Subjective Bayesianism is a major school of uncertain reasoning and statistical inference. It is often criticized for a lack of objectivity: it opens the door to the influence of values and biases, evidence judgments can vary substantially between scientists, it is not suited for informing policy decisions. My paper rebuts these concerns by connecting the debates on scientific objectivity and statistical method. First, I show that the above concerns arise equally for standard frequentist inference with null hypothesis significance (...) tests. Second, the criticisms are based on specific senses of objectivity with unclear epistemic value. Third, I show that Subjective Bayesianism promotes other, epistemically relevant senses of scientific objectivity—most notably by increasing the transparency of scientific reasoning. (shrink)

This paper poses a problem for Lewis’ Principal Principle in a subjective Bayesian framework: we show that, where chances inform degrees of belief, subjective Bayesianism fails to validate normal informal standards of what is reasonable. This problem points to a tension between the Principal Principle and the claim that conditional degrees of belief are conditional probabilities. However, one version of objective Bayesianism has a straightforward resolution to this problem, because it avoids this latter claim. The problem, (...) then, offers some support to this version of objective Bayesianism. (shrink)

Though not monolithic, Bayesianism offers a powerful and compelling set of methods for drawing inductive inferences. Its unifying ideas are (a) Pascal’s recognition that uncertainty is best expressed probabilistically and that values of unknown quantities are best estimated using the principle of mathematical expectation, and (b) Bayes’s insight that learning and inductive inference can be fruitfully modeled using conditional probabilities and Bayes’s theorem. The two central challenges for Bayesianism are the problem of the priors, and the development of (...) general methods for Bayesian conditioning. Bayesians have responded to the problem of the priors by proposing the use of ignorance priors that are justified a priori, embracing a radical subjectivism in which probabilities are mere degrees of coherent credence, or have sought refuge in the idea that subjective prejudices will wash out as evidence increases. On the conditioning front, Jeffrey has extended Bayes’s basic approach to account for non-dogmatic learning experiences, and further developments based on measures of divergence among probabilities seem promising. Bayesians have a vexed relationship with objective chance. Some reject the notion outright and portray chances as projections of personal inductive tastes onto the world. Others hope to make room for chances by developing chance/credence principles that clarify and explain the evidential relationships between the two kinds of probability. At bottom, however, all Bayesians agree that inductive reasoning involves drawing conclusions from new data on the basis of prior information using update rules that require conditioning on the evidence. -/- . (shrink)

