Scoring rules measure the deviation between a forecast, which assigns degrees of confidence to various events, and reality. Strictly proper scoring rules have the property that for any forecast, the mathematical expectation of the score of a forecast p by the lights of p is strictly better than the mathematical expectation of any other forecast q by the lights of p. Forecasts need not satisfy the axioms of the probability calculus, but Predd et al. [9] have shown that given a (...) finite sample space and any strictly proper additive and continuous scoring rule, the score for any forecast that does not satisfy the axioms of probability is strictly dominated by the score for some probabilistically consistent forecast. Recently, this result has been extended to non-additive continuous scoring rules. In this paper, a condition weaker than continuity is given that suffices for the result, and the condition is proved to be optimal. (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)

Bayesians standardly claim that there is rational pressure for agents’ credences to cohere across time because they face bad (epistemic or practical) consequences if they fail to diachronically cohere. But as David Christensen has pointed out, groups of individual agents also face bad consequences if they fail to interpersonally cohere, and there is no general rational pressure for one agent's credences to cohere with another’s. So it seems that standard Bayesian arguments may prove too much. Here, we agree with Christensen (...) that there is no general rational pressure to diachronically cohere, but we argue that there are particular cases in which there is rational pressure to diachronically cohere, as well as particular cases in which interpersonal probabilistic coherence is rationally required. More generally, we suggest that Bayesian arguments for coherence apply whenever a collection (of agents or time slices) has a shared dimension of value and an ability to coordinate their actions in a range of cases relevant to that value. Typically, this shared value and ability to coordinate is very strong across the time slices of one human being, and very weak across different human beings, but there are special cases where these can switch—i.e., some groups of humans will have as much reason for their beliefs to cohere across a particular range of cases as the time slices of one human usually do, but some time slices of a human will have as much freedom to differ in their beliefs from the others as the members of a group usually do. (shrink)

Had we grown up elsewhere or been educated differently, our view of the world would likely be radically different. What to make of this? This paper takes an accuracy-centered first-personal approach to the question of how to respond to the arbitrary nature in which many of our beliefs are formed. I show how considerations of accuracy motivate different responses to this sort of information depending on the type of attitude we take towards the belief in question upon subjecting the belief (...) to doubt. (shrink)

Scoring rules measure the accuracy or epistemic utility of a credence assignment. A significant literature uses plausible conditions on scoring rules on finite sample spaces to argue for both probabilism—the doctrine that credences ought to satisfy the axioms of probabilism—and for the optimality of Bayesian update as a response to evidence. I prove a number of formal results regarding scoring rules on infinite sample spaces that impact the extension of these arguments to infinite sample spaces. A common condition in the (...) arguments for probabilism and Bayesian update is strict propriety: that according to each probabilistic credence, the expected accuracy of any other credence is worse. Much of the discussion needs to divide depending on whether we require finite or countable additivity of our probabilities. I show that in a number of natural infinite finitely additive cases, there simply do not exist strictly proper scoring rules, and the prospects for arguments for probabilism and Bayesian update are limited. In many natural infinite countably additive cases, on the other hand, there do exist strictly proper scoring rules that are continuous on the probabilities, and which support arguments for Bayesian update, but which do not support arguments for probabilism. There may be more hope for accuracy-based arguments if we drop the assumption that scores are extended-real-valued. I sketch a framework for scoring rules whose values are nets of extended reals, and show the existence of a strictly proper net-valued scoring rules in all infinite cases, both for f.a. and c.a. probabilities. These can be used in an argument for Bayesian update, but it is not at present known what is to be said about probabilism in this case. (shrink)

In this paper I argue that de Finetti provided compelling reasons for rejecting countable additivity. It is ironical therefore that the main argument advanced by Bayesians against following his recommendation is based on the consistency criterion, coherence, he himself developed. I will show that this argument is mistaken. Nevertheless, there remain some counter-intuitive consequences of rejecting countable additivity, and one in particular has all the appearances of a full-blown paradox. I will end by arguing that in fact it is no (...) paradox, and that what it shows is that conditionalisation, often claimed to be integral to the Bayesian canon, has to be rejected as a general rule in a finitely additive environment. (shrink)

