Richard Pettigrew offers an extended investigation into a particular way of justifying the rational principles that govern our credences. The main principles that he justifies are the central tenets of Bayesian epistemology, though many other related principles are discussed along the way. Pettigrew looks to decision theory in order to ground his argument. He treats an agent's credences as if they were a choice she makes between different options, gives an account of the purely epistemic utility enjoyed by different sets (...) of credences, and then appeals to the principles of decision theory to show that, when epistemic utility is measured in this way, the credences that violate the principles listed above are ruled out as irrational. The account of epistemic utility set out here is the veritist's: the sole fundamental source of epistemic utility for credences is their accuracy. Thus, Pettigrew conducts an investigation in the version of epistemic utility theory known as accuracy-first epistemology. (shrink)

Jim Joyce argues for two amendments to probabilism. The first is the doctrine that credences are rational, or not, in virtue of their accuracy or “closeness to the truth” (1998). The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (2010). We argue that both amendments cannot be satisfied simultaneously. To do so, we employ a (slightly-generalized) impossibility theorem of Seidenfeld, Schervish, and Kadane (2012), who show that (...) there is no strictly proper scoring rule for imprecise probabilities. -/- The question then is what should give way. Joyce, who is well aware of this no-go result, thinks that a quantifiability constraint on epistemic accuracy should be relaxed to accommodate imprecision. We argue instead that another Joycean assumption — called strict immodesty— should be rejected, and we prove a representation theorem that characterizes all “mildly” immodest measures of inaccuracy. (shrink)

Recently many have argued that agents must sometimes have credences that are imprecise, represented by a set of probability measures. But opponents claim that fans of imprecise credences cannot provide a decision theory that protects agents who follow it from foregoing sure money. In particular, agents with imprecise credences appear doomed to act irrationally in diachronic cases, where they are called to make decisions at earlier and later times. I respond to this claim on behalf of imprecise credence fans. Once (...) we appreciate the complexity of our intuitions about rational decision making, we can see that diachronic cases are in fact evidence for the essential claims motivating imprecise credence models. I argue that our decision theory for imprecise agents should mirror our decision theory for agents in moral dilemmas, and I develop permissive norms that explain our intuitions about both sorts of agents. (shrink)

The modus ponens (A -> B, A :. B) is, along with modus tollens and the two logically not valid counterparts denying the antecedent (A -> B, ¬A :. ¬B) and affirming the consequent, the argument form that was most often investigated in the psychology of human reasoning. The present contribution reports the results of three experiments on the probabilistic versions of modus ponens and denying the antecedent. In probability logic these arguments lead to conclusions with imprecise probabilities. In the (...) modus ponens tasks the participants inferred probabilities that agreed much better with the coherent normative values than in the denying the antecedent tasks, a result that mirrors results found with the classical argument versions. For modus ponens a surprisingly high number of lower and upper probabilities agreed perfectly with the conjugacy property (upper probabilities equal one complements of the lower probabilities). When the probabilities of the premises are imprecise the participants do not ignore irrelevant (“silent”) boundary probabilities. The results show that human mental probability logic is close to predictions derived from probability logic for the most elementary argument form, but has considerable difficulties with the more complex forms involving negations. (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)

Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

According to Bayesian epistemology, the epistemically rational agent updates her beliefs by conditionalization: that is, her posterior subjective probability after taking account of evidence X, pnew, is to be set equal to her prior conditional probability pold(·|X). Bayesians can be challenged to provide a justification for their claim that conditionalization is recommended by rationality—whence the normative force of the injunction to conditionalize? There are several existing justifications for conditionalization, but none directly addresses the idea that conditionalization will be epistemically rational (...) if and only if it can reasonably be expected to lead to epistemically good outcomes. We apply the approach of cognitive decision theory to provide a justification for conditionalization using precisely that idea. We assign epistemic utility functions to epistemically rational agents; an agent’s epistemic utility is to depend both upon the actual state of the world and on the agent’s credence distribution over possible states. We prove that, under independently motivated conditions, conditionalization is the unique updating rule that maximizes expected epistemic utility. (shrink)

It has been claimed that, in response to certain kinds of evidence, agents ought to adopt imprecise credences: doxastic states that are represented by sets of credence functions rather than single ones. In this paper I argue that, given some plausible constraints on accuracy measures, accuracy-centered epistemologists must reject the requirement to adopt imprecise credences. I then show that even the claim that imprecise credences are permitted is problematic for accuracy-centered epistemology. It follows that if imprecise credal states are permitted (...) or required in the cases that their defenders appeal to, then the requirements of rationality can outstrip what would be warranted by an interest in accuracy. (shrink)

