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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 2008 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. C. J. Adcock (1928). Law and Chance. Australasian Journal of Philosophy 6 (3):210 – 212.
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  2. D. M. Borchert (ed.) (2006). Encyclopedia of Philosophy, Second Edition.
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  3. W. Büchel (1975). Statistische Wahrscheinlichkeit Und Statistische Physik. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 6 (1):7-18.
    W. Stegmüller sees the decisive difficulty of the Laplacean interpretation of Carnaps probability in the lack of the required equiprobable possibilities. It is argued that the required equiprobabilities in physics are given by statistical mechanics and can easily be transferred from physics to general statistical problems.
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  4. Arthur W. Burks (1979). Chance, Cause, Reason: An Inquiry Into the Nature of Scientific Evidence. Philosophical Review 88 (3):500-502.
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  5. H. W. Capel, J. S. Cramer, O. Estevez-Uscanga, C. A. J. Klaassen & G. J. Mellenbergh (eds.) (2002). Chance and Uncertainty. 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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  6. Rudolf Carnap (1963). The Logical Foundations of Probability. Journal of Philosophy 60 (13):362-364.
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  7. John L. Casti (2001). Rooting Out Randomness. Complexity 6 (4):13-15.
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  8. Robert Charles Clark (1970). Total Control and Chance in Musics. Part II. Reflections on Criticism and Judgment. Journal of Aesthetics and Art Criticism 29 (1):43-46.
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  9. Carol E. Cleland (1985). Causality, Chance and Weak Non-Super Venience. American Philosophical Quarterly 22 (4):287 - 298.
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  10. John Cohen (1960). Chance, Skill, and Luck. Baltimore, Penguin Books.
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  11. Marcel Conche (1999). L'aléatoire / Marcel Conche. Monograph Collection (Matt - Pseudo).
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  12. Arthur H. Copeland (1962). Statistical Induction and the Foundations of Probability. Theoria 28 (2):87-109.
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  13. D. Costantini (1985). Probability and Laws. Erkenntnis 22 (1-3):33 - 49.
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  14. Mark Crovelli (2009). Has David Howden Vindicated Richard von Mises's Definition of Probability? Libertarian Papers 1.
    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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  15. Mark Crovelli (2009). On the Possibility of Assigning Probabilities to Singular Cases, Or: Probability Is Subjective Too! Libertarian Papers 1.
    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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  16. Bruno De Finetti (2008). Philosophical Lectures on Probability. Collected, Edited and Annotated by Alberto Mura. Springer.
    The book contains the transcription of a course on the foundations of probability given by the Italian mathematician Bruno de Finetti in 1979 at the a oeNational Institute of Advanced Mathematicsa in Rome.
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  17. P. G. de Gennes (1977). Chance and Necessity in Cooperative Phenomena. Diogenes 25 (100):198-217.
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  18. Agustin de Herrera & Sven K. Knebel (1996). A Treatise on Aleatory Probability. Modern Schoolman 73 (3):199-264.
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  19. Arthur Dewing (1910). Chance as a Category of Science. Journal of Philosophy, Psychology and Scientific Methods 7 (3):70-73.
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  20. Phil Dowe (2003). A Dilemma for Objective Chance. In Jr Kyburg & Mariam Thalos (eds.), Probability is the Very Guide of Life: The Philosophical Uses of Chance. Open Court 153--64.
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  21. Antony Eagle, Frequency, Laws, and Time-Dependent Chances.
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  22. Ralph M. Eaton (1921). The Meaning of Chance. The Monist 31 (2):280-296.
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  23. Brian Ellis (1999). A Review Essay on God, Chance & Necessity. Sophia 38 (1):89-98.
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  24. Douglas Fawcett (1927). Chance and Creation. Mind 36 (142):261-262.
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  25. Milton Fisk (1980). Chance, Cause, Reason. International Studies in Philosophy 12 (1):93-95.
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  26. Henry J. Folse (1997). Physics and Chance. International Studies in Philosophy 29 (1):150-151.
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  27. Roman Frigg, Probability in Boltzmannian Statistical Mechanics.
    In two recent papers Barry Loewer (2001, 2004) has suggested to interpret probabilities in statistical mechanics as Humean chances in David Lewis’ (1994) sense. I first give a precise formulation of this proposal, then raise two fundamental objections, and finally conclude that these can be overcome only at the price of interpreting these probabilities epistemically.