How should we reason in science? Jan Sprenger and Stephan Hartmann offer a refreshing take on classical topics in philosophy of science, using a single key concept to explain and to elucidate manifold aspects of scientific reasoning. They present good arguments and good inferences as being characterized by their effect on our rational degrees of belief. Refuting the view that there is no place for subjective attitudes in 'objective science', Sprenger and Hartmann explain the value of convincing evidence in terms (...) of a cycle of variations on the theme of representing rational degrees of belief by means of subjective probabilities (and changing them by Bayesian conditionalization). In doing so, they integrate Bayesian inference—the leading theory of rationality in social science—with the practice of 21st century science. Bayesian Philosophy of Science thereby shows how modeling such attitudes improves our understanding of causes, explanations, confirming evidence, and scientific models in general. It combines a scientifically minded and mathematically sophisticated approach with conceptual analysis and attention to methodological problems of modern science, especially in statistical inference, and is therefore a valuable resource for philosophers and scientific practitioners. (shrink)

James Joyce's article “A Nonpragmatic Vindication of Probabilism” introduced an approach to arguing for credal norms by appealing to the epistemic value of accuracy. The central thought was that credences ought to accurately represent the world, a guiding thought that has gone on to generate an entire research paradigm on the rationality of credences. Recently, a number of epistemologists have begun to apply this same thought to full beliefs, attempting to explain and argue for norms of belief in terms of (...) epistemic value. This paper examines these recent attempts, showing how they interact with work on the accuracy of credences. It then examines how differing judgments about epistemic value give rise to distinct rational requirements for belief, concluding by considering some of the fundamental questions and issues yet to be fully explored. (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)

Traditionally, epistemologists have distinguished between epistemic and pragmatic goals. In so doing, they presume that much of game theory is irrelevant to epistemic enterprises. I will show that this is a mistake. Even if we restrict attention to purely epistemic motivations, members of epistemic groups will face a multitude of strategic choices. I illustrate several contexts where individuals who are concerned solely with the discovery of truth will nonetheless face difficult game theoretic problems. Examples of purely epistemic coordination problems and (...) social dilemmas will be presented. These show that there is a far deeper connection between economics and epistemology than previous appreciated. (shrink)

Two of the most influential arguments for Bayesian updating ("Conditionalization") -- Hilary Greaves' and David Wallace's Accuracy Argument and David Lewis' Diachronic Dutch Book Argument-- turn out to impose a strong and surprising limitation on rational uncertainty: that one can never be rationally uncertain of what one's evidence is. Many philosophers ("externalists") reject that claim, and now seem to face a difficult choice: either to endorse the arguments and give up Externalism, or to reject the arguments and lose some of (...) the best justifications of Bayesianism. The author argues that the key to resolving this conflict lies in recognizing that both arguments are plan-based, in that they argue for Conditionalization by first arguing that one should planto conditionalize. With this in view, we can identify the culprit common to both arguments: for an externalist, they misconceive the requirement to carry out a plan made at an earlier time. They should therefore not persuade us to reject Externalism. Furthermore, rethinking the nature of this requirement allows us to give two new arguments for Conditionalization that do not rule out rational uncertainty about one's evidence and that can thus serve as common ground in the debate between externalists and their opponents. (shrink)

The debate between Uniqueness and Permissivism concerns whether a body of evidence sometimes allows multiple doxastic attitudes towards a proposition. An important motivation for Uniqueness is the so-called ‘arbitrariness argument,’ which says that Permissivism leads to some unacceptable arbitrariness with regard to one's beliefs. An influential response to the argument says that the arbitrariness in beliefs can be avoided by invoking epistemic standards. In this paper, I argue that such a response to the arbitrariness argument is unsuccessful. Then I defend (...) a new response: contrary to common conception, the arbitrariness resulted by Permissivism is acceptable. The basic idea is that the arbitrariness resulted by Permissivism is analogous to the arbitrariness in permissive actions and the latter arbitrariness is intuitively acceptable. I answer three possible objections against this analogy, which are all motivated by the thought that beliefs aim at the truth. In addressing the last objection, I draw inspiration from the recent debate on transformative experience. (shrink)

Philosophy and Phenomenological Research, EarlyView.

