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Philosophy of Probability

Edited by Darrell Rowbottom (Lingnan University)
Assistant editor: Joshua Luczak (University of Western Ontario)
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  1. A. R. A. (1957). Probability in Logic. Review of Metaphysics 11 (2):348-348.
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  2. A. R. A. (1956). Risk and Gambling. Review of Metaphysics 10 (1):174-174.
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  3. Andre Ariew (2009). What Fitness Can't Be. Erkenntnis 71 (3):289 - 301.
    Recently advocates of the propensity interpretation of fitness have turned critics. To accommodate examples from the population genetics literature they conclude that fitness is better defined broadly as a family of propensities rather than the propensity to contribute descendants to some future generation. We argue that the propensity theorists have misunderstood the deeper ramifications of the examples they cite. These examples demonstrate why there are factors outside of propensities that determine fitness. We go on to argue for the more general (...)
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  4. Horacio Arlo-Costa & Jeffrey Helzner, Iterated Random Selection as Intermediate Between Risk and Uncertainty.
    In (Hertwig et al. , 2003) Hertwig et al. draw a distinction between decisions from experience and decisions from description. In a decision from experience an agent does not have a summary description of the possible outcomes or their likelihoods. A career choice, deciding whether to back up a computer hard drive, cross a busy street, etc., are typical examples of decisions from experience. In such decisions agents can rely only of their encounters with the corresponding prospects. By contrast, an (...)
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  5. Horacio Arlo-Costa & Richmond H. Thomason, Iterative Probability Kinematics.
    Following the pioneer work of Bruno De Finetti, conditional probability spaces (allowing for conditioning with events of measure zero) have been studied since (at least) the 1950's.
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  6. David Atkinson & Jeanne Peijnenburg (2006). Probability All the Way Up. Synthese 153 (2):187 - 197.
    Richard Jeffrey's radical probabilism ('probability all the way down') is augmented by the claim that probability cannot be turned into certainty, except by data that logically exclude all alternatives. Once we start being uncertain, no amount of updating will free us from the treadmill of uncertainty. This claim is cast first in objectivist and then in subjectivist terms.
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  7. Gergely Bana & Thomas Durt (1997). Proof of Kolmogorovian Censorship. Foundations of Physics 27 (10):1355-1373.
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  8. Dror Bar-Natan (1989). Two Examples in Noncommutative Probability. Foundations of Physics 19 (1):97-104.
    A simple noncommutative probability theory is presented, and two examples for the difference between that theory and the classical theory are shown. The first example is the well-known formulation of the Heisenberg uncertainty principle in terms of a variance inequality and the second example is an interpretatio of the Bell paradox in terms of noncommuntative probability.
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  9. Jean Baratgin, David E. Over & Guy Politzer (2011). Betting on Conditionals. Thinking and Reasoning 16 (3):172-197.
    A study is reported testing two hypotheses about a close parallel relation between indicative conditionals, if A then B , and conditional bets, I bet you that if A then B . The first is that both the indicative conditional and the conditional bet are related to the conditional probability, P(B|A). The second is that de Finetti's three-valued truth table has psychological reality for both types of conditional— true , false , or void for indicative conditionals and win , lose (...)
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  10. Howard Barnum, Carl Philipp Gaebler & Alexander Wilce (2013). Ensemble Steering, Weak Self-Duality, and the Structure of Probabilistic Theories. Foundations of Physics 43 (12):1411-1427.
    In any probabilistic theory, we say that a bipartite state ω on a composite system AB steers its marginal state ω B if, for any decomposition of ω B as a mixture ω B =∑ i p i β i of states β i on B, there exists an observable {a i } on A such that the conditional states $\omega_{B|a_{i}}$ are exactly the states β i . This is always so for pure bipartite states in quantum mechanics, a fact (...)
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  11. David Bellhouse (1996). Book Reviews. [REVIEW] Philosophia Mathematica 4 (3):290-291.
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  12. Joseph Louis François Bertrand (1888). Calcul des Probabilités. Gauthier-Villars Et Fils.