Whilst Bayesian epistemology is widely regarded nowadays as our best theory of knowledge, there are still a relatively large number of incompatible and competing approaches falling under that umbrella. Very recently, Wallmann and Williamson wrote an interesting article that aims at showing that a subjective Bayesian who accepts the principal principle and uses a known physical chance as her degree of belief for an event A could end up having incoherent or very implausible beliefs if she subjectively chooses the (...) probability of an event F for which she has much poorer evidence. They also argued that their own version of objective Bayesianism is completely immune to that challenge. In this article, after having presented the strongest version of Wallmann’s and Williamson’s argument, I will show that if successful, it has far-reaching consequences and would not only invalidate moderate subjective Bayesianism and imprecise probalism but also a form of objective Bayesianism that relies on conditionalisation, the principal principle, reference classes, and the principle of indifference applied to the most basic partitions. I then argue that their argument can be defeated by adding the rule that it is always irrational to choose a probability that can be computed from the known probabilities associated to one’s other beliefs. I finally argue that the authors’ main intuition that probabilities have different degrees of reliability favours imprecise Bayesianism over precise Bayesianism. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume Studies Volume 28, Number 1, April 2002, pp. 113-130 Bayesianism, Analogy, and Hume's Dialogues concerning Natural Religion SALLY FERGUSON Introduction Analyses of the argument from design in Hume's Dialogues concerning Natural Religion have generally treated that argument as an example of reasoning by analogy.1 In this paper I examine whether it is in accord with Hume's thinking about the argument to subsume the version of it given (...) in the Dialogues under the model of probabilistic reasoning offered by Bayes's theorem. Wesley Salmon attempted this project in 1978.2 In related projects, David Owen3 as well as Philip Dawid and Donald Gillies4 have more recently attempted to construct Bayesian analyses of Hume's argument concerning testimony in "Of Miracles." I want to be careful at this stage to note exactly what I will claim. It is not that Bayesian reasoning sheds no light on the argument from design, or on arguments concerning testimony. All of the analyses mentioned above are beneficial in that they have been able to expose subtleties in these arguments that had previously gone unnoticed. Salmon's paper, in particular, contributes nicely to an understanding of just how the design argument may function in relation to contemporary scientific reasoning. In this paper I argue that, nonetheless, the attempt to apply Bayesian reasoning to the argument as presented in the Dialogues is not well supported as a reconstruction of Hume's own approach to the argument from design. Sally Ferguson is Assistant Professor of Philosophy, University of West Florida, UOOO University Parkway, Pensacola, FL 32514, USA. e-mail: sallyf@uwf.edu 114 Sally Ferguson There are two stages to my treatment of the issue. I begin by considering how much Hume knew of Bayes's theorem, and what consequence that knowledge might have had on his treatment of the argument in the Dialogues. This discussion includes a consideration of exactly what has been claimed by other authors on this subject, including what some have argued concerning Hume's reasonings in "Of Miracles," section 10 of An Enquiry concerning Human Understanding. I conclude that, based on the historical data, there is little reason to think of Hume's approach to the argument from design as anything more than proto-Bayesian at best. I then argue further, through a close textual analysis of the Dialogues, that there are good reasons for not treating Hume's reasoning there as even proto-Bayesian. In the end, the benefits that have been claimed for that approach, in terms of exposing both the subtleties of the argument and of Hume's reasoning about it, can equally well be derived from a careful analysis of the argument under a model of analogical reasoning, without need of Bayes's theorem. Section One Perhaps one might think that there is not much use for a consideration of the question whether Hume himself conceived of any of his arguments along specifically Bayesian lines. As Gower argues,5 Hume's knowledge of mathematics in general was fairly limited, and Bayes's theorem was not well known even up until Hume's death. It is important, therefore, for me to establish that there have not only been those who thought that Bayesian reasoning illuminates the arguments Hume gave, but also his own thinking about those arguments. It is also important for me to establish that it is not obvious that knowledge of Bayes's theorem did not affect Hume's reasonings. Each of these points will be addressed in the following. As to the first point, the claims of some authors on the subject are ambiguous. Dawid and Gillie, for example, make no statement to the effect that the probabilities involved in Bayes's theorem were in fact examined in "Of Miracles," nor do they attempt to produce any passages from Hume in support of that view. Thus it would be assumed that they see their attempt not as an attempt to provide an analysis that represents Hume's own approach to the argument, but rather simply as one that provides an illuminating method of analysis and support for an argument that Hume happened to give. Indeed, their conclusion, to the effect that a... (shrink)

Bayesianism claims to provide a unified theory of epistemic and practical rationality based on the principle of mathematical expectation. In its epistemic guise it requires believers to obey the laws of probability. In its practical guise it asks agents to maximize their subjective expected utility. Joyce’s primary concern is Bayesian epistemology, and its five pillars: people have beliefs and conditional beliefs that come in varying gradations of strength; a person believes a proposition strongly to the extent that she (...) presupposes its truth in her practical and theoretical reasoning; rational graded beliefs must conform to the laws of probability; evidential relationships should be analyzed subjectively in terms of relations among a person’s graded beliefs and conditional beliefs; empirical learning is best modeled as probabilistic conditioning. Joyce explains each of these claims and evaluates some of the justifications that have been offered for them, including “Dutch book,” “decision-theoretic,” and “non-pragmatic” arguments for and. He also addresses some common objections to Bayesianism, in particular the “problem of old evidence” and the complaint that the view degenerates into an untenable subjectivism. The essay closes by painting a picture of Bayesianism as an “internalist” theory of reasons for action and belief that can be fruitfully augmented with “externalist” principles of practical and epistemic rationality. (shrink)

Bayesianism has been dubbed as the most adequate and successful theory of scientific rationality. Its success mainly lies in its ability to combine two mutually exclusive elements involved in the process of theory-selection in science, viz.: the subjective and objective elements. My aim in this paper is to explain and evaluate Bayesianism’s account of scientific rationality by contrasting it with two other accounts.

Objective Bayesianism has been criticised on the grounds that objective Bayesian updating, which on a finite outcome space appeals to the maximum entropy principle, differs from Bayesian conditionalisation. The main task of this paper is to show that this objection backfires: the difference between the two forms of updating reflects negatively on Bayesian conditionalisation rather than on objective Bayesian updating. The paper also reviews some existing criticisms and justifications of conditionalisation, arguing in particular that the diachronic Dutch book justification (...) fails because diachronic Dutch book arguments are subject to a reductio: in certain circumstances one can Dutch book an agent however she changes her degrees of belief . One may also criticise objective Bayesianism on the grounds that its norms are not compulsory but voluntary, the result of a stance. It is argued that this second objection also misses the mark, since objective Bayesian norms are tied up in the very notion of degrees of belief. (shrink)