In “A Nonpragmatic Vindication of Probabilism”, Jim Joyce argues that our credences should obey the axioms of the probability calculus by showing that, if they don't, there will be alternative credences that are guaranteed to be more accurate than ours. But it seems that accuracy is not the only goal of credences: there is also the goal of matching one's credences to one's evidence. I will consider four ways in which we might make this latter goal precise: on the first, (...) the norms to which this goal gives rise act as ‘side constraints’ on our choice of credences; on the second, matching credences to evidence is a goal that is weighed against accuracy to give the overall cognitive value of credences; on the third, as on the second, proximity to the evidential goal and proximity to the goal of accuracy are both sources of value, but this time they are incomparable; on the fourth, the evidential goal is not an independent goal at all, but rather a byproduct of the goal of accuracy. All but the fourth way of making the evidential goal precise are pluralist about credal virtue: there is the virtue of being accurate and there is the virtue of matching the evidence and neither reduces to the other. The fourth way is monist about credal virtue: there is just the virtue of being accurate. The pluralist positions lead to problems for Joyce's argument; the monist position avoids them. I endorse the latter. (shrink)

A number of Bayesians claim that, if one has no evidence relevant to a proposition P, then one's credence in P should be spread over the interval [0, 1]. Against this, I argue: first, that it is inconsistent with plausible claims about comparative levels of confidence; second, that it precludes inductive learning in certain cases. Two motivations for the view are considered and rejected. A discussion of alternatives leads to the conjecture that there is an in-principle limitation on formal representations (...) of belief: they cannot be both fully accurate and maximally specific. (shrink)

The pragmatic character of the Dutch book argument makes it unsuitable as an "epistemic" justification for the fundamental probabilist dogma that rational partial beliefs must conform to the axioms of probability. To secure an appropriately epistemic justification for this conclusion, one must explain what it means for a system of partial beliefs to accurately represent the state of the world, and then show that partial beliefs that violate the laws of probability are invariably less accurate than they could be otherwise. (...) The first task can be accomplished once we realize that the accuracy of systems of partial beliefs can be measured on a gradational scale that satisfies a small set of formal constraints, each of which has a sound epistemic motivation. When accuracy is measured in this way it can be shown that any system of degrees of belief that violates the axioms of probability can be replaced by an alternative system that obeys the axioms and yet is more accurate in every possible world. Since epistemically rational agents must strive to hold accurate beliefs, this establishes conformity with the axioms of probability as a norm of epistemic rationality whatever its prudential merits or defects might be. (shrink)

Unspecific evidence calls for imprecise credence. My aim is to vindicate this thought. First, I will pin down what it is that makes one's imprecise credences more or less epistemically valuable. Then I will use this account of epistemic value to delineate a class of reasonable epistemic scoring rules for imprecise credences. Finally, I will show that if we plump for one of these scoring rules as our measure of epistemic value or utility, then a popular family of decision rules (...) recommends imprecise credences. In particular, a range of Hurwicz criteria, which generalise the Maximin decision rule, recommend imprecise credences. If correct, the moral is this: an agent who adopts precise credences, rather than imprecise ones, in the face of unspecific and incomplete evidence, goes wrong by gambling with the epistemic utility of her doxastic state in too risky a fashion. Precise credences represent an overly risky epistemic bet, according to the Hurwicz criteria. (shrink)

We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required . Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our second argument begins with our (...) describing a world that plausibly has indeterminate chances. Rationality requires a certain alignment of your credences with corresponding hypotheses about the chances. Thus, if you hypothesize the chances to be indeterminate, your will inherit their indeterminacy in your corresponding credences. Our third argument is motivated by a dilemma. Epistemic rationality requires you to stay open-minded about contingent matters about which your evidence has not definitively legislated. Practical rationality requires you to be able to act decisively at least sometimes. These requirements can conflict with each other-for thanks to your open-mindedness, some of your options may have undefined expected utility, and if you are choosing among them, decision theory has no advice to give you. Such an option is playing Nover and Hájek’s Pasadena Game , and indeed any option for which there is a positive probability of playing the Pasadena Game. You can serve both masters, epistemic rationality and practical rationality, with an indeterminate credence to the prospect of playing the Pasadena game. You serve epistemic rationality by making your upper probability positive-it ensures that you are open-minded. You serve practical rationality by making your lower probability 0-it provides guidance to your decision-making. No sharp credence could do both. (shrink)

One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its prequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In the prequel, we made this norm mathematically precise; in this paper, we derive its consequences. We show that the two core tenets of Bayesianism (...) follow from the norm, while the characteristic claim of the Objectivist Bayesian follows from the norm along with an extra assumption. Finally, we consider Richard Jeffrey’s proposed generalization of conditionalization. We show not only that his rule cannot be derived from the norm, unless the requirement of Rigidity is imposed from the start, but further that the norm reveals it to be illegitimate. We end by deriving an alternative updating rule for those cases in which Jeffrey’s is usually supposed to apply. (shrink)

