In a penetrating investigation of the relationship between belief and quantitative degrees of confidence (or degrees of belief) Richard Foley (1992) suggests the following thesis: ... it is epistemically rational for us to believe a proposition just in case it is epistemically rational for us to have a sufficiently high degree of confidence in it, sufficiently high to make our attitude towards it one of belief. Foley goes on to suggest that rational belief may be just rational degree of confidence (...) above some threshold level that the agent deems sufficient for belief. He finds hints of this view in Locke’s discussion of probability and degrees of assent, so he calls it the Lockean Thesis.1 The Lockean Thesis has important implications for the logic of belief. Most prominently, it implies that even a logically ideal agent whose degrees of confidence satisfy the axioms of probability theory may quite rationally believe each of a large body of propositions that are jointly inconsistent. For example, an agent may legitimately believe that on each given occasion her well-maintained car will start, but nevertheless believe that she will eventually encounter a.. (shrink)

In his Treatise, Hume confronted the tensions between his project of uncovering the causal operations of the human mind and the extreme skeptical tendencies of his system. Louis Loeb argues that Hume overreaches, and he advances a controversial interpretation of Hume's epistemological framework that shows how Hume could have avoided the more destructive positions in his work.

The distinguished philosopher Louis Loeb examines the epistemological framework of Scottish philosopher David Hume, as employed in his celebrated work A Treatise of Human Nature. Loeb's project is to advance an integrated interpretation of Hume's accounts of belief and justification. His thesis is that Hume, in his Treatise, has a "stability-based" theory of justification which posits that his belief is justified if it is the result of a belief producing mechanism that engenders stable beliefs. But Loeb argues that the striking (...) corollary to this theory is that no belief generating mechanism is fully stable - or fully justified - for a fully reflective person. This carefully argued and original interpretation of Hume makes sense of seemingly contradictory ideas and will provoke serious discussion among Hume scholars. (shrink)

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

We defend a set of acceptance rules that avoids the lottery paradox, that is closed under classical entailment, and that accepts uncertain propositions without ad hoc restrictions. We show that the rules we recommend provide a semantics that validates exactly Adams’ conditional logic and are exactly the rules that preserve a natural, logical structure over probabilistic credal states that we call probalogic. To motivate probalogic, we first expand classical logic to geo-logic, which fills the entire unit cube, and then we (...) project the upper surfaces of the geo-logical cube onto the plane of probabilistic credal states by means of standard, linear perspective, which may be interpreted as an extension of the classical principle of indifference. Finally, we apply the geometrical/logical methods developed in the paper to prove a series of trivialization theorems against question-invariance as a constraint on acceptance rules and against rational monotonicity as an axiom of conditional logic in situations of uncertainty. (shrink)

In the course of the discussion, Professor Quine pinpoints the difficulties involved in translation, brings to light the anomalies and conflicts implicit in our ...

This comprehensive discussion of the problem of rational belief develops the subject on the pattern of Bayesian decision theory. The analogy with decision theory introduces philosophical issues not usually encountered in logical studies and suggests some promising new approaches to old problems."We owe Professor Levi a debt of gratitude for producing a book of such excellence. His own approach to inductive inference is not only original and profound, it also clarifies and transforms the work of his predecessors. In short, the (...) book deserves to become a classic....There is a great deal of interest in the book besides these basic matters [forumlating rules of acceptance]. Some of the most interesting chapters are those that examine the implications of such rules. The discussions of probability, generalization, and various forms of inference are brilliant and enlightening. Indeed, the problems and methods elaborated by Professor Levi in his book serve as a new foundation for the study of inductive inference."--Keith Lehrer, Nous"Levi's book is an extremely interesting report on 'tentative and speculative first steps' toward a decision-theoretic approach to inductive inference....Professor Levi is to be congratulated on his ingenious development and application of this approach...."--Richard C. Jeffrey, The Journal of Philosophy. (shrink)

A theory of evidential probability is developed from two assumptions:(1) the evidential probability of a proposition is its probability conditional on the total evidence;(2) one's total evidence is one's total knowledge. Evidential probability is distinguished from both subjective and objective probability. Loss as well as gain of evidence is permitted. Evidential probability is embedded within epistemic logic by means of possible worlds semantics for modal logic; this allows a natural theory of higher-order probability to be developed. In particular, it is (...) emphasized that it is sometimes uncertain which propositions are part of one's total evidence; some surprising implications of this fact are drawn out. (shrink)

