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Summary Perhaps the most natural way to understand probability is as an epistemic phenomenon. A probability function is an attempt to quantify a degree of uncertainty -- a state of mind. But some probabilities appear to be objective features of the world. A well constructed die has a probability of one in six that it will land on any given side, for instance. Such objective probabilities, or chances, explain why events happen with typical frequencies, while they cannot be predicted with certainty on any given trial. Philosophical controversies primarily arise regarding: the relationship between chances and epistemic states (under what circumstances should our degree of confidence match the chance, and why?); and also regarding the relationship between chances and frequencies (if chances are not reducible to frequencies, how do they explain those frequencies?).
Key works Popper 1959 puts forth the propensity interpretation of probability, which has been an influential way of understanding chances; Lewis 2010 focuses upon epistemic aspects of chance, and is the focus of much literature relating to Humeanism and chance; Loewer 2004 is a helpful paper further exploring Lewis's metaphysics of chance; Albert 2000 discusses the time asymmetry of chance and its relation to temporal symmetries in physics.
Introductions Consult Handfield 2012 for an exclusive focus upon chance; Hájek 2007 is about broader topic of probability, but has much that is of relevance to chance; Eagle 2010 contains many classic papers.
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  1. Against an Argument for Objective Probabilities of Undetermined Choices.Daniele Conti - 2024 - American Philosophical Quarterly 61 (2):127–137.
    According to libertarianism about free will, at least some of the choices we make are free and undetermined. Many libertarians also accept the thesis that, before we make an undetermined choice, there is a nontrivial objective probability that we will make that choice. In the literature on free will, the ascription of objective probabilities is sometimes justified via an “Argument from Motivation,” which adverts to the fact that typically, in situations of choice, we are more motivated to choose some options (...)
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  2. Discussion Note: Non-Measurability, Imprecise Credences, and Imprecise Chances.Joshua Thong - forthcoming - Mind.
    This paper is a discussion note on Isaacs et al. (2022), who have claimed to offer a new motivation for imprecise probabilities, based on the mathematical phenomenon of non-measurability. In this note, I clarify some consequences of their proposal. In particular, I show that if their proposal is applied to a bounded 3-dimensional space, then they have to reject at least one of the following: (i) If A is at most as probable as B and B is at most as (...)
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  3. How a pure risk of harm can itself be a harm: A reply to Rowe.H. Orri Stefánsson - 2024 - Analysis 84 (1):112-116.
    Rowe has recently argued that pure risk of harm cannot itself be a harm. I respond to Rowe and argue that given an appropriate understanding of objective probabilities, pure objective risk of harm can itself be a harm.
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  4. Type I error rates are not usually inflated.Mark Rubin - manuscript
    The inflation of Type I error rates is thought to be one of the causes of the replication crisis. Questionable research practices such as p-hacking are thought to inflate Type I error rates above their nominal level, leading to unexpectedly high levels of false positives in the literature and, consequently, unexpectedly low replication rates. In this article, I offer an alternative view. I argue that questionable and other research practices do not usually inflate relevant Type I error rates. I begin (...)
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  5. Fairness and risk attitudes.Richard Bradley & Stefánsson H. Orri - 2023 - Philosophical Studies 180 (10-11):3179-3204.
    According to a common judgement, a social planner should often use a lottery to decide which of two people should receive a good. This judgement undermines one of the best-known arguments for utilitarianism, due to John C. Harsanyi, and more generally undermines axiomatic arguments for utilitarianism and similar views. In this paper we ask which combinations of views about (a) the social planner’s attitude to risk and inequality, and (b) the subjects’ attitudes to risk are consistent with the aforementioned judgement. (...)
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  6. The Stochastic-Quantum Theorem.Jacob A. Barandes - manuscript
    This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called generalized stochastic systems, collectively encompass many important kinds of stochastic processes, including Markov chains and random dynamical systems. This paper then states and proves a new theorem that establishes a precise correspondence between any generalized stochastic system and a unitarily evolving quantum system. This theorem therefore leads to a new formulation of (...)
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  7. "Hasard hypostasié et hasard réprimé : pour en finir avec certains mythes".Philippe Gagnon - 2023 - In Philippe Quentin (ed.), Hasard et création. Actes du colloque 7 et 8 mars 2022. Presses universitaires de l'ICES. pp. 155-175.
