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Summary

One can think of belief in a binary way--you either believe something or you don't. One can also think of belief as something that comes in degrees--you can believe something to a number of different degrees. It has been popular in formal epistemology to think of beliefs in the latter way, as things which come in degrees, and to further maintain that such degrees of belief should should satisfy the probability axioms. Given this picture, it has been debated whether there are other normative constraints on what an agent's degrees of belief should be like. The probabilistic principles discussed in this area are largely proposals about what these further normative constraints on degrees of belief should be like.

Key works A classic description and defense of conditionalization can be found in Urbach & Howson 1993. An influential and critical discussion of Indifference Principles can be found in Van Fraassen 1989. Important discussions and applications of scoring rules are given in Oddie 1997 and Joyce 1998. An early and influential discussion of chance-credence principles is given by Lewis 2010. Reflection Principles were introduced and defended in van Fraassen 1984 and van Fraassen 1995. Influential discussions of direct inference principles are given in Kyburg 1974 and Pollock 1990.
Introductions Good introductory discussions that cover many of the principles discussed in this section can be found in a number of places, including Urbach & Howson 1993Strevens ms and Weisberg 2011.
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  1. Probability and Paradox.F. Granger - 1929 - Aristotelian Society Supplementary Volume 9 (1):1-18.
  2. Special issue on Combining Probability and Logic.Jon Williamson & Dov Gabbay - 2003 - Journal of Applied Logic 1 (3-4):135-138.
  3. XIII.—The Philosophy of Probability.A. Wolf - 1913 - Proceedings of the Aristotelian Society 13 (1):328-361.
  4. Lorraine Daston. Classical Probability in the Enlightenment. Princeton: Princeton University Press, 1988. Pp. xviii + 423. ISBN 0-691-08497-1, £27.50, $49.50. [REVIEW]Theodore M. Porter - 1989 - British Journal for the History of Science 22 (4):444-446.
  5. Dutch Pioneers of Science. Leo Beek.Willem Hackmann - 1988 - Isis 79 (1):132-134.
  6. Heuristics can produce surprisingly rational probability estimates: Comment on Costello and Watts (2014).Håkan Nilsson, Peter Juslin & Anders Winman - 2016 - Psychological Review 123 (1):103-111.
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  7. Probability theory, not the very guide of life.Peter Juslin, Håkan Nilsson & Anders Winman - 2009 - Psychological Review 116 (4):856-874.
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  8. The principle of belief congruence and the congruity principle as models of cognitive interaction.Milton Rokeach & Gilbert Rothman - 1965 - Psychological Review 72 (2):128-142.
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  9. The Quantification of Judgment: Some Methodological Suggestions.Robert L. Winkler - 1967 - Journal of the American Statistical Association 62 (320):1105-1120.
    The personalistic theory of probability prescribes that a person should use personal probability assessments in decision-making and that these assessments should correspond with his judgments. Since the judgments exist solely in the assessor's mind, there is no way to prove whether or not this requirement is satisfied. De Finetti has proposed the development of methods which should oblige the assessor to make his assessments correspond with his judgments. An ideal Assessor is hypothesized and his behavior is investigated under a number (...)
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  10. 9. The de Finetti Lottery and Equiprobability.Paul Bartha - 2005 - In Kent A. Peacock & Andrew D. Irvine, Mistakes of reason: essays in honour of John Woods. Buffalo: University of Toronto Press. pp. 158-172.
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  11. Chapter 7. Absolute Probability Functions Construed as Representing Degrees of Logical Truth.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hugues Leblanc, Probability Theory and Probability Semantics. University of Toronto Press. pp. 114-141.
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  12. Chapter 3. Relative Probability Functions and Their T-Restrictions.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hugues Leblanc, Probability Theory and Probability Semantics. University of Toronto Press. pp. 45-58.
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  13. Significance testing, p-values and the principle of total evidence.Bengt Autzen - 2016 - European Journal for Philosophy of Science 6 (2):281-295.
