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  1. Ernest W. Adams (1964). On Rational Betting Systems. Archiv für Mathematische Logik Und Grundlagenforschung 6:7-29.
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  2. Brad Armendt (2010). Stakes and Beliefs. Philosophical Studies 147 (1):71 - 87.
    The idea that beliefs may be stake-sensitive is explored. This is the idea that the strength with which a single, persistent belief is held may vary and depend upon what the believer takes to be at stake. The stakes in question are tied to the truth of the belief—not, as in Pascal’s wager and other cases, to the belief’s presence. Categorical beliefs and degrees of belief are considered; both kinds of account typically exclude the idea and treat belief as stake-invariant (...)
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  3. Frank Arntzenius, Adam Elga & and John Hawthorne (2004). Bayesianism, Infinite Decisions, and Binding. Mind 113 (450):251-283.
    We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as ‘Trumped’ (Arntzenius and McCarthy 1997), ‘Rouble trouble’ (Arntzenius and Barrett 1999), ‘The airtight Dutch book’ (McGee 1999), and ‘The two envelopes puzzle’ (Broome 1999). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably (...)
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  4. Frank Arntzenius & Ned Hall (2003). On What We Know About Chance. British Journal for the Philosophy of Science 54 (2):171-179.
    The ‘Principal Principle’ states, roughly, that one's subjective probability for a proposition should conform to one's beliefs about that proposition's objective chance of coming true. David Lewis has argued (i) that this principle provides the defining role for chance; (ii) that it conflicts with his reductionist thesis of Humean supervenience, and so must be replaced by an amended version that avoids the conflict; hence (iii) that nothing perfectly deserves the name ‘chance’, although something can come close enough by playing the (...)
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  5. Helen Beebee & David Papineau (1997). Probability as a Guide to Life. Journal of Philosophy 94 (5):217-243.
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  6. Helen Beebee & David Papineau (1997). Probability as a Guide to Life. Journal of Philosophy 94 (5):217-243.
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  7. Richard Bradley (2001). Ramsey and the Measurement of Belief. In David Corfield & Jon Williamson (eds.), Foundations of Bayesianism.
    Foundations of Bayesianism is an authoritative collection of papers addressing the key challenges that face the Bayesian interpretation of probability today. Some of these papers seek to clarify the relationships between Bayesian, causal and logical reasoning. Others consider the application of Bayesianism to artificial intelligence, decision theory, statistics and the philosophy of science and mathematics. The volume includes important criticisms of Bayesian reasoning and also gives an insight into some of the points of disagreement amongst advocates of the Bayesian approach. (...)
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  8. Jeffrey Bub (2007). Quantum Probabilities as Degrees of Belief. Studies in History and Philosophy of Science Part B 38 (2):232-254.
  9. Lara Buchak (forthcoming). Rational Faith and Justified Belief. In Tim O'Connor & Laura Goins (eds.), Religious Faith and Intellectual Virtue.
    In “Can it be rational to have faith?”, it was argued that to have faith in some proposition consists, roughly speaking, in stopping one’s search for evidence and committing to act on that proposition without further evidence. That paper also outlined when and why stopping the search for evidence and acting is rationally required. Because the framework of that paper was that of formal decision theory, it primarily considered the relationship between faith and degrees of belief, rather than between faith (...)
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  10. Lara Buchak (2013). Belief, Credence, and Norms. Philosophical Studies (2):1-27.
    There are currently two robust traditions in philosophy dealing with doxastic attitudes: the tradition that is concerned primarily with all-or-nothing belief, and the tradition that is concerned primarily with degree of belief or credence. This paper concerns the relationship between belief and credence for a rational agent, and is directed at those who may have hoped that the notion of belief can either be reduced to credence or eliminated altogether when characterizing the norms governing ideally rational agents. It presents a (...)
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  11. Wesley Buckwalter, David Rose & John Turri (2013). Belief Through Thick and Thin. Noûs 47 (3).
    We distinguish between two categories of belief—thin belief and thick belief—and provide evidence that they approximate genuinely distinct categories within folk psychology. We use the distinction to make informative predictions about how laypeople view the relationship between knowledge and belief. More specifically, we show that if the distinction is genuine, then we can make sense of otherwise extremely puzzling recent experimental findings on the entailment thesis (i.e. the widely held philosophical thesis that knowledge entails belief). We also suggest that the (...)
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  12. Jake Chandler (2010). The Lottery Paradox Generalized? British Journal for the Philosophy of Science 61 (3):667-679.
    In a recent article, Douven and Williamson offer both (i) a rebuttal of various recent suggested sufficient conditions for rational acceptability and (ii) an alleged ‘generalization’ of this rebuttal, which, they claim, tells against a much broader class of potential suggestions. However, not only is the result mentioned in (ii) not a generalization of the findings referred to in (i), but in contrast to the latter, it fails to have the probative force advertised. Their paper does however, if unwittingly, bring (...)