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  13. John Bigelow & Robert Pargetter (1987). An Analysis of Indefinite Probability Statements. Synthese 73 (2):361 - 370.
    An analysis of indefinite probability statements has been offered by Jackson and Pargetter (1973). We accept that this analysis will assign the correct probability values for indefinite probability claims. But it does so in a way which fails to reflect the epistemic state of a person who makes such a claim. We offer two alternative analyses: one employing de re (epistemic) probabilities, and the other employing de dicto (epistemic) probabilities. These two analyses appeal only to probabilities which are accessible to (...)
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  14. Jean-Francois Bonnefon & Denis J. Hilton (2002). The Suppression of Modus Ponens as a Case of Pragmatic Preconditional Reasoning. Thinking and Reasoning 8 (1):21 – 40.
    The suppression of the Modus Ponens inference is described as a loss of confidence in the conclusion C of an argument ''If A1 then C; If A2 then C; A1'' where A2 is a requirement for C to happen. It is hypothesised that this loss of confidence is due to the derivation of the conversational implicature ''there is a chance that A2 might not be satisfied'', and that different syntactic introductions of the requirement A2 (e.g., ''If C then A2'') will (...)
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  15. R. Bradley (2012). Multidimensional Possible-World Semantics for Conditionals. Philosophical Review 121 (4):539-571.
    Adams’s Thesis, the claim that the probabilities of indicative conditionals equal the conditional probabilities of their consequents given their antecedents, has proven impossible to accommodate within orthodox possible-world semantics. This essay proposes a modification to the orthodoxy that removes this impossibility. The starting point is a proposal by Jeffrey and Stalnaker that conditionals take semantic values in the unit interval, interpreting these (à la McGee) as their expected truth-values at a world. Their theories imply a false principle, namely, that the (...)
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  16. B. C. (1982). Philosophical Problems of Statistical Inference. Review of Metaphysics 35 (4):907-909.
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  17. Rolando Chuaqui (1991). Truth, Possibility and Probability: New Logical Foundations of Probability and Statistical Inference Vol. 166. Access Online Via Elsevier.
    This unique book presents a new interpretation of probability, rooted in the traditional interpretation that was current in the 17th and 18th centuries.
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  18. Co-Authored & Helen Beebee (2003). Probability as a Guide to Life. In David Papineau (ed.), The Roots of Reason: Philosophical Essays on Rationality, Evolution, and Probability. Oxford University Press.
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  19. R. Eugene Collins (1977). Quantum Theory: A Hilbert Space Formalism for Probability Theory. [REVIEW] Foundations of Physics 7 (7-8):475-494.
    It is shown that the Hilbert space formalism of quantum mechanics can be derived as a corrected form of probability theory. These constructions yield the Schrödinger equation for a particle in an electromagnetic field and exhibit a relationship of this equation to Markov processes. The operator formalism for expectation values is shown to be related to anL 2 representation of marginal distributions and a relationship of the commutation rules for canonically conjugate observables to a topological relationship of two manifolds is (...)
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  20. Allan Combs (1996). Synchronicity: Science, Myth, and the Trickster. Marlowe & Co..
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  21. D. R. Cousin (1954). Probability. Philosophical Quarterly 4 (14):82-84.
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  22. Mark R. Crovelli, 9. “All Probabilistic Methods Assume a Subjective Definition of Probability”.
    In previous publications on probability, I have followed I.J. Good in arguing that probability must be defined subjectively if we accept that the world is causally deterministic. In this article I go significantly beyond this position, arguing that we are forced to accept a subjective definition of probability if we [...].
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  23. Simon D'Alfonso (2014). Review of 'Quitting Certainties'. [REVIEW] Philosophy in Review 34:34-36.
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  24. David W. Green David, E. Over Robin & A. Pyne (1997). Probability and Choice in the Selection Task. Thinking and Reasoning 3 (3):209 – 235.
