About this topic

One can think of belief in a binary way--you either believe something or you don't. One can also think of belief as something that comes in degrees--you can believe something to a number of different degrees. It has been popular in formal epistemology to think of beliefs in the latter way, as things which come in degrees, and to further maintain that such degrees of belief should should satisfy the probability axioms. Given this picture, it has been debated whether there are other normative constraints on what an agent's degrees of belief should be like. The probabilistic principles discussed in this area are largely proposals about what these further normative constraints on degrees of belief should be like.

Key works A classic description and defense of conditionalization can be found in Urbach & Howson 1993. An influential and critical discussion of Indifference Principles can be found in van Fraassen 1989. Important discussions and applications of scoring rules are given in Oddie 1997 and Joyce 1998. An early and influential discussion of chance-credence principles is given by Lewis 1980. Reflection Principles were introduced and defended in Van Fraassen 1984 and Van Fraassen 1995. Influential discussions of direct inference principles are given in Kyburg 1974 and Pollock 1990.
Introductions Good introductory discussions that cover many of the principles discussed in this section can be found in a number of places, including Urbach & Howson 1993Strevens manuscript and Weisberg manuscript.
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  1. Symmetry Arguments Against Regular Probability: A Reply to Recent Objections.Matthew W. Parker - 2018 - European Journal for Philosophy of Science 9 (1):8.
    A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson is speaking (...)
  2. In Search of Good Probability Assessors: An Experimental Comparison of Elicitation Rules for Confidence Judgments.Guillaume Hollard, Sébastien Massoni & Jean-Christophe Vergnaud - 2016 - Theory and Decision 80 (3):363-387.
  3. Vague Credence.Aidan Lyon - 2017 - Synthese 194 (10):3931-3954.
    It is natural to think of precise probabilities as being special cases of imprecise probabilities, the special case being when one’s lower and upper probabilities are equal. I argue, however, that it is better to think of the two models as representing two different aspects of our credences, which are often vague to some degree. I show that by combining the two models into one model, and understanding that model as a model of vague credence, a natural interpretation arises that (...)
  4. Rationality and Reflection: How to Think About What to Think.Jim Slagle - 2017 - Philosophical Quarterly 67 (266):212-214.
  5. V—Expressing Credences.Daniel Rothschild - 2012 - Proceedings of the Aristotelian Society 112 (1pt1):99-114.
    After presenting a simple expressivist account of reports of probabilistic judgements, I explore a classic problem for it, namely the Frege‐Geach problem. I argue that it is a problem not just for expressivism but for any reasonable account of ascriptions of graded judgements. I suggest that the problem can be resolved by appropriately modelling imprecise credences.
  6. Rewording the Rules on Disjunctive Probability.Ronald Cordero - 2016 - Metaphilosophy 47 (4-5):719-727.
    Logic is a central and highly useful part of philosophy. Its value is particularly evident when it comes to keeping our thinking about disjunctive probabilities clear. Because of the two meanings of “or”, logic can show how the likelihood of a disjunction being true can be determined quite easily. To gauge the chance that one of two or more exclusive alternatives is true, one need only sum up their respective likelihoods. And to know the chance that at least one of (...)
  7. Probability. [REVIEW]Mauricio Suárez - 2011 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 26 (1):99-103.
  8. A Treatise on Probability.Clarence Irving Lewis & John Maynard Keynes - 1922 - Philosophical Review 31 (2):180.
  9. Probabilities Cannot Be Rationally Neglected.Yoaav Isaacs - 2016 - Mind 125 (499):759-762.
    In response to Smith, I argue that probabilities cannot be rationally neglected. I show that Smith’s proposal for ignoring low-probability outcomes must, on pain of violating dominance reasoning, license taking arbitrarily high risk for arbitrarily little reward.
  10. Could the Probability of Doom Be Zero or One?Martin H. Krieger - 1995 - Journal of Philosophy 92 (7):382-387.
  11. A Famous Dutch Convert.A. W. G. Randall - 1922 - New Blackfriars 3 (28):183-189.
  12. Dutch Pioneers of Science. Leo Beek.Willem D. Hackmann - 1988 - Isis 79 (1):132-134.
  13. Heuristics Can Produce Surprisingly Rational Probability Estimates: Comment on Costello and Watts.Håkan Nilsson, Peter Juslin & Anders Winman - 2016 - Psychological Review 123 (1):103-111.
  14. Probability Theory, Not the Very Guide of Life.Peter Juslin, Håkan Nilsson & Anders Winman - 2009 - Psychological Review 116 (4):856-874.
  15. The Principle of Belief Congruence and the Congruity Principle as Models of Cognitive Interaction.Milton Rokeach & Gilbert Rothman - 1965 - Psychological Review 72 (2):128-142.
  16. On the Subjective Probability of Compound Events.Maya Bar-Hillel - 1973 - Organizational Behavior and Human Performance 9 (3):396-406.