    This is the outline : I - Quelques étapes aux avancées significatives II - La pensée chrétienne et le hasard d’ignorance III - De quelques difficultés de raisonner sur le probable IV - Téléologie et évolutionnisme V - Où est l’« étage » qui permette de parler d’indépendance ? VI. Qu’y a-t-il à la base de nos concepts d’ordre ? VII - Quelle place pour le hasard ? VIII. Le hasard appréhendé de dos ?
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  8. John Venn's Logic of Chance.Wesley C. Salmon - 1981 - In Jaakko Hintikka, David Gruender & Evandro Agazzi (eds.), Probabilistic Thinking, Thermodynamics and the Interaction of the History and Philosophy of Science: Proceedings of the 1978 Pisa Conference on the History and Philosophy of Science. D. Reidel. pp. 125--138.
  9. A New Dialogue on Yijing -The Book of Changes in a World of Changes, Instability, Disequilibrium and Turbulence.David Leong - manuscript
    This paper proposes a reinterpretation of the Chinese worldview on equilibrium/nonequilibrium and yin-yang. Important terminologies and concepts that constitute Yijing have correlative aspects with irreversible thermodynamics and quantum reality- instability, nonlinearity, nonequilibrium and temporality. Ilya Prigogine is a Nobel laureate noted for his contribution to dissipative structures and their role in thermodynamic systems far from equilibrium, complexity and irreversibility. His expressions, as argued in this paper, resonate with the principles in Yijing. Thus, this paper attempts to re-state existing interpretations of (...)
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  10. The Physical Foundation of Quantum Theory.Mehran Shaghaghi - 2023 - Foundations of Physics 53 (1):1-36.
    The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems with only one adjustable property cannot carry more than a single message at a time. We demonstrate that this is true for the photons in the double-slit experiment, and that this is what leads to the fundamental limit on measuring the complementary aspect of the photons. Next, we illustrate that systems with a single adjustable property exhibit other quantum (...)
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  11. The Complex Nexus of Evolutionary Fitness.Mauricio Suárez - 2022 - European Journal for Philosophy of Science 12 (1):1-26.
    The propensity nature of evolutionary fitness has long been appreciated and is nowadays amply discussed. The discussion has, however, on occasion followed long standing conflations in the philosophy of probability literature between propensities, probabilities, and frequencies. In this paper, I apply a more recent conception of propensities in modelling practice to some of the key issues, regarding the mathematical representation of fitness and how it may be regarded as explanatory. The ensuing complex nexus of fitness emphasises the distinction between biological (...)
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  12. The Design Inference: Eliminating Chance through Small Probabilities.Jordan Howard Sobel - 2003 - Mind 112 (447):521-525.
  13. 4. Physical Chance.Richard Johns - 2002 - In A Theory of Physical Probability. University of Toronto Press. pp. 84-108.
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  14. Interpreting Probability: Controversies and Developments in the Early Twentieth Century.David Howie - 2002 - Cambridge University Press.
    The term probability can be used in two main senses. In the frequency interpretation it is a limiting ratio in a sequence of repeatable events. In the Bayesian view, probability is a mental construct representing uncertainty. This 2002 book is about these two types of probability and investigates how, despite being adopted by scientists and statisticians in the eighteenth and nineteenth centuries, Bayesianism was discredited as a theory of scientific inference during the 1920s and 1930s. Through the examination of a (...)
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  15. Gillies, Donald, "An Objective Theory of Probability". [REVIEW]Colin Howson - 1979 - Erkenntnis 14:87.
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  16. An Analysis of Probability Interpretations for the Physical and Biological Sciences.Kimberly Ann Maricic - 1993 - Dissertation, Washington University
    In this work, five different interpretations of "probability" are analyzed: the classical, logical, subjective, relative frequency, and propensity interpretations. The objective is to determine which of these interpretations is most suitable for probability applications in the physical and biological sciences. The first state of this analysis involves evaluating the different interpretations with respect to the probability calculus. The objective at this point is not to reject any interpretations outright, but rather to keep in mind any difficulties in adherence to the (...)
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  17. Patrick Suppes, Probabilistic Metaphysics. [REVIEW]Alasdair Urquhart - 1985 - Philosophy in Review 5:478-480.
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  18. Inquiries in the Philosophy of Probability: Randomness and Independence.Paul William Humphreys - 1976 - Dissertation, Stanford University
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  19. Some Remarks of Foundations of Probability Theory.Michal Heller - 1985 - Roczniki Filozoficzne 33 (3):82.
