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Probabilistic Reasoning

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Summary What principles govern uncertain reasoning?  And how do they apply to other philosophical problems; like whether a decision is rational, or whether one thing is a cause of another? Most philosophers think uncertain reasoning should at least obey the axioms of the mathematical theory of probability; though some prefer other axioms, like those of Dempster-Shafer theory or ranking theory.  Many also endorse principles governing beliefs about physical probabilities (chance-credence principles), and principles for responding to new evidence (updating principles).  Some also endorse principles for reasoning in the absence of relevant information (indifference principles).  A perennial question is how many principles we should accept: how "objective" is probabilistic reasoning? Probabilistic principles have traditionally been applied to the study of scientific reasoning (confirmation theory) and practical rationality (decision theory).  But they also apply to more traditional epistemological issues, like foundationalism vs. coherentism, and to metaphysical questions, e.g. about the nature of causality and our access to it.
Key works Key works defending the probability axioms as normative principles are Ramsey 1926, De 1989, Savage 1954, and Joyce 1998.  Locus classici for additional probabilistic principles are Lewis 1980 (chance-credence), van Fraassen 1984 (reflection), Carnap 1950, Jaynes 1973 (indifference), and Lewis 1999 (updating). Alternative axiomatic frameworks originate with Shafer 1976 (Dempster-Shafer theory) and Spohn 1988 (ranking theory). Some classic applications of probabilistic principles to epistemological and other problems are Good 1960 (the raven paradox), Pearl 2000 (causal inference), and Elga 2000 (sleeping beauty and self-location). 
Introductions Skyrms 1966 is an excellent and gentle introduction for non-initiates.  A next step up is Jeffrey 1965.  More advanced introductions are Urbach & Howson 1993 and Earman 1992.  More recently, Halpern 2003 provides an excellent overview of the mathematical options.  A recent overview of the more philosophical issues can be found in Weisberg 2011.
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  1. Four Approaches to Supposition.Benjamin Eva, Ted Shear & Branden Fitelson - manuscript
    The primary purpose of this paper is to shed light on the structure of four varieties of normative theories of supposition by systematically explicating the relationships between canonical representatives of each. These include qualitative and quantitative theories of indicative and subjunctive supposition. We approach this project by treating supposition as a form of 'provisional belief revision' in which a person temporarily accepts the supposition as true and makes some appropriate changes to her other opinions so as to accommodate their supposition. (...)
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  2. Reconsidering the Rule of Consideration: Probabilistic Knowledge and Legal Proof.Tim Smartt - forthcoming - Episteme:1-16.
    In this paper, I provide an argument for rejecting Sarah Moss's recent account of legal proof. Moss's account is attractive in a number of ways. It provides a new version of a knowledge-based theory of legal proof that elegantly resolves a number of puzzles about mere statistical evidence in the law. Moreover, the account promises to have attractive implications for social and moral philosophy, in particular about the impermissibility of racial profiling and other harmful kinds of statistical generalisation. In this (...)
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  3. Sensitivity and Closure.Sherrilyn Roush - 2012 - In Kelly Becker & Tim Black (eds.), The Sensitivity Principle in Epistemology. Cambridge, UK: pp. 242-268.
    This paper argues that if knowledge is defined in terms of probabilistic tracking then the benefits of epistemic closure follow without the addition of a closure clause. (This updates my definition of knowledge in Tracking Truth 2005.) An important condition on this result is found in "Closure Failure and Scientific Inquiry" (2017).
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  4. Calibrating Generative Models: The Probabilistic Chomsky-Schützenberger Hierarchy.Thomas Icard - forthcoming - Journal of Mathematical Psychology 95.
  5. Overconfidence in Overconfidence.Kevin Dorst - manuscript
    Do people tend to be overconfident in their opinions? Many psychologists think so. They have run calibration studies in which they ask people a variety of questions, and then test whether their confidence in their answers matches the proportions of those answers that are true. Under certain conditions, an “overconfidence effect” is robust—for example, of the answers people are 80% confident in, only 60% are true. Psychologists have inferred that people tend to be irrationally overconfident. My question is when and (...)
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  6. The Logic of Conditional Belief.Benjamin Eva - forthcoming - Philosophical Quarterly.
