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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 1980 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. The Mechanism Behind Probability (Version 2.0).Sydney Ernest Grimm - manuscript
    Changes within observable reality at the lowest level of reality seem to occur in accordance with the probabil­ity theory in mathematics. It is quite remarkable that nature itself has chosen the probability theory to ar­range all the changes within the structure of the basic quantum fields. This rises a question about the distri­bution of properties in space and time. DOI: 10.5281/zenodo.5515861.
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  2. The 'Noncausal Causality' of Quantum Information.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (45):1-7.
    The paper is concentrated on the special changes of the conception of causality from quantum mechanics to quantum information meaning as a background the revolution implemented by the former to classical physics and science after Max Born’s probabilistic reinterpretation of wave function. Those changes can be enumerated so: (1) quantum information describes the general case of the relation of two wave functions, and particularly, the causal amendment of a single one; (2) it keeps the physical description to be causal by (...)
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  3. The Design Inference: Eliminating Chance Through Small Probabilities.Jordan Howard Sobel - 2003 - Mind 112 (447):521-525.
  4. 4. Physical Chance.Richard Johns - 2002 - In A Theory of Physical Probability. University of Toronto Press. pp. 84-108.
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  5. Gillies, Donald, "An Objective Theory of Probability". [REVIEW]Colin Howson - 1979 - Erkenntnis 14:87.
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  6. The Enterprise of Knowledge: An Essay on Knowledge, Credal Probability, and Chance. [REVIEW]H. T. R. - 1982 - Review of Metaphysics 35 (3):610-612.
    Levi in this book develops the views on inductive logic which he put forward in 1967 in Gambling with Truth. He extends the account given there of inductive expansion and supplements it with an account of routine expansion and contraction with the aim of constructing a view of how revisions of bodies of knowledge should be evaluated. He is concerned to give an account of the revision of probability judgments and gives the contexts of specific enquiries an important place in (...)
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  7. 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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  8. Patrick Suppes, Probabilistic Metaphysics. [REVIEW]Alasdair Urquhart - 1985 - Philosophy in Review 5:478-480.
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  9. Inquiries in the Philosophy of Probability: Randomness and Independence.Paul William Humphreys - 1976 - Dissertation, Stanford University
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  10. Some Remarks of Foundations of Probability Theory.Michal Heller - 1985 - Roczniki Filozoficzne 33 (3):82.
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  11. The Logical Structure of Probability.Stephen Martin Spielman - 1967 - Dissertation, University of Pennsylvania
  12. Probability.S. E. Toulmin & L. J. Russell - 1950 - Aristotelian Society Supplementary Volume 24:27-74.
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  13. Objective Chance: Lonergan and Peirce on Scientific Generalization.S. Vincent Potter - 1994 - Method 12 (1):91-108.
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  14. R.A. Fisher And The Interpretation Of Probability.Howard H. Harriott - 1998 - ProtoSociology 12:176-193.
  15. 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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  16. 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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  17. HACKING, I.: "The Emergence of Probability". [REVIEW]D. C. Stove - 1976 - Australasian Journal of Philosophy 54:180.
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  18. ILLIES, D. A.: "An Objective Theory of Probability". [REVIEW]M. von Thun - 1975 - Australasian Journal of Philosophy 53:267.
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  19. 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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  20. THORPE, W. H. "Purpose in a World of Chance". [REVIEW]Hugo Meynell - 1979 - Philosophy 54:425.
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  21. Purpose in a World of Chance.W. H. Thorpe, Donald M. Mackay & Jacob Bronowski - 1979 - Philosophy 54 (209):425-427.
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  22. 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 - 1888 - Macmillan.
    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, and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may (...)
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  23. 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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  24. 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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  25. The Empire of Chance: How Probability Changed Science and Everyday Life.Gerd Gigerenzer, Zeno Swijtink, Theodore Porter, Lorraine Daston, John Beatty & Lorenz Kruger - 1989 - 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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  26. L'aléatoire / Marcel Conche.Marcel Conche - 1999
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  27. Ian Hacking, "The Emergence of Probability". [REVIEW]Henry E. Kyburg - 1978 - Theory and Decision 9 (2):205.
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  28. J. Venn, The Logic of Chance. [REVIEW]W. R. Sorley - 1904 - Mind 13:268.
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  29. 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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  30. Some Recent Work on Probability. [REVIEW]David Miller - 1986 - Philosophical Quarterly 36 (45):536.
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  31. The Logical Foundations of Probability.Rudolf Carnap - 1950 - Journal of Philosophy 60 (13):362-364.
  32. A Statistical Study of Belief.F. B. Sumner - 1899 - Philosophical Review 8:192.
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  33. Chance, Cause, Reason: An Inquiry Into the Nature of Scientific Evidence.Henry E. Kyburg Jr - 1979 - Philosophical Review 88 (3):500-502.
  34. World of Chance, A. [REVIEW]Clement A. Green - 1936 - Modern Schoolman 14:67.
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  35. 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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  36. 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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  37. 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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  38. 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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  39. 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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  40. 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.
  41. Probabilistic Metaphysics by Patrick Suppes. [REVIEW]Henry E. Kyburg - 1987 - Journal of Philosophy 84 (1):45-49.
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  42. 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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  43. 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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  44. Two Interpretations of Objective Probability. On the Ambiguity of Popper's Conception of Propensities.Christina Schneider - 1994 - Philosophia Naturalis 31 (1):107-131.
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  45. GILLIES, D.-Philosophical Theories of Probability. [REVIEW]Nicholas Shackel - 2003 - Philosophical Books 44 (1):92-94.
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  46. Frequencies and Propensities: Inference to the Best Explanation.James H. Fetzer - 2002 - Synthese 132 (1-2):27-61.
    An approach to inference to the best explanation integrating a Popperianconception of natural laws together with a modified Hempelian account of explanation, one the one hand, and Hacking's law of likelihood, on the other, which provides a robust abductivist model of sciencethat appears to overcome the obstacles that confront its inductivist,deductivist, and hypothetico-deductivist alternatives.This philosophy of scienceclarifies and illuminates some fundamental aspects of ontology and epistemology, especially concerning the relations between frequencies and propensities. Among the most important elements of this (...)
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  47. Probability.Ronald A. Fisher - 1922 - The Eugenics Review 14 (1):46.
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  48. Patrick Suppes, Probabilistic Metaphysics Reviewed By.Alasdair Urquhart - 1985 - Philosophy in Review 5 (10):478-480.
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  49. Probabilistic Metaphysics.James H. Fetzer - 2010 - In Ellery Eells & James H. Fetzer (eds.), The Place of Probability in Science. Springer. pp. 81--98.
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  50. The Mathematization of Chance in the Middle of the 17th Century.Ivo Schneider - 2000 - In Emily Grosholz & Herbert Breger (eds.), The Growth of Mathematical Knowledge. Kluwer Academic Publishers. pp. 59--75.
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