In everyday life we either express our beliefs in all-or-nothing terms or we resort to numerical probabilities: I believe it's going to rain or my chance of winning is one in a million. The Stability of Belief develops a theory of rational belief that allows us to reason with all-or-nothing belief and numerical belief simultaneously.

In this paper, I discuss Whiting’s (2021) account of rational belief and discuss some unresolved issues arising from its reliance on epistemic possibility and, by extension, perspective-relative aprioricity.

This paper uses Popper's treatment of probability and an epistemic constraint on probability assignments to conditionals to extend the Bayesian representation of rational belief so that revision of previously accepted evidence is allowed for. Results of this extension include an epistemic semantics for Lewis' theory of counterfactual conditionals and a representation for one kind of conceptual change.

A theory of rational belief should get the cases right. It should also reach its verdicts using the right theoretical assumptions. Leading theories seem to predict the wrong things. With only one exception, they don't accommodate principles that we should use to explain these verdicts. We offer a theory of rational belief that combines an attractive picture of epistemic desirability with plausible principles connecting desirability to rationality. On our view, it's rational to believe when it's (...) sufficiently likely that you'd know because believing when it's sufficiently likely that you'd know minimises expected objective epistemic undesirability. (shrink)

This book is a wide-ranging treatment of central topics in epistemology. It provides conceptions of belief and knowledge, offers a theory of how they are grounded in our experience and in the social context of testimony, and connects them with the will and with action, moral responsibility, and intellectual virtue.

Intuitively, it seems that some belief-forming practices have the following three properties: 1. They are rational practices, and the beliefs that we form by means of these practices are themselves rational or justified beliefs. 2. Even if in most cases these practices reliably lead to correct beliefs (i.e., beliefs in true propositions), they are not infallible: it is possible for beliefs that are formed by means of these practices to be incorrect (i.e., to be beliefs in false (...) propositions). 3. The rationality of these practices is basic or primitive. That is, the rationality of these practices is not due simply to the availability, by means of some process of reasoning that relies purely on other practices, of a rational or justified belief in the reliability of these practices. -/- How can there be such practices? This paper offers an answer to that question. (shrink)

Beliefs can be evaluated from a number of perspectives. Epistemic evaluation involves epistemic standards and appropriate epistemic goals. On a truthconducive account of epistemic justification, a justified belief is one that serves the goal of believing truths and avoiding falsehoods. Beliefs are also prompted by nonepistemic reasons. This raises the question of whether, say, the pragmatic benefits of a belief are able to rationalize it. In this paper, after criticizing certain responses to this question, I shall argue that, (...) as far as beliefs are concerned, justification has an essentially epistemic character. This conclusion is then qualified by considering the conditions under which pragmatic consequences of a belief can be epistemically relevant. (shrink)

We are fallible creatures, prone to making all sorts of mistakes. So, we should be open to evidence of error. But what constitutes such evidence? And what is it to rationally accommodate it? I approach these questions by considering an evolutionary debunking argument according to which (a) we have good, scientific, reason to think our moral beliefs are mistaken, and (b) rationally accommodating this requires revising our confidence in, or altogether abandoning the suspect beliefs. I present a dilemma for such (...) debunkers, which shows that either we have no reason to worry about our moral beliefs, or we do but we can self-correct. Either way, moral skepticism doesn’t follow. That the evolutionary debunking argument fails is important; also important, however, is what its failure reveals about rational belief revision. Specifically, it suggests that getting evidence of error is a non-trivial endeavor and that we cannot learn that we are likely to be mistaken about some matter from a neutral stance on that matter. (shrink)

In this paper I scrutinize the “rational beliefs” in the concept of rationalizability in strategic games [Bernheim, Pearce ]. I illustrate through an example that a rationalizable strategy may not be supported by a “rational belief”, at least under one plausible interpretation of “rational belief”. I offer an alternative formulation of “rational belief” in the concept of rationalizability, which yields a novel epistemic interpretation of the notion of point-rationalizability.

