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  1. Reflecting on diachronic Dutch books.Michael Rescorla - 2023 - Noûs 57 (3):511-538.
    Conditionalization governs how to reallocate credence in light of new evidence. One prominent argument in favor of Conditionalization holds that an agent who violates it is vulnerable to a diachronic Dutch book: a series of acceptable bets offered at multiple times that inflict a sure loss. van Fraassen argues that an agent who violates the Principle of Reflection is likewise vulnerable to a diachronic Dutch book. He concludes that agents should conform to both Conditionalization and Reflection. Some authors reply that (...)
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  • A Remark on Probabilistic Measures of Coherence.Sergi Oms - 2020 - Notre Dame Journal of Formal Logic 61 (1):129-140.
    In recent years, some authors have proposed quantitative measures of the coherence of sets of propositions. Such probabilistic measures of coherence (PMCs) are, in general terms, functions that take as their argument a set of propositions (along with some probability distribution) and yield as their value a number that is supposed to represent the degree of coherence of the set. In this paper, I introduce a minimal constraint on PMC theories, the weak stability principle, and show that any correct, coherent, (...)
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  • Knowledge of Our Own Beliefs.Sherrilyn Roush - 2016 - Philosophy and Phenomenological Research 93 (3):45-69.
    There is a widespread view that in order to be rational we must mostly know what we believe. In the probabilistic tradition this is defended by arguments that a person who failed to have this knowledge would be vulnerable to sure loss, or probabilistically incoherent. I argue that even gross failure to know one's own beliefs need not expose one to sure loss, and does not if we follow a generalization of the standard bridge principle between first-order and second-order beliefs. (...)
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  • Fading Foundations: Probability and the Regress Problem.Jeanne Peijnenburg - 2017 - Cham, Switzerland: Springer. Edited by Jeanne Peijnenburg.
    This Open Access book addresses the age-old problem of infinite regresses in epistemology. How can we ever come to know something if knowing requires having good reasons, and reasons can only be good if they are backed by good reasons in turn? The problem has puzzled philosophers ever since antiquity, giving rise to what is often called Agrippa's Trilemma. The current volume approaches the old problem in a provocative and thoroughly contemporary way. Taking seriously the idea that good reasons are (...)
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  • The structure of radical probabilism.Brian Skyrms - 1996 - Erkenntnis 45 (2-3):285 - 297.
    Does the philosophy of Radical Probabilism have enough structure to enable it to address fundamental epistemological questions? The requirement of dynamic coherence provides the structure for radical probabilist epistemology. This structure is sufficient to establish (i) the value of knowledge and (ii) long run convergence of degrees of belief.
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  • A Consistent Set of Infinite-Order Probabilities.David Atkinson & Jeanne Peijnenburg - 2013 - International Journal of Approximate Reasoning 54:1351-1360.
    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 (...)
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  • Biased Coins: A model for higher-order probabilities.Jeanne Peijnenburg & David Atkinson - 2014 - In Maria Carla Galavotti, Elisabeth Nemeth & Friedrich Stadler (eds.), European Philosophy of Science: Philosophy of Science in Europe and the Vienna Heritage. Cham: 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.
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  • Higher order probabilities.Zoltan Domotor - 1981 - Philosophical Studies 40 (1):31 - 46.
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  • Probability logic and F-coherence.A. I. Dale - 1976 - Philosophy of Science 43 (2):254-265.
    In order that a degree-of-belief function be coherent it is necessary and sufficient that it satisfy the axioms of probability theory. This theorem relies heavily for its proof on the two-valued sentential calculus, which emerges as a limiting case of a continuous scale of truth-values. In this “continuum of certainty” a theorem analogous to that instanced above is proved.
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