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Summary

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 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 2011.
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  1. Ernest W. Adams (1996). Four Probability-Preserving Properties of Inferences. Journal of Philosophical Logic 25 (1):1 - 24.
    Different inferences in probabilistic logics of conditionals 'preserve' the probabilities of their premisses to different degrees. Some preserve certainty, some high probability, some positive probability, and some minimum probability. In the first case conclusions must have probability I when premisses have probability 1, though they might have probability 0 when their premisses have any lower probability. In the second case, roughly speaking, if premisses are highly probable though not certain then conclusions must also be highly probable. In the third case (...)
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  2. Evandro Agazzi (1988). Probability in the Sciences. Monograph Collection (Matt - Pseudo).
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  3. Arjun Appadurai (1995). Locating the Subject. In Richard Fardon (ed.), Counterworks: Managing the Diversity of Knowledge. Routledge. 192.
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  4. A. Balakrishnan & A. K. Shanmukham (1968). Equipment for Calibration of Bathythermograph and Preparation of Grids. In Peter Koestenbaum (ed.), Proceedings. [San Jose? Calif.. 38--334.
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  5. Lee R. Beach & Lawrence D. Phillips (1967). Subjective Probabilities Inferred From Estimates and Bets. Journal of Experimental Psychology 75 (3):354.
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  6. Lee Roy Beach, Richard M. Rose, Yutaka Sayeki, James A. Wise & William B. Carter (1970). Probability Learning: Response Proportions and Verbal Estimates. Journal of Experimental Psychology 86 (2):165.
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  7. Manuel Bilsky (1953). The Significance of Locating the Art Object. Philosophy and Phenomenological Research 13 (4):531-536.
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  8. D. J. Bradley (2012). Four Problems About Self-Locating Belief. Philosophical Review 121 (2):149-177.
    This article defends the Doomsday Argument, the Halfer Position in Sleeping Beauty, the Fine-Tuning Argument, and the applicability of Bayesian confirmation theory to the Everett interpretation of quantum mechanics. It will argue that all four problems have the same structure, and it gives a unified treatment that uses simple models of the cases and no controversial assumptions about confirmation or self-locating evidence. The article will argue that the troublesome feature of all these cases is not self-location but selection effects.
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  9. Philip Brickman & Scott M. Pierce (1972). Estimates of Conditional Probabilities of Confirming Versus Disconfirming Events as a Function of Inference Situation and Prior Evidence. Journal of Experimental Psychology 95 (1):235.
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  10. Lucas N. H. Bunt (1967). Probability and Statistical Inference in the Secondary School. Dialectica 21 (1‐4):366-382.
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  11. John Cantwell (2002). The Pragmatic Stance, Whither Dutch Books and Money Pumps? Croatian Journal of Philosophy 6 (3):319-336.
    The view that decision methods can only be justified by appeal to pragmatic considerations is defended. Pragmatic considerations are viewed as providing the underlying subject matter of decision theories. It is argued that other approaches fail to provide grounds for a normative decision theory.It is argued that preferences that can lead to pragmatically adverse outcomes in a relevantly similar possible decision situation are pragmatically unsound, even if the decision situation never arises. This rebuts several standard objections to money-pump and Dutch (...)
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  12. Roderick M. Chisholm (1984). What is the Problem of Objective Reference? Dialectica 38 (2‐3):131-142.
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  13. David Christensen (2010). Rational Reflection. Philosophical Perspectives 24 (1):121-140.
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  14. Rolando Chuaqui (1991). Truth, Possibility and Probability: New Logical Foundations of Probability and Statistical Inference Vol. 166. Access Online Via Elsevier.
    This unique book presents a new interpretation of probability, rooted in the traditional interpretation that was current in the 17th and 18th centuries.
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  15. Anne Colby (1987). Standard Issue Scoring Manual. In , The Measurement of Moral Judgment. Cambridge University Press.
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  16. Marcello D'Agostino & Corrado Sinigaglia (2010). Epistemic Accuracy and Subjective Probability. In M. Dorato M. Suàrez (ed.), Epsa Epistemology and Methodology of Science. Springer. 95--105.
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  17. A. I. Dale (1980). Personal Probabilities of Probabilities in the Case of Sampling Without Replacement. Theory and Decision 12 (1):75-77.
