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  1. 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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  • The material theory of induction.John D. Norton - 2021 - Calgary, Alberta, Canada: University of Calgary Press.
    The inaugural title in the new, Open Access series BSPS Open, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single (...)
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  • Peirce, Pedigree, Probability.Rush T. Stewart & Tom F. Sterkenburg - 2022 - Transactions of the Charles S. Peirce Society 58 (2):138-166.
    An aspect of Peirce’s thought that may still be underappreciated is his resistance to what Levi calls _pedigree epistemology_, to the idea that a central focus in epistemology should be the justification of current beliefs. Somewhat more widely appreciated is his rejection of the subjective view of probability. We argue that Peirce’s criticisms of subjectivism, to the extent they grant such a conception of probability is viable at all, revert back to pedigree epistemology. A thoroughgoing rejection of pedigree in the (...)
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  • The theory of games as a tool for the social epistemologist.Kevin J. S. Zollman - 2020 - Philosophical Studies 178 (4):1381-1401.
    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 (...)
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  • Desirability foundations of robust rational decision making.Marco Zaffalon & Enrique Miranda - 2018 - Synthese 198 (Suppl 27):6529-6570.
    Recent work has formally linked the traditional axiomatisation of incomplete preferences à la Anscombe-Aumann with the theory of desirability developed in the context of imprecise probability, by showing in particular that they are the very same theory. The equivalence has been established under the constraint that the set of possible prizes is finite. In this paper, we relax such a constraint, thus de facto creating one of the most general theories of rationality and decision making available today. We provide the (...)
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  • Is There a Conjunction Fallacy in Legal Probabilistic Decision Making?Bartosz W. Wojciechowski & Emmanuel M. Pothos - 2018 - Frontiers in Psychology 9.
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  • Bayesian conditionalisation and the principle of minimum information.P. M. Williams - 1980 - British Journal for the Philosophy of Science 31 (2):131-144.
  • On the foundations of constructive mathematics – especially in relation to the theory of continuous functions.Frank Waaldijk - 2004 - Foundations of Science 10 (3):249-324.
    We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely related to the definition in BISH of (...)
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  • Biased information and the exchange paradox.Anubav Vasudevan - 2019 - Synthese 196 (6):2455-2485.
    This paper presents a new solution to the well-known exchange paradox, or what is sometimes referred to as the two-envelope paradox. Many recent commentators have analyzed the paradox in terms of the agent’s biased concern for the contents of his own arbitrarily chosen envelope, claiming that such bias violates the manifest symmetry of the situation. Such analyses, however, fail to make clear exactly how the symmetry of the situation is violated by the agent’s hypothetical conclusion that he ought to switch (...)
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  • The Brandeis Dice Problem and Statistical Mechanics.Steven J. van Enk - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 48 (1):1-6.
  • How Percepts and Concepts Engage the Future.Roberto Torretti - 2011 - Foundations of Physics 41 (11):1717-1728.
    With Humean empiricism and its agnostic stance regarding the future as a foil, I take a bird’s eye view of the links between past and future prescribed by ordinary concepts of everyday things and processes, and by scientific models of phenomenal situations. I argue that they entitle us to claim knowledge of the future—including, where appropriate, its necessary course—in a humanly affordable sense of ‘knowledge’.
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  • Dismissal of the illusion of uncertainty in the assessment of a likelihood ratio.Franco Taroni, Silvia Bozza, Alex Biedermann & Colin Aitken - unknown
    The use of the Bayes factor (BF) or likelihood ratio as a metric to assess the probative value of forensic traces is largely supported by operational standards and recommendations in different forensic disciplines. However, the progress towards more widespread consensus about foundational principles is still fragile as it raises new problems about which views differ. It is not uncommon e.g. to encounter scientists who feel the need to compute the probability distribution of a given expression of evidential value (i.e. a (...)
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  • Two Forms of Inconsistency in Quantum Foundations.Jer Steeger & Nicholas Teh - 2021 - British Journal for the Philosophy of Science 72 (4):1083-1110.
    Recently, there has been some discussion of how Dutch Book arguments might be used to demonstrate the rational incoherence of certain hidden variable models of quantum theory. In this paper, we argue that the 'form of inconsistency' underlying this alleged irrationality is deeply and comprehensively related to the more familiar 'inconsistency' phenomenon of contextuality. Our main result is that the hierarchy of contextuality due to Abramsky and Brandenburger corresponds to a hierarchy of additivity/convexity-violations which yields formal Dutch Books of different (...)
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  • Vagueness, Uncertainty and Degrees of Belief: Two Kinds of Indeterminacy—One Kind of Credence.Nicholas J. J. Smith - 2014 - Erkenntnis 79 (5):1027-44.