We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey-Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of nonmonotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).'Expectation' is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form (...) of belief weaker than absolute certainty. Our model offers a modified and extended version of an account of qualitative belief in terms of conditional probability, first presented in (van Fraassen, 1995). We use this model to relate probabilistic and qualitative models of non-monotonic relations in terms of expectations. In doing so we propose a probabilistic model of the notion of expectation. We provide characterization results both for logically finite languages and for logically infinite, but countable, languages. The latter case shows the relevance of the axiom of countable additivity for our probability functions. We show that a rational logic defined over a logically infinite language can only be fully characterized in terms of finitely additive conditional probability. (shrink)

David Hume's A Treatise of Human Nature is famous for its extreme skepticism. Louis Loeb argues that Hume's destructive conclusions have in fact obscured a constructive stage that Hume abandons prematurely. Working within a philosophical tradition that values tranquillity, Hume favors an epistemology that links justification with settled belief. Hume appeals to psychological stability to support his own epistemological assessments, both favorable regarding causal inference, and unfavorable regarding imaginative propensities. The theory's success in explaining Hume's epistemic distinctions gives way to (...) pessimism, since Hume contends that reflection on beliefs is deeply destabilizing. So much the worse, Hume concludes, for placing a premium on reflection. Hume endorses and defends the position that stable beliefs of unreflective persons are justified, though they would not survive reflection. At the same time, Hume relishes the paradox that unreflective beliefs enjoy a preferred epistemic status and strains to establish it. Loeb introduces a series of amendments to the Treatise that secures a more positive result for justified belief while maintaining Hume's fundamental principles. In his review of Hume's applications of his epistemology, Loeb uncovers a stratum of psychological doctrine beyond associationism, a theory of conditions in which beliefs are felt to conflict and of the resolution of this uneasiness or dissonance. This theory of mental conflict is also essential to Hume's strategy for integrating empiricism about meaning with his naturalism. However, Hume fails to provide a general account of the conditions in which conflicting beliefs lead to persisting instability, so his theory is incomplete. Loeb explores Hume's concern with stability in reference to his discussions of belief, education, the probability of causes, unphilosophical probability, the belief in body, sympathy and moral judgment, and the passions, among other topics. (shrink)

Stability and Justification in Hume's Treatise. LOUIS LOEB. Knowledge by Agreement: The Programme of Communitarian Epistemology. MARTIN KUSCH. A Philosophy of Culture: The Scope of Holistic Pragmatism, MORTON WHITE. Resemblance Nominalism: A Solution to the Problem of Universals. GONZALO RODRIGUEZ‐PEREYRA.

This paper concerns the extent to which uncertain propositional reasoning can track probabilistic reasoning, and addresses kinematic problems that extend the familiar Lottery paradox. An acceptance rule assigns to each Bayesian credal state p a propositional belief revision method B p , which specifies an initial belief state B p (T) that is revised to the new propositional belief state B(E) upon receipt of information E. An acceptance rule tracks Bayesian conditioning when B p (E) = B p|E (T), for (...) every E such that p(E) > 0; namely, when acceptance by propositional belief revision equals Bayesian conditioning followed by acceptance. Standard proposals for uncertain acceptance and belief revision do not track Bayesian conditioning. The "Lockean" rule that accepts propositions above a probability threshold is subject to the familiar lottery paradox (Kyburg 1961), and we show that it is also subject to new and more stubborn paradoxes when the tracking property is taken into account. Moreover, we show that the familiar AGM approach to belief revision (Harper, Synthese 30(1-2):221-262, 1975; Alchourrón et al., J Symb Log 50:510-530, 1985) cannot be realized in a sensible way by any uncertain acceptance rule that tracks Bayesian conditioning. Finally, we present a plausible, alternative approach that tracks Bayesian conditioning and avoids all of the paradoxes. It combines an odds-based acceptance rule proposed originally by Levi (1996) with a non-AGM belief revision method proposed originally by Shoham (1987). (shrink)

David Lewis (1941-2001) was Class of 1943 University Professor of Philosophy at Princeton University. His contributions spanned philosophical logic, philosophy of language, philosophy of mind, philosophy of science, metaphysics, and epistemology. In On the Plurality of Worlds, he defended his challenging metaphysical position, "modal realism." He was also the author of the books Convention, Counterfactuals, Parts of Classes, and several volumes of collected papers.

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.

