Alongside science and law, argumentation is also of central importance in everyday life. But what characterizes a good argument? This question has occupied philosophers and psychologists for centuries. The theory of Bayesian argumentation is particularly suitable for clarifying it, because it allows us to take into account in a natural way the role of uncertainty, which is central to much argumentation. Moreover, it offers the possibility of measuring the strength of an argument in probabilistic terms. One way to do this, (...) implicit in much work, is to identify the strength of an argument with the degree to which the premises of the argument confirm the conclusion. We criticize this prima facie plausible proposal and suggest instead that the strength of an argument has something to do with how much the premises and the conclusion of the argument cohere with each other. This leads to a new probabilistic measure whose properties we examine in more detail. (shrink)

Do epistemic and aesthetic values ever conflict? The answer might appear to be no, given that background knowledge generally enhances aesthetic experience, and aesthetic experience in turn generates new knowledge. As Keats writes, ‘Beauty is truth, truth beauty’ (Keats, 1996). Contra this line of thought, I argue that epistemic and aesthetic values can conflict when we over-rely on aesthetically enhancing background beliefs. The true and the beautiful can pull in different directions, forcing us to choose between flavours of normativity.

Reasoning from inconclusive evidence, or ‘induction’, is central to science and any applications we make of it. For that reason alone it demands the attention of philosophers of science. This Element explores the prospects of using probability theory to provide an inductive logic, a framework for representing evidential support. Constraints on the ideal evaluation of hypotheses suggest that overall support for a hypothesis is represented by its probability in light of the total evidence, and incremental support, or confirmation, indicated by (...) an increased probability given the evidence than otherwise. This proposal is shown to have the capacity to reconstruct many canons of the scientific method and inductive inference. Along the way, significant objections are discussed, such as the challenge from inductive scepticism and the objection that the probabilistic approach makes evidential support arbitrary. (shrink)

In response to two trenchant objections, radical subjective Bayesianism has been widely rejected. In this paper, I seek, if not to rehabilitate subjectivism, at least to show its critic what is attractive about the position. I argue that what is at stake in the subjectivism/anti-subjectivism debate is not, as is commonly thought, which norms of rationality are true, but rather, the conception of rationality that we adopt: there is an alternative approach to the widespread telic approach to rationality, which I (...) call the poric approach, on which subjectivism is an attractive position. I then argue that the poric approach—and therefore subjectivism—cannot be easily dismissed. (shrink)

Our scientific theories, like our cognitive structures in general, consist of propositions linked by evidential, explanatory, probabilistic, and logical connections. Those theoretical webs ‘impinge on the world at their edges,’ subject to a continuing barrage of incoming evidence. Our credences in the various elements of those structures change in response to that continuing barrage of evidence, as do the perceived connections between them. Here we model scientific theories as Bayesian nets, with credences at nodes and conditional links between them modelled (...) as conditional probabilities. We update those networks, in terms of both credences at nodes and conditional probabilities at links, through a temporal barrage of random incoming evidence. Robust patterns of punctuated equilibrium, suggestive of ‘normal science’ alternating with ‘paradigm shifts,’ emerge prominently in that change dynamics. The suggestion is that at least some of the phenomena at the core of the Kuhnian tradition are predictable in the typical dynamics of scientific theory change captured as Bayesian nets under even a random evidence barrage. (shrink)

Hájek (Erkenntnis 70(2):211–235, 2009) argues that probabilities cannot be the limits of relative frequencies in counterfactual infinite sequences. I argue for a different understanding of these limits, drawing on Norton’s (Philos Sci 79(2):207–232, 2012) distinction between approximations (inexact descriptions of a target) and idealizations (separate models that bear analogies to the target). Then, I adapt Hájek’s arguments to this new context. These arguments provide excellent reasons not to use hypothetical frequencies as idealizations, but no reason not to use them as (...) approximations. (shrink)