A general form is proposed for epistemological theories, the relevant factors being: the family of epistemic judgments, the epistemic state, the epistemic commitment, and the family of possible epistemic inputs. First a simple theory is examined in which the states are probability functions, and the subject of probability kinematics introduced by Richard Jeffrey is explored. Then a second theory is examined in which the state has as constituents a body of information and a recipe that determines the accepted epistemic judgments (...) on the basis of this corpus. Through an examination of several approaches to the statistical syllogism, a relation is again established with Jeffrey's generalized conditionalization. (shrink)

A general form is proposed for epistemological theories, the relevant factors being: the family of epistemic judgments, the epistemic state, the epistemic commitment , and the family of possible epistemic inputs . First a simple theory is examined in which the states are probability functions, and the subject of probability kinematics introduced by Richard Jeffrey is explored. Then a second theory is examined in which the state has as constituents a body of information and a recipe that determines the accepted (...) epistemic judgments on the basis of this corpus. Through an examination of several approaches to the statistical syllogism, a relation is again established with Jeffrey's generalized conditionalization. (shrink)

Intelligent problem-solving depends on consciously applied methods of thinking as well as inborn or trained skills. The latter are like resident programs which control processes of the kind called (in Unix) daemons. Such a computational process is a fitting reaction to situations (defined in the program in question) which is executed without any command of a computer user (or without any intention of the conscious subject). The study of intelligence should involve methods of recognizing those beliefs whose existence is due (...) to daemons. Once having been aware of so produced belief, one can assess it critically and, if possible and necessary, make it more rational. Eg, beliefs concerning properties of time are produced by a daemon-like intuition, likewise the Euclidean properties of space. The merit of getting aware of such daemon's activities, and so transforming implicit beliefs into explicit ones, lies mainly in the axiomatic characterization of the properties involved. That makes possible to improve a daemon-like conceptual equipment (producing beliefs) by suitable modifications of the axioms, or postulates. Such postulate sets can also define artificial daemons to either emulate or improve natural intelligence. (shrink)

We must change our beliefs, and change them in particular ways, in response to new information. But not all changes are created equal: some are rational changes, some not. The Problem of Epistemic Change is the problem of specifying the rational constraints on how the epistemic state of an agent ought to change in the face of new information. This dissertation is about the philosophical and logical investigation of rational belief change. I start by arguing that (...) the familiar foundations---coherence distinction from static epistemology does not adequately carve up the logical space of theories of epistemic change. It is better to think of theories as being loosely ordered along a continuum from more to less foundational. The ordering, however, is "clumpy" in the sense that there are large regions in the ordering which remain unexplored. I then present and develop GDEC which is a new foundations model of belief revision that fills a gap in this ordering of theories of epistemic change. The key insight in GDEC is that belief that...is ambiguous between the attitudes of accept that...and expect that... GDEC respects the difference and how it matters for epistemic change. I show that GDEC is a genuine competitor to the AGM theory of belief revision in the sense that the two approaches are incompatible. The remainder of the dissertation is devoted to exploring the logical dynamics of GDEC and the models I develop here which extend it by applying them to a series of richer epistemic environments. I show how puzzles and paradoxes which confound other theories of belief revision are solved in a unified way by GDEC and its extensions. In particular, I give solutions to Moore's Paradox, Fuhrmann's Impossibility Theorem, the Reduction Problem of Epistemic Conditionals, and the Gardenfors Impossibility Theorem. (shrink)

There are two ways of representing rational belief: qualitatively as yes-or-no belief, and quantitatively as degrees of belief. Standard rationality conditions are: consistency and logical closure, for qualitative belief, satisfaction of the probability axioms, for quantitative belief, and a relationship between qualitative and quantitative beliefs in accordance with the Lockean thesis. In this paper, it is shown that these conditions are inconsistent with each of three further rationality conditions: fallibilism, open-mindedness, and invariance under independent (...) conceptual expansions. Restrictions of the Lockean thesis that have been suggested in the literature cannot remove the inconsistency. In the outlook we discuss two alternative ways of dealing with this problem: restricting conjunctive closure or going for a dual system account. (shrink)

Game theory poses problems for modeling rational belief, but it does not need a new theory of rationality. Experimental results that suggest otherwise often reveal difficulties in testing game theory, rather than mistakes or paradoxes. Even though the puzzles Colman discusses show no inadequacy in the standard theory of rationality, they show that improved models of belief are needed.

Philosophers disagree about the role of reflection for rationality, understood as the capacity to (properly) respond to genuine, normative reasons. Here, ‘reflection’ means the capacity for self-conscious normative meta-cognition. This article develops and rejects a novel argument – the argument from undercutting defeaters – in favor of the ‘one-level view’ that holds that having the concept of a belief (and of a reason) is necessary for responding to reasons. It will be argued that the ‘two-level view’, which allows for (...) rational subjects that can only non-reflectively respond to reasons, is supported by considerations dealing with the role of responding to reasons for rational action. Rationality is not as unified as the one-level view wants to have it. We start with the non-reflective way of rationally forming beliefs and then grow into the reflective way. (shrink)