Is it possible to give an explicit definition of belief in terms of subjective probability, such that believed propositions are guaranteed to have a sufficiently high probability, and yet it is neither the case that belief is stripped of any of its usual logical properties, nor is it the case that believed propositions are bound to have probability 1? We prove the answer is ‘yes’, and that given some plausible logical postulates on belief that involve a contextual “cautiousness” threshold, there (...) is but one way of determining the extension of the concept of belief that does the job. The qualitative concept of belief is not to be eliminated from scientific or philosophical discourse, rather, by reducing qualitative belief to assignments of resiliently high degrees of belief and a “cautiousness” threshold, qualitative and quantitative belief turn out to be governed by one unified theory that offers the prospects of a huge range of applications. Within that theory, logic and probability theory are not opposed to each other but go hand in hand. (shrink)

Many philosophers have believed that the laws of nature differ from the accidental truths in their invariance under counterfactual perturbations. Roughly speaking, the laws would still have held had q been the case, for any q that is consistent with the laws. (Trivially, no accident would still have held under every such counterfactual supposition.) The main problem with this slogan (even if it is true) is that it uses the laws themselves to delimit qs range. I present a means of (...) distinguishing the laws (and their logical consequences) from the accidents, in terms of their range of invariance under counterfactual antecedents, that does not appeal to physical modalities (or any cognate notion) in delimiting the relevant range of counterfactual perturbations. I then argue that this approach explicates the sense in which the laws possess a kind of necessity. (shrink)

Coping with uncertainty is a necessary part of ordinary life and is crucial to an understanding of how the mind works. For example, it is a vital element in developing artificial intelligence that will not be undermined by its own rigidities. There have been many approaches to the problem of uncertain inference, ranging from probability to inductive logic to nonmonotonic logic. Thisbook seeks to provide a clear exposition of these approaches within a unified framework. The principal market for the book (...) will be students and professionals in philosophy, computer science, and AI. Among the special features of the book are a chapter on evidential probability, which has not received a basic exposition before; chapters on nonmonotonic reasoning and theory replacement, matters rarely addressed in standard philosophical texts; and chapters on Mill's methods and statistical inference that cover material sorely lacking in the usual treatments of AI and computer science. (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)

We chart the ways in which closure properties of consequence relations for uncertain inference take on different forms according to whether the relations are generated in a quantitative or a qualitative manner. Among the main themes are: the identification of watershed conditions between probabilistically and qualitatively sound rules; failsafe and classicality transforms of qualitatively sound rules; non-Horn conditions satisfied by probabilistic consequence; representation and completeness problems; and threshold-sensitive conditions such as `preface' and `lottery' rules.

Knowledge and Lotteries is organized around an epistemological puzzle: in many cases, we seem consistently inclined to deny that we know a certain class of propositions, while crediting ourselves with knowledge of propositions that imply them. In its starkest form, the puzzle is this: we do not think we know that a given lottery ticket will be a loser, yet we normally count ourselves as knowing all sorts of ordinary things that entail that its holder will not suddenly acquire a (...) large fortune. After providing a number of specific and general characterizations of the puzzle, Hawthorne carefully examines the competing merits of candidate solutions. In so doing, he explores a number of central questions concerning the nature and importance of knowledge, including the relationship of knowledge to assertion and practical reasoning, the status of epistemic closure principles, the merits of various brands of scepticism, the prospects for a contextualist account of knowledge, and the potential for other sorts of salience-sensitive accounts. Along the way, he offers a careful treatment of pertinent issues at the foundations of semantics. His book will be of interest to anyone working in the field of epistemology, as well as to philosophers of language. (shrink)

This paper is concerned with formal solutions to the lottery paradox on which high probability defeasibly warrants acceptance. It considers some recently proposed solutions of this type and presents an argument showing that these solutions are trivial in that they boil down to the claim that perfect probability is sufficient for rational acceptability. The argument is then generalized, showing that a broad class of similar solutions faces the same problem. An argument against some formal solutions to the lottery paradox The (...) argument generalized Some variations Adding modalities Anticipated objections. (shrink)

The detailed analysis of a particular quasi-historical numerical example is used to illustrate the way in which a Bayesian personalist approach to scientific inference resolves the Duhemian problem of which of a conjunction of hypotheses to reject when they jointly yield a prediction which is refuted. Numbers intended to be approximately historically accurate for my example show, in agreement with the views of Lakatos, that a refutation need have astonishingly little effect on a scientist's confidence in the ‘hard core’ of (...) a successful research programme even when a comparable confirmation would greatly enhance that confidence. Timeo Danaos et dona ferentis. (shrink)

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...) its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are "relational" and "transitively relational", are studied in detail, and their connections with certain "supplementary postulates" of Gardenfors investigated, with a further representation theorem established. (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)