One very popular framework in contemporary epistemology is Bayesian. The central epistemic state is subjective confidence, or credence. Traditional epistemic states like belief and knowledge tend to be sidelined, or even dispensed with entirely. Credences are often introduced as familiar mental states, merely in need of a special label for the purposes of epistemology. But whether they are implicitly recognized by the folk or posits of a sophisticated scientific psychology, they do not appear to fit well with perception, as is (...) often noted. -/- This paper investigates the tension between probabilistic cognition and non-probabilistic perception. The tension is real, and the solution—to adapt a phrase from Quine and Goodman—is to renounce credences altogether. (shrink)

In attempts to compare different distributions with regards to need, so-called “measures of need-based distributive justice” have emerged in recent years. Each of the proposed measures relies on a single dimension of need that is taken into account. This is shown to be problematic since humans experience different kinds of need that appear to be incommensurable. A strategy to deal with this problem is introduced by using multidimensional measures.

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

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

A probability distribution is regular if it does not assign probability zero to any possible event. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson and Benci et al. have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s “isomorphic” events are not in fact isomorphic, but Howson is speaking (...) of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson is speaking (...) of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

to appear in Lambert, E. and J. Schwenkler (eds.) Transformative Experience (OUP) -/- L. A. Paul (2014, 2015) argues that the possibility of epistemically transformative experiences poses serious and novel problems for the orthodox theory of rational choice, namely, expected utility theory — I call her argument the Utility Ignorance Objection. In a pair of earlier papers, I responded to Paul’s challenge (Pettigrew 2015, 2016), and a number of other philosophers have responded in similar ways (Dougherty, et al. 2015, Harman (...) 2015) — I call our argument the Fine-Graining Response. Paul has her own reply to this response, which we might call the Authenticity Reply. But Sarah Moss has recently offered an alternative reply to the Fine-Graining Response on Paul’s behalf (Moss 2017) — we’ll call it the No Knowledge Reply. This appeals to the knowledge norm of action, together with Moss’ novel and intriguing account of probabilistic knowledge. In this paper, I consider Moss’ reply and argue that it fails. I argue first that it fails as a reply made on Paul’s behalf, since it forces us to abandon many of the features of Paul’s challenge that make it distinctive and with which Paul herself is particularly concerned. Then I argue that it fails as a reply independent of its fidelity to Paul’s intentions. (shrink)

So-called “traditional epistemology” and “Bayesian epistemology” share a word, but it may often seem that the enterprises hardly share a subject matter. They differ in their central concepts. They differ in their main concerns. They differ in their main theoretical moves. And they often differ in their methodology. However, in the last decade or so, there have been a number of attempts to build bridges between the two epistemologies. Indeed, many would say that there is just one branch of philosophy (...) here—epistemology. There is a common subject matter after all. In this paper, we begin by playing the role of a “bad cop,” emphasizing many apparent points of disconnection, and even conflict, between the approaches to epistemology. We then switch role, playing a “good cop” who insists that the approaches are engaged in common projects after all. We look at various ways in which the gaps between them have been bridged, and we consider the prospects for bridging them further. We conclude that this is an exciting time for epistemology, as the two traditions can learn, and have started learning, from each other. (shrink)

This paper presents a general-purpose update semantics for expressions of subjective uncertainty in natural language. First, a set of desiderata are established for how expressions of subjective uncertainty should behave in dynamic, update-based semantic systems; then extant implementations of expressions of subjective uncertainty in such models are evaluated and found wanting; finally, a new update semantics is proposed. The desiderata at the heart of this paper center around the contention that expressions of subjective uncertainty express beliefs which are not persistent, (...) whereas propositions express beliefs that are persistent. I argue that if we make the move of treating updates in a dynamic semantics as Bayesian updates, i.e. as conditionalization, then expressions of subjective uncertainty will behave the way we want them to without altering the way propositions behave. (shrink)

