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  1. A. R. A. (1957). Probability in Logic. Review of Metaphysics 11 (2):348-348.
  2. Edward H. Allen (1976). Negative Probabilities and the Uses of Signed Probability Theory. Philosophy of Science 43 (1):53-70.
    The use of negative probabilities is discussed for certain problems in which a stochastic process approach is indicated. An extension of probability theory to include signed (negative and positive) probabilities is outlined and both philosophical and axiomatic examinations of negative probabilities are presented. Finally, a class of applications illustrates the use and implications of signed probability theory.
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  3. Arnold Baise (2013). Probability, Objectivity, and Induction. Journal of Ayn Rand Studies 13 (2):81-95.
    The main purpose of this article is to use Ayn Rand’s analysis of the meaning of objectivity to clarify the much-discussed question of whether probability is “objective” or “subjective.” This results in a classification of probability theories as frequentist, subjective Bayesian, or objective Bayesian. The work of objective Bayesian E. T. Jaynes is emphasized, and is used to provide a formal definition of probability. The relation between probability and induction is covered briefly, with probability theory presented as the basis of (...)
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  4. Sorin Bangu (2010). On Bertrand's Paradox. Analysis 70 (1):30-35.
    The Principle of Indifference is a central element of the ‘classical’ conception of probability, but, for all its strong intuitive appeal, it is widely believed that it faces a devastating objection: the so-called (by Poincare´) ‘Bertrand paradoxes’ (in essence, cases in which the same probability question receives different answers). The puzzle has fascinated many since its discovery, and a series of clever solutions (followed promptly by equally clever rebuttals) have been proposed. However, despite the long-standing interest in this problem, an (...)
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  5. Jean Baratgin & Guy Politzer (2011). Updating: A Psychologically Basic Situation of Probability Revision. Thinking and Reasoning 16 (4):253-287.
    The Bayesian model has been used in psychology as the standard reference for the study of probability revision. In the first part of this paper we show that this traditional choice restricts the scope of the experimental investigation of revision to a stable universe. This is the case of a situation that, technically, is known as focusing. We argue that it is essential for a better understanding of human probability revision to consider another situation called updating (Katsuno & Mendelzon, 1992), (...)
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  6. G. Spencer Brown & G. B. Keene (1957). Symposium: Randomness. Aristotelian Society Supplementary Volume 31:145 - 160.
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  7. Franz Dietrich & Christian List (forthcoming). Probabilistic Opinion Pooling. In A. Hajek & C. Hitchcock (eds.), Oxford Handbook of Philosophy and Probability. Oxford University Press
    Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This article reviews several proposed solutions to this problem. We focus on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). We present axiomatic characterisations of each class of (...)
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  8. Antony Eagle, Chance Versus Randomness. Stanford Encyclopedia of Philosophy.
    This article explores the connection between objective chance and the randomness of a sequence of outcomes. Discussion is focussed around the claim that something happens by chance iff it is random. This claim is subject to many objections. Attempts to save it by providing alternative theories of chance and randomness, involving indeterminism, unpredictability, and reductionism about chance, are canvassed. The article is largely expository, with particular attention being paid to the details of algorithmic randomness, a topic (...)
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  9. Antony Eagle (2005). Randomness Is Unpredictability. British Journal for the Philosophy of Science 56 (4):749-790.
    The concept of randomness has been unjustly neglected in recent philosophical literature, and when philosophers have thought about it, they have usually acquiesced in views about the concept that are fundamentally flawed. After indicating the ways in which these accounts are flawed, I propose that randomness is to be understood as a special case of the epistemic concept of the unpredictability of a process. This proposal arguably captures the intuitive desiderata for the concept of randomness; at least it should suggest (...)
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  10. Kenny Easwaran (2011). Varieties of Conditional Probability. In Prasanta Bandyopadhyay & Malcolm Forster (eds.), Handbook for Philosophy of Statistics. North Holland
    I consider the notions of logical probability, degree of belief, and objective chance, and argue that a different formalism for conditional probability is appropriate for each.
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  11. Kenny Easwaran (2010). Logic and Probability. Journal of the Indian Council of Philosophical Research 27 (2):229-253.
    As is clear from the other articles in this volume, logic has applications in a broad range of areas of philosophy. If logic is taken to include the mathematical disciplines of set theory, model theory, proof theory, and recursion theory (as well as first-order logic, second-order logic, and modal logic), then the only other area of mathematics with such wide-ranging applications in philosophy is probability theory.
