Many philosophers have argued that statistical evidence regarding group characteristics (particularly stereotypical ones) can create normative conflicts between the requirements of epistemic rationality and our moral obligations to each other. In a recent article, Johnson-King and Babic argue that such conflicts can usually be avoided: what ordinary morality requires, they argue, epistemic rationality permits. In this article, we show that as data get large, Johnson-King and Babic’s approach becomes less plausible. More constructively, we build on their project and develop a (...) generalized model of reasoning about stereotypes under which one can indeed avoid normative conflicts, even in a big data world, when data contain some noise. In doing so, we also articulate a general approach to rational belief updating for noisy data. (shrink)

According to Humean theories of objective chance, the chances reduce to patterns in the history of occurrent events, such as frequencies. According to non-Humean accounts, the chances are metaphysically fundamental, existing independently of the "Humean Mosaic" of actually-occurring events. It is therefore possible, by the lights of non-Humeanism, for the chances and the frequencies to diverge wildly. Humeans often allege that this undermines the ability of non-Humean accounts of chance to rationalize adherence to David Lewis' Principal Principle (PP), which states (...) that an agent's degrees of belief should match what they take to be the objective chances. In this paper, I propose two approaches to justifying (PP) for non-Humean chance, hence defusing the Humean objection. The first approach justifies (PP) via the role it plays in informing outright beliefs about long-run frequencies. The second approach justifies (PP) by showing that adherence to (PP), even for non-Humean chance, maximizes expected epistemic utility according to the actual objective chance function. I then address an objection to this approach, concerning the alleged circularity of the derivations. (shrink)

Impurism says that practical factors encroach on knowledge. An important version of impurism is called ‘Threshold-Impurism,’ which says that practical factors encroach on the threshold that rational credence must pass in order for one to have knowledge. A prominent kind of argument for Threshold-Impurism is the so-called ‘principle-based argument,’ which relies on a principle of fallibilism and a knowledge-action principle. This paper offers a new challenge against Threshold-Impur- ism. I attempt to show that the two principles Threshold-Impurists are committed to—KJ (...) and Fallibilism—are jointly in tension with a widely-held principle of credence that’s called ‘Truth-Directedness,’ in the sense that the former two principles cannot both apply to those who know the third. This tension constitutes a serious challenge to Threshold-Impurists, because it leaves them two options, both of which are undesirable: denying Truth-Directedness, or accepting Truth-Directedness and accepting that whether KJ and Fallibilism apply to a person depends on whether she knows Truth-Directedness. (shrink)

How much does rationality constrain what we should believe on the basis of our evidence? According to this book, not very much. For most people and most bodies of evidence, there is a wide range of beliefs that rationality permits them to have in response to that evidence. The argument, which takes inspiration from William James' ideas in 'The Will to Believe', proceeds from two premises. The first is a theory about the basis of epistemic rationality. It's called epistemic utility (...) theory, and it says that what it is epistemically rational for you to believe is what it would be rational for you to choose if you were given the chance to pick your beliefs and, when picking them, you were to care only about their epistemic value. So, to say which beliefs are permitted, we must say how to measure epistemic value, and which decision rule to use when picking your beliefs. The second premise is a claim about attitudes to epistemic risk, and it says that rationality permits many different such attitudes. These attitudes can show up in epistemic utility theory in two ways: in the way you measure epistemic value; and in the decision rule you use to pick beliefs. This book explores the latter. The result is permissivism about epistemic rationality: different attitudes to epistemic risk lead to different choices of prior beliefs; given most bodies of evidence, different priors lead to different posteriors; and even once we fix your attitudes to epistemic risk, if they are at all risk-inclined, there is a range of different priors and therefore different posteriors they permit. (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.

(This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with examples such as (...) Hilbert’s programme and Gödel’s incompleteness theorems; social choice theory, with examples such as Condorcet’s paradox and Arrow’s theorem; ‘how possibly’ results, with examples such as Condorcet’s jury theorem and recent work on intersectionality theory; and the application of advanced mathematics in philosophy, with examples such as accuracy-first epistemology. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that govern a logically ignorant individual at any given time; (...) an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence; and an account of when logical ignorance is irrational and when it isn’t. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations. (shrink)