    The logic of indicative conditionals remains the topic of deep and intractable philosophical disagreement. I show that two influential epistemic norms -- the Lockean theory of belief and the Ramsey test for conditional belief -- are jointly sufficient to ground a powerful new argument for a particular conception of the logic of indicative conditionals. Specifically, the argument demonstrates, contrary to the received historical narrative, that there is a real sense in which Stalnaker's semantics for the indicative did succeed in capturing (...)
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  7. Probability, Coherent Belief and Coherent Belief Changes.John Cantwell & Hans Rott - 2019 - Annals of Mathematics and Artificial Intelligence 87 (3):259-291.
    This paper is about the statics and dynamics of belief states that are represented by pairs consisting of an agent's credences (represented by a subjective probability measure) and her categorical beliefs (represented by a set of possible worlds). Regarding the static side, we argue that the latter proposition should be coherent with respect to the probability measure and that its probability should reach a certain threshold value. On the dynamic side, we advocate Jeffrey conditionalisation as the principal mode of changing (...)
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  8. Evidential Probabilities and Credences.Anna-Maria Asunta Eder - 2019 - British Journal for the Philosophy of Science:1-21.
    Enjoying great popularity in decision theory, epistemology, and philosophy of science, Bayesianism as understood here is fundamentally concerned with epistemically ideal rationality. It assumes a tight connection between evidential probability and ideally rational credence, and usually interprets evidential probability in terms of such credence. Timothy Williamson challenges Bayesianism by arguing that evidential probabilities cannot be adequately interpreted as the credences of an ideal agent. From this and his assumption that evidential probabilities cannot be interpreted as the actual credences of human (...)
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  9. Speed-Optimal Induction and Dynamic Coherence.Michael Nielsen & Eric Wofsey - forthcoming - British Journal for the Philosophy of Science:axz030.
    A standard way to challenge convergence-based accounts of inductive success is to claim that they are too weak to constrain inductive inferences in the short run. We respond to such a challenge by answering some questions raised by Juhl (1994). When it comes to predicting limiting relative frequencies in the framework of Reichenbach, we show that speed-optimal convergence—a long-run success condition—induces dynamic coherence in the short run.
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  10. Counterexamples to Some Characterizations of Dilation.Michael Nielsen & Rush T. Stewart - 2019 - Erkenntnis:1-12.
    Pedersen and Wheeler (2014) and Pedersen and Wheeler (2015) offer a wide-ranging and in-depth exploration of the phenomenon of dilation. We find that these studies raise many interesting and important points. However, purportedly general characterizations of dilation are reported in them that, unfortunately, admit counterexamples. The purpose of this note is to show in some detail that these characterization results are false.
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  11. Mathematical Models of Games of Chance: Epistemological Taxonomy and Potential in Problem-Gambling Research.Catalin Barboianu - 2015 - UNLV Gaming Research and Review Journal 19 (1):17-30.
    Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of (...)
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  12. The Epistemology of the Near Miss and Its Potential Contribution in the Prevention and Treatment of Problem-Gambling.Catalin Barboianu - 2019 - Journal of Gambling Studies 1:1-16.
    The near-miss has been considered an important factor of reinforcement in gambling behavior, and previous research has focused more on its industry-related causes and effects and less on the gaming phenomenon itself. The near-miss has usually been associated with the games of slots and scratch cards, due to the special characteristics of these games, which include the possibility of pre-manipulation of award symbols in order to increase the frequency of these “engineered” near-misses. In this paper, we argue that starting from (...)
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  13. From Probabilities to Categorical Beliefs: Going Beyond Toy Models.Igor Douven & Hans Rott - 2018 - Journal of Logic and Computation 28 (6):1099-1124.
    According to the Lockean thesis, a proposition is believed just in case it is highly probable. While this thesis enjoys strong intuitive support, it is known to conflict with seemingly plausible logical constraints on our beliefs. One way out of this conflict is to make probability 1 a requirement for belief, but most have rejected this option for entailing what they see as an untenable skepticism. Recently, two new solutions to the conflict have been proposed that are alleged to be (...)
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  14. The Representation of Belief.Isaac Wilhelm - 2018 - Journal of Philosophical Logic 47 (4):715-732.
    I derive a sufficient condition for a belief set to be representable by a probability function: if at least one comparative confidence ordering of a certain type satisfies Scott’s axiom, then the belief set used to induce that ordering is representable. This provides support for Kenny Easwaran’s project of analyzing doxastic states in terms of belief sets rather than credences.
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  15. Attitudes in Active Reasoning.Julia Staffel - forthcoming - In Magdalena Balcerak Jackson & Brendan Balcerak Jackson (eds.), Reasoning: New Essays on Theoretical and Practical Thinking. Oxford University Press.
