Bayesianism is a collection of positions in several related fields, centered on the interpretation of probability as something like degree of belief, as contrasted with relative frequency, or objective chance. However, Bayesianism is far from a unified movement. Bayesians are divided about the nature of the probability functions they discuss; about the normative force of this probability function for ordinary and scientific reasoning and decision making; and about what relation (if any) holds between Bayesian and non-Bayesian concepts.

Orthodox Bayesianism tells a story about the epistemic trajectory of an ideally rational agent. The agent begins with a ‘prior’ probability function; thereafter, it conditionalizes on its evidence as it comes in. Consider, then, such an agent at the very beginning of its trajectory. It is ideally rational, but completely ignorant of which world is actual. Call this agent ‘Superbaby’.1 Superbaby personifies the Bayesian story. We argue that it must believe ‘Moorish’ propositions of the form.

Bayesianism tells a story about the epistemic trajectory of an ideally rational agent. The agent begins with a ‘prior’ probability function; thereafter, it conditionalizes on its evidence as it comes in. Consider, then, such an agent at the very beginning of its trajectory. It is ideally rational, but completely ignorant of which world is actual. Let us call this agent ‘superbaby’. We show that superbaby is committed to sincerely asserting propositions of the form [p and I am not justified (...) in believing that p]. (shrink)

First published in 1998. Routledge is an imprint of Taylor & Francis, an informa company.

This paper argues that professionals who make boundary-related decisions should be guided by relationship-based practice. In our roles as service users and professionals, drawing from our lived experiences of professional relationships, we argue we need to move away from distance-based practice. This includes understanding the boundary stories and narratives that exist for all of us – including the people we support, other professionals, as well as the organisations and systems within which we work. When we are dealing with professional boundary (...) issues, we should centre relationship-building skills that are central to many other aspects of our work. Skills that foster relationships at all levels – between professionals, service users, and services – need to be revalued. Our final recommendation is to create, develop, and foster safer spaces within and outside of organisations, as well as inter-professionally, for the discussion and exploration of boundary-related issues and practice. We are interested in hearing from those with experiences of being marginalised by boundaries so that they can inform a reshaping of our collective ideas around boundary related practices. To foster relationship-based practices in organisations, we have outlined several recommendations here; however, we recognize that these do not go far enough, and that collective action is needed to inform systemic change. (shrink)

This paper (first published under the same title in Journal of Mathematical Economics, 29, 1998, p. 331-361) is a sequel to "Consistent Bayesian Aggregation", Journal of Economic Theory, 66, 1995, p. 313-351, by the same author. Both papers examine mathematically whether the the following assumptions are compatible: the individuals and the group both form their preferences according to Subjective Expected Utility (SEU) theory, and the preferences of the group satisfy the Pareto principle with respect to those of the individuals. While (...) the 1995 paper explored these assumptions in the axiomatic context of Savage's (1954-1972) SEU theory, the present paper explores them in the context of Anscombe and Aumann's (1963) alternative SEU theory. We first show that the problematic assumptions become compatible when the Anscombe-Aumann utility functions are state-dependent and no subjective probabilities are elicited. Then we show that the problematic assumptions become incompatible when the Anscombe-Aumann utility functions are state-dependent, like before, but subjective probabilities are elicited using a relevant technical scheme. This last result reinstates the impossibilities proved by the 1995 paper, and thus shows them to be robust with respect to the choice of the SEU axiomatic framework. The technical scheme used for the elicitation of subjective probabilities is that of Karni, Schmeidler and Vind (1983). (shrink)

State of the art paper on the problem of induction: how to justify the conclusion that ‘all Fs are Gs’ from the premise that ‘all observed Fs are Gs’. The most prominent theories of contemporary philosophical literature are discussed and analysed, such as: inductivism, reliabilism, perspective of laws of nature, rationalism, falsificationism, the material theory of induction and probabilistic approaches, according to Carnap, Reichenbach and Bayesianism. In the end, we discuss the new problem of induction of Goodman, raised by (...) the grue predicate. (shrink)

