This is a three-part exchange on the relationship between belief and credence. It begins with an opening essay by Roger Clarke that argues for the claim that the notion of credence generalizes the notion of belief. Julia Staffel argues in her reply that we need to distinguish between mental states and models representing them, and that this helps us explain what it could mean that belief is a special case of credence. Roger Clarke's final essay reflects on the compatibility of (...) the previously discussed views with dualist and monist interpretations of our mental states and our ways of modeling them. (shrink)

How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences. However, standard representation theorems make strong rationality assumptions, in particular expected utility maximization. How do we ascribe subjective probability to agents which do not satisfy these strong rationality assumptions? I present a representation theorem with weak rationality assumptions which can be used to define or measure (...) subjective probability for partly irrational agents. (shrink)

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)

‘Bayesian epistemology’ became an epistemological movement in the 20th century, though its two main features can be traced back to the eponymous Reverend Thomas Bayes (c. 1701-61). Those two features are: (1) the introduction of a formal apparatus for inductive logic; (2) the introduction of a pragmatic self-defeat test (as illustrated by Dutch Book Arguments) for epistemic rationality as a way of extending the justification of the laws of deductive logic to include a justification for the laws of inductive logic. (...) The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of conditionalization. (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)

We defend three controversial claims about preference, credence, and choice. First, all agents (not just rational ones) have complete preferences. Second, all agents (again, not just rational ones) have real-valued credences in every proposition in which they are confident to any degree. Third, there is almost always some unique thing we ought to do, want, or believe.

How do multiple reasons combine to support a conclusion about what to do or believe? This question raises two challenges: How can we represent the strength of a reason? How do the strengths of multiple reasons combine? Analogous challenges about confirmation have been answered using probabilistic tools. Can reductive and nonreductive theories of reasons use these tools to answer their challenges? Yes, or more exactly: reductive theories can answer both challenges. Nonreductive theories, with the help of a result in confirmation (...) theory, can answer one, and there are grounds for optimism that they can answer the other. (shrink)

It is a consequence of the theory of imprecise credences that there exist situations in which rational agents inevitably become less opinionated toward some propositions as they gather more evidence. The fact that an agent's imprecise credal state can dilate in this way is often treated as a strike against the imprecise approach to inductive inference. Here, we show that dilation is not a mere artifact of this approach by demonstrating that opinion loss is countenanced as rational by a substantially (...) broader class of normative theories than has been previously recognised. Specifically, we show that dilation-like phenomena arise even when one abandons the basic assumption that agents have (precise or imprecise) credences of any kind, and follows directly from bedrock norms for rational comparative confidence judgements of the form `I am at least as confident in p as I am in q'. We then use the comparative confidence framework to develop a novel understanding of what exactly gives rise to dilation-like phenomena. By considering opinion loss in this more general setting, we are able to provide a novel assessment of the prospects for an account of inductive inference that is not saddled with the inevitability of rational opinion loss. (shrink)

Policymakers who seek to make scientifically informed decisions are constantly confronted by scientific uncertainty and expert disagreement. This thesis asks: how can policymakers rationally respond to expert disagreement and scientific uncertainty? This is a work of non-ideal theory, which applies formal philosophical tools developed by ideal theorists to more realistic cases of policymaking under scientific uncertainty. I start with Bayesian approaches to expert testimony and the problem of expert disagreement, arguing that two popular approaches— supra-Bayesianism and the standard model of (...) expert deference—are insufficient. I develop a novel model of expert deference and show how it can deal with many of these problems raised for them. I then turn to opinion pooling, a popular method for dealing with disagreement. I show that various theoretical motivations for pooling functions are irrelevant to realistic policymaking cases. This leads to a cautious recommendation of linear pooling. However, I then show that any pooling method relies on value judgements, that are hidden in the selection of the scoring rule. My focus then narrows to a more specific case of scientific uncertainty: multiple models of the same system. I introduce a particular case study involving hurricane models developed to support insurance decision-making. I recapitulate my analysis of opinion pooling in the context of model ensembles, confirming that my hesitations apply. This motivates a shift of perspective, to viewing the problem as a decision theoretic one. I rework a recently developed ambiguity theory, called the confidence approach, to take input from model ensembles. I show how it facilitates the resolution of the policymaker’s problem in a way that avoids the issues encountered in previous chapters. This concludes my main study of the problem of expert disagreement. In the final chapter, I turn to methodological reflection. I argue that philosophers who employ the mathematical methods of the prior chapters are modelling. Employing results from the philosophy of scientific models, I develop the theory of normative modelling. I argue that it has important methodological conclusions for the practice of formal epistemology, ruling out popular moves such as searching for counterexamples. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