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  20. The Logical Structure of Probability.Stephen Martin Spielman - 1967 - Dissertation, University of Pennsylvania
  21. Symposium: “Probability”.S. E. Toulmin & L. J. Russell - 1950 - Aristotelian Society Supplementary Volume 24 (1):27-74.
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  22. Objective Chance: Lonergan and Peirce on Scientific Generalization.S. Vincent Potter - 1994 - Method 12 (1):91-108.
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  23. R.A. Fisher and the Interpretation of Probability.Howard H. Harriott - 1998 - ProtoSociology 12:176-193.
  24. Counterfactuals, Dispositions, and Conscious Experience: Essays on Entropy.Adam Newman Elga - 2001 - Dissertation, Massachusetts Institute of Technology
    Chapter 1 of this thesis concerns counterfactual conditionals. David Lewis has offered a natural and influential analysis of counterfactuals. But the analysis fails to take into account the asymmetry of entropy, and comes to grief precisely because of that failure. The cause of the grief is that processes involving the increase of entropy are exceedingly sensitive to small changes in their final conditions. ;Chapter 2 concerns robust dispositions. Drop an ordinary rock into hydrofluoric acid, and---almost no matter what is going (...)
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  25. Chance and Choice by Cardpack and Chessboard: An Introduction to Probability in Practice by Visual Aids. Vol. I.Lancelot Hogben - 1952 - Philosophy and Phenomenological Research 12 (3):434-436.
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  26. HACKING, I.: "The Emergence of Probability". [REVIEW]D. C. Stove - 1976 - Australasian Journal of Philosophy 54:180.
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  27. ILLIES, D. A.: "An Objective Theory of Probability". [REVIEW]M. von Thun - 1975 - Australasian Journal of Philosophy 53:267.
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  28. Propensities, Chance, Causation, and Contrastive Explanation.Christopher S. I. Mccurdy - 1994 - Dissertation, The University of Western Ontario (Canada)
    A pragmatic account of scientific understanding is used both to examine and to unify fundamental questions concerning the propensity interpretation of probability and theories of chance, causation, and explanation. One of the most important problems to be addressed is the problem of defining homogeneous reference classes in theories of chance, causation, and explanation. The consistency of the propensity interpretation is defended against traditional criticisms such as "Humphreys's paradox." It is demonstrated that the application of this interpretation to theories of chance (...)
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  29. THORPE, W. H. "Purpose in a World of Chance". [REVIEW]Hugo Meynell - 1979 - Philosophy 54:425.
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  30. Purpose in a World of Chance.W. H. Thorpe, Donald M. Mackay & Jacob Bronowski - 1979 - Philosophy 54 (209):425-427.
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  31. The Logic of Chance: An Essay on the Foundations and Province of the Theory of Probability, with Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science, and to Statistics.John Venn - 2015 - Palala Press.
    This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...)
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  32. The Logic of Chance an Essay on the Foundations and Province of the Theory of Probability, with Especial Reference to its Logical Bearings and its Application to Moral and Social Science.John Venn - 1866 - London, England: Macmillan.
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  33. The Empire of Chance: How Probability Changed Science and Everyday Life.Gerd Gigerenzer, Zeno Swijtink, Theodore Porter, Lorraine Daston, John Beatty & Lorenz Kruger - 1990 - Cambridge University Press.
    The Empire of Chance tells how quantitative ideas of chance transformed the natural and social sciences, as well as daily life over the last three centuries. A continuous narrative connects the earliest application of probability and statistics in gambling and insurance to the most recent forays into law, medicine, polling and baseball. Separate chapters explore the theoretical and methodological impact in biology, physics and psychology. Themes recur - determinism, inference, causality, free will, evidence, the shifting meaning of probability - but (...)
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  34. L'aléatoire / Marcel Conche.Marcel Conche - 1999
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  35. Ian Hacking, "The Emergence of Probability". [REVIEW]Henry E. Kyburg - 1978 - Theory and Decision 9 (2):205.
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  36. J. Venn, The Logic of Chance. [REVIEW]W. R. Sorley - 1904 - Mind 13:268.
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  37. Les chances de l'Église dans la révolution tranquille de Hongrie.L. Lukács - 1991 - Nouvelle Revue Théologique 113 (4):543-553.
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  38. Some Recent Work on Probability. [REVIEW]David Miller - 1986 - Philosophical Quarterly 36 (45):536.