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  12. Ellery Eells, Brian Skyrms & Ernest W. Adams (eds.) (1994). Probability and Conditionals: Belief Revision and Rational Decision. Cambridge University Press.
    This is a 'state of the art' collection of essays on the relation between probabilities, especially conditional probabilities, and conditionals. It provides new negative results which sharply limit the ways conditionals can be related to conditional probabilities. There are also positive ideas and results which will open up new areas of research. The collection is intended to honour Ernest W. Adams, whose seminal work is largely responsible for creating this area of inquiry. As well as describing, evaluating, and (...)
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  13. David Ellerman, On the Duality Between Existence and Information.
    Recent developments in pure mathematics (category theory) and in mathematical logic (partition logic) have uncovered a fundamental duality between "existence" and "information." In logic, the duality is between the Boolean logic of subsets (mis-specified as the logic of "propositions") and the logic of quotient sets, equivalence relations, or partitions. The analogue to an element of a subset is the notion of a distinction (a pair of elements in different blocks) of a partition, and that leads to a whole stream of (...)
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  14. Branden Fitelson & Lara Buchak, Separability Assumptions in Scoring-Rule-Based Arguments for Probabilism.
    - In decision theory, an agent is deciding how to value a gamble that results in different outcomes in different states. Each outcome gets a utility value for the agent.
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  15. Joseph S. Fulda, Remarks on the Argument From Design.
    Gives two pared-down versions of the argument from design, which may prove more persuasive as to a Creator, discusses briefly the mathematics underpinning disbelief and nonbelief and its misuse and some proper uses, moves to why the full argument is needed anyway, viz., to demonstrate Providence, offers a theory as to how miracles (open and hidden) occur, viz. the replacement of any particular mathematics underlying a natural law (save logic) by its most appropriate nonstandard variant. -/- Note: This is an (...)
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  16. Shan Gao, Derivation of the Meaning of the Wave Function.
    We show that the physical meaning of the wave function can be derived based on the established parts of quantum mechanics. It turns out that the wave function represents the state of random discontinuous motion of particles, and its modulus square determines the probability density of the particles appearing in certain positions in space.
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  17. Shan Gao, Protective Measurement and the Meaning of the Wave Function.
    This article analyzes the implications of protective measurement for the meaning of the wave function. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus square of its wave function. It is shown that the mass and charge density is not real but effective, formed by the ergodic motion of a localized particle with the total mass and charge of the system. Moreover, it is argued that the ergodic motion is not continuous but (...)
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  18. Shan Gao, The Wave Function and Its Evolution.
    The meaning of the wave function and its evolution are investigated. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and (...)
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  19. D. Gillies (2007). Maria Carla Galavotti. Philosophical Introduction to Probability. Stanford: Center for the Study of Language and Information Publications, 2005. Pp. X + 265. ISBN 1-57586-490-8 (Pbk), 1-57586-489-4 (Hardback). [REVIEW] Philosophia Mathematica 15 (1):129-132.
    Galavotti begins her book by stressing the centrality of probability to a whole range of philosophical problems. She writes 1: "Probability invests all branches of philosophical investigation, from epistemology to moral and political philosophy, and impinges upon major controversies, like that between determinism and indeterminism, or between free will and moral obligation, and problems such as: ‘What degree of certainty can human knowledge attain?’ ‘What is the relationship between probability and certainty?’" She then explains that her book will focus on (...)
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  20. Donald Gillies (2010). An Objective Theory of Probability (Routledge Revivals). Routledge.
    This reissue of D. A. Gillies highly influential work, first published in 1973, is a philosophical theory of probability which seeks to develop von Mises’ views on the subject. In agreement with von Mises, the author regards probability theory as a mathematical science like mechanics or electrodynamics, and probability as an objective, measurable concept like force, mass or charge. On the other hand, Dr Gillies rejects von Mises’ definition of probability in terms of limiting frequency and claims that probability should (...)
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  21. Donald Gillies (1994). Review of John Earman Bayes or Bust? [REVIEW] Mind 103 (411):376-379.
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  22. James Goetz (2006). Classical Probability, Shakespearean Sonnets, and Multiverse Hypotheses. International Society for Complexity, Information, and Design Archive.