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  13. Jake Chandler (2009). Review of Franz Huber and Christoph Schmidt-Petri, Eds. Degrees of Belief. Philosophy in Review 296 (6):422-424.
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  14. Shoutir Kishore Chatterjee (2003). Statistical Thought: A Perspective and History. OUP Oxford.
    In this unique monograph, based on years of extensive work, Chatterjee presents the historical evolution of statistical thought from the perspective of various approaches to statistical induction. Developments in statistical concepts and theories are discussed alongside philosophical ideas on the ways we learn from experience. -/- Suitable for researchers, lecturers and students in statistics and the history of science this book is aimed at those who have had some exposure to statistical theory. It is also useful to logicians and philosophers (...)
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  15. David Christensen (2007). Epistemic Self-Respect. Proceedings of the Aristotelian Society 107 (1pt3):319-337.
  16. David Christensen (2001). Preference-Based Arguments for Probabilism. Philosophy of Science 68 (3):356-376.
    Both Representation Theorem Arguments and Dutch Book Arguments support taking probabilistic coherence as an epistemic norm. Both depend on connecting beliefs to preferences, which are not clearly within the epistemic domain. Moreover, these connections are standardly grounded in questionable definitional/metaphysical claims. The paper argues that these definitional/metaphysical claims are insupportable. It offers a way of reconceiving Representation Theorem arguments which avoids the untenable premises. It then develops a parallel approach to Dutch Book Arguments, and compares the results. In each case (...)
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  17. David Christensen (1991). Clever Bookies and Coherent Beliefs. Philosophical Review 100 (2):229-247.
  18. David Phiroze Christensen (2004). Putting Logic in its Place: Formal Constraints on Rational Belief. Oxford University Press.
    What role, if any, does formal logic play in characterizing epistemically rational belief? Traditionally, belief is seen in a binary way - either one believes a proposition, or one doesn't. Given this picture, it is attractive to impose certain deductive constraints on rational belief: that one's beliefs be logically consistent, and that one believe the logical consequences of one's beliefs. A less popular picture sees belief as a graded phenomenon.
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  19. Roger Clarke (2013). Belief Is Credence One (In Context). Philosophers' Imprint 13 (11):1-18.
    This paper argues for two theses: (a) that degrees of belief are context sensitive; (b) that outright belief is belief to degree 1. The latter thesis is rejected quickly in most discussions of the relationship between credence and belief, but the former thesis undermines the usual reasons for doing so. Furthermore, identifying belief with credence 1 allows nice solutions to a number of problems for the most widely-held view of the relationship between credence and belief, the threshold view. I provide (...)
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  20. David Corfield & Jon Williamson (eds.) (2001). Foundations of Bayesianism. Kluwer Academic Publishers.
    The volume includes important criticisms of Bayesian reasoning and also gives an insight into some of the points of disagreement amongst advocates of the ...
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  21. A. I. Dale (1976). Probability, Likelihood and Support: A Metamathematical Approach to a System of Axioms for Upper and Lower Degrees of Belief. Philosophical Papers 5 (2):153-161.
    (1976). PROBABILITY, LIKELIHOOD AND SUPPORT: A METAMATHEMATICAL APPROACH TO A SYSTEM OF AXIOMS FOR UPPER AND LOWER DEGREES OF BELIEF. Philosophical Papers: Vol. 5, No. 2, pp. 153-161.
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  22. Barbara Davidson & Robert Pargetter (1985). In Defence of the Dutch Book Argument. Canadian Journal of Philosophy 15 (3):405 - 423.
  23. Donald Davidson (1980). Toward a Unified Theory of Meaning and Action. Grazer Philosophische Studien 11:1-12.
    The central propositional attitudes of belief, desire, and meaning are interdependent; it is therefore fruitless to analyse one or two of them in terms of the others. A method is outlined in this paper that yields a theory for interpreting speech, a measure of degree of belief, and a measure of desirability. The method combines in a novel way features of Bayesean decision theory, and a Quinean approach to radical interpretation.
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  24. Bruno de Finetti (1972). Probability, Induction, and Statistics. New York: John Wiley.
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  25. Bruno de Finetti (1970). Theory of Probability. New York: John Wiley.
  26. Bruno de Finetti (1937). La Prévision: Ses Lois Logiques, Ses Sources Subjectives. Annales de l'Institut Henri Poincaré 17:1-68.
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  27. Henk de Regt, Samir Okasha & Stephan Hartmann (eds.) (forthcoming). Proceedings of EPSA09. Springer.
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  28. Patryk Dziurosz-Serafinowicz (2009). Subjective Probability and the Problem of Countable Additivity. Filozofia Nauki 1.