Philosophy and Phenomenological Research, EarlyView.

Philosophy and Phenomenological Research, EarlyView.

Jeff Paris proves a generalized Dutch Book theorem. If a belief state is not a generalized probability then one faces ‘sure loss’ books of bets. In Williams I showed that Joyce’s accuracy-domination theorem applies to the same set of generalized probabilities. What is the relationship between these two results? This note shows that both results are easy corollaries of the core result that Paris appeals to in proving his dutch book theorem. We see that every point of accuracy-domination defines a (...) dutch book, but we only have a partial converse. (shrink)

Drawing on a passage from Ramsey's Truth and Probability, we formulate a simple, plausible constraint on evaluating the accuracy of credences: the Calibration Test. We show that any additive, continuous accuracy measure that passes the Calibration Test will be strictly proper. Strictly proper accuracy measures are known to support the touchstone results of accuracy-first epistemology, for example vindications of probabilism and conditionalization. We show that our use of Calibration is an improvement on previous such appeals by showing how it answers (...) or sidesteps problems that have been raised for previous work in this area. (shrink)

Forty years ago, Bayesian philosophers were just catching a new wave of technical innovation, ushering in an era of scoring rules, imprecise credences, and infinitesimal probabilities. Meanwhile, down the hall, Gettier’s 1963 paper [28] was shaping a literature with little obvious interest in the formal programs of Reichenbach, Hempel, and Carnap, or their successors like Jeffrey, Levi, Skyrms, van Fraassen, and Lewis. And how Bayesians might accommodate the discourses of full belief and knowledge was but a glimmer in the eye (...) of Isaac Levi. Forty years later, scoring rules, imprecise credences, and infinitesimal probabilities are all the rage. And the formal and “informal” traditions are increasingly coming together as Bayesian arguments spill over into debates about the foundations of empirical knowledge, skepticism, and more. Relatedly, Bayesian interest in full belief and knowledge has never been greater. Much more besides has happened in the last forty years of Bayesian philosophy, .. (shrink)

Inference to the Best Explanation (IBE) and Bayesianism are our two most prominent theories of scientific inference. Are they compatible? Van Fraassen famously argued that they are not, concluding that IBE must be wrong since Bayesianism is right. Writers since then, from both the Bayesian and explanationist camps, have usually considered van Fraassen’s argument to be misguided, and have plumped for the view that Bayesianism and IBE are actually compatible. I argue that van Fraassen’s argument is actually not so misguided, (...) and that it causes more trouble for compatibilists than is typically thought. Bayesianism in its dominant, subjectivist form, can only be made compatible with IBE if IBE is made subservient to conditionalization in a way that robs IBE of much of its substance and interest. If Bayesianism and IBE are to be fit together, I argue, a strongly objective Bayesianism is the preferred option. I go on to sketch this objectivist, IBE-based Bayesianism, and offer some preliminary suggestions for its development. (shrink)

If beliefs are subject to a basic norm of correctness—roughly, to the principle that a belief is correct only if the proposition believed is true—how can this norm guide believers in forming their beliefs? Answer: this norm guides believers indirectly: believers are directly guided by requirements of rationality—which are themselves explained by this norm of correctness. The fundamental connection between rationality and correctness is probabilistic. Incorrectness comes in degrees; for beliefs, these degrees of incorrectness are measured by quadratic scoring rules, (...) such as the so-called Brier score. This account is defended against objections; and its implications for suspension of judgement are explored. (shrink)

