance- or resource-based constraints, nor by the authors’ brief discussion of reference repulsion. Can resource rationality accommodate them?

How should we reason in science? Jan Sprenger and Stephan Hartmann offer a refreshing take on classical topics in philosophy of science, using a single key concept to explain and to elucidate manifold aspects of scientific reasoning. They present good arguments and good inferences as being characterized by their effect on our rational degrees of belief. Refuting the view that there is no place for subjective attitudes in 'objective science', Sprenger and Hartmann explain the value of convincing evidence in terms (...) of a cycle of variations on the theme of representing rational degrees of belief by means of subjective probabilities (and changing them by Bayesian conditionalization). In doing so, they integrate Bayesian inference—the leading theory of rationality in social science—with the practice of 21st century science. Bayesian Philosophy of Science thereby shows how modeling such attitudes improves our understanding of causes, explanations, confirming evidence, and scientific models in general. It combines a scientifically minded and mathematically sophisticated approach with conceptual analysis and attention to methodological problems of modern science, especially in statistical inference, and is therefore a valuable resource for philosophers and scientific practitioners. (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)

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)

Duncan Pritchard’s Epistemic Angst promises a novel solution to the closure-based sceptical problem that, unlike more traditional solutions, does not entail revising our fundamental epistemological commitments. In order to do this, it appeals to a Wittgensteinian account of rational evaluation, the overarching theme of which is that it neither makes sense to doubt nor to believe in our anti-sceptical hinge commitments. The purpose of this paper is to show that the argument for the claim that there can be no rational (...) basis to believe our anti-sceptical hinge commitments relies upon an implicit assumption about rational support that I label The Pritchensteinian Rational Grounds Principle. I argue that, insofar as this principle is intended to apply to closure-style inferences, it leads to irrational doxastic attitudes. I consider a seemingly plausible modification of the principle that would avoid this result but show that this modified principle faces serious problems of its own. -/- . (shrink)

According to the traditional Bayesian view of credence, its structure is that of precise probability, its objects are descriptive propositions about the empirical world, and its dynamics are given by conditionalization. Each of the three essays that make up this thesis deals with a different variation on this traditional picture. The first variation replaces precise probability with sets of probabilities. The resulting imprecise Bayesianism is sometimes motivated on the grounds that our beliefs should not be more precise than the evidence (...) calls for. 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 the first essay I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid without compromising the initial evidentialist motivation. The second variation replaces descriptive claims with moral claims as the objects of credence. I consider three standard arguments for probabilism with respect to descriptive uncertainty—representation theorem arguments, Dutch book arguments, and accuracy arguments—in order to examine whether such arguments can also be used to establish probabilism with respect to moral uncertainty. In the second essay, I argue that by and large they can, with some caveats. First, I don’t examine whether these arguments can be given sound non-cognitivist readings, and any conclusions therefore only hold conditional on cognitivism. Second, decision-theoretic representation theorems are found to be less convincing in the moral case, because there they implausibly commit us to thinking that intertheoretic comparisons of value are always possible. Third and finally, certain considerations may lead one to think that imprecise probabilism provides a more plausible model of moral epistemology. The third variation considers whether, in addition to conditionalization, agents may also change their minds by becoming aware of propositions they had not previously entertained, and therefore not previously assigned any probability. More specifically, I argue that if we wish to make room for reflective equilibrium in a probabilistic moral epistemology, we must allow for awareness growth. In the third essay, I sketch the outline of such a Bayesian account of reflective equilibrium. Given that this account gives a central place to awareness growth, and that the rationality constraints on belief change by awareness growth are much weaker than those on belief change by conditionalization, it follows that the rationality constraints on the credences of agents who are seeking reflective equilibrium are correspondingly weaker. (shrink)

This paper looks at three ways of addressing probabilism’s implausible requirement of logical omniscience. The first and most common strategy says it’s okay to require an ideally rational person to be logically omniscient. I argue that this view is indefensible on any interpretation of ‘ideally rational’. The second strategy says probabilism should be formulated not in terms of logically possible worlds but in terms of doxastically possible worlds, ways you think the world might be. I argue that, on the interpretation (...) of this approach that lifts the requirement of certainty in all logical truths, the view becomes vacuous, issuing no requirements on rational believers at all. Finally, I develop and endorse a new solution to the problem. This view proposes dynamic norms for reasoning with credences. The solution is based on an old proposal of Ian Hacking’s that says you’re required to be sensitive to logical facts only when you know they are logical facts. (shrink)