Following Kuhn's main thesis according to which theory revision and acceptance is always paradigm relative, I propose to outline some possible consequences of such a view. First, asking the question in what sense Bayesian decision theory could serve as the appropriate (normative) theory of rationality examined from the point of view of the epistemology of theory acceptance, I argue that Bayesianism leads to a narrow conception of theory acceptance. Second, regarding the different types of theory revision, i.e. expansion, contraction, (...) replacement and residuals shifts, I extract from Kuhn's view a series of indications showing that theory replacement cannot be rationalized within the framework of Bayesian decision theory, not even within a more sophisticated version of that model. Third, and finally, I will point to the need for a more comprehensive model of rationality than the Bayesian expected utility maximization model, the need for a model which could better deal with the different aspects of theory replacement. I will show that Kuhn's distinction between normal and revolutionary science gives us several hints for a more adequate theory of rationality in science. I will also show that Kuhn is not in a position to fully articulate his main ideas and that he well be confronted with a serious problem concerning collective choice of a paradigm. (shrink)

Foundations of Bayesianism is an authoritative collection of papers addressing the key challenges that face the Bayesian interpretation of probability today. Some of these papers seek to clarify the relationships between Bayesian, causal and logical reasoning. Others consider the application of Bayesianism to artificial intelligence, decision theory, statistics and the philosophy of science and mathematics. The volume includes important criticisms of Bayesian reasoning and also gives an insight into some of the points of disagreement amongst advocates of the (...) Bayesian approach. The upshot is a plethora of new problems and directions for Bayesians to pursue.The book will be of interest to graduate students or researchers who wish to learn more about Bayesianism than can be provided by introductory textbooks to the subject. Those involved with the applications of Bayesian reasoning will find essential discussion on the validity of Bayesianism and its limits, while philosophers and others interested in pure reasoning will find new ideas on normativity and the logic of belief. (shrink)

“Evidence” in the form of data collected and analysis thereof is fundamental to medicine, health and science. In this paper, we discuss the “evidence-based” aspect of evidence-based medicine in terms of statistical inference, acknowledging that this latter field of statistical inference often also goes by various near-synonymous names—such as inductive inference (amongst philosophers), econometrics (amongst economists), machine learning (amongst computer scientists) and, in more recent times, data mining (in some circles). Three central issues to this discussion of “evidence-based” are (i) (...) whether or not the statistical analysis can and/or should be objective and/or whether or not (subjective) prior knowledge can and/or should be incorporated, (ii) whether or not the analysis should be invariant to the framing of the problem (e.g. does it matter whether we analyse the ratio of proportions of morbidity to non-morbidity rather than simply the proportion of morbidity?), and (iii) whether or not, as we get more and more data, our analysis should be able to converge arbitrarily closely to the process which is generating our observed data. For many problems of data analysis, it would appear that desiderata (ii) and (iii) above require us to invoke at least some form of subjective (Bayesian) prior knowledge. This sits uncomfortably with the understandable but perhaps impossible desire of many medical publications that at least all the statistical hypothesis testing has to be classical non-Bayesian—i.e. it is not permitted to use any (subjective) prior knowledge. (shrink)

J. Howard Sobel has long been recognized as an important figure in philosophical discussions of rational decision. He has done much to help formulate the concept of causal decision theory. In this volume of essays Sobel explores the Bayesian idea that rational actions maximize expected values, where an action's expected value is a weighted average of its agent's values for its possible total outcomes. Newcomb's Problem and The Prisoner's Dilemma are discussed, and Allais-type puzzles are viewed from the perspective of (...) causal world Bayesianism. The author establishes principles for distinguishing options in decision problems, and studies ways in which perfectly rational causal maximizers can be capable of resolute choices. Sobel also views critically Gauthier's revisionist ideas about maximizing rationality. This collection will be a desideratum for anyone working in the field of rational choice theory, whether in philosophy, economics, political science, psychology or statistics. Howard Sobel's work in decision theory is certainly among the most important, interesting and challenging that is being done by philosophers. (shrink)

