Bayesian probability has recently been proposed as a normative theory of argumentation. In this article, we provide a Bayesian formalisation of the ad Hitlerum argument, as a special case of the ad hominem argument. Across three experiments, we demonstrate that people's evaluation of the argument is sensitive to probabilistic factors deemed relevant on a Bayesian formalisation. Moreover, we provide the first parameter-free quantitative evidence in favour of the Bayesian approach to argumentation. Quantitative Bayesian prescriptions were derived from participants' stated subjective (...) probabilities (Experiments 1 and 2), as well as from frequency information explicitly provided in the experiment (Experiment 3). Participants' stated evaluations of the convincingness of the argument were well matched to these prescriptions. (shrink)

(2013). Rational argument, rational inference. Argument & Computation: Vol. 4, Formal Models of Reasoning in Cognitive Psychology, pp. 21-35. doi: 10.1080/19462166.2012.689327.

We continue the investigations initiated in the recent papers where Bayes logics have been introduced to study the general laws of Bayesian belief revision. In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using the Bayes rule. In this paper we take the more general Jeffrey formula as a conditioning device and study the corresponding modal logics that we call Jeffrey logics, focusing mainly on the countable case. The containment relations among (...) these modal logics are determined and it is shown that the logic of Bayes and Jeffrey updating are very close. It is shown that the modal logic of belief revision determined by probabilities on a finite or countably infinite set of elementary propositions is not finitely axiomatizable. The significance of this result is that it clearly indicates that axiomatic approaches to belief revision might be severely limited. (shrink)

We investigate the general properties of general Bayesian learning, where “general Bayesian learning” means inferring a state from another that is regarded as evidence, and where the inference is conditionalizing the evidence using the conditional expectation determined by a reference probability measure representing the background subjective degrees of belief of a Bayesian Agent performing the inference. States are linear functionals that encode probability measures by assigning expectation values to random variables via integrating them with respect to the probability measure. If (...) a state can be learned from another this way, then it is said to be Bayes accessible from the evidence. It is shown that the Bayes accessibility relation is reflexive, antisymmetric and non-transitive. If every state is Bayes accessible from some other defined on the same set of random variables, then the set of states is called weakly Bayes connected. It is shown that the set of states is not weakly Bayes connected if the probability space is standard. The set of states is called weakly Bayes connectable if, given any state, the probability space can be extended in such a way that the given state becomes Bayes accessible from some other state in the extended space. It is shown that probability spaces are weakly Bayes connectable. Since conditioning using the theory of conditional expectations includes both Bayes’ rule and Jeffrey conditionalization as special cases, the results presented generalize substantially some results obtained earlier for Jeffrey conditionalization. (shrink)

Recent work on conditional reasoning argues that denying the antecedent [DA] and affirming the consequent [AC] are defeasible but cogent patterns of argument, either because they are effective, rational, albeit heuristic applications of Bayesian probability, or because they are licensed by the principle of total evidence. Against this, we show that on any prevailing interpretation of indicative conditionals the premises of DA and AC arguments do not license their conclusions without additional assumptions. The cogency of DA and AC inferences rather (...) depends on contingent factors extrinsic to, and independent of, what is asserted by DA and AC arguments. arguments do not license their conclusions without additional assumptions. The cogency of DA and AC inferences rather depends on contingent factors extrinsic to, and independent of, what is asserted by DA and AC arguments. (shrink)

This paper offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency. Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: change in the commitment to the reason, the reason’s sensitivity and selectivity to the claim, one’s prior commitment to the claim, and the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, and (...) may indeed serve to correct, the informal understanding and applications of the RSA criteria concerning their conceptual dependence, their function as update-thresholds, and their status as obligatory rather than permissive norms, but also show how these formal and informal normative approachs can in fact align. (shrink)

The propensity interpretation of probability was introduced by Popper ([1957]), but has subsequently been developed in different ways by quite a number of philosophers of science. This paper does not attempt a complete survey, but discusses a number of different versions of the theory, thereby giving some idea of the varieties of propensity. Propensity theories are classified into (i) long-run and (ii) single-case. The paper argues for a long-run version of the propensity theory, but this is contrasted with two single-case (...) propensity theories, one due to Miller and the later Popper, and the other to Fetzer. The three approaches are compared by examining how they deal with a key problem for the propensity approach, namely the relationship between propensity and causality and Humphreys' paradox. (shrink)