Accuracy-first accounts of rational learning attempt to vindicate the intuitive idea that, while rationally-formed belief need not be true, it is nevertheless likely to be true. To this end, they attempt to show that the Bayesian's rational learning norms are a consequence of the rational pursuit of accuracy. Existing accounts fall short of this goal, for they presuppose evidential norms which are not and cannot be vindicated in terms of the single-minded pursuit of accuracy. I propose an alternative account, according (...) to which learning experiences rationalize changes in the way you value accuracy, which in turn rationalize changes in belief. I show that this account is capable of vindicating the Bayesian's rational learning norms in terms of the single-minded pursuit of accuracy, so long as accuracy is rationally valued. (shrink)

In this paper, I present an argument for a rational norm involving a kind of credal attitude called a quantificational credence – the kind of attitude we can report by saying that Lucy thinks that each record in Schroeder’s collection is 5% likely to be scratched. I prove a result called a Dutch Book Theorem, which constitutes conditional support for the norm. Though Dutch Book Theorems exist for norms on ordinary and conditional credences, there is controversy about the epistemic significance (...) of these results. So, my conclusion is that if Dutch Book Theorems do, in general, support norms on credal states, then we have support for the suggested norm on quantificational credences. Providing conditional support for this norm gives us a fuller picture of the normative landscape of credal states. (shrink)

The main question of this paper is: how do we manage to know what our own degrees of belief are? Section 1 briefly reviews and criticizes the traditional functionalist view, a view notably associated with David Lewis and sometimes called the theory-theory. I use this criticism to motivate the approach I want to promote. Section 2, the bulk of the paper, examines and begins to develop the view that we have a special kind of introspective access to our degrees of (...) belief. I give an initial assessment of the view by examining its compatibility with leading theories of introspection. And I identify a challenge for the view, and explain why I'm optimistic that the view can overcome it. (shrink)

This paper considers two questions. First, what is the scope of the Equal Weight View? Is it the case that meeting halfway is the uniquely rational method of belief-revision in all cases of known peer disagreement? The answer is no. It is sometimes rational to maintain your own opinion in the face of peer disagreement. But this leaves open the possibility that the Equal Weight View is indeed sometimes the uniquely rational method of belief revision. Precisely what is the skeptical (...) import of this fact; is it the case that some form of skepticism triumphs in such cases? The answer to this question is also no. As it turns out, the situations in which it is most plausible that the Equal Weight view is a rational requirement are the ones in which meeting halfway with a disagreeing peer brings you closer to, and not farther from, knowledge. I argue for these theses in a novel way; by looking at the comparative reliability of belief- invariance and meeting halfway using measures of reliability for degrees of belief, and by drawing normative conclusions from such results. The conclusions here can have the effect of reframing the entire debate in the epistemology of disagreement. (shrink)

The twin goals of this essay are: to investigate a family of cases in which the goal of guaranteed convergence to the truth is beyond our reach; and to argue that each of three strands prominent in contemporary epistemological thought has undesirable consequences when confronted with the existence of such problems. Approaches that follow Reichenbach in taking guaranteed convergence to the truth to be the characteristic virtue of good methods face a vicious closure problem. Approaches on which there is a (...) unique rational doxastic response to any given body of evidence can avoid incoherence only by rendering epistemology a curiously limited enterprise. Bayesian approaches rule out humility about one’s prospects of success in certain situations in which failure is typical. (shrink)

In Bayesian epistemology, the problem of the priors is this: How should we set our credences (or degrees of belief) in the absence of evidence? That is, how should we set our prior or initial credences, the credences with which we begin our credal life? David Lewis liked to call an agent at the beginning of her credal journey a superbaby. The problem of the priors asks for the norms that govern these superbabies. -/- The Principle of Indifference gives a (...) very restrictive answer. It demands that such an agent divide her credences equally over all possibilities. That is, according to the Principle of Indifference, only one initial credence function is permissible, namely, the uniform distribution. In this paper, we offer a novel argument for the Principle of Indifference. I call it the Argument from Accuracy. (shrink)