Coherence is a key concept in many accounts of epistemic justification within ‘traditional’ analytic epistemology. Within formal epistemology, too, there is a substantial body of research on coherence measures. However, there has been surprisingly little interaction between the two bodies of literature. The reason is that the existing formal literature on coherence measure operates with a notion of belief system that is very different from—what we argue is—a natural Bayesian formalisation of the concept of belief system from traditional epistemology. Therefore, (...) formal epistemology has so far only been concerned with one particular—arguably not even very natural—way of formalising coherence of belief systems; it has by no means refuted the viability of coherentism. In contrast to the existing literature, we formalise belief systems as families of assignments of (conditional) degrees of belief (which may be compatible with several subjective probability measures). Within this framework, we propose a Bayesian formalisation of the thrust of BonJour’s coherence concept in The structure of empirical knowledge (Harvard University Press, Cambridge, 1985), using a combination of Bayesian confirmation theory and basic graph theory. In excursions, we introduce graded notions for both logical and probabilistic consistency of belief systems—the latter being based on certain geometrical structures induced by probabilistic belief systems. For illustration, we reconsider BonJour’s “ravens” challenge (op. cit., p. 95f.). Finally, potential objections to our proposed formal coherence notion are explored. (shrink)

The problem of how to rationally aggregate probability measures occurs in particular when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and when an individual whose belief system is compatible with several probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory. We investigate this problem by first recalling some negative results from preference and judgment (...) aggregation theory which show that the aggregate of several probability measures should not be conceived as the probability measure induced by the aggregate of the corresponding expected utility preferences. We describe how McConway’s :410–414, 1981) theory of probabilistic opinion pooling can be generalised to cover the case of the aggregation of infinite profiles of finitely additive probability measures, too; we prove the existence of aggregation functionals satisfying responsiveness axioms à la McConway plus additional desiderata even for infinite electorates. On the basis of the theory of propositional-attitude aggregation, we argue that this is the most natural aggregation theory for probability measures. Our aggregation functionals for the case of infinite electorates are neither oligarchic nor integral-based and satisfy a weak anonymity condition. The delicate set-theoretic status of integral-based aggregation functionals for infinite electorates is discussed. (shrink)

Conditionalization is one of the central norms of Bayesian epistemology. But there are a number of competing formulations, and a number of arguments that purport to establish it. In this paper, I explore which formulations of the norm are supported by which arguments. In their standard formulations, each of the arguments I consider here depends on the same assumption, which I call Deterministic Updating. I will investigate whether it is possible to amend these arguments so that they no longer depend (...) on it. As I show, whether this is possible depends on the formulation of the norm under consideration. (shrink)

Despite the recent backlash against epistemic consequentialism, an explicit systematic alternative has yet to emerge. This paper articulates and defends a novel alternative, Epistemic Kantianism, which rests on a requirement of respect for the truth. §1 tackles some preliminaries concerning the proper formulation of the epistemic consequentialism / non-consequentialism divide, explains where Epistemic Kantianism falls in the dialectical landscape, and shows how it can capture what seems attractive about epistemic consequentialism while yielding predictions that are harder for the latter to (...) secure in a principled way. §2 presents Epistemic Kantianism. §3 argues that it is uniquely poised to satisfy the desiderata set out in §1 on an ideal theory of epistemic justification. §4 gives three further arguments, suggesting that it (i) best explains the objective normative significance of the subject's perspective in epistemology, (ii) follows from the kind of axiology needed to solve the swamping problem together with modest assumptions about the relation between the evaluative and the deontic, and (iii) illuminates certain asymmetries in epistemic value and obligation. §5 takes stock and reassesses the score in the debate. (shrink)

The accuracy-first program attempts to ground epistemology in the norm that one’s beliefs should be as accurate as possible, where accuracy is measured using a scoring rule. We argue that considerations of scientific progress suggest that such a monism about epistemic value is untenable. In particular, we argue that counterexamples to the standard scoring rules are ubiquitous in the history of science, and hence that these scoring rules cannot be regarded as a precisification of our intuitive concept of epistemic value.

This paper aims to provide hyperintensional foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...) Hale and Wright and examined in Hale (2013), and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest that observational type theory can be applied to first-order abstraction principles in order to make abstraction principles recursively enumerable. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Evolutionary reliabilism is the view that natural selection likely favoured reliable cognitive faculties in humans. While ER enjoys some plausibility, Stephen Stich and Alvin Plantinga have presented well-known challenges to the view. Their arguments rely on a common premiss; namely, that natural selection is indifferent to truth. This article shows that this premiss is both imprecise and too weak to support their conclusions and, therefore, that their challenges to ER fail.

