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Probabilistic Reasoning

Assistant editor: Joshua Luczak (University of Western Ontario, Georgetown University)
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), van 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 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 manuscript.
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  1. Robert P. Abelson (1954). Critical Comment on "Learning and the Principle of Inverse Probability.". Psychological Review 61 (4):276-278.
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  2. Martin Barrett & Elliott Sober (1994). The Second Law of Probability Dynamics. British Journal for the Philosophy of Science 45 (4):941-953.
    When the probability of causes, and the probability of effects, given causes, are each randomly assigned, entropy ‘usually’ increases.
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  3. Seamus Bradley & Katie Steele, Can Free Evidence Be Bad? Value of Information for the Imprecise Probabilist.
    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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  4. William Forbes Cooley (1912). The Principles of Science a College Text-Book. H. Holt and Company.
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  5. Christian Dahlman, Farhan Sarwar, Rasmus Bååth, Lena Wahlberg & Sverker Sikström, The Effect of Imprecise Expressions in Argumentation-Theory and Experimental Results.
    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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  6. J. Acacio de Barros, Carlos Montemayor & Leonardo De Assis (forthcoming). Contextuality in the Integrated Information Theory. 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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  7. Luis J. Flores (2015). Therapeutic Inferences for Individual Patients. 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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  8. Patrick Forber (2012). Modeling Scientific Evidence: The Challenge of Specifying Likelihoods. In Henk W. de Regt (ed.), Epsa Philosophy of Science: Amsterdam 2009. Springer. pp. 55--65.
    Evidence is an objective matter. This is the prevailing view within science, and confirmation theory should aim to capture the objective nature of scientific evidence. Modeling an objective evidence relation in a probabilistic framework faces two challenges: the probabilities must have the right epistemic foundation, and they must be specifiable given the hypotheses and data under consideration. Here I will explore how Sober's approach to confirmation handles these challenges of foundation and specification. In particular, I will argue that the specification (...)
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  9. Malcolm Forster (2007). A Philosopher's Guide to Empirical Success. Philosophy of Science 74 (5):588-600.
    The simple question, what is empirical success? turns out to have a surprisingly complicated answer. We need to distinguish between meritorious fit and ‘fudged fit', which is akin to the distinction between prediction and accommodation. The final proposal is that empirical success emerges in a theory dependent way from the agreement of independent measurements of theoretically postulated quantities. Implications for realism and Bayesianism are discussed. ‡This paper was written when I was a visiting fellow at the Center for Philosophy of (...)
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  10. C. R. Gallistel, Monika Krishan, Ye Liu, Reilly Miller & Peter E. Latham (2014). The Perception of Probability. Psychological Review 121 (1):96-123.
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  11. Benjamin Ginzburg (1934). Probability and the Philosophical Foundations of Scientific Knowledge. Philosophical Review 43 (3):258-278.
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  12. James G. Greeno (1970). Theoretical Entities in Statistical Explanation. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1970:3 - 26.
  13. Robin M. Hogarth (1975). Cognitive Processes and the Assessment of Subjective Probability Distributions. 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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  14. Philip E. B. Jourdain (1919). Causality, Induction, and Probability (I.). Mind 28 (110):162-179.
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  15. Martin H. Krieger (1995). Could the Probability of Doom Be Zero or One? Journal of Philosophy 92 (7):382-387.
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  16. Theo A. F. Kuipers (2009). Empirical Progress and Truth Approximation by the 'Hypothetico-Probabilistic Method'. Erkenntnis 70 (3):313 - 330.
    Three related intuitions are explicated in this paper. The first is the idea that there must be some kind of probabilistic version of the HD-method, a ‘Hypothetico-Probabilistic (HP-) method’, in terms of something like probabilistic consequences, instead of deductive consequences. According to the second intuition, the comparative application of this method should also be functional for some probabilistic kind of empirical progress, and according to the third intuition this should be functional for something like probabilistic truth approximation. In all three (...)
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  17. Theo A. F. Kuipers (1983). Non-Inductive Explication of Two Inductive Intuitions. British Journal for the Philosophy of Science 34 (3):209-223.