In the recent philosophical literature on inquiry, epistemologists point out that their subject has often begun at the point at which you already have your evidence and then focussed on identifying the beliefs for which that evidence provides justification. But we are not mere passive recipients of evidence. While some comes to us unbidden, we often actively collect it. This has long been recognised, but typically epistemologists have taken the norms that govern inquiry to be practical, not epistemic. The recent (...) literature challenges this assumption and uncovers a rich range of questions about the epistemic normativity of inquiry. In this paper, I approach these questions from the formal side of epistemology. Developing out of the philosophy of science, as it did, this branch of epistemology has long discussed inquiry. And, building on the insights of David Blackwell (1951) and I. J. Good (1967), it has produced a reasonably well-developed framework in which to understand norms of inquiry, both epistemic and practical. In the first half of the paper, I will present the pragmatic versions of this framework due to Blackwell and Good, and the epistemic version due to Wayne Myrvold (2012); in the second half of the paper, I put this framework to work, turning to some of the questions from the recent debate about inquiry and asking how the Blackwell-Good-Myrvold approach can help us answer them. Questions will include: Are there purely epistemic norms that govern these actions (Flores and Woodard forthcoming)? When should we initiate an inquiry, when should we continue it, when should we conclude it, and when should we reopen it? How should we understand Julia Staffel's distinction between transitional attitudes and terminal attitudes (Staffel 2021a,b)? How do epistemic norms of inquiry relate to epistemic norms of belief or credence, and can they conflict (Friedman 2020)? And how should we understand the epistemic error that occurs when someone is resistant to evidence (Simion 2023)? (shrink)

Science is about evaluation, persuasion and logic. In scientific debate, scientists collectively evaluate theories by persuading each other in regard to epistemological qualities such as deduction and fact. There is, however, a flaw intrinsic to evaluation-by-persuasion: an individual can attempt and even succeed in persuading others by asserting that their reasoning is logical when it is not. This is a problem since, from an epistemological perspective, it is not always transparent nor obvious when a persuasive assertion is actually deductively warranted. (...) Empirical research upon reasoning, indeed, supports the notion that assertions are often strongly persuasive for reasons other than their logic. The unreliability of the link between persuasion and logic raises an important methodological issue: how do scientists debate in a manner such that claimed but false “logical” arguments are ignored, and only warranted arguments get to determine theory preference? This need for soundness in debate is a particularly important epistemological concern in cases where the deductive qualities of persuasive argument are not overt, and so cannot be directly checked --such as when they are founded upon Bayesianism probabilistic coherence. The argument presented here is that scientists make the qualities of probabilistic and nonprobabilistic inference sound (and so warranted) through how they organize their debate. Scientists, I argue, abide by “epistemological quality control practices” that limit the persuasive power of unsound arguments upon theory evaluation. Examples of such debate quality control practices are publicness, clarity, openness to criticism, and the collective promotion of attempts at theory conjecture and refutation. Methodologically, these quality control practices are extralogical since they do not directly provide scientific inferences with additional logical warrantedness. They function instead in science to generate an epistemological evaluative environment in which persuasiveness is due, and only due, to logic (i.e. sound). Their methodological role is therefore to make what is warranted de papyri (in our principles of rationality – epistemologically competence) also what is persuasive in evaluation and debate de cognitio (in our exercise of such principles – epistemologically performance). Several limitations exist upon the soundness of Bayesian inferential coherence – surreptitious revision, logical omniscience, uncertain evidence, old evidence, and new hypotheses. Bayesianism, as a result, can only exist if it is pursued in a debate that is regulated by quality control practices over its inferences (for instance, practices that ensure there is autonomy of inference, diligence of inference, probity of evidence, auditability of inference and assiduousness of conjecture). In this context, one can reinterpret Popper’s concern with criticism, openness, refutation and conjecture, as deriving not (as he thought) directly from the needs of logic, but, indirectly, from the need of scientists to create epistemological soundness. (shrink)

We analyse the issue of using prior information in frequentist statistical inference. For that purpose, we scrutinise different kinds of sampling designs in Jerzy Neyman’s theory to reveal a variety of ways to explicitly and objectively engage with prior information. Further, we turn to the debate on sampling paradigms (design-based vs. model-based approaches) to argue that Neyman’s theory supports an argument for the intermediate approach in the frequentism vs. Bayesianism debate. We also demonstrate that Neyman’s theory, by allowing non-epistemic (...) values to influence evidence collection and formulation of statistical conclusions, does not compromise the epistemic reliability of the procedures and may improve it. This undermines the value-free ideal of scientific inference. (shrink)