Following the standard practice in sociology, cultural anthropology and history, sociologists, historians of science and some philosophers of science define scientific communities as groups with shared beliefs, values and practices. In this paper it is argued that in real cases the beliefs of the members of such communities often vary significantly in important ways. This has rather dire implications for the convergence defense against the charge of the excessive subjectivity of subjective Bayesianism because that defense requires that communities (...) of Bayesian inquirers share a significant set of modal beliefs. The important implication is then that given the actual variation in modal beliefs across individuals, either Bayesians cannot claim that actual theories have been objectively confirmed or they must accept that such theories have been confirmed relative only to epistemically insignificant communities. (shrink)

The idea that the quantum probabilities are best construed as the personal/subjective degrees of belief of Bayesian agents is an old one. In recent years the idea has been vigorously pursued by a group of physicists who fly the banner of quantum Bayesianism. The present paper aims to identify the prospects and problems of implementing QBism, and it critically assesses the claim that QBism provides a resolution of some of the long-standing foundations issues in quantum mechanics, including the (...) measurement problem and puzzles of nonlocality. (shrink)

Key Terms in Logic offers the ideal introduction to this core area in the study of philosophy, providing detailed summaries of the important concepts in the study of logic and the application of logic to the rest of philosophy. A brief introduction provides context and background, while the following chapters offer detailed definitions of key terms and concepts, introductions to the work of key thinkers and lists of key texts. Designed specifically to meet the needs of students and assuming no (...) prior knowledge of the subject, this is the ideal reference tool for those coming to Logic for the first time. (shrink)

Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities, they should be calibrated to our evidence of physical probabilities, and they should otherwise equivocate sufficiently between the basic propositions that we can express. The three norms are sometimes explicated by appealing to the maximum entropy principle, which says that a belief function should be a probability function, from all those that are calibrated to evidence, that has maximum entropy. However, the three norms of objective (...) class='Hi'>Bayesianism are usually justified in different ways. In this paper we show that the three norms can all be subsumed under a single justification in terms of minimising worst-case expected loss. This, in turn, is equivalent to maximising a generalised notion of entropy. We suggest that requiring language invariance, in addition to minimising worst-case expected loss, motivates maximisation of standard entropy as opposed to maximisation of other instances of generalised entropy. Our argument also provides a qualified justification for updating degrees of belief by Bayesian conditionalisation. However, conditional probabilities play a less central part in the objective Bayesian account than they do under the subjective view of Bayesianism, leading to a reduced role for Bayes’ Theorem. (shrink)

The inductive reliability of Bayesian methods is explored. The first result presented shows that for any solvable inductive problem of a general type, there exists a subjective prior which yields a Bayesian inductive method that solves the problem, although not all subjective priors give rise to a successful inductive method for the problem. The second result shows that the same does not hold for computationally bounded agents, so that Bayesianism is "inductively incomplete" for such agents. Finally a (...) consistency proof shows that inductive agents do not need to disregard inductive failure on sets of subjective probability 0 in order to be ideally rational. Together the results reveal the inadequacy of the subjective Bayesian norms for scientific methodology. (shrink)

The Bayesian approach to quantum mechanics of Caves, Fuchs and Schack is presented. Its conjunction of realism about physics along with anti-realism about much of the structure of quantum theory is elaborated; and the position defended from common objections: that it is solipsist; that it is too instrumentalist; that it cannot deal with Wigner's friend scenarios. Three more substantive problems are raised: Can a reasonable ontology be found for the approach? Can it account for explanation in quantum theory? Are (...) class='Hi'>subjective probabilities on their own adequate in the quantum domain? The first question is answered in the affirmative, drawing on elements from Nancy Cartwright's philosophy of science. The second two are not: it is argued that these present outstanding difficulties for the project. A quantum Bayesian version of Moore's paradox is developed to illustrate difficulties with the subjectivist account of pure state assignments. (shrink)

This is a review essay about David Corfield and Jon Williamson's anthology Foundations of Bayesianism. Taken together, the fifteen essays assembled in the book assess the state of the art in Bayesianism. Such an assessment is timely, because decision theory and formal epistemology have become disciplines that are no longer taught on a routine basis in good philosophy departments. Thus we need to ask: Quo vadis, Bayesianism? The subjects of the articles include Bayesian group decision theory, approaches (...) to the concept of probability, Bayesian approaches in the philosophy of mathematics, reflections on the relationship between causation and probability, the Independence axiom, and a range of criticisms of Bayesianism, among other subjects. While critical of some of the arguments presented in the articles, this review recommends Corfield and Williamson's volume to anyone who is trying to stay abreast of Bayesian research. (shrink)

