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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. Ernest W. Adams (1986). On the Logic of High Probability. Journal of Philosophical Logic 15 (3):255 - 279.
  2. C. J. Adcock (1928). Law and Chance. Australasian Journal of Philosophy 6 (3):210 – 212.
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  3. Translated as‘Probabilism (1989). A Critical Essay on the Theory of Probability and on the Value of Science,'. Erkenntnis 31:169-223.
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  4. Patrick K. Bastable (1971). The Concept of Probability. Philosophical Studies 20:337-338.
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  5. Zygmunt Bauman (2008). Introduction Threats or Chances? In Does Ethics Have a Chance in a World of Consumers? Harvard University Press. pp. 1-30.
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  6. Claus Beisbart (2016). A Humean Guide to Spielraum Probabilities. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 47 (1):189-216.
    The most promising accounts of ontic probability include the Spielraum conception of probabilities, which can be traced back to J. von Kries and H. Poincaré, and the best system account by D. Lewis. This paper aims at comparing both accounts and at combining them to obtain the best of both worlds. The extensions of both Spielraum and best system probabilities do not coincide because the former only apply to systems with a special dynamics. Conversely, Spielraum probabilities may not be part (...)
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  7. Claus Beisbart & Stephan Hartmann (eds.) (2011). Probabilities in Physics. Oxford University Press.
    This volume is the first to provide a philosophical appraisal of probabilities in all of physics.
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  8. F. C. Benenson (1977). Randomness and the Frequency Definition of Probability. Synthese 36 (2):207 - 233.
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  9. Gustav Bergmann (1945). Frequencies, Probabilities, and Positivism. Philosophy and Phenomenological Research 6 (1):26-44.
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  10. John Bigelow & Robert Pargetter (1987). An Analysis of Indefinite Probability Statements. Synthese 73 (2):361 - 370.
    An analysis of indefinite probability statements has been offered by Jackson and Pargetter (1973). We accept that this analysis will assign the correct probability values for indefinite probability claims. But it does so in a way which fails to reflect the epistemic state of a person who makes such a claim. We offer two alternative analyses: one employing de re (epistemic) probabilities, and the other employing de dicto (epistemic) probabilities. These two analyses appeal only to probabilities which are accessible to (...)
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  11. Simon Blackburn (1980). Opinions and Chances. In D. H. Mellor (ed.), Prospects for Pragmatism. Cambridge University Press. pp. 175--96.
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  12. Simon Blackburn (1976). HACKING, IAN "The Emergence of Probability". [REVIEW] Philosophy 51:476.
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  13. D. M. Borchert (ed.) (2006). Encyclopedia of Philosophy, Second Edition.
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  14. Nicolas Bouleau, What Are the Philosophical Probabilities ?
  15. Richard Boyd (1972). Determinism, Laws, and Predictability in Principle. Philosophy of Science 39 (4):431-450.
    This paper examines commonly offered arguments to show that human behavior is not deterministic because it is not predictable. These arguments turn out to rest on the assumption that deterministic systems must be governed by deterministic laws, and that these give rise to predictability "in principle" of determined events. A positive account of determinism is advanced and it is shown that neither of these assumptions is true. The relation between determinism, laws, and prediction in practice is discussed as a question (...)
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  16. Bob Brier (1970). Randomness, Statistics and Emergence.
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  17. 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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  18. 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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  19. 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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  20. Rudolf Carnap (1963). The Logical Foundations of Probability. Journal of Philosophy 60 (13):362-364.
  21. John L. Casti (2001). Rooting Out Randomness. Complexity 6 (4):13-15.
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  22. 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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  23. Carol E. Cleland (1985). Causality, Chance and Weak Non-Super Venience. American Philosophical Quarterly 22 (4):287 - 298.
  24. John Cohen (1960). Chance, Skill, and Luck. Baltimore: Penguin Books.
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  25. Marcel Conche (1999). L'aléatoire / Marcel Conche.