    We evaluate classical probability in relation to the random generation of a Shakespearean sonnet by a typing monkey and the random generation of universes in a World Ensemble based on various multiverse models involving eternal inflation. We calculate that it would take a monkey roughly 10^942 years to type a Shakespearean sonnet, which pushes the scenario into a World Ensemble. The evaluation of a World Ensemble based on various models of eternal inflation suggests that there is no middle ground between (...)
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  23. Amit Hagar (2014). Demons in Physics. [REVIEW] Metascience 23 (2):1-10.
    In their book The Road to Maxwell's Demon Hemmo & Shenker re-describe the foundations of statistical mechanics from a purely empiricist perspective. The result is refreshing, as well as intriguing, and it goes against much of the literature on the demon. Their conclusion, however, that Maxwell's demon is consistent with statistical mechanics, still leaves open the question of why such a demon hasn't yet been observed on a macroscopic scale. This essay offers a sketch of what a possible answer could (...)
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  24. Alan Hájek (2008). A Philosopher’s Guide to Probability. In G. Bammer & M. Smithson (eds.), Uncertainty and Risk: Multidisciplinary Perspectives. Routledge
    Uncertainty governs our lives. From the unknowns of living with the risks of terrorism to developing policies on genetically modified foods, or disaster planning for catastrophic climate change, how we conceptualize, evaluate and cope with uncertainty drives our actions and deployment of resources, decisions and priorities.
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  25. Sven Ove Hansson (2009). From the Casino to the Jungle. Synthese 168 (3):423 - 432.
    Clear-cut cases of decision-making under risk (known probabilities) are unusual in real life. The gambler’s decisions at the roulette table are as close as we can get to this type of decision-making. In contrast, decision-making under uncertainty (unknown probabilities) can be exemplified by a decision whether to enter a jungle that may contain unknown dangers. Life is usually more like an expedition into an unknown jungle than a visit to the casino. Nevertheless, it is common in decision-supporting disciplines to proceed (...)
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  26. James Hawthorne (2004). Three Models of Sequential Belief Updating on Uncertain Evidence. Journal of Philosophical Logic 33 (1):89-123.
    Jeffrey updating is a natural extension of Bayesian updating to cases where the evidence is uncertain. But, the resulting degrees of belief appear to be sensitive to the order in which the uncertain evidence is acquired, a rather un-Bayesian looking effect. This order dependence results from the way in which basic Jeffrey updating is usually extended to sequences of updates. The usual extension seems very natural, but there are other plausible ways to extend Bayesian updating that maintain order-independence. I will (...)
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  27. James Hawthorne (1996). On the Logic of Nonmonotonic Conditionals and Conditional Probabilities. Journal of Philosophical Logic 25 (2):185-218.
    I will describe the logics of a range of conditionals that behave like conditional probabilities at various levels of probabilistic support. Families of these conditionals will be characterized in terms of the rules that their members obey. I will show that for each conditional, →, in a given family, there is a probabilistic support level r and a conditional probability function P such that, for all sentences C and B, 'C → B' holds just in case P[B | C] ≥ (...)
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  28. Wesley H. Holliday & Thomas F. Icard (2013). Measure Semantics and Qualitative Semantics for Epistemic Modals. Proceedings of SALT 23:514-534.
    In this paper, we explore semantics for comparative epistemic modals that avoid the entailment problems shown to result from Kratzer’s (1991) semantics by Yalcin (2006, 2009, 2010). In contrast to the alternative semantics presented by Yalcin and Lassiter (2010, 2011), based on finitely additive probability measures, we introduce semantics based on qualitatively additive measures, as well as semantics based on purely qualitative orderings, including orderings on propositions derived from orderings on worlds in the tradition of Kratzer (1991). All of these (...)
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  29. Andrew Holster, The Time Flow Manifesto CHAPTER 2 TIME SYMMETRY IN PHYSICS.
    This chapter starts with a simple conventional presentation of time reversal in physics, and then returns to analyse it, rejects the conventional analysis, and establishes correct principles in their place.
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  30. Andrew Holster, The Time Flow Manifesto CHAPTER 3 REVERSIBILTY IN PHYSICS.
    The conventional claims and concepts of 5* - 8* are a hang-over from the classical theory of thermodynamics – i.e. thermodynamics based on a fully deterministic micro-theory, developed in the time of Boltzmann, Loschmidt and Gibbs in the late C19th. The classical theory has well-known ‘reversibility paradoxes’ when applied to the universe as a whole. But the introduction of intrinsic probabilities in quantum mechanics, and its consequent time asymmetry, fundamentally changes the picture.
