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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 1980. 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. Epistemology and Inference. Henry E. Kyburg, Jr. [REVIEW]Stephen Spielman - 1986 - Philosophy of Science 53 (1):149-150.
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  2. Similarities as Evidence for Common Ancestry: A Likelihood Epistemology.Elliott Sober & Mike Steel - 2015 - British Journal for the Philosophy of Science:axv052.
    Darwin claims in the Origin that similarity is evidence for common ancestry, but that adaptive similarities are ‘almost valueless’ as evidence. This second claim seems reasonable for some adaptive similarities but not for others. Here we clarify and evaluate these and related matters by using the law of likelihood as an analytic tool and by considering mathematical models of three evolutionary processes: directional selection, stabilizing selection, and drift. Our results apply both to Darwin’s theory of evolution and to modern evolutionary (...)
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  3. Probability, Induction and Statistics.Henry E. Kyburg - 1973 - Philosophy of Science 40 (3):451-453.
  4. Probability. [REVIEW]Mauricio Suárez - 2011 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 26 (1):99-103.
  5. A Treatise on Probability.Clarence Irving Lewis - 1922 - Philosophical Review 31 (2):180.
  6. A Famous Dutch Convert.A. W. G. Randall - 1922 - New Blackfriars 3 (28):183-189.
  7. Probability and Paradox.F. Granger - 1929 - Aristotelian Society Supplementary Volume 9 (1):1-18.
  8. Special Issue on Combining Probability and Logic.Jon Williamson & Dov Gabbay - 2003 - Journal of Applied Logic 1 (3-4):135-138.
  9. XIII.—The Philosophy of Probability.A. Wolf - 1913 - Proceedings of the Aristotelian Society 13 (1):328-361.
  10. Dutch Pioneers of Science. Leo Beek.Willem D. Hackmann - 1988 - Isis 79 (1):132-134.
  11. Heuristics Can Produce Surprisingly Rational Probability Estimates: Comment on Costello and Watts.Håkan Nilsson, Peter Juslin & Anders Winman - 2016 - Psychological Review 123 (1):103-111.
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  12. 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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  13. 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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  14. On the Subjective Probability of Compound Events.Maya Bar-Hillel - 1973 - Organizational Behavior and Human Performance 9 (3):396-406.
    Subjects were requested to choose between gambles, where the outcome of one gamble depended on a single elementary event, and the other depended on an event compounded of a series of such elementary events. The data supported the hypothesis that the subjective probability of a compound event is systematically biased in the direction of the probability of its components resulting in overestimation of conjunctive events and underestimation of disjunctive events. Studies pertaining to this topic are discussed.
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  15. 9. The de Finetti Lottery and Equiprobability.Paul Bartha - 2005 - In Kent A. Peacock & Andrew D. Irvine (eds.), Mistakes of Reason: Essays in Honour of John Woods. University of Toronto Press. pp. 158-172.
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  16. Chapter 7. Absolute Probability Functions Construed as Representing Degrees of Logical Truth.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 114-141.
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  17. Chapter 3. Relative Probability Functions and Their T-Restrictions.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 45-58.
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  18. 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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  19. An Airtight Dutch Book.V. McGee - 1999 - Analysis 59 (4):257-265.
  20. It All Adds Up: The Dynamic Coherence of Radical Probabilism.S. L. Zabell - 2002 - Philosophy of Science 69 (S3):S98-S103.
  21. 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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  22. A New Way to Block a Dutch Book Argument, or The Stubborn Non-Probabilist.Leszek Wronski - manuscript
    We point out a yet unnoticed flaw in Dutch Book arguments that relates to a link between degrees of belief and betting quotients. We offer a set of precise conditions governing when a nonprobabilist is immune to the classical Dutch Book argument. We suggest that diachronic Dutch Book arguments are also affected.
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  23. The Axioms and Algebra of Intuitive Probability.Bernard O. Koopman - 1940 - Annals of Mathematics:269--292.
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  24. The Modern Epistemic Interpretations of Probability: Logicism and Subjectivism.Maria Carla Galavotti - 2011 - In Dov M. Gabby & John Woods (eds.), Handbook of the History of Logic: Inductive Logic. North Holland: Amsterdam. pp. 153--203.
  25. Bruno de Finetti and Imprecision.Paolo Vicig & Teddy Seidenfeld - unknown
    We review several of de Finetti’s fundamental contributions where these have played and continue to play an important role in the development of imprecise probability research. Also, we discuss de Finetti’s few, but mostly critical remarks about the prospects for a theory of imprecise probabilities, given the limited development of imprecise probability theory as that was known to him.
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  26. Rational Credences Are Private.Randall G. McCutcheon - manuscript
    Anti-expertise, or self-defeating belief, leads to incoherent personal credences. Some philosophers think that anti-expertise is irrational but avoidable, others think that some cases of anti-expertise are rational, and still others think that anti-expertise is irrational and unavoidable. Taking as premises some standard assumptions about the Sleeping Beauty Problem, I prove that if Beauty maintains public credences then she is prone to anti-expertise unless she embraces optimism, i.e. denies that she will experience multiple awakenings if tails.
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  27. HACKING, I. "The Emergence of Probability". [REVIEW]J. R. Lucas - 1977 - Mind 86:466.
  28. The Pragmatic Justification of Induction: A Critical Examination.Lewis Graham Creary - 1969 - Dissertation, Princeton University
    The dissertation is a detailed critique of the main elements of Hans Reichenbach's pragmatic treatment of the problem of induction. In the introductory Chapter I we give a broad overview of Reichenbach's theory of probability and induction, indicating that he approaches the problem of justifying inductive inference in general by attempting first to reduce all kinds of non-deductive reasoning to combinations of inferences in accordance with the rules of deductive logic together with RRI -- the "rule of induction." Having thus (...)