In standard decision theory, the probability function ought to be updated in light of evidence, but the utility function generally stays fixed. However, there is nothing in the formal theory that prevents one from instead updating the utility function, while keeping the probability function fixed. Moreover, there are good arguments for updating the utilities and not just the probabilities. Hence, the first puzzle is whether there is anything that justifies updating beliefs, but not desires, in light of evidence. The paper (...) argues that there is not, but that this raises a second puzzle. (shrink)

Bayesian inference is limited in scope because it cannot be applied in idealized contexts where none of the hypotheses under consideration is true and because it is committed to always using the likelihood as a measure of evidential favouring, even when that is inappropriate. The purpose of this article is to study inductive inference in a very general setting where finding the truth is not necessarily the goal and where the measure of evidential favouring is not necessarily the likelihood. I (...) use an accuracy argument to argue for probabilism and I develop a new kind of argument to argue for two general updating rules, both of which are reasonable in different contexts. One of the updating rules has standard Bayesian updating, Bissiri et al.’s general Bayesian updating, Douven’s IBE-based updating, and Vassend’s ]) quasi-Bayesian updating as special cases. The other updating rule is novel. (shrink)

The Sleeping Beauty Problem attracts so much attention because it connects to a wide variety of unresolved issues in formal epistemology, decision theory, and the philosophy of science. The problem raises unanswered questions concerning relative frequencies, objective chances, the relation between self-locating and non-self-locating information, the relation between self-location and updating, Dutch Books, accuracy arguments, memory loss, indifference principles, the existence of multiple universes, and many-worlds interpretations of quantum mechanics. After stating the problem, this article surveys its connections to all (...) of these areas. (shrink)

What goes wrong, from a rational point of view, when an agent’s beliefs change while her evidence remains constant? I canvass a number of answers to this question suggested by recent literature, then identify some desiderata I would like any potential answer to meet. Finally, I suggest that the rational problem results from the undermining of reasoning processes that are necessarily extended in time.

In attempting to form rational personal probabilities by direct inference, it is usually assumed that one should prefer frequency information concerning more specific reference classes. While the preceding assumption is intuitively plausible, little energy has been expended in explaining why it should be accepted. In the present article, I address this omission by showing that, among the principled policies that may be used in setting one’s personal probabilities, the policy of making direct inferences with a preference for frequency information for (...) more specific reference classes yields personal probabilities whose accuracy is optimal, according to all proper scoring rules, in situations where all of the relevant frequency information is point-valued. Assuming that frequency information for narrower reference classes is preferred, when the relevant frequency statements are point-valued, a dilemma arises when choosing whether to make a direct inference based upon relatively precise-valued frequency information for a broad reference class, R, or upon relatively imprecise-valued frequency information for a more specific reference class, R*. I address such cases, by showing that it is often possible to make a precise-valued frequency judgment regarding R* based on precise-valued frequency information for R, using standard principles of direct inference. Having made such a frequency judgment, the dilemma of choosing between and is removed, and one may proceed by using the precise-valued frequency estimate for the more specific reference class as a premise for direct inference. (shrink)

Accuracy‐first epistemology is an approach to formal epistemology which takes accuracy to be a measure of epistemic utility and attempts to vindicate norms of epistemic rationality by showing how conformity with them is beneficial. If accuracy‐first epistemology can actually vindicate any epistemic norms, it must adopt a plausible account of epistemic value. Any such account must avoid the epistemic version of Derek Parfit's “repugnant conclusion.” I argue that the only plausible way of doing so is to say that accurate credences (...) in certain propositions have no, or almost no, epistemic value. I prove that this is incompatible with standard accuracy‐first arguments for probabilism, and argue that there is no way for accuracy‐first epistemology to show that all credences of all agents should be coherent. (shrink)

Ideal agents are role models whose perfection in some normative domain we try to approximate. But which form should this striving take? It is well known that following ideal rules of practical reasoning can have disastrous results for non-ideal agents. Yet, this issue has not been explored with respect to rules of theoretical reasoning. I show how we can extend Bayesian models of ideally rational agents in order to pose and answer the question of whether non-ideal agents should form new (...) degrees of belief in the same way as their ideal counterparts. I demonstrate that the epistemic and the practical case are parallel: following ideal rules does not always lead to optimal outcomes for non-ideal agents. (shrink)