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  18. J. P. Das (1962). Supplementary Report: Semantic Generalization in Probability Learning. Journal of Experimental Psychology 64 (4):423.
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  19. Bruno De Finetti (2008). Philosophical Lectures on Probability. Collected, Edited and Annotated by Alberto Mura. Springer.
    The book contains the transcription of a course on the foundations of probability given by the Italian mathematician Bruno de Finetti in 1979 at the a oeNational Institute of Advanced Mathematicsa in Rome.
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  20. R. W. Ditchburn (1937). Contribution to Discussion on Probability. Erkenntnis 7 (1):352-353.
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  21. Zoltan Domotor, Mario Zanotti & Henson Graves (1980). Probability Kinematics. Synthese 44 (3):421 - 442.
    Probability kinematics is studied in detail within the framework of elementary probability theory. The merits and demerits of Jeffrey's and Field's models are discussed. In particular, the principle of maximum relative entropy and other principles are used in an epistemic justification of generalized conditionals. A representation of conditionals in terms of Bayesian conditionals is worked out in the framework of external kinematics.
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  22. Ward Edwards (1961). Probability Learning in 1000 Trials. Journal of Experimental Psychology 62 (4):385.
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  23. Gloria J. Fischer (1971). Number of Event Choices and the Difference Between Event Probabilities in Human Probability Learning. Journal of Experimental Psychology 89 (1):192.
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  24. Patrizio Frederic, Mario Di Bacco & Frank Lad (2012). Combining Expert Probabilities Using the Product of Odds. Theory and Decision 73 (4):605-619.
    We resolve a useful formulation of the question how a statistician can coherently incorporate the information in a consulted expert’s probability assessment for an event into a personal posterior probability assertion. Using a framework that recognises the total information available as composed of units available only to each of them along with units available to both, we show: that a sufficient statistic for all the information available to both the expert and the statistician is the product of their odds ratios (...)
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  25. Robin Hanson, Book Orders for Market Scoring Rules.
    This explains how to smoothly integrate booked orders with a combinatorial market maker, all for the general case of bets on E[x|A] for arbitrary random variables x and sets A.
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  26. Matthew Harrison-Trainor, Wesley H. Holliday & Thomas F. Icard (forthcoming). A Note on Cancellation Axioms for Comparative Probability. Theory and Decision.
    We prove that the generalized cancellation axiom for incomplete comparative probability relations introduced by Rios Insua (1992) and Alon and Lehrer (2014) is stronger than the standard cancellation axiom for complete comparative probability relations introduced by Scott (1964), relative to their other axioms for comparative probability in both the finite and infinite cases. This result has been suggested but not proved in the previous literature.
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  27. E. Henry Jr (forthcoming). Kyburg.'The Rule of Adjunction and Reasonable Inference,'. Journal of Philosophy.
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  28. Leendert Huisman (forthcoming). On Indeterminate Updating of Credences. 81 (4):537-557,.
    The strategy of updating credences by minimizing the relative entropy has been questioned by many authors, most strongly by means of the Judy Benjamin puzzle. I present a new analysis of Judy Benjamin–like forms of new information and defend the thesis that in general the rational posterior is indeterminate, meaning that a family of posterior credence functions rather than a single one is the rational response when that type of information becomes available. The proposed thesis extends naturally to all cases (...)
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  29. Keith Hutchison (2012). Dutch-Book Arguments Against Using Conditional Probabilities for Conditional Bets. Open Journal of Philosophy 2 (3):195.
    We consider here an important family of conditional bets, those that proceed to settlement if and only if some agreed evidence is received that a condition has been met. Despite an opinion widespread in the literature, we observe that when the evidence is strong enough to generate certainty as to whether the condition has been met or not, using traditional conditional probabilities for such bets will NOT preserve a gambler from having a synchronic Dutch Book imposed upon him. On the (...)
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  30. W. E. Johnson (1932). Probability: Axioms. Mind 41 (163):281-296.
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  31. Brad J. Kallenberg (2003). On Locating Disaster. Teaching Ethics 4 (1):85-88.
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  32. Kevin T. Kelly (1999). Iterated Belief Revision, Reliability, and Inductive Amnesia. Erkenntnis 50 (1):11-58.
