Permissivism is the view that, sometimes, there is more than one doxastic attitude that is perfectly rationalised by the evidence. Impermissivism is the denial of Permissivism. Several philosophers, with the aim to defend either Impermissivism or Permissivism, have recently discussed the value of (im)permissive rationality. This paper focuses on one kind of value-conferring considerations, stemming from the so-called “truth-connection” enjoyed by rational doxastic attitudes. The paper vindicates the truth-connected value of permissive rationality by pursuing a novel strategy which rests on (...) two main planks: first, there is a distinction between a fine-grained and a coarse-grained type-individuation of belief-forming methods. Secondly, different kinds of decision-theoretic reasoning, i.e. expected-accuracy reasoning and accuracy-domination reasoning, must be paired with a fine-grained and a coarse-grained type-individuation of methods, respectively. I argue that while the first pair is wholly irrelevant to the question of the truth-connection, the second affords the means to a permissivist explanation of the truth-connected value of rationality. (shrink)

Accuracy arguments for the core tenets of Bayesian epistemology differ mainly in the conditions they place on the legitimate ways of measuring the inaccuracy of our credences. The best existing arguments rely on three conditions: Continuity, Additivity, and Strict Propriety. In this paper, I show how to strengthen the arguments based on these conditions by showing that the central mathematical theorem on which each depends goes through without assuming Additivity.

In response to two trenchant objections, radical subjective Bayesianism has been widely rejected. In this paper, I seek, if not to rehabilitate subjectivism, at least to show its critic what is attractive about the position. I argue that what is at stake in the subjectivism/anti-subjectivism debate is not, as is commonly thought, which norms of rationality are true, but rather, the conception of rationality that we adopt: there is an alternative approach to the widespread telic approach to rationality, which I (...) call the poric approach, on which subjectivism is an attractive position. I then argue that the poric approach—and therefore subjectivism—cannot be easily dismissed. (shrink)

Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...) that is, by employing tools from logic and mathematics. The goal of this entry is to give the reader an overview of the formal tools available to epistemologists for the representation of belief. A particular focus will be the relation between formal representations of qualitative belief and formal representations of quantitative degrees of belief. (shrink)

In the recent philosophical literature on inquiry, epistemologists point out that their subject has often begun at the point at which you already have your evidence and then focussed on identifying the beliefs for which that evidence provides justification. But we are not mere passive recipients of evidence. While some comes to us unbidden, we often actively collect it. This has long been recognised, but typically epistemologists have taken the norms that govern inquiry to be practical, not epistemic. The recent (...) literature challenges this assumption and uncovers a rich range of questions about the epistemic normativity of inquiry. In this paper, I approach these questions from the formal side of epistemology. Developing out of the philosophy of science, as it did, this branch of epistemology has long discussed inquiry. And, building on the insights of Janina Hosiasson (1931), David Blackwell (1951), and I. J. Good (1967), it has produced a reasonably well-developed framework in which to understand norms of inquiry, both epistemic and practical. In the first half of the paper, I will present the pragmatic versions of this framework due to Hosiasson, Blackwell, and Good, and the epistemic version due to Graham Oddie (1997); in the second half of the paper, I put this framework to work, turning to some of the questions from the recent debate about inquiry and asking how the framework can help us answer them. Questions include: When should we initiate an inquiry, when should we continue it, when should we conclude it, and when should we reopen it? How do epistemic norms of inquiry relate to epistemic norms of belief or credence, and can they conflict, as Jane Friedman (2020) contends? How should we resolve the apparent puzzle raised by Friedman's example of counting the windows in the Chrysler Building? How should we direct our attention, as Georgi Gardiner (2022) asks? How should we choose and reason after receiving evidence we'd rather not have received? And how should we understand the epistemic error that occurs when someone is resistant to evidence in the way Mona Simion (2023) describes? (shrink)

I develop a broadly reliabilist theory of non-ideal epistemic rationality and argue that if it is correct we should reject the recently popular idea that the standards of non-ideal epistemic rationality are mere social conventions.

Katie Steele and H. Orri Stefánsson argue that, to reflect an agent’s limited awareness, the algebra of propositions on which that agent’s credences are defined should be relativised to their awareness state. I argue that this produces insurmountable difficulties. But the project of relativising the agent’s algebra to reflect their partial perspective need not be abandoned: the algebra can be relativised, not to the agent’s awareness state, but to what we might call their subjective modality.