    The aim of this paper is to present and analyse Bruno de Finetti's view that the axiom of countable additivity of the probability calculus cannot be justified in terms of the subjective interpretation of probability. After presenting the core of the subjective theory of probability and the main de Finetti's argument against the axiom of countable additivity (the so called de Finetti's infinite lottery) I argue against de Finetti's view. In particular, I claim that de Finetti does not prove the (...)
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  29. Patryk Dziurosz-Serafinowicz (2009). Subiektywne prawdopodobieństwo i problem przeliczalnej addytywności. Filozofia Nauki 1.
    The aim of this paper is to present and analyse Bruno de Finetti's view that the axiom of countable additivity of the probability calculus cannot be justified in terms of the subjective interpretation of probability. After presenting the core of the subjective theory of probability and the main de Finetti's argument against the axiom of countable additivity (the so called de Finetti's infinite lottery) I argue against de Finetti's view. In particular, I claim that de Finetti does not prove the (...)
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  30. Kenny Easwaran (2014). Regularity and Hyperreal Credences. Philosophical Review 123 (1):1-41.
    Many philosophers have become worried about the use of standard real numbers for the probability function that represents an agent's credences. They point out that real numbers can't capture the distinction between certain extremely unlikely events and genuinely impossible ones—they are both represented by credence 0, which violates a principle known as “regularity.” Following Skyrms 1980 and Lewis 1980, they recommend that we should instead use a much richer set of numbers, called the “hyperreals.” This essay argues that this popular (...)
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  31. Kenny Easwaran & Branden Fitelson (2012). An 'Evidentialist' Worry About Joyce's Argument for Probabilism. Dialetica 66 (3):425-433.
    To the extent that we have reasons to avoid these “bad B -properties”, these arguments provide reasons not to have an incoherent credence function b — and perhaps even reasons to have a coherent one. But, note that these two traditional arguments for probabilism involve what might be called “pragmatic” reasons (not) to be (in)coherent. In the case of the Dutch Book argument, the “bad” property is pragmatically bad (to the extent that one values money). But, it is not clear (...)
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  32. Philip A. Ebert & Martin Smith (2012). Introduction: Outright Belief and Degrees of Belief. Dialectica 66 (3):305-308.
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  33. Ellery Eells & Branden Fitelson (2000). Comments and Criticism: Measuring Confirmation and Evidence. Journal of Philosophy 97 (12):663-672.
    Bayesian epistemology suggests various ways of measuring the support that a piece of evidence provides a hypothesis. Such measures are defined in terms of a subjective probability assignment, pr, over propositions entertained by an agent. The most standard measure (where “H” stands for “hypothesis” and “E” stands for “evidence”) is: the difference measure: d(H,E) = pr(H/E) - pr(H).0 This may be called a “positive (probabilistic) relevance measure” of confirmation, since, according to it, a piece of evidence E qualitatively confirms a (...)
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  34. 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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  35. Lina Eriksson & Alan Hájek (2007). What Are Degrees of Belief? Studia Logica 86 (2):185-215.
    Probabilism is committed to two theses: 1) Opinion comes in degrees—call them degrees of belief, or credences. 2) The degrees of belief of a rational agent obey the probability calculus. Correspondingly, a natural way to argue for probabilism is: i) to give an account of what degrees of belief are, and then ii) to show that those things should be probabilities, on pain of irrationality. Most of the action in the literature concerns stage ii). Assuming that stage i) has been (...)
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  36. J. Fetzer (ed.) (1988). Probability and Causality. D. Reidel.
  37. Richard Foley (2009). Beliefs, Degrees of Belief, and the Lockean Thesis. In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of Belief. Springer. 37-47.
    What propositions are rational for one to believe? With what confidence is it rational for one to believe these propositions? Answering the first of these questions requires an epistemology of beliefs, answering the second an epistemology of degrees of belief.
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  38. Keith Frankish (2009). Partial Belief and Flat-Out Belief. In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of Belief. Springer. 75--93.
    There is a duality in our everyday view of belief. On the one hand, we sometimes speak of credence as a matter of degree. We talk of having some level of confidence in a claim (that a certain course of action is safe, for example, or that a desired event will occur) and explain our actions by reference to these degrees of confidence – tacitly appealing, it seems, to a probabilistic calculus such as that formalized in Bayesian decision theory. On (...)
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  39. Jane Friedman (2013). Rational Agnosticism and Degrees of Belief. Oxford Studies in Epistemology 4:57.
    There has been much discussion about whether traditional epistemology's doxastic attitudes are reducible to degrees of belief. In this paper I argue that what I call the Straightforward Reduction - the reduction of all three of believing p, disbelieving p, and suspending judgment about p, not-p to precise degrees of belief for p and not-p that ought to obey the standard axioms of the probability calculus - cannot succeed. By focusing on suspension of judgment (agnosticism) rather than belief, we can (...)