Popper's writings cover a remarkably wide range of subjects. The spectrum runs from Plato's theory of politics to the foundations of quantum mechanics. Yet even amidst this variety the philosophy of probability occupies a prominent place. David Miller once pointed out to me that more than half of Popper's The Logic of Scientific Discovery is taken up with discussions of probability. I checked this claim using the 1972 6th revised impression of The Logic of Scientific Discovery , and found that (...) of the approximately 450 pages of text, approximately 250 are to do with probability. Thus Miller's claim is amply justified. It seems indeed that the philosophy of probability was one of Popper's favourite subjects, and, as we shall see, Popper certainly enriched the field with several striking innovations. In this area, as in others, Popper held very definite views, and criticized his opponents in no uncertain terms. Popper was an objectivist and anti-Bayesian, and his criticisms were directed against subjectivism and Bayesianism. (shrink)

It is sometimes thought that randomized study group allocation is uniquely proficient at producing comparison groups that are evenly balanced for all confounding causes. Philosophers have argued that in real randomized controlled trials this balance assumption typically fails. But is the balance assumption an important ideal? I run a thought experiment, the CONFOUND study, to answer this question. I then suggest a new account of causal inference in ideal and real comparative group studies that helps clarify the roles of confounding (...) variables and randomization. 1Confounders and Causes2The Balance Assumption3The CONFOUND Study 3.1CONFOUND 13.2CONFOUND 24Disjunction C and the Ideal Study 4.1The ultimate ‘other cause’: C4.2The ideal comparative group study4.3Required conditions for causal inference5Confounders as Causes, Confounders as Correlates6Summary. (shrink)

Does confirmation holism imply meaning holism? A plausible and novel argument, all of whose premises enjoy significant support among contemporary philosophers, links the two theses. This article presents this argument and diagnoses it with a weakness. The weakness illustrates a general difficulty with drawing morals for the nature of ordinary thought and language from claims about the nature of science. The diagnosis is instructive: It suggests more fruitful relations between theories of scientific theory confirmation and semantic theories of our everyday (...) thoughts and statements. (shrink)

GRW Theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as either single (...) case propensities or Humean objective chances. Although single case propensities have some intuitive appeal in the context of GRW theory, on balance it seems that Humean objective chances are preferable on conceptual grounds because single case propensities suffer from various well know problems such as unlimited frequency tolerance and lack of a rationalisation of the principal principle. (shrink)

Traditional analyses of the curve fitting problem maintain that the data do not indicate what form the fitted curve should take. Rather, this issue is said to be settled by prior probabilities, by simplicity, or by a background theory. In this paper, we describe a result due to Akaike [1973], which shows how the data can underwrite an inference concerning the curve's form based on an estimate of how predictively accurate it will be. We argue that this approach throws light (...) on the theoretical virtues of parsimoniousness, unification, and non ad hocness, on the dispute about Bayesianism, and on empiricism and scientific realism. * Both of us gratefully acknowledge support from the Graduate School at the University of Wisconsin-Madison, and NSF grant DIR-8822278 (M.F.) and NSF grant SBE-9212294 (E.S.). Special thanks go to A. W. F. Edwards.William Harper. Martin Leckey. Brian Skyrms, and especially Peter Turney for helpful comments on an earlier draft. (shrink)

The central problem with Bayesian philosophy of science is that it cannot take account of the relevance of simplicity and unification to confirmation, induction, and scientific inference. The standard Bayesian folklore about factoring simplicity into the priors, and convergence theorems as a way of grounding their objectivity are some of the myths that Earman's book does not address adequately. 1Review of John Earman: Bayes or Bust?, Cambridge, MA. MIT Press, 1992, £33.75cloth.

Wayne (1995) critiques the Bayesian explication of the confirmational significance of evidential diversity (CSED) offered by Horwich (1982). Presently, I argue that Wayne’s reconstruction of Horwich’s account of CSED is uncharitable. As a result, Wayne’s criticisms ultimately present no real problem for Horwich. I try to provide a more faithful and charitable rendition of Horwich’s account of CSED. Unfortunately, even when Horwich’s approach is charitably reconstructed, it is still not completely satisfying.

