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  1. A. R. A. (1957). Probability in Logic. Review of Metaphysics 11 (2):348-348.
  2. 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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  3. Sorin Bangu (2010). On Bertrand's Paradox. Analysis 70 (1):30-35.
    The Principle of Indifference is a central element of the ‘classical’ conception of probability, but, for all its strong intuitive appeal, it is widely believed that it faces a devastating objection: the so-called (by Poincare´) ‘Bertrand paradoxes’ (in essence, cases in which the same probability question receives different answers). The puzzle has fascinated many since its discovery, and a series of clever solutions (followed promptly by equally clever rebuttals) have been proposed. However, despite the long-standing interest in this problem, an (...)
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  4. Jean Baratgin & Guy Politzer (2011). Updating: A Psychologically Basic Situation of Probability Revision. Thinking and Reasoning 16 (4):253-287.
    The Bayesian model has been used in psychology as the standard reference for the study of probability revision. In the first part of this paper we show that this traditional choice restricts the scope of the experimental investigation of revision to a stable universe. This is the case of a situation that, technically, is known as focusing. We argue that it is essential for a better understanding of human probability revision to consider another situation called updating (Katsuno & Mendelzon, 1992), (...)
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  5. Franz Dietrich & Christian List, Probabilistic Opinion Pooling Generalized -- Part One: General Agendas.
    How can different individuals' probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events -- the agenda -- is a sigma-algebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interest-rate increase, but not in the probability of rain or (...)
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  6. Franz Dietrich & Christian List, Probabilistic Opinion Pooling Generalised -- Part Two: The Premise-Based Approach.
    How can different individuals' probability functions on a given sigma-algebra of events be aggregated into a collective probability function? Classic approaches to this problem often require 'event-wise independence': the collective probability for each event should depend only on the individuals' probabilities for that event. In practice, however, some events may be 'basic' and others 'derivative', so that it makes sense first to aggregate the probabilities for the former and then to let these constrain the probabilities for the latter. We formalize (...)
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  7. Antony Eagle, Chance Versus Randomness. Stanford Encyclopedia of Philosophy.
    This article explores the connection between objective chance and the randomness of a sequence of outcomes. Discussion is focussed around the claim that something happens by chance iff it is random. This claim is subject to many objections. Attempts to save it by providing alternative theories of chance and randomness, involving indeterminism, unpredictability, and reductionism about chance, are canvassed. The article is largely expository, with particular attention being paid to the details of algorithmic randomness, a topic relatively unfamiliar to philosophers.
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  8. Antony Eagle (2005). Randomness Is Unpredictability. British Journal for the Philosophy of Science 56 (4):749-790.
    The concept of randomness has been unjustly neglected in recent philosophical literature, and when philosophers have thought about it, they have usually acquiesced in views about the concept that are fundamentally flawed. After indicating the ways in which these accounts are flawed, I propose that randomness is to be understood as a special case of the epistemic concept of the unpredictability of a process. This proposal arguably captures the intuitive desiderata for the concept of randomness; at least it should suggest (...)
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  9. Kenny Easwaran (2011). Varieties of Conditional Probability. In Prasanta Bandyopadhyay & Malcolm Forster (eds.), Handbook for Philosophy of Statistics. North Holland.
    I consider the notions of logical probability, degree of belief, and objective chance, and argue that a different formalism for conditional probability is appropriate for each.
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  10. Kenny Easwaran (2010). Logic and Probability. Journal of the Indian Council of Philosophical Research 27 (2):229-253.
    As is clear from the other articles in this volume, logic has applications in a broad range of areas of philosophy. If logic is taken to include the mathematical disciplines of set theory, model theory, proof theory, and recursion theory (as well as first-order logic, second-order logic, and modal logic), then the only other area of mathematics with such wide-ranging applications in philosophy is probability theory.
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  11. Ellery Eells, Brian Skyrms & Ernest W. Adams (eds.) (1994). Probability and Conditionals: Belief Revision and Rational Decision. Cambridge University Press.
    This is a 'state of the art' collection of essays on the relation between probabilities, especially conditional probabilities, and conditionals. It provides new negative results which sharply limit the ways conditionals can be related to conditional probabilities. There are also positive ideas and results which will open up new areas of research. The collection is intended to honour Ernest W. Adams, whose seminal work is largely responsible for creating this area of inquiry. As well as describing, evaluating, and applying Adams' (...)
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  12. Branden Fitelson & Lara Buchak, Separability Assumptions in Scoring-Rule-Based Arguments for Probabilism.
