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  1. Yann Benétreau-Dupin (forthcoming). Blurring Out Cosmic Puzzles. Philosophy of Science.
    The Doomsday argument and anthropic arguments are illustrations of a paradox. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, the paradox constitutes a challenge to Bayesianism. Several attempts, some successful, have been made to avoid these conclusions, but some versions of the paradox cannot be dissolved within the framework of orthodox Bayesianism. I show that adopting an imprecise framework of probabilistic reasoning allows for a more adequate representation of ignorance (...)
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  2. Seamus Bradley (2012). Dutch Book Arguments and Imprecise Probabilities. In Dennis Dieks, Stephan Hartmann, Michael Stoeltzner & Marcel Weber (eds.), Probabilities, Laws and Structures. Springer.
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  3. Jake Chandler (forthcoming). Subjective Probabilities Need Not Be Sharp. Erkenntnis:1-14.
    It is well known that classical, aka ‘sharp’, Bayesian decision theory, which models belief states as single probability functions, faces a number of serious difficulties with respect to its handling of agnosticism. These difficulties have led to the increasing popularity of so-called ‘imprecise’ models of decision-making, which represent belief states as sets of probability functions. In a recent paper, however, Adam Elga has argued in favour of a putative normative principle of sequential choice that he claims to be borne out (...)
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  4. Horacio Arlo Costa & Jeffrey Helzner, Iterated Random Selection as Intermediate Between Risk and Uncertainty. ISIPTA'09 ELECTRONIC PROCEEDINGS.
  5. Eleonora Cresto (2010). Belief and Contextual Acceptance. Synthese 177 (1):41-66.
    I develop a strategy for representing epistemic states and epistemic changes that seeks to be sensitive to the difference between voluntary and involuntary aspects of our epistemic life, as well as to the role of pragmatic factors in epistemology. The model relies on a particular understanding of the distinction between full belief and acceptance , which makes room for the idea that our reasoning on both practical and theoretical matters typically proceeds in a contextual way. Within this framework, I discuss (...)
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  6. John Earman (ed.) (1984). Testing Scientific Theories. Minneapolis: University of Minnesota Press.
    Rich with historical and cultural value, these works are published unaltered from the original University of Minnesota Press editions.
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  7. Adam Elga (2010). Subjective Probabilities Should Be Sharp. Philosophers' Imprint 10 (05).
    Many have claimed that unspecific evidence sometimes demands unsharp, indeterminate, imprecise, vague, or interval-valued probabilities. Against this, a variant of the diachronic Dutch Book argument shows that perfectly rational agents always have perfectly sharp probabilities.
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  8. Angelo Gilio (2005). Probabilistic Logic Under Coherence, Conditional Interpretations, and Default Reasoning. Synthese 146 (1-2):139 - 152.
    We study a probabilistic logic based on the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence). We examine probabilistic conditional knowledge bases associated with imprecise probability assessments defined on arbitrary families of conditional events. We introduce a notion of conditional interpretation defined directly in terms of precise probability assessments. We also examine a property of strong satisfiability which is related to the notion of toleration well known in default reasoning. In our framework we give more (...)
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  9. Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler & Jon Williamson (2011). Probabilistic Logics and Probabilistic Networks. Synthese Library.
    Additionally, the text shows how to develop computationally feasible methods to mesh with this framework.
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  10. Alan Hájek & Michael Smithson (2012). Rationality and Indeterminate Probabilities. Synthese 187 (1):33-48.
    We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required . Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our second argument begins with our (...)
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  11. James Hawthorne (2009). The Lockean Thesis and the Logic of Belief. In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of Belief. Synthese Library: Springer. 49--74.
    In a penetrating investigation of the relationship between belief and quantitative degrees of confidence (or degrees of belief) Richard Foley (1992) suggests the following thesis: ... it is epistemically rational for us to believe a proposition just in case it is epistemically rational for us to have a sufficiently high degree of confidence in it, sufficiently high to make our attitude towards it one of belief. Foley goes on to suggest that rational belief may be just rational degree of confidence (...)
