Brian Hedden defends a radical view about the relationship between rationality, personal identity, and time. On the standard view, personal identity over time plays a central role in thinking about rationality, because there are rational norms for how a person's attitudes and actions at one time should fit with her attitudes and actions at other times. But these norms are problematic. They make what you rationally ought to believe or do depend on facts about your past that aren't part of (...) your current perspective on the world, and they make rationality depend on controversial, murky metaphysical facts about what binds different instantaneous snapshots into a single person extended in time. Hedden takes a different approach, treating the relationship between different time-slices of the same person as no different from the relationship between different people. On his account, the locus of rationality is the time-slice rather than the temporally extended agent. This impersonal, time-slice-centric approach to rationality yields a unified approach to the rationality of beliefs, preferences, and actions where what rationality demands of you is solely determined by your evidence, with no special weight given to your past beliefs or actions. (shrink)

How should thinkers cope with uncertainty? Julia Staffel breaks new ground in the study of rationality by answering this question and many others. She also explains how it is better to be less irrational, because less irrational degrees of belief are generally more accurate and better at guiding our actions.

Many philosophers have argued that "degree of belief" or "credence" is a more fundamental state grounding belief. Many other philosophers have been skeptical about the notion of "degree of belief", and take belief to be the only meaningful notion in the vicinity. This paper shows that one can take belief to be fundamental, and ground a notion of "degree of belief" in the patterns of belief, assuming that an agent has a collection of beliefs that isn't dominated by some other (...) collection in terms of the overall balance of truth and falsity that it could contain. (shrink)

Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory (...) to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives. (shrink)

Vagueness is the study of concepts that admit borderline cases. The epistemology of vagueness concerns attitudes we should have towards propositions we know to be borderline. On this basis Andrew Bacon develops a new theory of vagueness in which vagueness is fundamentally a property of propositions, explicated in terms of its role in thought.

An adequate account of laws should satisfy at least five desiderata: it should provide a unified account of laws and chances, it should yield plausible relations between laws and chances, it should vindicate numerical chance assignments, it should accommodate dynamical and non-dynamical chances, and it should accommodate a plausible range of nomic possibilities. No extant account of laws satisfies these desiderata. This paper presents a non-Humean account of laws, the Nomic Likelihood Account, that does.

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)

Traditional Bayesianism requires that an agent’s degrees of belief be represented by a real-valued, probabilistic credence function. However, in many cases it seems that our evidence is not rich enough to warrant such precision. In light of this, some have proposed that we instead represent an agent’s degrees of belief as a set of credence functions. This way, we can respect the evidence by requiring that the set, often called the agent’s credal state, includes all credence functions that are in (...) some sense compatible with the evidence. One known problem for this evidentially motivated imprecise view is that in certain cases, our imprecise credence in a particular proposition will remain the same no matter how much evidence we receive. In this article I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid it without compromising the initial evidentialist motivation. _1_ Introduction _2_ Precision and Its Problems _3_ Imprecise Bayesianism and Respecting Ambiguous Evidence _4_ Local Belief Inertia _5_ From Local to Global Belief Inertia _6_ Responding to Global Belief Inertia _7_ Conclusion. (shrink)

Abstract:This paper explores the contrast between mentalistic and behaviouristic interpretations of decision theory. The former regards credences and utilities as psychologically real, while the latter regards them as mere representations of an agent's preferences. Philosophers typically adopt the former interpretation, economists the latter. It is argued that the mentalistic interpretation is preferable if our aim is to use decision theory for descriptive purposes, but if our aim is normative then the behaviouristic interpretation cannot be dispensed with.