Hempel first introduced the paradox of confirmation in (Hempel 1937). Since then, a very extensive literature on the paradox has evolved (Vranas 2004). Much of this literature can be seen as responding to Hempel’s subsequent discussions and analyses of the paradox in (Hempel 1945). Recently, it was noted that Hempel’s intuitive (and plausible) resolution of the paradox was inconsistent with his official theory of confirmation (Fitelson & Hawthorne 2006). In this article, we will try to explain how this inconsistency affects (...) the historical dialectic about the paradox and how it illuminates the nature of confirmation. In the end, we will argue that Hempel’s intuitions about the paradox of confirmation were (basically) correct, and that it is his theory that should be rejected, in favor of a (broadly) Bayesian account of confirmation. (shrink)

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 applying Bayes’s theorem to the history of science, Bayesians sometimes assume – often without argument – that they can safely ignore very implausible theories. This assumption is false, both in that it can seriously distort the history of science as well as the mathematics and the applicability of Bayes’s theorem. There are intuitively very plausible counter-examples. In fact, one can ignore very implausible or unknown theories only if at least one of two conditions is satisfied: (i) one is certain (...) that there are no unknown theories which explain the phenomenon in question, or (ii) the likelihood of at least one of the known theories used in the calculation of the posterior is reasonably large. Often in the history of science, a very surprising phenomenon is observed, and neither of these criteria is satisfied. (shrink)

has proposed an interesting and novel Bayesian analysis of the Quine-Duhem (Q–D) problem (i.e., the problem of auxiliary hypotheses). Strevens's analysis involves the use of a simplifying idealization concerning the original Q–D problem. We will show that this idealization is far stronger than it might appear. Indeed, we argue that Strevens's idealization oversimplifies the Q–D problem, and we propose a diagnosis of the source(s) of the oversimplification. Some background on Quine–Duhem Strevens's simplifying idealization Indications that (I) oversimplifies Q–D Strevens's argument (...) for the legitimacy of (I). (shrink)

outlined. This account is partly inspired by the work of C.S. Peirce. When we want to consider how degree of confirmation varies with changing I show that a large class of quantitative Bayesian measures of con-.

This paper critically analyzes Sherrilyn Roush's (Tracking truth: knowledge, evidence and science, 2005) definition of evidence and especially her powerful defence that in the ideal, a claim should be probable to be evidence for anything. We suggest that Roush treats not one sense of 'evidence' but three: relevance, leveraging and grounds for knowledge; and that different parts of her argument fare differently with respect to different senses. For relevance, we argue that probable evidence is sufficient but not necessary for Roush's (...) own two criteria of evidence to be met. With respect to grounds for knowledge, we agree that high probability evidence is indeed ideal for the central reason Roush gives: When believing a hypothesis on the basis of e it is desirable that e be probable. But we maintain that her further argument that Bayesians need probable evidence to warrant the method they recommend for belief revision rests on a mistaken interpretation of Bayesian conditionalization. Moreover, we argue that attempts to reconcile Roush's arguments with Bayesianism fail. For leveraging, which we agree is a matter of great importance, the requirement that evidence be probable suffices for leveraging to the probability of the hypothesis if either one of Roush's two criteria for evidence are met. Insisting on both then seems excessive. To finish, we show how evidence, as Roush defines it, can fail to track the hypothesis. This can remedied by adding a requirement that evidence be probable, suggesting another rationale for taking probable evidence as ideal—but only for a grounds-for-knowledge sense of evidence. (shrink)

If knowledge is the norm of practical reasoning, then we should be able to alter people's behavior by affecting their knowledge as well as by affecting their beliefs. Thus, as Roy Sorensen (2010) suggests, we should expect to find people telling lies that target knowledge rather than just lies that target beliefs. In this paper, however, I argue that Sorensen's discovery of “knowledge-lies” does not support the claim that knowledge is the norm of practical reasoning. First, I use a Bayesian (...) framework to show that in each of Sorensen's examples, knowledge-lies alter people's behavior by affecting their beliefs. Second, I show that while we can imagine lies that target knowledge without targeting beliefs, they cannot alter people's behavior. In other words, knowledge-lies actually work (i.e., manipulate behavior) by targeting beliefs or they do not work at all. (shrink)

We provide a Bayesian justification of the idea that, under certain conditions, the absence of an argument in favour of the truth of a hypothesis H constitutes a good argument against the truth of H.