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  12. Colin Howson & Peter Urbach (1993). Scientific Reasoning: The Bayesian Approach. Open Court.
    Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...
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  13. Franz Huber & Christoph Schmidt-Petri (eds.) (2009). Degrees of Belief. Springer.
    Various theories try to give accounts of how measures of this confidence do or ought to behave, both as far as the internal mental consistency of the agent as ...
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  14. Richard C. Jeffrey (1983). Bayesianism With A Human Face. In John Earman (ed.), Testing Scientific Theories. University of Minnesota Press. 133--156.
  15. James M. Joyce (2010). A Defense of Imprecise Credences in Inference and Decision Making1. Philosophical Perspectives 24 (1):281-323.
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  16. James M. Joyce (2000). Why We Still Need the Logic of Decision. Philosophy of Science 67 (3):13.
    In The Logic of Decision Richard Jeffrey defends a version of expected utility theory that advises agents to choose acts with an eye to securing evidence for thinking that desirable results will ensue. Proponents of "causal" decision theory have argued that Jeffrey's account is inadequate because it fails to properly discriminate the causal features of acts from their merely evidential properties. Jeffrey's approach has also been criticized on the grounds that it makes it impossible to extract a unique probability/utility representation (...)
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  17. Henry E. Kyburg Jr (2001). Probability as a Guide in Life. The Monist 84 (2):135 - 152.
    Bishop Butler, [Butler, 1736], said that probability was the very guide of life. But what interpretations of probability can serve this function? It isn't hard to see that empirical (frequency) views won't do, and many recent writers—for example John Earman, who has said that Bayesianism is "the only game in town"—have been persuaded by various dutch book arguments that only subjective probability will perform the function required. We will defend the thesis that probability construed in this way offers very little (...)
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  18. Mark Kaplan (2010). In Defense of Modest Probabilism. Synthese 176 (1):41 - 55.
    Orthodox Probabilists hold that an inquirer ought to harbor a precise degree of confidence in each hypothesis about which she is concerned. Modest Probabilism is one of a family doctrines inspired by the thought that Orthodox Probabilists are thereby demanding that an inquirer effect a precision that is often unwarranted by her evidence. The purpose of this essay is (i) to explain the particular way in which Modest Probabilism answers to this thought, and (ii) to address an alleged counterexample to (...)
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  19. Henry E. Kyburg Jr (2001). Probability as a Guide in Life. The Monist 84 (2):135-152.
    Bishop Butler, [Butler, 1736], said that probability was the very guide of life. But what interpretations of probability can serve this function? It isn’t hard to see that empirical (frequency) views won’t do, and many recent writers-for example John Earman, who has said that Bayesianism is “the only game in town”-have been persuaded by various dutch book arguments that only subjective probability will perform the function required. We will defend the thesis that probability construed in this way offers very little (...)
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  20. Henry E. Kyburg (1992). Getting Fancy with Probability. Synthese 90 (2):189-203.
    There are a number of reasons for being interested in uncertainty, and there are also a number of uncertainty formalisms. These formalisms are not unrelated. It is argued that they can all be reflected as special cases of the approach of taking probabilities to be determined by sets of probability functions defined on an algebra of statements. Thus, interval probabilities should be construed as maximum and minimum probabilities within a set of distributions, Glenn Shafer's belief functions should be construed as (...)
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  21. Isaac Levi (1980). The Enterprise of Knowledge: An Essay on Knowledge, Credal Probability, and Chance. The Mit Press.
    This major work challenges some widely held positions in epistemology - those of Peirce and Popper on the one hand and those of Quine and Kuhn on the other.
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  22. Isaac Levi (1974). On Indeterminate Probabilities. Journal of Philosophy 71 (13):391-418.
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  23. Thomas Lukasiewicz (2005). Nonmonotonic Probabilistic Reasoning Under Variable-Strength Inheritance with Overriding. Synthese 146 (1-2):153 - 169.
    We present new probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment, called Zλ- and lexλ-entailment, which are parameterized through a value λ ∈ [0,1] that describes the strength of the inheritance of purely probabilistic knowledge. In the special cases of λ = 0 and λ = 1, the notions of Zλ- and lexλ-entailment coincide with probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment that have been recently introduced by the author. We show (...)
