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  1. Modeling Rational Players: Part I.Ken Binmore - 1987 - Economics and Philosophy 3 (2):179-214.
    Game theory has proved a useful tool in the study of simple economic models. However, numerous foundational issues remain unresolved. The situation is particularly confusing in respect of the non-cooperative analysis of games with some dynamic structure in which the choice of one move or another during the play of the game may convey valuable information to the other players. Without pausing for breath, it is easy to name at least 10 rival equilibrium notions for which a serious case can (...)
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  • Prediction in forensic science: a critical examination of common understandings.Alex Biedermann, Silvia Bozza & Franco Taroni - 2015 - Frontiers in Psychology 6.
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  • Probability logic, logical probability, and inductive support.Isaac Levi - 2010 - Synthese 172 (1):97-118.
    This paper seeks to defend the following conclusions: The program advanced by Carnap and other necessarians for probability logic has little to recommend it except for one important point. Credal probability judgments ought to be adapted to changes in evidence or states of full belief in a principled manner in conformity with the inquirer’s confirmational commitments—except when the inquirer has good reason to modify his or her confirmational commitment. Probability logic ought to spell out the constraints on rationally coherent confirmational (...)
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  • (1 other version)Probabilistic abstract argumentation: an investigation with Boltzmann machines.Régis Riveret, Dimitrios Korkinof, Moez Draief & Jeremy Pitt - 2015 - Argument and Computation 6 (2):178-218.
    Probabilistic argumentation and neuro-argumentative systems offer new computational perspectives for the theory and applications of argumentation, but their principled construction involves two entangled problems. On the one hand, probabilistic argumentation aims at combining the quantitative uncertainty addressed by probability theory with the qualitative uncertainty of argumentation, but probabilistic dependences amongst arguments as well as learning are usually neglected. On the other hand, neuro-argumentative systems offer the opportunity to couple the computational advantages of learning and massive parallel computation from neural networks (...)
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  • Aggregating infinitely many probability measures.Frederik Herzberg - 2015 - Theory and Decision 78 (2):319-337.
    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 (...)
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  • Subjective Probability as Sampling Propensity.Thomas Icard - 2016 - Review of Philosophy and Psychology 7 (4):863-903.
    Subjective probability plays an increasingly important role in many fields concerned with human cognition and behavior. Yet there have been significant criticisms of the idea that probabilities could actually be represented in the mind. This paper presents and elaborates a view of subjective probability as a kind of sampling propensity associated with internally represented generative models. The resulting view answers to some of the most well known criticisms of subjective probability, and is also supported by empirical work in neuroscience and (...)
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  • Scoring Imprecise Credences: A Mildly Immodest Proposal.Conor Mayo-Wilson & Gregory Wheeler - 2016 - Philosophy and Phenomenological Research 92 (1):55-78.
    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 (...)
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  • Looking for Those Natural Numbers: Dimensionless Constants and the Idea of Natural Measurement.Philip Mirowski - 1992 - Science in Context 5 (1):165-188.
    The ArgumentMany find it “notoriously difficult to see how societal context can affect in any essential way how someone solves a mathematical problem or makes a measurement.” That may be because it has been a habit of western scientists to assert their numerical schemes were untainted by any hint of anthropomorphism. Nevertheless, that Platonist penchant has always encountered obstacles in practice, primarily because the stability of any applied numerical scheme requires some alien or external warrant.This paper surveys the history of (...)
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  • Finite additivity, another lottery paradox and conditionalisation.Colin Howson - 2014 - Synthese 191 (5):1-24.
    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 (...)
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  • Demystifying Dilation.Arthur Paul Pedersen & Gregory Wheeler - 2014 - Erkenntnis 79 (6):1305-1342.
    Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically (...)
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  • The main two arguments for probabilism are flawed.Luigi Secchi - 2014 - Synthese 191 (3):287-295.
