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Probabilistic Reasoning

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, 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 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 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 manuscript.
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  1. Critical Comment on "Learning and the Principle of Inverse Probability.".Robert P. Abelson - 1954 - Psychological Review 61 (4):276-278.
  2. Mr. Kneale on Probability and Induction I.F. J. Anscombe - 1951 - Mind 60 (239):299-309.
  3. Transitivity and Partial Screening Off.David Atkinson & Jeanne Peijnenburg - 2013 - Theoria 79 (4):294-308.
    The notion of probabilistic support is beset by well-known problems. In this paper we add a new one to the list: the problem of transitivity. Tomoji Shogenji has shown that positive probabilistic support, or confirmation, is transitive under the condition of screening off. However, under that same condition negative probabilistic support, or disconfirmation, is intransitive. Since there are many situations in which disconfirmation is transitive, this illustrates, but now in a different way, that the screening-off condition is too restrictive. We (...)
  4. The Second Law of Probability Dynamics.Martin Barrett & Elliott Sober - 1994 - 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.
  5. Probabilistic Modeling in Physics.Claus Beisbart - 2011 - In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford University Press. pp. 143.
  6. Can Free Evidence Be Bad? Value of Information for the Imprecise Probabilist.Seamus Bradley & Katie Steele - 2016 - 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 (...)
  7. 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.
  8. Principles and Procedures of Statistics, with Special Reference to the Biological Sciences.R. G. Carpenter - 1960 - The Eugenics Review 52 (3):172.
  9. Can Coherence Generate Warrant "Ex Nihilo"? Probability and the Logic of Concurring Witnesses.Cleve James van - 2011 - Philosophy and Phenomenological Research 82 (2):337 - 380.
    Most foundationalists allow that relations of coherence among antecedently justified beliefs can enhance their overall level of justification or warrant. In light of this, some coherentists ask the following question: if coherence can elevate the epistemic status of a set of beliefs, what prevents it from generating warrant entirely on its own? Why do we need the foundationalist's basic beliefs? I address that question here, drawing lessons from an instructive series of attempts to reconstruct within the probability calculus the classical (...)
  10. Probability as a Guide to Life. Co-Authored & Helen Beebee - 2003 - In David Papineau (ed.), The Roots of Reason: Philosophical Essays on Rationality, Evolution, and Probability. Oxford University Press.
  11. The Principles of Science a College Text-Book.William Forbes Cooley - 1912 - H. Holt and Company.
  12. Review of 'Quitting Certainties'. [REVIEW]Simon D'Alfonso - 2014 - Philosophy in Review 34:34-36.
  13. A Theory of Conclusions.Raymond Dacey - 1978 - Philosophy of Science 45 (4):563-574.
    This paper presents a theory of conclusions based upon the suggestions of Tukey [21]. The logic offered here is based upon two rules of detachment that occur naturally in probabilistic inference, a traditional rule of acceptance, and a rule of rejection. The rules of detachment provide flexibility: the theory of conclusions can account for both statistical and deductive arguments. The rule of acceptance governs the acceptance of new conclusions, is a variant of the rule of high probability, and is a (...)
  14. 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 (...)
  15. Hempel Revisited.A. J. Dale - 1984 - Analysis 44 (2):90 - 92.
  16. 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, (...)
  17. 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 (...)
  18. The Epistemic Status of Probabilistic Proof.Don Fallis - 1997 - Journal of Philosophy 94 (4):165.
  19. Therapeutic Inferences for Individual Patients.Luis J. 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 (...)
  20. Modeling Scientific Evidence: The Challenge of Specifying Likelihoods.Patrick Forber - 2012 - 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 (...)
  21. A Philosopher's Guide to Empirical Success.Malcolm Forster - 2007 - 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 (...)
  22. Distance From Indifference.Ivan Fox - 1978 - Erkenntnis 12 (2):249 - 279.
  23. The Perception of Probability.C. R. Gallistel, Monika Krishan, Ye Liu, Reilly Miller & Peter E. Latham - 2014 - Psychological Review 121 (1):96-123.
