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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 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 manuscript.
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  1. Direct Inference in the Material Theory of Induction.William Peden - unknown
    John D. Norton’s “Material Theory of Induction” has been one of the most intriguing recent additions to the philosophy of induction. Norton’s account appears to be a notably natural account of actual inductive practices, though his theory has attracted considerable criticisms. I detail several novel issues for his theory, but argue that supplementing the Material Theory with a theory of direct inference could address these problems. I argue that if this combination is possible, a stronger theory of inductive reasoning emerges, (...)
  2. 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 (...)
  3. The Promise of Pick-the-Winners Contests for Producing Crowd Probability Forecasts.Phillip E. Pfeifer - 2016 - Theory and Decision 81 (2):255-278.
  4. 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 (...)
  5. 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 (...)
  6. 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 (...)
  7. Hempel's Paradox, Law-Likeness and Causal Relations.Severin Schroeder - unknown
  8. 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 (...)
  9. 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, (...)
  10. 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.
  11. The Perception of Probability.C. R. Gallistel, Monika Krishan, Ye Liu, Reilly Miller & Peter E. Latham - 2014 - Psychological Review 121 (1):96-123.
  12. Critical Comment on "Learning and the Principle of Inverse Probability.".Robert P. Abelson - 1954 - Psychological Review 61 (4):276-278.
  13. 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 (...)
  14. 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 (...)
  15. 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 (...)
  16. Probability and Causality in the Early Works of Hans Reichenbach.Flavia Padovani - 2008 - Dissertation, University of Geneva
  17. Pluralism in Probabilistic Justification.David Atkinson & Jeanne Peijnenburg - unknown
  18. 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 (...)
  19. 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 (...)
  20. HEMPEL and ROST, Von Ugarit Nach Qumran. [REVIEW]Paul Winter - 1958 - Hibbert Journal 57:204.
  21. The Principles of Science a College Text-Book.William Forbes Cooley - 1912 - H. Holt and Company.
  22. Gott Und Das Denken Nach Schellings Spätphilosophie. [REVIEW]J. V. M. - 1972 - Review of Metaphysics 25 (4):755-756.
  23. 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.
  24. Michael G. Titelbaum , Quitting Certainties . Reviewed By.Simon D.’Alfonso - 2014 - Philosophy in Review 34 (1-2):34-36.
  25. 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.
  26. Biasing Frequency Estimates by Dichotomous Questions.Dj Mingay, Mt Greenwell & Cl Kelley - 1989 - Bulletin of the Psychonomic Society 27 (6):520-520.
  27. Hempel and Oppenbeim Revisited, Again.Herman E. Stark - 2003 - Epistemologia 26 (2):237-266.
  28. Principles and Procedures of Statistics, with Special Reference to the Biological Sciences.R. G. Carpenter - 1960 - The Eugenics Review 52 (3):172.
  29. Probabilistic Modeling in Physics.Claus Beisbart - 2011 - In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford University Press. pp. 143.
  30. 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.
  31. Stopping the Murdering Martyrs.Ahm Van Iersel - 2005 - In Wim Smit (ed.), Just War and Terrorism: The End of the Just War Concept? Peeters.
  32. 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.
  33. Essai Sur le Phénomène de L'Indifférence.Liubava Moreva - 2004 - Diogène 206 (2):47.
  34. Locating and Identifying the Baths of Bab Al-Mardun (or of the Cross).Jean Passini - 2010 - Al-Qantara: Revista de Estudios Árabes 31 (1):211 - 223.
  35. 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 (...)
  36. The Confirmational Significance of Agreeing Measurements.Casey Helgeson - 2013 - Philosophy of Science 80 (5):721-732.
    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".
  37. Formalna ocena argumentacji.Marcin Selinger - 2012 - Przeglad Filozoficzny - Nowa Seria 81 (1):89-109.
    Naszym celem jest dostarczenie formalnego modelu oceny możliwie szerokiej klasy argumentacji, w szczególności tych, które pojawiają się w kontekstach naturalnych. We wprowadzeniu przedstawiamy elementarne sposoby rozbudowywania argumentacji prostych w coraz bardziej złożone struktury. W drugim rozdziale podajemy ścisłe definicje pojęć służących do opisu tych struktur — argumentację definiujemy jako niepusty i skończony zbiór sekwentów, tj. jako niepustą i skończoną relację zachodzącą pomiędzy niepustymi i skończonymi zbio-rami zdań a pojedynczymi zdaniami danego języka; wprowadzamy także kilka pojęć (nie-spójność, rozbieżność, kolistość), które pozwalają (...)
  38. Probability: A Graduate Course.Allan Gut - 2005 - Springer.
  39. Can Coherence Generate Warrant "Ex Nihilo"? Probability and the Logic of Concurring Witnesses.James Van Cleve - 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 (...)
  40. 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 (...)
  41. Probabilidad, causalidad y explicación.Marc Meléndez Schofield - 2011 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 26 (1):109-112.
  42. Reden von Gott. Reflexionen Zur Analytischen Philosophie der Religiösen Sprache.G. H. H. - 1976 - Review of Metaphysics 29 (4):732-733.
  43. Metaphysics and Probability.John King-Farlow - 1968 - Philosophical Studies 17:38-59.
  44. When Adjunction Fails.Choh Man Teng - 2012 - Synthese 186 (2):501-510.
    The rule of adjunction is intuitively appealing and uncontroversial for deductive inference, but in situations where information can be uncertain, the rule is neither needed nor wanted for rational acceptance, as illustrated by the lottery paradox. Practical certainty is the acceptance of statements whose chances of error are smaller than a prescribed threshold parameter, when evaluated against an evidential corpus. We examine the failure of adjunction in relation to the threshold parameter for practical certainty, with an eye towards reinstating the (...)
  45. The Pre-Objective Reconsidered.Thomas N. Munson - 1958 - Review of Metaphysics 12 (4):624 - 632.
  46. Theoretical Entities in Statistical Explanation.James G. Greeno - 1970 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1970:3 - 26.
  47. Hempel Revisited.A. J. Dale - 1984 - Analysis 44 (2):90 - 92.
  48. Probabilistic Justification.Jeanne Peijnenburg & David Atkinson - unknown
    We discuss two objections that foundationalists have raised against infinite chains of probabilistic justification. We demonstrate that neither of the objections can be maintained.
  49. Objective Probability-Like Things with and Without Objective Indeterminism.László E. Szabó - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (3):626-634.
    I shall argue that there is no such property of an event as its “probability.” This is why standard interpretations cannot give a sound definition in empirical terms of what “probability” is, and this is why empirical sciences like physics can manage without such a definition. “Probability” is a collective term, the meaning of which varies from context to context: it means different — dimensionless [0, 1]-valued — physical quantities characterising the different particular situations. In other words, probability is a (...)
  50. Probability Perplexities.Robert Gilson - 1996 - World Futures 47 (4):311-317.
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