There is a tension between normative and descriptive elements in the theory of rational belief. This tension has been reflected in work in psychology and decision theory as well as in philosophy. Canons of rationality should be tailored to what is humanly feasible. But rationality has normative content as well as descriptive content.A number of issues related to both deductive and inductive logic can be raised. Are there full beliefs – statements that are categorically accepted? Should statements be (...) accepted when they become overwhelmingly probable? What is the structure imposed on these beliefs by rationality? Are they consistent? Are they deductively closed? What parameters, if any, does rational acceptance depend on? How can accepted statements come to be rejected on new evidenceShould degrees of belief satisfy the probability calculus? Does conformity to the probability calculus exhaust the rational constraints that can be imposed on partial beliefs? With the acquisition of new evidence, should beliefs change in accord with Bayes' theorem? Are decisions made in accord with the principle of maximizing expected utility? Should they be?A systematic set of answers to these questions is developed on the basis of a probabilistic rule of acceptance and a conception of interval-valued logical probability according to which probabilities are based onknownfrequencies. This leads to limited deductive closure, a demand for only limited consistency, and the rejection of Bayes' theorem as universally applicable to changes of belief. It also becomes possible, given new evidence, to reject previously accepted statements. (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.

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)

It is usually maintained that a subject with manifestly contradictory beliefs is irrational. How can we account, then, for the intuitive rationality of dialetheists, who believe that some manifest contradictions are true? My paper aims to answer this question. Its ultimate goal is to determine a characterization of (or rather a constraint for) rational belief approvable by both the theorists of Dialetheism and its opponents. In order to achieve this goal, a two-step strategy will be adopted. First, a (...) characterization of rational belief applicable to non-dialetheist believers will be determined; this characterization will involve the semantic apparatus of Nathan Salmon’s Millian Russellianism but will get rid of the problematic and obscure notion of mode of presentation (guise in his own terminology), replacing it with a couple of novel devices, belief subsystems and cognitive coordination. Second, using ideas from Graham Priest, the leading proponent of Dialetheism, such a characterization will be modified, so as to devise a new one able to account for the intuitive rationality of both dialetheist and non-dialetheist believers. (shrink)

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.

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.

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)

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)

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.

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)

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)

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.

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)

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)

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)

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)

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)

This chapter argues that the common view that believing a contradiction is the nadir of rationality should be rejected, and that rational considerations may require one to believe contradictions. An informal model of rationality as an optimization procedure under constraint is given.

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.

Argues that rational belief is important in so far as we are interested in the truth, and that deference to authority does not provide an attractive alternative. Also argues that it cannot be made out that it would be good to have an irrational belief in God by appealing to the importance of trust or, as Pascal's wager does, to the good consequences of belief in God, if he exists. I go on to consider the value (...) of belief in God, when conceived in the way proposed. I conclude that, valuable as this may be, what is most valuable is the knowledge of God's will; because that is knowledge of what is good and what is bad. (shrink)

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.

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)

I wish to consider what can helpfully be meant by the phrase “rational to believe” as it might appear in the statement “It is rational for the person S in his circumstances at t to place more confidence in p than in q, provided his overriding interest at the time is to place confidence, among any propositions he is considering, in true propositions and not in false ones.” The reference here to the interest of the person is intended (...) to avoid discussing persons for whom it is rational to believe something for extraneous reasons, e.g., for a man to believe his wife is loyal to him irrespective of the evidence. I shall take this term as paradigmatic of “epistemic terms”, examples of which philosophers take to be such terms as “is epistemically justified in believing”, “is warranted in believing”, “is credible”, and so on. I do not claim that all these terms have or should bear the same meaning, but I propose to ignore possible distinctions. (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...

The Stability of Belief: How Rational Belief Coheres with Probability, by LeitgebHannes. Oxford: Oxford University Press, 2017. Pp. xiv + 365.

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)

Although the AGM theory established a paradigm for the theory of belief revision, which is generally regarded as a kind of standard in the field, it is also frequently criticized as inadequate because it neglects justificational structures. Other theories of belief revision are similarly remiss in this regard. So far, little has been done to address this shortcoming. This paper aims to fill this gap. Following a critical analysis of the AGM theory, a justification operator is introduced as (...) a formal means to incorporate justificational structures into a belief revision theory. An AGM style belief revision theory is proposed that is based on such a justification operator. The theory is presented in an axiomatic form. Representation theorems link the axioms with constructive belief change mechanisms. The proposed theory addresses the problems of the AGM theory and similar approaches that neglect justificational structures. (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)