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  31. James M. Joyce (2005). How Probabilities Reflect Evidence. Philosophical Perspectives 19 (1):153–178.
  32. Pawel Kawalec (2012). Bayesianizm w polskiej tradycji probabilizmu – studium stanowiska Kazimierza Ajdukiewicza. Ruch Filozoficzny 1 (1).
    Abstract The opening section outlines probabilism in the 20th century philosophy and shortly discusses the major accomplishments of Polish probabilist thinkers. A concise characterization of Bayesianism as the major recent form of probabilism follows. It builds upon the core personalist version of Bayesianism towards more objectively oriented versions thereof. The problem of a priori probability is shortly discussed. A tentative characterization of Kazimierz Ajdukiewicz’s standpoint regarding the inductive inference is cast in Bayesian terms. His objections against it presented in Pragmatic (...)
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  33. John-Michael Kuczynski (2006). THE ANALOGUE-DIGITAL DISTINCTION AND THE COGENCY OF KANT'S TRANSCENDENTAL ARGUMENTS. Existentia: An International Journal of Philosophy (3-4):279-320.
    Hume's attempt to show that deduction is the only legitimate form of inference presupposes that enumerative induction is the only non-deductive form of inference. In actuality, enumerative induction is not even a form of inference: all supposed cases of enumerative induction are disguised cases of Inference to the Best Explanation (IBE), so far as they aren't simply cases of mentation of a purely associative kind and, consequently, of a kind that is non-inductive and otherwise non-inferential. The justification for IBE lies (...)
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  34. Michael LaPorte (2013). Philosophy Paper.
  35. Christian List & Marcus Pivato (2015). Emergent Chance. Philosophical Review 124 (1):119-152.
    We offer a new argument for the claim that there can be non-degenerate objective chance (“true randomness”) in a deterministic world. Using a formal model of the relationship between different levels of description of a system, we show how objective chance at a higher level can coexist with its absence at a lower level. Unlike previous arguments for the level-specificity of chance, our argument shows, in a precise sense, that higher-level chance does not collapse into epistemic probability, despite higher-level properties (...)
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  36. Rupert Macey-Dare, Expected Loss Balance of Probability Theorem.
    This paper shows how for every Contingent Loss whose associated probability fails the Balance of Probability test, there is a corresponding Expected Loss whose probability passes the Balance of Probability test and so constitutes a preferable head of damage for a civil claim. Recent English Mesothelioma and Asbestos-related judgements including Gregg v Scott 2005, Fairchild v Glenhaven 2002 and Barker v Corus 2006 are considered in the light of this theorem.
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  37. Rupert Macey-Dare, Expected Loss Divisibility Theorem.
    This paper proposes and analyses the following theorem: For every total actual loss caused to a claimant with given probabilities by a single unidentified member of a defined group, there is a corresponding total expected loss, divisible and separable into discrete component expected sub-losses, each individually "caused" by a corresponding specific member of that defined group. Moreover, for every total estimated loss caused to a claimant in the past or present or prospectively in the future with estimable probabilities by one (...)
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  38. Rupert Macey-Dare, Expected Loss Interest-Adjustment Theorem.
    This paper proposes and analyses the following theorem: Every legal claim or award that includes interest rate adjustment also incorporates an implicit head of loss or counterclaim for the expected opportunity cost or time value of the underlying claim amount. This expected opportunity cost satisfies no-arbitrage when compared with the parallel interest rate market. The inflation and discounting of nominal damage awards forwards and backwards in time and the relationship between indemnity interest rates and equity are all examined.
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  39. Enrique Morata, On Random as a Cause. Academia.
    On absolute random and restricted random .
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  40. Charles Morgan & Hughes LeBlanc (1983). Probabilistic Semantics for Formal Logic. Notre Dame Journal of Formal Logic 24:161-180.
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  41. Flavia Padovani (2011). Hans Reichenbach.The Concept of Probability in the Mathematical Representation of Reality. Trans. And Ed. Frederick Eberhardt and Clark Glymour. Chicago: Open Court, 2008. Pp. Xi+154. $34.97. [REVIEW] Hopos: The Journal of the International Society for the History of Philosophy of Science 1 (2):344-347.