It is commonly assumed that if one's beliefs are epistemically rational, then those beliefs must at least be consistent with one another. I argue that this assumption is false. I argue that it can be epistemically rational for a person to believe an inconsistent set of statements. I argue further that while one can rationally believe an inconsistent set of statements, one cannot rationally believe a set of statements that she or he knows to be inconsistent. ;In opposition, (...) versions of the "Preface Paradox" and the "Lottery Paradox" seem to show that one can be epistemically rational in believing a set of statements that she or he knows is inconsistent. More specifically, these paradoxes seem to show that one can be epistemically rational in believing a set of statements of the form . ;I carefully examine both paradoxes and argue for solutions that preserve all of the epistemic principles that generate these paradoxes and the assumption that it is not rational to believe a set of statements that is known to be inconsistent. (shrink)

An account of how a rational agent should revise beliefs in the light of new evidence.

Descartes, and many of the other great epistemologists of the modern period, looked to epistemology to put science and intellectual inquiry generally on a secure foundation. Epistemology’s role was to provide assurances of the reliability of properly conducted inquiry. Indeed, its role was nothing less than to be czar of the sciences and of intellectual inquiry in general. This conception of epistemology is now almost universally regarded as overly grandiose. Nonetheless, Descartes and the other great epistemologists of the modern era (...) were not completely mistaken. Epistemology does have a foundational role to play, but not that of a guarantor of knowledge. Its role, rather, is the less flamboyant but nonetheless theoretically crucial one of providing a philosophically respectable foundation for a general theory of rationality. (shrink)

The importance of mathematics in the context of the scientific and technological development of humanity is determined by the possibility of creating mathematical models of the objects studied under the different branches of Science and Technology. The arithmetisation process that took place during the nineteenth century consisted of the quest to discover a new mathematical reality in which the validity of logic would stand as something essential and central. Nevertheless, in contrast to this process, the development of mathematical analysis within (...) a framework that largely involves intuition and geometry is a fact that cannot go unnoticed amongst the mathematics community, as we shall show in this paper through the research made by Bernhard Riemann on complex variables. (shrink)

There are several ways of conceiving objectivity -- scientific objectivity in particular -- and, accordingly, several ways of defending or attacking particular construals of it. According to one conception sometimes labelled "realism", objectivity in science is a semantic, modal and metaphysical notion: a scientific theory is objective insofar as it tells the truth about the way the world is independently of its epistemic accessibility to us. So, for instance, the Newtonian theory of gravition is objective insofar as it tells the (...) truth about the motion of particles submitted to gravitational forces. What it tells us, the realist contends, holds or is the case whether or not the physical world is accessible to us. The conception is semantic insofar as the notion of truth is involved, modal insofar as the conception of the possibility of a mind-independent natural world is involved and metaphysical insofar as a conception of a certain way the world is is involved. Philosophers as diverse as Berkeley, Kant and Dummett's antirealist will then ask: if this were the case, how could we know anything about it? How could we even form a bona fide conception of its possibility? (shrink)

We talk and think about our beliefs both in a categorical and in a graded way. How do the two kinds of belief hang together? The most straightforward answer is that we believe something categorically if we believe it to a high enough degree. But this seemingly obvious, near-platitudinous claim is known to give rise to a paradox commonly known as the 'lottery paradox' – at least when it is coupled with some further seeming near-platitudes about belief. How (...) to resolve that paradox has been a matter of intense philosophical debate for over fifty years. This volume offers a collection of newly commissioned essays on the subject, all of which provide compelling reasons for rethinking many of the fundamentals of the debate. (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.

Choquet expected utility substitutes capacities for subjective probabilities to explain uncertainty aversion and related phenomena. This paper studies capacities as models of belief. The notions of inner and outer acceptance context are defined. These are shown to be the natural acceptance contexts when belief expansion is described by naïve Bayesian and Dempster–Shafer updating of capacities respectively. We also show that Eichberger and Kelsey's use of Dempster–Shafer updating as a model of belief revision may lead to violations of (...) the AGM axioms for rational belief change. (shrink)

The papers collected in this volume were originally presented at a sym posium held at the University of Pennsylvania in December of 1968. Each of the papers has been revised in light of the discussions that took place during this symposium. None of the papers has appeared in print previously. The extensive bibliography that appears at the end of the volume was originally distributed during the symposium and was revised on the basis of many helpful suggestions made by those who (...) participated. The symposium was made possible by a grant from The National Science Foundation and funds contributed by the Philosophy Depart ment of the University of Pennsylvania. On behalf of the contributors to this volume, I would like to express my thanks to these organizations for their generous support. In addition, I would like to express my gratitude to the members of the Graduate Philosophy Students Organization at the University of Penn sylvania for the considerable assistance they gave me during the sym posium. My thanks, also, to Judith Sofranko and Lynn Luckett for their very responsible efforts in the preparation of the manuscript. Finally, I would like to thank Professor James Cornman for his invaluable advice and encouragement. (shrink)