In this paper, I present and defend a novel account of doubt. In Part 1, I make some preliminary observations about the nature of doubt. In Part 2, I introduce a new puzzle about the relationship between three psychological states: doubt, belief, and confidence. I present this puzzle because my account of doubt emerges as a possible solution to it. Lastly, in Part 3, I elaborate on and defend my account of doubt. Roughly, one has doubt if and only if (...) one believes one might be wrong; I argue that this is superior to the account that says that one has doubt if and only if one has less than the highest degree of confidence. (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)

Causal reasoning is one of our most central cognitive competencies, enabling us to adapt to our world. Causal knowledge allows us to predict future events, or diagnose the causes of observed facts. We plan actions and solve problems using knowledge about cause-effect relations. Without our ability to discover and empirically test causal theories, we would not have made progress in various empirical sciences. In the past decades, the important role of causal knowledge has been discovered in many areas of cognitive (...) psychology. Despite the ubiquity of causal reasoning, textbooks of cognitive psychology have neglected this growing field. The goal of The Oxford Handbook of Causal Reasoning is to fill this gap. The handbook brings together the leading researchers in the field of causal reasoning and offers state-of-the-art presentations of theories and research. It provides introductions of competing theories of causal reasoning, and discusses its role in various cognitive functions and domains. The final section presents research from neighboring fields. 1. Causal Reasoning: An Introduction Michael R. Waldmann Part I: Theories of Causal Cognition 2. Associative Accounts of Causal Cognition Mike E. Le Pelley, Oren Griffiths, and Tom Beesley 3. Rules of Causal Judgment: Mapping Statistical Information Onto Causal Beliefs José C. Perales, Andrés Catena, Antonio Cándido, and Antonio Maldonado 4. The Inferential Reasoning Theory of Causal Learning: Toward a Multi- Process Propositional Account Yannick Boddez, Jan De Houwer, and Tom Beckers 5. Causal Invariance as an Essential Constraint for Creating a Causal Representation of the World: Generalizing the Invariance of Causal Power Patricia W. Cheng and Hongjing Lu 6. The Acquisition and Use of Causal Structure Knowledge Benjamin Margolin Rottman 7. Formalizing Prior Knowledge in Causal Induction Thomas L. Griffiths 8. Causal Mechanisms Samuel G. B. Johnson and Woo-kyoung Ahn 9. Force Dynamics and Causation Phillip Wolff and Robert Thorstad 10. Mental Models and Causation P. N. Johnson- Laird and Sangeet S. Khemlani 11. Pseudocontingencies Klaus Fiedler and Florian Kutzner 12. Singular Causation David Danks 13. Cognitive Neuroscience of Causal Reasoning Joachim T. Operskalski and Aron K. Barbey Part II: Basic Cognitive Functions 14. Visual Impressions of Causality Peter White 15. Goal-Directed Actions Bernhard Hommel 16. Planning and Control Magda Osman 17. Reinforcement Learning and Causal Models Samuel J. Gershman 18. Causation and the Probability of Causal Conditionals David E. Over 19. Causal Models and Conditional Reasoning Mike Oaksford and Nick Chater 20. Concepts as Causal Models: Categorization Bob Rehder 21. Concepts as Causal Models: Induction Bob Rehder 22. Causal Explanation Tania Lombrozo and Nadya Vasilyeva 23. Diagnostic Reasoning Björn Meder and Ralf Mayrhofer 24. Inferring Causal Relations by Analogy Keith J. Holyoak and Hee-Seung Lee 25. Causal Argument Ulrike Hahn, Roland Bluhm, and Frank Zenker 26. Causality in Decision- Making York Hagmayer and Philip M. Fernbach Part III: Domains of Causal Reasoning 27. Intuitive Theories Tobias Gerstenberg and Joshua B. Tenenbaum 28. Space, Time, and Causality Marc J. Buehner 29. Causation in Legal and Moral Reasoning David A. Lagnado and Tobias Gerstenberg 30. The Role of Causal Knowledge in Reasoning About Mental Disorders Woo-kyoung Ahn, Nancy S. Kim, and Matthew S. Lebowitz 31. Causality and Causal Reasoning in Natural Language Torgrim Solstad and Oliver Bott 32. Social Attribution and Explanation Denis Hilton Part IV: Development, Phylogeny, and Culture 33. The Development of Causal Reasoning Paul Muentener and Elizabeth Bonawitz 34. Causal Reasoning in Non-Human Animals Christian Schloegl and Julia Fischer 35. Causal Cognition and Culture Andrea Bender, Sieghard Beller, and Douglas L. Medin. (shrink)

