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Develops an extended version of the Preface Paradox to show how the counter-intuitive binary beliefs mandated by deductive consistency and deductive closure can cascade into massive irrationality. This highlights the Preface Paradox's severity and illuminates what is absurd about the beliefs required by deductive cogency Then shows that situations with Preface Paradox structure occur commonly in ordinary life. Finally, examines and rejects attempts to defend deductive constraints by explaining away our troublesome intuitions in Preface cases and in related cases involving the Lottery Paradox.

Examines and rejects several arguments claiming that the fundamental purposes of binary belief requires deductive cogency. The strongest such argument claims that if deductive cogency were not rationally required, deductive arguments would have no rational force. Develops and defends an alternative explanation of the epistemic importance of deductive arguments, rooted in a probabilistic coherence constraint on graded belief. Ends with a discussion of whether binary belief has any epistemic importance; argues that although our binary way of talking and thinking about belief may be very useful, it may not, in the end, capture any important aspect of rationality. Moreover, further development of extended Preface-type cases shows that the sort of binary belief that was subject to deductive cogency could not have the connections to central aspects of our practical reasoning, our assertions, and our emotions that seem to give belief its point.

There are situations in which the best strategy for a person depends on what intellectual virtues she possesses. The chapter discusses Pascal problems, where one has a motive to acquire beliefs one thinks are false, and preface problems, where one has reason to believe that specific beliefs that one holds are false. In all these cases there is equally persuasive advice leading to incompatible courses of action and thought. These include some situations in which one has beliefs that one knows to be inconsistent. The central claim is that which course of thinking is best for a particular person depends on her profile of intellectual virtues. This claim suggests that whether one virtue is to be recommended to someone depends on what other virtues she already possesses, an idea that the chapter elaborates by suggesting a taxonomy of virtues together with an ordering in which virtues of different kinds apply.

Chapter 4 looks at some paradoxes in recent epistemology that can be resolved in light of the Austinian view of assurances. The paradoxes considered are each driven by a closure principle, roughly to the effect that knowledge is closed under known implication. The key to resolving these closure-based paradoxes is to restrict closure to apply only when the situation is held stable. Other possible restrictions on closure are considered. The Austinian view explains how we sometimes know uncertain propositions (propositions with known probability less than one). It is also shown how, contrary to what some believe, a reasonable alternatives theory can provide an account of inductive knowledge. Once again appeal to a standard of reasonableness is central.

Is there an interesting relation between the Preface paradox and the Sorites paradox that might be used to illuminate either or both of those paradoxes and the phenomena of rationality and vagueness with which they, respectively, are bound up? In particular, if we consider the analogy alongside a familiar response to the Preface Paradox that employs degrees of belief, does this give any support to the thought that we should adopt some kind of degree-theoretic treatment of vagueness and the sorites? This chapter argues that it does not; indeed exploring the disanalogies contributes to a case against such a treatment of vagueness more generally. Among other views, it considers Edgington’s account of vagueness that employs a probabilistic structure of ‘verities’. It then contends that appeal to the framework of supervaluationism yields a better guide to reasoning in vague language than the degree-theoretic treatment can sustain.

Intellectual humility can be merely implicit, but can also be articulated. One context in which it is expressed gives rise to the preface paradox. The danger of this paradox is that it constitutes a threat to any account that places high value on intellectual humility. The present chapter aims to deflect this concern, showing how expressions of humility and fallibility are appropriate and generate no paradoxical consequences.

This chapter deals with the practical rationality of all-or-nothing belief and degrees of belief—the consequences that the stability theory of rational belief from the previous chapters has for: qualitative and quantitative decision-making, which are found to cohere with each other; the assertability of factual statements and indicative conditionals, for which stability plays a crucial role again; and the extreme stability that is afforded by the mental act of accepting a proposition. The chapter concludes with a rational reconstruction of the Preface Paradox that is compatible with the stability theory of belief developed in this book.

This chapter assimilates the Sorites Paradox and the Preface Paradox, drawing parallels between reasoning with uncertainty and reasoning with vague concepts (a theme that Dorothy Edgington has explored). It discusses experiments in which subjects are taken along soritical series of coloured patches, displaying so-called reverse hysteresis in their responses. The chapter offers an explanation of why reverse hysteresis is rational there. It presents a variant of the Preface Paradox—the Progressive Preface Paradox—that is analogous to the Sorites Paradox and its associated experiments, and it offers an analogous explanation of why reverse hysteresis is again rational. The explanation’s central idea is that ‘belief’ is context-dependent.

Paradoxes of individual coherence (e.g., the preface paradox for individual judgment) and group coherence (e.g., the doctrinal paradox for judgment aggregation) typically presuppose that deductive consistency is a coherence requirement for both individual and group judgment. This chapter introduces a new coherence requirement for (individual) full belief, and it explains how this new approach to individual coherence leads to an amelioration of the traditional paradoxes. In particular, it explains why this new coherence requirement gets around the standard doctrinal paradox. However, it also proves a new impossibility result, which reveals that (more complex) varieties of the doctrinal paradox can arise even for this new notion of coherence.