Following Kuhn's main thesis according to which theory revision and acceptance is always paradigm relative, I propose to outline some possible consequences of such a view. First, asking the question in what sense Bayesian decision theory could serve as the appropriate (normative) theory of rationality examined from the point of view of the epistemology of theory acceptance, I argue that Bayesianism leads to a narrow conception of theory acceptance. Second, regarding the different types of theory revision, i.e. expansion, contraction, (...) replacement and residuals shifts, I extract from Kuhn's view a series of indications showing that theory replacement cannot be rationalized within the framework of Bayesian decision theory, not even within a more sophisticated version of that model. Third, and finally, I will point to the need for a more comprehensive model of rationality than the Bayesian expected utility maximization model, the need for a model which could better deal with the different aspects of theory replacement. I will show that Kuhn's distinction between normal and revolutionary science gives us several hints for a more adequate theory of rationality in science. I will also show that Kuhn is not in a position to fully articulate his main ideas and that he well be confronted with a serious problem concerning collective choice of a paradigm. (shrink)

We demonstrate that Statistical significance (Chow 1996) includes straw man arguments against (1) effect size, (2) meta-analysis, and (3) Bayesianism. We agree with the author that in experimental designs, H0 “is the effect of chance influences on the data-collection procedure . . . it says nothing about the substantive hypothesis or its logical complement” (Chow 1996, p. 41).

The epistemic problem of assessing the support that some evidence confers on a hypothesis is considered using an extended example from the history of meteorology. In this case, and presumably in others, the problem is to develop techniques of data analysis that will link the sort of evidence that can be collected to hypotheses of interest. This problem is solved by applying mathematical tools to structure the data and connect them to the competing hypotheses. I conclude that mathematical innovations provide (...) crucial epistemic links between evidence and theories precisely because the evidence and theories are mathematically described.Keywords: J. N. Lockyer; Gilbert T. Walker; ENSO; Models; Bayesianism. (shrink)

J. Howard Sobel has long been recognized as an important figure in philosophical discussions of rational decision. He has done much to help formulate the concept of causal decision theory. In this volume of essays Sobel explores the Bayesian idea that rational actions maximize expected values, where an action's expected value is a weighted average of its agent's values for its possible total outcomes. Newcomb's Problem and The Prisoner's Dilemma are discussed, and Allais-type puzzles are viewed from the perspective of (...) causal world Bayesianism. The author establishes principles for distinguishing options in decision problems, and studies ways in which perfectly rational causal maximizers can be capable of resolute choices. Sobel also views critically Gauthier's revisionist ideas about maximizing rationality. This collection will be a desideratum for anyone working in the field of rational choice theory, whether in philosophy, economics, political science, psychology or statistics. Howard Sobel's work in decision theory is certainly among the most important, interesting and challenging that is being done by philosophers. (shrink)

Orthodox Bayesianism is a highly idealized theory of how we ought to live our epistemic lives. One of the most widely discussed idealizations is that of logical omniscience: the assumption that an agent’s degrees of belief must be probabilistically coherent to be rational. It is widely agreed that this assumption is problematic if we want to reason about bounded rationality, logical learning, or other aspects of non-ideal epistemic agency. Yet, we still lack a satisfying way to avoid logical omniscience (...) within a Bayesian framework. Some proposals merely replace logical omniscience with a different logical idealization; others sacrifice all traits of logical competence on the altar of logical non-omniscience. We think a better strategy is available: by enriching the Bayesian framework with tools that allow us to capture what agents can and cannot infer given their limited cognitive resources, we can avoid logical omniscience while retaining the idea that rational degrees of belief are in an important way constrained by the laws of probability. In this paper, we offer a formal implementation of this strategy, show how the resulting framework solves the problem of logical omniscience, and compare it to orthodox Bayesianism as we know it. (shrink)

