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Interpretation of Probability

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  1. Marshall Abrams, Toward a Mechanistic Interpretation of Probability.
    I sketch a new objective interpretation of probability, called "mechanistic probability", and more specifically what I call "far-flung frequency (FFF) mechanistic probability". FFF mechanistic probability is defined in terms of facts about the causal structure of devices and certain sets of collections of frequencies in the actual world. The relevant kind of causal structure is a generalization of what Strevens (2003) calls microconstancy. Though defined partly in terms of frequencies, FFF mechanistic probability avoids many drawbacks of well-known frequency theories. It (...)
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  2. Lennart Åqvist (2007). An Interpretation of Probability in the Law of Evidence Based on Pro-Et-Contra Argumentation. Artificial Intelligence and Law 15 (4).
    The purpose of this paper is to improve on the logical and measure-theoretic foundations for the notion of probability in the law of evidence, which were given in my contributions Åqvist [ (1990) Logical analysis of epistemic modality: an explication of the Bolding–Ekelöf degrees of evidential strength. In: Klami HT (ed) Rätt och Sanning (Law and Truth. A symposium on legal proof-theory in Uppsala May 1989). Iustus Förlag, Uppsala, pp 43–54; (1992) Towards a logical theory of legal evidence: semantic analysis (...)
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  3. E. Beth (1946). On the Interpretation of Probability Calculi Ernest Nagel. Synthese 5 (1-2).
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  4. Craig Callender (2007). The Emergence and Interpretation of Probability in Bohmian Mechanics. Studies in History and Philosophy of Science Part B 38 (2):351-370.
    A persistent question about the deBroglie–Bohm interpretation of quantum mechanics concerns the understanding of Born’s rule in the theory. Where do the quantum mechanical probabilities come from? How are they to be interpreted? These are the problems of emergence and interpretation. In more than 50 years no consensus regarding the answers has been achieved. Indeed, mirroring the foundational disputes in statistical mechanics, the answers to each question are surprisingly diverse. This paper is an opinionated survey of this literature. While acknowledging (...)
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  5. Rudolf Carnap (1945). The Two Concepts of Probability: The Problem of Probability. Philosophy and Phenomenological Research 5 (4):513-532.
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  6. Mark R. Crovelli, “A Challenge to Ludwig von Mises's Theory of Probability”.
    The most interesting and completely overlooked aspect of Ludwig von Mises’s theory of probability is the total absence of any explicit definition for probability in his theory. This paper examines Mises’s theory of probability in light of the fact that his theory possesses no definition for probability. It is argued, [...].
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  7. Branden Fitelson, Alan Hajek & Ned Hall (2006). Probability. In Jessica Pfeifer & Sahotra Sarkar (eds.), The Philosophy of Science: An Encyclopedia. Routledge.
    There are two central questions concerning probability. First, what are its formal features? That is a mathematical question, to which there is a standard, widely (though not universally) agreed upon answer. This answer is reviewed in the next section. Second, what sorts of things are probabilities---what, that is, is the subject matter of probability theory? This is a philosophical question, and while the mathematical theory of probability certainly bears on it, the answer must come from elsewhere. To see why, observe (...)
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  8. Roman Frigg, Probability in Boltzmannian Statistical Mechanics.
    In two recent papers Barry Loewer (2001, 2004) has suggested to interpret probabilities in statistical mechanics as Humean chances in David Lewis’ (1994) sense. I first give a precise formulation of this proposal, then raise two fundamental objections, and finally conclude that these can be overcome only at the price of interpreting these probabilities epistemically.
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  9. Maria Carla Galavotti (1995). Operationism, Probability and Quantum Mechanics. Foundations of Science 1 (1).
    This paper investigates the kind of empiricism combined with an operationalist perspective that, in the first decades of our Century, gave rise to a turning point in theoretical physics and in probability theory. While quantum mechanics was taking shape, the classical (Laplacian) interpretation of probability gave way to two divergent perspectives: frequentism and subjectivism. Frequentism gained wide acceptance among theoretical physicists. Subjectivism, on the other hand, was never held to be a serious candidate for application to physical theories, despite the (...)
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  10. Maria Carla Galavotti (1989). Anti-Realism in the Philosophy of Probability: Bruno de Finetti's Subjectivism. Erkenntnis 31 (2-3):239--261.
