I argue that the standard Bayesian solution to the ravens paradox— generally accepted as the most successful solution to the paradox—is insufficiently general. I give an instance of the paradox which is not solved by the standard Bayesian solution. I defend a new, more general solution, which is compatible with the Bayesian account of confirmation. As a solution to the paradox, I argue that the ravens hypothesis ought not to be held equivalent to its contrapositive; more interestingly, I argue that (...) how we formally represent hypotheses ought to vary with the context of inquiry. This explains why the paradox is compelling, while dealing with standard objections to holding hypotheses inequivalent to their contrapositives. (shrink)

This paper argues for a treatment of belief as essentially sensitive to certain features of context. The first part gives an argument that we must take belief to be context-sensitive in the same way that assertion is, if we are to preserve appealing principles tying belief to sincere assertion. In particular, whether an agent counts as believing that p in a context depends on the space of alternative possibilities the agent is considering in that context. One and the same doxastic (...) state may amount to belief that p in one context but not another. The second part of the paper gives a formal treatment of doxastic states, according to which belief is context-sensitive along just these lines. The model is applied to characterize (but not to refute) skeptical arguments. (shrink)

What role, if any, does formal logic play in characterizing epistemically rational belief? Traditionally, belief is seen in a binary way - either one believes a proposition, or one doesn't. Given this picture, it is attractive to impose certain deductive constraints on rational belief: that one's beliefs be logically consistent, and that one believe the logical consequences of one's beliefs. A less popular picture sees belief as a graded phenomenon.

What propositions are rational for one to believe? With what confidence is it rational for one to believe these propositions? Answering the first of these questions requires an epistemology of beliefs, answering the second an epistemology of degrees of belief.

There is a duality in our everyday view of belief. On the one hand, we sometimes speak of credence as a matter of degree. We talk of having some level of confidence in a claim (that a certain course of action is safe, for example, or that a desired event will occur) and explain our actions by reference to these degrees of confidence – tacitly appealing, it seems, to a probabilistic calculus such as that formalized in Bayesian decision theory. On (...) the other hand, we also speak of belief as an unqualified, or flat-out, state (‘plain belief’ as it is sometimes called), which is either categorically present or categorically absent. We talk of simply believing or thinking that something is the case, and we cite these flat-out attitudes in explanation of our actions – appealing to classical practical reasoning of the sort formalized in the so-called ‘practical syllogism’.1 This tension in everyday discourse is reflected in the theoretical literature on belief. In formal epistemology there is a division between those in the Bayesian tradition, who treat credence as graded, and those who think of it as a categorical attitude of some kind. The Bayesian perspective also contrasts with the dominant view in philosophy of mind, where belief is widely regarded as a categorical state (a token sentence of a mental language, inscribed in a functionally defined ‘belief box’, according to one popular account). A parallel duality is present in our everyday view of desire. Sometimes we talk of having degrees of preference or desirability; sometimes we speak simply of wanting or desiring something tout court, and, again, this tension is reflected in the theoretical literature. What should we make of these dualities? Are there two different types of belief and desire – partial and flat-out, as they are sometimes called? If so, how are they related? And how could both have a role in guiding rational action, as the everyday view has it? The last question poses a particular challenge in relation to flat-out belief and desire.. (shrink)

The abstract structure of inquiry - the process of acquiring and changing beliefs about the world - is the focus of this book which takes the position that the "pragmatic" rather than the "linguistic" approach better solves the philosophical problems about the nature of mental representation, and better accounts for the phenomena of thought and speech. It discusses propositions and propositional attitudes (the cluster of activities that constitute inquiry) in general and takes up the way beliefs change in response to (...) potential new information, suggesting that conditional propositions should be understood as projections of epistemic policies onto the world.Robert C. Stalnaker is a professor in the Sage School of Philosophy at Cornell University. A Bradford Book. (shrink)

By means of an example, shows the possibility of beliefs that are separately rational whilst together inconsistent.

Kolmogorov''s axiomatization of probability includes the familiarratio formula for conditional probability: 0).$$ " align="middle" border="0">.

To handle epistemic and pragmatic risks, Gärdenfors and Sahlin (1982, 1988) design a decision procedure for cases in which probabilities are indeterminate. Their procedure steps outside the traditional expected utility framework. Must it do this? Can the traditional framework handle risk? This paper argues that it can. The key is a comprehensive interpretation of an option's possible outcomes. Taking possible outcomes more broadly than Gärdenfors and Sahlin do, expected utility can give risk its due. In particular, Good's (1952) decision procedure (...) adequately handles indeterminate probabilities and the risks they generate. (shrink)

I consider the problem of how to derive what an agent believes from their credence function and utility function. I argue the best solution of this problem is pragmatic, i.e. it is sensitive to the kinds of choices actually facing the agent. I further argue that this explains why our notion of justified belief appears to be pragmatic, as is argued e.g. by Fantl and McGrath. The notion of epistemic justification is not really a pragmatic notion, but it is being (...) applied to a pragmatically defined concept, i.e. belief. (shrink)