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

This paper examines the debate between permissive and impermissive forms of Bayesianism. It briefly discusses some considerations that might be offered by both sides of the debate, and then replies to some new arguments in favor of impermissivism offered by Roger White. First, it argues that White’s (Oxford studies in epistemology, vol 3. Oxford University Press, Oxford, pp 161–186, 2010) defense of Indifference Principles is unsuccessful. Second, it contends that White’s (Philos Perspect 19:445–459, 2005) arguments against permissive views do (...) not succeed. (shrink)

This book explores the Bayesian approach to the logic and epistemology of scientific reasoning. Section 1 introduces the probability calculus as an appealing generalization of classical logic for uncertain reasoning. Section 2 explores some of the vast terrain of Bayesian epistemology. Three epistemological postulates suggested by Thomas Bayes in his seminal work guide the exploration. This section discusses modern developments and defenses of these postulates as well as some important criticisms and complications that lie in wait for the Bayesian epistemologist. (...) Section 3 applies the formal tools and principles of the first two sections to a handful of topics in the epistemology of scientific reasoning: confirmation, explanatory reasoning, evidential diversity and robustness analysis, hypothesis competition, and Ockham's Razor. (shrink)

We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as 'Trumped' (Arntzenius and McCarthy 1997), 'Rouble trouble' (Arntzenius and Barrett 1999), 'The airtight Dutch book' (McGee 1999), and 'The two envelopes puzzle' (Broome 1995). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably (...) additive. The resolution also shows that when infinitely many decisions are involved, the difference between making the decisions simultaneously and making them sequentially can be the difference between riches and ruin. Finally, the resolution reveals a new way in which the ability to make binding commitments can save perfectly rational agents from sure losses. (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)

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)

Two of the most influential theories about scientific inference are inference to the best explanation and Bayesianism. How are they related? Bas van Fraassen has claimed that IBE and Bayesianism are incompatible rival theories, as any probabilistic version of IBE would violate Bayesian conditionalization. In response, several authors have defended the view that IBE is compatible with Bayesian updating. They claim that the explanatory considerations in IBE are taken into account by the Bayesian because the Bayesian either does (...) or should make use of them in assigning probabilities to hypotheses. I argue that van Fraassen has not succeeded in establishing that IBE and Bayesianism are incompatible, but that the existing compatibilist response is also not satisfactory. I suggest that a more promising approach to the problem is to investigate whether explanatory considerations are taken into account by a Bayesian who assigns priors and likelihoods on his or her own terms. In this case, IBE would emerge from the Bayesian account, rather than being used to constrain priors and likelihoods. I provide a detailed discussion of the case of how the Copernican and Ptolemaic theories explain retrograde motion, and suggest that one of the key explanatory considerations is the extent to which the explanation a theory provides depends on its core elements rather than on auxiliary hypotheses. I then suggest that this type of consideration is reflected in the Bayesian likelihood, given priors that a Bayesian might be inclined to adopt even without explicit guidance by IBE. The aim is to show that IBE and Bayesianism may be compatible, not because they can be amalgamated, but rather because they capture substantially similar epistemic considerations. 1 Introduction2 Preliminaries3 Inference to the Best Explanation4 Bayesianism5 The Incompatibilist View : Inference to the Best Explanation Contradicts Bayesianism5. 1 Criticism of the incompatibilist view6 Constraint - Based Compatibilism6. 1 Criticism of constraint - based compatibilism7 Emergent Compatibilism7. 1 Analysis of inference to the best explanation7. 1. 1 Inference to the best explanation on specific hypotheses7. 1. 2 Inference to the best explanation on general theories7. 1. 3 Copernicus versus Ptolemy7. 1. 4 Explanatory virtues7. 1. 5 Summary7. 2 Bayesian account8 Conclusion. (shrink)