    If we think, as Ramsey did, that a degree of belief that P is a stronger or weaker tendency to act as if P, then it is clear that not only uncertainty, but also vagueness, gives rise to degrees of belief. If I like hot coffee and do not know whether the coffee is hot or cold, I will have some tendency to reach for a cup; if I like hot coffee and know that the coffee is borderline hot, I (...)
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  • Problems of Precision in Fuzzy Theories of Vagueness and Bayesian Epistemology.Nicholas J. J. Smith - 2019 - In Richard Dietz (ed.), Vagueness and Rationality in Language Use and Cognition. Springer Verlag. pp. 31-48.
    A common objection to theories of vagueness based on fuzzy logics centres on the idea that assigning a single numerical degree of truth -- a real number between 0 and 1 -- to each vague statement is excessively precise. A common objection to Bayesian epistemology centres on the idea that assigning a single numerical degree of belief -- a real number between 0 and 1 -- to each proposition is excessively precise. In this paper I explore possible parallels between these (...)
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  • The Insufficiency of the Dutch Book Argument.Darrell Patrick Rowbottom - 2007 - Studia Logica 87 (1):65-71.
    It is a common view that the axioms of probability can be derived from the following assumptions: probabilities reflect degrees of belief, degrees of belief can be measured as betting quotients; and a rational agent must select betting quotients that are coherent. In this paper, I argue that a consideration of reasonable betting behaviour, with respect to the alleged derivation of the first axiom of probability, suggests that and are incorrect. In particular, I show how a rational agent might assign (...)
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  • Evidence, computation and AI: why evidence is not just in the head.Darrell P. Rowbottom, André Curtis-Trudel & William Peden - 2023 - Asian Journal of Philosophy 2 (1):1-17.
    Can scientific evidence outstretch what scientists have mentally entertained, or could ever entertain? This article focuses on the plausibility and consequences of an affirmative answer in a special case. Specifically, it discusses how we may treat automated scientific data-gathering systems—especially AI systems used to make predictions or to generate novel theories—from the point of view of confirmation theory. It uses AlphaFold2 as a case study.
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  • 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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  • Can quantum probability provide a new direction for cognitive modeling?Emmanuel M. Pothos & Jerome R. Busemeyer - 2013 - Behavioral and Brain Sciences 36 (3):255-274.
    Classical (Bayesian) probability (CP) theory has led to an influential research tradition for modeling cognitive processes. Cognitive scientists have been trained to work with CP principles for so long that it is hard even to imagine alternative ways to formalize probabilities. However, in physics, quantum probability (QP) theory has been the dominant probabilistic approach for nearly 100 years. Could QP theory provide us with any advantages in cognitive modeling as well? Note first that both CP and QP theory share the (...)
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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.
  • You say you want a revolution: two notions of probabilistic independence.Alexander Meehan - 2021 - Philosophical Studies 178 (10):3319-3351.
    Branden Fitelson and Alan Hájek have suggested that it is finally time for a “revolution” in which we jettison Kolmogorov’s axiomatization of probability, and move to an alternative like Popper’s. According to these authors, not only did Kolmogorov fail to give an adequate analysis of conditional probability, he also failed to give an adequate account of another central notion in probability theory: probabilistic independence. This paper defends Kolmogorov, with a focus on this independence charge. I show that Kolmogorov’s sophisticated theory (...)
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  • Processing Probability Information in Nonnumerical Settings – Teachers’ Bayesian and Non-bayesian Strategies During Diagnostic Judgment.Timo Leuders & Katharina Loibl - 2020 - Frontiers in Psychology 11.
    A diagnostic judgment of a teacher can be seen as an inference from manifest observable evidence on a student’s behavior to his or her latent traits. This can be described by a Bayesian model of in-ference: The teacher starts from a set of assumptions on the student (hypotheses), with subjective probabilities for each hypothesis (priors). Subsequently, he or she uses observed evidence (stu-dents’ responses to tasks) and knowledge on conditional probabilities of this evidence (likelihoods) to revise these assumptions. Many systematic (...)
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  • Quantum physical symbol systems.Kathryn Blackmond Laskey - 2006 - Journal of Logic, Language and Information 15 (1-2):109-154.
    Because intelligent agents employ physically embodied cognitive systems to reason about the world, their cognitive abilities are constrained by the laws of physics. Scientists have used digital computers to develop and validate theories of physically embodied cognition. Computational theories of intelligence have advanced our understanding of the nature of intelligence and have yielded practically useful systems exhibiting some degree of intelligence. However, the view of cognition as algorithms running on digital computers rests on implicit assumptions about the physical world that (...)