    Probabilism, the view that agents have numerical degrees of beliefs that conform to the axioms of probability, has been defended by the vast majority of its proponents by way of either of two arguments, the Dutch Book Argument and the Representation Theorems Argument. In this paper I argue that both arguments are flawed. The Dutch Book Argument is based on an unwarranted, ad hoc premise that cannot be dispensed with. The Representation Theorems Argument hinges on an invalid implication.
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  • You've Come a Long Way, Bayesians.Jonathan Weisberg - 2015 - Journal of Philosophical Logic 44 (6):817-834.
    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 (...)
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  • Quantum Theory: A Pragmatist Approach.Richard Healey - 2012 - British Journal for the Philosophy of Science 63 (4):729-771.
    While its applications have made quantum theory arguably the most successful theory in physics, its interpretation continues to be the subject of lively debate within the community of physicists and philosophers concerned with conceptual foundations. This situation poses a problem for a pragmatist for whom meaning derives from use. While disputes about how to use quantum theory have arisen from time to time, they have typically been quickly resolved, and consensus reached, within the relevant scientific sub-community. Yet rival accounts of (...)
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  • Accuracy and Coherence: Prospects for an Alethic Epistemology of Partial Belief.James M. Joyce - 2009 - In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of belief. London: Springer. pp. 263-297.
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  • (1 other version)Quantum probability and many worlds.Meir Hemmo - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):333-350.
    We discuss the meaning of probabilities in the many worlds interpretation of quantum mechanics. We start by presenting very briefly the many worlds theory, how the problem of probability arises, and some unsuccessful attempts to solve it in the past. Then we criticize a recent attempt by Deutsch to derive the quantum mechanical probabilities from the nonprobabilistic parts of quantum mechanics and classical decision theory. We further argue that the Born probability does not make sense even as an additional probability (...)
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  • Advancing the rationality debate.Keith E. Stanovich & Richard F. West - 2000 - Behavioral and Brain Sciences 23 (5):701-717.
    In this response, we clarify several misunderstandings of the understanding/acceptance principle and defend our specific operationalization of that principle. We reiterate the importance of addressing the problem of rational task construal and we elaborate the notion of computational limitations contained in our target article. Our concept of thinking dispositions as variable intentional-level styles of epistemic and behavioral regulation is explained, as is its relation to the rationality debate. Many of the suggestions of the commentators for elaborating two-process models are easily (...)
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  • Bayes' theorem.James Joyce - 2008 - Stanford Encyclopedia of Philosophy.
    Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, (...)
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  • Quantum probability and decision theory, revisited [2002 online-only paper].David Wallace - 2002
    An extended analysis is given of the program, originally suggested by Deutsch, of solving the probability problem in the Everett interpretation by means of decision theory. Deutsch's own proof is discussed, and alternatives are presented which are based upon different decision theories and upon Gleason's Theorem. It is argued that decision theory gives Everettians most or all of what they need from `probability'. Contact is made with Lewis's Principal Principle linking subjective credence with objective chance: an Everettian Principal Principle is (...)
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  • Countable additivity and subjective probability.Jon Williamson - 1999 - British Journal for the Philosophy of Science 50 (3):401-416.
    While there are several arguments on either side, it is far from clear as to whether or not countable additivity is an acceptable axiom of subjective probability. I focus here on de Finetti's central argument against countable additivity and provide a new Dutch book proof of the principle, To argue that if we accept the Dutch book foundations of subjective probability, countable additivity is an unavoidable constraint.
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  • Should we respond to evil with indifference?Brian Weatherson - 2005 - Philosophy and Phenomenological Research 70 (3):613–635.
    In a recent article, Adam Elga outlines a strategy for “Defeating Dr Evil with Self-Locating Belief”. The strategy relies on an indifference principle that is not up to the task. In general, there are two things to dislike about indifference principles: adopting one normally means confusing risk for uncertainty, and they tend to lead to incoherent views in some ‘paradoxical’ situations. I argue that both kinds of objection can be levelled against Elga’s indifference principle. There are also some difficulties with (...)
