This is a three-part exchange on the relationship between belief and credence. It begins with an opening essay by Roger Clarke that argues for the claim that the notion of credence generalizes the notion of belief. Julia Staffel argues in her reply that we need to distinguish between mental states and models representing them, and that this helps us explain what it could mean that belief is a special case of credence. Roger Clarke's final essay reflects on the compatibility of (...) the previously discussed views with dualist and monist interpretations of our mental states and our ways of modeling them. (shrink)

Several authors have investigated the question of whether canonical logic-based accounts of belief revision, and especially the theory of AGM revision operators, are compatible with the dynamics of Bayesian conditioning. Here we show that Leitgeb's stability rule for acceptance, which has been offered as a possible solution to the Lottery paradox, allows to bridge AGM revision and Bayesian update: using the stability rule, we prove that AGM revision operators emerge from Bayesian conditioning by an application of the principle of maximum (...) entropy. In situations of information loss, or whenever the agent relies on a qualitative description of her information state - such as a plausibility ranking over hypotheses, or a belief set - the dynamics of AGM belief revision are compatible with Bayesian conditioning; indeed, through the maximum entropy principle, conditioning naturally generated AGM revision operators. This mitigates an impossibility theorem of Lin and Kelly for tracking Bayesian conditioning with AGM revision, and suggests an approach to the compatibility problem that highlights the information loss incurred by acceptance rules in passing from probabilistic to qualitative representations of beliefs. (shrink)

It seems obvious that when higher-order evidence makes it rational for one to doubt that one’s own belief on some matter is rational, this can undermine the rationality of that belief. This is known as higher-order defeat. However, despite its intuitive plausibility, it has proved puzzling how higher-order defeat works, exactly. To highlight two prominent sources of puzzlement, higher-order defeat seems to defy being understood in terms of conditionalization; and higher-order defeat can sometimes place agents in what seem like epistemic (...) dilemmas. This chapter draws attention to an overlooked aspect of higher-order defeat, namely that it can undermine the resilience of one’s beliefs. The notion of resilience was originally devised to understand how one should reflect the ‘weight’ of one’s evidence. But it can also be applied to understand how one should reflect one’s higher-order evidence. The idea is particularly useful for understanding cases where one’s higher-order evidence indicates that one has failed in correctly assessing the evidence, without indicating whether one has over- or underestimated the degree of evidential support for a proposition. But it is exactly in such cases that the puzzles of higher-order defeat seem most compelling. (shrink)

Pérez Carballo adopts an epistemic utility theory picture of epistemic norms where epistemic utility functions measure the value of degrees of belief, and rationality consists in maximizing expected epistemic utility. Within this framework he seeks to show that we can make sense of the intuitive idea that some true beliefs—say true beliefs about botany—are more valuable than other true beliefs—say true beliefs about the precise number of plants in North Dakota. To do so, however, Pérez Carballo argues that we must (...) think of the value of epistemic states as consisting in more than simply accuracy. This sheds light on which questions it is most epistemically valuable to pursue. (shrink)

An aspect of Peirce’s thought that may still be underappreciated is his resistance to what Levi calls _pedigree epistemology_, to the idea that a central focus in epistemology should be the justification of current beliefs. Somewhat more widely appreciated is his rejection of the subjective view of probability. We argue that Peirce’s criticisms of subjectivism, to the extent they grant such a conception of probability is viable at all, revert back to pedigree epistemology. A thoroughgoing rejection of pedigree in the (...) context of probabilistic epistemology, however, _does_ challenge prominent subjectivist responses to the problem of the priors. (shrink)

Focusing on cases which involve binding into epistemic modals with definite descriptions and quantifiers, I raise some new problems for standard approaches to all of these expressions. The difficulties are resolved in a semantic framework that is dynamic in character. I close with a new class of problems about de re readings within the scope of modals.

When a proposition is established, it can be taken as evidence for other propositions. Can the Bayesian theory of rational belief and action provide an account of establishing? I argue that it can, but only if the Bayesian is willing to endorse objective constraints on both probabilities and utilities, and willing to deny that it is rationally permissible to defer wholesale to expert opinion. I develop a new account of deference that accommodates this latter requirement.