    In section I the notions of logical and inductive probability will be discussed as well as two explicanda, viz. degree of confirmation, the base for inductive probability, and degree of evidential support, Popper's favourite explicandum. In section II it will be argued that Popper's paradox of ideal evidence is no paradox at all; however, it will also be shown that Popper's way out has its own merits.
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  18. Johannes Lenhard (2006). Models and Statistical Inference: The Controversy Between Fisher and Neyman–Pearson. British Journal for the Philosophy of Science 57 (1):69-91.
    The main thesis of the paper is that in the case of modern statistics, the differences between the various concepts of models were the key to its formative controversies. The mathematical theory of statistical inference was mainly developed by Ronald A. Fisher, Jerzy Neyman, and Egon S. Pearson. Fisher on the one side and Neyman–Pearson on the other were involved often in a polemic controversy. The common view is that Neyman and Pearson made Fisher's account more stringent mathematically. It is (...)
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  19. Isaac Levi (1983). Kyburg on Random Designators. Philosophy of Science 50 (4):635-642.
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  20. Isaac Levi (1971). Certainty, Probability and the Correction of Evidence. Noûs 5 (3):299-312.
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  21. Patrick Maher (1993). Howson and Franklin on Prediction. Philosophy of Science 60 (2):329-340.
    Evidence for a hypothesis typically confirms the hypothesis more if the evidence was predicted than if it was accommodated. Or so I argued in previous papers, where I also developed an analysis of why this should be so. But this was all a mistake if Howson and Franklin (1991) are to be believed. In this paper, I show why they are not to be believed. I also identify a grain of truth that may have been dimly grasped by those Bayesians (...)
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  22. Ilkka Niiniluoto (1978). High Probability and Inductive Systematization. Journal of Philosophy 75 (12):737-739.
  23. Jeanne Peijnenburg & David Atkinson, Probabilistic Justification.
    We discuss two objections that foundationalists have raised against infinite chains of probabilistic justification. We demonstrate that neither of the objections can be maintained.
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  24. Phillip E. Pfeifer (forthcoming). The Promise of Pick-the-Winners Contests for Producing Crowd Probability Forecasts. Theory and Decision.
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  25. Michael Redhead (1985). On the Impossibility of Inductive Probability. British Journal for the Philosophy of Science 36 (2):185-191.
  26. A. D. Ritchie (1926). Induction and Probability. Mind 35 (139):301-318.
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  27. Chester Townsend Ruddick (1940). Cournot's Doctrine of Philosophical Probability. Philosophical Review 49 (4):415-423.
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  28. Ferdinand Schoeman (1987). Statistical Vs. Direct Evidence. Noûs 21 (2):179-198.
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  29. Marc Meléndez Schofield (2011). Probabilidad, causalidad y explicación. Theoria 26 (1):109-112.
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  30. Severin Schroeder, Hempel's Paradox, Law-Likeness and Causal Relations.
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  31. Severin Schroeder, Hempel's Paradox, Law-Likeness and Causal Relations.
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  32. Seamus Bradley and Katie Steele (2015). Can Free Evidence Be Bad? Value of Information for the Imprecise Probabilist. Philosophy of Science 83 (1):1-28.
    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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  33. László E. Szabó (2007). Objective Probability-Like Things with and Without Objective Indeterminism. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (3):626-634.
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  34. Bas C. van Fraassen (2005). The Day of the Dolphins: Puzzling Over Epistemic Partnership. 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.
  35. Jie Zheng, Marcelline R. Harris, Anna Maria Masci, Lin Yu, Alfred Hero, Barry Smith & Yongqun He (2016). The Ontology of Biological and Clinical Statistics (OBCS) for Standardized and Reproducible Statistical Analysis. 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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Bayesian Reasoning
  1. Balazs Aczel, Aba Szollosi & Bence Bago (forthcoming). Lax Monitoring Versus Logical Intuition: The Determinants of Confidence in Conjunction Fallacy. Lax Monitoring Versus Logical Intuition: The Determinants of Confidence in Conjunction Fallacy:1-19.
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  2. Balazs Aczel, Aba Szollosi & Bence Bago (2015). Lax Monitoring Versus Logical Intuition: The Determinants of Confidence in Conjunction Fallacy. Thinking and Reasoning 22 (1):99-117.