Bayesians defend norms of ideal rationality such as probabilism, which they claim should be approximated by non-ideal thinkers. Yet, it is not often discussed exactly in what sense it is beneficial for an agent’s credence function to approximate probabilistic coherence. Some existing research indicates that approximating coherence leads to improvements in accuracy, whereas other research suggests that it decreases Dutch book vulnerability. Yet, the existing results don’t settle whether there is a way of approximating coherence that delivers both benefits at (...) once. We show that there is. (shrink)

This paper investigates the relationship between two evaluative claims about agents’ de- grees of belief: (i) that it is better to have more, rather than less accurate degrees of belief, and (ii) that it is better to have less, rather than more probabilistically incoherent degrees of belief. We show that, for suitable combinations of inaccuracy measures and incoherence measures, both claims are compatible, although not equivalent; moreover, certain ways of becoming less incoherent always guarantee improvements in accuracy. Incompatibilities between particular (...) incoherence and inaccuracy measures can be exploited to argue against particular ways of measuring either inaccuracy or incoherence. (shrink)

According to Bayesian orthodoxy, an agent should update---or at least should plan to update---her credences by conditionalization. Some have defended this claim by means of a diachronic Dutch book argument. They say: an agent who does not plan to update her credences by conditionalization is vulnerable (by her own lights) to a diachronic Dutch book, i.e., a sequence of bets which, when accepted, guarantee loss of utility. Here, I show that this argument is in tension with evidence externalism, i.e., the (...) view that an agent's evidence can entail non-trivial propositions about the external world. I argue that this tension casts doubt on the idea that diachronic Dutch books can be used to justify or vindicate updating plans. (shrink)

What is structural rationality? Specifically, what is the distinctive feature of structural requirements of rationality? Some philosophers have argued, roughly, that the distinctive feature of structural requirements is coherence. But what does coherence mean, exactly? Or, at least, what do structuralists about rationality have in mind when they claim that structural rationality is coherence? This issue matters for making progress in various active debates concerning rationality. In this paper, I analyze three strategies for figuring out what coherence means in the (...) debates on structural rationality. I argue that these strategies face problems. (shrink)

Some epistemologists think that the Bayesian ideals matter because we can approximate them. That is, our attitudes can be more or less close to the ones of our ideal Bayesian counterpart. In this paper, I raise a worry for this justification of epistemic ideals. The worry is this: In order to correctly compare agents to their ideal counterparts, we need to imagine idealized agents who have the same relevant information, knowledge, or evidence. However, there are cases in which one’s ideal (...) counterpart cannot have one’s information, knowledge, or evidence. In these situations, agents cannot compare themselves to their ideal counterpart. (shrink)

We argue that there is a tension between two monistic claims that are the core of recent work in epistemic consequentialism. The first is a form of monism about epistemic value, commonly known as veritism: accuracy is the sole final objective to be promoted in the epistemic domain. The other is a form of monism about a class of epistemic scoring rules: that is, strictly proper scoring rules are the only legitimate measures of inaccuracy. These two monisms, we argue, are (...) in tension with each other. If only accuracy has final epistemic value, then there are legitimate alternatives to strictly proper scoring rules. Our argument relies on the way scoring rules are used in contexts where accuracy is rewarded, such as education. (shrink)

Structural requirements of rationality prohibit various things, like having inconsistent combinations of attitudes, having means-end incoherent combinations of attitudes, and so on. But what is the distinctive feature of structural requirements of rationality? And do we fall under an obligation to be structurally rational? These issues have been at the heart of significant debates over the past fifteen years. Some philosophers have recently argued that we can unify the structural requirements of rationality by analyzing what is constitutive of our attitudes (...) (Lee, 2020; Worsnip, 2018a). It has also been suggested that, in the course of good first-personal deliberation, agents should treat structurally irrational combinations of attitudes as off-limits (Worsnip, 2021). In this paper, I raise a worry for these two theses concerning structural rationality. Roughly, I argue that some imperfect epistemic agents (like us) can be disposed to have structurally irrational combinations of attitudes. Also, when these imperfect agents deliberate, they should not treat structurally irrational combinations of attitudes as off-limits. Given our imperfections, being structurally irrational can very well be the best option we have. More generally, these observations reveal that structural rationality should not always be theorized independently from more “substantive” norms, like responsiveness to reasons or expected value optimization. (shrink)

