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Probabilistic Reasoning

Edited by Jonathan Weisberg (University of Toronto)
Assistant editor: Joshua Luczak (University of Western Ontario)
About this topic
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 2010, Finetti 1989, Savage 1954, and Joyce 1998.  Locus classici for additional probabilistic principles are Lewis 1980 (chance-credence), Fraassen 1984 (reflection), Carnap 1962, Jaynes 1973 (indifference), and Lewis 2010 (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 1975 is an excellent and gentle introduction for non-initiates.  A next step up is Jeffrey 1983.  More advanced introductions are Howson & Urbach 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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Bayesian Reasoning
  1. David Cox & Deborah G. Mayo (2010). Objectivity and Conditionality in Frequentist Inference. In Deborah G. Mayo & Aris Spanos (eds.), Error and Inference: Recent Exchanges on Experimental Reasoning, Reliability, and the Objectivity and Rationality of Science. Cambridge University Press 276.
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  2. Donald Gillies (1990). Bayesianism Versus Falsifigationism. Ratio 3 (1):82-98.
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  3. T. R. Girill (1978). Are Requirement and Confirmation Analogous? Philosophical Studies 33 (4):339 - 349.
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  4. R. Goldstone (1992). The Effects of Feature Distribution on Estimation. Bulletin of the Psychonomic Society 30 (6):480-481.
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  5. Rebecca Gómez (2009). Statistical Learning in Infant Language Development. In Gareth Gaskell (ed.), Oxford Handbook of Psycholinguistics. OUP Oxford
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  6. Christophe Gonzales & Pierre-Henri Wuillemin (2011). PRM Inference Using Jaffray & Faÿ's Local Conditioning. Theory and Decision 71 (1):33-62.
    Probabilistic Relational Models (PRMs) are a framework for compactly representing uncertainties (actually probabilities). They result from the combination of Bayesian Networks (BNs), Object-Oriented languages, and relational models. They are specifically designed for their efficient construction, maintenance and exploitation for very large scale problems, where BNs are known to perform poorly. Actually, in large-scale problems, it is often the case that BNs result from the combination of patterns (small BN fragments) repeated many times. PRMs exploit this feature by defining these patterns (...)
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  7. I. J. Good, Ian Hacking, R. C. Jeffrey & Håkan Törnebohm (1966). The Estimation of Probabilities: An Essay on Modern Bayesian Methods. Synthese 16 (2):234-244.
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  8. Mark Goodale (2011). Becoming Irrelevant. In Thomas Cushman (ed.), Handbook of Human Rights. Routledge 180.
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  9. Nelson Goodman (1947). On Infirmities of Confirmation-Theory. Philosophy and Phenomenological Research 8 (1):149-151.
  10. Noah D. Goodman, Chris L. Baker & Joshua B. Tenenbaum (2009). Cause and Intent: Social Reasoning in Causal Learning. In N. A. Taatgen & H. van Rijn (eds.), Proceedings of the 31st Annual Conference of the Cognitive Science Society. 2759--2764.
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  11. Jacqueline Jarrett Goodnow & Leo Postman (1955). Probability Learning in a Problem-Solving Situation. Journal of Experimental Psychology 49 (1):16.
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  12. Alison Gopnik, Causal Learning Across Domains.
    Five studies investigated (a) children’s ability to use the dependent and independent probabilities of events to make causal inferences and (b) the interaction between such inferences and domain-specific knowledge. In Experiment 1, preschoolers used patterns of dependence and independence to make accurate causal inferences in the domains of biology and psychology. Experiment 2 replicated the results in the domain of biology with a more complex pattern of conditional dependencies. In Experiment 3, children used evidence about patterns of dependence and independence (...)
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  13. Gerd Graßhoff (2011). Inferences to Causal Relevance From Experiments. In Dennis Dieks, Wenceslao Gonzalo, Thomas Uebel, Stephan Hartmann & Marcel Weber (eds.), Explanation, Prediction, and Confirmation. Springer 167--182.
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  14. Christopher D. Green (2002). Comment on Chow's "Issues in Statistical Inference". Philosophical Explorations.
    Contrary to Chow, Wilkinson's report, though more tentative than it might have been, is a reasoned and valuable contribution to psychological science. For those who are quite familiar with the details of statistical methods, it confirms much of what has been happening in the literature over the past few decades. For those who have not been keeping abreast of new developments on the statistical scene, it alerts them in a gentle way that there have been some important changes since they (...)