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  40. A. J. B. Fugard, Niki Pfeifer & B. Mayerhofer (2011). Probabilistic Theories of Reasoning Need Pragmatics Too: Modulating Relevance in Uncertain Conditionals. Journal of Pragmatics 43:2034–2042.
    According to probabilistic theories of reasoning in psychology, people's degree of belief in an indicative conditional `if A, then B' is given by the conditional probability, P(B|A). The role of language pragmatics is relatively unexplored in the new probabilistic paradigm. We investigated how consequent relevance a ects participants' degrees of belief in conditionals about a randomly chosen card. The set of events referred to by the consequent was either a strict superset or a strict subset of the set of events referred (...)
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  41. Haim Gaifman (2012). Deceptive Updating and Minimal Information Methods. Synthese 187 (1):147 - 178.
    The technique of minimizing information (infomin) has been commonly employed as a general method for both choosing and updating a subjective probability function. We argue that, in a wide class of cases, the use of infomin methods fails to cohere with our standard conception of rational degrees of belief. We introduce the notion of a deceptive updating method and argue that non-deceptiveness is a necessary condition for rational coherence. Infomin has been criticized on the grounds that there are no higher (...)
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  42. Dorit Ganson (2008). Evidentialism and Pragmatic Constraints on Outright Belief. Philosophical Studies 139 (3):441 - 458.
    Evidentialism is the view that facts about whether or not an agent is justified in having a particular belief are entirely determined by facts about the agent’s evidence; the agent’s practical needs and interests are irrelevant. I examine an array of arguments against evidentialism (by Jeremy Fantl, Matthew McGrath, David Owens, and others), and demonstrate how their force is affected when we take into account the relation between degrees of belief and outright belief. Once we are sensitive to one of (...)
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  43. Donald Gillies (1991). Intersubjective Probability and Confirmation Theory. British Journal for the Philosophy of Science 42 (4):513-533.
    This paper introduces what is called the intersubjective interpretation of the probability calculus. Intersubjective probabilities are related to subjective probabilities, and the paper begins with a particular formulation of the familiar Dutch Book argument. This argument is then extended, in Section 3, to social groups, and this enables the concept of intersubjective probability to be introduced in Section 4. It is then argued that the intersubjective interpretation is the appropriate one for the probabilities which appear in confirmation theory whether of (...)
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  44. Clark Glymour (1980). Theory and Evidence. Princeton University Press.
  45. D. Goldstick (2000). Three Epistemic Senses of Probability. Philosophical Studies 101 (1):59-76.
  46. James Hawthorne, Voting in Search of the Public Good: The Probabilistic Logic of Majority Judgments.
    I argue for an epistemic conception of voting, a conception on which the purpose of the ballot is at least in some cases to identify which of several policy proposals will best promote the public good. To support this view I first briefly investigate several notions of the kind of public good that public policy should promote. Then I examine the probability logic of voting as embodied in two very robust versions of the Condorcet Jury Theorem and some related results. (...)
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  47. 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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  48. James Hawthorne (2005). Degree-of-Belief and Degree-of-Support: Why Bayesians Need Both Notions. Mind 114 (454):277-320.
    I argue that Bayesians need two distinct notions of probability. We need the usual degree-of-belief notion that is central to the Bayesian account of rational decision. But Bayesians also need a separate notion of probability that represents the degree to which evidence supports hypotheses. Although degree-of-belief is well suited to the theory of rational decision, Bayesians have tried to apply it to the realm of hypothesis confirmation as well. This double duty leads to the problem of old evidence, a problem (...)
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  49. James Hawthorne (2004). Three Models of Sequential Belief Updating on Uncertain Evidence. Journal of Philosophical Logic 33 (1):89-123.
    Jeffrey updating is a natural extension of Bayesian updating to cases where the evidence is uncertain. But, the resulting degrees of belief appear to be sensitive to the order in which the uncertain evidence is acquired, a rather un-Bayesian looking effect. This order dependence results from the way in which basic Jeffrey updating is usually extended to sequences of updates. The usual extension seems very natural, but there are other plausible ways to extend Bayesian updating that maintain order-independence. I will (...)
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  50. James Hawthorne & Luc Bovens (1999). The Preface, the Lottery, and the Logic of Belief. Mind 108 (430):241-264.
    John Locke proposed a straightforward relationship between qualitative and quantitative doxastic notions: belief corresponds to a sufficiently high degree of confidence. Richard Foley has further developed this Lockean thesis and applied it to an analysis of the preface and lottery paradoxes. Following Foley's lead, we exploit various versions of these paradoxes to chart a precise relationship between belief and probabilistic degrees of confidence. The resolutions of these paradoxes emphasize distinct but complementary features of coherent belief. These features suggest principles that (...)
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