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  28. Maria Carla Galavotti (1987). Comments on Patrick Suppes “Propensity Interpretations of Probability”. Erkenntnis 26 (3):359 - 368.
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  29. Christopher Gauker (1987). Mind and Chance. Canadian Journal of Philosophy 17 (September):533-52.
  30. Quentin Gibson (1953). Argument From Chances. Australasian Journal of Philosophy 31 (3):170 – 183.
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  31. Ronald N. Giere (2010). Objective Single-Case Probabilities and the Foundations of Statistics. In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge
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  32. Gerd Gigerenzer (1989). The Empire of Chance How Probability Changed Science and Everyday Life. Monograph Collection (Matt - Pseudo).
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  33. Leon J. Goldstein (1978). Purpose in a World of Chance. International Studies in Philosophy 10:206-206.
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  34. Clement A. Green (1936). World of Chance, A. [REVIEW] Modern Schoolman 14:67.
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  35. Paulos Mar Gregorios (1992). Method and Epistemology in Science: Some Counter-Comments on Chance. In Jayant Vishnu Narlikar, Indu Banga & Chhanda Gupta (eds.), Philosophy of Science: Perspectives From Natural and Social Sciences. Munshiram Manoharlal Publishers 137.
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  36. L. Groot (2000). Roger Caillois, Games of Chance and the Superstar. Diogenes 48 (190):33-42.
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  37. David Grünberg (unknown). T-Theoretical Single-Case Ontic Probability. Yeditepe'de Felsefe (Philosophy at Yeditepe) 4.
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  38. G. J. Gustafson (1950). A Note on Chance. New Scholasticism 24 (2):174-177.
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  39. John Haigh (2006). What Are Your Chances? Think 4 (12):37-42.
    John Haigh provides us with some mind-expanding puzzles concerning probabilities.
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  40. John F. Halpin, Halpin@Oakland.Edu.
    The best-system account of scientific law proposes that laws and chances are to be defined in terms of systematic interpretation of all occurrences: L is a law and the chance of X is p just in case L and the chance p of X are consequences of the ideal axiom system for the totality of events. So, what seem to be further facts beyond the occurrences are just matters of the best way to interpret the totality of physical events. This (...)
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  41. M. Hammerton (1973). A Case of Radical Probability Estimation. Journal of Experimental Psychology 101 (2):252.
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  42. Sandra Harding (1994). Ist Die Westliche Wissenschaft Eine Ethnowissenschaft? Herausforderung Und Chance Für Die Feministische Wissenschaftsforschung. Die Philosophin 5 (9):26-44.
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  43. Howard Harriott (1999). R.A. Fisher And The Interpretation Of Probability. Protosociology 12.
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  44. Michal Heller (1985). Some Remarks of Foundations of Probability Theory. Roczniki Filozoficzne 33 (3):82.
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  45. Vincent F. Hendricks, Stig Andur Pederson & Klaus Frovin Jørgensen (eds.) (2001). Probability Theory: Philosophy, Recent History and Relations to Science. Synthese Library, Kluwer.
    This book sheds light on some recent discussions of the problems in probability theory and their history, analysing their philosophical and mathematical significance, and the role pf mathematical probability theory in other sciences.
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  46. T. Hibbard (1987). Freedom by Chance. In Tom Hibbard (ed.), Surrealist Philosophy. Arjuna Library
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  47. M. J. S. Hodge (1991). The Empire of Chance. How Probability Changed Science and Everyday Life. [REVIEW] British Journal for the History of Science 24 (1):124-126.
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  48. Lancelot Hogben (1952). Chance and Choice by Cardpack and Chessboard: An Introduction to Probability in Practice by Visual Aids. Vol. I. Philosophy and Phenomenological Research 12 (3):434-436.
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  49. Wolfram Hogrebe (1983). From Hidden Necessity to Chance Remarks on the Roots of Scientific Rationality. American Philosophical Quarterly 20 (3):305 - 308.
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  50. David Howden (2009). Single Trial Probability Applications: Can Subjectivity Evade Frequency Limitations? Libertarian Papers 1.
    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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