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  24. Daniel J. Mckaughan & John M. Drake (2012). Representing Vague Opinion. Principia 16 (2):341-344.
    http://dx.doi.org/10.5007/1808-1711.2012v16n2p341 Current supervaluation models of opinion, notably van Fraassen’s (1984; 1989; 1990; 1998; 2005; 2006) use of intervals to characterize vague opinion, capture nuances of ordinary reflection which are overlooked by classic measure theoretic models of subjective probability. However, after briefly explaining van Fraassen’s approach, we present two limitations in his current framework which provide clear empirical reasons for seeking a refinement. Any empirically adequate account of our actual judgments must reckon with the fact that these are typically neither uniform (...)
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  25. Cesaltina Pacheco Pires (2002). A Rule For Updating Ambiguous Beliefs. Theory and Decision 53 (2):137-152.
    When preferences are such that there is no unique additive prior, the issue of which updating rule to use is of extreme importance. This paper presents an axiomatization of the rule which requires updating of all the priors by Bayes rule. The decision maker has conditional preferences over acts. It is assumed that preferences over acts conditional on event E happening, do not depend on lotteries received on Ec, obey axioms which lead to maxmin expected utility representation with multiple priors, (...)
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  26. Arthur Paul Pedersen & Gregory Wheeler (2013). Demystifying Dilation. Erkenntnis:1-38.
    Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically (...)
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  27. Susanna Rinard (forthcoming). A Decision Theory for Imprecise Credences. Philosophers' Imprint.
    Those who model doxastic states with a set of probability functions, rather than a single function, face a pressing challenge: can they provide a plausible decision theory compatible with their view? Adam Elga (2010) and others claim that they cannot, and that the set of functions model should be rejected for this reason. This paper aims to answer this challenge. The key insight is that the set of functions model can be seen as an instance of the supervaluationist approach to (...)
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  28. Susanna Rinard (2014). The Principle of Indifference and Imprecise Probability. Thought: A Journal of Philosophy 3 (2):110-114.
    Sometimes different partitions of the same space each seem to divide that space into propositions that call for equal epistemic treatment. Famously, equal treatment in the form of equal point-valued credence leads to incoherence. Some have argued that equal treatment in the form of equal interval-valued credence solves the puzzle. This paper shows that, once we rule out intervals with extreme endpoints, this proposal also leads to incoherence.
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  29. Susanna Rinard (2013). Against Radical Credal Imprecision. Thought: A Journal of Philosophy 2 (1):157-165.
    A number of Bayesians claim that, if one has no evidence relevant to a proposition P, then one's credence in P should be spread over the interval [0, 1]. Against this, I argue: first, that it is inconsistent with plausible claims about comparative levels of confidence; second, that it precludes inductive learning in certain cases. Two motivations for the view are considered and rejected. A discussion of alternatives leads to the conjecture that there is an in-principle limitation on formal representations (...)
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  30. Daniel Rothschild (2012). Expressing Credences. 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.
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  31. Miriam Schoenfield (2012). Chilling Out on Epistemic Rationality. Philosophical Studies 158 (2):197-219.
    A defense of imprecise credences (and other imprecise doxastic attitudes).
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  32. Gerhard Schurz & Paul D. Thorn (2012). REWARD VERSUS RISK IN UNCERTAIN INFERENCE: THEOREMS AND SIMULATIONS. Review of Symbolic Logic 5 (4):574-612.
    Systems of logico-probabilistic (LP) reasoning characterize inference from conditional assertions that express high conditional probabilities. In this paper we investigate four prominent LP systems, the systems O, P, Z, and QC. These systems differ in the number of inferences they licence (O ⊂ P ⊂ Z ⊂ QC). LP systems that license more inferences enjoy the possible reward of deriving more true and informative conclusions, but with this possible reward comes the risk of drawing more false or uninformative conclusions. In (...)