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)

Say that an agent is "epistemically humble" if she is less than certain that her opinions will converge to the truth, given an appropriate stream of evidence. Is such humility rationally permissible? According to the orgulity argument : the answer is "yes" but long-run convergence-to-the-truth theorems force Bayesians to answer "no." That argument has no force against Bayesians who reject countable additivity as a requirement of rationality. Such Bayesians are free to count even extreme humility as rationally permissible.

The concept of randomness has been unjustly neglected in recent philosophical literature, and when philosophers have thought about it, they have usually acquiesced in views about the concept that are fundamentally flawed. After indicating the ways in which these accounts are flawed, I propose that randomness is to be understood as a special case of the epistemic concept of the unpredictability of a process. This proposal arguably captures the intuitive desiderata for the concept of randomness; at least it should suggest (...) that the commonly accepted accounts cannot be the whole story and more philosophical attention needs to be paid. 1. Randomness in science1.1Random systems1.2Random behaviour1.3Random sampling1.4Caprice, arbitrariness and noise2. Concepts of randomness2.1Von Mises/church/martin-löf randomness2.2KCS-randomness3. Randomness is unpredictability: preliminaries3.1Process and product randomness3.2Randomness is indeterminism?4. Predictability4.1Epistemic constraints on prediction4.2Computational constraints on prediction4.3Pragmatic constraints on prediction4.4Prediction defined5. Unpredictability6. Randomness is unpredictability6.1Clarification of the definition of randomness6.2Randomness and probability6.3Subjectivity and context sensitivity of randomness7. Evaluating the analysis[R]andomness … is going to be a concept which is relative to our body of knowledge, which will somehow reflect what we know and what we don't know. Henry E. Kyburg, Jr ([1974], p. 217)Phenomena that we cannot predict must be judged random. Patrick Suppes ([1984], p. 32). (shrink)

I argue that any broadly dispositional analysis of probability will either fail to give an adequate explication of probability, or else will fail to provide an explication that can be gainfully employed elsewhere (for instance, in empirical science or in the regulation of credence). The diversity and number of arguments suggests that there is little prospect of any successful analysis along these lines.

In this article, the author focuses on Philip Kitcher's and Alvin Goldman's economic models of the social character of scientific knowledge production. After introducing some relevant methodological issues in the social sciences and characterizing Kitcher's and Goldman's models, the author goes on to show that special problems arise directly from the concept of an agent invoked in the models. The author argues that the two distinct concepts of agents, borrowed from economics and cognitive psychology, are inconsistent. Finally, the author discusses (...) some of the normative implications that arise from adopting economic concepts of agents in the study of science. (shrink)

Scientific researchers welcome disagreement as a way of furthering epistemic aims. Religious communities, by contrast, tend to regard it as a potential threat to their beliefs. But I argue that religious disagreement can help achieve religious epistemic aims. I do not argue this by comparing science and religion, however. For scientific hypotheses are ideally held with a scholarly neutrality, and my aim is to persuade those who arecommittedto religious beliefs that religious disagreement can be epistemically beneficial for them too.

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

Various scientific theories stand in a reductive relation to each other. In a recent article, we have argued that a generalized version of the Nagel-Schaffner model (GNS) is the right account of this relation. In this article, we present a Bayesian analysis of how GNS impacts on confirmation. We formalize the relation between the reducing and the reduced theory before and after the reduction using Bayesian networks, and thereby show that, post-reduction, the two theories are confirmatory of each other. We (...) then ask when a purported reduction should be accepted on epistemic grounds. To do so, we compare the prior and posterior probabilities of the conjunction of both theories before and after the reduction and ask how well each is confirmed by the available evidence. (shrink)