In this paper I argue that it is finally time to move beyond the Nagelian framework and to break new ground in thinking about epistemic reduction in biology. I will do so, not by simply repeating all the old objections that have been raised against Ernest Nagel’s classical model of theory reduction. Rather, I grant that a proponent of Nagel’s approach can handle several of these problems but that, nevertheless, Nagel’s general way of thinking about epistemic reduction in terms of (...) theories and their logical relations is entirely inadequate with respect to what is going on in actual biological research practice. (shrink)

In this paper we discuss the new Tweety puzzle. The original Tweety puzzle was addressed by approaches in non-monotonic logic, which aim to adequately represent the Tweety case, namely that Tweety is a penguin and, thus, an exceptional bird, which cannot fly, although in general birds can fly. The new Tweety puzzle is intended as a challenge for probabilistic theories of epistemic states. In the first part of the paper we argue against monistic Bayesians, who assume that epistemic states can (...) at any given time be adequately described by a single subjective probability function. We show that monistic Bayesians cannot provide an adequate solution to the new Tweety puzzle, because this requires one to refer to a frequency-based probability function. We conclude that monistic Bayesianism cannot be a fully adequate theory of epistemic states. In the second part we describe an empirical study, which provides support for the thesis that monistic Bayesianism is also inadequate as a descriptive theory of cognitive states. In the final part of the paper we criticize Bayesian approaches in cognitive science, insofar as their monistic tendency cannot adequately address the new Tweety puzzle. We, further, argue against monistic Bayesianism in cognitive science by means of a case study. In this case study we show that Oaksford and Chater’s (2007, 2008) model of conditional inference—contrary to the authors’ theoretical position—has to refer also to a frequency-based probability function. (shrink)

Jeff Paris proves a generalized Dutch Book theorem. If a belief state is not a generalized probability then one faces ‘sure loss’ books of bets. In Williams I showed that Joyce’s accuracy-domination theorem applies to the same set of generalized probabilities. What is the relationship between these two results? This note shows that both results are easy corollaries of the core result that Paris appeals to in proving his dutch book theorem. We see that every point of accuracy-domination defines a (...) dutch book, but we only have a partial converse. (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)

Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a result, we (...) should reject these claims, and lay the foundations of decision theory on firmer ground. (shrink)

Philosophers of science have often favoured reductive approaches to how-possibly explanation. This article identifies three alternative conceptions making how-possibly explanation an interesting phenomenon in its own right. The first variety approaches “how possibly X?” by showing that X is not epistemically impossible. This can sometimes be achieved by removing misunderstandings concerning the implications of one’s current belief system but involves characteristically a modification of this belief system so that acceptance of X does not result in contradiction. The second variety offers (...) a potential how-explanation of X. It is usually followed by a range of further potential how-explanations of the same phenomenon. In recent literature the factual claims implied by the second variety have been downplayed whereas the heuristic role of mapping the space of conceptual possibilities has been emphasized. I will focus especially on this truth-bracketing sense of potentiality when looking closer at the second variety in the paper. The third variety has attracted less interest. It presents a partial how-explanation of X. Typically it aims to establish the existence of a mechanism by which X could be and was generated. The third conception stands out as the natural alternative for the advocate of ontic how-possibly explanations. This article transfers Salmon’s view that explanation-concepts can be broadly divided into epistemic, modal, and ontic to the context of how-possibly explanations. Moreover, it is argued that each of the three above-mentioned varieties of how-possibly explanation occurs in science. To recognize this may be especially relevant for philosophers. We are often misled by the promises of various why-explanation accounts, and seem to have forgotten nearly everything about the diversity of how-possibly explanations. (shrink)

