「경험주의의 두 독단」에서 콰인은 인식론적 전체론에 근거해서 모든 문장이 원칙적으로 수정 가능하므로, 무슨 일이 있어도 수정되지 않는 것으로 가정된 분석 문장이 존재하지 않는다고 주장한다. 콰인에 맞서서, 차머스는 베이즈주의 인식론의 이론적 틀을 사용해서 분석성을 옹호한다. 특히 그는 인식론적 전체론을 받아들이는 콰인주의자들이 베이즈주의 조건화 원리를 위반한 합리적인 믿음 수정의 존재에 개입하게 된다는 것을 설득력 있게 논증한다. 그리고 더 나아가 그는 이러한 종류의 믿음 수정에는 개념 변화가 요구된다고 주장한다. 그런데 이것은 곧 콰인주의자들이 자신들이 거부하고자 하는 분석 문장의 존재를 거부할 수 없게 된다는 것을 (...) 의미한다. 이 글에서 나는 콰인주의자들이 조건화 원리를 위반한 합리적인 믿음 수정을 개념 변화에 호소하는 대신에 이론 변화에 호소해서 설명할 수 있다는 것을 논증한다. (shrink)

The paper takes thePrincipal Principle to be a norm demanding that subjective degrees of belief of a Bayesian agent be equal to the objective probabilities once the agent has conditionalized his subjective degrees of beliefs on the values of the objective probabilities, where the objective probabilities can be not only chances but any other quantities determined objectively. Weak and strong consistency of the Abstract Principal Principle are defined in terms of classical probability measure spaces. It is proved (...) that the Abstract Principal Principle is weakly consistent and that it is strongly consistent in the category of probability measure spaces where the Boolean algebra representing the objective random events is finite. It is argued that it is desirable to strengthen the Abstract Principal Principle by adding a stability requirement to it. Weak and strong consistency of the resulting Stable Abstract Principal Principle are defined, and the strong consistency of the Abstract Principal Principle is interpreted as necessary for a non-omniscient Bayesian agent to be able to have rational degrees of belief in all epistemic situations. It is shown that the Stable Abstract Principal Principle is weakly consistent, but the strong consistency of the Stable Abstract Principal principle remains an open question. We conclude that we do not yet have proof that Bayesian agents can have rational degrees of belief in every epistemic situation. (shrink)

This book grew out of previously published papers of mine composed over a period of years; they have been reworked (sometimes beyond recognition) so as to form a reasonably coherent whole. Part One treats of informative inference. I argue (Chapter 2) that the traditional principle of induction in its clearest formulation (that laws are confirmed by their positive cases) is clearly false. Other formulations in terms of the 'uniformity of nature' or the 'resemblance of the future to the past' (...) seem to me hopelessly unclear. From a Bayesian point of view, 'learning from experience' goes by conditionalization (Bayes' rule). The traditional stum bling block for Bayesians has been to fmd objective probability inputs to conditionalize upon. Subjective Bayesians allow any probability inputs that do not violate the usual axioms of probability. Many subjectivists grant that this liberality seems prodigal but own themselves unable to think of additional constraints that might plausibly be imposed. To be sure, if we could agree on the correct probabilistic representation of 'ignorance' (or absence of pertinent data), then all probabilities obtained by applying Bayes' rule to an 'informationless' prior would be objective. But familiar contra dictions, like the Bertrand paradox, are thought to vitiate all attempts to objectify 'ignorance'. BuUding on the earlier work of Sir Harold Jeffreys, E. T. Jaynes, and the more recent work ofG. E. P. Box and G. E. Tiao, I have elected to bite this bullet. In Chapter 3, I develop and defend an objectivist Bayesian approach. (shrink)