    Hans Reichenbach has been not only one of the founding fathers of logical empiricism but also one of the most prominent figures in the philosophy of science of the past century. While some of his ideas continue to be of interest in current philosophical programs, an important part of his early work has been neglected, and some of it has been unavailable to English readers. Among Reichenbach’s overlooked (and untranslated) early works, his doctoral thesis of 1915, The Concept of Probability (...)
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  42. Kawalec Paweł (2013). Cartwright’s Approach to Invariance Under Intervention. Zagadnienia Naukoznawstwa 49 (4):321-333.
    N. Cartwright’s results on invariance under intervention and causality (2003) are reconsidered. Procedural approach to causality elicited in this paper and contrasted with Cartwright’s apparently philosophical one unravels certain ramifications of her results. The procedural approach seems to license only a constrained notion of intervention and in consequence the “correctness to invariance” part of Cartwright’s first theorem fails for a class of cases. The converse “invariance to correctness” part of the theorem relies heavily on modeling assumptions which prove to be (...)
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  43. Anthony F. Peressini (forthcoming). Causation, Probability, and the Continuity Bind. British Journal for the Philosophy of Science.
    Analyses of singular (token-level) causation often make use of the idea that a cause in- creases the probability of its effect. Of particular salience in such accounts are the values of the probability function of the effect, conditional on the presence and absence of the putative cause, analyzed around the times of the events in question: causes are characterized by the effect’s probability function being greater when conditionalized upon them. Put this way it becomes clearer that the ‘behavior’ (continuity) (...)
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  44. Niki Pfeifer & G. D. Kleiter (2009). Framing Human Inference by Coherence Based Probability Logic. Journal of Applied Logic 7 (2):206--217.
  45. Niki Pfeifer & G. D. Kleiter (2006). Inference in Conditional Probability Logic. Kybernetika 42 (2):391--404.
    An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if . . . , then . . . ” by conditional probabilities and not by the probability of the material implication. An inference rule is probabilistically informative if the coherent probability interval of its conclusion is not necessarily equal to the unit interval (...)
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  46. Niki Pfeifer & G. D. Kleiter (2006). Towards a Probability Logic Based on Statistical Reasoning. In Proceedings of the 11 T H Ipmu International Conference (Information Processing and Management of Uncertainty in Knowledge-Based Systems). 2308--2315.
    Logical argument forms are investigated by second order probability density functions. When the premises are expressed by beta distributions, the conclusions usually are mixtures of beta distributions. If the shape parameters of the distributions are assumed to be additive (natural sampling), then the lower and upper bounds of the mixing distributions (P´olya-Eggenberger distributions) are parallel to the corresponding lower and upper probabilities in conditional probability logic.
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  47. Niki Pfeifer & G. D. Kleiter (2005). Towards a Mental Probability Logic. Psychologica Belgica 45 (1):71--99.
    We propose probability logic as an appropriate standard of reference for evaluating human inferences. Probability logical accounts of nonmonotonic reasoning with system p, and conditional syllogisms (modus ponens, etc.) are explored. Furthermore, we present categorical syllogisms with intermediate quantifiers, like the “most . . . ” quantifier. While most of the paper is theoretical and intended to stimulate psychological studies, we summarize our empirical studies on human nonmonotonic reasoning.
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  48. Karl Popper (1990). A World of Propensities. Thoemmes.
  49. Huw Price, The Lion, the 'Which?' And the Wardrobe -- Reading Lewis as a Closet One-Boxer.
    Newcomb problems turn on a tension between two principles of choice: roughly, a principle sensitive to the causal features of the relevant situation, and a principle sensitive only to evidential factors. Two-boxers give priority to causal beliefs, and one-boxers to evidential beliefs. A similar issue can arise when the modality in question is chance, rather than causation. In this case, the conflict is between decision rules based on credences guided solely by chances, and rules based on credences guided by other (...)
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  50. Susanna Rinard (2014). A New Bayesian Solution to the Paradox of the Ravens. Philosophy of Science 81 (1):81-100.
    The canonical Bayesian solution to the ravens paradox faces a problem: it entails that black non-ravens disconfirm the hypothesis that all ravens are black. I provide a new solution that avoids this problem. On my solution, black ravens confirm that all ravens are black, while non-black non-ravens and black non-ravens are neutral. My approach is grounded in certain relations of epistemic dependence, which, in turn, are grounded in the fact that the kind raven is more natural than the kind black. (...)
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