Bayesians standardly identify irrelevance with probabilistic irrelevance. However, there are cases where e is probabilistically irrelevant to h but intuitively e is relevant to h. For instance, ‘Die A came up 1 and die B came up 1, 3, 5 or 6’ is probabilistically irrelevant to ‘Die A came up odd and die B came up even’, yet, intuitively, it is not, irrelevant to that claim, in the sense that ‘Sydney has a harbour Bridge’ is irrelevant to it. In the (...) context of decision making this notion of irrelevance combined with such rules as ‘Do not expend resources on irrelevant evidence’ leads to bad results. A stronger notion of irrelevance fitting our intuitions and the contexts of decision making is proposed: e is irrelevant to h if and only if every part of e is probabilistically irrelevant to every part of h. However, we need to take care in determining what counts as part of a statement. (shrink)

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

This article explores the relationship between pragmatic encroachment and epistemic permissiveness. If the suggestion that all epistemic notions are interest-relative is viable , then it seems that a certain species of epistemic permissivism must be viable as well. For, if all epistemic notions are interest relative then, sometimes, parties in paradigmatic cases of shared evidence can be maximally rational in forming competing basic doxastic attitudes towards the same proposition. However, I argue that this total pragmatic encroachment is not tenable, and, (...) thus, epistemic permissivism cannot be vindicated in this way. (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)

Why should coherence be an epistemic desideratum? One response is that coherence is truth-conducive: mutually coherent propositions are more likely to be true, ceteris paribus, than mutually incoherent ones. But some sets of propositions are more coherent, while others are less so. How could coherence be measured? Probabilistic measures of coherence exist; some are identical to probabilistic measures of confirmation, while others are extensions of such measures. Probabilistic measures of coherence are fine when applicable, but many situations are so information-poor (...) that the requisite probabilities cannot be determined. To measure coherence in these cognitively impoverished situations, this article proposes that the discussion be broadened to include plausibilistic measures of coherence. It shows how plausibilistic measures of coherence can be defined using plausibilistic measures of confirmation. It then illustrates how plausibilisic coherence can be measured in situations where probabilistic coherence cannot be determined. The coherence values obtained through the use of plausibilistic measures are often, though not always, comparable. The article also shows that coherence can be instantiated on different levels, one of which permits connections to inductive strength and deductive validity. (shrink)

A familiar adage in the philosophy of science is that general hypotheses are better supported by varied evidence than by uniform evidence. Several studies suggest that young children do not respect this principle, and thus suffer from a defect in their inductive methodology. We argue that the diversity principle does not have the normative status that psychologists attribute to it, and should be replaced by a simple rule of probability. We then report experiments designed to detect conformity to the latter (...) rule in children's inductive judgment. The results suggest that young children in both the United States and Taiwan are sensitive to the constraints imposed by the rule on judgments of probability and evidential strength. We conclude with a suggested reinterpretation of the thesis that children's inductive methodology qualifies them as “little scientists.”. (shrink)

Inductive probability is the logical concept of probability in ordinary language. It is vague but it can be explicated by defining a clear and precise concept that can serve some of the same purposes. This paper presents a general method for doing such an explication and then a particular explication due to Carnap. Common criticisms of Carnap's inductive logic are examined; it is shown that most of them are spurious and the others are not fundamental.