    - In decision theory, an agent is deciding how to value a gamble that results in different outcomes in different states. Each outcome gets a utility value for the agent.
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  13. Joseph S. Fulda, Remarks on the Argument From Design.
    Gives two pared-down versions of the argument from design, which may prove more persuasive as to a Creator, discusses briefly the mathematics underpinning disbelief and nonbelief and its misuse and some proper uses, moves to why the full argument is needed anyway, viz., to demonstrate Providence, offers a theory as to how miracles (open and hidden) occur, viz. the replacement of any particular mathematics underlying a natural law (save logic) by its most appropriate nonstandard variant. -/- Note: This is an (...)
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  14. Shan Gao, The Wave Function and Its Evolution.
    The meaning of the wave function and its evolution are investigated. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and (...)
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  15. Shan Gao, Derivation of the Meaning of the Wave Function.
    We show that the physical meaning of the wave function can be derived based on the established parts of quantum mechanics. It turns out that the wave function represents the state of random discontinuous motion of particles, and its modulus square determines the probability density of the particles appearing in certain positions in space.
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  16. Shan Gao, Protective Measurement and the Meaning of the Wave Function.
    This article analyzes the implications of protective measurement for the meaning of the wave function. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus square of its wave function. It is shown that the mass and charge density is not real but effective, formed by the ergodic motion of a localized particle with the total mass and charge of the system. Moreover, it is argued that the ergodic motion is not continuous but (...)
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  17. D. Gillies (2007). Maria Carla Galavotti. Philosophical Introduction to Probability. Stanford: Center for the Study of Language and Information Publications, 2005. Pp. X + 265. ISBN 1-57586-490-8 (Pbk), 1-57586-489-4 (Hardback). [REVIEW] Philosophia Mathematica 15 (1):129-132.
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  18. Amit Hagar (2014). Demons in Physics. [REVIEW] Metascience 23 (2):1-10.
    In their book The Road to Maxwell's Demon Hemmo & Shenker re-describe the foundations of statistical mechanics from a purely empiricist perspective. The result is refreshing, as well as intriguing, and it goes against much of the literature on the demon. Their conclusion, however, that Maxwell's demon is consistent with statistical mechanics, still leaves open the question of why such a demon hasn't yet been observed on a macroscopic scale. This essay offers a sketch of what a possible answer could (...)
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  19. Sven Ove Hansson (2009). From the Casino to the Jungle. Synthese 168 (3):423 - 432.
    Clear-cut cases of decision-making under risk (known probabilities) are unusual in real life. The gambler’s decisions at the roulette table are as close as we can get to this type of decision-making. In contrast, decision-making under uncertainty (unknown probabilities) can be exemplified by a decision whether to enter a jungle that may contain unknown dangers. Life is usually more like an expedition into an unknown jungle than a visit to the casino. Nevertheless, it is common in decision-supporting disciplines to proceed (...)
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  20. 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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  21. James Hawthorne (1996). On the Logic of Nonmonotonic Conditionals and Conditional Probabilities. Journal of Philosophical Logic 25 (2):185-218.
    I will describe the logics of a range of conditionals that behave like conditional probabilities at various levels of probabilistic support. Families of these conditionals will be characterized in terms of the rules that their members obey. I will show that for each conditional, →, in a given family, there is a probabilistic support level r and a conditional probability function P such that, for all sentences C and B, 'C → B' holds just in case P[B | C] ≥ (...)
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  22. Wesley H. Holliday & Thomas F. Icard (forthcoming). Measure Semantics and Qualitative Semantics for Epistemic Modals. Proceedings of SALT 23.
    In this paper, we explore semantics for comparative epistemic modals that avoid the entailment problems shown to result from Kratzer’s (1991) semantics by Yalcin (2006, 2009, 2010). In contrast to the alternative semantics presented by Yalcin and Lassiter (2010, 2011), based on finitely additive probability measures, we introduce semantics based on qualitatively additive measures, as well as semantics based on purely qualitative orderings, including orderings on propositions derived from orderings on worlds in the tradition of Kratzer (1991). All of these (...)
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  23. James M. Joyce (2005). How Probabilities Reflect Evidence. Philosophical Perspectives 19 (1):153–178.
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  24. Pawel Kawalec (2012). Bayesianizm w polskiej tradycji probabilizmu – studium stanowiska Kazimierza Ajdukiewicza. Ruch Filozoficzny 1 (1).
