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  1. Jonathan E. Adler (1991). Double Standards, Racial Equality and the Right Reference Class. Journal of Applied Philosophy 8 (1):69-82.
  2. Max Albert (2005). Should Bayesians Bet Where Frequentists Fear to Tread? Philosophy of Science 72 (4):584-593.
  3. Peter Baumann (2005). Three Doors, Two Players, and Single-Case Probabilities. American Philosophical Quarterly 42 (1):71 - 79.
    The well known Monty Hall-problem has a clear solution if one deals with a long enough series of individual games. However, the situation is different if one switches to probabilities in a single case. This paper presents an argument for Monty Hall situations with two players (not just one, as is usual). It leads to a quite general conclusion: One cannot apply probabilistic considerations (for or against any of the strategies) to isolated single cases. If one does that, one cannot (...)
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  4. Lara Buchak (2013). Belief, Credence, and Norms. Philosophical Studies 2:1-27.
    There are currently two robust traditions in philosophy dealing with doxastic attitudes: the tradition that is concerned primarily with all-or-nothing belief, and the tradition that is concerned primarily with degree of belief or credence. This paper concerns the relationship between belief and credence for a rational agent, and is directed at those who may have hoped that the notion of belief can either be reduced to credence or eliminated altogether when characterizing the norms governing ideally rational agents. It presents a (...)
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  5. Shoutir Kishore Chatterjee (2003). Statistical Thought: A Perspective and History. OUP Oxford.
    In this unique monograph, based on years of extensive work, Chatterjee presents the historical evolution of statistical thought from the perspective of various approaches to statistical induction. Developments in statistical concepts and theories are discussed alongside philosophical ideas on the ways we learn from experience.
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  6. Edward K. Cheng (2009). A Practical Solution to the Reference Class Problem. Columbia Law Review 109 (8).
    The “reference class problem” is a serious challenge to the use of statistical evidence that arises in a wide variety of cases, including toxic torts, property valuation, and even drug smuggling. At its core, it observes that statistical inferences depend critically on how people, events, or things are classified. As there is (purportedly) no principle for privileging certain categories over others, statistics become manipulable, undermining the very objectivity and certainty that make statistical evidence valuable and attractive to legal actors. In (...)
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  7. Edward K. Cheng (2009). Law, Statistics, and the Reference Class Problem. Columbia Law Review, Sidebar 109.
    Preview of: Edward K. Cheng, A Practical Solution to the Reference Class Problem, 109 Colum. L. Rev. (forthcoming Dec. 2009).
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  8. Timothy Childers ( 2012). Objectifying Subjective Probabilities: Dutch Book Arguments for Principles of Direct Inference. In Probabilities, Laws, and Structures.
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  9. L. J. Cohen (1981). Subjective Probability and the Paradox of the Gatecrasher. Arizona State Law Journal 2 (2).
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  10. Mark Colyvan, Legal Decisions and the Reference-Class Problem.
    There has been a long history of discussion on the usefulness of formal methods in legal settings.1 Some of the recent debate has focussed on foundational issues in statistics, in particular, how the reference-class problem affects legal decisions based on certain types of statistical evidence.2 Here we examine aspects of this debate, stressing why the reference-class problem presents serious difficulties for the kinds of statistical inferences under consideration and the relevance of this for the use of statistics in the courtroom. (...)
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  11. Mark Colyvan, Helen M. Regan & Scott Ferson (2001). Is It a Crime to Belong to a Reference Class. Journal of Political Philosophy 9 (2):168–181.
    ON DECEMBER 10, 1991 Charles Shonubi, a Nigerian citizen but a resident of the USA, was arrested at John F. Kennedy International Airport for the importation of heroin into the United States.1 Shonubi's modus operandi was ``balloon swallowing.'' That is, heroin was mixed with another substance to form a paste and this paste was sealed in balloons which were then swallowed. The idea was that once the illegal substance was safely inside the USA, the smuggler would pass the balloons and (...)
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  12. I. Douven (2012). The Sequential Lottery Paradox. Analysis 72 (1):55-57.
    The Lottery Paradox is generally thought to point at a conflict between two intuitive principles, to wit, that high probability is sufficient for rational acceptability, and that rational acceptability is closed under logical derivability. Gilbert Harman has offered a solution to the Lottery Paradox that allows one to stick to both of these principles. The solution requires the principle that acceptance licenses conditionalization. The present study shows that adopting this principle alongside the principle that high probability is sufficient for rational (...)