Evidentialism is the doctrine that rational belief should be proportioned to one’s evidence. By “one’s evidence,” I mean evidence that we possess and know that we possess. I specifically exclude from “evidence” the following: information of which we are unaware that our brain might rely on in constructing experience or in the formation of beliefs. My initial interest is with the doctrine of Evidentialism as it applies to a quandary that arises in the Sci-Fi movie Contact, the “Contact (...) Paradox” as I will call it. In this movie one of the main characters, Ellie, is a cosmologist working in a radio-telescope research facility searching for signals from intelligent life in the cosmos. The entity whose epistemological status is at issue in her quandary is her deceased father but there is an obvious parallel between the quandary of a rational believer in God and Ellie’s quandary, a parallel extensively explored in the movie itself. My first thesis is that in Ellie’s case Evidentialism is false: in certain cases, it is rational to believe in the existence of an entity in spite of the fact that the empirical evidence overall is contrary, and the Contact Paradox is one such case. Later in the paper I turn attention to the issue of Evidentialism regarding beliefs in the existence of God. My second thesis is that Evidentialism is false there as well. (shrink)

This collection focuses on relations between probability or Bayesian credence on the one hand and rational belief or knowledge on the other, relations undergirding epistemic lottery paradoxes. A co...

Until recently, it seemed like no theory about the relationship between rational credence and rational outright belief could reconcile three independently plausible assumptions: that our beliefs should be logically consistent, that our degrees of belief should be probabilistic, and that a rational agent believes something just in case she is sufficiently confident in it. Recently a new formal framework has been proposed that can accommodate these three assumptions, which is known as “the stability theory of (...) belief” or “high probability cores.” In this paper, I examine whether the stability theory of belief can meet two further constraints that have been proposed in the literature: that it is irrational to outright believe lottery propositions, and that it is irrational to hold outright beliefs based on purely statistical evidence. I argue that these two further constraints create a dilemma for a proponent of the stability theory: she must either deny that her theory is meant to give an account of the common epistemic notion of outright belief, or supplement the theory with further constraints on rational belief that render the stability theory explanatorily idle. This result sheds light on the general prospects for a purely formal theory of the relationship between rational credence and belief, i.e. a theory that does not take into account belief content. I argue that it is doubtful that any such theory could properly account for these two constraints, and hence play an important role in characterizing our common epistemic notion of outright belief. (shrink)

In book 10 of the Republic we find a new argument for the division of the soul. The argument’s structure is similar to the arguments in book 4 but, unlike those arguments, it centres on a purely cognitive conflict: believing and disbelieving the same thing, at the same time. The argument presents two interpretive difficulties. First, it assumes that a conflict between a belief and an appearance—e.g. disbelieving that a stick partially immersed in water is, as it appears, bent—entails (...) a conflict between beliefs. Prima facie, there is only one belief, the belief that contradicts the appearance. Second, it is unclear what parts of the soul Plato intends to divide between: some argue that it is, as in book 4, a partition between a rational and a non-rational part; others argue that it is a new partition between a higher and a lower subdivision of the rational part. This paper offers solutions to both difficulties through an analysis of what Plato means by φαινόμενα, ‘appearances’, and δόξαι, ‘beliefs’. It is argued, first, that the relevant appearances are entirely sensory but nonetheless sufficiently belief-like to (a) warrant being called δόξαι and (b) oppose, by themselves, our beliefs; there is no need for a third mental state, a belief that assents to the appearance. A second claim concerns a central line in the argument, 602e4–6, that has served as the primary evidence that the partition is within the rational part of the soul. Those who wish to avoid this conclusion generally resort to alternative, and less natural, translations of 602e4–6. It is argued that this is unnecessary: once we have correctly understood sensory appearances, we see that the standard translation of 602e4–6 in fact entails a division between a rational and a non-rational part of the soul. (shrink)

Niceties aside, Reliabilism is the claim that a belief is justified or rational if and only if it has a reliable source. One way to arrive at a belief is by inferring it from others through the application of a rule of inference. Hence Reliabilism has the consequence that a belief arrived at by applying a given rule of inference is rational if and only if arriving at that belief by applying the rule is (...) reliable. This consequence of Reliabilism I will call the Reliabilist’s Thesis. (shrink)