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  15. Nicholas Griffin (1975). Has Harre Solved Hempel's Paradox? Mind 84 (335):426-430.
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  16. Geoffrey R. Grimmett (1986). Probability: An Introduction. Oxford University Press.
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  17. Charles Charles Miller Grinstead & James Laurie Snell (1997). Introduction to Probability. American Mathematical Soc..
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  18. Barbro Gustafsson & Ingmar Pörn (1994). A Motivational Approach to Confirmation: An Interpretation of Dysphagic Patients' Experiences. Theoretical Medicine and Bioethics 15 (4).
    In this paper we articulate confirmation and disconfirmation as components in human motivation. We develop a theory of motivation on the basis of a model of human action and we explore aspects of confirmation and disconfirmation in the context of the meeting of dysphagic patients with their physicians. We distinguish four central elements in confirmation and disconfirmation and use these and the relations between them for the purpose of constructing a typology. Finally, on the basis of the results obtained we (...)
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  19. Alan H.Ájek (1998). Agnosticism Meets Bayesianism. Analysis 58 (3):199-206.
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  20. Ian Hacking (1968). On Falling Short of Strict Coherence. Philosophy of Science 35 (3):284-286.
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  21. Alan Hajek (2008). Probability—A Phifosophical Overview. In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America 323.
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  22. Alan Hájek & James M. Joyce (2008). Confirmation. In S. Psillos & M. Curd (eds.), The Routledge Companion to the Philosophy of Science. Routledge
    Confirmation theory is intended to codify the evidential bearing of observations on hypotheses, characterizing relations of inductive “support” and “counter­support” in full generality. The central task is to understand what it means to say that datum E confirms or supports a hypothesis H when E does not logically entail H.
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  23. Marsha Hanen (1975). Confirmation, Explanation and Acceptance. In Keith Lehrer (ed.), Analysis and Metaphysics. Springer 93--128.
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  24. Marsha Pearlman Hanen (1970). An Examination of Adequacy Conditions for Confirmation. Dissertation, Brandeis University
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  25. Robin Hanson (2006). Uncommon Priors Require Origin Disputes. Theory and Decision 61 (4):319-328.
    In standard belief models, priors are always common knowledge. This prevents such models from representing agents’ probabilistic beliefs about the origins of their priors. By embedding standard models in a larger standard model, however, pre-priors can describe such beliefs. When an agent’s prior and pre-prior are mutually consistent, he must believe that his prior would only have been different in situations where relevant event chances were different, but that variations in other agents’ priors are otherwise completely unrelated to which events (...)
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  26. Maralee Harrell & Clark Glymour (2002). Confirmation And Chaos. Philosophy of Science 69 (2):256-265.
    Recently, Rueger and Sharp (1996) and Koperski (1998) have been concerned to show that certain procedural accounts of model confirmation are compromised by non-linear dynamics. We suggest that the issues raised are better approached by considering whether chaotic data analysis methods allow for reliable inference from data. We provide a framework and an example of this approach.
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  27. Maralee Harrell & Clark Glymour (2002). Confirmation and Chaos. Philosophy of Science 69 (2):256-265.
    Recently, Rueger and Sharp (1996) and Koperski (1998) have been concerned to show that certain procedural accounts of model confirmation are compromised by non‐linear dynamics. We suggest that the issues raised are better approached by considering whether chaotic data analysis methods allow for reliable inference from data. We provide a framework and an example of this approach.
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  28. Evan Heit (2008). Models of Inductive Reasoning. In Ron Sun (ed.), The Cambridge Handbook of Computational Psychology. Cambridge University Press 322--338.
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  29. Casey Helgeson, The Confirmational Significance of Agreeing Measurements.
    Agreement between \independent" measurements of a theoretically posited quantity is intuitively compelling evidence that a theory is, loosely speaking, on the right track. But exactly what conclusion is warranted by such agreement? I propose a new account of the phenomenon's epistemic significance within the framework of Bayesian epistemology. I contrast my proposal with the standard Bayesian treatment, which lumps the phenomenon under the heading of \evidential diversity.".
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  30. Carl G. Hempel (1945). Studies in the Logic of Confirmation (I.). Mind 54 (213):1-26.