    Active reasoning is the kind of reasoning that we do deliberately and consciously. In characterizing the nature of active reasoning and the norms it should obey, the question arises which attitudes we can reason with. Many authors take outright beliefs to be the attitudes we reason with. Others assume that we can reason with both outright beliefs and degrees of belief. Some think that we reason only with degrees of belief. In this paper I approach the question of what kinds (...)
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  16. The Promise of Pick-the-Winners Contests for Producing Crowd Probability Forecasts.Phillip E. Pfeifer - 2016 - Theory and Decision 81 (2):255-278.
    This paper considers pick-the-winners contests as a simple method for harnessing the wisdom of crowds to produce probability forecasts. Pick-the-winners contests are those in which players pick the outcomes of selected future binary events with a prize going to the player with the most correct picks. In contrast to soliciting probability forecasts from experts, this paper shows that competition among players is to be encouraged because it improves the accuracy of the resulting crowd probability forecasts. This improvement comes because the (...)
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  17. Probabilistic Justification Logic.Joseph Lurie - 2018 - Philosophies 3 (1):2-0.
    Justification logics are constructive analogues of modal logics. They are often used as epistemic logics, particularly as models of evidentialist justification. However, in this role, justification logics are defective insofar as they represent justification with a necessity-like operator, whereas actual evidentialist justification is usually probabilistic. This paper first examines and rejects extant candidates for solving this problem: Milnikel’s Logic of Uncertain Justifications, Ghari’s Hájek–Pavelka-Style Justification Logics and a version of probabilistic justification logic developed by Kokkinis et al. It then proposes (...)
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  18. The Fine-Tuning Argument and the Requirement of Total Evidence.Peter Fisher Epstein - 2017 - Philosophy of Science 84 (4):639-658.
    According to the Fine-Tuning Argument, the existence of life in our universe confirms the Multiverse Hypothesis. A standard objection to FTA is that it violates the Requirement of Total Evidence. I argue that RTE should be rejected in favor of the Predesignation Requirement, according to which, in assessing the outcome of a probabilistic process, we should only use evidence characterizable in a manner available before observing the outcome. This produces the right verdicts in some simple cases in which RTE leads (...)
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  19. Inferring Probability Comparisons.Matthew Harrison-Trainor, Wesley H. Holliday & Thomas Icard - 2018 - Mathematical Social Sciences 91:62-70.
    The problem of inferring probability comparisons between events from an initial set of comparisons arises in several contexts, ranging from decision theory to artificial intelligence to formal semantics. In this paper, we treat the problem as follows: beginning with a binary relation ≥ on events that does not preclude a probabilistic interpretation, in the sense that ≥ has extensions that are probabilistically representable, we characterize the extension ≥+ of ≥ that is exactly the intersection of all probabilistically representable extensions of (...)
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  20. Stability and Scepticism in the Modelling of Doxastic States: Probabilities and Plain Beliefs.Hans Rott - 2017 - Minds and Machines 27 (1):167-197.
    There are two prominent ways of formally modelling human belief. One is in terms of plain beliefs, i.e., sets of propositions. The second one is in terms of degrees of beliefs, which are commonly taken to be representable by subjective probability functions. In relating these two ways of modelling human belief, the most natural idea is a thesis frequently attributed to John Locke: a proposition is or ought to be believed just in case its subjective probability exceeds a contextually fixed (...)
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  21. Closure Failure and Scientific Inquiry.Sherri Roush - 2017 - Res Philosophica 94 (2):275-299.
    Deduction is important to scientific inquiry because it can extend knowledge efficiently, bypassing the need to investigate everything directly. The existence of closure failure—where one knows the premises and that the premises imply the conclusion but nevertheless does not know the conclusion—is a problem because it threatens this usage. It means that we cannot trust deduction for gaining new knowledge unless we can identify such cases ahead of time so as to avoid them. For philosophically engineered examples we have “inner (...)
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  22. Précis of Tracking Truth.Sherrilyn Roush - 2009 - Philosophy and Phenomenological Research 79 (1):213-222.
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  23. Probabilidad, causalidad y explicación. [REVIEW]Marc Meléndez Schofield - 2011 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 26 (1):109-112.