Direct inferences identify certain probabilistic credences or confirmation-function-likelihoods with values of objective chances or relative frequencies. The best known version of a direct inference principle is David Lewis’s Principal Principle. Certain kinds of statements undermine direct inferences. Lewis calls such statements inadmissible. We show that on any Bayesian account of direct inference several kinds of intuitively innocent statements turn out to be inadmissible. This may pose a significant challenge to Bayesian accounts of direct inference. We suggest some ways in which (...) these challenges may be addressed. (shrink)

Legal probabilism is the view that juridical fact-finding should be modeled using Bayesian methods. One of the alternatives to it is the narration view, according to which instead we should conceptualize the process in terms of competing narrations of what happened. The goal of this paper is to develop a reconciliatory account, on which the narration view is construed from the Bayesian perspective within the framework of formal Bayesian epistemology.

The Stability of Belief: How Rational Belief Coheres with Probability, by LeitgebHannes. Oxford: Oxford University Press, 2017. Pp. xiv + 365.

The world is said to contain crystal balls whenever the present carries news of the as-yet-undetermined parts of the future. Many philosophers believe that crystal balls are metaphysically possible. In this essay, I argue that they are not. Whether crystal balls are possible matters, for at least two reasons. The first is epistemological. According to a simple, user-friendly chance norm for credence, which I call the Present Principle, agents are rationally required to conform their credences to their expectations of the (...) present chances, deferring to the present chances as they would to an expert. I would like to defend the Present Principle since its truth would do much to simplify the relation between chance and credence. But the Present Principle is counterexample-free, and hence defensible, only if crystal balls are impossible. The second reason is decision-theoretic. The problem of crystal balls is one of the main objections to causal decision theory. But crystal ball cases can be counterexample to causal decision theory only if crystal balls are possible, and, as I argue, crystal balls are not possible. (shrink)

William Roche and Elliott Sober argue that explanatoriness is evidentially irrelevant. This conclusion is surprising since it conflicts with a plausible assumption—the fact that a hypothesis best explains a given set of data is evidence that the hypothesis is true. We argue that Roche and Sober's screening-off argument fails to account for a key aspect of evidential strength: the weight of a body of evidence. The weight of a body of evidence affects the resiliency of probabilities in the light of (...) new evidence. Thus, Roche and Sober are mistaken. Explanatoriness is evidentially relevant. (shrink)

The aim of this paper is to provide a detailed characterisation of some ways in which our preferences reflect our reasons. I will argue that practical reasons can be characterised along two dimensions that influence our preferences: their balance and their weight. This is analogous to a similar characterisation of the way in which probabilities reflect the balance and weight of evidence in epistemology. In this paper, I will illustrate the distinction between the balance and weight of reasons, and show (...) how this is crucial for an adequate account of preference and choice. The upshot is a more complete picture of a particular kind of decision, labelled by Isaac Levi and, more recently, Ruth Chang as ‘hard choices’. These are choices in which one option is better than another in some ways, the other is better than the first in some ways, but neither seems better overall. The distinction between the balance and weight of reasons presents a new way of understanding how hard choices vary by degree and what it is that makes them so hard. (shrink)

This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, this essay will show that this combination of principles is satisfiable (and indeed nontrivially so) and that the principles (...) are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as will be argued in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc and that has various philosophical features that are plausible independently. In particular, this essay shows that the theory allows for a solution to the Lottery Paradox, and it has nice applications to formal epistemology. The price that is to be paid for this theory is a strong dependency of belief on the context, where a context involves both the agent's degree of belief function and the partitioning or individuation of the underlying possibilities. But as this essay argues, that price seems to be affordable. (shrink)

Is it possible to give an explicit definition of belief in terms of subjective probability, such that believed propositions are guaranteed to have a sufficiently high probability, and yet it is neither the case that belief is stripped of any of its usual logical properties, nor is it the case that believed propositions are bound to have probability 1? We prove the answer is ‘yes’, and that given some plausible logical postulates on belief that involve a contextual “cautiousness” threshold, there (...) is but one way of determining the extension of the concept of belief that does the job. The qualitative concept of belief is not to be eliminated from scientific or philosophical discourse, rather, by reducing qualitative belief to assignments of resiliently high degrees of belief and a “cautiousness” threshold, qualitative and quantitative belief turn out to be governed by one unified theory that offers the prospects of a huge range of applications. Within that theory, logic and probability theory are not opposed to each other but go hand in hand. (shrink)