    Subjects were requested to choose between gambles, where the outcome of one gamble depended on a single elementary event, and the other depended on an event compounded of a series of such elementary events. The data supported the hypothesis that the subjective probability of a compound event is systematically biased in the direction of the probability of its components resulting in overestimation of conjunctive events and underestimation of disjunctive events. Studies pertaining to this topic are discussed.
  17. 9. The de Finetti Lottery and Equiprobability.Paul Bartha - 2005 - In Kent A. Peacock & Andrew D. Irvine (eds.), Mistakes of Reason: Essays in Honour of John Woods. University of Toronto Press. pp. 158-172.
  18. Chapter 7. Absolute Probability Functions Construed as Representing Degrees of Logical Truth.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 114-141.
  19. Chapter 3. Relative Probability Functions and Their T-Restrictions.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hughes Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 45-58.
  20. An Airtight Dutch Book.V. McGee - 1999 - Analysis 59 (4):257-265.
  21. How Probable is an Infinite Sequence of Heads?Timothy Williamson - 2007 - Analysis 67 (3):173-180.
    Isn't probability 1 certainty? If the probability is objective, so is the certainty: whatever has chance 1 of occurring is certain to occur. Equivalently, whatever has chance 0 of occurring is certain not to occur. If the probability is subjective, so is the certainty: if you give credence 1 to an event, you are certain that it will occur. Equivalently, if you give credence 0 to an event, you are certain that it will not occur. And so on for other (...)
  22. It All Adds Up: The Dynamic Coherence of Radical Probabilism.S. L. Zabell - 2002 - Philosophy of Science 69 (S3):S98-S103.
  23. Indifference, Neutrality and Informativeness: Generalizing the Three Prisoners Paradox.Sergio Wechsler, L. G. Esteves, A. Simonis & C. Peixoto - 2005 - Synthese 143 (3):255-272.
    . The uniform prior distribution is often seen as a mathematical description of noninformativeness. This paper uses the well-known Three Prisoners Paradox to examine the impossibility of maintaining noninformativeness throughout hierarchization. The Paradox has been solved by Bayesian conditioning over the choice made by the Warder when asked to name a prisoner who will be shot. We generalize the paradox to situations of N prisoners, k executions and m announcements made by the Warder. We then extend the consequences of hierarchically (...)
  24. An Empirical Approach to Symmetry and Probability.Jill North - 2010 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (1):27-40.
    We often use symmetries to infer outcomes’ probabilities, as when we infer that each side of a fair coin is equally likely to come up on a given toss. Why are these inferences successful? I argue against answering this with an a priori indifference principle. Reasons to reject that principle are familiar, yet instructive. They point to a new, empirical explanation for the success of our probabilistic predictions. This has implications for indifference reasoning in general. I argue that a priori (...)
  25. The Axioms and Algebra of Intuitive Probability.Bernard O. Koopman - 1940 - Annals of Mathematics:269--292.
  26. Bruno de Finetti and Imprecision.Paolo Vicig & Teddy Seidenfeld - unknown
    We review several of de Finetti’s fundamental contributions where these have played and continue to play an important role in the development of imprecise probability research. Also, we discuss de Finetti’s few, but mostly critical remarks about the prospects for a theory of imprecise probabilities, given the limited development of imprecise probability theory as that was known to him.
  27. A Consistent Set of Infinite-Order Probabilities.David Atkinson & Jeanne Peijnenburg - unknown
    Some philosophers have claimed that it is meaningless or paradoxical to consider the probability of a probability. Others have however argued that second-order probabilities do not pose any particular problem. We side with the latter group. On condition that the relevant distinctions are taken into account, second-order probabilities can be shown to be perfectly consistent. May the same be said of an infinite hierarchy of higher-order probabilities? Is it consistent to speak of a probability of a probability, and of a (...)
  28. Avoiding Both the Garbage-In/Garbage-Out and the Borel Paradox in Updating Probabilities Given Experimental Information.Robert F. Bordley - 2015 - Theory and Decision 79 (1):95-105.
  29. The Role of Second-Order Probabilities in Decision Making.Nils-Eric Sahlin & Robert Goldsmith - unknown
    The importance, legitimacy and role of second-order probabilities are discussed. Two descriptive models of the use of second-order probabilities in decisions are presented. The results of two empirical studies of the effects of second-order probabilities upon the rank orderings of bets are summarized briefly. The bets were of three basic types and involved a wide variety of first- and second-order probabilities as subjectively assessed by the subjects. Support was obtained for the assumption that the majority of subjects make use of (...)
  30. HACKING, I. "The Emergence of Probability". [REVIEW]J. R. Lucas - 1977 - Mind 86:466.
  31. Probability and Opinion: A Study in the Medieval Presuppositions of Post-Medieval Theories of Probability.Edmund F. Byrne (ed.) - 1968 - The Hague: Martinus Nijhoff.