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  11. Donald Gillies (2000). Philosophical Theories of Probability. Routledge.
    This book presents a comprehensive and systematic account of the various philosophical theories of probability and explains how they are related. It covers the classical, logical, subjective, frequency, and propensity views of probability. Donald Gillies even provides a new theory of probability -the intersubjective-a development of the subjective theory. He argues for a pluralist view, where there can be more than one valid interpretation of probabiltiy, each appropriate in a different context. The relation of the various interpretations to the Bayesian (...)
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  12. Alan Hájek, Australasian Philosophy of Probability, and Probability in Australasian Philosophy.
    The philosophy of probability has been alive and well for several decades in Australia and New Zealand. Some distinctive lines of thought have emerged, resonating with broader themes that have come to be associated with Australasian philosophers: realist/objectivist accounts of various theoretical entities; an ongoing concern with logic, including the development of non­classical logics; and enthusiasm for conceptual analysis, rooted in commonsense but informed by science. In this article I concentrate on work by philosophers on the interpretation of probability, its (...)
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  13. Alan Hájek, Interpretations of Probability. Stanford Encyclopedia of Philosophy.
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  14. Alan Hájek (2007). The Reference Class Problem is Your Problem Too. Synthese 156 (3):563--585.
    The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference (...)
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  15. Michael Heidelberger (2001). Origins of the Logical Theory of Probability: Von Kries, Wittgenstein, Waismann. International Studies in the Philosophy of Science 15 (2):177 – 188.
    The physiologist and neo-Kantian philosopher Johannes von Kries (1853-1928) wrote one of the most philosophically important works on the foundation of probability after P.S. Laplace and before the First World War, his Principien der Wohrscheinlich-keitsrechnung (1886, repr. 1927). In this book, von Kries developed a highly original interpretation of probability, which maintains it to be both logical and objectively physical. After presenting his approach I shall pursue the influence it had on Ludwig Wittgenstein and Friedrich Waismann. It seems that von (...)
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  16. Jürgen Humburg (1986). Foundations of a New System of Probability Theory. Topoi 5 (1):39-50.
    The aim of my book is to explain the content of the different notions of probability.Based on a concept of logical probability, which is modified as compared with Carnap, we succeed by means of the mathematical results of de Finetti in defining the concept of statistical probability.
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  17. Patrick Maher (2006). The Concept of Inductive Probability. Erkenntnis 65 (2):185 - 206.
    The word ‘probability’ in ordinary language has two different senses, here called inductive and physical probability. This paper examines the concept of inductive probability. Attempts to express this concept in other words are shown to be either incorrect or else trivial. In particular, inductive probability is not the same as degree of belief. It is argued that inductive probabilities exist; subjectivist arguments to the contrary are rebutted. Finally, it is argued that inductive probability is an important concept and that it (...)
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  18. Peter Milne (1986). Can There Be a Realist Single-Case Interpretation of Probability? Erkenntnis 25 (2):129 - 132.
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  19. Paul K. Moser (1988). The Foundations of Epistemological Probability. Erkenntnis 28 (2):231 - 251.
    Epistemological probability is the kind of probability relative to a body of evidence. Many philosophers, including Henry Kyburg and Roderick Chisholm, hold that all epistemological probabilities reflect a relation between an evidential body of propositions and other propositions. But this article argues that some epistemological probabilities for empirical propositions must be relative to non-propositional evidence, specifically the contents of non-propositional perceptual states. In doing so, the article distinguishes between internalism and externalism regarding epistemological probability, and argues for a version of (...)
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  20. Jan Plato (1982). The Significance of the Ergodic Decomposition of Stationary Measures for the Interpretation of Probability. Synthese 53 (3).
    De Finetti's representation theorem is a special case of the ergodic decomposition of stationary probability measures. The problems of the interpretation of probabilities centred around de Finetti's theorem are extended to this more general situation. The ergodic decomposition theorem has a physical background in the ergodic theory of dynamical systems. Thereby the interpretations of probabilities in the cases of de Finetti's theorem and its generalization and in ergodic theory are systematically connected to each other.
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  21. T. V. Reeves (1988). A Theory of Probability. British Journal for the Philosophy of Science 39 (2):161-182.