Proponents of Bayesian confirmation theory believe that they have the solution to a significant, recalcitrant problem in philosophy of science. It is the identification of the logic that governs evidence and its inductive bearing in science. That is the logic that lets us say that our catalog of planetary observations strongly confirms Copernicus’ heliocentric hypothesis; or that the fossil record is good evidence for the theory of evolution; or that the 3oK cosmic background radiation supports big bang cosmology. The definitive (...) solution to this problem would be a significant achievement. The problem is of central importance to philosophy of science, for, in the end, what distinguishes science from myth making is that we have good evidence for the content of science, or at least of mature sciences, whereas myths are evidentially ungrounded fictions. The core ideas shared by all versions of Bayesian confirmation theory are, at a good first approximation, that a scientist’s beliefs are or should conform to a probability measure; and that the incorporation of new evidence is through conditionalization using Bayes’ theorem. While the burden of this chapter will be to inventory why critics believe this theory may not be the solution after all, it is worthwhile first to summarize here the most appealing virtues of this simple account. There are three. First, the theory reduces the often nebulous notion of a logic of.. (shrink)

The paper provides an argument for the thesis that an agent’s degrees of disbelief should obey the ranking calculus. This Consistency Argument is based on the Consistency Theorem. The latter says that an agent’s belief set is and will always be consistent and deductively closed iff her degrees of entrenchment satisfy the ranking axioms and are updated according to the ranktheoretic update rules.

Recent literature on Stalnaker's Thesis, which seeks to vindicate it from Lewis (1976)'s triviality results, has featured linguistic data that is prima facie incompatible with Conditionalization in iterated cases (McGee 1989, 2000; Kaufmann 2015; Khoo & Santorio, 2018). In a recent paper (2021), Goldstein & Santorio make a bold claim: they hold that these departures light the way to a new, non‐conditionalizing theory of rational update.Here, I consider whether this new form of update is subject to a Dutch book. On (...) the official, invariantist version of the theory, I show that the answer is “yes”. On a competing, contextualist theory of indicative conditionals (Bacon, 2015), the answer is “no”, for reasons that have familiar connections to the limits of textbook Bayesianism. After presenting a concrete case, I explore the dialectical ramifications. The upshot is some hard choices for theories that seek to save the linguistic phenomena. (shrink)

– 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)

Policymakers who seek to make scientifically informed decisions are constantly confronted by scientific uncertainty and expert disagreement. This thesis asks: how can policymakers rationally respond to expert disagreement and scientific uncertainty? This is a work of non-ideal theory, which applies formal philosophical tools developed by ideal theorists to more realistic cases of policymaking under scientific uncertainty. I start with Bayesian approaches to expert testimony and the problem of expert disagreement, arguing that two popular approaches— supra-Bayesianism and the standard model of (...) expert deference—are insufficient. I develop a novel model of expert deference and show how it can deal with many of these problems raised for them. I then turn to opinion pooling, a popular method for dealing with disagreement. I show that various theoretical motivations for pooling functions are irrelevant to realistic policymaking cases. This leads to a cautious recommendation of linear pooling. However, I then show that any pooling method relies on value judgements, that are hidden in the selection of the scoring rule. My focus then narrows to a more specific case of scientific uncertainty: multiple models of the same system. I introduce a particular case study involving hurricane models developed to support insurance decision-making. I recapitulate my analysis of opinion pooling in the context of model ensembles, confirming that my hesitations apply. This motivates a shift of perspective, to viewing the problem as a decision theoretic one. I rework a recently developed ambiguity theory, called the confidence approach, to take input from model ensembles. I show how it facilitates the resolution of the policymaker’s problem in a way that avoids the issues encountered in previous chapters. This concludes my main study of the problem of expert disagreement. In the final chapter, I turn to methodological reflection. I argue that philosophers who employ the mathematical methods of the prior chapters are modelling. Employing results from the philosophy of scientific models, I develop the theory of normative modelling. I argue that it has important methodological conclusions for the practice of formal epistemology, ruling out popular moves such as searching for counterexamples. (shrink)

We point out a yet unnoticed flaw in Dutch Book arguments that relates to a link between degrees of belief and betting quotients. We offer a set of precise conditions governing when a nonprobabilist is immune to the classical Dutch Book argument. We suggest that diachronic Dutch Book arguments are also affected.

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.