Knowledge-first epistemology includes a knowledge norm of action: roughly, act only on what you know. This norm has been criticized, especially from the perspective of so-called standard decision theory. Mueller and Ross provide example decision problems which seem to show that acting properly cannot require knowledge. I argue that this conclusion depends on applying a particular decision theory which is ill-motivated in this context. Agents’ knowledge is often most plausibly formalized as an ambiguous epistemic state, and the theory of decision (...) under ambiguity is then the appropriate modeling tool. I show how to model agents as acting rationally on the basis of their knowledge according to such a theory. I conclude that the tension between the knowledge norm of action and formal decision theory is illusory; the knowledge-first paradigm should be used to actively select the decision-theoretical tools that can best capture the knowledge-based decisions in any given situation. (shrink)

A number of philosophers have thought that fair lotteries over countably infinite sets of outcomes are conceptually incoherent by virtue of violating countable additivity. In this article, I show that a qualitative analogue of this argument generalizes to an argument against the conceptual coherence of a much wider class of fair infinite lotteries—including continuous uniform distributions. I argue that this result suggests that fair lotteries over countably infinite sets of outcomes are no more conceptually problematic than continuous uniform distributions. Along (...) the way, I provide a novel argument for a weak qualitative, epistemic version of regularity. (shrink)

Imprecise probabilities are often modelled with representors, or sets of probability functions. In the recent literature, two ways of interpreting representors have emerged as especially prominent: vagueness interpretations, according to which each probability function in the set represents how the agent's beliefs would be if any vagueness were precisified away; and comparativist interpretations, according to which the set represents those comparative confidence relations that are common to all probability functions therein. I argue that these interpretations have some important limitations. I (...) also propose an alternative—the functional interpretation—according to which representors are best interpreted by reference to the roles they play in the theories that make use of them. (shrink)

What are credences? Where do the numbers come from? Some have argued that they are brute and primitive; others, that they model our dispositions to bet, our comparative confidence judgments, or our all‐out beliefs. This paper explores a new answer to this question: credences model our dispositions to guess. I argue that we can think of credences this way, and then consider: should we?

Moss (2018) argues that rational agents are best thought of not as having degrees of belief in various propositions but as having beliefs in probabilistic contents, or probabilistic beliefs. Probabilistic contents are sets of probability functions. Probabilistic belief states, in turn, are modeled by sets of probabilistic contents, or sets of sets of probability functions. We argue that this Mossean framework is of considerable interest quite independently of its role in Moss’ account of probabilistic knowledge or her semantics for epistemic (...) modals and probability operators. It is an extremely general model of uncertainty. Indeed, it is at least as general and expressively powerful as every other current imprecise probability framework, including lower probabilities, lower previsions, sets of probabilities, sets of desirable gambles, and choice functions. In addition, we partially answer an important question that Moss leaves open, viz., why should rational agents have consistent probabilistic beliefs? We show that an important subclass of Mossean believers avoid Dutch bookability iff they have consistent probabilistic beliefs. (shrink)

My dissertation is about Bayesian rationality for non-ideal agents. I show how to derive subjective probabilities from preferences using much weaker rationality assumptions than other standard representation theorems. I argue that non-ideal agents might be uncertain about how they will update on new information and consider two consequences of this uncertainty: such agents should sometimes reject free information and make choices which, taken together, yield sure loss. The upshot is that Bayesian rationality for non-ideal agents makes very different normative demands (...) than ideal Bayesian rationality. (shrink)