    Abstract The opening section outlines probabilism in the 20th century philosophy and shortly discusses the major accomplishments of Polish probabilist thinkers. A concise characterization of Bayesianism as the major recent form of probabilism follows. It builds upon the core personalist version of Bayesianism towards more objectively oriented versions thereof. The problem of a priori probability is shortly discussed. A tentative characterization of Kazimierz Ajdukiewicz’s standpoint regarding the inductive inference is cast in Bayesian terms. His objections against it presented in Pragmatic (...)
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  25. Christian List & Marcus Pivato, Emergent Chance.
    We offer a new argument for the claim that there can be non-degenerate objective chance (“true randomness”) in a deterministic world. Using a formal model of the relationship between different levels of description of a system, we show how objective chance at a higher level can coexist with its absence at a lower level. Unlike previous arguments for the level-specificity of chance, our argument shows, in a precise sense, that higher-level chance does not collapse into epistemic probability, despite higher-level properties (...)
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  26. Charles Morgan & Hughes LeBlanc (1983). Probabilistic Semantics for Formal Logic. Notre Dame Journal of Formal Logic 24:161-180.
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  27. Niki Pfeifer & G. D. Kleiter (2009). Framing Human Inference by Coherence Based Probability Logic. Journal of Applied Logic 7 (2):206--217.
  28. Niki Pfeifer & G. D. Kleiter (2006). Inference in Conditional Probability Logic. Kybernetika 42 (2):391--404.
    An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if . . . , then . . . ” by conditional probabilities and not by the probability of the material implication. An inference rule is probabilistically informative if the coherent probability interval of its conclusion is not necessarily equal to the unit interval (...)
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  29. Niki Pfeifer & G. D. Kleiter (2006). Towards a Probability Logic Based on Statistical Reasoning. In Proceedings of the 11 T H Ipmu International Conference (Information Processing and Management of Uncertainty in Knowledge-Based Systems). 2308--2315.
    Logical argument forms are investigated by second order probability density functions. When the premises are expressed by beta distributions, the conclusions usually are mixtures of beta distributions. If the shape parameters of the distributions are assumed to be additive (natural sampling), then the lower and upper bounds of the mixing distributions (P´olya-Eggenberger distributions) are parallel to the corresponding lower and upper probabilities in conditional probability logic.
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  30. Niki Pfeifer & G. D. Kleiter (2005). Towards a Mental Probability Logic. Psychologica Belgica 45 (1):71--99.
    We propose probability logic as an appropriate standard of reference for evaluating human inferences. Probability logical accounts of nonmonotonic reasoning with system p, and conditional syllogisms (modus ponens, etc.) are explored. Furthermore, we present categorical syllogisms with intermediate quantifiers, like the “most . . . ” quantifier. While most of the paper is theoretical and intended to stimulate psychological studies, we summarize our empirical studies on human nonmonotonic reasoning.
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  31. Karl Popper (1990). A World of Propensities. Thoemmes.
  32. Huw Price, The Lion, the 'Which?' And the Wardrobe -- Reading Lewis as a Closet One-Boxer.
    Newcomb problems turn on a tension between two principles of choice: roughly, a principle sensitive to the causal features of the relevant situation, and a principle sensitive only to evidential factors. Two-boxers give priority to causal beliefs, and one-boxers to evidential beliefs. A similar issue can arise when the modality in question is chance, rather than causation. In this case, the conflict is between decision rules based on credences guided solely by chances, and rules based on credences guided by other (...)
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  33. Susanna Rinard (2014). A New Bayesian Solution to the Paradox of the Ravens. Philosophy of Science 81 (1):81-100.
    The canonical Bayesian solution to the ravens paradox faces a problem: it entails that black non-ravens disconfirm the hypothesis that all ravens are black. I provide a new solution that avoids this problem. On my solution, black ravens confirm that all ravens are black, while non-black non-ravens and black non-ravens are neutral. My approach is grounded in certain relations of epistemic dependence, which, in turn, are grounded in the fact that the kind raven is more natural than the kind black. (...)
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  34. 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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  35. Andrew Sepielli (2012). Normative Uncertainty for Non-Cognitivists. Philosophical Studies 160 (2):191-207.
    Normative judgments involve two gradable features. First, the judgments themselves can come in degrees; second, the strength of reasons represented in the judgments can come in degrees. Michael Smith has argued that non-cognitivism cannot accommodate both of these gradable dimensions. The degrees of a non-cognitive state can stand in for degrees of judgment, or degrees of reason strength represented in judgment, but not both. I argue that (a) there are brands of noncognitivism that can surmount Smith’s challenge, and (b) any (...)
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  36. Michael J. Shaffer (2004). Probability and Tempered Modal Eliminativism. History and Philosophy of Logic 25 (4):305-318.