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  • (1 other version)Review. [REVIEW]Brian Skyrms - 1996 - British Journal for the Philosophy of Science 47 (4):627-629.
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  • What are conditional probabilities conditional upon?Keith Hutchison - 1999 - British Journal for the Philosophy of Science 50 (4):665-695.
    This paper rejects a traditional epistemic interpretation of conditional probability. Suppose some chance process produces outcomes X, Y,..., with probabilities P(X), P(Y),... If later observation reveals that outcome Y has in fact been achieved, then the probability of outcome X cannot normally be revised to P(X|Y) ['P&Y)/P(Y)]. This can only be done in exceptional circumstances - when more than just knowledge of Y-ness has been attained. The primary reason for this is that the weight of a piece of evidence varies (...)
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  • The preface paradox revisited.Igor Douven - 2003 - Erkenntnis 59 (3):389 - 420.
    The Preface Paradox has led many philosophers to believe that, if it isassumed that high probability is necessary for rational acceptability, the principleaccording to which rational acceptability is closed under conjunction (CP)must be abandoned. In this paper we argue that the paradox is far less damaging to CP than is generally believed. We describe how, given certain plausibleassumptions, in a large class of cases in which CP seems to lead tocontradiction, it does not do so after all. A restricted version (...)
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  • A dutch book and subjective probabilities.P. G. Moore - 1983 - British Journal for the Philosophy of Science 34 (3):263-266.
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  • Varieties of Bayesianism.Jonathan Weisberg - 2011
    Handbook of the History of Logic, vol. 10, eds. Dov Gabbay, Stephan Hartmann, and John Woods, forthcoming.
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  • Theories of probability.Colin Howson - 1995 - British Journal for the Philosophy of Science 46 (1):1-32.
    My title is intended to recall Terence Fine's excellent survey, Theories of Probability [1973]. I shall consider some developments that have occurred in the intervening years, and try to place some of the theories he discussed in what is now a slightly longer perspective. Completeness is not something one can reasonably hope to achieve in a journal article, and any selection is bound to reflect a view of what is salient. In a subject as prone to dispute as this, there (...)
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  • Logic with numbers.Colin Howson - 2007 - Synthese 156 (3):491-512.
    Many people regard utility theory as the only rigorous foundation for subjective probability, and even de Finetti thought the betting approach supplemented by Dutch Book arguments only good as an approximation to a utility-theoretic account. I think that there are good reasons to doubt this judgment, and I propose an alternative, in which the probability axioms are consistency constraints on distributions of fair betting quotients. The idea itself is hardly new: it is in de Finetti and also Ramsey. What is (...)
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  • (1 other version)Waging War on Pascal’s Wager.Alan Hájek - 2003 - Philosophical Review 112 (1):27-56.
    Pascal’s Wager is simply too good to be true—or better, too good to be sound. There must be something wrong with Pascal’s argument that decision-theoretic reasoning shows that one must (resolve to) believe in God, if one is rational. No surprise, then, that critics of the argument are easily found, or that they have attacked it on many fronts. For Pascal has given them no dearth of targets.
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  • Twenty-one arguments against propensity analyses of probability.Antony Eagle - 2004 - Erkenntnis 60 (3):371–416.
    I argue that any broadly dispositional analysis of probability will either fail to give an adequate explication of probability, or else will fail to provide an explication that can be gainfully employed elsewhere (for instance, in empirical science or in the regulation of credence). The diversity and number of arguments suggests that there is little prospect of any successful analysis along these lines.
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  • Bertrand’s Paradox and the Principle of Indifference.Nicholas Shackel - 2024 - Abingdon: Routledge.
    Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand’s chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum sized state spaces. Articulating the nature of such spaces involves some deep mathematics and that is perhaps why the recent literature on Bertrand’s Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication. At the same time, the (...)
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  • An Improved Argument for Superconditionalization.Julia Staffel & Glauber De Bona - forthcoming - Erkenntnis:1-27.