The Sleeping Beauty problem has attracted considerable attention in the literature as a paradigmatic example of how self-locating uncertainty creates problems for the Bayesian principles of Conditionalization and Reflection. Furthermore, it is also thought to raise serious issues for diachronic Dutch Book arguments. I show that, contrary to what is commonly accepted, it is possible to represent the Sleeping Beauty problem within a standard Bayesian framework. Once the problem is correctly represented, the ‘thirder’ solution satisfies standard rationality (...) principles, vindicating why it is not vulnerable to diachronic Dutch Book arguments. Moreover, the diachronic Dutch Books against the ‘halfer’ solutions fail to undermine the standard arguments for Conditionalization. The main upshot that emerges from my discussion is that the disagreement between different solutions does not challenge the applicability of Bayesian reasoning to centered settings, nor the commitment to Conditionalization, but is instead an instance of the familiar problem of choosing the priors. (shrink)

The likelihood principle (LP) is a core issue in disagreements between Bayesian and frequentist statistical theories. Yet statements of the LP are often ambiguous, while arguments for why a Bayesian must accept it rely upon unexamined implicit premises. I distinguish two propositions associated with the LP, which I label LP1 and LP2. I maintain that there is a compelling Bayesian argument for LP1, based upon strict conditionalization, standard Bayesian decision theory, and a proposition I (...) call the practical relevance principle. In contrast, I argue that there is no similarly compelling argument for or against LP2. I suggest that these conclusions lead to a restrictedly pluralistic view of Bayesian confirmation measures. (shrink)

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

Probabilism in epistemology does not have to be of the Bayesian variety. The probabilist represents a person''s opinion as a probability function; the Bayesian adds that rational change of opinion must take the form of conditionalizing on new evidence. I will argue that this is the correct procedure under certain special conditions. Those special conditions are important, and instantiated for example in scientific experimentation, but hardly universal. My argument will be related to the much maligned Reflection Principle (...) (van Fraassen, 1984, 1995), and partly inspired by the work of Brian Skyrms (1987). (shrink)

The applicability of Bayesian conditionalization in setting one’s posterior probability for a proposition, α, is limited to cases where the value of a corresponding prior probability, PPRI(α|∧E), is available, where ∧E represents one’s complete body of evidence. In order to extend probability updating to cases where the prior probabilities needed for Bayesian conditionalization are unavailable, I introduce an inference schema, defeasible conditionalization, which allows one to update one’s personal probability in a proposition by conditioning on (...) a proposition that represents a proper subset of one’s complete body of evidence. While defeasible conditionalization has wider applicability than standard Bayesian conditionalization (since it may be used when the value of a relevant prior probability, PPRI(α|∧E), is unavailable), there are circumstances under which some instances of defeasible conditionalization are unreasonable. To address this difficulty, I outline the conditions under which instances of defeasible conditionalization are defeated. To conclude the article, I suggest that the prescriptions of direct inference and statistical induction can be encoded within the proposed system of probability updating, by the selection of intuitively reasonable prior probabilities. (shrink)

The principle of maximum entropy is a method for assigning values to probability distributions on the basis of partial information. In usual formulations of this and related methods of inference one assumes that this partial information takes the form of a constraint on allowed probability distributions. In practical applications, however, the information consists of empirical data. A constraint rule is then employed to construct constraints on probability distributions out of these data. Usually one adopts the rule that equates the (...) expectation values of certain functions with their empirical averages. There are, however, various other ways in which one can construct constraints from empirical data, which makes the maximum entropy principle lead to very different probability assignments. This paper shows that an argument by Jaynes to justify the usual constraint rule is unsatisfactory and investigates several alternative choices. The choice of a constraint rule is also shown to be of crucial importance to the debate on the question whether there is a conflict between the methods of inference based on maximum entropy and Bayesian conditionalization. (shrink)

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

I re-examine Coherence Arguments (Dutch Book Arguments, No Arbitrage Arguments) for diachronic constraints on Bayesian reasoning. I suggest to replace the usual game–theoretic coherence condition with a new decision–theoretic condition ('Diachronic Sure Thing Principle'). The new condition meets a large part of the standard objections against the Coherence Argument and frees it, in particular, from a commitment to additive utilities. It also facilitates the proof of the Converse Dutch Book Theorem. I first apply the improved Coherence Argument to (...) van Fraassen's (1984) Reflection principle. I then point out the failure of a Coherence Argument that is intended to support Conditionalization as a naive, universal, update rule. I also point out that Reflection is incompatible with the universal use of Conditionalization thus interpreted. The Coherence Argument therefore defeats the naive view on Bayesian learning that it was originally designed to justify. (shrink)