    This paper argues that probability is not an objective phenomenon that can be identified with either the configurational properties of sequences, or the dynamic properties of sources that generate sequences. Instead, it is proposed that probability is a function of subjective as well as objective conditions. This is explained by formulating a nation of probability that is a modification of Laplace‘s classical enunciation. This definition is then used to explain why probability is strongly associated with disordered sequences, and is also (...)
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  22. Federica Russo (2006). Salmon and Van Fraassen on the Existence of Unobservable Entities: A Matter of Interpretation of Probability. Foundations of Science 11 (3).
    A careful analysis of Salmon’s Theoretical Realism and van Fraassen’s Constructive Empiricism shows that both share a common origin: the requirement of literal construal of theories inherited by the Standard View. However, despite this common starting point, Salmon and van Fraassen strongly disagree on the existence of unobservable entities. I argue that their different ontological commitment towards the existence of unobservables traces back to their different views on the interpretation of probability via different conceptions of induction. In fact, inferences to (...)
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  23. Simon Saunders (forthcoming). What is Probability? Arxiv Preprint Quant-Ph/0412194.
    Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's Copenhagen interpretation, nor the pilot-wave theory, nor stochastic state-reduction theories, give a satisfactory answer to the question of what objective probabilities are in quantum mechanics, or why they should satisfy the Born rule; nor do they give any reason why subjective probabilities should track objective ones. But (...)
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  24. Niall Shanks (1993). Time and the Propensity Interpretation of Probability. Journal for General Philosophy of Science 24 (2):293 - 302.
    The prime concern of this paper is with the nature of probability. It is argued that questions concerning the nature of probability are intimately linked to questions about the nature of time. The case study here concerns the single case propensity interpretation of probability. It is argued that while this interpretation of probability has a natural place in the quantum theory, the metaphysical picture of time to be found in relativity theory is incompatible with such a treatment of probability.
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  25. Lawrence Sklar (1970). Is Probability a Dispositional Property? Journal of Philosophy 67 (11):355-366.
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  26. Patrick Suppes (2010). The Nature of Probability. Philosophical Studies 147 (1).
    The thesis of this article is that the nature of probability is centered on its formal properties, not on any of its standard interpretations. Section 2 is a survey of Bayesian applications. Section 3 focuses on two examples from physics that seem as completely objective as other physical concepts. Section 4 compares the conflict between subjective Bayesians and objectivists about probability to the earlier strident conflict in physics about the nature of force. Section 5 outlines a pragmatic approach to the (...)
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  27. James E. Tomberlin (1974). J. L. Mackie's Truth, Probability, and Paradox: Studies in Philosophical Logic. Philosophy and Phenomenological Research 34 (4):591-592.
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  28. David Wallace (2006). Epistemology Quantized: Circumstances in Which We Should Come to Believe in the Everett Interpretation. British Journal for the Philosophy of Science 57 (4):655-689.
    I consider exactly what is involved in a solution to the probability problem of the Everett interpretation, in the light of recent work on applying considerations from decision theory to that problem. I suggest an overall framework for understanding probability in a physical theory, and conclude that this framework, when applied to the Everett interpretation, yields the result that that interpretation satisfactorily solves the measurement problem. Introduction What is probability? 2.1 Objective probability and the Principal Principle 2.2 Three ways of (...)
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  29. Margaret D. Wilson (1971). Possibility, Propensity, and Chance: Some Doubts About the Hacking Thesis. Journal of Philosophy 68 (19):610-617.
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Classical Probability
  1. Ernest W. Adams (1996). Four Probability-Preserving Properties of Inferences. Journal of Philosophical Logic 25 (1):1 - 24.
    Different inferences in probabilistic logics of conditionals preserve the probabilities of their premisses to different degrees. Some preserve certainty, some high probability, some positive probability, and some minimum probability. In the first case conclusions must have probability 1 when premisses have probability 1, though they might have probability 0 when their premisses have any lower probability. In the second case, roughly speaking, if premisses are highly probable though not certain then conclusions must also be highly probable. In the third case (...)
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  2. Leon Cohen (1966). Can Quantum Mechanics Be Formulated as a Classical Probability Theory? Philosophy of Science 33 (4):317-322.