    The paper examines the claim that significance testing violates the Principle of Total Evidence. I argue that p-values violate PTE for two-sided tests but satisfy PTE for one-sided tests invoking a sufficient test statistic independent of the preferred theory of evidence. While the focus of the paper is to evaluate a particular claim about the relationship of significance testing and PTE, I clarify the reading of this methodological principle along the way.
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  14. A Continuum of Inductive Methods Arising from a Generalized Principle of Instantial Relevance.C. J. Nix & J. B. Paris - 2006 - Journal of Philosophical Logic 35 (1):83-115.
    In this paper we consider a natural generalization of the Principle of Instantial Relevance and give a complete characterization of the probabilistic belief functions satisfying this principle as a family of discrete probability functions parameterized by a single real δ ∊ [0, 1).
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  15. (1 other version)The Axioms and Algebra of Intuitive Probability.Bernard O. Koopman - 1940 - Annals of Mathematics:269--292.
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  16. HACKING, I. "The Emergence of Probability". [REVIEW]J. R. Lucas - 1977 - Mind 86:466.
  17. Biased Coins: A model for higher-order probabilities.Jeanne Peijnenburg & David Atkinson - 2014 - In Maria Carla Galavotti, Elisabeth Nemeth & Friedrich Stadler, European Philosophy of Science: Philosophy of Science in Europe and the Vienna Heritage. Cham: Springer. pp. 241-248.
    Is it coherent to speak of the probability of a probability, and the probability of a probability of a probability, and so on? We show that it is, in the sense that a regress of higher-order probabilities can lead to convergent sequences that determine all these probabilities. By constructing an implementable model which is based on coin-making machines, we demonstrate the consistency of our regress.
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  18. Probability in the Philosophy of Religion.D. H. Mellor - 2013 - Analysis 73 (3):548-554.
  19. The Carnapian Tolerance in the Foundations of Probability'.Wilhelm K. Essler - 1984 - Epistemologia 7:171-190.
  20. On the probability of particular events.Alfred Jules Ayer - 1961 - Revue Internationale de Philosophie 15 (58):366-75.
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  21. On representation of source reliability in weight of evidence.Daniel E. O'Leary - 1991 - In Bernadette Bouchon-Meunier, Ronald R. Yager & Lotfi A. Zadeh, Uncertainty in Knowledge Bases: 3rd International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU'90, Paris, France, July 2 - 6, 1990. Proceedings. Springer. pp. 115--123.
  22. De Finetti's generalizations of exchangeability.Persi Diaconis & David Freedman - 1971 - In Richard C. Jeffrey, Studies in Inductive Logic and Probability. Berkeley: University of California Press. pp. 2--233.
  23. Factors determining the probability of recollection of intraoperative events.L. Goldman - 1990 - In B. Bonke, W. Fitch & K. Millar, Memory and Awareness In Anesthesia. Swets & Zeitlinger. pp. 45--9.
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  24. Philosophical foundations of probability.Hans Reichenbach - 1996 - In Sahotra Sarkar, Logic, probability, and epistemology: the power of semantics. New York: Garland Pub. Co.. pp. 3--115.
  25. From probabilities to percepts.Bjorn Merker - 2012 - In Shimon Edelman, Tomer Fekete & Neta Zach, Being in Time: Dynamical Models of Phenomenal Experience. Philadelphia: John Benjamins. pp. 88--37.
  26. Reinforcement probability and concurrent operants.Jordan Rosenberg - 1974 - Bulletin of the Psychonomic Society 4 (6):582-584.
  27. The modification of background frequency information.Philip H. Marshall, Clay E. George & Pamela Cohen - 1985 - Bulletin of the Psychonomic Society 23 (1):9-11.
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  28. (1 other version)Bruno de Finetti. Philosophical Lectures on Probability. Collected, edited, and annotated by Alberto Mura. Translated by Hykel Hosni. Synthese Library; 340. [REVIEW]Jon Williamson - 2010 - Philosophia Mathematica 18 (1):130-135.