This paper suggests a bridge principle for all-or-nothing belief and degrees of belief to the effect that belief corresponds to stably high degree of belief. Different ways of making this Humean thesis on belief precise are discussed, and one of them is shown to stand out by unifying the others. The resulting version of the thesis proves to be fruitful in entailing the logical closure of belief, the Lockean thesis on belief, and coherence between decision-making based on all-or-nothing beliefs and (...) on degrees of belief. (shrink)

A new justification of probabilism is developed that pays close attention to the structure of the underlying space of possibilities. Its central assumption is that rational numerical degrees of bel...

(2014). Exploring the Stability of Belief: Resiliency and Temptation. Inquiry: Vol. 57, The Nature of Belief, pp. 1-27. doi: 10.1080/0020174X.2014.858414.

While practitioners think highly of randomized studies, some philosophers argue that there is no epistemic reason to randomize. Here I show that their arguments do not entail their conclusion. Moreover, I provide novel reasons for randomizing in the context of interventional studies. The overall discussion provides a unified framework for assessing baseline balance, one that holds for interventional and observational studies alike. The upshot: practitioners’ strong preference for randomized studies can be defended in some cases, while still offering a nuanced (...) approach to evidence-appraisal, one where not all non-randomized studies are treated equally. (shrink)

Weight of evidence continues to be a powerful metaphor within formal approaches to epistemology. But attempts to construe the metaphor in precise and useful ways have encountered formidable obstacles. This paper shows that two quite different understandings of evidential weight can be traced back to one 1878 article by C.S. Peirce. One conception, often associated with I.J. Good, measures the balance or net weight of evidence, while the other, generally associated with J.M. Keynes, measures the gross weight of evidence. Conflations (...) of these two notions have contributed to misunderstandings in the literature on weight. This paper shows why Peirce developed each conception of weight, why he distinguished them, and why they are easily mistaken for one another. (shrink)

Peirce makes it clear that doubt and belief oppose one another. But that slogan admits of a weaker and a stronger reading. The weaker reading permits and the stronger reading forbids one to be in a state of doubt and of belief with respect to the same proposition at the same time. The stronger claim is standardly attributed to Peirce, for textual and philosophical reasons. This paper maintains that this standard construal is excessively strong. It argues that the secondary literature (...) tends to presuppose the strong reading and that it often does so by confusing sufficient conditions for belief with necessary ones. It acknowledges some textual evidence on behalf of the strong reading but maintains that,taken as a whole, the relevant passages are as friendly to the weak as to the strong interpretation of Peirce. The paper then links the doubt–belief theory of“The Fixation of Belief” to the papers on probability that occupy the bulk of the Illustrations of the Logic of Science. It shows that Peirce's discussion of probability, strength of belief, and weight of evidence makes room for confidence, but not belief, to be undermined and thus offers a more flexible version of Peirce's theory of inquiry. (shrink)

Most legal evidence scholars agree that proof of guilt beyond a reasonable doubt requires the belief that the defendant probably committed the alleged acts. However, they also agree that this is not a sufficient condition, as this belief may be unreasonable. I focus on two popular proposals for additional conditions: (i) that the degree of belief should be robust and (ii) that it should be reasonable given the available evidence (should be an evidential probability). Both criteria face difficulties regarding their (...) meaning and utility. I propose an interpretation which overcomes these difficulties and which combines the two conditions into a single criterion on which both conditions are about the possibility of overlooked, exculpatory information. Proof of guilt beyond a reasonable doubt requires that we are sufficiently certain that we did not miss such information for the sake of achieving accurate beliefs and a just error distribution. How certain we can be that we did not miss anything relevant depends on our higher-order evidence. One important type of higher-order evidence is whether the hypotheses under consideration are sufficiently detailed. This point leads to a novel way of combining the Bayesian and explanation-based accounts of rational legal proof. (shrink)