    Two experiments using a realistic version of the selection task examined the relationship between participants probability estimates of finding a counter example and their selections. Experiment 1 used everyday categories in the context of a scenario to determine whether or not the number of instances in a category affected the estimated probability of a counter-example. Experiment 2 modified the scenario in order to alter participants estimates of finding a specific counter-example. Unlike Kirby 1994a , but consistent with his proposals, (...)
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  25. Bruno De Finetti (2008). Philosophical Lectures on Probability. Collected, Edited and Annotated by Alberto Mura. Springer.
    The book contains the transcription of a course on the foundations of probability given by the Italian mathematician Bruno de Finetti in 1979 at the a oeNational Institute of Advanced Mathematicsa in Rome.
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  26. Mark de Rond & Iain Morley (eds.) (2010). Serendipity: Fortune and the Prepared Mind. Cambridge University Press.
    Machine generated contents note: Introduction. Fortune and the prepared mind Iain Morley and Mark de Rond; 1. The stratigraphy of serendipity Susan E. Alcock; 2. Understanding humans - serendipity and anthropology Richard Leakey; 3. HIV and the naked ape Robin Weiss; 4. Cosmological serendipity Simon Singh; 5. Serendipity in astronomy Andrew C. Fabian; 6. Serendipity in physics Richard Friend; 7. Liberalism and uncertainty Oliver Letwin; 8. The unanticipated pleasures of the writing life Simon Winchester.
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  27. Georg J. W. Dorn (1997). Deductive, Probabilistic and Inductive Dependence. An Axiomatic Study in Probability Semantics. Verlag Peter Lang.
    This work is in two parts. The main aim of part 1 is a systematic examination of deductive, probabilistic, inductive and purely inductive dependence relations within the framework of Kolmogorov probability semantics. The main aim of part 2 is a systematic comparison of (in all) 20 different relations of probabilistic (in)dependence within the framework of Popper probability semantics (for Kolmogorov probability semantics does not allow such a comparison). Added to this comparison is an examination of (in all) 15 purely inductive (...)
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  28. 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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  29. J. Dubucs (ed.) (1993). Philosophy of Probability. Kluwer, Dordrecht.
    Philosophy of Probability provides a comprehensive introduction to theoretical issues that occupy a central position in disciplines ranging from philosophy of ...
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  30. Antony Eagle, Randomness and Probability.
    Von Mises thought that an adequate account of objective probability required a condition of randomness. For frequentists, some such condition is needed to rule out those sequences where the relative frequencies converge towards definite limiting values, and where it is nevertheless not appropriate to speak of probability … [because such a sequence] obeys an easily recognizable law (von Mises, Probability, Statistics, and Truth). But is a condition of randomness required for an adequate account of probability, given the existence of decisive (...)
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  31. J. Ellenberg & E. Sober (2011). Objective Probabilities in Number Theory. Philosophia Mathematica 19 (3):308-322.
    Philosophers have explored objective interpretations of probability mainly by considering empirical probability statements. Because of this focus, it is widely believed that the logical interpretation and the actual-frequency interpretation are unsatisfactory and the hypothetical-frequency interpretation is not much better. Probabilistic assertions in pure mathematics present a new challenge. Mathematicians prove theorems in number theory that assign probabilities. The most natural interpretation of these probabilities is that they describe actual frequencies in finite sets and limits of actual frequencies in infinite sets. (...)
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  32. Roger Andreas Fischer (2010). Vom Offenen Geschehen Und Seiner Bewältigung: Ein Essay. Centaurus.
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  33. Branden Fitelson (2003). Review of I. Hacking, An Introduction to Probability and Inductive Logic. [REVIEW] Bulletin of Symbolic Logic 9 (4):5006-5008.
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  34. James Franklin, Home | Archives | Announcements | About the Journal | Submission Information | Contact Us.
    Decision under conditions of uncertainty is an unavoidable fact of life. The available evidence rarely suffices to establish a claim with complete confidence, and as a result a good deal of our reasoning about the world must employ criteria of probable judgment. Such criteria specify the conditions under which rational agents are justified in accepting or acting upon propositions whose truth cannot be ascertained with certainty. Since the seventeenth century philosophers and mathematicians have been accustomed to consider belief under uncertainty (...)