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

Rescorla (Erkenntnis, 2020) has recently pointed out that the standard arguments for Bayesian Conditionalization assume that whenever I become certain of something, it is true. Most people would reject this assumption. In response, Rescorla offers an improved Dutch Book argument for Bayesian Conditionalization that does not make this assumption. My purpose in this paper is two-fold. First, I want to illuminate Rescorla’s new argument by giving a very general Dutch Book argument that applies to many cases (...) of updating beyond those covered by Conditionalization, and then showing how Rescorla’s version follows as a special case of that. Second, I want to show how to generalise R. A. Briggs and Richard Pettigrew’s Accuracy Dominance argument to avoid the assumption that Rescorla has identified (Briggs and Pettigrew in Noûs, 2018). In both cases, these arguments proceed by first establishing a very general reflection principle. (shrink)

This develops a framework for second-order conditionalization on statements about one's own epistemic reliability. It is the generalization of the framework of "Second-Guessing" (2009) to the case where the subject is uncertain about her reliability. See also "Epistemic Self-Doubt" (2017).

Hume bases his argument against miracles on an informal principle. This paper gives a formal explication of this principle of Hume’s, and then shows that this explication can be rigorously proved in a Bayesian framework.

The principle of proportionality is seen as the highest peak of structural, logical thinking that enables balancing between constitutional principles and their interferences. So far, Alexy's weight formula has been the most advanced approach in structured balancing of proportionality stricto sensu, while this paper shows it as still too subjective. Despite judicial tests—or different, manifestly inappropriate reasonableness tests—proportionality stricto sensu hides some form of the jumping-to-conclusions bias, because the inference is made through a subjective lens. The paper presents structured (...) legal balancing (and hence reasoning) based on Bayes’ theorem. This paper, based on the connection between probability and hypothetical legal norms, transfers the four-part structure of proportionality into the relevant four-part structure of the Bayes tree. This transfer shows the first as flawed due to its failing to consider means that can have the same effects as the considered ones. Only by inclusion of the latter can the total probability of a considered case be established. Numerical proportionality à la Bayes can be further improved through the use of public-value weights that are obtained from surveys or online communities of people giving weights in the real time (collective wisdom). The Bayesian approach can also be used in adjudication as a control in assessing judicial standards in use. (shrink)

Recently, some have challenged the idea that there are genuine norms of diachronic rationality. Part of this challenge has involved offering replacements for diachronic principles. Skeptics about diachronic rationality believe that we can provide an error theory for it by appealing to synchronic updating rules that, over time, mimic the behavior of diachronic norms. In this paper, I argue that the most promising attempts to develop this position within the Bayesian framework are unsuccessful. I sketch a new synchronic surrogate (...) that draws upon some of the features of each of these earlier attempts. At the heart of this discussion is the question of what exactly it means to say that one norm is a surrogate for another. I argue that surrogacy, in the given context, can be taken as a proxy for the degree to which formal and traditional epistemology can be made compatible. (shrink)

This paper develops a trivalent semantics for indicative conditionals and extends it to a probabilistic theory of valid inference and inductive learning with conditionals. On this account, (i) all complex conditionals can be rephrased as simple conditionals, connecting our account to Adams's theory of p-valid inference; (ii) we obtain Stalnaker's Thesis as a theorem while avoiding the well-known triviality results; (iii) we generalize Bayesian conditionalization to an updating principle for conditional sentences. The final result is a unified (...) semantic and probabilistic theory of conditionals with attractive results and predictions. (shrink)

This paper suggests a new principle for confirmation theory which is called the principle of explanatory surplus. This principle is shown to be non-Bayesian in character, and to lead to a treatment of simplicity in science. Two cases of the principle of explanatory surplus are considered. The first (number of parameters) is illustrated by curve-fitting examples, while the second (number of theoretical assumptions) is illustrated by the examples of Newton's Laws and Adler's Theory of the (...) Inferiority Complex. (shrink)