Abstract:The standard, Bayesian account of rational belief and decision is often argued to be unable to cope properly with severe uncertainty, of the sort ubiquitous in some areas of policy making. This paper tackles the question of what should replace it as a guide for rational decision making. It defends a recent proposal, which reserves a role for the decision maker’s confidence in beliefs. Beyond being able to cope with severe uncertainty, the account has strong normative credentials on the main (...) fronts typically evoked as relevant for rational belief and decision. It fares particularly well, we argue, in comparison to other prominent non-Bayesian models in the literature. (shrink)

There has been considerable puzzlement over how to respond to higher-order evidence. The existing dilemmas can be defused by adopting a ‘two-dimensional’ representation of doxastic attitudes which incorporates not only substantive uncertainty about which first-order state of affairs obtains but also the degree of conviction with which we hold the attitude. This makes it possible that in cases of higher-order evidence the evidence sometimes impacts primarily on our conviction, rather than our substantive uncertainty. I argue that such a two-dimensional representation (...) is naturally developed by making use of imprecise probabilities. (shrink)

We argue that social deliberation may increase an agent’s confidence and credence under certain circumstances. An agent considers a proposition H and assigns a probability to it. However, she is not fully confident that she herself is reliable in this assignment. She then endorses H during deliberation with another person, expecting him to raise serious objections. To her surprise, however, the other person does not raise any objections to H. How should her attitudes toward H change? It seems plausible that (...) she should increase the credence she assigns to H and, at the same time, increase the reliability she assigns to herself concerning H. A Bayesian model helps us to investigate under what conditions, if any, this is rational. (shrink)

The strongest possible Lewisian triviality result for the indicative conditional is proven.

Wilcox proposed an argument against imprecise probabilities and for the principle of indifference based on a thought experiment where he argues that it is very intuitive to feel that one’s confidence in drawing a ball of a given colour out of an unknown urn should decrease while the number of potential colours in the urn increases. In my response to him, I argue that one’s intuitions may be unreliable because it is very hard to truly feel completely ignorant in such (...) a situation. I further argue that Wilcox must also account for the conflicting intuition that it is absurd to have to feel completely convinced that a specific claim about reality is true _in the absence of any evidence_ in order to avoid being irrational. It is dubious that this intuition is considerably less universal and strongly-held than Wilcox’s own intuition. Finally, I point out that even if Wilcox’s intuition were to be universally shared among members of our biological species, it is far from being clear that someone refusing to let that intuition dictate his or her beliefs would be irrational. For all these reasons, I believe that Wilcox was not successful in proving that philosophers and scientists representing uncertainty through imprecise probabilities are violating the principles of rationality. (shrink)

I argue that there is a prima facie tension between solutions to the problem of fake news and solutions to the problem presented by various cognitive biases that dispose us to dismiss evidence against our prior beliefs (what might seem to be the driving force behind echo chambers). We can guard against fake news by strengthening belief. But we can exit echo chambers by becoming more sensitive to counterevidence, which seems to require weakening our beliefs. I resolve the tension by (...) arguing against an injunction to weaken belief in the required ways. In particular, there is no injunction to be open-minded in all circumstances toward various counterarguments, even those whose premises seem compelling and in which we can’t expose a flaw. On the contrary, there are circumstances in which you should, in the relevant sense, be closed-minded toward such counterarguments. (shrink)

It is bad news to find out that one's cognitive or perceptual faculties are defective. Furthermore, it’s not always transparent how one ought to revise one's beliefs in light of such news. Two sorts of news should be distinguished. On the one hand, there is news that a faculty is unreliable -- that it doesn't track the truth particularly well. On the other hand, there is news that a faculty is anti-reliable -- that it tends to go positively wrong. These (...) two sorts of news call for extremely different responses. We provide accounts of these responses, and prove bounds on the degree to which one can reasonably count oneself as mistaken about a given subject matter. (shrink)