  24. The Ontology of Biological and Clinical Statistics (OBCS) for Standardized and Reproducible Statistical Analysis.Jie Zheng, Marcelline R. Harris, Anna Maria Masci, Lin Yu, Alfred Hero, Barry Smith & Yongqun He - 2016 - Journal of Biomedical Semantics 7 (53).
    Statistics play a critical role in biological and clinical research. However, most reports of scientific results in the published literature make it difficult for the reader to reproduce the statistical analyses performed in achieving those results because they provide inadequate documentation of the statistical tests and algorithms applied. The Ontology of Biological and Clinical Statistics (OBCS) is put forward here as a step towards solving this problem. Terms in OBCS, including ‘data collection’, ‘data transformation in statistics’, ‘data visualization’, ‘statistical data (...)
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  25. Contextuality in the Integrated Information Theory.J. Acacio de Barros, Carlos Montemayor & Leonardo De Assis - forthcoming - In J. A. de Barros, B. Coecke & E. Pothos (eds.), Lecture Notes on Computer Science.
    Integrated Information Theory (IIT) is one of the most influential theories of consciousness, mainly due to its claim of mathematically formalizing consciousness in a measurable way. However, the theory, as it is formulated, does not account for contextual observations that are crucial for understanding consciousness. Here we put forth three possible difficulties for its current version, which could be interpreted as a trilemma. Either consciousness is contextual or not. If contextual, either IIT needs revisions to its axioms to include contextuality, (...)
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  26. Probabilistic Thinking, Thermodynamics, and the Interaction of the History and Philosophy of Science: Proceedings of the 1978 Pisa Conference on the History and Philosophy of Science, Volume IIJaakko Hintikka David Gruender Evandro Agazzi.Stephen G. Brush - 1982 - Isis 73 (2):286-287.
  27. The Perception of Probability.C. R. Gallistel, Monika Krishan, Ye Liu, Reilly Miller & Peter E. Latham - 2014 - Psychological Review 121 (1):96-123.
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  28. Critical Comment on "Learning and the Principle of Inverse Probability.".Robert P. Abelson - 1954 - Psychological Review 61 (4):276-278.
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  29. Can Free Evidence Be Bad? Value of Information for the Imprecise Probabilist.Seamus Bradley & Katie Steele - unknown
    This paper considers a puzzling conflict between two positions that are each compelling: it is irrational for an agent to pay to avoid `free' evidence before making a decision, and rational agents may have imprecise beliefs and/or desires. Indeed, we show that Good's theorem concerning the invariable choice-worthiness of free evidence does not generalise to the imprecise realm, given the plausible existing decision theories for handling imprecision. A key ingredient in the analysis, and a potential source of controversy, is the (...)
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  30. Cognitive Processes and the Assessment of Subjective Probability Distributions.Robin M. Hogarth - 1975 - Journal of the American Statistical Association 70 (350):271-289.
    This article considers the implications of recent research on judgmental processes for the assessment of subjective probability distributions. It is argued that since man is a selective, sequential information processing system with limited capacity, he is ill-suited for assessing probability distributions. Various studies attesting to man's difficulties in acting as an "intuitive statistician" are summarized in support of this contention. The importance of task characteristics on judgmental performance is also emphasized. A critical survey of the probability assessment literature is provided (...)
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  31. Foundations of a Probabilistic Theory of Causal Strength.Jan Sprenger - 2018 - Philosophical Review 127 (3):371-398.
    This paper develops axiomatic foundations for a probabilistic-interventionist theory of causal strength. Transferring methods from Bayesian confirmation theory, I proceed in three steps: I develop a framework for defining and comparing measures of causal strength; I argue that no single measure can satisfy all natural constraints; I prove two representation theorems for popular measures of causal strength: Pearl's causal effect measure and Eells' difference measure. In other words, I demonstrate these two measures can be derived from a set of plausible (...)
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  32. Argumenty kondukcyjne.Marcin Selinger - 2014 - Studia Philosophica Wratislaviensia 9 (4):53-63.
    The term "conduction" introduced by Wellman in 1971 is almost absent in the Polish literature on arguments. Contemporarily, conductive arguments are mostly understood as pro and contra arguments, which consist not only of normal pro-premises supporting a conclusion, but also of contra-premises (exceptions) denying it. We explain why such an interpretation seems to be attractive from the logical point of view, and we propose a formal method of representing conductive arguments and calculating the acceptability of their conclusions. The method allows (...)