When P(E) > 0, conditional probabilities P(H|E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(H|E)$$\end{document} are given by the ratio formula. An agent engages in ratio conditionalization when she updates her credences using conditional probabilities dictated by the ratio formula. Ratio conditionalization cannot eradicate certainties, including certainties gained through prior exercises of ratio conditionalization. An agent who updates her credences only through ratio conditionalization risks permanent certainty in propositions against which she has overwhelming evidence. To (...) avoid this undesirable consequence, I argue that we should supplement ratio conditionalization with Kolmogorov conditionalization, a strategy for updating credences based on propositions E such that P(E) = 0. Kolmogorov conditionalization can eradicate certainties, including certainties gained through prior exercises of conditionalization. Adducing general theorems and detailed examples, I show that Kolmogorov conditionalization helps us model epistemic defeat across a wide range of circumstances. (shrink)

Bayesian analyses are prominent among recent and allegedly novel interpretations of Hume’s argument against the justified belief in miracles. However, since there is no consensus on just what Hume’s argument is any Bayesian analysis will beg crucial issues of interpretation. Apart from independent philosophical arguments—arguments that would undermine the relevance of a Bayesian analysis to the question of the credibility of reports of the miraculous—no such analysis can, in principle, prove that no testimony can (or cannot) (...) establish the credibility of a miracle. Bayesian analyses of Hume’s argument are not analyses of Hume’s argument at all—but superfluous representations of it. (shrink)

Conditionalization is a norm that governs the rational reallocation of credence. I distinguish between factive and non-factive formulations of Conditionalization. Factive formulations assume that the conditioning proposition is true. Non-factive formulations allow that the conditioning proposition may be false. I argue that non-factive formulations provide a better foundation for philosophical and scientific applications of Bayesian decision theory. I furthermore argue that previous formulations of Conditionalization, factive and non-factive alike, have almost universally ignored, downplayed, or mishandled a (...) crucial causal aspect of Conditionalization. To formulate Conditionalization adequately, one must explicitly address the causal structure of the transition from old credences to new credences. I offer a formulation of Conditionalization that takes these considerations into account, and I compare my preferred formulation with some prominent formulations found in the literature. (shrink)

The goal of the paper is to review existing work on consciousness within the frameworks of Predictive Processing, Active Inference, and Free Energy Principle. The emphasis is put on the role played by the precision and complexity of the internal generative model. In the light of those proposals, these two properties appear to be the minimal necessary components for the emergence of conscious experience—a Minimal Unifying Model of consciousness.

This article examines the effect of material evidence upon historiographic hypotheses. Through a series of successive Bayesian conditionalizations, I analyze the extended competition among several hypotheses that offered different accounts of the transition between the Bronze Age and the Iron Age in Palestine and in particular to the “emergence of Israel”. The model reconstructs, with low sensitivity to initial assumptions, the actual outcomes including a complete alteration of the scientific consensus. Several known issues of Bayesian confirmation, including the (...) problem of old evidence, the introduction and confirmation of novel theories and the sensitivity of convergence to uncertain and disputed evidence are discussed in relation to the model’s result and the actual historical process. The most important result is that convergence of probabilities and of scientific opinion is indeed possible when advocates of rival hypotheses hold similar judgment about the factual content of evidence, even if they differ sharply in their historiographic interpretation. This speaks against the contention that understanding of present remains is so irrevocably biased by theoretical and cultural presumptions as to make an objective assessment impossible. (shrink)

This paper discusses and rejects some objections raised by Chihara to the book Scientific Reasoning: the Bayesian Approach, by Howson and Urbach. Some of Chihara's objections are of independent interest because they reflect widespread misconceptions. One in particular, that the Bayesian theory presupposes logical omniscience, is widely regarded as being fatal to the entire Bayesian enterprise, It is argued here that this is no more true than the parallel charge that the theory of deductive logic is fatally (...) comprised because it presupposes logical omniscience. Neither theory presupposes logical omniscience. (shrink)