In this paper I develop an account of member obligation: the obligations that fall on the members of an obligated collective in virtue of that collective obligation. I use this account to argue that unorganized collections of individuals can constitute obligated agents. I argue first that, to know when a collective obligation entails obligations on that collective’s members, we have to know not just what it would take for each member to do their part in satisfying (...) the collective obligation, but also what they should do if they cannot do their part because others will not do theirs. I go on to argue (contra recent proposals) that it is not good enough for members in this situation to reasonably believe that others will not do their part. Rather, for a member of an obligated collective to permissibly escape doing her part in a collective obligation, she must both reasonably doubt that others will do their part and stand ready to act in case others do as well. -/- This necessary condition for collective obligation points the way to plausible sufficient conditions – conditions that, I argue, allow unstructured collectives to bear obligations. For (a) if a collective’s members are individually obligated to be ready to do their part, in a given collective action, and (b) if that individual readiness makes it sufficiently likely that the collective will in fact act, then it is hard to see what could block an attribution of collective obligation. In particular, in that case there ought to be no additional objection that there is no existing, organized “agent” on which the obligation might fall. For agents are, simply, things that can act. To be able to act is just to be able to succeed by trying. Unstructured collectives try to do something, I argue, when each member acts on their willingness to do their part in that thing if others do theirs; sometimes they succeed, producing a collective action. Some unstructured collectives, therefore, can succeed by trying; therefore, they can act; therefore they are agents. (shrink)

A Bayesian mind is, at its core, a rational mind. Bayesianism is thus well-suited to predict and explain mental processes that best exemplify our ability to be rational. However, evidence from belief acquisition and change appears to show that we do not acquire and update information in a Bayesian way. Instead, the principles of belief acquisition and updating seem grounded in maintaining a psychological immune system rather than in approximating a Bayesian processor.

Proponents of IBE claim that the ability of a hypothesis to explain a range of phenomena in a unifying way contributes to the hypothesis’s credibility in light of these phenomena. I propose a Bayesian justification of this claim that reveals a hitherto unnoticed role for explanatory unification in evaluating the plausibility of a hypothesis: considerations of explanatory unification enter into the determination of a hypothesis’s prior by affecting its ‘explanatory coherence’, that is, the extent to which the hypothesis offers mutually (...) cohesive explanations of various phenomena. (shrink)

A study of the possibility of casting plausible matheamtical inference in Bayesian terms.

Likelihoodists and Bayesians seem to have a fundamental disagreement about the proper probabilistic explication of relational (or contrastive) conceptions of evidential support (or confirmation). In this paper, I will survey some recent arguments and results in this area, with an eye toward pinpointing the nexus of the dispute. This will lead, first, to an important shift in the way the debate has been couched, and, second, to an alternative explication of relational support, which is in some sense a "middle way" (...) between Likelihoodism and Bayesianism. In the process, I will propose some new work for an old probability puzzle: the "Monty Hall" problem. (shrink)

In the first paper, I discussed the basic claims of Bayesianism (that degrees of belief are important, that they obey the axioms of probability theory, and that they are rationally updated by either standard or Jeffrey conditionalization) and the arguments that are often used to support them. In this paper, I will discuss some applications these ideas have had in confirmation theory, epistemol- ogy, and statistics, and criticisms of these applications.

Many philosophers in the field of meta-ethics believe that rational degrees of confidence in moral judgments should have a probabilistic structure, in the same way as do rational degrees of belief. The current paper examines this position, termed “moral Bayesianism,” from an empirical point of view. To this end, we assessed the extent to which degrees of moral judgments obey the third axiom of the probability calculus, ifP(A∩B)=0thenP(A∪B)=P(A)+P(B), known as finite additivity, as compared to degrees of beliefs on the (...) one hand and degrees of desires on the other. Results generally converged to show that degrees of moral judgment are more similar to degrees of belief than to degrees of desire in this respect. This supports the adoption of a Bayesian approach to the study of moral judgments. To further support moral Bayesianism, we also demonstrated its predictive power. Finally, we discuss the relevancy of our results to the meta-ethical debate between moral cognitivists and moral non-cognitivists. (shrink)

Objective Bayesianism is a methodological theory that is currently applied in statistics, philosophy, artificial intelligence, physics and other sciences. This book develops the formal and philosophical foundations of the theory, at a level accessible to a graduate student with some familiarity with mathematical notation.

An important line of response to scepticism appeals to the best explanation. But anti-sceptics have not engaged much with work on explanation in the philosophy of science. I plan to investigate whether plausible assumptions about best explanations really do favour anti-scepticism. I will argue that there are ways of constructing sceptical hypotheses in which the assumptions do favour anti-scepticism, but the size of the support for anti-scepticism is small.