This paper formally explores the common ground between mild versions of epistemological coherentism and infinitism; it proposes—and argues for—a hybrid, coherentist–infinitist account of epistemic justification. First, the epistemological regress argument and its relation to the classical taxonomy regarding epistemic justification—of foundationalism, infinitism and coherentism—is reviewed. We then recall recent results proving that an influential argument against infinite regresses of justification, which alleges their incoherence on account of probabilistic inconsistency, cannot be maintained. Furthermore, we prove that the Principle of Inferential Justification (...) has rather unwelcome consequences—formally resembling the Sorites paradox—as soon as it is iterated and combined with a natural Bayesian perspective on probabilistic inferences. We conclude that strong versions of foundationalism and infinitism should be abandoned. Positively, we provide a rough sketch for a graded formal coherence notion, according to which infinite regresses of epistemic justification will often have more than a minimal degree of coherence. (shrink)

In standard probability theory, probability zero is not the same as impossibility. But many have suggested that only impossible events should have probability zero. This can be arranged if we allow infinitesimal probabilities, but infinitesimals do not solve all of the problems. We will see that regular probabilities are not invariant over rigid transformations, even for simple, bounded, countable, constructive, and disjoint sets. Hence, regular chances cannot be determined by space-time invariant physical laws, and regular credences cannot satisfy seemingly reasonable (...) symmetry principles. Moreover, the examples here are immune to the objections against Williamson’s infinite coin flips. (shrink)

This paper argues for two theses: that degrees of belief are context sensitive; that outright belief is belief to degree 1. The latter thesis is rejected quickly in most discussions of the relationship between credence and belief, but the former thesis undermines the usual reasons for doing so. Furthermore, identifying belief with credence 1 allows nice solutions to a number of problems for the most widely-held view of the relationship between credence and belief, the threshold view. I provide a sketch (...) of a formal framework on which both theses are true. This is a modified Bayesian framework; I argue that despite making credences context-sensitive, the framework lets Bayesians hold on to their signature explanatory successes. The sort of context-sensitivity claimed for credences here mirrors the sort of context-sensitivity I have elsewhere claimed for outright belief: one's credences depend, in part, on the space of alternative possibilities one takes seriously in a context. (shrink)

A measure of coherence is said to be reliability conducive if and only if a higher degree of coherence (as measured) results in a higher likelihood that the witnesses are reliable. Recently, it has been proved that several coherence measures proposed in the literature are reliability conducive in a restricted scenario (Olsson and Schubert 2007, Synthese 157:297–308). My aim is to investigate which coherence measures turn out to be reliability conducive in the more general scenario where it is any finite (...) number of witnesses that give equivalent reports. It is shown that only the so-called Shogenji measure is reliability conducive in this scenario. I take that to be an argument for the Shogenji measure being a fruitful explication of coherence. (shrink)

This paper develops a probabilistic model of belief change under interpretation shifts, in the context of a problem case from dynamic epistemic logic. Van Benthem [4] has shown that a particular kind of belief change, typical for dynamic epistemic logic, cannot be modelled by standard Bayesian conditioning. I argue that the problems described by van Benthem come about because the belief change alters the semantics in which the change is supposed to be modelled: the new information induces a shift in (...) the interpretation of the sentences. In this paper I show that interpretation shifts can be modeled in terms of updating by conditioning. The model derives from the knowledge structures developed by Fagin et al [8], and hinges on a distinction between the propositional and informational content of sentences. Finally, I show that Dempster-Shafer theory provides the appropriate probability kinematics for the model. (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)

Additionally, the text shows how to develop computationally feasible methods to mesh with this framework.