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  31. Carl G. Hempel (1945). Studies in the Logic of Confirmation (II.). Mind 54 (214):97-121.
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  32. Carl G. Hempel & Paul Oppenheim (1945). A Definition of "Degree of Confirmation". Philosophy of Science 12 (2):98-115.
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  33. Vincent F. Hendricks, Stig Andur Pederson & Klaus Frovin Jørgensen (eds.) (2001). Probability Theory: Philosophy, Recent History and Relations to Science. Synthese Library, Kluwer.
    This book sheds light on some recent discussions of the problems in probability theory and their history, analysing their philosophical and mathematical significance, and the role pf mathematical probability theory in other sciences.
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  34. Christian Hennig (2012). Deborah G. Mayo & Aris Spanos, Eds. 2009. Error and Inference (Christian Hennig). Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 27 (2):245-247.
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  35. Jaakko Hintikka (1970). Unknown Probabilities, Bayesianism, and de Finetti's Representation Theorem. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1970:325 - 341.
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  36. R. J. Hirst & S. F. Barker (1960). Induction and Hypothesis: A Study of the Logic of Confirmation. Philosophical Quarterly 10 (41):375.
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  37. Gábor Hofer-Szabó (forthcoming). Relating Bell’s Local Causality to the Causal Markov Condition. Foundations of Physics:1-27.
    The aim of the paper is to relate Bell’s notion of local causality to the Causal Markov Condition. To this end, first a framework, called local physical theory, will be introduced integrating spatiotemporal and probabilistic entities and the notions of local causality and Markovity will be defined. Then, illustrated in a simple stochastic model, it will be shown how a discrete local physical theory transforms into a Bayesian network and how the Causal Markov Condition arises as a special case of (...)
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  38. Ulrich Hoffrage & Gerd Gigerenzer (1996). The Impact of Information Representation on Bayesian Reasoning. In Garrison W. Cottrell (ed.), Proceedings of the Eighteenth Annual Conference of the Cognitive Science Society. Lawrence Erlbaum 126--130.
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  39. C. A. Hooker & D. Stove (1968). Relevance and the Ravens. British Journal for the Philosophy of Science 18 (4):305-315.
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  40. Paul Horwich (1993). Wittgensteinian bayesianism. Midwest Studies in Philosophy 18 (1):62-75.
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  41. Hykel Hosni, Book Review: In Defence of Objective Bayesianism. [REVIEW]
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  42. Colin Howson (2007). An Interview with Colin Howson. The Reasoner 1 (6):1-3.
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  43. Colin Howson (1984). Bayesianism and Support by Novel Facts. British Journal for the Philosophy of Science 35 (3):245-251.
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  44. Franz Huber (2007). The Logic of Theory Assessment. Journal of Philosophical Logic 36 (5):511-538.
    This paper starts by indicating the analysis of Hempel's conditions of adequacy for any relation of confirmation (Hempel, 1945) as presented in Huber (submitted). There I argue contra Carnap (1962, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausible theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. The main part of the paper (...)
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  45. Franz Huber (2005). The Logic of Confirmation and Theory Assessment. In L. Behounek & M. Bilkova (eds.), The Logica Yearbook. Filosofia
    This paper discusses an almost sixty year old problem in the philosophy of science -- that of a logic of confirmation. We present a new analysis of Carl G. Hempel's conditions of adequacy (Hempel 1945), differing from the one Carnap gave in §87 of his Logical Foundations of Probability (1962). Hempel, it is argued, felt the need for two concepts of confirmation: one aiming at true theories and another aiming at informative theories. However, he also realized that these two concepts (...)
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  46. Paul Humphreys (1980). Inference, Method, and Decision. International Studies in Philosophy 12 (1):90-91.
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  47. B. Hutton (forthcoming). Hydrography: Compiling and Updating the Nautical Chart. Veritas: Revista de Filosofia da PUCRS.
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  48. Christiaan Huygens (2009). Successful Hypotheses and High Probability. In Timothy J. McGrew, Marc Alspector-Kelly & Fritz Allhoff (eds.), The Philosophy of Science: An Historical Anthology. Wiley-Blackwell 162.
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  49. Compresence is A. Bundle (forthcoming). Jeffrey Grupp. Metaphysica.
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  50. R. Jardine (1965). The Resolution of the Confirmation Paradox. Australasian Journal of Philosophy 43 (3):359 – 368.
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