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  1. Edward H. Allen (1976). Negative Probabilities and the Uses of Signed Probability Theory. Philosophy of Science 43 (1):53-70.
    The use of negative probabilities is discussed for certain problems in which a stochastic process approach is indicated. An extension of probability theory to include signed (negative and positive) probabilities is outlined and both philosophical and axiomatic examinations of negative probabilities are presented. Finally, a class of applications illustrates the use and implications of signed probability theory.
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  2. Antony Eagle (forthcoming). Probability and Randomness. In Alan Hájek & Christopher Hitchcock (eds.), Oxford Handbook of Probability and Philosophy. Oxford University Press
  3. David Ellerman (2016). Quantum Mechanics Over Sets: A Pedagogical Model with Non-Commutative Finite Probability Theory as its Quantum Probability Calculus. Synthese 2016:1-34.
    This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability calculus. The previous attempts (...)
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  4. Dale C. Gillman (2014). On the Search For Objective Truths of Reality and Human Society: Part 1. Dissertation, Kennesaw State University
    Abstract Pioneers in the respective field of philosophy have made remarkable progress in the world. Thinkers starting with Plato and more contemporary thinkers such as Descartes and many others have tried pushing the limits of what humans can learn about the world around us. In my paper I am trying to establish probability as a recognized law of our physical reality. I also briefly discuss logic, reason and the need for modern philosophy. My hopes are also to show that though (...)
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  5. Alan Hájek (2001). Probability, Logic, and Probability Logic. In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Blackwell Publishers 362--384.
  6. Thomas Hofweber (2014). Infinitesimal Chances. Philosophers' Imprint 14 (2).
    It is natural to think that questions in the metaphysics of chance are independent of the mathematical representation of chance in probability theory. After all, chance is a feature of events that comes in degrees and the mathematical representation of chance concerns these degrees but leaves the nature of chance open. The mathematical representation of chance could thus, un-controversially, be taken to be what it is commonly taken to be: a probability measure satisfying Kolmogorov’s axioms. The metaphysical questions about chance (...)
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  7. Conor Mayo‐Wilson & Gregory Wheeler (2016). Scoring Imprecise Credences: A Mildly Immodest Proposal. Philosophy and Phenomenological Research 92 (1):55-78.
    Jim Joyce argues for two amendments to probabilism. The first is the doctrine that credences are rational, or not, in virtue of their accuracy or “closeness to the truth” (1998). The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (2010). We argue that both amendments cannot be satisfied simultaneously. To do so, we employ a (slightly-generalized) impossibility theorem of Seidenfeld, Schervish, and Kadane (2012), who show that (...)
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  8. Arthur Paul Pedersen & Gregory Wheeler (2015). Dilation, Disintegrations, and Delayed Decisions. In Thomas Augistin, Serena Dora, Enrique Miranda & Erik Quaeghebeur (eds.), Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications (ISIPTA 2015). Aracne Editrice 227–236.
    Both dilation and non-conglomerability have been alleged to conflict with a fundamental principle of Bayesian methodology that we call \textit{Good's Principle}: one should always delay making a terminal decision between alternative courses of action if given the opportunity to first learn, at zero cost, the outcome of an experiment relevant to the decision. In particular, both dilation and non-conglomerability have been alleged to permit or even mandate choosing to make a terminal decision in deliberate ignorance of relevant, cost-free information. Although (...)
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  9. Arthur Paul Pedersen & Gregory Wheeler (2014). Demystifying Dilation. Erkenntnis 79 (6):1305-1342.
    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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  10. Alexander R. Pruss (2012). Infinite Lotteries, Perfectly Thin Darts and Infinitesimals. Thought: A Journal of Philosophy 1 (2):81-89.
    One of the problems that Bayesian regularity, the thesis that all contingent propositions should be given probabilities strictly between zero and one, faces is the possibility of random processes that randomly and uniformly choose a number between zero and one. According to classical probability theory, the probability that such a process picks a particular number in the range is zero, but of course any number in the range can indeed be picked. There is a solution to this particular problem on (...)
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  11. Lukas M. Verburgt (2013). Robert Leslie Ellis's Work on Philosophy of Science and the Foundations of Probability Theory. Historia Mathematica 40 (4):423-454.
    The goal of this paper is to provide an extensive account of Robert Leslie Ellisʼs largely forgotten work on philosophy of science and probability theory. On the one hand, it is suggested that both his ‘idealist’ renovation of the Baconian theory of induction and a ‘realism’ vis-à-vis natural kinds were the result of a complex dialogue with the work of William Whewell. On the other hand, it is shown to what extent the combining of these two positions contributed to Ellisʼs (...)
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