    It is shown that quantum mechanics cannot be formulated as a stochastic theory involving a probability distribution function of position and momentum. This is done by showing that the most general distribution function which yields the proper quantum mechanical marginal distributions cannot consistently be used to predict the expectations of observables if phase space integration is used. Implications relating to the possibility of establishing a "hidden" variable theory of quantum mechanics are discussed.
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  3. G. Gerlich (1981). Some Remarks on Classical Probability Theory in Quantum Mechanics. Erkenntnis 16 (3):335 - 338.
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  4. Michal Marczyk & Leszek Wronski, Exhaustive Classication of Finite Classical Probability Spaces with Regard to the Notion of Causal Up-to-N-Closedness.
    Extending the ideas from (Hofer-Szabó and Rédei [2006]), we introduce the notion of causal up-to-n-closedness of probability spaces. A probability space is said to be causally up-to-n-closed with respect to a relation of independence R_ind iff for any pair of correlated events belonging to R_ind the space provides a common cause or a common cause system of size at most n. We prove that a finite classical probability space is causally up-to-3-closed w.r.t. the relation of logical independence iff its probability (...)
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  5. Joseph D. Sneed (1970). Quantum Mechanics and Classical Probability Theory. Synthese 21 (1):34 - 64.
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Frequentism
  1. Marshall Abrams, Short-Run Mechanistic Probability.
    This paper sketches a concept of higher-level objective probability (“short-run mechanistic probability”, SRMP) inspired partly by a style of explanation of relative frequencies known as the “method of arbitrary functions”. SRMP has the potential to fill the need for a theory of objective probability which has wide application at higher levels and which gives probability causal connections to observed relative frequency (without making it equivalent to relative frequency). Though this approach provides probabilities on a space of event types, it does (...)
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  2. Alan Hájek (2009). Fifteen Arguments Against Hypothetical Frequentism. Erkenntnis 70 (2):211 - 235.
    This is the sequel to my "Fifteen Arguments Against Finite Frequentism" (Erkenntnis 1997), the second half of a long paper that attacks the two main forms of frequentism about probability. Hypothetical frequentism asserts: The probability of an attribute A in a reference class B is p iff the limit of the relative frequency of A's among the B's would be p if there were an infinite sequence of B's. I offer fifteen arguments against this analysis. I consider various frequentist responses, (...)
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  3. David Atkinson & Jeanne Peijnenburg (2008). Reichenbach's Posits Reposited. Erkenntnis 69 (1):93 - 108.
    Reichenbach’s use of ‘posits’ to defend his frequentistic theory of probability has been criticized on the grounds that it makes unfalsifiable predictions. The justice of this criticism has blinded many to Reichenbach’s second use of a posit, one that can fruitfully be applied to current debates within epistemology. We show first that Reichenbach’s alternative type of posit creates a difficulty for epistemic foundationalists, and then that its use is equivalent to a particular kind of Jeffrey conditionalization. We conclude that, under (...)
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  4. J. Berkovitz (2001). On Chance in Causal Loops. Mind 110 (437):1-23.
    A common line of argument for the impossibility of closed causal loops is that they would involve causal paradoxes. The usual reply is that such loops impose heavy consistency constraints on the nature of causal connections in them; constraints that are overlooked by the impossibility arguments. Hugh Mellor has maintained that arguments for the possibility of causal loops also overlook some constraints, which are related to the chances (single-case, objective probabilities) that causes give to their effects. And he argues that (...)
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  5. Noëul Bonneuil (2004). Repertoires, Frequentism, and Predictability. History and Theory 43 (1):117–123.
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  6. Bas C. Fraassen (1977). Relative Frequencies. Synthese 34 (2):133 - 166.
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  7. Amit Hagar & Giuseppe Sergioli, Counting Steps: A New Interpretation of Objective Probability in Physics.
    We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set--up in the lab, or a subsystem of the universe), and quantifies (1) the difficulty to realize a physical state given another, (2) the 'distance' (in terms of physical resources) from a physical state to another, and (3) the size of the set of time--complexity functions that are compatible with the physical (...)
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  8. Alan Hájek (2010). Mises Redux-Redux : Fifteen Arguments Against Finite Frequentism. In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge.
    According to finite frequentism, the probability of an attribute A in a finite reference class B is the relative frequency of actual occurrences of A within B. I present fifteen arguments against this position.