  24. 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.
  25. Conditional Random Quantities and Compounds of Conditionals.Angelo Gilio & Giuseppe Sanfilippo - 2014 - Studia Logica 102 (4):709-729.
    In this paper we consider conditional random quantities (c.r.q.’s) in the setting of coherence. Based on betting scheme, a c.r.q. X|H is not looked at as a restriction but, in a more extended way, as \({XH + \mathbb{P}(X|H)H^c}\) ; in particular (the indicator of) a conditional event E|H is looked at as EH + P(E|H)H c . This extended notion of c.r.q. allows algebraic developments among c.r.q.’s even if the conditioning events are different; then, for instance, we can give a (...)
  26. Probability Perplexities.Robert Gilson - 1996 - World Futures 47 (4):311-317.
  27. Probability and the Philosophical Foundations of Scientific Knowledge.Benjamin Ginzburg - 1934 - Philosophical Review 43 (3):258-278.
  28. Theoretical Entities in Statistical Explanation.James G. Greeno - 1970 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1970:3 - 26.
  29. Probability: A Graduate Course.Allan Gut - 2005 - Springer.
  30. Reden von Gott. Reflexionen Zur Analytischen Philosophie der Religiösen Sprache.G. H. H. - 1976 - Review of Metaphysics 29 (4):732-733.
  31. 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.
  32. LHC Forecasts: Better Than Horoscopes?Robin Hanson - unknown
    My horoscope today says, “Focus on the small stuff.” Now, such advice does have content. It predicts that when readers interpret its words in the usual way as a guide to action, those who do what they think it recommends will, on average, feel they got more of what they wanted than those who ignored it. Even so, astrologers sure don’t make it easy for us to test their claims. If they wanted to make it easier, they would do what (...)
  33. Inferring Probability Comparisons.Matthew Harrison-Trainor, Wesley H. Holliday & Thomas Icard - forthcoming - Mathematical Social Sciences.
    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 (...)
  34. 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.
  35. 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 (...)
  36. Stopping the Murdering Martyrs.Ahm Van Iersel - 2005 - In Wim Smit (ed.), Just War and Terrorism: The End of the Just War Concept? Peeters.
  37. Causality, Induction, and Probability (I.).Philip E. B. Jourdain - 1919 - Mind 28 (110):162-179.
  38. Metaphysics and Probability.John King-Farlow - 1968 - Philosophical Studies 17:38-59.
  39. Probability and Induction II.William Kneale - 1951 - Mind 60 (239):310-317.
  40. Could the Probability of Doom Be Zero or One?Martin H. Krieger - 1995 - Journal of Philosophy 92 (7):382-387.
  41. Empirical Progress and Truth Approximation by the 'Hypothetico-Probabilistic Method'.Theo A. F. Kuipers - 2009 - 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 (...)
  42. Non-Inductive Explication of Two Inductive Intuitions.Theo A. F. Kuipers - 1983 - 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.
  43. Models and Statistical Inference: The Controversy Between Fisher and Neyman–Pearson.Johannes Lenhard - 2006 - 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 (...)
  44. Kyburg on Random Designators.Isaac Levi - 1983 - Philosophy of Science 50 (4):635-642.
  45. Certainty, Probability and the Correction of Evidence.Isaac Levi - 1971 - Noûs 5 (3):299-312.
  46. Gott Und Das Denken Nach Schellings Spätphilosophie. [REVIEW]J. V. M. - 1972 - Review of Metaphysics 25 (4):755-756.
  47. Howson and Franklin on Prediction.Patrick Maher - 1993 - 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 (...)
  48. Biasing Frequency Estimates by Dichotomous Questions.Dj Mingay, Mt Greenwell & Cl Kelley - 1989 - Bulletin of the Psychonomic Society 27 (6):520-520.
  49. Essai Sur le Phénomène de L'Indifférence.Liubava Moreva - 2004 - Diogène 206 (2):47.
  50. The Pre-Objective Reconsidered.N. Munson Thomas - 1958 - Review of Metaphysics 12 (4):624 - 632.
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