Karl Popper (1902-1994) was one of the most influential philosophers of science of the 20th century. He made significant contributions to debates concerning general scientific methodology and theory choice, the demarcation of science from non-science, the nature of probability and quantum mechanics, and the methodology of the social sciences. His work is notable for its wide influence both within the philosophy of science, within science itself, and within a broader social context. Popper’s early work attempts to solve the problem of (...) demarcation and offer a clear criterion that distinguishes scientific theories from metaphysical or mythological claims. Popper’s falsificationist methodology holds that scientific theories are characterized by entailing predictions that future observations might reveal to be false. When theories are falsified by such observations, scientists can respond by revising the theory, or by rejecting the theory in favor of a rival or by maintaining the theory as is and changing an auxiliary hypothesis. In either case, however, this process must aim at the production of new, falsifiable predictions. While Popper recognizes that scientists can and do hold onto theories in the face of failed predictions when there are no predictively superior rivals to turn to. He holds that scientific practice is characterized by its continual effort to test theories against experience and make revisions based on the outcomes of these tests. By contrast, theories that are permanently immunized from falsification by the introduction of untestable ad hoc hypotheses can no longer be classified as scientific. Among other things, Popper argues that his falsificationist proposal allows for a solution of the problem of induction, since inductive reasoning plays no role in his account of theory choice. Along with his general proposals regarding falsification and scientific methodology, Popper is notable for his work on probability and quantum mechanics and on the methodology of the social sciences. Popper defends a propensity theory of probability, according to which probabilities are interpreted as objective, mind-independent properties of experimental setups. Popper then uses this theory to provide a realist interpretation of quantum mechanics, though its applicability goes beyond this specific case. With respect to the social sciences, Popper argued against the historicist attempt to formulate universal laws covering the whole of human history and instead argued in favor of methodological individualism and situational logic. Table of Contents 1. Background 2. Falsification and the Criterion of Demarcation a. Popper on Physics and Psychoanalysis b. Auxiliary and Ad Hoc Hypotheses c. Basic Sentences and the Role of Convention d. Induction, Corroboration, and Verisimilitude 3. Criticisms of Falsificationism 4. Realism, Quantum Mechanics, and Probability 5. Methodology in the Social Sciences 6. Popper’s Legacy 7. References and Further Reading a. Primary Sources b. Secondary Sources -/- . (shrink)

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...) of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

This paper surveys and critically assesses existing theories of evidence with respect to four desiderata. A good theory of evidence should be both a theory of evidential support (i.e., be informative about what kinds of facts speak in favour of a hypothesis), and of warrant (i.e., be informative about how strongly a given set of facts speaks in favour of the hypothesis), it should apply to the non-ideal cases in which scientists typically find themselves, and it should be ‘descriptively adequate’, (...) i.e., able to adequately represent typical episodes of evidentiary reasoning. The theories surveyed here—Bayesianism, hypotheticodeductivism,satisfaction theories, error statistics as well as Achinstein’s and Cartwright’s theories—are all found wanting in important respects. I finally argue that a deficiency all these theories have in common is a neglect or underplaying of the epistemic context in which the episode of evidentiary reasoning takes place.Este artículo describe y valora críticamente diversas teorías de la evidencia en relación a cuatro desiderata. Una buena teoría de la evidencia debería ser tanto una teoría sobre el apoyo evidencial [evidential support] (ser informativa sobre qué tipos de hechos hablan a favor de la hipótesis) como sobre la justificación [warrant]; debería aplicarse en las situaciones no ideales en las que normalmente se encuentran los científicos; y debería ser ‘descriptivamente adecuada’, esto es, capaz de representar correctamente episodios típicos de razonamiento evidencial. Las teorías aquí revisadas—bayesianismo, hipotético-deductivismo, teorías de la satisfacibilidad, la estadística del error, así como las propuestas de Achinstein y Cartwright—se consideran deficientes en aspectos básicos. Argumentaré que un defecto común en todas ellas es que olvidan, o minusvaloran, el contexto epistémico en el que el episodio de razonamiento evidencial tiene lugar. (shrink)

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, (...) the Theorem's central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology. (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)

Handbook of the History of Logic, vol. 10, eds. Dov Gabbay, Stephan Hartmann, and John Woods, forthcoming.

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