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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. 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. -/- Suitable for researchers, lecturers and students in statistics and the history of science this book is aimed at those who have had some exposure to statistical theory. It is also useful to logicians and philosophers (...)
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  3. 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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  4. 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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  5. 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.
    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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  6. James H. Fetzer (1977). Reichenbach, Reference Classes, and Single Case 'Probabilities'. Synthese 34 (2):185 - 217.
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  7. 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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  8. 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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  9. 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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  10. 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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  11. 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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  12. 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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  13. 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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  14. 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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  15. Henry E. Kyburg Jr (1983). Levi, Petersen, and Direct Inference. Philosophy of Science 50 (4):630-634.
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  16. Henry E. Kyburg Jr (1977). Randomness and the Right Reference Class. Journal of Philosophy 74 (9):501-521.
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  17. Henry E. Kyburg Jr (1970). More on Maximal Specificity. Philosophy of Science 37 (2):295-300.
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  18. He Kyburg (1985). A Problem About Frequencies in Direct Inference-Reply to Leeds. Philosophical Studies 48 (1):145-148.
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  19. Henry E. Kyburg (1985). Another Reply to Leeds. Philosophical Studies 48 (1):145 - 148.
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  20. Henry E. Kyburg (1963). Probability and Randomness. Theoria 29 (1):27-55.
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  21. Stephen Leeds (1994). A Note on Pollock's System of Direct Inference. Theory and Decision 36 (3):247-256.
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  22. Stephen Leeds (1985). Postscript to 'a Problem About Frequencies in Direct Inference'. Philosophical Studies 48 (1):149 - 152.
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  23. 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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  24. Isaac Levi (2001). Objective Modality and Direct Inference. The Monist 84 (2):179-207.
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  25. 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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  26. 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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  27. Isaac Levi (1977). Direct Inference. Journal of Philosophy 74 (1):5-29.
  28. Hanti Lin & Kevin T. Kelly (2012). A Geo-Logical Solution to the Lottery Paradox, with Applications to Conditional Logic. Synthese 186 (2):531-575.
  29. P. J. M. (1966). Studies in Subjective Probability. Review of Metaphysics 19 (3):611-611.
  30. Timothy McGrew (2001). Direct Inference and the Problem of Induction. The Monist 84 (2):153-178.
  31. D. H. Mellor, Articles.
    Isaac Levi's principle of direct inference, from an agent's knowledge of a chance to that agent's corresponding credence, is central to his account of chance. He holds moreover that this principle shows the 'gratuitous, diversionary and obscurantist character' of frequency, propensity and other metaphysical theories of what chances are. In this contribution to Levi's Festschrift, I argue that, on the contrary, his direct inference principle commits him to just such a theory, the propensity theory.
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  32. G.�Nter Menges (1970). On Subjective Probability and Related Problems. Theory and Decision 1 (1):40-60.
  33. 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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  34. James Willard Oliver (1953). Deduction and the Statistical Syllogism. Journal of Philosophy 50 (26):805-807.
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  35. Jl Pollock (1985). A Problem About Frequencies in Direct Inference-Reply to Leeds. Philosophical Studies 48 (1):141-144.
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  36. John Pollock, Probable Probabilities.
    In concrete applications of probability, statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q&R), and we may not have the data required to assess that directly. The probability calculus is of no help here. Given prob(P/Q) and prob(P/R), it is consistent with the probability calculus (...)
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  37. John Pollock, Direct Inference and Probable Probabilities.
    New results in the theory of nomic probability have led to a theory of probable probabilities, which licenses defeasible inferences between probabilities that are not validated by the probability calculus. Among these are classical principles of direct inference together with some new more general principles that greatly strengthen direct inference and make it much more useful.
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  38. John Pollock, The y-Function.
    Direct inference derives values for definite (single-case) probabilities from those of related indefinite (general) probabilities. But direct inference is less useful than might be supposed, because we often have too much information, with the result that we can make conflicting direct inferences, and hence they all undergo collective defeat, leaving us without any conclusion to draw about the value of the definite probabilities. This paper presents reason for believing that there is a function — the Y- function — that can (...)
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  39. John Pollock, Joint Probabilities.
    When combining information from multiple sources and attempting to estimate the probability of a conclusion, we often find ourselves in the position of knowing the probability of the conclusion conditional on each of the individual sources, but we have no direct information about the probability of the conclusion conditional on the combination of sources. The probability calculus provides no way of computing such joint probabilities. This paper introduces a new way of combining probabilistic information to estimate joint probabilities. It is (...)
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  40. John Pollock (2011). Reasoning Defeasibly About Probabilities. Synthese 181 (2):317 - 352.
    In concrete applications of probability, statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q& R), and we may not have the data required to assess that directly. The probability calculus is of no help here. Given prob(P/Q) and prob(P/R), it is consistent with the probability (...)
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  41. John Pollock (1992). The Theory of Nomic Probability. Synthese 90 (2):263 - 299.
    This article sketches a theory of objective probability focusing on "nomic probability", which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the "statistical syllogism". It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of induction. The theory of induction (...)
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  42. John L. Pollock, Probabilities for AI.
    Probability plays an essential role in many branches of AI, where it is typically assumed that we have a complete probability distribution when addressing a problem. But this is unrealistic for problems of real-world complexity. Statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q&R), and (...)
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  43. John L. Pollock (1994). Foundations for Direct Inference. Theory and Decision 17 (3):221-255.
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  44. John L. Pollock (1992). The Theory of Nomic Probability. Synthese 90 (2):263 - 299.
    This article sketches a theory of objective probability focusing on nomic probability, which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the statistical syllogism. It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of induction. The theory of induction (...)
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  45. John L. Pollock (1991). How to Use Probabilities in Reasoning. Philosophical Studies 64 (1):65 - 85.
    Probabilities are important in belief updating, but probabilistic reasoning does not subsume everything else (as the Bayesian would have it). On the contrary, Bayesian reasoning presupposes knowledge that cannot itself be obtained by Bayesian reasoning, making generic Bayesianism an incoherent theory of belief updating. Instead, it is indefinite probabilities that are of principal importance in belief updating. Knowledge of such indefinite probabilities is obtained by some form of statistical induction, and inferences to non-probabilistic conclusions are carried out in accordance with (...)
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  46. John L. Pollock (1990). Nomic Probability and the Foundations of Induction. Oxford University Press.
    In this book Pollock deals with the subject of probabilistic reasoning, making general philosophical sense of objective probabilities and exploring their ...
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  47. John L. Pollock (1983). A Theory of Direct Inference. Theory and Decision 15 (1):29-95.
  48. Joel Pust (2011). Sleeping Beauty and Direct Inference. Analysis 71 (2):290-293.
    One argument for the thirder position on the Sleeping Beauty problem rests on direct inference from objective probabilities. In this paper, I consider a particularly clear version of this argument by John Pollock and his colleagues (The Oscar Seminar 2008). I argue that such a direct inference is defeated by the fact that Beauty has an equally good reason to conclude on the basis of direct inference that the probability of heads is 1/2. Hence, neither thirders nor halfers can find (...)
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  49. W. C. S. (1978). Erratum: Objectively Homogeneous Reference Classes. Synthese 37 (2):253 -.
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  50. Wesley C. Salmon (1977). Objectively Homogeneous Reference Classes. Synthese 36 (4):399 - 414.
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