Key Terms in Logic offers the ideal introduction to this core area in the study of philosophy, providing detailed summaries of the important concepts in the study of logic and the application of logic to the rest of philosophy. A brief introduction provides context and background, while the following chapters offer detailed definitions of key terms and concepts, introductions to the work of key thinkers and lists of key texts. Designed specifically to meet the needs of students and assuming no (...) prior knowledge of the subject, this is the ideal reference tool for those coming to Logic for the first time. (shrink)

Key Terms in Logic offers the ideal introduction to this core area in the study of philosophy, providing detailed summaries of the important concepts in the study of logic and the application of logic to the rest of philosophy. A brief introduction provides context and background, while the following chapters offer detailed definitions of key terms and concepts, introductions to the work of key thinkers and lists of key texts. Designed specifically to meet the needs of students and assuming no (...) prior knowledge of the subject, this is the ideal reference tool for those coming to Logic for the first time. (shrink)

Bayesianism is the position that scientific reasoning is probabilistic and that probabilities are adequately interpreted as an agent's actual subjective degrees of belief, measured by her betting behaviour. Confirmation is one important aspect of scientific reasoning. The thesis of this paper is the following: if scientific reasoning is at all probabilistic, the subjective interpretation has to be given up in order to get right confirmation—and thus scientific reasoning in general. The Bayesian approach to scientific reasoning Bayesian confirmation (...) theory The example The less reliable the source of information, the higher the degree of Bayesian confirmation Measure sensitivity A more general version of the problem of old evidence Conditioning on the entailment relation The counterfactual strategy Generalizing the counterfactual strategy The desired result, and a necessary and sufficient condition for it Actual degrees of belief The common knock-down feature, or ‘anything goes’ The problem of prior probabilities. (shrink)

The foundations of probability deal with the problem of modelling reasoning in face of uncertainty by a mathematical calculus, usually the standard probability calculus .The three dominating schools in the foundations of probability interpret probabilities as limiting long-run frequencies conceived as an objective property of series of repeatable experiments , or rational betting rates for an individual to bet on the unknown outcome of experiments depending on the individual’s prior assessments updated by evidence , or rational betting rates to bet (...) on the unknown outcome of experiments depending on evidence only, but not on subjective assessments .Apart from the interpretation of probability, frequentism and Bayesianism in particular also differ with respect to the advocated methodology for inference. Frequentists use tests, estimators, and confidence intervals . Bayesians usually start with a prior distribution and use the posterior distribution, which is obtained by conditioning on the evidence, in order to carry out inferences. The prior distribution either models the individual’s personal prior probability assessments or, in objective Bayesianism, is chosen according to some rules in order to allow the evidence to determine the posterior.All three approaches are riddled with difficulties . Frequentism is often accused of circularity, because the assumption of independent identically distributed outcomes is needed in order to connect observations to frequentist probabilities, but ‘iid’ is itself defined probabilistically. Subjective Bayesianism is attacked for being too …. (shrink)

We argue that subjective Bayesians face a dilemma: they must offend against the spirit of their permissivism about rational credence or reject the principle that one should avoid accuracy dominance.

This chapter is a philosophical survey of some leading approaches in formal epistemology in the so-called ‘Bayesian’ tradition. According to them, a rational agent’s degrees of belief—credences—at a time are representable with probability functions. We also canvas various further putative ‘synchronic’ rationality norms on credences. We then consider ‘diachronic’ norms that are thought to constrain how credences should respond to evidence. We discuss some of the main lines of recent debate, and conclude with some prospects for future research.

In the Bayesian approach to quantum mechanics, probabilities—and thus quantum states—represent an agent’s degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept of certainty in quantum mechanics. Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations on the other. We first review the main arguments for the general claim that probabilities (...) always represent degrees of belief. We then argue that a quantum state prepared by some physical device always depends on an agent’s prior beliefs, implying that the probability-1 predictions derived from that state also depend on the agent’s prior beliefs. Quantum certainty is therefore always some agent’s certainty. Conversely, if facts about an experimental setup could imply agent-independent certainty for a measurement outcome, as in many Copenhagen-like interpretations, that outcome would effectively correspond to a preexisting system property. The idea that measurement outcomes occurring with certainty correspond to preexisting system properties is, however, in conflict with locality. We emphasize this by giving a version of an argument of Stairs [(1983). Quantum logic, realism, and value-definiteness. Philosophy of Science, 50, 578], which applies the Kochen–Specker theorem to an entangled bipartite system. (shrink)

Options and the subjective ought Content Type Journal Article Pages 1-18 DOI 10.1007/s11098-012-9880-0 Authors Brian Hedden, Department of Linguistics and Philosophy, Massachusetts Institute of Technology, Cambridge, MA, USA Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116.