  29. Relative importance of probabilities and payoffs in risk taking.Paul Slovic & Sarah Lichtenstein - 1968 - Journal of Experimental Psychology 78 (3p2):1.
  30. Strength of the relationship between the value of an event and its subjective probability as a function of method of measurement.Dean G. Pruitt & Robert D. Hoge - 1965 - Journal of Experimental Psychology 69 (5):483.
  31. Probabilities all the way down.Adam LaCaze - 2006 - Metascience 15 (3):547-551.
  32. An Endless Hierarchy of Probabilities.Jeanne Peijnenburg & David Atkinson - 2012 - American Philosophical Quarterly 49 (3):267-276.
    Suppose q is some proposition, and let P(q) = v0 (1) be the proposition that the probability of q is v0.1 How can one know that (1) is true? One cannot know it for sure, for all that may be asserted is a further probabilistic statement like P(P(q) = v0) = v1, (2) which states that the probability that (1) is true is v1. But the claim (2) is also subject to some further statement of an even higher probability: P(P(P(q) (...)
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  33. Embedded probabilities.J. Dubucs - 1991 - Theory and Decision 30 (3):279-284.
  34. Qualitative independence in probability theory.R. Duncan Luce & Louis Narens - 1978 - Theory and Decision 9 (3):225-239.
  35. Probabilities of probabilities.Karl Borch - 1975 - Theory and Decision 6 (2):155-159.
  36. Good Thinking: The Foundations of Probability and its Applications.Irving John Good - 1983 - Univ Minnesota Pr.
    ... Press for their editorial perspicacity, to the National Institutes of Health for the partial financial support they gave me while I was writing some of the chapters, and to Donald Michie for suggesting the title Good Thinking.
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  37. Is Probability Inapplicable -- in Principle -- to the God-Hypothesis?Robert A. Oakes - 1970 - New Scholasticism 44 (3):426-430.
  38. (1 other version)Probability as a guide to life.Helen Beebee & David Papineau - 2003 - In David Papineau, The Roots of Reason: Philosophical Essays on Rationality, Evolution, and Probability. New York: Oxford University Press. pp. 217-243.
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  39. Epistemological Probability.Henry E. Kyburg Jr - 1971 - Synthese 23 (2/3):309 - 326.
  40. Symposium: Probability.S. E. Toulmin & L. J. Russell - 1950 - Aristotelian Society Supplementary Volume 24 (1):27 - 74.
  41. The Logic of Probability.Bruno De Finetti & Brad Angell - 1995 - Philosophical Studies 77 (1):181 - 190.
  42. Pragmatic Probability.Newton C. A. Da Costa - 1986 - Erkenntnis 25 (2):141 - 162.
  43. Probabilism: A Critical Essay on the Theory of Probability and on the Value of Science.Finetti Bruno De - 1989 - Erkenntnis 31 (2-3):169 - 223.
  44. Review: The Plain Man's Guide to Probability. [REVIEW]Colin Howson - 1972 - British Journal for the Philosophy of Science 23 (2):157 - 170.
  45. More about Probability.C. H. Whiteley - 1947 - Analysis 8 (5):76 - 80.
  46. Rejoinder to Barker and Kyburg.Wesley C. Salmon - 1965 - American Philosophical Quarterly 2 (4):277 - 280.
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  47. Probability and Lycan’s Paradox.S. K. Wertz - 1988 - Southwest Philosophy Review 4 (2):85-85.
  48. Probability in Philosophy.Brian Weatherson - manuscript
    I’m not sure how much knowledge everyone already has, so I’d like to start with a little questionnaire. On a card, say for each of the following topics whether you’re familiar with the topic, have heard of it but aren’t familiar with it, or have never heard of it.
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  49. The Sweep of Probability.David Miller - 1993 - Philosophical Books 34 (1):29-30.
  50. Ramsey, truth, and probability.S. L. Zabell - 1991 - Theoria 57 (3):211-238.
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