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  13. Igor Douven (2012). The Lottery Paradox and the Pragmatics of Belief. Dialectica 66 (3):351-373.
    The thesis that high probability suffices for rational belief, while initially plausible, is known to face the Lottery Paradox. The present paper proposes an amended version of that thesis which escapes the Lottery Paradox. The amendment is argued to be plausible on independent grounds.
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  14. Ian Evans, Don Fallis, Peter Gross, Terry Horgan, Jenann Ismael, John Pollock, Paul D. Thorn, Jacob N. Caton, Adam Arico, Daniel Sanderman, Orlin Vakerelov, Nathan Ballantyne, Matthew S. Bedke, Brian Fiala & Martin Fricke (2007). An Objectivist Argument for Thirdism. Analysis 68 (2):149-155.
    Bayesians take “definite” or “single-case” probabilities to be basic. Definite probabilities attach to closed formulas or propositions. We write them here using small caps: PROB(P) and PROB(P/Q). Most objective probability theories begin instead with “indefinite” or “general” probabilities (sometimes called “statistical probabilities”). Indefinite probabilities attach to open formulas or propositions. We write indefinite probabilities using lower case “prob” and free variables: prob(Bx/Ax). The indefinite probability of an A being a B is not about any particular A, but rather about the (...)
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  15. James H. Fetzer (1977). Reichenbach, Reference Classes, and Single Case 'Probabilities'. Synthese 34 (2):185 - 217.
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  16. Bas C. Van Fraassen (1980). Rational Belief and Probability Kinematics. Philosophy of Science 47 (2):165-187.
    A general form is proposed for epistemological theories, the relevant factors being: the family of epistemic judgments, the epistemic state, the epistemic commitment, and the family of possible epistemic inputs. First a simple theory is examined in which the states are probability functions, and the subject of probability kinematics introduced by Richard Jeffrey is explored. Then a second theory is examined in which the state has as constituents a body of information and a recipe that determines the accepted epistemic judgments (...)
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  17. J. Franklin (2001). Resurrecting Logical Probability. Erkenntnis 55 (2):277-305.
    The logical interpretation of probability, or ``objective Bayesianism''''– the theory that (some) probabilitiesare strictly logical degrees of partial implication – is defended.The main argument against it is that it requires the assignment ofprior probabilities, and that any attempt to determine them by symmetryvia a ``principle of insufficient reason'''' inevitably leads to paradox.Three replies are advanced: that priors are imprecise or of little weight, sothat disagreement about them does not matter, within limits; thatit is possible to distinguish reasonable from unreasonable priorson (...)
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  18. Ori Friedman & John Turri (2015). Is Probabilistic Evidence a Source of Knowledge? Cognitive Science 39 (5):1062-1080.
    We report a series of experiments examining whether people ascribe knowledge for true beliefs based on probabilistic evidence. Participants were less likely to ascribe knowledge for beliefs based on probabilistic evidence than for beliefs based on perceptual evidence or testimony providing causal information. Denial of knowledge for beliefs based on probabilistic evidence did not arise because participants viewed such beliefs as unjustified, nor because such beliefs leave open the possibility of error. These findings rule out traditional philosophical accounts for why (...)
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  19. Alan Hájek (2007). The Reference Class Problem is Your Problem Too. Synthese 156 (3):563--585.
    The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference (...)
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  20. Howard Hugh Harriott (1988). Levi and the Defense of Bayesianism. Dissertation, The University of Rochester
    Bayesianism as an intellectual movement promises much, if the views of some statisticians and some philosophers are to be believed. But increasingly, the pat answers to the problems raised by the critics cannot stand up to philosophical scrutiny. While the formalism of Bayesianism is easy to understand, its interpretation is less clear. I take Professor Isaac Levi's work The Enterprise of Knowledge to be the most philosophically satisfactory defense of Bayesianism which remains faithful to an objective view of scientific practice. (...)
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  21. James Hawthorne, Jürgen Landes, Christian Wallmann & Jon Williamson (forthcoming). The Principal Principle Implies the Principle of Indifference. British Journal for the Philosophy of Science:axv030.