Consider a group of people whose preferences satisfy the axioms of one of the current versions of utility theory, such as von Neumann-Morgenstern (1944), Savage (1954), or Bolker-Jeffrey (1965). There are political and economic contexts in which it is of interest to find ways of aggregating these individual preferences into a group preference ranking. The question then arises of whether methods of aggregation exist in which the group’s preferences also satisfy the axioms of the chosen utility theory, and in which (...) at the same time the aggregation process satisfies certain plausible conditions (e.g., the Pareto conditions below). (shrink)

A measure of coherence is said to be reliability conducive if and only if a higher degree of coherence (as measured) among testimonies implies a higher probability that the witnesses are reliable. Recently, it has been proved that several coherence measures proposed in the literature are reliability conducive in scenarios of equivalent testimonies (Olsson and Schubert 2007; Schubert, to appear). My aim is to investigate which coherence measures turn out to be reliability conducive in the more general scenario where the (...) testimonies do not have to be equivalent. It is shown that four measures are reliability conducive in the present scenario, all of which are ordinally equivalent to the Shogenji measure. I take that to be an argument for the Shogenji measure being a fruitful explication of coherence. (shrink)

The Dutch Book argument, like Route 66, is about to turn 80. It is arguably the most celebrated argument for subjective Bayesianism. Start by rejecting the Cartesian idea that doxastic attitudes are ‘all-or-nothing’; rather, they are far more nuanced degrees of belief, for short credences, susceptible to fine-grained numerical measurement. Add a coherentist assumption that the rationality of a doxastic state consists in its internal consistency. The remaining problem is to determine what consistency of credences amounts to. The Dutch Book (...) argument, in a nutshell, says that if your credences do not obey the probability calculus, you are ‘incoherent’—susceptible to sure losses at the hands of a ‘Dutch Bookie’—and thus irrational. Conclusion: rationality requires your credences to obey the probability calculus. And like Route 66, the fortunes of the Dutch Book argument have been mixed. Opinions on the argument are sharply divided. The list of its proponents is quite a ‘who’s who’ of philosophers of probability; they include de Finetti (1937, 1980), Carnap (1950, 1962, and more fully, 1955), Kemeny (1955), Lehman (1955), Shimony (1955), Adams (1962), Mellor (1971), Rosenkrantz (1981), van Fraassen (1989), Jeffrey (1983, 1992). (shrink)

To clarify and illuminate the place of probability in science Ellery Eells and James H. Fetzer have brought together some of the most distinguished philosophers ...

Various theories try to give accounts of how measures of this confidence do or ought to behave, both as far as the internal mental consistency of the agent as ...

The concept of evidence is among the central concerns of epistemology broadly construed. As such, it has long engaged the intellectual energies of both philosophers of science and epistemologists of a more traditional variety. Here I briefly survey some of the more important ideas to have emerged from this tradition of reflection. I then look somewhat more closely at an issue that has recently come to the fore, largely as a result of Williamson's Knowledge and Its Limits: that of whether (...) one's evidence supervenes on one's non-factive mental states. (shrink)

A person who does not have good intellectual reasons for believing in God can, depending on his probabilities and values for consequences of believing, have good practical reasons. Pascalian wagers founded on a variety of possible probability/value profiles are examined from a Bayesian perspective central to which is the idea that states and options are pragmatically reasonable only if they maximize subjective expected value. Attention is paid to problems posed by representations of values by Cantorian infinities. An appendix attends to (...) Robinsonian hyperreals. Another appendix presents for comparison Newcomb's Problem and a problem in some ways like it suggested, I think, by ideas of John Calvin. (shrink)

I argue that Bayesians need two distinct notions of probability. We need the usual degree-of-belief notion that is central to the Bayesian account of rational decision. But Bayesians also need a separate notion of probability that represents the degree to which evidence supports hypotheses. Although degree-of-belief is well suited to the theory of rational decision, Bayesians have tried to apply it to the realm of hypothesis confirmation as well. This double duty leads to the problem of old evidence, a problem (...) that, we will see, is much more extensive than usually recognized. I will argue that degree-of-support is distinct from degree-of-belief, that it is not just a kind of counterfactual degree-of-belief, and that it supplements degree-of-belief in a way that resolves the problems of old evidence and provides a richer account of the logic of scientific inference and belief. (shrink)