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  35. Marie Gaudard (1984). The Correspondence Between Credibilities and Induced Betting Rate Assignments. Foundations of Physics 14 (5):431-441.
    Operational statistics is an operational theory of probability and statistics which generalizes classical probability and statistics and provides a formalism particularly suited to the needs of quantum mechanics. Within this formalism, statistical inference can be accomplished using the Bayesian inference strategy. In a hierarchical Bayesian approach, a second-order probability measure, or credibility, represents degrees of belief in statistical hypotheses. A credibility determines an assignment of simple and conditioned betting rates to events in a natural way. In the setting of operational (...)
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  36. Christian George (1997). Reasoning From Uncertain Premises. Thinking and Reasoning 3 (3):161 – 189.
    Previous studies have shown that 1 participants are reluctant to accept a conclusion as certainly true when it is derived from a valid conditional argument that includes a doubtful premise, and 2 participants typically link the degree of uncertainty found in a given premise set to its conclusion. Two experiments were designed to further investigate these phenomena. Ninety adult participants in Experiment 1 were first asked to judge the validity of three conditional arguments Modus Ponens, Denial of the Antecedent, and (...)
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  37. Clark Glymour (2014). Poincaré's Probabilities, Kantified, Post-Modernized. Biological Theory 9 (1):113-114.
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  38. Clark Glymour (2001). Instrumental Probability. The Monist 84 (2):284-300.
    The claims of science and the claims of probability combine in two ways. In one, probability is part of the content of science, as in statistical mechanics and quantum theory and an enormous range of "models" developed in applied statistics. In the other, probability is the tool used to explain and to justify methods of inference from records of observations, as in every science from psychiatry to physics. These intimacies between science and probability are logical sports, for while we think (...)
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  39. W. T. Grandy Jr (2004). Book Review: Probability Theory: The Logic of Science. By Edwin T. Jaynes, Edited by G. Larry Bretthorst. Cambridge University Press, Cambridge, United Kingdom, 2003, Xxix + 727 Pp., S60.00 (Hardcover). ISBN 0-521-59271-2. [REVIEW] Foundations of Physics 34 (3):533-536.
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  40. S. Gudder (2000). What Is Fuzzy Probability Theory? Foundations of Physics 30 (10):1663-1678.
    The article begins with a discussion of sets and fuzzy sets. It is observed that identifying a set with its indicator function makes it clear that a fuzzy set is a direct and natural generalization of a set. Making this identification also provides simplified proofs of various relationships between sets. Connectives for fuzzy sets that generalize those for sets are defined. The fundamentals of ordinary probability theory are reviewed and these ideas are used to motivate fuzzy probability theory. Observables (fuzzy (...)
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  41. Stan Gudder (1999). Observables and Statistical Maps. Foundations of Physics 29 (6):877-897.
    This article begins with a review of the framework of fuzzy probability theory. The basic structure is given by the σ-effect algebra of effects (fuzzy events) $\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ and the set of probability measures $M_1^ + {\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ on a measurable space $\left( {\Omega ,\mathcal{A}} \right)$ . An observable $X:\mathcal{B} \to {\text{ }}\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ is defined, where $\begin{gathered} X:\mathcal{B} \to {\text{ }}\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right) \\ \left( {\Lambda ,{\text{ }}\mathcal{B}} \right) (...)
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  42. Ian Hacking (1995). The Emergence of Probability. Cambridge : Cambridge University Press.
    Ian Hacking here presents a philosophical critique of early ideas about probability, induction and statistical inference and the growth of this new family of ...
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  43. Ian Hacking (1978). Hume's Species of Probability. Philosophical Studies 33 (1):21 - 37.
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  44. Joseph Y. Halpern & Riccardo Pucella (2009). Evidence with Uncertain Likelihoods. Synthese 171 (1):111 - 133.