This paper shows how a particular resiliency-centered approach to chance lends support for two conditions characterizing chance. The first condition says that the present chance of some proposition A conditional on the proposition about some later chance of A should be set equal to that later chance of A. The second condition requires the present chance of some proposition A to be equal to the weighted average of possible later chances of A. I first introduce, motivate, and make precise a (...) resiliency-centered approach to chance whose basic idea is that any chance distribution should be maximally invariant under variation of experimental factors. Second, I show that any present chance distribution that violates the two conditions can be replaced by another present chance distribution that satisfies them and is more resilient under variation of experimental factors. This shows that the two conditions are an essential feature of chances that maximize resiliency. Finally, I explore the relationship between the idea of resilient chances so understood and so-called Humean accounts of chance—one of the most promising recent philosophical accounts of chance. (shrink)

This paper argues that there is an important connection between Inference to the Best Explanation and Bayesianism, in the medical context of the interplay between mechanisms and population studies. It is argued that the criteria for evaluating mechanistic evidence can be used in Inference to the Best Explanation and such use thereby increases the resilience of probabilities in a Bayesian framework. This point grows out of the emerging literature on evidence-based medicine and naturally strengthens McCain and Poston's proposal that explanatory (...) information is evidentially relevant. (shrink)

Does rationality require imprecise credences? Many hold that it does: imprecise evidence requires correspondingly imprecise credences. I argue that this is false. The imprecise view faces the same arbitrariness worries that were meant to motivate it in the first place. It faces these worries because it incorporates a certain idealization. But doing away with this idealization effectively collapses the imprecise view into a particular kind of precise view. On this alternative, our attitudes should reflect a kind of normative uncertainty: uncertainty (...) about what to believe. This view refutes the claim that precise credences are inappropriately informative or committal. Some argue that indeterminate evidential support requires imprecise credences; but I argue that indeterminate evidential support instead places indeterminate requirements on credences, and is compatible with the claim that rational credences may always be precise. (shrink)

This paper offers a theory of how epistemic and practical reasons for belief can be combined into all‐things‐considered reason. Unlike alternative theories, it does not involve any sharp cut‐offs or lexical priorities among types of reason. The theory allows that the relative strengths of the practical and epistemic reasons matter, as does the distance between the epistemically rational credence and the practically rational credence. Although there are important differences between the structure of epistemic and practical reason, they can still be (...) combined in a satisfactory way. The central idea is that epistemic reason determines an epistemically rational doxastic state, and practical reason can push it around. (shrink)

We propose a new model for forming and revising beliefs about unknown probabilities. To go beyond what is known with certainty and represent the agent’s beliefs about probability, we consider a plausibility map, associating to each possible distribution a plausibility ranking. Beliefs are defined as in Belief Revision Theory, in terms of truth in the most plausible worlds. We consider two forms of conditioning or belief update, corresponding to the acquisition of two types of information: learning observable evidence obtained by (...) repeated sampling from the unknown distribution; and learning higher-order information about the distribution. The first changes only the plausibility map, but leaves the given set of possible distributions essentially unchanged; the second rules out some distributions, thus shrinking the set of possibilities, without changing their plausibility ordering.. We look at stability of beliefs under either of these types of learning, defining two related notions, as well as a measure of the verisimilitude of a given plausibility model. We prove a number of convergence results, showing how our agent’s beliefs track the true probability after repeated sampling, and how she eventually gains in a sense knowledge of that true probability. Finally, we sketch the contours of a dynamic doxastic logic for statistical learning. (shrink)

This book illustrates the program of Logical-Informational Dynamics. Rational agents exploit the information available in the world in delicate ways, adopt a wide range of epistemic attitudes, and in that process, constantly change the world itself. Logical-Informational Dynamics is about logical systems putting such activities at center stage, focusing on the events by which we acquire information and change attitudes. Its contributions show many current logics of information and change at work, often in multi-agent settings where social behavior is essential, (...) and often stressing Johan van Benthem's pioneering work in establishing this program. However, this is not a Festschrift, but a rich tapestry for a field with a wealth of strands of its own. The reader will see the state of the art in such topics as information update, belief change, preference, learning over time, and strategic interaction in games. Moreover, no tight boundary has been enforced, and some chapters add more general mathematical or philosophical foundations or links to current trends in computer science. The theme of this book lies at the interface of many disciplines. Logic is the main methodology, but the various chapters cross easily between mathematics, computer science, philosophy, linguistics, cognitive and social sciences, while also ranging from pure theory to empirical work. Accordingly, the authors of this book represent a wide variety of original thinkers from different research communities. And their interconnected themes challenge at the same time how we think of logic, philosophy and computation. Thus, very much in line with van Benthem's work over many decades, the volume shows how all these disciplines form a natural unity in the perspective of dynamic logicians (broadly conceived) exploring their new themes today. And at the same time, in doing so, it offers a broader conception of logic with a certain grandeur, moving its horizons beyond the traditional study of consequence relations. (shrink)