According to the principle of multiple premise closure, if one has justification for believing each of a series of propositions, one has justification for believing their joint deductive consequences. A powerful objection to this principle arises from the phenomenon of risk aggregation, made vivid by the preface paradox. In this chapter two theories of justification are outlined—a pure normic theory that respects multiple premise closure and a hybrid theory that violates it. It is shown that multiple premise closure is derivable from a range of further formal principles for justification and, as such, the formal consequences of rejecting multiple premise closure are difficult to anticipate. A case is made for the possibility of justifiably believing propositions that run a high risk of falsity, and some consequences for the psychology of human reasoning are explored.

This chapter develops a stability theory of rational all-or-nothing belief and degrees of belief again, but the starting point differs from that of Chapter 2. The theory in Chapter 3 is based on three assumptions: the logic of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis. Contrary to common belief, this combination of principles is satisfiable and indeed non-trivially so, and the principles are jointly satisfied if and only if the Humean thesis from Chapter 2 holds with a Humean threshold of 1/2. The downside of the theory is that rational belief turns out to be context-sensitive in a sense that is explained in the chapter. But the same context-sensitivity also paves the way for solutions to the Lottery Paradox and the Preface Paradox.

A definition of fallibility shows that agents are fallible about necessary truths. It is shown that fallibility of agents implies a denial of parity reasoning. Moorean paradoxes appear to undercut fallibility, but they are due entirely to the factivity of “know.” Kripke’s dogmatism paradox is explained: the key is recognizing that knowledge fallibility applies to the knowledge that all evidence against something one knows is misleading. That we do not know we will lose a lottery is denied. Fallibility shows this. And that people argue over this also indicates this. Knowledge closure fails because of fallibility; so does aggregation of assumptions. Vagueness shows why debates about whether we know outcomes of lotteries before winning tickets are drawn are irresolvable. Irrational penny reasoning is analyzed; it applies to nonfactive attitudes such as being really really sure. Preface paradoxes are explained. That it is sometimes rational to believe contradictory propositions is explained.

After introducing the three principles of Judaism, and the structure of the rest of the book, this chapter addresses a paradox. This book seeks to lay out the fundamental principles of Judaism, and yet (allegedly) Judaism thinks that some of its fundamental principles are unsayable. Can this paradox be escaped? This chapter explores three routes out, and endorses the third.

Several problems plague acceptance. First, it is unclear how a context of acceptance is to be construed. Second, the possibility of conjoining an epistemic component and a utility component is merely posited rather than derived from the rational structure of acceptance. Finally, the norm of acceptance is generally seen as related to truth, which turns out to be often inapplicable. These various problems are addressed. The specific context-dependence of acceptances is derived from their being mental actions, each embedded in a complex hierarchy of acceptances composing, together, a planning sequence. Second, acceptances come in several varieties, corresponding to the specific epistemic norm(s) that constitute them. Once a type of acceptance is selected, on the basis of utility, the epistemic norm constitutive for that acceptance strictly applies. Third, context-dependence superimposes a decision criterion on the output of the initial epistemic acceptance, to form a strategic acceptance regulated by expected utility.

Argues that, far from presenting an insurmountable obstacle to the project of constructive epistemology, the deployment of Austin’s requirement of fidelity enables us to find new solutions to epistemological problems; argues, in particular, that, once we embrace Austin’s fidelity requirement, we can see that we must reject solutions to the paradoxes of the lottery and preface that would have us effect an indifference to whether our set of beliefs is consistent or deductively cogent; offers a solution to the paradox of the lottery; argues that Austin’s insights, into how to think about knowledge and fallibility, enable us see how properly to solve the paradox of the preface.

To earn their keep, theories of justification must be shown to have fruitful applications and to provide the means to address well-known puzzles and paradoxes. It is argued that the present account of justification does very well on this score. Not only does it prove amenable to the idea that standards for knowledge and justification may shift, it allows for an explanation of why they shift in tandem. It lends itself to a justificationist conception of the rules that may guide the formation of beliefs, to the extent that these beliefs aspire to be knowledgeable. The present account moreover affords principled solutions to the preface paradox, the lottery paradox, the related but distinct lottery puzzle, and a more recent sceptical challenge targeting doxastic justification.

This chapter generalizes the modal theory of subjective reasons to the epistemic domain and combines it with the first-order commitment that truth is the sole right-maker for belief. The result is a modal account of epistemic rationality, according to which there is a safety condition on rational belief distinct from but mirroring the more familiar safety condition on knowledge. The chapter shows that the account delivers plausible closure principles on rational belief and offers a straightforward resolution of the lottery paradox. It also explores the implications of the view for whether it is rational to believe necessary propositions, preface propositions, and Moorean propositions.

Core theses of the novel account of justification to be developed are first stated: one has propositional justification for p just in case one is in no position to know that one is in no position to know p; and one has doxastic justification for p just in case one is in no position to know that one does not know p. Unlike other theories that conceive of justification in terms of the metaphysical possibility of knowing, the present account thus construes it as a distinctive kind of epistemic possibility. It treats propositional justification as non-factive, both its presence and its absence as luminous conditions, and by assuming a weak non-normal modal logic for knowledge and being in a position to know, validates principles of positive and negative introspection for it. The account thereby attributes features to justification that internalists care about. But it does so without construing justification as an internal condition. The account allows one to systematically distinguish between the condition of being justified and the metaphysical grounds for its obtaining, thereby heeding externalist insights into the difference between the good cases and the bad cases envisaged by radical scepticism. Lines of argument that show the account’s potential, e.g. in dealing with the preface and lottery paradoxes, are previewed, and so are lines of defence against challenges and objections, including prominent anti-luminosity arguments.