    Standard arguments for Bayesian conditionalizing rely on assumptions that many epistemologists have criticized as being too strong: (i) that conditionalizers must be logically infallible, which rules out the possibility of rational logical learning, and (ii) that what is learned with certainty must be true (factivity). In this paper, we give a new factivity-free argument for the superconditionalization norm in a personal possibility framework that allows agents to learn empirical and logical falsehoods. We then discuss how the resulting framework should be (...)
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  • Coherence as Joint Satisfiability.Samuel Fullhart & Camilo Martinez - forthcoming - Australasian Journal of Philosophy.
    According to many philosophers, rationality is, at least in part, a matter of one’s attitudes cohering with one another. Theorists who endorse this idea have devoted much attention to formulating various coherence requirements. Surprisingly, they have said very little about what it takes for a set of attitudes to be coherent in general. We articulate and defend a general account on which a set of attitudes is coherent just in case and because it is logically possible for the attitudes to (...)
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  • Una revisión de la condicionalización bayesiana.Rodrigo Iván Barrera Guajardo - 2021 - Culturas Cientificas 2 (1):24-54.
    La epistemología bayesiana tiene como concepto capital la condicionalización simple. Para comprender de buena forma cómo opera esta regla, se debe dar cuenta de la concepción subjetiva de la probabilidad. Sobre la base de lo anterior es posible esclarecer alcances y límites de la condicionalización simple. En general, cuando esta regla enfrenta una dificultad se hacen esfuerzos por resolver dicha particular cuestión, pero no es usual encontrar propuestas unificadas con la intención de resolver varias de las complicaciones subyacentes al bayesianismo (...)
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  • Hypothetical Frequencies as Approximations.Jer Steeger - 2024 - Erkenntnis 89 (4):1295-1325.
    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 (...)
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  • Proper scoring rules in epistemic decision theory.Maomei Wang - 2020 - Dissertation, Lingnan University
    Epistemic decision theory aims to defend a variety of epistemic norms in terms of their facilitation of epistemic ends. One of the most important components of EpDT is known as a scoring rule. This thesis addresses some problems about scoring rules in EpDT. I consider scoring rules both for precise credences and for imprecise credences. For scoring rules in the context of precise credences, I examine the rationale for requiring a scoring rule to be strictly proper, and argue that no (...)
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  • A Gentle Approach to Imprecise Probabilities.Gregory Wheeler - 2022 - In Thomas Augustin, Fabio Gagliardi Cozman & Gregory Wheeler (eds.), Reflections on the Foundations of Probability and Statistics: Essays in Honor of Teddy Seidenfeld. Springer. pp. 37-67.
    The field of of imprecise probability has matured, in no small part because of Teddy Seidenfeld’s decades of original scholarship and essential contributions to building and sustaining the ISIPTA community. Although the basic idea behind imprecise probability is (at least) 150 years old, a mature mathematical theory has only taken full form in the last 30 years. Interest in imprecise probability during this period has also grown, but many of the ideas that the mature theory serves can be difficult to (...)
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  • Towards the Inevitability of Non-Classical Probability.Giacomo Molinari - 2023 - Review of Symbolic Logic 16 (4):1053-1079.
    This paper generalises an argument for probabilism due to Lindley [9]. I extend the argument to a number of non-classical logical settings whose truth-values, seen here as ideal aims for belief, are in the set $\{0,1\}$, and where logical consequence $\models $ is given the “no-drop” characterization. First I will show that, in each of these settings, an agent’s credence can only avoid accuracy-domination if its canonical transform is a (possibly non-classical) probability function. In other words, if an agent values (...)
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  • Non-Measurability, Imprecise Credences, and Imprecise Chances.Yoaav Isaacs, Alan Hájek & John Hawthorne - 2021 - Mind 131 (523):892-916.
    – We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...)
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  • (1 other version)Perception and probability.Alex Byrne - 2021 - Philosophy and Phenomenological Research 104 (2):1-21.