Epistemic utility theory seeks to establish epistemic norms by combining principles from decision theory and social choice theory with ways of determining the epistemic utility of agents’ attitudes. Recently, Moss, 1053–69, 2011) has applied this strategy to the problem of finding epistemic compromises between disagreeing agents. She shows that the norm “form compromises by maximizing average expected epistemic utility”, when applied to agents who share the same proper epistemic utility function, yields the result that agents must form compromises by splitting (...) the difference between their credence functions. However, this “split the difference” norm is in conflict with conditionalization, since applications of the two norms don’t commute. A common response in the literature seems to be to abandon the procedure of splitting the difference in favor of compromise strategies that avoid non-commutativity. This would also entail abandoning Moss’ norm. I explore whether a different response is feasible. If agents can use epistemic utility-based considerations to agree on an order in which they will apply the two norms, they might be able to avoid diachronic incoherence. I show that this response can’t save Moss’ norm, because the agreements concerning the order of compromising and updating it generates are not stable over time, and hence cannot avoid diachronic incoherence. I also show that a variant of Moss’ norm, which requires that the weights given to each agent’s epistemic utility change in a way that ensures commutativity, cannot be justified on epistemological grounds. (shrink)

Objective standards for justification or for being a reason would be desirable, but inductive skepticism tells us that they cannot be presupposed. Rather, we have to start from subjective-relative notions of justification and of being a reason. The paper lays out the strategic options we have given this dilemma. The paper explains the requirements for this subject-relative notion and how they may be satisfied. Then it discusses four quite heterogeneous ways of providing more objective standards, which combine without guaranteeing complete (...) success. (shrink)

When a belief has been influenced, in part or whole, by factors that, by the believer's own lights, do not bear on the truth of the believed proposition, we can say that the belief has been, in a sense, arbitrarily formed. Can such beliefs ever be rational? It might seem obvious that they can't. After all, belief, supposedly, “aims at the truth.” But many epistemologists have come to think that certain kinds of arbitrary beliefs can, indeed, be rational. In this (...) paper, I want to do two things. First, I want to show that the claim that arbitrary beliefs can be rational is inconsistent with the conjunction of two other attractive claims: one saying that rationality requires a certain kind of epistemic immodesty, and one saying that rationality forbids certain kinds of self-ascriptions of epistemic luck. Second, I want to evaluate different ways one might respond to this inconsistent triad. I won't defend any response in particular, but I'll draw out some notable costs and benefits of each response, which may help shed light on the question of whether arbitrary beliefs can be rational. (shrink)

Don’t form beliefs on the basis of coin flips or random guesses. More generally, don’t take belief gambles: if a proposition is no more likely to be true than false given your total body of evidence, don’t go ahead and believe that proposition. Few would deny this seemingly innocuous piece of epistemic advice. But what, exactly, is wrong with taking belief gambles? Philosophers have debated versions of this question at least since the classic dispute between William Clifford and William James (...) near the end of the nineteenth century. Here I reassess the normative standing of belief gambles from the perspective of epistemic decision theory. The main lesson of the paper is a negative one: it turns out that we need to make some surprisingly strong and hard-to-motivate assumptions to establish a general norm against belief gambles within a decision-theoretic framework. I take this to pose a dilemma for epistemic decision theory: it forces us to either make seemingly unmotivated assumptions to secure a norm against belief gambles, or concede that belief gambles can be rational after all. (shrink)