Richard Jeffrey has labelled his philosophy of probability radical probabilism and qualified this position as Bayesian, nonfoundational and anti-rationalist. This paper explores the roots of radical probabilism, to be traced back to the work of Frank P. Ramsey and Bruno de Finetti.

The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference (...) class problem. Other versions of these interpretations apparently evade the problem. But I contend that they are all “no-theory” theories of probability - accounts that leave quite obscure why probability should function as a guide to life, a suitable basis for rational inference and action. The reference class problem besets those theories that are genuinely informative and that plausibly constrain our inductive reasonings and decisions. I distinguish a “metaphysical” and an “epistemological” reference class problem. I submit that we can dissolve the former problem by recognizing that probability is fundamentally a two-place notion: conditional probability is the proper primitive of probability theory. However, I concede that the epistemological problem remains. (shrink)

Mainstream epistemology is a highly theoretical and abstract enterprise. Traditional epistemologists rarely present their deliberations as critical to the practical problems of life, unless one supposes—as Hume, for example, did not—that skeptical worries should trouble us in our everyday affairs. But some issues in epistemology are both theoretically interesting and practically quite pressing. That holds of the problem to be discussed here: how laypersons should evaluate the testimony of experts and decide which of two or more rival experts is most (...) credible. It is of practical importance because in a complex, highly specialized world people are constantly confronted with situations in which, as comparative novices, they must turn to putative experts for intellectual guidance or assistance. It is of theoretical interest because the appropriate epistemic considerations are far from transparent; and it is not clear how far the problems lead to insurmountable skeptical quandaries. This paper does not argue for flat-out skepticism in this domain; nor, on the other hand, does it purport to resolve all pressures in the direction of skepticism. It is an exploratory paper, which tries to identify problems and examine some possible solutions, not to establish those solutions definitively. (shrink)

I begin with a rather unpromising dispute that Nozick once had with Ian Hacking in the pages of the London Review of Books, in which both vied with one another in their enthusiasm to repudiate the thesis that some human people or peoples are closer than others to animality. I shall attempt to show that one can build, on the basis of Nozick’s discussion of rationality, a defense of the view that the capacity tor language places human rationality out of (...) reach of a comparison with animals. The difference rests, paradoxically, on the human capacity tor irratianality. Irrationality depends on the capacity tor language, which allows the detachment of explicit thoughts from their underlying dynamic implementation; these, in turn, condition the essential disputability of principles of rationality. That is what places every human potentially -- if not actually -- on the other side of an unbridgeable gulf that separates us from other animals. (shrink)

Given someone’s fully specified posterior probability distribution q and information about the revision method that they employed to produce q, what can you infer about their prior probabilistic commitments? This question provides an entrée into a thoroughgoing discussion of a class of parameterizations of Jeffrey conditioning in which the parameters furnish information above and beyond that incorporated in \. Our analysis highlights the ubiquity of Bayes factors in the study of probability revision.

How should we understand the relationship between binary belief and degree of belief? To answer this question, we should look to desire. Whatever relationship we think holds between desire and degree of desire should be used as our model for the relationship we think holds between belief and degree of belief. This parity pushes us towards an account that treats the binary attitudes as primary. But if we take binary beliefs as primary, we seem to face a serious problem. Binary (...) beliefs are insufficiently discriminating. If we treat them as primary, we will lack the resources needed for fruitful theorizing. This problem can, I argue, be solved if we think of an agent’s degree of belief that p as reducible to her binary believing that p and the change in the apparent reasons that would be needed to get her to withhold. (shrink)