This paper discusses and rejects some objections raised by Chihara to the book Scientific Reasoning: the Bayesian Approach, by Howson and Urbach. Some of Chihara's objections are of independent interest because they reflect widespread misconceptions. One in particular, that the Bayesian theory presupposes logical omniscience, is widely regarded as being fatal to the entire Bayesian enterprise, It is argued here that this is no more true than the parallel charge that the theory of deductive logic is fatally (...) comprised because it presupposes logical omniscience. Neither theory presupposes logical omniscience. (shrink)

The paper considers the legal tools that have been developed in German pharmaceutical regulation as a result of the precautionary attitude inaugurated by the Contergan decision. These tools are the notion of “well-founded suspicion”, which attenuates the requirements for safety intervention by relaxing the requirement of a proved causal connection between danger and source, and the introduction of the reversal of proof burden in liability norms. The paper focuses on the first and proposes seeing the precautionary principle as an (...) instance of the requirement that one should maximise expected utility. In order to maximise expected utility certain probabilities are required and it is argued that objective Bayesianism offers the most plausible means to determine the optimal decision in cases where evidence supports diverging choices. (shrink)

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology – namely, Behaviorism and evolutionary psychology – that set aside mechanistic explanations or make use of optimality assumptions. (...) Through these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls that have plagued previous theoretical movements. (shrink)

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

Various sexist and racist beliefs ascribe certain negative qualities to people of a given sex or race. Epistemic allies are people who think that in normal circumstances rationality requires the rejection of such sexist and racist beliefs upon learning of many counter-instances, i.e. members of these groups who lack the target negative quality. Accordingly, epistemic allies think that those who give up their sexist or racist beliefs in such circumstances are rationally responding to their evidence, while those who do not (...) are irrational in failing to respond to their evidence by giving up their belief. This is a common view among philosophers and non-philosophers. But epistemic allies face three problems. First, sexist and racist beliefs often involve generic propositions. These sorts of propositions are notoriously resilient in the face of counter-instances since the truth of generic propositions is typically compatible with the existence of many counter-instances. Second, background beliefs can enable one to explain away counter-instances to one’s beliefs. So even when counter-instances might otherwise constitute strong evidence against the truth of the generic, the ability to explain the counter-instances away with relevant background beliefs can make it rational to retain one’s belief in the generic despite the existence of many counter-instances. The final problem is that the kinds of judgements epistemic allies want to make about the irrationality of sexist and racist beliefs upon encountering many counter-instances is at odds with the judgements that we are inclined to make in seemingly parallel cases about the rationality of non-sexist and non-racist generic beliefs. Thus epistemic allies may end up having to give up on plausible normative supervenience principles. All together, these problems pose a significant prima facie challenge to epistemic allies. In what follows I explain how a Bayesian approach to the relation between evidence and belief can neatly untie these knots. The basic story is one of defeat: Bayesianism explains when one is required to become increasingly confident in chance propositions, and confidence in chance propositions can make belief in corresponding generics irrational. (shrink)

Many philosophers regard the imprecise credence framework as a more realistic model of probabilistic inferences with imperfect empirical information than the traditional precise credence framework. Hence, it is surprising that the literature lacks any discussion on how to update one’s imprecise credences when the given evidence itself is imprecise. To fill this gap, I consider two updating principles. Unfortunately, each of them faces a serious problem. The first updating principle, which I call “generalized conditionalization,” sometimes forces an agent (...) to change her imprecise degrees of belief even though she does not have new evidence. The second updating principle, which I call “the generalized dynamic Keynesian model,” may result in a very precise credal state although the agent does not have sufficiently strong evidence to justify such an informative doxastic state. This means that it is much more difficult to come up with an acceptable updating principle for the imprecise credence framework than one might have thought it would be. (shrink)