Epistemic consequentialists think that epistemic norms are about believing the truth and avoiding error. Recently, a number of authors have rejected epistemic consequentialism on the basis that it incorrectly sanctions tradeoffs of epistemic goodness. Here, I argue that epistemic consequentialists should borrow two lessons from ethical consequentialists to respond to these worries. Epistemic consequentialists should construe their view as an account of right belief, which they distinguish from other notions like rational and justified belief. Epistemic consequentialists should also make their (...) view ‘sophisticated,’ in the sense of Railton. Epistemic consequentialism, I conclude, is best construed as sharing much of its structure with prominent act-consequentialist views in ethics. Epistemic consequentialism has an advantage over its ethical counterpart though: the key claim of the view is practically universally accepted, which gives us an additional reason to think it’s true. (shrink)

In this paper, we compare and contrast two methods for the revision of qualitative beliefs. The first method is generated by a simplistic diachronic Lockean thesis requiring coherence with the agent’s posterior credences after conditionalization. The second method is the orthodox AGM approach to belief revision. Our primary aim is to determine when the two methods may disagree in their recommendations and when they must agree. We establish a number of novel results about their relative behavior. Our most notable finding (...) is that the inverse of the golden ratio emerges as a non-arbitrary bound on the Bayesian method’s free-parameter—the Lockean threshold. This “golden threshold” surfaces in two of our results and turns out to be crucial for understanding the relation between the two methods. (shrink)

In this paper I’ll suggest that a certain challenge facing defeatist views about higher-order evidence cannot be met, namely, motivating principles that recommend abandoning belief in cases of higher order defeat, but do not recommend global scepticism. I’ll propose that, ultimately, the question of whether to abandon belief in response to the realization that our belief can’t be recovered from what I’ll call ‘a perspective of doubt’ can’t be answered through rational deliberation aimed at truth or accuracy.

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 this essay, I develop and defend a virtue-theoretic conception of rationality as a capacity whose function is understanding, as opposed to mere truth or correctness. I focus on two main potential advantages of this view. First, its ability to explain the rationality of forms of explanatory reasoning, and second, its ability to offer a more unified account of theoretical and practical rationality.

How should rational beliefs change over time? The standard Bayesian answer is: by conditionalization (a.k.a. Bayes’ Rule). But conditionalization is not an adequate rule for updating beliefs in “centred” propositions whose truth-value may itself change over time. In response, some have suggested that the objects of belief must be uncentred; others have suggested that beliefs in centred propositions are not subject to diachronic norms. Iargue that these views do not offer a satisfactory account of self-locating beliefs and their dynamics. A (...) third response is to replace conditionalization by a new norm that can deal with centred propositions. I critically survey anumber of new norms that have been proposed, and defend one particular approach. (shrink)

Greaves and Wallace argue that conditionalization maximizes expected accuracy. In this paper I show that their result only applies to a restricted range of cases. I then show that the update procedure that maximizes expected accuracy in general is one in which, upon learning P, we conditionalize, not on P, but on the proposition that we learned P. After proving this result, I provide further generalizations and show that much of the accuracy-first epistemology program is committed to KK-like iteration principles (...) and to the existence of a class of propositions that rational agents will be certain of if and only if they are true. (shrink)

When an agent undergoes fission, how should the beliefs of the fission results relate to the pre-fission beliefs? This question is important for the Everett interpretation of quantum mechanics, but it is of independent philosophical interest. Among other things, fission scenarios demonstrate that ‘self-locating’ information can affect the probability of uncentred propositions even if an agent has no essentially self-locating uncertainty. I present a general update rule for centred beliefs that gives sensible verdicts in cases of fission, without relying on (...) controversial metaphysical or linguistic assumptions. The rule is supported by the same considerations that support standard conditioning in the traditional framework of uncentred propositions. (shrink)

It seems like we care about at least two features of our credence function: gradational-accuracy and verisimilitude. Accuracy-first epistemology requires that we care about one feature of our credence function: gradational-accuracy. So if you want to be a verisimilitude-valuing accuracy-firster, you must be able to think of the value of verisimilitude as somehow built into the value of gradational-accuracy. Can this be done? In a recent article, Oddie has argued that it cannot, at least if we want the accuracy measure (...) to be proper. I argue that it can. 1Introduction2Some Nuts and Bolts3First Attempts4Oddie’s Constraint5The Good5.1Proximity over the disagreement metric 5.2Proximity over the magnitude metric 6The Bad and the Ugly 7Some More Good: The Role of Evenness of Distribution 8Some More Bad: Which Propositions to Privilege? 9Concluding Thoughts: Accuracy and Practical Value. (shrink)