The idea that probability is a degree of rational belief seemed too vague for a foundation of a mathematical theory. It was certainly not obvious that degrees of rational belief had to be governed by the probability axioms as used by Laplace and other prestatistical probabilityst. The axioms seemed arbitrary in their interpretation. To eliminate the arbitrariness, the stat- isticians of the early 20th century drastically restricted the possible applications of the probability theory, by insisting that probabilities had to be (...) interpreted as relative frequencies, which obviously satisfied the probability axioms, and so the arbitrariness was removed. But the frequentist approach turned more subjective than the prestatistical approach, because the identifications of outcome spaces, the choices of test statistics, the declarations of what rejection regions are, the choices of null-hypothesis among alternatives, the contradictory choices between sizes and powers etc., depend on thoughts or even whims of the experimenter. Frequentists thus failed to solve the problems that motivated their approach, they even exacerbated them. The subjective Bayesianism of Ramsey and de Finetti did not solve the problems either. Finally Cox provided the missing foundation for probability as a degree of rational belief, which makes the Bayesian probability theory (which is based on this foundation) the best theory of probable inference we have. Hence, it is quite unbelievable that it is not even mentioned in recent philosophy textbooks devoted to the probable inference. The reason could be that it requires fairly sophisticated mathematics. But not even to mention it? We explain the history and prove Cox theorem in a novel way. (shrink)

Many philosophers claimed that there might be fertile ground for collaboration between IBE and the objective end of the Bayesian methodology. Recent literature is investigated in this chapter, to highlight the latest developments about the possibility of such a collaboration. The merits of the convergence of the two methods are presented. It is argued that arriving on this end is not an easy goal as there are four ways by which subjective considerations may overshadow the objective picture. The existence (...) of subjective virtues, the vagueness of the mapping, the absence of an accurate weighting, and the existence of partial virtues allow the generation of infinitely many different initializations of priors and likelihoods, thus keeping the explanationist away from the objective extreme. Hence, either the explanationist successfully faces up with each one of the four problems so as to converge to the objective end or she ends up in a semi-objective position, whereby the explanatory restrictions allow a bunch of equally good probability distributions. (shrink)

Christopher Fuchs has recently offered a provocative version of quantum mechanical realism, which is based on the suggestion that quantum probabilities merit a subjective interpretation. His proposal, however, has been charged with inconsistency by Amit Hagar (2003), who argues that interpreting quantum probabilities subjectively is inconsistent with the realist claims Fuchs wants to maintain for the quantum system and the dimensionality of the Hilbert space that accompanies it. In this paper I first outline the fundamentals of Fuchs's approach and (...) then take up the task of rebutting Hagar's charge by demonstrating the internal coherence of Fuchs's realism. (shrink)

Many philosophers hold that the probability axioms constitute norms of rationality governing degrees of belief. This view, known as subjective Bayesianism, has been widely criticized for being too idealized. It is claimed that the norms on degrees of belief postulated by subjective Bayesianism cannot be followed by human agents, and hence have no normative force for beings like us. This problem is especially pressing since the standard framework of subjective Bayesianism only allows us to (...) distinguish between two kinds of credence functions—coherent ones that obey the probability axioms perfectly, and incoherent ones that don’t. An attractive response to this problem is to extend the framework of subjective Bayesianism in such a way that we can measure differences between incoherent credence functions. This lets us explain how the Bayesian ideals can be approximated by humans. I argue that we should look for a measure that captures what I call the ‘overall degree of incoherence’ of a credence function. I then examine various incoherence measures that have been proposed in the literature, and evaluate whether they are suitable for measuring overall incoherence. The competitors are a qualitative measure that relies on finding coherent subsets of incoherent credence functions, a class of quantitative measures that measure incoherence in terms of normalized Dutch book loss, and a class of distance measures that determine the distance to the closest coherent credence function. I argue that one particular Dutch book measure and a corresponding distance measure are particularly well suited for capturing the overall degree of incoherence of a credence function. (shrink)

The justificatory force of empirical reasoning always depends upon the existence of some synthetic, a priori justification. The reasoner must begin with justified, substantive constraints on both the prior probability of the conclusion and certain conditional probabilities; otherwise, all possible degrees of belief in the conclusion are left open given the premises. Such constraints cannot in general be empirically justified, on pain of infinite regress. Nor does subjective Bayesianism offer a way out for the empiricist. Despite often-cited convergence (...) theorems, subjective Bayesians cannot hold that any empirical hypothesis is ever objectively justified in the relevant sense. Rationalism is thus the only alternative to an implausible skepticism. (shrink)