    Recognizing that probability (the Greek doxa) was understood in pre-modern theories as the polar opposite of certainty (episteme), the author of this study elaborates the forms which these polar opposites have taken in some twentieth century writers and then, in greater detail, in the writings of Thomas Aquinas. Profiting from subsequent more sophisticated theories of probability, he examines how Aquinas’s judgments about everything from God to gossip depend on schematizations of the polarity between the systematic and the non-systematic: revelation/reason, science/opinion, (...)
  32. Biased Coins: A Model for Higher-Order Probabilities.Jeanne Peijnenburg & David Atkinson - 2014 - In Maria Clara Galavotti, Elisabeth Nemeth & Friedrich Stadler (eds.), European Philosophy of Science: Philosophy of Science in Europe and the Vienna Heritage. Springer. pp. 241-248.
    Is it coherent to speak of the probability of a probability, and the probability of a probability of a probability, and so on? We show that it is, in the sense that a regress of higher-order probabilities can lead to convergent sequences that determine all these probabilities. By constructing an implementable model which is based on coin-making machines, we demonstrate the consistency of our regress.
  33. Carnap and Reichenbach on Probability with Neurath the Winner.Keith Lehrer - 1993 - Vienna Circle Institute Yearbook 1:143-155.
    Carnap and Reichenbach made extraordinary contributions to our understanding of the foundations of probability.1 Each of them provided a precise logical and mathematical analysis of probability that satisfied the formal calculus of probability. Reichenbach’s theory of probability analysed probability as the limit of relative frequency, while Carnap’s theory of probability explicated probability as a degree of logical connection. Carnap articulated his account of the foundations of probability by insisting that there were two concepts of probability, his own, probability one, and (...)
  34. Classical Probability in the Enlightenment. [REVIEW]Theodore Porter - 1989 - British Journal for the History of Science 22 (4):444-446.
  35. 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.
  36. Probability in the Philosophy of Religion.D. H. Mellor - 2013 - Analysis 73 (3):548-554.
  37. The Carnapian Tolerance in the Foundations of Probability'.Wilhelm K. Essler - 1984 - Epistemologia 7:171-190.
  38. Probabilities and Causes, 82 J.David Papineau - 1985 - Philosophy 57 (10.2307):202655557.
  39. Dutch-Books and Money Pumps.E. F. McClennen & P. Found - forthcoming - Theory and Decision.
  40. Varieties of Subjective-Probability.Rs Lockhart - 1992 - Bulletin of the Psychonomic Society 30 (6):483-483.
  41. On the Probability of Absolute Truth for And/Or Formulas.Alan Woods - 2005 - Bulletin of Symbolic Logic 12 (3).
  42. 10. It All Adds Up: The Dynamic Coherence of Radical Probabilism It All Adds Up: The Dynamic Coherence of Radical Probabilism (Pp. S98-S103). [REVIEW]S. L. Zabell, Brian Skyrms, Elliott Sober, Malcolm R. Forster, Wayne C. Myrvold, William L. Harper, Rob Clifton, Itamar Pitowsky, Robyn M. Dawes & David Faust - 2002 - Philosophy of Science 69 (S3).
  43. Locating Opportunities for Brownfield Redevelopment in St. Louis.Kristi Walker - forthcoming - Emergence: Complexity and Organization.
  44. On the Probability of Particular Events.Alfred Jules Ayer - 1961 - Revue Internationale de Philosophie 15 (58):366-75.
  45. Fronting in Dutch.Jan G. Kooij - 1978 - In Frank Jansen (ed.), Studies on Fronting. Peter de Ridder Press.
  46. Representation Theorems of the de Finetti Type for (Partially) Symmetric Probability Measures.Godehard Link - 1980 - In Richard C. Jeffrey (ed.), Studies in Inductive Logic and Probability. Berkeley: University of California Press. pp. 2--207.
  47. Pragmatic Control of Specificity and Scope: Evidence From Dutch L1A.William Philip - 2005 - In Emar Maier, Corien Bary & Janneke Huitink (eds.), Proceedings of Sub9. pp. 271--285.
  48. Factors Determining the Probability of Recollection of Intraoperative Events.L. Goldman - 1990 - In B. Bonke, W. Fitch & K. Millar (eds.), Memory and Awareness in Anesthesia. Swets & Zeitlinger. pp. 45--9.
  49. Philosophical Foundations of Probability.Hans Reichenbach - 1996 - In Sahotra Sarkar (ed.), Logic, Probability, and Epistemology: The Power of Semantics. Garland Pub. Co.. pp. 3--115.
  50. Interpreting Imprecise Diagrams.Neil Smith, Pete Thomas & Kevin Waugh - 2004 - In A. Blackwell, K. Marriott & A. Shimojima (eds.), Diagrammatic Representation and Inference. Springer. pp. 239--241.
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