This thesis explores attempts to characterise the structure of reality. Three notions stand out: Lewisian naturalness, Sider’s ‘structure’, and grounding, where the latter has become the most popular way to characterise the structure of reality in the contemporary literature. I argue that none of these notions, as they are currently understood, are suited for limning the metaphysical structure of reality. In the first part of the thesis I argue that, by the lights of the relevant theories, both naturalness and structure (...) fall short of the theoretical role carved out for those posits. In the second part of the thesis I present two challenges to the ‘orthodox’ conception of grounding. The first contests the standard assumption that grounding is asymmetric, both by citing what I take to be best described as symmetric instances of grounding, and by developing and arguing for a new theory of metaphysical structure – ‘metaphysical interdependence’ – which takes grounding to be nonsymmetric. The second challenge concerns the relationship between grounding and explanation, and leads to a dilemma for the grounding theorist. My proposed resolution to the dilemma is to adopt an antirealist approach to grounding, which I further motivate and develop in the final chapter. (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)

My dissertation asks how we affect conversational context and how it affects us when we participate in any conversation—including philosophical conversations. Chapter 1 argues that speakers make pragmatic presuppositions when they use proper names. I appeal to these presuppositions in giving a treatment of Frege’s puzzle that is consistent with the claim that coreferential proper names have the same semantic value. I outline an explanation of the way presupposition carrying expressions in general behave in belief ascriptions, and suggest that substitutivity (...) failure is a special case of this behavior. Chapter 2 develops a compositional probabilistic semantics for the language of subjective uncertainty, including epistemic adjectives scoped under quantifiers. I argue that we should distinguish sharply between the effects that epistemically hedged statements have on conversational context, and the effects that they have on belief states. I also suggest that epistemically hedged statements are a kind of doxastic advice, and explain how this hypothesis illuminates some otherwise puzzling phenomena. Chapter 3 argues that ordinary causal talk is deeply sensitive to conversational context. The principle that I formulate to characterize that context sensitivity explains at least some of the oddness of ‘systematic causal overdetermination,’ and explains why some putative overgenerated causes are never felicitously counted, in conversation, as causes. But the principle also makes metaphysical theorizing about causation rather indirectly constrained by ordinary language judgments. (shrink)

Intellectual progress involves forming a more accurate picture of the world. But it also figuring out which concepts to use for theorizing about the world. Bayesian epistemology has had much to say about the former aspect of our cognitive lives, but little if at all about the latter. I outline a framework for formulating questions about conceptual change in a broadly Bayesian framework. By enriching the resources of Epistemic Utility Theory with a more expansive conception of epistemic value, I offer (...) a picture of our cognitive economy on which adopting new conceptual tools can sometimes be epistemically rational. (shrink)

