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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. Mark Alfano (2007). A Critical Discussion Of The Compatibility Of Bayesianism And Inference To The Best Explanation. Philosophical Writings 34 (1).
    In this paper I critique Peter Lipton’s attempt to deal with the threat of Bayesianism to the normative aspect of his project in Inference to the Best Explanation. I consider the five approaches Lipton proposes for reconciling the doxastic recommendations of Inference to the Best Explanation with BA’s: IBE gives a ‘boost’ to the posterior probability of particularly ‘lovely’ hypotheses after the Bayesian calculation is performed; IBE helps us to set the likelihood of evidence on a given hypothesis; IBE helps (...)
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  2. Margaret Atack (1986). Sheila Jeffrey, The Spinster and Her Enemies. [REVIEW] Radical Philosophy 44:42.
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  3. Paul Frank Andrew Bartha (1994). Analogical Reasoning and Plausibility in the Sciences. Dissertation, University of Pittsburgh
    Analogical reasoning plays a significant role in the evolution of scientific thought. Not only is analogy extensively used in the early stages of investigation to demonstrate the plausibility of hypotheses, but in some fields, such as archaeology and evolutionary biology, it is often the strongest possible form of theoretical confirmation. This widely used form of reasoning, however, has seldom been subjected to rigorous examination by philosophers of science. Not surprisingly, there is a notable absence of standards for distinguishing between 'good' (...)
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  4. F. C. Benenson (1976). Probability, Frequency and Evidence.
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  5. S. Blackburn (1975). SWINBURNE, R. "An Introduction to Confirmation Theory". [REVIEW] Mind 84:146.
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  6. H. Bourgeois (1993). La Place de la Confirmation Dans l'Initiation Chrétienne. Nouvelle Revue Théologique 115 (4):516-542.
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  7. Susanta Chakrabarti (1993). Heuristic Approach to Scientific Theory-Confirmation. Indian Philosophical Quarterly 20 (2):189.
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  8. A. F. Chalmers (1981). Howson, Colin , "Method and Appraisal in the Physical Sciences". [REVIEW] Erkenntnis 16:167.
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  9. Kelly James Clark (1985). Probabilistic Confirmation Theory and the Existence of God. Dissertation, University of Notre Dame
    A recent development in the philosophy of religion has been the attempt to justify belief in God using Bayesian confirmation theory. My dissertation critically discusses two prominent spokesmen for this approach--Richard Swinburne and J. L. Mackie. Using probabilistic confirmation theory, these philosophers come to wildly divergent conclusions with respect to the hypothesis of theism; Swinburne contends that the evidence raises the overall probability of the hypothesis of theism, whereas Mackie argues that the evidence disconfirms the existence of God. After a (...)
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  10. 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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  11. Yehudah Freundlich (1976). Resurrecting the Ravens. Synthese 33 (1):341 - 354.
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  12. Lisbeth S. Fried & Cameron R. Peterson (1969). Information Seeking: Optional Versus Fixed Stopping. Journal of Experimental Psychology 80 (3p1):525.
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  13. Michael Friedman (1979). Truth and Confirmation. Journal of Philosophy 76 (7):361-382.
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  14. Zoubin Ghahramani (2002). Graphical Models: Parameter Learning. In M. Arbib (ed.), The Handbook of Brain Theory and Neural Networks. Mit Press. 2--486.
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  15. Jerzy Giedymin (1968). Confirmation, Counterfactuals and Projectibility. In Raymond Klibansky (ed.), Contemporary Philosophy. Firenze, la Nuova Italia. 2--70.
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  16. Ronald Nelson Giere (1968). Prediction and Confirmation. Dissertation, Cornell University
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  17. George F. Gilder & John Wohlstetter (forthcoming). Broadband or Bust! Inquiry.
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  18. Daniel Gile (1999). Testing the Effort Models' Tightrope Hypothesis in Simultaneous Interpreting-A Contribution. Hermes 23 (1999):153-172.
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  19. D. A. Gillies (1972). The Subjective Theory of Probability. [REVIEW] British Journal for the Philosophy of Science 23 (2):138-157.
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  20. Donald Gillies (2001). Bayesianism and the Fixity of the Theoretical Framework. In David Corfield & Jon Williamson (eds.), Foundations of Bayesianism. Kluwer Academic Publishers. 363--379.
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  21. Donald Gillies (2001). Critical Notices-Judea Pearl Causality: Models, Reasoning, and Inference. British Journal for the Philosophy of Science 52 (3):613-622.
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  22. Donald Gillies (1990). Bayesianism Versus Falsifigationism. Ratio 3 (1):82-98.
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  23. T. R. Girill (1978). Are Requirement and Confirmation Analogous? Philosophical Studies 33 (4):339 - 349.
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  24. R. Goldstone (1992). The Effects of Feature Distribution on Estimation. Bulletin of the Psychonomic Society 30 (6):480-481.
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  25. Rebecca Gómez (2009). Statistical Learning in Infant Language Development. In Gareth Gaskell (ed.), Oxford Handbook of Psycholinguistics. Oup Oxford.
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  26. 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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  27. 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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  28. Mark Goodale (2011). Becoming Irrelevant. In Thomas Cushman (ed.), Handbook of Human Rights. Routledge. 180.
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  29. Nelson Goodman (1947). On Infirmities of Confirmation-Theory. Philosophy and Phenomenological Research 8 (1):149-151.
  30. 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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  31. Jacqueline Jarrett Goodnow & Leo Postman (1955). Probability Learning in a Problem-Solving Situation. Journal of Experimental Psychology 49 (1):16.
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  32. 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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  33. 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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  34. 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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  35. Nicholas Griffin (1975). Has Harre Solved Hempel's Paradox? Mind 84 (335):426-430.
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  36. Geoffrey R. Grimmett (1986). Probability: An Introduction. Oxford University Press.
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  37. Charles Charles Miller Grinstead & James Laurie Snell (1997). Introduction to Probability. American Mathematical Soc..
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  38. 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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  39. Alan H.Ájek (1998). Agnosticism Meets Bayesianism. Analysis 58 (3):199-206.
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  40. Ian Hacking (1968). On Falling Short of Strict Coherence. Philosophy of Science 35 (3):284-286.
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  41. 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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  42. 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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  43. Marsha Hanen (1975). Confirmation, Explanation and Acceptance. In Keith Lehrer (ed.), Analysis and Metaphysics. Springer. 93--128.
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  44. Marsha Pearlman Hanen (1970). An Examination of Adequacy Conditions for Confirmation. Dissertation, Brandeis University
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  45. 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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  46. 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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  47. 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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  48. 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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  49. 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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  50. Carl G. Hempel (1945). Studies in the Logic of Confirmation (I.). Mind 54 (213):1-26.
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