Naive versions of decision theory take probabilities and utilities as primitive and use expected value to give norms on rational decision. However, standard decision theory takes rational preference as primitive and uses it to construct probability and utility. This paper shows how to justify a version of the naive theory, by taking dominance as the most basic normatively required preference relation, and then extending it by various conditions under which agents should be indifferent between acts. The resulting theory can make (...) all the decisions of classical expected utility theory, plus more in cases where expected utilities are infinite or undefined. Although the theory requires similarly strong assumptions to classical expected utility theory, versions of the theory can be developed with slightly weaker assumptions, without having to prove a new representation theorem for the weaker theory. This alternate foundation is particularly useful if probability is prior to preference, as suggested by the recent program to base probabilism on accuracy and alethic considerations rather than pragmatic ones. (shrink)

Credences are similar to levels of confidence, represented as a value on the [0,1] interval. This chapter sheds light on questions about credence, including its relationship to full belief, with an eye toward the empirical relevance of credence. First, I’ll provide a brief epistemological history of credence and lay out some of the main theories of the nature of credence. Then, I’ll provide an overview of the main views on how credences relate to full beliefs. Finally, I’ll turn to the (...) empirical, and suggest some ways that cognitive science does and could answer questions about credence, such as what credences one has, how credences relate to beliefs, and the extent to which we can control our credences. (shrink)

Deontologists have long been upbraided for lacking an account of justified decision- making under risk and uncertainty. One response is to develop a deontological decision theory—a set of necessary and sufficient conditions for an act’s being permissible given an agent’s imperfect information. In this article, I show that deontologists can make more use of regular decision theory than some might have thought, but that we must adapt decision theory to accommodate agent- centered options—permissions to favor or sacrifice our own interests, (...) when doing so is overall morally worse. Accommodating options requires more than just amend- ing the decision-theoretic ‘value function’. We must change the decision rule as well. (shrink)

How should deontologists concerned with the ethics of killing apply their moral theory when we don’t know all the facts relevant to the permissibility of our action? Though the stakes couldn’t be higher, and uncertainty is endemic where killing is concerned, few deontologists have an answer to this question. In this paper I canvass two possibilities: that we should apply a threshold standard, equivalent to the ‘beyond a reasonable doubt’ standard applied for criminal punishment; and that we should fit our (...) deontological ethical theory into the apparatus of decision theory. I show that the first approach faces insurmountable obstacles, while the second holds much more promise for deontologists than they might first have assumed. (shrink)

Should economics study the psychological basis of agents' choice behaviour? I show how this question is multifaceted and profoundly ambiguous. There is no sharp distinction between "mentalist'' answers to this question and rival "behavioural'' answers. What's more, clarifying this point raises problems for mentalists of the "functionalist'' variety (Dietrich and List, 2016). Firstly, functionalist hypotheses collapse into hypotheses about input--output dispositions, I show, unless one places some unwelcome restrictions on what counts as a cognitive variable. Secondly, functionalist hypotheses make some (...) risky commitments about the plasticity of agents' choice dispositions. (shrink)

How ought you to evaluate your options if you’re uncertain about which axiology is true? One prominent response is Expected Moral Value Maximisation, the view that under axiological uncertainty, an option is better than another if and only if it has the greater expected moral value across axiologies. EMVM raises two fundamental questions. First, there’s a question about what it should even mean. In particular, it presupposes that we can compare moral value across axiologies. So to even understand EMVM, we (...) need to explain what it is for such comparisons to hold. Second, assuming that we understand it, there’s a question about whether EMVM is true. Since there are many plausible rivals, we need an argument to defend it. In this paper, I’ll introduce a representation theorem for axiological uncertainty to answer these two questions. Roughly, the theorem shows that if all our axiologies satisfy the von Neumann–Morgenstern axioms, and if the facts about which options are better than which in light of your uncertainty also satisfy these axioms as well as a Pareto condition, then these facts have a relevantly unique expected utility representation. If I’m right, this theorem at once affords us a compelling way to understand EMVM—and specifically intertheoretic comparisons—and a systematic argument for its truth. (shrink)