What kind of thing do you believe when you believe that you are in a certain place, that it is a certain time, and that you are a certain individual? What happens if you get lost, or lose track of the time? Can you ever be unsure of your own identity? These are the kind of questions considered in my thesis. Beliefs about where, when and who you are are what are called in the literature de se, or self-locating beliefs. (...) This thesis examines how we can represent de se beliefs, and how we can reason about de se uncertainty. In the first part of the thesis, I present and motivate a specific account of the content of de se belief, based on the one given by David Lewis. On this account, the content of de se beliefs are centred propositions. I defend this view against a rival account, put forward by Robert Stalnaker, according to whom the content of de se beliefs are ordinary propositions. In the second part of the thesis, I explore how we can reason probabilistically about de se uncertainty. I start by defining probabilities over centred propositions, and investigate what probabilities mean in this context. As it turns out, all the main interpretations of probability can be extended to centred propositions. The only trouble seems to arise for the Bayesian principle of updating via conditionalization. After giving a diagnosis of the problem, I offer a solution by formulating a natural extension of conditionalization, which I argue preserves the essential features of Bayesian reasoning. In the final chapter, I apply my view and show that it leads to a natural resolution of a puzzle that is generally taken to be a test case for any account of centred updating. (shrink)

Charles Chihara has presented a problem he claims Bayesian confirmation theory cannot handle. Chihara gives examples in which he claims the change in belief cannot be construced as conditionalizing on new evidence. These are situations in which the agent suddenly thinks of new possibilities. I propose a solution that incorporates the important ideas of Bayesian theory. In particular, I present a principle which shows that the change of belief in Chihara's example is due to simple conditionalization.

Van Fraassen does not merely perform Bayesian conditionalization on his pragmatic theory of scientific explanation; he uses inference to the best explanation (IBE) to justify it, contrary to what Prasetya thinks. Without first using IBE, we cannot carry out Bayesian conditionalization, contrary to what van Fraassen thinks. The argument from a bad lot, which van Fraassen constructs to criticize IBE, backfires on both the pragmatic theory and Bayesian conditionalization, pace van Fraassen and Prasetya.

This paper presents a new argument for the Principle of Indifference. This argument can be thought of in two ways: as a pragmatic argument, justifying the principle as needing to hold if one is to minimise worst-case expected loss, or as an epistemic argument, justifying the principle as needing to hold in order to minimise worst-case expected inaccuracy. The question arises as to which interpretation is preferable. I show that the epistemic argument contradicts Evidentialism and suggest that (...) the relative plausibility of Evidentialism provides grounds to prefer the pragmatic interpretation. If this is right, it extends to a general preference for pragmatic arguments for the Principle of Indifference, and also to a general preference for pragmatic arguments for other norms of Bayesian epistemology. (shrink)

The proportional weight view in epistemology of disagreement generalizes the equal weight view and proposes that we assign to judgments of different people weights that are proportional to their epistemic qualifications. It is shown that if the resulting degrees of confidence are to constitute a probability function, they must be the weighted arithmetic means of individual degrees of confidence, while if the resulting degrees of confidence are to obey the Bayesian rule of conditionalization, they must be the weighted (...) geometric means of individual degrees of confidence. The double bind entails that the proportional weight view (and its moderate adjustment in favor of one’s own judgment) is inconsistent with Bayesianism. (shrink)

This paper presents a new argument for the Principle of Indifference. This argument can be thought of in two ways: as a pragmatic argument, justifying the principle as needing to hold if one is to minimise worst-case expected loss, or as an epistemic argument, justifying the principle as needing to hold in order to minimise worst-case expected inaccuracy. The question arises as to which interpretation is preferable. I show that the epistemic argument contradicts Evidentialism and suggest that (...) the relative plausibility of Evidentialism provides grounds to prefer the pragmatic interpretation. If this is right, it extends to a general preference for pragmatic arguments for the Principle of Indifference, and also to a general preference for pragmatic arguments for other norms of Bayesian epistemology. (shrink)

The principle of compositionality claims that the content of a complex concept is determined by its constituent concepts and the way in which they are composed. However, for prototype concepts this principle is often too rigid. Blurring the division between conceptual composition and belief update has therefore been suggested. Inspired by this idea, we develop a normative account of how belief revision and meaning composition should interact in modifications such as “red apple” or “pet hamster”. We do this (...) by combining the well-known selective modification model :485–527 1988) with the rules of Bayesian belief update. Moreover, we relate this model to systems of defeasible reasoning as discussed in the field of artificial intelligence. (shrink)