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  39. A Statistical Study of Belief.F. B. Sumner - 1899 - Philosophical Review 8:192.
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  40. Chance, Cause, Reason: An Inquiry into the Nature of Scientific Evidence.Henry E. Kyburg Jr - 1979 - Philosophical Review 88 (3):500-502.
  41. The Creature, Man. [REVIEW]Clement A. Green - 1937 - Modern Schoolman 14 (3):67-67.
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  42. Statistical and Inductive Probabilities. [REVIEW]H. T. R. - 1964 - Review of Metaphysics 18 (1):179-179.
    A careful presentation of the foundations of probability theory, containing many valuable innovations. Two accounts of probability are adduced: probability as a measure on the subsets of a probability set, and as a measure on the sentences of a formal language. The book stresses connections between these two accounts; of particular interest is its thesis that statistical probabilities may be regarded as estimates of inductive probabilities.—R. H. T.
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  43. Elements of the Theory of Probability. [REVIEW]S. P. - 1966 - Review of Metaphysics 20 (1):147-148.
    Introduces probability theory largely by way of precept. Results of theory are stated, not derived, and then problems are proposed and solved by way of illustration. Although there is a commendable number of such problems, it should be noted that no exercises are concocted and left for the reader. Other topics touched upon besides discrete probability are continuous probability and probability of causes. The treatment lays bare some philosophical issues.—P. S.
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  44. Has David Howden Vindicated Richard von Mises’s Definition of Probability?Mark R. Crovelli - 2009 - Libertarian Papers 1:44.
    In my recent article on these pages I argued that members of the Austrian School of economics have adopted and defended a faulty definition of probability. I argued that the definition of probability necessarily depends upon the nature of the world in which we live. I claimed that if the nature of the world is such that every event and phenomenon which occurs has a cause of some sort, then probability must be defined subjectively; that is, “as a measure of (...)
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  45. On the Possibility of Assigning Probabilities to Singular Cases, or: Probability Is Subjective Too!Mark R. Crovelli - 2009 - Libertarian Papers 1:26.
    Both Ludwig von Mises and Richard von Mises claimed that numerical probability could not be legitimately applied to singular cases. This paper challenges this aspect of the von Mises brothers’ theory of probability. It is argued that their denial that numerical probability could be applied to singular cases was based solely upon Richard von Mises’ exceptionally restrictive definition of probability. This paper challenges Richard von Mises’ definition of probability by arguing that the definition of probability necessarily depends upon whether the (...)
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  46. Single Trial Probability Applications: Can Subjectivity Evade Frequency Limitations?David Howden - 2009 - Libertarian Papers 1:42.
    Frequency probability theorists define an event’s probability distribution as the limit of a repeated set of trials belonging to a homogeneous collective. The subsets of this collective are events which we have deficient knowledge about on an individual level, although for the larger collective we have knowledge its aggregate behavior. Hence, probabilities can only be achieved through repeated trials of these subsets arriving at the established frequencies that define the probabilities. Crovelli argues that this is a mistaken approach, and that (...)
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  47. The Empire of Chance. How Probability Changed Science and Everyday Life. [REVIEW]M. J. S. Hodge - 1991 - British Journal for the History of Science 24 (1):124-126.
  48. Probabilistic Metaphysics by Patrick Suppes. [REVIEW]Henry E. Kyburg - 1987 - Journal of Philosophy 84 (1):45-49.
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  49. Chance and Uncertainty: Their Role in Various Disciplines.H. W. Capel, J. S. Cramer, O. Estevez-Uscanga, C. A. J. Klaassen & G. J. Mellenbergh (eds.) - 1995 - Amsterdam University Press.
    'Uncertainty and chance' is a subject with a broad span, in that there is no academic discipline or walk of life that is not beset by uncertainty and chance. In this book a range of approaches is represented by authors from varied disciplines: natural sciences, mathematics, social sciences and medical sciences. At one extreme, this volume is concerned with the foundations of probability. At the other extreme, we have scholars who acknowledge the concept of chance and uncertainty but do not (...)
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  50. Frequency-driven Probabilities In Quantitative Causal Analysis.Frederica Russo - unknown
    This paper addresses the problem of the interpretation of probability in quantitative causal analysis. I argue that probability has to be interpreted according to a Bayesian framework in which degrees of belief are frequency-driven. This interpretation can account for the peculiar use and meaning of probability in generic and single-case causal inferences involved in this domain.
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