    An agent often has a number of hypotheses, and must choose among them based on observations, or outcomes of experiments. Each of these observations can be viewed as providing evidence for or against various hypotheses. All the attempts to formalize this intuition up to now have assumed that associated with each hypothesis h there is a likelihood function μ h , which is a probability measure that intuitively describes how likely each observation is, conditional on h being the correct hypothesis. (...)
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  45. Sven Ove Hansson (2010). Past Probabilities. Notre Dame Journal of Formal Logic 51 (2):207-223.
    The probability that a fair coin tossed yesterday landed heads is either 0 or 1, but the probability that it would land heads was 0.5. In order to account for the latter type of probabilities, past probabilities, a temporal restriction operator is introduced and axiomatically characterized. It is used to construct a representation of conditional past probabilities. The logic of past probabilities turns out to be strictly weaker than the logic of standard probabilities.
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  46. Sven Ove Hansson (2008). Do We Need Second-Order Probabilities? Dialectica 62 (4):525-533.
    Although it has often been claimed that all the information contained in second-order probabilities can be contained in first-order probabilities, no practical recipe for the elimination of second-order probabilities without loss of information seems to have been presented. Here, such an elimination method is introduced for repeatable events. However, its application comes at the price of losses in cognitive realism. In spite of their technical eliminability, second-order probabilities are useful because they can provide models of important features of the world (...)
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  47. Gilbert Harman (1983). Problems with Probabilistic Semantics. In Alex Orenstein & Rafael Stern (eds.), Developments in Semantics. Haven. 243-237.
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  48. Alois Hartkämper & Heinz-Jürgen Schmidt (1983). On the Foundations of the Physical Probability Concept. Foundations of Physics 13 (7):655-672.
    An exact formulation of the frequency interpretation of probability is proposed on the basis of G. Ludwig's concept of physical theories. Starting from a short outline of this concept, a formal definition of weak approximate reduction is developed, which covers the reduction of probability to frequency as a special case.
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  49. James Hawthorne & Luc Bovens (1999). The Preface, the Lottery, and the Logic of Belief. Mind 108 (430):241 - 264.
    John Locke proposed a straightforward relationship between qualitative and quantitative doxastic notions: belief corresponds to a sufficiently high degree of confidence. Richard Foley has further developed this Lockean thesis and applied it to an analysis of the preface and lottery paradoxes. Following Foley's lead, we exploit various versions of these paradoxes to chart a precise relationship between belief and probabilistic degrees of confidence. The resolutions of these paradoxes emphasize distinct but complementary features of coherent belief. These features suggest principles that (...)
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  50. Richard Jeffrey (1996). Unknown Probabilities. Erkenntnis 45 (2-3):327 - 335.
    From a point of view like de Finetti's, what is the judgmental reality underlying the objectivistic claim that a physical magnitude X determines the objective probability that a hypothesis H is true? When you have definite conditional judgmental probabilities for H given the various unknown values of X, a plausible answer is sufficiency, i.e., invariance of those conditional probabilities as your probability distribution over the values of X varies. A different answer, in terms of conditional exchangeability, is offered for use (...)
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     Induction
     Probabilistic Reasoning
     Scientific Change
     Inference to the Best Explanation
     Theoretical Virtues
     Scientific Method, Misc
    Interpretation of Probability
     Chance and Objective Probability
     Classical Probability
     Frequentism
     Logical Probability
     Propensities
     Subjective Probability
     Interpretion of Probability, Misc
    Mathematics of Probability
     Axioms of Probability
     Infinitesimals and Probability
     Mathematics of Probability, Misc
    Probabilistic Reasoning
     Bayesian Reasoning
     Probabilistic Principles
     Probabilistic Frameworks
     Probabilistic Puzzles
     Subjective Probability
    Phil of Statistics
    Applications of Probability
     Probability in the Philosophy of Religion
     Probability in the Physical Sciences
     Applications of Probability, Misc
     Decision Theory
     Probabilistic Reasoning
    Phil of Probability, Misc
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