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  33. Probability and Causality in the Early Works of Hans Reichenbach.Flavia Padovani - 2008 - Dissertation, University of Geneva
  34. Pluralism in Probabilistic Justification.David Atkinson & Jeanne Peijnenburg - unknown
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  35. Therapeutic Inferences for Individual Patients.Luis Flores - 2015 - Journal of Evaluation in Clinical Practice 21 (3):440-447.
    RATIONALE, AIMS AND OBJECTIVES: Increased awareness of the gap between controlled research and medical practice has raised concerns over whether the special attention of doctors to probability estimates from clinical trials really improves the care of individuals. Evidence-based medicine has acknowledged that research results are not applicable to all kinds of patients, and consequently, has attempted to overcome this limitation by introducing improvements in the design and analysis of clinical trials. METHODS: A clinical case is used to highlight the premises (...)
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  36. The Effect of Imprecise Expressions in Argumentation-Theory and Experimental Results.Christian Dahlman, Farhan Sarwar, Rasmus Bååth, Lena Wahlberg & Sverker Sikström - unknown
    We investigate argumentation where an expression is substituted with a less precise expression. We propose that the effect that this deprecization has on the audience be called deprecization effect. When the audience agrees more with the less precise version of the argument, there is a positive deprecization effect. We conducted an experiment where the participants were presented with a court room scenario. The results of the experiment confirm the following hypothesis: If the participants find it hard to agree with the (...)
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  37. HEMPEL and ROST, Von Ugarit Nach Qumran. [REVIEW]Paul Winter - 1958 - Hibbert Journal 57:204.
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  38. The Principles of Science a College Text-Book.William Forbes Cooley - 1912 - H. Holt and Company.
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  39. Gott Und Das Denken Nach Schellings Spätphilosophie. [REVIEW]J. V. M. - 1972 - Review of Metaphysics 25 (4):755-756.
    Author of a short study on Franz von Baader Klaus, Hemmerle presents us now with a longer study on the last philosophy of Schelling. The book sets out to be an exercise in Mitdenken. Instead of accumulating footnotes and going through the usual painstaking ways of a scholarly exegesis of texts, Hemmerle tries to think with Schelling, along the lines of Schelling's thought; and he does this a rather original way. Motivated by a genuine enthusiasm for Schelling, Hemmerle paraphrases and (...)
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  40. Some Aesthetic Decisions: The Photographs of Judy Fiskin.Virginia Heckert - 2011 - J. Paul Getty Museum.
    "A monograph of the work of Los Angeles-based artist Judy Fiskin.
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  41. Michael G. Titelbaum , Quitting Certainties . Reviewed By.Simon D.’Alfonso - 2014 - Philosophy in Review 34 (1-2):34-36.
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  42. Fixed or Probable Ideas?Hugh Gash - 2014 - Foundations of Science 19 (3):283-284.
    This commentary on Nescolarde-Selva and Usó-Doménech (Found Sci, 2013) raises questions about the dynamic versus static nature of the model proposed, and in addition asks whether the model might be used to explain ethical flexibility and rigidity.
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  43. Biasing Frequency Estimates by Dichotomous Questions.Dj Mingay, Mt Greenwell & Cl Kelley - 1989 - Bulletin of the Psychonomic Society 27 (6):520-520.
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  44. Hempel and Oppenbeim Revisited, Again.Herman E. Stark - 2003 - Epistemologia 26 (2):237-266.
  45. Principles and Procedures of Statistics, with Special Reference to the Biological Sciences.R. G. Carpenter - 1960 - The Eugenics Review 52 (3):172.
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  46. Probabilistic Modeling in Physics.Claus Beisbart - 2011 - In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford University Press. pp. 143.
  47. The Day of the Dolphins: Puzzling Over Epistemic Partnership.Bas C. Van Fraassen - 2005 - In John Woods, Kent A. Peacock & A. D. Irvine (eds.), Mistakes of Reason: Essays in Honour of John Woods. University of Toronto Press. pp. 111-133.
  48. Stopping the Murdering Martyrs.Ahm Van Iersel - 2005 - In Wim Smit (ed.), Just War and Terrorism: The End of the Just War Concept? Peeters.
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  49. Empty Time and Indifference to Being.Michel Haar - 1999 - In James Risser (ed.), Heidegger Toward the Turn: Essays on the Work of the 1930s. State University of New York Press. pp. 295--318.
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  50. Essai Sur le Phénomène de L'Indifférence.Liubava Moreva - 2004 - Diogène 206 (2):47.
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