I present a puzzle about belief and credence, which takes the form of three independently supported views that are mutually inconsistent. The first is the view that S has a modal belief that p (e.g., S believes that probably-p) if and only if S has a corresponding credence that p. The second is the view that S believes that p only if S has some credence that p. The third is the view that, possibly, S believes that p without a (...) modal belief that p. [Word Count: 85]. (shrink)

According to comparativism, degrees of belief are reducible to a system of purely ordinal comparisons of relative confidence. (For example, being more confident that P than that Q, or being equally confident that P and that Q.) In this paper, I raise several general challenges for comparativism, relating to (i) its capacity to illuminate apparently meaningful claims regarding intervals and ratios of strengths of belief, (ii) its capacity to draw enough intuitively meaningful and theoretically relevant distinctions between doxastic states, and (...) (iii) its capacity to handle common instances of irrationality. (shrink)

The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk (like Pascal's Mugging), and intolerably paradoxical in cases like the St. Petersburg and Pasadena games. In this paper I show that, under certain conditions, stochastic dominance reasoning can capture most of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given sufficient background uncertainty (...) about the choiceworthiness of one's options, many expectation-maximizing gambles that do not stochastically dominate their alternatives "in a vacuum" become stochastically dominant in virtue of that background uncertainty. But, even under these conditions, stochastic dominance will not require agents to accept options whose expectational superiority depends on sufficiently small probabilities of extreme payoffs. The sort of background uncertainty on which these results depend looks unavoidable for any agent who measures the choiceworthiness of her options in part by the total amount of value in the resulting world. At least for such agents, then, stochastic dominance offers a plausible general principle of choice under uncertainty that can explain more of the apparent rational constraints on such choices than has previously been recognized. (shrink)

This paper defends two related claims about belief. First, the claim that unlike numerical degrees of belief, comparative beliefs are primitive and psychologically real. Second, the claim that the fundamental norm of Probabilism is not that numerical degrees of belief should satisfy the probability axioms, but rather that comparative beliefs should satisfy certain constraints.

There are decision problems where the preferences that seem rational to many people cannot be accommodated within orthodox decision theory in the natural way. In response, a number of alternatives to the orthodoxy have been proposed. In this paper, I offer an argument against those alternatives and in favour of the orthodoxy. I focus on preferences that seem to encode sensitivity to risk. And I focus on the alternative to the orthodoxy proposed by Lara Buchak’s risk-weighted expected utility theory. I (...) will show that the orthodoxy can be made to accommodate all of the preferences that Buchak’s theory can accommodate. (shrink)

Consequentialists often assume rational monism: the thesis that options are always made rationally permissible by the maximization of the selfsame quantity. This essay argues that consequentialists should reject rational monism and instead accept rational pluralism: the thesis that, on different occasions, options are made rationally permissible by the maximization of different quantities. The essay then develops a systematic form of rational pluralism which, unlike its rivals, is capable of handling both the Newcomb problems that challenge evidential decision theory and the (...) unstable problems that challenge causal decision theory. (shrink)

The main question of this paper is: how do we manage to know what our own degrees of belief are? Section 1 briefly reviews and criticizes the traditional functionalist view, a view notably associated with David Lewis and sometimes called the theory-theory. I use this criticism to motivate the approach I want to promote. Section 2, the bulk of the paper, examines and begins to develop the view that we have a special kind of introspective access to our degrees of (...) belief. I give an initial assessment of the view by examining its compatibility with leading theories of introspection. And I identify a challenge for the view, and explain why I'm optimistic that the view can overcome it. (shrink)