Real human agents, even when they are rational by everyday standards, sometimes assign different credences to objectively equivalent statements, such as ‘Orwell is a writer’ and ‘E.A. Blair is a writer’, or credences less than 1 to necessarily true statements, such as not-yet-proven theorems of arithmetic. Anna Mahtani calls this the phenomenon of ‘opacity’. Opaque credences seem probabilistically incoherent, which goes against a key modelling assumption of probability theory. I sketch a modelling strategy for capturing opaque credence assignments without abandoning (...) probabilistic coherence. I draw on ideas from judgement-aggregation theory, where we face similar challenges of defining the ‘objects of judgement’. (shrink)

Paying attention to the inner workings of mathematicians has led to a proliferation of new themes in the philosophy of mathematics. Several of these have to do with epistemology. Philosophers of mathematical practice, however, have not (yet) systematically engaged with general (analytic) epistemology. To be sure, there are some exceptions, but they are few and far between. In this chapter, I offer an explanation of why this might be the case and show how the situation could be remedied. I contend (...) that it is only by conceiving the knowing subject(s) as embodied, fallible, and embedded in a specific context (along the lines of what has been done within social and feminist epistemology) that we can pursue an epistemology of mathematics sensitive to actual mathematical practice. I further suggest that this reconception of the knowing subject(s) does not force us to abandon the traditional framework of epistemology in which knowledge requires justified true belief. It does, however, lead to a fallible conception of mathematical justification that, among other things, makes Gettier cases possible. This shows that topics considered to be far removed from the interests of philosophers of mathematical practice might reveal to be relevant to them. (shrink)

Standard arguments for Bayesian conditionalizing rely on assumptions that many epistemologists have criticized as being too strong: (i) that conditionalizers must be logically infallible, which rules out the possibility of rational logical learning, and (ii) that what is learned with certainty must be true (factivity). In this paper, we give a new factivity-free argument for the superconditionalization norm in a personal possibility framework that allows agents to learn empirical and logical falsehoods. We then discuss how the resulting framework should be (...) interpreted. Does it still model norms of rationality, or something else, or nothing useful at all? We discuss five ways of interpreting our results, three that embrace them and two that reject them. We find one of each kind wanting, and leave readers to choose among the remaining three. (shrink)

According to epistemic utility theory, epistemic rationality is teleological: epistemic norms are instrumental norms that have the aim of acquiring accuracy. What’s definitive of these norms is that they can be expected to lead to the acquisition of accuracy when followed. While there’s much to be said in favor of this approach, it turns out that it faces a couple of worrisome extensional problems involving the future. The first problem involves credences about the future, and the second problem involves future (...) credences. Examining prominent solutions to a different extensional problem for this approach reinforces the severity of the two problems involving the future. Reflecting on these problems reveals the source: the teleological assumption that epistemic rationality aims at acquiring accuracy. (shrink)

The best and most popular argument for probabilism is the accuracy-dominance argument, which purports to show that alethic considerations alone support the view that an agent’s degrees of belief should always obey the axioms of probability. I argue that extant versions of the accuracy-dominance argument face a problem. In order for the mathematics of the argument to function as advertised, we must assume that every omniscient credence function is classically consistent; there can be no worlds in the set of dominance-relevant (...) worlds that obey some other logic. This restriction cannot be motivated on alethic grounds unless we’re also willing to accept that rationality requires belief in every metaphysical necessity, as the distinction between a priori logical necessities and a posteriori metaphysical ones is not an alethic distinction. To justify the restriction to classically consistent worlds, non-alethic motivation is required. And thus, if there is a version of the accuracy-dominance argument in support of probabilism, it isn’t one that is grounded in alethic considerations alone. (shrink)

Three natural assumptions about rationality lead to conflict when they are formalized in natural ways. The paper examines how the assumptions are built into formal frameworks and why they lead to conflict. Several lessons are learned for the type of rationality ordinary people manifest in everyday life.

I develop a broadly reliabilist theory of non‐ideal epistemic rationality and argue that if it is correct we should reject the recently popular idea that the standards of non‐ideal epistemic rationality are mere social conventions.

Analogy has received attention as a form of inductive reasoning in the empirical sciences. Its role in mathematics has, instead, received less consideration. This paper provides a novel account of how an analogy with a more familiar mathematical domain can contribute to the confirmation of a mathematical conjecture. By reference to case-studies, we propose a distinction between an _incremental_ and a _non-incremental_ form of confirmation by mathematical analogy. We offer an account of the former within the popular framework of Bayesian (...) confirmation theory. As for the non-incremental notion, we defend its role in rationally informing the prior credences of mathematicians in those circumstances in which no new mathematical evidence is introduced. The resulting framework captures many important aspects of the use of analogical inference in the domain of pure mathematics. (shrink)

Traditional epistemologists assumed that the most important doxastic norms were rational requirements on belief. This orthodoxy has recently been challenged by the work of revolutionary epistemologists on the rational requirements on credences. Revolutionary epistemology takes it that such contemporary work is important precisely because traditional epistemologists are mistaken—credal norms are more fundamental than, and determinative of, belief norms. To make sense of their innovative project, many revolutionary epistemologists have also adopted another commitment, that norms on credences are governed by a (...) fundamental accuracy norm. Unfortunately for the revolutionary epistemologist, it has been difficult to define a measure of accuracy while maintaining that credal norms are more basic than belief norms. In this paper, I criticize one such proposal for measuring accuracy, that the accuracy of our credences should be assessed in terms of what we know, arguing that this picture ultimately cannot vindicate the revolutionary approach. (shrink)