What is the relationship between Immodesty and Permissivism? For permissivists, epistemically rational agents are sometimes permitted to take incompatible doxastic attitudes towards P. Immodesty is a requirement governing our estimations or beliefs about our own credences and standards. If agents believe that their standards and credences are not among the most truth-conducive ones available to them, they are not immodest. Some philosophers think that Immodesty is incompatible with Intrapersonal Permissivism :41–56, 2014, J Philos 116:237–262, 2019). Others think that Immodesty can (...) be used to respond to some objections against Interpersonal Permissivism :193–218). In this paper, we argue that Immodesty neither supports nor disproves Permissivism. (shrink)

We recast subjective probabilities by rejecting behaviourist accounts of belief by explicitly distinguishing between judgements of uncertainty and expressions of those judgements. We argue that this entails rejecting that orderings of uncertainty be complete. This in turn leads naturally to several generalizations of the probability calculus. We define probability-like functions over incomplete algebras that reflect a subject’s incomplete judgements of uncertainty. These functions can be further generalized to inner and outer measures that reflect approximate elicitations.

One of the main goals of Bayesian epistemology is to justify the rational norms credence functions ought to obey. Accuracy arguments attempt to justify these norms from the assumption that the source of value for credences relevant to their epistemic status is their accuracy. This assumption and some standard decision-theoretic principles are used to argue for norms like Probabilism, the thesis that an agent’s credence function is rational only if it obeys the probability axioms. We introduce an example that shows (...) that the accuracy arguments for Probabilism given by Joyce and Pettigrew fail, and that Probabilism in fact turns out to be false given Pettigrew’s way of conceiving of the goal of having accurate credences. Finally, we use our discussion of Pettigrew’s framework to draw an important general lesson about normative theorizing that relies on the positing of ideal agents. (shrink)

This paper considers a problem for Bayesian epistemology and proposes a solution to it. On the traditional Bayesian framework, an agent updates her beliefs by Bayesian conditioning, a rule that tells her how to revise her beliefs whenever she gets evidence that she holds with certainty. In order to extend the framework to a wider range of cases, Jeffrey (1965) proposed a more liberal version of this rule that has Bayesian conditioning as a special case. Jeffrey conditioning is a rule (...) that tells the agent how to revise her beliefs whenever she gets evidence that she holds with any degree of confidence. The problem? While Bayesian conditioning has a foundationalist structure, this foundationalism disappears once we move to Jeffrey conditioning. If Bayesian conditioning is a special case of Jeffrey conditioning, then they should have the same normative structure. The solution? To reinterpret Bayesian updating as a form of diachronic coherentism. (shrink)

Epistemic rationality is typically taken to be immodest at least in this sense: a rational epistemic state should always take itself to be doing at least as well, epistemically and by its own light, than any alternative epistemic state. If epistemic states are probability functions and their alternatives are other probability functions defined over the same collection of proposition, we can capture the relevant sense of immodesty by claiming that epistemic utility functions are (strictly) proper. In this paper I examine (...) what happens if we allow for the alternatives to an epistemic state to include probability functions with different domains. I first prove an impossibility result: on minimal assumptions, I show that there is no way of vindicating strong immodesty principles to the effect that any probability function should take itself to be doing at least as well than any alternative probability function, regardless of its domain. I then consider alternative, weaker generalizations of the traditional immodesty principle and prove some characterization results for some classes of epistemic utility functions satisfying each of the relevant principles. (shrink)

How should rational believers pursue the aim of truth? Epistemic utility theorists have argued that by combining the tools of decision theory with an epistemic form of value—gradational accuracy, proximity to the truth—we can justify various epistemological norms. I argue that deriving these results requires using decision rules that are different in important respects from those used in standard (practical) decision theory. If we use the more familiar decision rules, we can’t justify the epistemic coherence norms that epistemic utility theory (...) had hoped to justify. In short, those of us who are attracted to the project of epistemic utility theory face a dilemma. If we choose “consequentialist” rules, then we can vindicate the idea that rational belief has the aim of accuracy—but at the cost of giving up attractive epistemic norms. (shrink)

Epistemology should take seriously the possibility of rationally evaluable changes in conceptual resources. Epistemic decision theory compares belief states in terms of epistemic value. But it's standardly restricted to belief states that don't differ in their conceptual resources. I argue that epistemic decision theory should be generalized to make belief states with differing concepts comparable. I characterize some possible constraints on epistemic utility functions. Traditionally, the epistemic utility of a total belief state has been understood as a function of the (...) epistemic utility of individual (partial) beliefs. The most natural ways of generalizing this account generate a kind of repugnant conclusion. I characterize some possible alternatives, reflecting different epistemic norms. (shrink)