How ought you to evaluate your options if you're uncertain about what's fundamentally valuable? A prominent response is Expected Value Maximisation (EVM)—the view that under axiological uncertainty, an option is better than another if and only if it has the greater expected value across axiologies. But the expected value of an option depends on quantitative probability and value facts, and in particular on value comparisons across axiologies. We need to explain what it is for such facts to hold. Also, EVM (...) is by no means self-evident. We need an argument to defend that it’s true. This book introduces an axiomatic approach to answer these worries. It provides an explication of what EVM means by use of representation theorems: intertheoretic comparisons can be understood in terms of facts about which options are better than which, and mutatis mutandis for intratheoretic comparisons and axiological probabilities. And it provides a systematic argument to the effect that EVM is true: the theory can be vindicated through simple axioms. The result is a formally cogent and philosophically compelling extension of standard decision theory, and original take on the problem of axiological or normative uncertainty. (shrink)

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)

In this new explanationist account of epistemic justification, Poston argues that the explanatory virtues provide all the materials necessary for a plausible account of justified belief. There are no purely autonomous reasons. Rather reasons occur only within an explanatory coherent set of beliefs.

Normative ethical theories owe us an account of how to evaluate decisions under risk and uncertainty. Deontologists seem at a disadvantage here: our best decision theories seem tailor-made for consequentialism. For example, decision theory enjoins us to always perform our best option; deontology is more permissive. In this paper, we discuss and defend the idea that, when some pro-tanto wrongful act is all-things considered permissible, because it is a ‘lesser evil’, it is often merely permissible, by the lights of deontology. (...) We show that this raises new problems for deontological decision theory, and we show that to resolve them, we need to take a more innovative approach to morally evaluating decision-making under risk and uncertainty. (shrink)

Credal reductivism is the view that outright belief is reducible to degrees of confidence or ‘credence’. The most popular versions of credal reductivism all have the consequence that if you are near-maximally confident that p in a low-stakes situation, then you outright believe p. This paper addresses a recent objection to this consequence—the Correctness Objection— introduced by Jeremy Fantl and Matthew McGrath and further developed by Jacob Ross and Mark Schroeder. The objection is that near-maximal confidence cannot entail outright belief (...) because when you believe a false proposition, you are wrong or incorrect, whereas you can be highly confident of a false proposition in a low-stakes situation without being incorrect. Both Fantl and McGrath’s and Ross and Schoeder’s versions of the Correctness Objection admit of multiple interpretations. But it is argued that even on the most charitable interpretations the objection fails. (shrink)

This paper discusses a challenge for Comparativists about belief, who hold that numerical degree of belief (in particular, subjective probability) is a useful fiction, unlike comparative belief, which they regard as real. The challenge is to make sense of claims like ‘I am twice as confident in A as in B’ in terms of comparative belief only. After showing that at least some Comparativists can meet this challenge, I discuss implications for Zynda’s [2000] and Stefánsson’s [2017] defences of Comparativism.

– 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)

The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility. However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being always probabilistically coherent with infinitely precise degrees (...) of belief and full knowledge of all a priori truths. Ordinary subjects do not look very rational when compared to the kinds of agents usually talked about in decision theory. In this paper, I will develop an expected utility representation theorem aimed at the representation of those who are neither probabilistically coherent, logically omniscient, nor expected utility maximisers across the board—that is, agents who are frequently irrational. The agents in question may be deductively fallible, have incoherent credences, limited representational capacities, and fail to maximise expected utility for all but a limited class of gambles. (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 this paper I examine a neglected question concerning the centerpiece of Carnap's philosophy: the principle of tolerance. The principle of tolerance states that we are free to devise and adopt any well-defined form of language or linguistic framework we please. A linguistic framework defines framework-internal standards of correct reasoning that guide us in our first-order scientific pursuits. The choice of a linguistic framework, on the other hand, is an ‘external’ question to be settled on pragmatic grounds and so not (...) itself constrained by these standards. However, even if choosing a framework is a practical matter, we would nevertheless expect the process of framework selection to be subject to rational norms. But which norms might those be? And where do they come from? I begin by showing that these questions are crucial to the success of Carnap's entire philosophical project. I then offer a response on behalf of the Carnapian which guarantees the rationality of the process of framework selection, while remaining true to Carnap's firm commitment to tolerance. (shrink)