According to Hempel's paradox, evidence (E) that an object is a nonblack nonraven confirms the hypothesis (H) that every raven is black. According to the standard Bayesian solution, E does confirm H but only to a minute degree. This solution relies on the almost never explicitly defended assumption that the probability of H should not be affected by evidence that an object is nonblack. I argue that this assumption is implausible, and I propose a way out for Bayesians. Introduction Hempel's (...) paradox, the standard Bayesian solution, and the disputed assumption Attempts to defend the disputed assumption Attempts to refute the disputed assumption A way out for Bayesians Conclusion. (shrink)

Is Bayesian decision theory a panacea for many of the problems in epistemology and the philosophy of science, or is it philosophical snake-oil? For years a debate had been waged amongst specialists regarding the import and legitimacy of this body of theory. Mark Kaplan had written the first accessible and non-technical book to address this controversy. Introducing a new variant on Bayesian decision theory the author offers a compelling case that, while no panacea, decision theory does in fact have the (...) most profound consequences for the way in which philosophers think about inquiry, criticism and rational belief. The new variant on Bayesian theory is presented in such a way that a non-specialist will be able to understand it. The book also offers new solutions to some classic paradoxes. It focuses on the intuitive motivations of the Bayesian approach to epistemology and addresses the philosophical worries to which it has given rise. (shrink)

This major work challenges some widely held positions in epistemology - those of Peirce and Popper on the one hand and those of Quine and Kuhn on the other.

One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its prequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In the prequel, we made this norm mathematically precise; in this paper, we derive its consequences. We show that the two core tenets of Bayesianism (...) follow from the norm, while the characteristic claim of the Objectivist Bayesian follows from the norm along with an extra assumption. Finally, we consider Richard Jeffrey’s proposed generalization of conditionalization. We show not only that his rule cannot be derived from the norm, unless the requirement of Rigidity is imposed from the start, but further that the norm reveals it to be illegitimate. We end by deriving an alternative updating rule for those cases in which Jeffrey’s is usually supposed to apply. (shrink)

One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its sequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In this paper, we make this norm mathematically precise in various ways. We describe three epistemic dilemmas that an agent might face if she attempts (...) to follow Accuracy, and we show that the only inaccuracy measures that do not give rise to such dilemmas are the quadratic inaccuracy measures. In the sequel, we derive the main tenets of Bayesianism from the relevant mathematical versions of Accuracy to which this characterization of the legitimate inaccuracy measures gives rise, but we also show that Jeffrey conditionalization has to be replaced by a different method of update in order for Accuracy to be satisfied. (shrink)

Is Bayesian decision theory a panacea for many of the problems in epistemology and the philosophy of science, or is it philosophical snake-oil? For years a debate had been waged amongst specialists regarding the import and legitimacy of this body of theory. Mark Kaplan had written the first accessible and non-technical book to address this controversy. Introducing a new variant on Bayesian decision theory the author offers a compelling case that, while no panacea, decision theory does in fact have the (...) most profound consequences for the way in which philosophers think about inquiry, criticism and rational belief. The new variant on Bayesian theory is presented in such a way that a non-specialist will be able to understand it. The book also offers new solutions to some classic paradoxes. It focuses on the intuitive motivations of the Bayesian approach to epistemology and addresses the philosophical worries to which it has given rise. (shrink)

The pragmatic character of the Dutch book argument makes it unsuitable as an "epistemic" justification for the fundamental probabilist dogma that rational partial beliefs must conform to the axioms of probability. To secure an appropriately epistemic justification for this conclusion, one must explain what it means for a system of partial beliefs to accurately represent the state of the world, and then show that partial beliefs that violate the laws of probability are invariably less accurate than they could be otherwise. (...) The first task can be accomplished once we realize that the accuracy of systems of partial beliefs can be measured on a gradational scale that satisfies a small set of formal constraints, each of which has a sound epistemic motivation. When accuracy is measured in this way it can be shown that any system of degrees of belief that violates the axioms of probability can be replaced by an alternative system that obeys the axioms and yet is more accurate in every possible world. Since epistemically rational agents must strive to hold accurate beliefs, this establishes conformity with the axioms of probability as a norm of epistemic rationality whatever its prudential merits or defects might be. (shrink)

John Locke proposed a straightforward relationship between qualitative and quantitative doxastic notions: belief corresponds to a sufficiently high degree of confidence. Richard Foley has further developed this Lockean thesis and applied it to an analysis of the preface and lottery paradoxes. Following Foley's lead, we exploit various versions of these paradoxes to chart a precise relationship between belief and probabilistic degrees of confidence. The resolutions of these paradoxes emphasize distinct but complementary features of coherent belief. These features suggest principles that (...) tie together qualitative and quantitative doxastic notions. We show how these principles may be employed to construct a quantitative model - in terms of degrees of confidence - of an agent's qualitative doxastic state. This analysis fleshes out the Lockean thesis and provides the foundation for a logic of belief that is responsive to the logic of degrees of confidence. (shrink)