Joyce () argues that for any credence function that doesn't satisfy the probability axioms, there is another function that dominates it in terms of accuracy. But if some potential credence functions are ruled out as violations of the Principal Principle, then some non‐probabilistic credence functions fail to be dominated. We argue that to fix Joyce's argument, one must show that all epistemic values for credence functions derive from accuracy.

Many philosophers have become worried about the use of standard real numbers for the probability function that represents an agent's credences. They point out that real numbers can't capture the distinction between certain extremely unlikely events and genuinely impossible ones—they are both represented by credence 0, which violates a principle known as “regularity.” Following Skyrms 1980 and Lewis 1980, they recommend that we should instead use a much richer set of numbers, called the “hyperreals.” This essay argues that this popular (...) view is the result of two mistakes. The first mistake, which this essay calls the “numerical fallacy,” is to assume that a distinction that isn't represented by different numbers isn't represented at all in a mathematical representation. In this case, the essay claims that although the real numbers do not make all relevant distinctions, the full mathematical structure of a probability function does. The second mistake is that the hyperreals make too many distinctions. They have a much more complex structure than credences in ordinary propositions can have, so they make distinctions that don't exist among credences. While they might be useful for generating certain mathematical models, they will not appear in a faithful mathematical representation of credences of ordinary propositions. (shrink)

If we add as an extra premise that the agent does know H, then it is possible for her to know E — H, we get the conclusion that the agent does not really know H. But even without that closure premise, or something like it, the conclusion seems quite dramatic. One possible response to the argument, floated by both Descartes and Hume, is to accept the conclusion and embrace scepticism. We cannot know anything that goes beyond our evidence, so (...) we do not know very much at all. This is a remarkably sceptical conclusion, so we should resist it if at all possible. A more modern response, associated with externalists like John McDowell and Timothy Williamson, is to accept the conclusion but deny it is as sceptical as it first appears. The Humean argument, even if it works, only shows that our evidence and our knowledge are more closely linked than we might have thought. Perhaps that’s true because we have a lot of evidence, not because we have very little knowledge. There’s something right about this response I think. We have more evidence than Descartes or Hume thought we had. But I think we still need the idea of ampliative knowledge. It stretches the concept of evidence to breaking point to suggest that all of our knowledge, including knowledge about the future, is part of our evidence. So the conclusion really is unacceptable. Or, at least, I think we should try to see what an epistemology that rejects the conclusion looks like. (shrink)

Elga (2010) argues that no plausible decision rule governs action with imprecise credences. I follow Moss (2015a) in claiming that the solution to Elga’s challenge is found in the philosophy of mind, not in devising a special new decision rule. Moss suggests that in decision situations that involve imprecise credences, we must identify with a precise credence, but she says little about identification. By reflecting on the common conception of identification and on what is necessary for Moss’s solution to succeed, (...) I argue that identifying with a precise credence is fundamentally accepting (in the sense of Bratman 1992; Cohen 1989) a proposition about probabilities. The norm on action with imprecise credences is then a special case of the general norm on action and acceptance. I delineate a number of attractive features of this position. (shrink)

I give a Dutch book argument for CDT thirders in the context of a generalized Sleeping Beauty scenario. In combination with the Briggs (2010) Dutch book for EDT thirders, this amounts to a purely decision-theoretic argument for halfing in Sleeping Beauty. In combination with the Hitchcock (2004) Dutch book for CDT halfers, this amounts to a Dutch book argument against CDT. The combined Dutch book against CDT invites a plausible diagnosis of the reasons for CDT’s failure: CDT is incompatible with (...) the Dutch book requirement because it allows the values of epistemically impossible outcomes influence one’s decision. (shrink)

Norms—that is, specifications of what we ought to do—play a critical role in the study of informal argumentation, as they do in studies of judgment, decision-making and reasoning more generally. Specifically, they guide a recurring theme: are people rational? Though rules and standards have been central to the study of reasoning, and behavior more generally, there has been little discussion within psychology about why (or indeed if) they should be considered normative despite the considerable philosophical literature that bears on this (...) topic. In the current paper, we ask what makes something a norm, with consideration both of norms in general and a specific example: norms for informal argumentation. We conclude that it is both possible and desirable to invoke norms for rational argument, and that a Bayesian approach provides solid normative principles with which to do so. (shrink)