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  9. Alan Hájek (2009). Fifteen Arguments Against Hypothetical Frequentism. Erkenntnis 70 (2):211 - 235.
    This is the sequel to my “Fifteen Arguments Against Finite Frequentism” ( Erkenntnis 1997), the second half of a long paper that attacks the two main forms of frequentism about probability. Hypothetical frequentism asserts: The probability of an attribute A in a reference class B is p iff the limit of the relative frequency of A ’s among the B ’s would be p if there were an infinite sequence of B ’s. I offer fifteen arguments against this analysis. I (...)
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  10. Alan Hájek (1996). “Mises Redux” — Redux: Fifteen Arguments Against Finite Frequentism. Erkenntnis 45 (2-3):209--27.
    According to finite frequentism, the probability of an attribute A in a finite reference class B is the relative frequency of actual occurrences of A within B. I present fifteen arguments against this position.
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  11. Paul Humphreys (2004). Some Thoughts on Wesley Salmon's Contributions to the Philosophy of Probability. Philosophy of Science 71 (5):942-949.
    Wesley Salmon provided three classic criteria of adequacy for satisfactory interpretations of probability. A fourth criterion is suggested here. A distinction is drawn between frequency‐driven probability models and theory‐driven probability models and it is argued that single case accounts of chance are superior to frequency accounts at least for the latter. Finally it is suggested that theories of chance should be required only to be contingently true, a position which is a natural extension of Salmon's ontic account of probabilistic causality (...)
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  12. Berna Kilinç (2000). Robert Leslie Ellis and John Stuart Mill on the One and the Many of Frequentism. British Journal for the History of Philosophy 8 (2):251-274.
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  13. Berna Kilinç (2000). Robert Leslie Ellis and John Stuart Mill on the One and the Many of Frequentism. British Journal for the History of Philosophy 8 (2):251 – 274.
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  14. Wesley C. Salmon (1977). Objectively Homogeneous Reference Classes. Synthese 36 (4):399 - 414.
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  15. Wesley C. Salmon (1965). What Happens in the Long Run? Philosophical Review 74 (3):373-378.
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  16. Wesley C. Salmon (1953). The Frequency Interpretation and Antecedent Probabilities. Philosophical Studies 4 (3):44 - 48.
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  17. Lawrence Sklar (1973). Unfair to Frequencies. Journal of Philosophy 70 (2):41-52.
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  18. M. Strevens (1996). Discussion. Quantum Mechanics and Frequentism: A Reply to Ismael. British Journal for the Philosophy of Science 47 (4):575-577.
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  19. Michael Strevens (2011). Probability Out Of Determinism. In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford University Press.
    This paper offers a metaphysics of physical probability in (or if you prefer, truth conditions for probabilistic claims about) deterministic systems based on an approach to the explanation of probabilistic patterns in deterministic systems called the method of arbitrary functions. Much of the appeal of the method is its promise to provide an account of physical probability on which probability assignments have the ability to support counterfactuals about frequencies. It is argued that the eponymous arbitrary functions are of little philosophical (...)
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  20. Michael Strevens (1996). Quantum Mechanics and Frequentism: A Reply to Ismael. British Journal for the Philosophy of Science 47 (4):575-577.
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  21. Peter M. Williams (1992). Review Essay: A Theory of Logical Frequentism. [REVIEW] Synthese 91 (3):337 - 346.
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Logical Probability
  1. Horacio Arló-Costa & Richmond H. Thomason (2001). Iterative Probability Kinematics. Journal of Philosophical Logic 30 (5):479-524.
    Following the pioneer work of Bruno De Finetti [12], conditional probability spaces (allowing for conditioning with events of measure zero) have been studied since (at least) the 1950's. Perhaps the most salient axiomatizations are Karl Popper's in [31], and Alfred Renyi's in [33]. Nonstandard probability spaces [34] are a well know alternative to this approach. Vann McGee proposed in [30] a result relating both approaches by showing that the standard values of infinitesimal probability functions are representable as Popper functions, and (...)
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  2. John C. Bigelow (1977). Semantics of Probability. Synthese 36 (4):459--72.
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  3. John C. Bigelow (1976). Possible Worlds Foundations for Probability. Journal of Philosophical Logic 5 (3):299--320.