Subjective Bayesianism is the current orthodoxy in confirmation theory. In broad outline, this view claims a) that confirmation is a relation of positive relevance, viz., that a piece of evidence confirms a theory if it increases its probability; b) that this relation of confirmation is captured by Bayes’s theorem; c) that, hence, the only factors relevant to confirmation of a theory are its prior probability, the likelihood of the evidence given the theory and the probability of the evidence; (...) d) that the specification of the prior probability of a theory is a purely subjective matter; e) that the only constraint on an assignment of prior probabilities to several theories should be that they obey the axioms of the probability calculus; f) that, hence, the reasonableness of a belief does not depend on its content; nor, ultimately, on whether the belief is made reasonable by the evidence; and g) that degrees of belief are probabilities and that belief is always a matter of degree. This theory has had many successes. Old tangles, like the ravens paradox or the grue problem, are resolved. New tangles, like the problem of old evidence, have been, to some extent, resolved. But there is still a pervasive dissatisfaction with subjective Bayesianism. This dissatisfaction concerns all of the theses to above, but it is centred mostly around the point that subjective Bayesianism is too subjective to offer an adequate theory of confirmation and of rational belief. Yet, up until recently this dissatisfaction had not borne fruits in a fully developed alternative theory of confirmation. Perhaps, only Deborah Mayo’s error-statistical approach was a fully developed alternative, but this too faced considerable problems, one central among them being that she takes all probabilities to be relative frequencies. One thing is sure. Probability theory should place a central role in a theory of confirmation. But how are we to interpret probabilities if we want to avoid the subjective element of Bayesianism and the objective element of the error-statistical approach? (shrink)

The Dutch Book Argument shows that an agent will lose surely in a gamble (a Dutch Book is made) if his degrees of belief do not satisfy the laws of the probability. Yet a question arises here: What does the Dutch Book imply? This paper firstly argues that there exists a utility function following Ramsey’s axioms. And then, it explicates the properties of the utility function and degree of belief respectively. The properties show that coherence in partial beliefs for (...) class='Hi'>Subjective Bayesianism means that the degree of belief, representing a belief ordering, satisfies the laws of probability, and that coherence in preferences means that the preferences are represented by expected utilities. A coherent belief ordering and a utility scale induce a coherent preference ordering; a coherent preference ordering induces a coherent belief ordering which can be uniquely represented by a degree-of-belief function. The preferences (values) and beliefs are both incoherent or disordered if a Dutch Book is made. (shrink)

We argue that David Lewis’s principal principle implies a version of the principle of indifference. The same is true for similar principles that need to appeal to the concept of admissibility. Such principles are thus in accord with objective Bayesianism, but in tension with subjective Bayesianism. 1 The Argument2 Some Objections Met.

In response to two trenchant objections, radical subjective Bayesianism has been widely rejected. In this paper, I seek, if not to rehabilitate subjectivism, at least to show its critic what is attractive about the position. I argue that what is at stake in the subjectivism/anti-subjectivism debate is not, as is commonly thought, which norms of rationality are true, but rather, the conception of rationality that we adopt: there is an alternative approach to the widespread telic approach to rationality, (...) which I call the poric approach, on which subjectivism is an attractive position. I then argue that the poric approach—and therefore subjectivism—cannot be easily dismissed. (shrink)

In this paper I am concerned with the question of whether degrees of belief can figure in reasoning processes that are executed by humans. It is generally accepted that outright beliefs and intentions can be part of reasoning processes, but the role of degrees of belief remains unclear. The literature on subjective Bayesianism, which seems to be the natural place to look for discussions of the role of degrees of belief in reasoning, does not address the question of (...) whether degrees of belief play a role in real agents’ reasoning processes. On the other hand, the philosophical literature on reasoning, which relies much less heavily on idealizing assumptions about reasoners than Bayesianism, is almost exclusively concerned with outright belief. One possible explanation for why no philosopher has yet developed an account of reasoning with degrees of belief is that reasoning with degrees of belief is not possible for humans. In this paper, I will consider three arguments for this claim. I will show why these arguments are flawed, and conclude that, at least as far as these arguments are concerned, it seems like there is no good reason why the topic of reasoning with degrees of belief has received so little attention. (shrink)

The Dutch Book argument, like Route 66, is about to turn 80. It is arguably the most celebrated argument for subjective Bayesianism. Start by rejecting the Cartesian idea that doxastic attitudes are ‘all-or-nothing’; rather, they are far more nuanced degrees of belief, for short credences, susceptible to fine-grained numerical measurement. Add a coherentist assumption that the rationality of a doxastic state consists in its internal consistency. The remaining problem is to determine what consistency of credences amounts to. The (...) Dutch Book argument, in a nutshell, says that if your credences do not obey the probability calculus, you are ‘incoherent’—susceptible to sure losses at the hands of a ‘Dutch Bookie’—and thus irrational. Conclusion: rationality requires your credences to obey the probability calculus. And like Route 66, the fortunes of the Dutch Book argument have been mixed. Opinions on the argument are sharply divided. The list of its proponents is quite a ‘who’s who’ of philosophers of probability; they include de Finetti (1937, 1980), Carnap (1950, 1962, and more fully, 1955), Kemeny (1955), Lehman (1955), Shimony (1955), Adams (1962), Mellor (1971), Rosenkrantz (1981), van Fraassen (1989), Jeffrey (1983, 1992). (shrink)