What does it mean to say that one event is a cause of another? The simplest counterfactual analyses identify causation with one of two counterfactual-dependence relations: if event c had not occurred, then event e would not have occurred; if c had not occurred, e's probability would have been lower. These analyses enjoy some success. For the first: the dart-throw caused the balloon-pop, because if the throw had not occurred, the pop would not have occurred. For the second: suppose two (...) radioactive samples, A and B, are introduced into a room containing a Geiger counter, and the counter clicks once due to an emission from an A-atom; then the introduction of A is a cause of the click; the click might have occurred without the A-introduction , but we can say at least that without the A-introduction, the probability of the click would have been lower. ;Ultimately, however, these analyses fail, for two clear reasons. Preemption: add to the dart scene that Lucy would have thrown her dart if I had refrained---then although my throw caused the pop, the pop is not dependent on my throw. Failed potential causes: the probability of the click would have been lower without the B-introduction, but the B-introduction did not actually succeed in causing of the click. ;I defend the two simple analyses against various other objections; I then try to home in on the precise nature of their genuine problems; I examine almost all the attempts to date to improve upon the simple analyses; and finally I propose two new analyses. One of my analyses is deterministic, the other is confined to worlds that are purely indeterministic. Both analyses take causation to be primarily a matter of counterfactual dependence in the circumstances: holding certain features of the world fixed, effects and their probabilities do indeed depend on their causes . ;My discussion of background issues---counterfactual semantics, objective chance, events---includes arguments for substantial simplifications of David Lewis's theory of events. (shrink)

In this paper, a concept of chance is introduced that is compatible with deterministic physical laws, yet does justice to our use of chance-talk in connection with typical games of chance. We take our cue from what Poincaré called "the method of arbitrary functions," and elaborate upon a suggestion made by Savage in connection with this. Comparison is made between this notion of chance, and David Lewis' conception.

Bayesian confirmation theory—abbreviated to in these notes—is the predominant approach to confirmation in late twentieth century philosophy of science. It has many critics, but no rival theory can claim anything like the same following. The popularity of the Bayesian approach is due to its flexibility, its apparently effortless handling of various technical problems, the existence of various a priori arguments for its validity, and its injection of subjective and contextual elements into the process of confirmation in just the places where (...) critics of earlier approaches had come to think that subjectivity and sensitivity to context were necessary. (shrink)

The aim of this thesis is to improve our understanding of how to assess and communicate uncertainty in areas of research deeply afflicted by it, the assessment and communication of which are made more fraught still by the studies’ immediate policy implications. The IPCC is my case study throughout the thesis, which consists of three parts. In Part 1, I offer a thorough diagnosis of conceptual problems faced by the IPCC uncertainty framework. The main problem I discuss is the persistent (...) ambiguity surrounding the concepts of ‘confidence’ and ‘likelihood’; I argue that the lack of a conceptually valid interpretation of these concepts compatible with the IPCC uncertainty guide’s recommendations has worrying implications for both the IPCC authors’ treatment of uncertainties and the interpretability of the information provided in the AR5. Finally, I show that an understanding of the reasons behind the IPCC’s decision to include two uncertainty scales can offer insights into the nature of this problem. In Part 2, I review what philosophers have said about model-based robustness analysis. I assess several arguments that have been offered for its epistemic import and relate this discussion to the context of climate model ensembles. I also discuss various measures of independence in the climate literature, and assess the extent to which these measures can help evaluate the epistemic import of model robustness. In Part 3, I explore the notion of the ‘weight of evidence’ typically associated with Keynes. I argue that the Bayesian is bound to struggle with this notion, and draw some lessons from this fact. Finally, I critically assess some recent proposals for a new IPCC uncertainty framework that significantly depart from the current one. (shrink)

This thesis concerns the measurement of freedom, and its value. Specifically, I am concerned with three overarching questions. First, can we measure the extent of an individual’s freedom? It had better be that we can, otherwise much ordinary and intuitive talk that we would like to vindicate – say, about free persons being freer than slaves – will turn out to be false or meaningless. Second, in what ways is freedom valuable, and how is this value measured? It matters, for (...) example, whether freedom is valuable only insofar as it enables us to pursue specific ends we happen to value for independent reasons, or whether it is also valuable in itself. In the latter case, but not the former, more freedom will always be better. Likewise, it’s important to get clarity on what ends, exactly, freedom is especially instrumentally valuable in promoting, since this goes to how much we should care about it. And finally, the liberal political tradition asserts that there is a special sphere of personal choices within which individuals should be free to do as they please, for reasons over and above the value of freedom itself. Now, can we measure the extent to which states and individuals respect individual liberties, and can we weigh the importance of respecting liberty against competing values like social welfare? To answer these questions, I follow the axiomatic tradition of social choice theory, and I develop several novel measures of freedom – including the first measure of freedom ever proposed that is sensitive to how modally robustly our options are available – a novel approach to measuring the diversity of an opportunity set, and I develop an account of the value of freedom according to which an important part of why freedom matters is that it enables us to improve our preferences through learning, and I construct ways of measuring the value of freedom along this dimension of value. Finally, in later chapters, I provide a representation result for a measure of illiberalism, i.e. of the degree to which states fail to respect the rights of their citizens, and I extend this result to provide a characterization of moral theories that express concern for respecting the rights of others. The final chapter closes by discussing how this concern may be weighed against concerns for social welfare. (shrink)