The aim of this paper is to apply the accuracy based approach to epistemology to the case of higher order evidence: evidence that bears on the rationality of one's beliefs. I proceed in two stages. First, I show that the accuracy based framework that is standardly used to motivate rational requirements supports steadfastness—a position according to which higher order evidence should have no impact on one's doxastic attitudes towards first order propositions. The argument for this will require a generalization of (...) an important result by Greaves and Wallace for the claim that conditionalization maximizes expected accuracy. The generalization I provide will, among other things, allow us to apply the result to cases of self-locating evidence. In the second stage, I develop an alternative framework. Very roughly, what distinguishes the traditional approach from the alternative one is that, on the traditional picture, we're interested in evaluating the expected accuracy of conforming to an update procedure. On the alternative picture that I develop, instead of considering how good an update procedure is as a plan to conform to, we consider how good it is as a plan to make. I show how, given the use of strictly proper scoring rules, the alternative picture vindicates calibrationism: a view according to which higher order evidence should have a significant impact on our beliefs. I conclude with some thoughts about why higher order evidence poses a serious challenge for standard ways of thinking about rationality. (shrink)

Quine taught us the difference between a theory’s ontology and its ideology. Ontology is the things a theory’s quantifiers must range over if it is true, Ideology is the primitive concepts that must be used to state the theory. This allows us to split the theoretical virtue of parsimony into two kinds: ontological parsimony and ideological parsimony. My goal is help illuminate the virtue of ideological parsimony by giving a criterion for ideological innocence—a rule for when additional ideology does not (...) count against parsimony. I propose the expressive power innocence criterion: if the ideology of theory one is expressively equivalent to that of theory two, then neither is ideologically simpler than the other. In its favor I offer the argument from accuracy, showing that any account of a theoretical virtue that is supposed to make theories that have it more likely to be true than theories that do not must respect it. Next I consider its ramifications, eliminating rival views and passing judgment on some arguments from parsimony that can be found in the literature. Finally, I consider two objections. First: I address an objection arising from the possibility of languages with a ‘primitive’ operator that allows us to list a theory’s primitives in the object-language. Second: I address an objection raised by Nelson Goodman against attempts to reckon simplicity by expressive power. Both objections fail. (shrink)

Conditionalization is a norm that governs the rational reallocation of credence. I distinguish between factive and non-factive formulations of Conditionalization. Factive formulations assume that the conditioning proposition is true. Non-factive formulations allow that the conditioning proposition may be false. I argue that non-factive formulations provide a better foundation for philosophical and scientific applications of Bayesian decision theory. I furthermore argue that previous formulations of Conditionalization, factive and non-factive alike, have almost universally ignored, downplayed, or mishandled a crucial causal aspect of (...) Conditionalization. To formulate Conditionalization adequately, one must explicitly address the causal structure of the transition from old credences to new credences. I offer a formulation of Conditionalization that takes these considerations into account, and I compare my preferred formulation with some prominent formulations found in the literature. (shrink)

Lewis proved a Dutch book theorem for Conditionalization. The theorem shows that an agent who follows any credal update rule other than Conditionalization is vulnerable to bets that inflict a sure loss. Lewis’s theorem is tailored to factive formulations of Conditionalization, i.e. formulations on which the conditioning proposition is true. Yet many scientific and philosophical applications of Bayesian decision theory require a non-factive formulation, i.e. a formulation on which the conditioning proposition may be false. I prove a Dutch book theorem (...) tailored to non-factive Conditionalization. I also discuss the theorem’s significance. (shrink)