We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several incompatible measurements. One of the measurements is subsequently chosen and performed and the money placed on the other measurements is returned to the agent. We show how the rules of rational betting imply all the interesting features of quantum probability, even in such finite gambles. These include the (...) uncertainty principle and the violation of Bell's inequality among others. Quantum gambles are closely related to quantum logic and provide a new semantics to it. We conclude with a philosophical discussion on the interpretation of quantum mechanics. (shrink)

Can self-locating beliefs be relevant to non-self-locating claims? Traditional Bayesian modeling techniques have trouble answering this question because their updating rule fails when applied to situations involving contextsensitivity. This essay develops a fully general framework for modeling stories involving context-sensitive claims. The key innovations are a revised conditionalization rule and a principle relating models of the same story with different modeling languages. The essay then applies the modeling framework to the Sleeping Beauty Problem, showing that when Beauty (...) awakens her degree of belief in heads should be one-third. This demonstrates that it can be rational for an agent who gains only self-locating beliefs between two times to alter her degree of belief in a non-self-locating claim. (shrink)

We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance, the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One of the measurements is subsequently chosen and performed and the money placed on the other measurements is returned to the agent. We show how the rules of rational betting imply all the interesting features of quantum probability, even in such finite gambles. These (...) include the uncertainty principle and the violation of Bell's inequality among others. Quantum gambles are closely related to quantum logic and provide a new semantics for it. We conclude with a philosophical discussion on the interpretation of quantum mechanics. (shrink)

According to the Bayesian paradigm in the psychology of reasoning, the norms by which everyday human cognition is best evaluated are probabilistic rather than logical in character. Recently, the Bayesian paradigm has been applied to the domain of argumentation, where the fundamental norms are traditionally assumed to be logical. Here, we present a major generalisation of extant Bayesian approaches to argumentation that utilizes a new class of Bayesian learning methods that are better suited to modelling dynamic (...) and conditional inferences than standard Bayesian conditionalization, is able to characterise the special value of logically valid argument schemes in uncertain reasoning contexts, greatly extends the range of inferences and argumentative phenomena that can be adequately described in a Bayesian framework, and undermines some influential theoretical motivations for dual function models of human cognition. We conclude that the probabilistic norms given by the Bayesian approach to rationality are not necessarily at odds with the norms given by classical logic. Rather, the Bayesian theory of argumentation can be seen as justifying and enriching the argumentative norms of classical logic. (shrink)

I show that David Lewis’s principal principle is not preserved under Jeffrey conditionalization. Using this observation, I argue that Lewis’s reason for rejecting the desire as belief thesis and Adams’s thesis applies also to his own principal principle. 1 Introduction2 Adams’s Thesis, the Desire as Belief Thesis, and the Principal Principle3 Jeffrey Conditionalization4 The Principal Principles Not Preserved under Jeffrey Conditionalization5 Inadmissible Experiences.

The probabilities a Bayesian agent assigns to a set of events typically change with time, for instance when the agent updates them in the light of new data. In this paper we address the question of how an agent's probabilities at different times are constrained by Dutch-book coherence. We review and attempt to clarify the argument that, although an agent is not forced by coherence to use the usual Bayesian conditioning rule to update his probabilities, coherence does require (...) the agent's probabilities to satisfy van Fraassen's [1984] reflection principle (which entails a related constraint pointed out by Goldstein [1983]). We then exhibit the specialized assumption needed to recover Bayesian conditioning from an analogous reflection-style consideration. Bringing the argument to the context of quantum measurement theory, we show that "quantum decoherence" can be understood in purely personalist terms---quantum decoherence (as supposed in a von Neumann chain) is not a physical process at all, but an application of the reflection principle. From this point of view, the decoherence theory of Zeh, Zurek, and others as a story of quantum measurement has the plot turned exactly backward. (shrink)