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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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  • Dutch-Book Arguments against using Conditional Probabilities for Conditional Bets.Keith Hutchison - 2012 - Open Journal of Philosophy 2 (3):195.
    We consider here an important family of conditional bets, those that proceed to settlement if and only if some agreed evidence is received that a condition has been met. Despite an opinion widespread in the literature, we observe that when the evidence is strong enough to generate certainty as to whether the condition has been met or not, using traditional conditional probabilities for such bets will NOT preserve a gambler from having a synchronic Dutch Book imposed upon him. On the (...)
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  • The dialectics of infinitism and coherentism: inferential justification versus holism and coherence.Frederik Herzberg - 2014 - Synthese 191 (4):701-723.
    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 (...)
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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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  • A Graded Bayesian Coherence Notion.Frederik Herzberg - 2014 - Erkenntnis 79 (4):843-869.
    Coherence is a key concept in many accounts of epistemic justification within ‘traditional’ analytic epistemology. Within formal epistemology, too, there is a substantial body of research on coherence measures. However, there has been surprisingly little interaction between the two bodies of literature. The reason is that the existing formal literature on coherence measure operates with a notion of belief system that is very different from—what we argue is—a natural Bayesian formalisation of the concept of belief system from traditional epistemology. Therefore, (...)
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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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  • 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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  • Lockeans Maximize Expected Accuracy.Kevin Dorst - 2019 - Mind 128 (509):175-211.
    The Lockean Thesis says that you must believe p iff you’re sufficiently confident of it. On some versions, the 'must' asserts a metaphysical connection; on others, it asserts a normative one. On some versions, 'sufficiently confident' refers to a fixed threshold of credence; on others, it varies with proposition and context. Claim: the Lockean Thesis follows from epistemic utility theory—the view that rational requirements are constrained by the norm to promote accuracy. Different versions of this theory generate different versions of (...)
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  • A Bayesian Mixed-Methods Analysis of Basic Psychological Needs Satisfaction through Outdoor Learning and Its Influence on Motivational Behavior in Science Class.Ulrich Dettweiler, Gabriele Lauterbach, Christoph Becker & Perikles Simon - 2017 - Frontiers in Psychology 8.
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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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  • Normative decision analysis in forensic science.A. Biedermann, S. Bozza & F. Taroni - 2020 - Artificial Intelligence and Law 28 (1):7-25.
    This paper focuses on the normative analysis—in the sense of the classic decision-theoretic formulation—of decision problems that arise in connection with forensic expert reporting. We distinguish this analytical account from other common types of decision analyses, such as descriptive approaches. While decision theory is, since several decades, an extensively discussed topic in legal literature, its use in forensic science is more recent, and with an emphasis on goals such as the analysis of the logical structure of forensic expert conclusions regarding, (...)
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  • D-separation, forecasting, and economic science: a conjecture. [REVIEW]David A. Bessler & Zijun Wang - 2012 - Theory and Decision 73 (2):295-314.
    The paper considers the conjecture that forecasts from preferred economic models or theories d-separate forecasts from less preferred models or theories from the Actual realization of the variable for which a scientific explanation is sought. D-separation provides a succinct notion to represent forecast dominance of one set of forecasts over another; it provides, as well, a criterion for model preference as a fundamental device for progress in economic science. We demonstrate these ideas with examples from three areas of economic modeling.
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  • The Weirdness Theorem and the Origin of Quantum Paradoxes.Alessio Benavoli, Alessandro Facchini & Marco Zaffalon - 2021 - Foundations of Physics 51 (5):1-39.
    We argue that there is a simple, unique, reason for all quantum paradoxes, and that such a reason is not uniquely related to quantum theory. It is rather a mathematical question that arises at the intersection of logic, probability, and computation. We give our ‘weirdness theorem’ that characterises the conditions under which the weirdness will show up. It shows that whenever logic has bounds due to the algorithmic nature of its tasks, then weirdness arises in the special form of negative (...)
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  • Everett’s Missing Postulate and the Born Rule.Per Arve - 2020 - Foundations of Physics 50 (7):665-692.
    Everett’s Relative State Interpretation has gained increasing interest due to the progress of understanding the role of decoherence. In order to fulfill its promise as a realistic description of the physical world, two postulates are formulated. In short they are for a system with continuous coordinates \, discrete variable j, and state \\), the density \=|\psi _j|^2\) gives the distribution of the location of the system with the respect to the variables \ and j; an equation of motion for the (...)
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  • Interpretations of probability.Alan Hájek - 2007 - Stanford Encyclopedia of Philosophy.
  • 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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  • IP Scoring Rules: Foundations and Applications.Jason Konek - 2019 - Proceedings of Machine Learning Research 103:256-264.