Orthodox Bayesianism endorses revising by conditionalization. This paper investigates the zero-raising problem, or equivalently the certainty-dropping problem of orthodox Bayesianism: previously neglected possibilities remain neglected, although the new evidence might suggest otherwise. Yet, one may want to model open-minded agents, that is, agents capable of raising previously neglected possibilities. Different reasons can be given for open-mindedness, one of which is fallibilism. The paper proposes a family of open-minded propositional revisions depending on a parameter ϵ. The basic idea is this: first (...) extend the prior to the newly suggested possibilities by mixing the prior with the uniform probability on these possibilities, then conditionalize. This may put the agent back on the right track when her beliefs or evidence happen to be false. The paper justifies this family of equivocal epsilon-conditionalizations as minimal non-biased open-minded modifications of conditionalization. Several variations are discussed, such as mixing with an ad hoc or silent prior instead of the uniform prior, and a generalization to probabilistic information is given. The approach is compared to other accounts, such as Jeffrey’s Bayesianism, Gärdenfors’s probabilistic revision, maximizing entropy, and minimal revision. _1_ Introduction _2_ Downsides of Certainty Conservation _3_ Why Raise Zeros? _3.1_ Accuracy defects _3.2_ Fallibilism and dissolutions _3.3_ Weak fallibilism and partial solutions _4_ Epsilon-Conditionalization _4.1_ Definitions _4.2_ Revision types and information assumptions _4.3_ Epsilon interpretation and flavours _5_ Justifications _5.1_ Open-minded orthodox Bayesianism _5.2_ Minimal revision _5.3_ Transitivity _6_ Conclusion Appendix. (shrink)

The debates between Bayesian, frequentist, and other methodologies of statistics have tended to focus on conceptual justifications, sociological arguments, or mathematical proofs of their long run properties. Both Bayesian statistics and frequentist (“classical”) statistics have strong cases on these grounds. In this article, we instead approach the debates in the “Statistics Wars” from a largely unexplored angle: simulations of different methodologies’ performance in the short to medium run. We conducted a large number of simulations using a straightforward decision problem based (...) around tossing a coin with unknown bias and then placing bets. In this simulation, we programmed four players, inspired by Bayesian statistics, frequentist statistics, Jon Williamson’s version of Objective Bayesianism, and a player who simply extrapolates from observed frequencies to general frequencies. The last player functions as a benchmark: a statistical methodology should at least outperform a crude form of induction. We focused on the performance of these methodologies in guiding the players towards good decisions. Unlike an earlier simulation study of this type, we found no systematic difference in performance between the Bayesian and frequentist players, provided the Bayesian used a flat prior and the frequentist used a low confidence level. Unlike that study, we were able to use Big Data methods to mitigate problems of random error in the simulation results. The Williamsonian player, who is a novel element of our study, also had no systematic differences in their performance, provided that they use a low confidence level. These players performed similarly even in the very short run, when players were making different decisions. Our study indicates that all three methodologies should be taken seriously by philosophers and practitioners of statistics. However, the frequentist and Williamsonian performed poorly when their confidence levels were high, and the Bayesian was surprisingly harmed by biased priors, providing some unexpected lessons for these methodologies when facing this type of decision problem. (shrink)

Epistemologists who study credences have a well-developed account of how you should change them when you learn new evidence; that is, when your body of evidence grows. What's more, they boast a diverse range of epistemic and pragmatic arguments that support that account. But they do not have a satisfactory account of when and how you should change your credences when you become aware of possibilities and propositions you have not entertained before; that is, when your awareness grows. In this (...) paper, I consider the arguments for the credal epistemologist's account of how to respond to evidence, and I ask whether they can help us generate an account of how to respond to awareness growth. The results are surprising: the arguments that all support the same norms for responding to evidence growth support a number of different norms when they are applied to awareness growth. Some of these norms seem too weak, others too strong. I ask what we should conclude from this, and argue that our credal response to awareness growth is considerably less rigorously constrained than our credal response to new evidence. (shrink)