    Belief revision theory concerns methods for reformulating an agent's epistemic state when the agent's beliefs are refuted by new information. The usual guiding principle in the design of such methods is to preserve as much of the agent's epistemic state as possible when the state is revised. Learning theoretic research focuses, instead, on a learning method's reliability or ability to converge to true, informative beliefs over a wide range of possible environments. This paper bridges the two perspectives by assessing the (...)
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  33. Hugues Leblanc & Peter Roeper (1990). What Are Absolute Probabilities a Function Of? In J. Dunn & A. Gupta (eds.), Truth or Consequences. Kluwer. 307--325.
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  34. Stephen Leeds (1981). Kyburg and Fiducial Inference. Philosophy of Science 48 (1):78-91.
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  35. Keith Lehrer (1981). The Evaluation of Method. Grazer Philosophische Studien 12:131-141.
    A theory of probabilities of probabilities is articulated and defended. Hume's argument against higher probabiHties is critically evaluated. Conflicting probability assignments for a hypothetis or theory may result from the appHcation of different methods or perspectives, for example, those of consensual authority and individual ratiocination. When we have conflicting probabilities we may assign probabilities to the diverse probabilities initially obtained. These second level probabilities may also conflict as a result of applying diverse methods or perspectives, and the same is true (...)
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  36. Isaac Levi (1980). The Enterprise of Knowledge an Essay on Knowledge, Credal Probability, and Chance /Isaac Levi. --. --. Mit Press, C1980.
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  37. H. Levy & L. Roth (1937). Elements of Probability. Journal of Philosophy 34 (5):137-137.
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  38. Sherry May (1976). Probability Kinematics: A Constrained Optimization Problem. [REVIEW] Journal of Philosophical Logic 5 (3):395 - 398.
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  39. Tim Milnes (2004). Charles Lamb: Professor of Indifference. Philosophy and Literature 28 (2):324-341.
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  40. Ronald D. Milo (1981). Moral Indifference. The Monist 64 (3):373-393.
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  41. Paul K. Moser (1988). The Foundations of Epistemological Probability. Erkenntnis 28 (2):231 - 251.
    Epistemological probability is the kind of probability relative to a body of evidence. Many philosophers, including Henry Kyburg and Roderick Chisholm, hold that all epistemological probabilities reflect a relation between an evidential body of propositions and other propositions. But this article argues that some epistemological probabilities for empirical propositions must be relative to non-propositional evidence, specifically the contents of non-propositional perceptual states. In doing so, the article distinguishes between internalism and externalism regarding epistemological probability, and argues for a version of (...)
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  42. Frederick L. Newman (1967). Differential Eyelid Conditioning as a Function of the Probability of Reinforcement. Journal of Experimental Psychology 75 (3):412.
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  43. Michael O'Hagan (1991). A Fuzzy Neuron Based Upon Maximum Entropy Ordered Weighted Averaging. In B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.), Uncertainty in Knowledge Bases. Springer. 598--609.
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  44. Robert Oakes (1978). Knowledge, Probability, and Nomic Connections: A Reply to Professor OLEN. Southern Journal of Philosophy 16 (2):133-135.
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  45. Rohert Oakes (1978). Knowledge, Probability and Nomic Connections. Southern Journal of Philosophy 16 (2):133-135.
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  46. Jeffrey OIen (1977). Knowledge, Probability, and Nomic Connections. Southern Journal of Philosophy 15 (4):521-526.
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  47. Jeffrey Olen (1977). Knowledge, Probability, and Nomic Connections. Southern Journal of Philosophy 15 (4):521-526.
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  48. Richard Pettigrew, Epistemic Utility Theory.
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  49. Itamar Pitowsky (1985). On the Status of Statistical Inferences. Synthese 63 (2):233 - 247.
    Can the axioms of probability theory and the classical patterns of statistical inference ever be falsified by observation? Various possible answers to this question are examined in a set theoretical context and in relation to the findings of microphysics.
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  50. John L. Pollock (2010). 10 Reasoning Defeasibly About Probabilities. In Joseph Keim Campbell, Michael O.’Rourke & Harry S. Silverstein (eds.), Knowledge and Skepticism. Mit Press. 219.
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