According to the preference-centric approach to understanding partial belief, the connection between partial beliefs and preferences is key to understanding what partial beliefs are and how they’re measured. As Ramsey put it, the ‘degree of a belief is a causal property of it, which we can express vaguely as the extent to which we are prepared to act on it’ The Foundations of Mathematics and Other Logical Essays, Routledge, Oxon, pp 156–198, 1931). But this idea is not as popular as (...) it once was. Nowadays, the preference-centric approach is frequently dismissed out-of-hand as behaviouristic, unpalatably anti-realist, and/or prone to devastating counterexamples. Cases like Eriksson and Hájek’s :183–213, 2007) preferenceless Zen monk and Christensen’s :356–376, 2001) other roles argument have suggested to many that any account of partial belief that ties them too closely to preferences is irretrievably flawed. In this paper I provide a defence of preference-centric accounts of partial belief. (shrink)

Comparativism is the view that comparative confidences (e.g., being more confident that P than that Q) are more fundamental than degrees of belief (e.g., believing that P with some strength x). In this paper, I outline the basis for a new, non-probabilistic version of comparativism inspired by a suggestion made by Frank Ramsey in `Probability and Partial Belief'. I show how, and to what extent, `Ramseyan comparativism' might be used to weaken the (unrealistically strong) probabilistic coherence conditions that comparativism traditionally (...) relies on. (shrink)

The topic of this thesis is axiological uncertainty – the question of how you should evaluate your options if you are uncertain about which axiology is true. As an answer, I defend Expected Value Maximisation (EVM), the view that one option is better than another if and only if it has the greater expected value across axiologies. More precisely, I explore the axiomatic foundations of this view. I employ results from state-dependent utility theory, extend them in various ways and interpret (...) them accordingly, and thus provide axiomatisations of EVM as a theory of axiological uncertainty. (shrink)

ABSTRACT In a recent article, Samir Okasha presented an argument that suggests that there is no rational way to choose among scientific theories. This would seriously undermine the view that science is a rational enterprise. In this article, I show how a suitably nuanced view of what scientific rationality requires allows us to sidestep this argument. In doing so, I present a new argument in favour of voluntarism of the type favoured by van Fraassen. I then show how such a (...) view of scientific rationality gives a precise interpretation of what Thomas Kuhn thought. _1_ Introduction _2_ Okasha’s Argument _3_ Rationality Can Be Silent _4_ Arrow Undermined _5_ The Informational-Basis Escape _6_ Theory Choice at the Level of the Individual Scientist _7_ Kuhn Vindicated _8_ Trade-offs and Partial Commensurability _9_ Conclusion. (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)

David Lewis (1974, 1994/1999) proposed to reduce the facts about mental representation to facts about sensory evidence, dispositions to act, and rationality. Recently, Robert Williams (2020) and Adam Pautz (2021) have taken up and developed Lewis’s project in sophisticated and novel ways. In this paper, we aim to present, clarify, and ultimately object to the core thesis that they all build their own views around. The different sophisticated developments and defenses notwithstanding, we think the core thesis is vulnerable. We pose (...) a dilemma by considering the two sides of a current epistemological controversy over the relation between evidence and rational belief: permissivism vs. uniqueness. As we argue, the prospects for the Lewisian project look dim when either supposition is clearly made. (shrink)

Frank Plumpton Ramsey (1903–30) made seminal contributions to philosophy, mathematics and economics. Whilst he was acknowledged as a genius by his contemporaries, some of his most important ideas were not appreciated until decades later; now better appreciated, they continue to bear an influence upon contemporary philosophy. His historic significance was to usher in a new phase of analytic philosophy, which initially built upon the logical atomist doctrines of Bertrand Russell and Ludwig Wittgenstein, raising their ideas to a new level of (...) sophistication, but ultimately he became their successor rather than remain a mere acolyte. (shrink)