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  4. F. Y. Edgeworth (1922). The Philosophy of Chance. Mind 31 (123):257-283.
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  5. F. Y. Edgeworth (1884). The Philosophy of Chance. Mind 9 (34):223-235.
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  6. J. Franklin (2001). Resurrecting Logical Probability. Erkenntnis 55 (2):277-305.
    The logical interpretation of probability, or ``objective Bayesianism''''– the theory that (some) probabilitiesare strictly logical degrees of partial implication – is defended.The main argument against it is that it requires the assignment ofprior probabilities, and that any attempt to determine them by symmetryvia a ``principle of insufficient reason'''' inevitably leads to paradox.Three replies are advanced: that priors are imprecise or of little weight, sothat disagreement about them does not matter, within limits; thatit is possible to distinguish reasonable from unreasonable priorson (...)
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  7. 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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  8. 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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  9. C. Howson (1973). Must the Logical Probability of Laws Be Zero? British Journal for the Philosophy of Science 24 (2):153-163.
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  10. Richard Johns, An Epistemic Theory of Objective Chance.
    A theory of objective, single-case chances is presented and defended. The theory states that the chance of an event E is its epistemic probability, given maximal knowledge of the possible causes of E. This theory is uniquely successful in entailing all the known properties of chance, but involves heavy metaphysical commitment. It requires an objective rationality that determines proper degrees of belief in some contexts.
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  11. John Maynard Keynes (1921/2004). A Treatise on Probability. Dover Publications.
    With this treatise, an insightful exploration of the probabilistic connection between philosophy and the history of science, the famous economist breathed new life into studies of both disciplines. Originally published in 1921, this important mathematical work represented a significant contribution to the theory regarding the logical probability of propositions. Keynes effectively dismantled the classical theory of probability, launching what has since been termed the “logical-relationist” theory. In so doing, he explored the logical relationships between classifying a proposition as “highly probable” (...)
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  12. Isaac Levi (2010). Probability Logic, Logical Probability, and Inductive Support. Synthese 172 (1).
    This paper seeks to defend the following conclusions: The program advanced by Carnap and other necessarians for probability logic has little to recommend it except for one important point. Credal probability judgments ought to be adapted to changes in evidence or states of full belief in a principled manner in conformity with the inquirer’s confirmational commitments—except when the inquirer has good reason to modify his or her confirmational commitment. Probability logic ought to spell out the constraints on rationally coherent confirmational (...)
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  13. Halina Mortimer (1973). A Rule of Acceptance Based on Logical Probability. Synthese 26 (2):259 - 263.
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  14. John F. Phillips (2005). A Theory of Objective Chance. Pacific Philosophical Quarterly 86 (2):267–283.
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  15. Darrell P. Rowbottom (forthcoming). Popper's Measure of Corroboration and P(H|B). British Journal for the Philosophy of Science.
    This paper shows that Popper’s measure of corroboration is inapplicable if, as Popper also argued, the logical probability of synthetic universal statements is zero relative to any evidence that we might possess. It goes on to show that Popper’s definition of degree of testability, in terms of degree of logical content, suffers from a similar problem.
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  16. Darrell P. Rowbottom (2008). On the Proximity of the Logical and 'Objective Bayesian' Interpretations of Probability. Erkenntnis 69 (3):335-349.
    In his Bayesian Nets and Causality, Jon Williamson presents an ‘Objective Bayesian’ interpretation of probability, which he endeavours to distance from the logical interpretation yet associate with the subjective interpretation. In doing so, he suggests that the logical interpretation suffers from severe epistemological problems that do not affect his alternative. In this paper, I present a challenge to his analysis. First, I closely examine the relationship between the logical and ‘Objective Bayesian’ views, and show how, and why, they are highly (...)
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  17. Darrell P. Rowbottom & Nicholas Shackel (2010). Bangu's Random Thoughts on Bertrand's Paradox. Analysis 70 (4):689-692.
    Bangu (2010) claims that Bertrand’s paradox rests on a hitherto unrecognized assumption, which assumption is sufficiently dubious to throw the burden of proof back onto ‘objectors to [the principle of indifference]’ (2010: 31). We show that Bangu’s objection to the assumption is ill-founded and that the assumption is provably true.