It’s been argued that there are no diachronic norms of epistemic rationality. These arguments come partly in response to certain kinds of counterexamples to Conditionalization, but are mainly motivated by a form of internalism that appears to be in tension with any sort of diachronic coherence requirements. I argue that there are, in fact, fundamentally diachronic norms of rationality. And this is to reject at least a strong version of internalism. But I suggest a replacement for Conditionalization that salvages internalist (...) intuitions, and carves a middle ground between conservatism and evidentialism. (shrink)

Epistemic Utility Theory is often identified with the project of *axiology-first epistemology*—the project of vindicating norms of epistemic rationality purely in terms of epistemic value. One of the central goals of axiology-first epistemology is to provide a justification of the central norm of Bayesian epistemology, Probabilism. The first part of this paper presents a new challenge to axiology first epistemology: I argue that in order to justify Probabilism in purely axiological terms, proponents of axiology first epistemology need to justify a (...) claim about epistemic value—what I label ‘Downwards Propriety’—much stronger than any they have offered justification. The second part of this paper offers an argument that this challenge cannot be met: that there is no hope for providing a purely axiological justification of Downwards Propriety, at least given widely accepted assumptions about epistemic value. (shrink)

This is a discussion of Richard Pettigrew's book "Accuracy and the Laws of Credence". I target Pettigrew's application of the accuracy framework to derive chance-credence principles. My principal contention is that Pettigrew's preferred version of the argument might in one sense be circular and, moreover, that Pettigrew's premises have content that go beyond that of standard chance-credence principles.

Can we extend accuracy-based epistemic utility theory to imprecise credences? There's no obvious way of proceeding: some stipulations will be necessary for either (i) the notion of accuracy or (ii) the epistemic decision rule. With some prima facie plausible stipulations, imprecise credences are always required. With others, they’re always impermissible. Care is needed to reach the familiar evidential view of imprecise credence: that whether precise or imprecise credences are required depends on the character of one's evidence. I propose an epistemic (...) utility theoretic defense of a common view about how evidence places demands on imprecise credence: that your spread of credence should cover the range of chance hypotheses left open by your evidence. I argue that objections to the form of epistemic utility theoretic argument that I use will extend to the standard motivation for epistemically mandatory imprecise credences. (shrink)

Accuracy-first epistemology aims to show that the norms of epistemic rationality can be derived from the effective pursuit of accuracy. This paper explores the prospects within accuracy-first epistemology for vindicating “modesty”: the thesis that ideal rationality permits uncertainty about one’s own rationality. I argue that accuracy-first epistemology faces serious challenges in accommodating three forms of modesty: uncertainty about what priors are rational, uncertainty about whether one’s update policy is rational, and uncertainty about what one’s evidence is. I argue that the (...) problem stems from the representation of epistemic decision problems. The appropriate representation of decision problems, and corresponding decision rules, for (diachronic) update policies should be a generalization of decision problems and decision rules for (synchronic) coherence. I argue that extant accounts build in conflicting assumptions about which kinds of information about the believer should be used to structure epistemic decision problems. In particular, extant accounts of update build in a form of epistemic consequentialism. Related forms of epistemic consequentialism have been shown to generate problems for accuracy-first epistemology’s purported justifications of probabilism, conditionalization, and the principal principle. These results are vindicated only with nonconsequentialist epistemic decision theories. I close with suggestive examples of how, with a fully nonconsequentialist representation of epistemic decision problems, accuracy-first epistemology can allow for rational modesty. (shrink)

We investigate how to assign probabilities to sentences that contain a type-free truth predicate. These probability values track how often a sentence is satisfied in transfinite revision sequences, following Gupta and Belnap’s revision theory of truth. This answers an open problem by Leitgeb which asks how one might describe transfinite stages of the revision sequence using such probability functions. We offer a general construction, and explore additional constraints that lead to desirable properties of the resulting probability function. One such property (...) is Leitgeb’s Probabilistic Convention T, which says that the probability of φ equals the probability that φ is true. (shrink)

In this article, I consider what sorts of chance credence norms can be justified by appeal to the idea that ideal credences should line up with the chances. I argue that the Principal Principle cannot be so justified but that an alternative norm, the Temporal Principle—which maintains that an agent’s credence in a proposition ϕ, conditional on the temporal proposition that says that the chance of ϕ is x, should be x—can be so justified.

In this paper, I argue that some plausible principles concerning which credences are rationally permissible for agents given information about one another’s epistemic and credal states have some surprising consequences for which credences an agent ought to have in light of self-locating information. I provide a framework that allows us to state these constraints and draw out these consequences precisely. I then consider and assess the prospects for rejecting these prima facie plausible principles.