    ABSTRACTThe general assumption that people fail to notice discrepancy between their answer and the normative answer in the conjunction fallacy task has been challenged by the theory of Logical Intuition. This theory suggests that people can detect the conflict between the heuristic and normative answers even if they do not always manage to inhibit their intuitive choice. This theory gained support from the finding that people report lower levels of confidence in their choice after they commit the conjunction fallacy compared (...)
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  3. Max Albert (1992). Die Falsifikation Statistischer Hypothesen. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 23 (1):1 - 32.
    The Falsification of Statistical Hypotheses. It is widely held that falsification of statistical hypotheses is impossible. This view is supported by an analysis of the most important theories of statistical testing: these theories are not compatible with falsificationism. On the other hand, falsificationism yields a basically viable solution to the problems of explanation, prediction and theory testing in a deterministic context. The present paper shows how to introduce the falsificationist solution into the realm of statistics. This is done mainly by (...)
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  4. F. J. Anscombe (1951). Mr. Kneale on Probability and Induction. Mind 60 (239):299-309.
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  5. Joseph L. Austerweil & Thomas L. Griffiths (2013). A Nonparametric Bayesian Framework for Constructing Flexible Feature Representations. Psychological Review 120 (4):817-851.
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  6. A. J. Ayer (1979). Probability and Evidence. Cambridge University Press.
    In _Probability and Evidence_, one of Britain's foremost twentieth-century philosophers addresses central questions in the theory of knowledge and the philosophy of science. This book contains A.J. Ayer's John Dewey Lectures delivered at Columbia University, together with two additional essays, "Has Harrod Answered Hume?" and "The Problem of Conditionals.".
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  7. David Bakan (1953). Learning and the Principle of Inverse Probability. Psychological Review 60 (6):360-370.
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  8. G. A. Barnard (1972). Two Points in the Theory of Statistical Inference. British Journal for the Philosophy of Science 23 (4):329-331.
  9. Eric Barnes (1996). Thoughts on Maher's Predictivism. Philosophy of Science 63 (3):401-410.
    Predictivism asserts that where evidence E confirms theory T, E provides stronger support for T when E is predicted on the basis of T and then confirmed than when E is known before T's construction and 'used', in some sense, in the construction of T. Among the most interesting attempts to argue that predictivism is a true thesis (under certain conditions) is that of Patrick Maher (1988, 1990, 1993). The purpose of this paper is to investigate the nature of predictivism (...)
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  10. Eric Christian Barnes (1998). Probabilities and Epistemic Pluralism. British Journal for the Philosophy of Science 49 (1):31-47.
    A pluralistic scientific method is one that incorporates a variety of points of view in scientific inquiry. This paper investigates one example of pluralistic method: the use of weighted averaging in probability estimation. I consider two methods of weight determination, one based on disjoint evidence possession and the other on track record. I argue that weighted averaging provides a rational procedure for probability estimation under certain conditions. I consider a strategy for calculating ‘mixed weights’ which incorporate mixed information about agent (...)
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  11. Thomas Bartelborth (2016). How Strong is the Confirmation of a Hypothesis by Significant Data? Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 47 (2):277-291.
    The aim of the article is to propose a way to determine to what extent a hypothesis H is confirmed if it has successfully passed a classical significance test. Bayesians have already raised many serious objections against significance testing, but in doing so they have always had to rely on epistemic probabilities and a further Bayesian analysis, which are rejected by classical statisticians. Therefore, I will suggest a purely frequentist evaluation procedure for significance tests that should also be accepted by (...)
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  12. Etienne-Emile Baulieu (1992). Updating RU 486 Development. Journal of Law, Medicine and Ethics 20 (3):154-156.
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  13. Darlene Bay & Alexey Nikitkov (2011). Subjective Probability Assessments of the Incidence of Unethical Behavior: The Importance of Scenario-Respondent Fit. Business Ethics: A European Review 20 (1):1-11.
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  14. A. G. Bearn & G. C. F. Bearn (1985). The Prevalence of Humbug and Other Essays by Max Black. Perspectives in Biology and Medicine 29 (1):170-174.
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  15. S. D. Belcher (2014). Can Grey Ravens Fly?: Beyond Frayling’s Categories. Arts and Humanities in Higher Education 13 (3):235-242.
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