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  33. Paul D. Thorn (2014). Defeasible Conditionalization. Journal of Philosophical Logic 43:283-302.
    The applicability of Bayesian conditionalization in setting one’s posterior probability for a proposition, α, is limited to cases where the value of a corresponding prior probability, PPRI(α|∧E), is available, where ∧E represents one’s complete body of evidence. In order to extend probability updating to cases where the prior probabilities needed for Bayesian conditionalization are unavailable, I introduce an inference schema, defeasible conditionalization, which allows one to update one’s personal probability in a proposition by conditioning on a proposition that represents a (...)
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  34. Paul D. Thorn (2013). Cognitivist Probabilism. In Vit Punochar & Petr Svarny (eds.), The Logica Yearbook 2012. College Publications. 201-213.
    In this article, I introduce the term “cognitivism” as a name for the thesis that degrees of belief are equivalent to full beliefs about truth-valued propositions. The thesis (of cognitivism) that degrees of belief are equivalent to full beliefs is equivocal, inasmuch as different sorts of equivalence may be postulated between degrees of belief and full beliefs. The simplest sort of equivalence (and the sort of equivalence that I discuss here) identifies having a given degree of belief with having a (...)
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  35. Paul D. Thorn (2012). Two Problems of Direct Inference. Erkenntnis 76 (3):299-318.
    The article begins by describing two longstanding problems associated with direct inference. One problem concerns the role of uninformative frequency statements in inferring probabilities by direct inference. A second problem concerns the role of frequency statements with gerrymandered reference classes. I show that past approaches to the problem associated with uninformative frequency statements yield the wrong conclusions in some cases. I propose a modification of Kyburg’s approach to the problem that yields the right conclusions. Past theories of direct inference have (...)
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  36. Paul D. Thorn (2007). Three Problems of Direct Inference. Dissertation, University of Arizona
  37. Paul D. Thorn & Gerhard Schurz (2014). A Utility Based Evaluation of Logico-Probabilistic Systems. Studia Logica 102 (4):867-890.
    Systems of logico-probabilistic (LP) reasoning characterize inference from conditional assertions interpreted as expressing high conditional probabilities. In the present article, we investigate four prominent LP systems (namely, systems O, P, Z, and QC) by means of computer simulations. The results reported here extend our previous work in this area, and evaluate the four systems in terms of the expected utility of the dispositions to act that derive from the conclusions that the systems license. In addition to conforming to the dominant (...)
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  38. B. Topey (2012). Coin Flips, Credences and the Reflection Principle. Analysis 72 (3):478-488.
    One recent topic of debate in Bayesian epistemology has been the question of whether imprecise credences can be rational. I argue that one account of imprecise credences, the orthodox treatment as defended by James M. Joyce, is untenable. Despite Joyce’s claims to the contrary, a puzzle introduced by Roger White shows that the orthodox account, when paired with Bas C. van Fraassen’s Reflection Principle, can lead to inconsistent beliefs. Proponents of imprecise credences, then, must either provide a compelling reason to (...)
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  39. Bas van Fraassen (1990). Figures in a Probability Landscape. In J. Dunn & A. Gupta (eds.), Truth or Consequences. Kluwer. 345-356.
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  40. Alex Voorhoeve, Ken Binmore & Lisa Stewart (2012). How Much Ambiguity Aversion? Finding Indifferences Between Ellsberg's Risky and Ambiguous Bets. Journal of Risk and Uncertainty 45 (3):215-38.
    Experimental results on the Ellsberg paradox typically reveal behavior that is commonly interpreted as ambiguity aversion. The experiments reported in the current paper find the objective probabilities for drawing a red ball that make subjects indifferent between various risky and uncertain Ellsberg bets. They allow us to examine the predictive power of alternative principles of choice under uncertainty, including the objective maximin and Hurwicz criteria, the sure-thing principle, and the principle of insufficient reason. Contrary to our expectations, the principle of (...)
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  41. Jonathan Weisberg, Upper & Lower Probabilities.
    An introduction to the motivations and mechanics of upper and lower probabilities, from a lecture given at the Northern Institute of Philosophy in 2010.
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