It is important to have an adequate model of uncertainty, since decisions must be made before the uncertainty can be resolved. For instance, flood defenses must be designed before we know the future distribution of flood events. It is standardly assumed that probability theory offers the best model of uncertain information. I think there are reasons to be sceptical of this claim. I criticise some arguments for the claim that probability theory is the only adequate model of uncertainty. In particular (...) I critique Dutch book arguments, representation theorems, and accuracy based arguments. Then I put forward my preferred model: imprecise probabilities. These are sets of probability measures. I offer several motivations for this model of uncertain belief, and suggest a number of interpretations of the framework. I also defend the model against some criticisms, including the so-called problem of dilation. I apply this framework to decision problems in the abstract. I discuss some decision rules from the literature including Levi’s E-admissibility and the more permissive rule favoured by Walley, among others. I then point towards some applications to climate decisions. My conclusions are largely negative: decision making under such severe uncertainty is inevitably difficult. I finish with a case study of scientific uncertainty. Climate modellers attempt to offer probabilistic forecasts of future climate change. There is reason to be sceptical that the model probabilities offered really do reflect the chances of future climate change, at least at regional scales and long lead times. Indeed, scientific uncertainty is multi-dimensional, and difficult to quantify. I argue that probability theory is not an adequate representation of the kinds of severe uncertainty that arise in some areas in science. I claim that this requires that we look for a better framework for modelling uncertainty. (shrink)

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

The use of probability theory is widespread in our daily life as well as in scientific theories. In virtually all cases, calculations can be carried out within the framework of classical probability theory. A special exception is given by quantum mechanics, which gives rise to a new probability theory: quantum probability theory. This dissertation deals with the question of how this formalism can be understood from a philosophical and physical perspective. The dissertation is divided into three parts. In the first (...) part, the formalism of quantum probability theory and its relation to quantum mechanics is presented. The second part considers the possibility of reformulating quantum probability theory to embed it within classical probability. Mathematically, this possibility overlaps with the possibility of the existence of hidden variables theories of quantum mechanics: theories that attempt to solve fundamental problems in quantum mechanics by introducing additional physical properties of systems. The conclusion of this part is that, although classical reformulations of quantum probability theory are formally possible, they offer little insight into the formalism of quantum probability theory itself. The third part regards a more direct investigation of quantum probability theory. A reformulation of quantum probability theory is obtained by constructing a quantum logic on the basis of empirical non-probabilistic predictions of quantum mechanics. In this reformulation quantum probability functions are conditional probability functions on an algebra of propositions about measurements and measurement outcomes. (shrink)

What should your reaction be when you find out that someone that you consider an "epistemic peer" disagrees with you? Two broad approaches to this question have gained support from different philosophers. Precise characterizations of these approaches will be given later, but consider for now the following approximations. First, there is the "conciliatory" approach, according to which the right reaction to a disagreement is to move one's opinion towards that of one's peer, in proportion to the degree of trust that (...) one accords to that peer—for instance, if you thought that, in case of disagreement, you are equally likely to be right, then the conciliatory approach would have it that you should meet your epistemic peer halfway. The other, "nonconciliatory" approach, holds that one's reaction to a disagreement need not be perfectly in line with one's prior degree of trust in the other party. Notice an important asymmetry between these two approaches: the conciliatory approach has it that conciliation is the right reaction to any disagreement, whereas the nonconciliatory approach has it that there are some possible disagreements the correct reaction to which is not to conciliate (or not to the extent mandated by conciliatory views). This article examines the dispute between conciliatory and nonconciliatory views by distinguishing and examining possible answers to four different questions. (shrink)