    In this paper the strategy for the eliminative reduction of the alethic modalities suggested by John Venn is outlined and it is shown to anticipate certain related contemporary empiricistic and nominalistic projects. Venn attempted to reduce the alethic modalities to probabilities, and thus suggested a promising solution to the nagging issue of the inclusion of modal statements in empiricistic philosophical systems. However, despite the promise that this suggestion held for laying the ‘ghost of modality’ to rest, this general approach, tempered (...)
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  37. Nathaniel Sharadin (forthcoming). Problems for Pure Probabilism About Promotion (and a Disjunctive Alternative). Philosophical Studies:1-16.
    Humean promotionalists about reasons think that whether there is a reason for an agent to ϕ depends on whether her ϕ-ing promotes the satisfaction of at least one of her desires. Several authors have recently defended probabilistic accounts of promotion, according to which an agent’s ϕ-ing promotes the satisfaction of one of her desires just in case her ϕ-ing makes the satisfaction of that desire more probable relative to some baseline. In this paper I do three things. First, I formalize (...)
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  38. Scott Sturgeon (2010). Confidence and Coarse-Grained Attitudes. In T. Szabo Gendler & J. Hawthorne (eds.), Oxford Studies in Epistemology. Oxford University Press. 3--126.
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  39. Eric Swanson (2009). How Not to Theorize About the Language of Subjective Uncertainty. In Andy Egan & B. Weatherson (eds.), Epistemic Modality. Oxford University Press.
    A successful theory of the language of subjective uncertainty would meet several important constraints. First, it would explain how use of the language of subjective uncertainty affects addressees’ states of subjective uncertainty. Second, it would explain how such use affects what possibilities are treated as live for purposes of conversation. Third, it would accommodate 'quantifying in' to the scope of epistemic modals. Fourth, it would explain the norms governing the language of subjective uncertainty, and the differences between them and the (...)
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  40. Nassim N. Taleb, The Future Has Thicker Tails Than the Past: Model Error as Branching Counterfactuals.
    Ex ante predicted outcomes should be interpreted as counterfactuals (potential histories), with errors as the spread between outcomes. But error rates have error rates. We reapply measurements of uncertainty about the estimation errors of the estimation errors of an estimation treated as branching counterfactuals. Such recursions of epistemic uncertainty have markedly different distributial properties from conventional sampling error, and lead to fatter tails in the projections than in past realizations. Counterfactuals of error rates always lead to fat tails, regardless of (...)
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  41. Nassim N. Taleb & Avital Pilpel (2007). Epistemology and Risk Management. Risk and Regulation 13:6--7.
  42. Vladislav Terekhovich (2013). Philosophical and Methodological Problems of the Principle of Least Action. Dissertation, St. Petersburg State University, Russia
    Twenty extremal principles of the natural sciences are reformulated to the general ontological scheme. The hypothesis is substantiated that the unique role of the principle of least action is based on its probabilistic interpretation. It is shown how most of the variational principles can be reduced to the principle of maximal probability, which is based on a realistic interpretation of Feynman’s path integral method.
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  43. Louis Vervoort, The Concept of Probability in Physics: An Analytic Version of von Mises’ Interpretation.
    In the following we will investigate whether von Mises’ frequency interpretation of probability can be modified to make it philosophically acceptable. We will reject certain elements of von Mises’ theory, but retain others. In the interpretation we propose we do not use von Mises’ often criticized ‘infinite collectives’ but we retain two essential claims of his interpretation, stating that probability can only be defined for events that can be repeated in similar conditions, and that exhibit frequency stabilization. The central idea (...)
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  44. J. R. G. Williams (2012). Gradational Accuracy and Nonclassical Semantics. Review of Symbolic Logic 5 (4):513-537.
    Joyce (1998) gives an argument for probabilism: the doctrine that rational credences should conform to the axioms of probability. In doing so, he provides a distinctive take on how the normative force of probabilism relates to the injunction to believe what is true. But Joyce presupposes that the truth values of the propositions over which credences are defined are classical. I generalize the core of Joyce’s argument to remove this presupposition. On the same assumptions as Joyce uses, the credences of (...)
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  45. Seth Yalcin (2010). Probability Operators. Philosophy Compass 5 (11):916-37.
    This is a study in the meaning of natural language probability operators, sentential operators such as probably and likely. We ask what sort of formal structure is required to model the logic and semantics of these operators. Along the way we investigate their deep connections to indicative conditionals and epistemic modals, probe their scalar structure, observe their sensitivity to contex- tually salient contrasts, and explore some of their scopal idiosyncrasies.
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