Probabilistic models have much to offer to philosophy. We continually receive information from a variety of sources: from our senses, from witnesses, from scientific instruments. When considering whether we should believe this information, we assess whether the sources are independent, how reliable they are, and how plausible and coherent the information is. Bovens and Hartmann provide a systematic Bayesian account of these features of reasoning. Simple Bayesian Networks allow us to model alternative assumptions about the nature of the information sources. (...) Measurement of the coherence of information is a controversial matter: arguably, the more coherent a set of information is, the more confident we may be that its content is true, other things being equal. The authors offer a new treatment of coherence which respects this claim and shows its relevance to scientific theory choice. Bovens and Hartmann apply this methodology to a wide range of much discussed issues regarding evidence, testimony, scientific theories, and voting. Bayesian Epistemology is an essential tool for anyone working on probabilistic methods in philosophy, and has broad implications for many other disciplines. (shrink)

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)

In ‘A Non-Pragmatic Vindication of Probabilism’, Jim Joyce attempts to ‘depragmatize’ de Finetti’s prevision argument for the claim that our partial beliefs ought to satisfy the axioms of probability calculus. In this paper, I adapt Joyce’s argument to give a non-pragmatic vindication of various versions of David Lewis’ Principal Principle, such as the version based on Isaac Levi's account of admissibility, Michael Thau and Ned Hall's New Principle, and Jenann Ismael's Generalized Principal Principle. Joyce enumerates properties that must be had (...) by any measure of the distance from a set of partial beliefs to the set of truth values; he shows that, on any such measure, and for any set of partial beliefs that violates the probability axioms, there is a set that satisfies those axioms that is closer to every possible set of truth values. I replace truth values by objective chances in his argument; I show that for any set of partial beliefs that violates the probability axioms or a version of the Principal Principle, there is a set that satisfies them that is closer to every possible set of objective chances. (shrink)

Why should a Bayesian bother performing an experiment, one the result of which might well upset his own favored credence function? The Ramsey-Good theorem provides a decision theoretic answer. Provided you base your decision on expected utility, and the the experiment is cost-free, performing the experiment and then choosing has at least as much expected utility as choosing without further ado. Furthermore, doing the experiment is strictly preferable just in case at least one possible outcome of the experiment could alter (...) your choice of options. That is, you should pursue the information just in case it could make a difference to what you do. The problem remains, however, why one should do an experiment when nothing of much practical consequence hangs in the balance. One possibility here is to invoke the pure cognitive utility of states. It is shown that one constraint on cognitive value (what I call cogency) guarantees the value of learning: from a cognitive point of view you are justified in performing an experiment if the outcome of the experiment could make a different to what you think. A bonus of the basic framework is that it provides a new decision theoretic argument for the rationality of conditionalization. (shrink)

We review de Finetti’s two coherence criteria for determinate probabilities: coherence1defined in terms of previsions for a set of events that are undominated by the status quo – previsions immune to a sure-loss – and coherence2 defined in terms of forecasts for events undominated in Brier score by a rival forecast. We propose a criterion of IP-coherence2 based on a generalization of Brier score for IP-forecasts that uses 1-sided, lower and upper, probability forecasts. However, whereas Brier score is a strictly (...) proper scoring rule for eliciting determinate probabilities, we show that there is no real-valuedstrictly proper IP-score. Nonetheless, with respect to either of two decision rules – Γ-maximin or E-admissibility-+-Γ-maximin – we give a lexicographic strictly proper IP-scoring rule that is based on Brier score. (shrink)

Expected accuracy arguments have been used by several authors (Leitgeb and Pettigrew, and Greaves and Wallace) to support the diachronic principle of conditionalization, in updates where there are only finitely many possible propositions to learn. I show that these arguments can be extended to infinite cases, giving an argument not just for conditionalization but also for principles known as ‘conglomerability’ and ‘reflection’. This shows that the expected accuracy approach is stronger than has been realized. I also argue that we should (...) be careful to distinguish diachronic update principles from related synchronic principles for conditional probability. (shrink)

Addresses ‘too-odd-not-to-be-true’ reasoning in the assessment of testimony. This is the curious phenomenon that an initially less plausible report from multiple independent witnesses may elicit more confidence than an initially more plausible report.

This major work challenges some widely held positions in epistemology - those of Peirce and Popper on the one hand and those of Quine and Kuhn on the other.

Bayesians often confuse insistence that probability judgment ought to be indeterminate (which is incompatible with Bayesian ideals) with recognition of the presence of imprecision in the determination or measurement of personal probabilities (which is compatible with these ideals). The confusion is discussed and illustrated by remarks in a recent essay by R. C. Jeffrey.