    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 (...)
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  • Regret Averse Opinion Aggregation.Lee Elkin - 2021 - Ergo: An Open Access Journal of Philosophy 8 (16):473-495.
    It is often suggested that when opinions differ among individuals in a group, the opinions should be aggregated to form a compromise. This paper compares two approaches to aggregating opinions, linear pooling and what I call opinion agglomeration. In evaluating both strategies, I propose a pragmatic criterion, No Regrets, entailing that an aggregation strategy should prevent groups from buying and selling bets on events at prices regretted by their members. I show that only opinion agglomeration is able to satisfy the (...)
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  • Respecting One’s Fellow: QBism’s Analysis of Wigner’s Friend.John B. DeBrota, Christopher A. Fuchs & Rüdiger Schack - 2020 - Foundations of Physics 50 (12):1859-1874.
    According to QBism, quantum states, unitary evolutions, and measurement operators are all understood as personal judgments of the agent using the formalism. Meanwhile, quantum measurement outcomes are understood as the personal experiences of the same agent. Wigner’s conundrum of the friend, in which two agents ostensibly have different accounts of whether or not there is a measurement outcome, thus poses no paradox for QBism. Indeed the resolution of Wigner’s original thought experiment was central to the development of QBist thinking. The (...)
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  • Chance and the Continuum Hypothesis.Daniel Hoek - 2020 - Philosophy and Phenomenological Research 103 (3):639-60.
    This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly pick (...)
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  • Belief, Credence and Statistical Evidence.Davide Fassio & Jie Gao - 2020 - Theoria 86 (4):500-527.
    According to the Rational Threshold View, a rational agent believes p if and only if her credence in p is equal to or greater than a certain threshold. One of the most serious challenges for this view is the problem of statistical evidence: statistical evidence is often not sufficient to make an outright belief rational, no matter how probable the target proposition is given such evidence. This indicates that rational belief is not as sensitive to statistical evidence as rational credence. (...)
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  • The Relationship Between Belief and Credence.Elizabeth G. Jackson - 2020 - Philosophy Compass 15 (6):1–13.
    Sometimes epistemologists theorize about belief, a tripartite attitude on which one can believe, withhold belief, or disbelieve a proposition. In other cases, epistemologists theorize about credence, a fine-grained attitude that represents one’s subjective probability or confidence level toward a proposition. How do these two attitudes relate to each other? This article explores the relationship between belief and credence in two categories: descriptive and normative. It then explains the broader significance of the belief-credence connection and concludes with general lessons from the (...)
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  • E.T. Jaynes’s Solution to the Problem of Countable Additivity.Colin Elliot - 2020 - Erkenntnis 87 (1):287-308.
    Philosophers cannot agree on whether the rule of Countable Additivity should be an axiom of probability. Edwin T. Jaynes attacks the problem in a way which is original to him and passed over in the current debate about the principle: he says the debate only arises because of an erroneous use of mathematical infinity. I argue that this solution fails, but I construct a different argument which, I argue, salvages the spirit of the more general point Jaynes makes. I argue (...)
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  • Logical ignorance and logical learning.Richard Pettigrew - 2020 - Synthese 198 (10):9991-10020.
    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; (...)
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  • Epistemic Decision Theory's Reckoning.Conor Mayo-Wilson & Gregory Wheeler - manuscript
    Epistemic decision theory (EDT) employs the mathematical tools of rational choice theory to justify epistemic norms, including probabilism, conditionalization, and the Principal Principle, among others. Practitioners of EDT endorse two theses: (1) epistemic value is distinct from subjective preference, and (2) belief and epistemic value can be numerically quantified. We argue the first thesis, which we call epistemic puritanism, undermines the second.
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  • Conditional Probabilities.Kenny Easwaran - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 131-198.
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  • (1 other version)Infinitesimal Probabilities.Sylvia Wenmackers - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 199-265.
    Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general.
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  • Decision Theory.Johanna Thoma - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 57-106.
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