    We argue that David Lewis’s principal principle implies a version of the principle of indifference. The same is true for similar principles that need to appeal to the concept of admissibility. Such principles are thus in accord with objective Bayesianism, but in tension with subjective Bayesianism. 1 The Argument2 Some Objections Met.
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  22. Carl G. Hempel (1968). Maximal Specificity and Lawlikeness in Probabilistic Explanation. Philosophy of Science 35 (2):116-133.
    The article is a reappraisal of the requirement of maximal specificity (RMS) proposed by the author as a means of avoiding "ambiguity" in probabilistic explanation. The author argues that RMS is not, as he had held in one earlier publication, a rough substitute for the requirement of total evidence, but is independent of it and has quite a different rationale. A group of recent objections to RMS is answered by stressing that the statistical generalizations invoked in probabilistic explanations must be (...)
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  23. Colin Howson (2012). Modelling Uncertain Inference. Synthese 186 (2):475-492.
    Kyburg’s opposition to the subjective Bayesian theory, and in particular to its advocates’ indiscriminate and often questionable use of Dutch Book arguments, is documented and much of it strongly endorsed. However, it is argued that an alternative version, proposed by both de Finetti at various times during his long career, and by Ramsey, is less vulnerable to Kyburg’s misgivings. This is a logical interpretation of the formalism, one which, it is argued, is both more natural and also avoids other, widely-made (...)
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  24. Manfred Jaeger (2005). A Logic for Inductive Probabilistic Reasoning. Synthese 144 (2):181 - 248.
    Inductive probabilistic reasoning is understood as the application of inference patterns that use statistical background information to assign (subjective) probabilities to single events. The simplest such inference pattern is direct inference: from “70% of As are Bs” and “a is an A” infer that a is a B with probability 0.7. Direct inference is generalized by Jeffrey’s rule and the principle of cross-entropy minimization. To adequately formalize inductive probabilistic reasoning is an interesting topic for artificial intelligence, as an autonomous system (...)
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  25. Henry E. Kyburg Jr (2001). Probability as a Guide in Life. The Monist 84 (2):135 - 152.
    Bishop Butler, [Butler, 1736], said that probability was the very guide of life. But what interpretations of probability can serve this function? It isn't hard to see that empirical (frequency) views won't do, and many recent writers—for example John Earman, who has said that Bayesianism is "the only game in town"—have been persuaded by various dutch book arguments that only subjective probability will perform the function required. We will defend the thesis that probability construed in this way offers very little (...)
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  26. Kyriakos N. Kotsoglou (2013). ,,Shonubi" revisited: Begründet die Zugehörigkeit zu einer Referenzklasse einen Schadensersatzanspruch? Archiv Fuer Rechts- Und Sozialphilosphie 99 (2):241-251.
    Nearly 20 years after the Shonubi case and an extended discussion in the Anglophone world on the admissibility and probative force of statistical evidence, the labour courts of Germany seem not to have learned a simple lesson: aleatory probabilities are not informative for the individual in question. In this paper I argue that innumeracy (that is the lack of ability to understand and apply simple numerical concepts) is underestimated – if not ignored – both within the German jurisprudence and legal (...)
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  27. Henry E. Kyburg Jr (2001). Probability as a Guide in Life. The Monist 84 (2):135-152.
    Bishop Butler, [Butler, 1736], said that probability was the very guide of life. But what interpretations of probability can serve this function? It isn’t hard to see that empirical (frequency) views won’t do, and many recent writers-for example John Earman, who has said that Bayesianism is “the only game in town”-have been persuaded by various dutch book arguments that only subjective probability will perform the function required. We will defend the thesis that probability construed in this way offers very little (...)
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  28. Henry E. Kyburg Jr (1983). Levi, Petersen, and Direct Inference. Philosophy of Science 50 (4):630-634.
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  29. Henry E. Kyburg Jr (1983). The Reference Class. Philosophy of Science 50 (3):374-397.
    The system presented by the author in The Logical Foundations of Statistical Inference (Kyburg 1974) suffered from certain technical difficulties, and from a major practical difficulty; it was hard to be sure, in discussing examples and applications, when you had got hold of the right reference class. The present paper, concerned mainly with the characterization of randomness, resolves the technical difficulties and provides a well structured framework for the choice of a reference class. The definition of randomness that leads to (...)
