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  1. 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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  2. 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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  3. 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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  4. 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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  5. 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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  6. Henry E. Kyburg Jr (1983). Levi, Petersen, and Direct Inference. Philosophy of Science 50 (4):630-634.
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  7. Stephen Leeds (1994). A Note on Pollock's System of Direct Inference. Theory and Decision 36 (3):247-256.
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  8. Stephen Leeds (1985). Postscript to 'a Problem About Frequencies in Direct Inference'. Philosophical Studies 48 (1):149 - 152.
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  9. 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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  10. Isaac Levi (2001). Objective Modality and Direct Inference. The Monist 84 (2):179-207.
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  11. 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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  12. Hanti Lin & Kevin T. Kelly (2012). A Geo-Logical Solution to the Lottery Paradox, with Applications to Conditional Logic. Synthese 186 (2):531-575.
  13. P. J. M. (1966). Studies in Subjective Probability. Review of Metaphysics 19 (3):611-611.
  14. Timothy McGrew (2001). Direct Inference and the Problem of Induction. The Monist 84 (2):153-178.
  15. 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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  16. G.�Nter Menges (1970). On Subjective Probability and Related Problems. Theory and Decision 1 (1):40-60.
  17. 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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  18. 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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  19. 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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  20. 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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  21. John L. Pollock (1994). Foundations for Direct Inference. Theory and Decision 17 (3):221-255.
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  22. 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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  23. 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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  24. John L. Pollock (1983). A Theory of Direct Inference. Theory and Decision 15 (1):29-95.
  25. 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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  26. Teddy Seidenfeld (1978). Direct Inference and Inverse Inference. Journal of Philosophy 75 (12):709-730.
    The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org.
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  27. Mark Stone (1987). Kyburg, Levi, and Petersen. Philosophy of Science 54 (2):244-255.
    In this paper I attempt to tie together a longstanding dispute between Henry Kyburg and Isaac Levi concerning statistical inferences. The debate, which centers around the example of Petersen the Swede, concerns Kyburg's and Levi's accounts of randomness and choosing reference classes. I argue that both Kyburg and Levi have missed the real significance of their dispute, that Levi's claim that Kyburg violates Confirmational Conditionalization is insufficient, and that Kyburg has failed to show that Levi's criteria for choosing reference class (...)
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  28. Paul D. Thorn (2013). Defeasible Conditionalization. Journal of Philosophical Logic:1-20.
    The applicability of Bayesian conditionalization in setting one’s posterior probability for a proposition, α, is limited to cases where the value of a corresponding prior probability, PPRI(α|∧E), is available, where ∧E represents one’s complete body of evidence. In order to extend probability updating to cases where the prior probabilities needed for Bayesian conditionalization are unavailable, I introduce an inference schema, defeasible conditionalization, which allows one to update one’s personal probability in a proposition by conditioning on a proposition that represents a (...)
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  29. Paul D. Thorn (2012). Two Problems of Direct Inference. Erkenntnis 76 (3):299-318.
    The article begins by describing two longstanding problems associated with direct inference. One problem concerns the role of uninformative frequency statements in inferring probabilities by direct inference. A second problem concerns the role of frequency statements with gerrymandered reference classes. I show that past approaches to the problem associated with uninformative frequency statements yield the wrong conclusions in some cases. I propose a modification of Kyburg’s approach to the problem that yields the right conclusions. Past theories of direct inference have (...)
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  30. Paul D. Thorn (2011). Undercutting Defeat Via Reference Properties of Differing Arity: A Reply to Pust. Analysis 71 (4):662-667.
    In a recent article, Joel Pust argued that direct inference based on reference properties of differing arity are incommensurable, and so direct inference cannot be used to resolve the Sleeping Beauty problem. After discussing the defects of Pust's argument, I offer reasons for thinking that direct inferences based on reference properties of differing arity are commensurable, and that we should prefer direct inferences based on logically stronger reference properties, regardless of arity.
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  31. Paul D. Thorn (2007). Three Problems of Direct Inference. Dissertation, University of Arizona
  32. Paul D. Thorn (2007). The Trouble with Pollock’s Principle of Agreement. The Reasoner 1 (8):9-10.