In this new book, Foley defends an epistemology that takes seriously the perspectives of individual thinkers. He argues that having rational opinions is a matter of meeting our own internal standards rather than standards that are somehow imposed upon us from the outside. It is a matter of making ourselves invulnerable to intellectual self-criticism. Foley also shows how the theory of rational belief is part of a general theory of rationality. He thus avoids treating the rationality of belief as a (...) fundamentally different kind of phenomenon from the rationality of decision or action. His approach generates promising suggestions about a wide range of issues--e.g., the distinction between epistemic and non-epistemic reasons for belief; the question of what aspects of the Cartesian project are still worth doing; the significance of simplicity and other theoretical virtues; the relevance of skeptical hypotheses; the difference between a theory of rational belief and a theory of knowledge; the difference between a theory of rational belief and a theory of rational degrees of belief; and the limits of idealization in epistemology. (shrink)

Introduction -- Fallibilism -- Contextualism -- Knowledge and reasons -- Justification -- Belief -- The value and importance of knowledge -- Infallibilism or pragmatic encroachment? -- Appendix I: Conflicts with bayesian decision theory? -- Appendix II: Does KJ entail infallibilism?

Probabilism is committed to two theses: 1) Opinion comes in degrees—call them degrees of belief, or credences. 2) The degrees of belief of a rational agent obey the probability calculus. Correspondingly, a natural way to argue for probabilism is: i) to give an account of what degrees of belief are, and then ii) to show that those things should be probabilities, on pain of irrationality. Most of the action in the literature concerns stage ii). Assuming that stage i) has been (...) adequately discharged, various authors move on to stage ii) with varied and ingenious arguments. But an unsatisfactory response at stage i) clearly undermines any gains that might be accrued at stage ii) as far as probabilism is concerned: if those things are not degrees of belief, then it is irrelevant to probabilism whether they should be probabilities or not. In this paper we scrutinize the state of play regarding stage i). We critically examine several of the leading accounts of degrees of belief: reducing them to corresponding betting behavior (de Finetti); measuring them by that behavior (Jeffrey); and analyzing them in terms of preferences and their role in decision-making more generally (Ramsey, Lewis, Maher). We argue that the accounts fail, and so they are unfit to subserve arguments for probabilism. We conclude more positively: ‘degree of belief’ should be taken as a primitive concept that forms the basis of our best theory of rational belief and decision: probabilism. (shrink)

There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes’s original paper to contemporary formal learning theory.In (...) a paper published posthumously in 1763, the Reverend Thomas Bayes made a seminal contribution to the understanding of "analogical or inductive reasoning." Building on his insights, modem Bayesians have developed an account of scientific inference that has attracted numerous champions as well as numerous detractors. Earman argues that Bayesianism provides the best hope for a comprehensive and unified account of scientific inference, yet the presently available versions of Bayesianisin fail to do justice to several aspects of the testing and confirming of scientific theories and hypotheses. By focusing on the need for a resolution to this impasse, Earman sharpens the issues on which a resolution turns. John Earman is Professor of History and Philosophy of Science at the University of Pittsburgh. (shrink)

This book is a major contribution to decision theory, focusing on the question of when it is rational to accept scientific theories. The author examines both Bayesian decision theory and confirmation theory, refining and elaborating the views of Ramsey and Savage. He argues that the most solid foundation for confirmation theory is to be found in decision theory, and he provides a decision-theoretic derivation of principles for how many probabilities should be revised over time. Professor Maher defines a notion of (...) accepting a hypothesis, and then shows that it is not reducible to probability and that it is needed to deal with some important questions in the philosophy of science. A Bayesian decision-theoretic account of rational acceptance is provided together with a proof of the foundations for this theory. A final chapter shows how this account can be used to cast light on such vexed issues as verisimilitude and scientific realism. (shrink)

There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes's original paper to contemporary formal learning theory. (...) In a paper published posthumously in 1763, the Reverend Thomas Bayes made a seminal contribution to the understanding of "analogical or inductive reasoning." Building on his insights, modem Bayesians have developed an account of scientific inference that has attracted numerous champions as well as numerous detractors. Earman argues that Bayesianism provides the best hope for a comprehensive and unified account of scientific inference, yet the presently available versions of Bayesianisin fail to do justice to several aspects of the testing and confirming of scientific theories and hypotheses. By focusing on the need for a resolution to this impasse, Earman sharpens the issues on which a resolution turns. John Earman is Professor of History and Philosophy of Science at the University of Pittsburgh. (shrink)

John Locke proposed a straightforward relationship between qualitative and quantitative doxastic notions: belief corresponds to a sufficiently high degree of confidence. Richard Foley has further developed this Lockean thesis and applied it to an analysis of the preface and lottery paradoxes. Following Foley's lead, we exploit various versions of these paradoxes to chart a precise relationship between belief and probabilistic degrees of confidence. The resolutions of these paradoxes emphasize distinct but complementary features of coherent belief. These features suggest principles that (...) tie together qualitative and quantitative doxastic notions. We show how these principles may be employed to construct a quantitative model - in terms of degrees of confidence - of an agent's qualitative doxastic state. This analysis fleshes out the Lockean thesis and provides the foundation for a logic of belief that is responsive to the logic of degrees of confidence. (shrink)