Standard accuracy-based approaches to imprecise credences have the consequence that it is rational to move between precise and imprecise credences arbitrarily, without gaining any new evidence. Building on the Educated Guessing Framework of Horowitz (2019), we develop an alternative accuracy-based approach to imprecise credences that does not have this shortcoming. We argue that it is always irrational to move from a precise state to an imprecise state arbitrarily, however it can be rational to move from an imprecise state to a (...) precise state arbitrarily. (shrink)

The foundations of probability are viewed through the lens of the subjectivist interpretation. This article surveys conditional probability, arguments for probabilism, probability dynamics, and the evidential and subjective interpretations of probability.

Epistemic decision theorists aim to justify Bayesian norms by arguing that these norms further the goal of epistemic accuracy—having beliefs that are as close as possible to the truth. The standard defense of Probabilism appeals to accuracy dominance: for every belief state that violates the probability calculus, there is some probabilistic belief state that is more accurate, come what may. The standard defense of Conditionalization, on the other hand, appeals to expected accuracy: before the evidence is in, one should expect (...) to do better by conditionalizing than by following any other rule. We present a new argument for Conditionalization that appeals to accuracy‐dominance, rather than expected accuracy. Our argument suggests that Conditionalization is a rule of coherence: plans that conflict with Conditionalization don't just prescribe bad responses to the evidence; they also give rise to inconsistent attitudes. (shrink)

We argue that philosophers ought to distinguish epistemic decision theory and epistemology, in just the way ordinary decision theory is distinguished from ethics. Once one does this, the internalist arguments that motivate much of epistemic decision theory make sense, given specific interpretations of the formalism. Making this distinction also causes trouble for the principle called Propriety, which says, roughly, that the only acceptable epistemic utility functions make probabilistically coherent credence functions immodest. We cast doubt on this requirement, but then argue (...) that epistemic decision theorists should never have wanted such a strong principle in any case. (shrink)

De Finetti is one of the founding fathers of the subjective school of probability. He held that probabilities are subjective, coherent degrees of expectation, and he argued that none of the objective interpretations of probability make sense. While his theory has been influential in science and philosophy, it has encountered various objections. I argue that these objections overlook central aspects of de Finetti’s philosophy of probability and are largely unfounded. I propose a new interpretation of de Finetti’s theory that highlights (...) these aspects and explains how they are an integral part of de Finetti’s instrumentalist philosophy of probability. I conclude by drawing an analogy between misconceptions about de Finetti’s philosophy of probability and common misconceptions about instrumentalism. (shrink)

Many have claimed that epistemic rationality sometimes requires us to have imprecise credal states (i.e. credal states representable only by sets of credence functions) rather than precise ones (i.e. credal states representable by single credence functions). Some writers have recently argued that this claim conflicts with accuracy-centered epistemology, i.e., the project of justifying epistemic norms by appealing solely to the overall accuracy of the doxastic states they recommend. But these arguments are far from decisive. In this essay, we prove some (...) new results, which show that there is little hope for reconciling the rationality of credal imprecision with accuracy-centered epistemology. (shrink)

If you utter sentence (1) ‘Obama was born in 1961’ now, you say something true about the past. Since the past will always be such that the year 1961 has the property of being a time in which Obama was born, it seems impossible that could ever be false in a future context of utterance. We shall consider the case of a sentence about the past exactly like (1), but which was true when uttered a few years ago and is (...) no longer true now. On this basis, we shall conclude that the past has changed. (shrink)

I propose a general alethic theory of epistemic risk according to which the riskiness of an agent’s credence function encodes her relative sensitivity to different types of graded error. After motivating and mathematically developing this approach, I show that the epistemic risk function is a scaled reflection of expected inaccuracy. This duality between risk and information enables us to explore the relationship between attitudes to epistemic risk, the choice of scoring rules in epistemic utility theory, and the selection of priors (...) in Bayesian epistemology more generally. (shrink)

Approximate coherentism suggests that imperfectly rational agents should hold approximately coherent credences. This norm is intended as a generalization of ordinary coherence. I argue that it may be unable to play this role by considering its application under learning experiences. While it is unclear how imperfect agents should revise their beliefs, I suggest a plausible route is through Bayesian updating. However, Bayesian updating can take an incoherent agent from relatively more coherent credences to relatively less coherent credences, depending on the (...) data observed. Thus, comparative rationality judgments among incoherent agents are unduly sensitive to luck. (shrink)