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  30. Henry E. Kyburg Jr (1977). Randomness and the Right Reference Class. Journal of Philosophy 74 (9):501-521.
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  31. Henry E. Kyburg Jr (1970). More on Maximal Specificity. Philosophy of Science 37 (2):295-300.
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  32. He Kyburg (1985). A Problem About Frequencies in Direct Inference-Reply to Leeds. Philosophical Studies 48 (1):145-148.
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  33. Henry E. Kyburg (1985). Another Reply to Leeds. Philosophical Studies 48 (1):145 - 148.
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  34. Henry E. Kyburg (1963). Probability and Randomness. Theoria 29 (1):27-55.
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  35. Stephen Leeds (1994). A Note on Pollock's System of Direct Inference. Theory and Decision 36 (3):247-256.
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  36. Stephen Leeds (1985). Postscript to 'a Problem About Frequencies in Direct Inference'. Philosophical Studies 48 (1):149 - 152.
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  37. Stephen Leeds (1981). Kyburg and Fiducial Inference. Philosophy of Science 48 (1):78-91.
  38. Stephen Leeds, John L. Pollock & Henry E. Kyburg (1985). A Problem About Frequencies in Direct Inference. Philosophical Studies 48 (1):137 - 140.
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  39. Isaac Levi (2001). Objective Modality and Direct Inference. The Monist 84 (2):179-207.
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  40. Isaac Levi (1982). Direct Inference and Randomization. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1982:447 - 463.
    There are two uses of randomization in efforts to control systematic bias in experimental design: (a) Alchemical uses seek to convert unavoidable systematic errors into random errors. (b) Hygienic uses seek to reduce the prospect of the experimenter's involvement with the implementation of the experiment contributing to bias. A few remarks are made at the end of the paper about the hygienic use of randomization as a preventative against sticky fingers. The bulk of the discussion addresses the alchemical applications. The (...)
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  41. Isaac Levi (1981). Direct Inference and Confirmational Conditionalization. Philosophy of Science 48 (4):532-552.
    The article responds to some of the points raised by B. van Fraassen concerning probability kinematics and direct inference within the framework of the approach to the revision of probability judgment proposed by Levi in The Enterprise of Knowledge. In particular, the critical importance of the question of direct inference is emphasized and explained.
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  42. Isaac Levi (1977). Direct Inference. Journal of Philosophy 74 (1):5-29.
  43. David Lewis (1980). A Subjectivist's Guide to Objective Chance. In Richard C. Jeffrey (ed.), Studies in Inductive Logic and Probability. University of California Press 83--132.
  44. Hanti Lin & Kevin T. Kelly (2012). A Geo-Logical Solution to the Lottery Paradox, with Applications to Conditional Logic. Synthese 186 (2):531-575.
  45. P. J. M. (1966). Studies in Subjective Probability. Review of Metaphysics 19 (3):611-611.
  46. Timothy McGrew (2001). Direct Inference and the Problem of Induction. The Monist 84 (2):153-178.
  47. GÜnter Menges (1970). On Subjective Probability and Related Problems. Theory and Decision 1 (1):40.
  48. Bradley Monton (2002). Sleeping Beauty and the Forgetful Bayesian. Analysis 62 (1):47–53.
    1. Consider the case of Sleeping Beauty: on Sunday she is put to sleep, and she knows that on Monday experimenters will wake her up, and then put her to sleep with a memory-erasing drug that causes her to forget that waking-up. The researchers will then flip a fair coin; if the result is Heads, they will allow her to continue to sleep, and if the result is Tails, they will wake her up again on Tuesday. Thus, when she is (...)
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  49. Martine Nida-Rümelin (1993). Probability and Direct Reference: Three Puzzles of Probability Theory: The Problem of the Two Boys, Freund's Problem and the Problem of the Three Prisoners. Erkenntnis 39 (1):51 - 78.
    I discuss three puzzles of probability theory which seem connected with problems of direct reference and rigid designation. The resolution of at least one of them requires referential use of definite descriptions in probability statements. I argue that contrary to common opinion all these puzzles are in a way still unsolved: They seem to exemplify cases in which a change of probabilities is rationally required, even though any specific change presupposes unjustified assumptions.
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  50. James Willard Oliver (1953). Deduction and the Statistical Syllogism. Journal of Philosophy 50 (26):805-807.
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