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  18. Hermann Vetter (1969). Logical Probability, Mathematical Statistics, and the Problem of Induction. Synthese 20 (1):56 - 71.
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Propensities
  1. M. Albert (2007). The Propensity Theory: A Decision-Theoretic Restatement. Synthese 156 (3):587 - 603.
    Probability theory is important because of its relevance for decision making, which also means: its relevance for the single case. The propensity theory of objective probability, which addresses the single case, is subject to two problems: Humphreys’ problem of inverse probabilities and the problem of the reference class. The paper solves both problems by restating the propensity theory using (an objectivist version of) Pearl’s approach to causality and probability, and by applying a decision-theoretic perspective. Contrary to a widely held view, (...)
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  2. Thomas Bartelborth (2011). Propensities and Transcendental Assumptions. Erkenntnis 74 (3):363-381.
    In order to comprehend the world around us and construct explaining theories for this purpose, we need a conception of physical probability, since we come across many (apparently) probabilistic phenomena in our world. But how should we understand objective probability claims? Since pure frequency approaches of probability are not appropriate, we have to use a single case propensity interpretation. Unfortunately, many philosophers believe that this understanding of probability is burdened with significant difficulties. My main aim is to show that we (...)
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  3. Nuel Belnap (2007). Propensities and Probabilities. Studies in History and Philosophy of Science Part B 38 (3):593-625.
    Popper’s introduction of ‘‘propensity’’ was intended to provide a solid conceptual foundation for objective single-case probabilities. By considering the partly opposed contributions of Humphreys and Miller and Salmon, it is argued that when properly understood, propensities can in fact be understood as objective single-case causal probabilities of transitions between concrete events. The chief claim is that propensities are well-explicated by describing how they fit into the existing formal theory of branching space-times, which is simultaneously indeterministic and causal. Several problematic examples, (...)
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  4. John C. Bigelow (1977). Semantics of Probability. Synthese 36 (4):459--72.
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  5. John C. Bigelow (1976). Possible Worlds Foundations for Probability. Journal of Philosophical Logic 5 (3):299--320.
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  6. David Bohm (1957/1999). Causality and Chance in Modern Physics. University of Pennsylvania Press.
    CHAPTER ONE Causality and Chance in Natural Law. INTRODUCTION IN nature nothing remains constant. Everything is in a perpetual state of transformation, ...
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  7. T. E. Burke (1991). A World of Propensities. Cogito 5 (3):179-180.
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  8. Richard N. Burnor (1984). What's the Matter with the Matter of Chance? Philosophical Studies 46 (3):349 - 365.
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  9. Antoine Côté (2009). Simplicius and James of Viterbo on Propensities. Vivarium 47 (1):24-53.
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  10. Antony Eagle (2004). Twenty-One Arguments Against Propensity Analyses of Probability. Erkenntnis 60 (3):371–416.
    I argue that any broadly dispositional analysis of probability will either fail to give an adequate explication of probability, or else will fail to provide an explication that can be gainfully employed elsewhere (for instance, in empirical science or in the regulation of credence). The diversity and number of arguments suggests that there is little prospect of any successful analysis along these lines.
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  11. James H. Fetzer (2002). Propensities and Frequencies: Inference to the Best Explanation. Synthese 132 (1-2):27 - 61.
    An approach to inference to the best explanation integrating a Popperianconception of natural laws together with a modified Hempelian account of explanation, one the one hand, and Hacking's law of likelihood (in its nomicguise), on the other, which provides a robust abductivist model of sciencethat appears to overcome the obstacles that confront its inductivist,deductivist, and hypothetico-deductivist alternatives.This philosophy of scienceclarifies and illuminates some fundamental aspects of ontology and epistemology, especially concerning the relations between frequencies and propensities. Among the most important (...)
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  12. Ronald N. Giere (1976). A Laplacean Formal Semantics for Single-Case Propensities. Journal of Philosophical Logic 5 (3):321 - 353.
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  13. Donald Gillies (2002). Causality, Propensity, and Bayesian Networks. Synthese 132 (1-2):63 - 88.
    This paper investigates the relations between causality and propensity. Aparticular version of the propensity theory of probability is introduced, and it is argued that propensities in this sense are not causes. Some conclusions regarding propensities can, however, be inferred from causal statements, but these hold only under restrictive conditions which prevent cause being defined in terms of propensity. The notion of a Bayesian propensity network is introduced, and the relations between such networks and causal networks is investigated. It is argued (...)