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  26. Neil Cooper (1965). The Concept of Probability. British Journal for the Philosophy of Science 16 (63):226-238.
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  27. Arthur H. Copeland (1962). Statistical Induction and the Foundations of Probability. Theoria 28 (2):87-109.
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  28. D. Costantini (1985). Probability and Laws. Erkenntnis 22 (1-3):33 - 49.
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  29. 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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  30. 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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  31. David Howie (2002). Interpreting Probability Controversies and Developments in the Early Twentieth Century. 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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  32. A. P. Dawid (1985). Probability, Symmetry and Frequency. British Journal for the Philosophy of Science 36 (2):107-128.
    We consider the meaning of the assignment of probabilities to events implied by the kind of model regularly used by Statisticians. Traditional frequentist understandings are reviewed and rejected. It is argued that many statistical models may be justified purely on the basis of the symmetry properties enjoyed by the observables being modelled.
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  33. 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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  34. P. G. de Gennes (1977). Chance and Necessity in Cooperative Phenomena. Diogenes 25 (100):198-217.
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  35. Agustin de Herrera & Sven K. Knebel (1996). A Treatise on Aleatory Probability. Modern Schoolman 73 (3):199-264.
  36. Arthur Dewing (1910). Chance as a Category of Science. Journal of Philosophy, Psychology and Scientific Methods 7 (3):70-73.
  37. Dennis Dieks, Wenceslao J. Gonzalez, Stephan Hartmann, Michael Stöltzner & Weber ( 2012). Probabilities, Laws, and Structures. Springer.
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  38. Dennis Dieks, Wenceslao Gonzalez, Hartmann J., Stöltzner Stephan, Weber Michael & Marcel (eds.) (2012). Probabilities, Laws, and Structures. Springer: Netherlands.
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  39. 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. pp. 153--64.
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  40. Homer H. Dubs (1939). Empirical Induction by Probability and the External World. Philosophy of Science 6 (3):371.
  41. Antony Eagle, Frequency, Laws, and Time-Dependent Chances.
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  42. Ralph M. Eaton (1921). The Meaning of Chance. The Monist 31 (2):280-296.
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  43. J. Ellenberg & E. Sober (2011). Objective Probabilities in Number Theory. Philosophia Mathematica 19 (3):308-322.
    Philosophers have explored objective interpretations of probability mainly by considering empirical probability statements. Because of this focus, it is widely believed that the logical interpretation and the actual-frequency interpretation are unsatisfactory and the hypothetical-frequency interpretation is not much better. Probabilistic assertions in pure mathematics present a new challenge. Mathematicians prove theorems in number theory that assign probabilities. The most natural interpretation of these probabilities is that they describe actual frequencies in finite sets and limits of actual frequencies in infinite sets. (...)
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  44. Brian Ellis (1999). A Review Essay on God, Chance & Necessity. Sophia 38 (1):89-98.
  45. N. Emery (2015). Chance, Possibility, and Explanation. British Journal for the Philosophy of Science 66 (1):95-120.
    I argue against the common and influential view that non-trivial chances arise only when the fundamental laws are indeterministic. The problem with this view, I claim, is not that it conflicts with some antecedently plausible metaphysics of chance or that it fails to capture our everyday use of ‘chance’ and related terms, but rather that it is unstable. Any reason for adopting the position that non-trivial chances arise only when the fundamental laws are indeterministic is also a reason for adopting (...)
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  46. Douglas Fawcett (1927). Chance and Creation. Mind 36 (142):261-262.
  47. J. H. Fetzer (forthcoming). Frequencies and Propensities: Inference to the Best Explanation. Synthese.
  48. Milton Fisk (1980). Chance, Cause, Reason. International Studies in Philosophy 12 (1):93-95.
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  49. Henry J. Folse (1997). Physics and Chance. International Studies in Philosophy 29 (1):150-151.
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  50. 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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