We argue that David Lewis’s principal principle implies a version of the principle of indifference. The same is true for similar principles that need to appeal to the concept of admissibility. Such principles are thus in accord with objective Bayesianism, but in tension with subjective Bayesianism. 1 The Argument2 Some Objections Met.

This paper aims to make explicit the methodological conditions that should be satisfied for the Bayesian model to be used as a normative model of human probability judgment. After noticing the lack of a clear definition of Bayesianism in the psychological literature and the lack of justification for using it, a classic definition of subjective Bayesianism is recalled, based on the following three criteria: an epistemic criterion, a static coherence criterion and a dynamic coherence criterion. Then it (...) is shown that the adoption of this framework has two kinds of implications. The first one regards the methodology of the experimental study of probability judgment. The Bayesian framework creates pragmatic constraints on the methodology that are linked to the interpretation of, and the belief in, the information presented, or referred to, by an experimenter in order for it to be the basis of a probability judgment by individual participants. It is shown that these constraints have not been satisfied in the past, and the question of whether they can be satisfied in principle is raised and answered negatively. The second kind of implications consists of two limitations in the scope of the Bayesian model. They regard (1) the background of revision (the Bayesian model considers only revising situations but not updating situations), and (2) the notorious case of the null priors. In both cases Lewis’ rule is an appropriate alternative to Bayes’ rule, but its use faces the same operational difficulties. (shrink)

What is guilt beyond a reasonable doubt (BARD) for a Bayesian? Is thinking of BARD in terms of probabilities a nonstarter? I propose an account of BARD compatible with Subjective Bayesianism that rejects the view that BARD is met by a threshold probability. BARD is a judgment, not merely about the credal state the factfinder endorses as her own (i.e. not merely as one’s own credence in guilt), but as about alternative possible credences, specifically those the factfinder does (...) not endorse, but finds reasonable. To this end, I employ a Bayesian framework, expounded by Lange (1999), that permits revision of past prior probability assignments. Such a framework presupposes a point of view free from one’s prior from which a prior is judged. A trier-of-fact asks whether doubt persists among any reasonable starting point one might take; if it does, acquittal is warranted. (shrink)

How should we make decisions when we do not know the relevant physical probabilities? In these ambiguous situations, we cannot use our knowledge to determine expected utilities or payoffs. The traditional Bayesian answer is that we should create a probability distribution using some mix of subjective intuition and objective constraints. Imprecise Bayesians argue that this approach is inadequate for modelling ambiguity. Instead, they represent doxastic states using credal sets. Generally, insofar as we are more uncertain about the physical probability (...) of an event, there is more divergence in the credal set. Hence, their approach can represent these ambiguities via the extent of the divergence. Imprecise Bayesianism has mostly been advocated for its epistemological features. In this article, we examine its properties for decision-making. We develop a model for comparing standard and Imprecise Bayesianism by testing their performances in a classic decision problem. We find that the representational tools of Imprecise Bayesianism also cause it to underperform in our tests. This issue has been overlooked, because previous research on Imprecise Bayesianism has not utilised agent-based modelling to provide information about its performance in the short-run. Overall, we reveal the Ambiguity Dilemma for Imprecise Bayesianism: To what extent should one value representational power or decision-making performance? (shrink)

Thomas Reid is often misread as defending common sense, if at all, only by relying on illicit premises about God or our natural faculties. On these theological or reliabilist misreadings, Reid makes common sense assertions where he cannot give arguments. This paper attempts to untangle Reid's defense of common sense by distinguishing four arguments: (a) the argument from madness, (b) the argument from natural faculties, (c) the argument from impotence, and (d) the argument from practical commitment. Of these, (a) and (...) (c) do rely on problematic premises that are no more secure than claims of common sense itself. Yet (b) and (d) do not. This conclusion can be established directly by considering the arguments informally, but one might still worry that there is an implicit premise in them. In order to address this concern, I reconstruct the arguments in the framework of subjective Bayesianism. The worry becomes this: Do the arguments rely on specific values for the prior probability of some premises? Reid's appeals to our prior cognitive and practical commitments do not. Rather than relying on specific probability assignments, they draw on things that are part of the Bayesian framework itself, such as the nature of observation and the connection between belief and action. Contra the theological or reliabilist readings, the defense of common sense does not require indefensible premises. (shrink)