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  14. Donald Gillies (2000). Varieties of Propensity. British Journal for the Philosophy of Science 51 (4):807-835.
    The propensity interpretation of probability was introduced by Popper ([1957]), but has subsequently been developed in different ways by quite a number of philosophers of science. This paper does not attempt a complete survey, but discusses a number of different versions of the theory, thereby giving some idea of the varieties of propensity. Propensity theories are classified into (i) long-run and (ii) single-case. The paper argues for a long-run version of the propensity theory, but this is contrasted with two single-case (...)
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  15. Donald Gillies (1991). A World of Propensities By Karl R. Popper Thoemmes Antiquarian Books Ltd., 64 Pp., £5.00 Paper. Philosophy 66 (257):392-.
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  16. N. Gisin (1991). Propensities in a Non-Deterministic Physics. Synthese 89 (2):287 - 297.
    Propensities are presented as a generalization of classical determinism. They describe a physical reality intermediary between Laplacian determinism and pure randomness, such as in quantum mechanics. They are characterized by the fact that their values are determined by the collection of all actual properties. It is argued that they do not satisfy Kolmogorov axioms; other axioms are proposed.
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  17. J. W. Grove (1995). Karl Popper, in Search of a Better World: Lectures and Essays From Thirty Years. Routledge, London and New York, 1992. Pp. X, 245. £25.00. Karl Popper, a World of Propensities. Thoemmes, Bristol, 1990. Pp. IX, 51. £5.99 (Paper). John R. Wettersten, the Roots of Critical Rationalism. Rodopi, Amsterdam and Atlanta, Ga, 1992. Pp. 254. $68.97. Philosophy of the Social Sciences 25 (3):376-383.
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  18. Joseph F. Hanna (1981). Single Case Propensities and the Explanation of Particular Events. Synthese 48 (3):409 - 436.
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  19. Christian Hennig (2007). Falsification of Propensity Models by Statistical Tests and the Goodness-of-Fit Paradox. Philosophia Mathematica 15 (2):166-192.
    Gillies introduced a propensity interpretation of probability which is linked to experience by a falsifying rule for probability statements. The present paper argues that general statistical tests should qualify as falsification rules. The ‘goodness-of-fit paradox’ is introduced: the confirmation of a probability model by a test refutes the model's validity. An example is given in which an independence test introduces dependence. Several possibilities to interpret the paradox and to deal with it are discussed. It is concluded that the propensity interpretation (...)
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  20. Colin Howson (1984). Probabilities, Propensities, and Chances. Erkenntnis 21 (3):279 - 293.
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  21. Paul Humphreys (1985). Why Propensities Cannot Be Probabilities. Philosophical Review 94 (4):557-570.
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  22. Frank Jackson & Robert Pargetter (1982). Physical Probability as a Propensity. Noûs 16 (4):567-583.
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  23. I. C. Jarvie (1991). Book Reviews : Karl R. Popper, A World of Propensities. Thoemmes, Bristol, 1990. Pp. 51. 5.00. Philosophy of the Social Sciences 21 (3):407-409.
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  24. Henry Krips (1984). Popper, Propensities, and Quantum Theory. British Journal for the Philosophy of Science 35 (3):253-274.
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  25. Review author[S.]: Henry E. Kyberg (1974). Propensities and Probabilities. British Journal for the Philosophy of Science 25 (4):358-375.
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  26. Christopher S. I. Mccurdy (1996). Humphrey's Paradox and the Interpretation of Inverse Conditional Propensities. Synthese 108 (1):105 - 125.
    The aim of this paper is to distinguish between, and examine, three issues surrounding Humphreys's paradox and interpretation of conditional propensities. The first issue involves the controversy over the interpretation of inverse conditional propensities — conditional propensities in which the conditioned event occurs before the conditioning event. The second issue is the consistency of the dispositional nature of the propensity interpretation and the inversion theorems of the probability calculus, where an inversion theorem is any theorem of probability that makes explicit (...)
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  27. D. H. Mellor (2000). Possibility, Chance and Necessity. Australasian Journal of Philosophy 78 (1):16 – 27.
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