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  29. Probability and Human Rationality.Lyle David Zynda - 1995 - Dissertation, Princeton University
    I argue for the moderate probabilist view that probability theory plays much the same role in epistemology as does logic, and so is as indispensable to epistemology as is logic; but probability theory by itself does not constitute a theory of rational degree of belief, just as deductive logic does not by itself constitute a theory of rational belief. I defend a version of Ramsey's view that degrees of belief, which are defined using the notion of mathematical expectation, must obey (...)
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  30. Probability and Opinion: A Study in the Medieval Presuppositions of Post-Medieval Theories of Probability.Edmund F. Byrne (ed.) - 1968 - The Hague: Martinus Nijhoff.
    Recognizing that probability (the Greek doxa) was understood in pre-modern theories as the polar opposite of certainty (episteme), the author of this study elaborates the forms which these polar opposites have taken in some twentieth century writers and then, in greater detail, in the writings of Thomas Aquinas. Profiting from subsequent more sophisticated theories of probability, he examines how Aquinas’s judgments about everything from God to gossip depend on schematizations of the polarity between the systematic and the non-systematic: revelation/reason, science/opinion, (...)
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  31. Biased Coins: A Model for Higher-Order Probabilities.Jeanne Peijnenburg & David Atkinson - 2014 - In Maria Clara Galavotti, Elisabeth Nemeth & Friedrich Stadler (eds.), European Philosophy of Science: Philosophy of Science in Europe and the Vienna Heritage. 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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  32. Classical Probability in the Enlightenment. [REVIEW]Theodore Porter - 1989 - British Journal for the History of Science 22 (4):444-446.
  33. Probability in the Philosophy of Religion.D. H. Mellor - 2013 - Analysis 73 (3):548-554.
  34. The Carnapian Tolerance in the Foundations of Probability'.Wilhelm K. Essler - 1984 - Epistemologia 7:171-190.
  35. Varieties of Subjective-Probability.Rs Lockhart - 1992 - Bulletin of the Psychonomic Society 30 (6):483-483.
  36. It All Adds Up: The Dynamic Coherence of Radical Probabilism It All Adds Up: The Dynamic Coherence of Radical Probabilism (Pp. S98-S103). [REVIEW]S. L. Zabell - 2002 - Philosophy of Science 69 (S3):S98-S103.
    Brian Skyrms (1987, 1990, 1993, 1997) has discussed the role of dynamic coherence arguments in the theory of personal or subjective probability. In particular, Skryms (1997) both reviews and discusses the utility of martingale arguments in establishing the convergence of beliefs within the context of radical probabilism. The classical martingale converence theorem, however, assumes the countable additivity of the underlying probability measure; an assumption rejected by some subjectivists such as Bruno de Finetti (see, e.g., de Finetti 1930 and 1972). This (...)
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  37. On the Probability of Particular Events.Alfred Jules Ayer - 1961 - Revue Internationale de Philosophie 15 (58):366-75.
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  38. On Representation of Source Reliability in Weight of Evidence.Daniel E. O'Leary - 1991 - In B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.), Uncertainty in Knowledge Bases. Springer. pp. 115--123.
  39. Fronting in Dutch.Jan G. Kooij - 1978 - In Frank Jansen (ed.), Studies on Fronting. Peter de Ridder Press.
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  40. De Finetti's Generalizations of Exchangeability.Persi Diaconis & David Freedman - 1980 - In Richard C. Jeffrey (ed.), Studies in Inductive Logic and Probability. Berkeley: University of California Press. pp. 2--233.
  41. Factors Determining the Probability of Recollection of Intraoperative Events.L. Goldman - 1990 - In B. Bonke, W. Fitch & K. Millar (eds.), Memory and Awareness in Anesthesia. Swets & Zeitlinger. pp. 45--9.
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  42. Philosophical Foundations of Probability.Hans Reichenbach - 1996 - In Sahotra Sarkar (ed.), Logic, Probability, and Epistemology: The Power of Semantics. Garland Pub. Co.. pp. 3--115.
  43. From Probabilities to Percepts.Bjorn Merker - 2012 - In Shimon Edelman, Tomer Fekete & Neta Zach (eds.), Being in Time: Dynamical Models of Phenomenal Experience. John Benjamins. pp. 88--37.
  44. Reinforcement Probability and Concurrent Operants.Jordan Rosenberg - 1974 - Bulletin of the Psychonomic Society 4 (6):582-584.
  45. 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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  46. 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.
  47. "Boekbalie" — a Unique Dutch Website.Adriaan Langendonk - 2006 - Logos. Anales Del Seminario de Metafísica [Universidad Complutense de Madrid, España] 17 (4):198-200.
  48. Relative Importance of Probabilities and Payoffs in Risk Taking.Paul Slovic & Sarah Lichtenstein - 1968 - Journal of Experimental Psychology 78 (3p2):1.
  49. 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.
  50. Reichenbachian Common Cause Systems of Arbitrary Finite Size Exist.Gábor Hofer-Szabó & Miklós Rédei - 2006 - Foundations of Physics 36 (5):745-756.
    A partition $\{C_i\}_{i\in I}$ of a Boolean algebra Ω in a probability measure space (Ω, p) is called a Reichenbachian common cause system for the correlation between a pair A,B of events in Ω if any two elements in the partition behave like a Reichenbachian common cause and its complement; the cardinality of the index set I is called the size of the common cause system. It is shown that given any non-strict correlation in (Ω, p), and given any finite (...)
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