Expert probability forecasts can be useful for decision making . But levels of uncertainty escalate: however the forecaster expresses the uncertainty that attaches to a forecast, there are good reasons for her to express a further level of uncertainty, in the shape of either imprecision or higher order uncertainty . Bayesian epistemology provides the means to halt this escalator, by tying expressions of uncertainty to the propositions expressible in an agent’s language . But Bayesian epistemology comes in three main varieties. (...) Strictly subjective Bayesianism and empirically-based subjective Bayesianism have difficulty in justifying the use of a forecaster’s probabilities for decision making . On the other hand, objective Bayesianism can justify the use of these probabilities, at least when the probabilities are consistent with the agent’s evidence . Hence objective Bayesianism offers the most promise overall for explaining how testimony of uncertainty can be useful for decision making. Interestingly, the objective Bayesian analysis provided in Sect. 5 can also be used to justify a version of the Principle of Reflection. (shrink)

Quantum Bayesianism, or QBism, is a recent development of the epistemic view of quantum states, according to which the state vector represents knowledge about a quantum system, rather than the true state of the system. QBism explicitly adopts the subjective view of probability, wherein probability assignments express an agent’s personal degrees of belief about an event. QBists claim that most if not all conceptual problems of quantum mechanics vanish if we simply take a proper epistemic and probabilistic perspective. (...) Although this judgement is largely subjective and logically consistent, I explain why I do not share it. (shrink)

The idea that a serious threat to scientific realism comes from unconceived alternatives has been proposed by van Fraassen, Sklar, Stanford and Wray among others. Peter Lipton's critique of this threat from underconsideration is examined briefly in terms of its logic and its applicability to the case of space-time and particle physics. The example of space-time and particle physics indicates a generic heuristic for quantitative sciences for constructing potentially serious cases of underdetermination, involving one-parameter family of rivals T_m that work (...) as a team rather than as a single rival against default theory T_0. In important examples this new parameter has a physical meaning and makes a crucial _conceptual_ difference, shrinking the symmetry group and in some case putting gauge freedom, formal indeterminism vs. determinism, the presence of the hole argument, etc., at risk. Methodologies akin to eliminative induction or tempered subjective Bayesianism are more demonstrably reliable than the custom of attending only to "our best theory": they can lead either to a serious rivalry or to improved arguments for the favorite theory. The example of General Relativity vs. massive spin 2 gravity, a recent topic in the physics literature, is discussed. Arguably the General Relativity and philosophy literatures have ignored the most serious rival to General Relativity. (shrink)

I argue that information is a goal-relative concept for Bayesians. More precisely, I argue that how much information is provided by a piece of evidence depends on whether the goal is to learn the truth or to rank actions by their expected utility, and that different confirmation measures should therefore be used in different contexts. I then show how information measures may reasonably be derived from confirmation measures, and I show how to derive goal-relative non-informative and informative priors given background (...) information. Finally, I argue that my arguments have important implications for both objective and subjective Bayesianism. In particular, the Uniqueness Thesis is either false or must be modified. Moreover, objective Bayesians must concede that pragmatic factors systematically influence which priors are rational, and subjective Bayesians must concede that pragmatic factors sometimes partly determine which prior distribution most accurately represents an agent's epistemic state. (shrink)

The chapter bases a theory of evidential probability on the equation of knowledge with evidence. It is a form of objective rather than subjective Bayesianism. Updating on new evidence is structured in a way that allows propositions to lose as well as gain probability. The account is integrated with possible worlds models of epistemic logic. Since one does not always know what one knows, the accessibility relation is not an equivalence relation, which has the effect that prior probability (...) can diverge from expected posterior probability. (shrink)

This paper begins by distinguishing intrinsic and extrinsic contributions of mathematics to scientific representation. This leads to two investigations into how these different sorts of contributions relate to confirmation. I present a way of accommodating both contributions that complicates the traditional assumptions of confirmation theory. In particular, I argue that subjective Bayesianism does best accounting for extrinsic contributions, while objective Bayesianism is more promising for intrinsic contributions.

The underdetermination thesis poses a threat to rational choice of scientific theories. We discuss two arguments for the thesis. One draws its strength from deductivism together with the existence thesis, and the other is defended on the basis of the failure of a reliable inductive method. We adopt a partially subjective/objective pragmatic Bayesian epistemology of science framework, and reject both arguments for the thesis. Thus, in science we are able to reinstate rational choice called into question by the underdetermination (...) thesis. (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)