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Summary Perhaps the most natural way to understand probability is as an epistemic phenomenon. A probability function is an attempt to quantify a degree of uncertainty -- a state of mind. But some probabilities appear to be objective features of the world. A well constructed die has a probability of one in six that it will land on any given side, for instance. Such objective probabilities, or chances, explain why events happen with typical frequencies, while they cannot be predicted with certainty on any given trial. Philosophical controversies primarily arise regarding: the relationship between chances and epistemic states (under what circumstances should our degree of confidence match the chance, and why?); and also regarding the relationship between chances and frequencies (if chances are not reducible to frequencies, how do they explain those frequencies?).
Key works Popper 1959 puts forth the propensity interpretation of probability, which has been an influential way of understanding chances; Lewis 1980 focuses upon epistemic aspects of chance, and is the focus of much literature relating to Humeanism and chance; Loewer 2004 is a helpful paper further exploring Lewis's metaphysics of chance; Albert 2000 discusses the time asymmetry of chance and its relation to temporal symmetries in physics.
Introductions Consult Handfield 2012 for an exclusive focus upon chance; Hájek 2008 is about broader topic of probability, but has much that is of relevance to chance; Eagle 2010 contains many classic papers.
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  1. C. J. Adcock (1928). Law and Chance. Australasian Journal of Philosophy 6 (3):210 – 212.
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  2. D. M. Borchert (ed.) (2006). Encyclopedia of Philosophy, Second Edition.
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  3. Phil Dowe (2003). A Dilemma for Objective Chance. In Jr Kyburg & Mariam Thalos (eds.), Probability is the Very Guide of Life: The Philosophical Uses of Chance. Open Court. 153--64.
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  4. Iñaki San Pedro (2011). Venetian Sea Levels, British Bread Prices and the Principle of the Common Cause: A Reassessment. In H. de Regt, S. Okasha & S. Hartmann (eds.), EPSA Philosophy of Science: Amsterdam 2009. Springer. 341-354.
    It is still a controversial issue whether Reichenbach’s Principle of the Common Cause (RPCC) is a sound method for causal inference. In fact, the status of the principle has been a subject of intense philosophical debate. An extensive literature has been thus generated both with arguments in favor and against the adequacy of the principle. A remarkable argument against the principle, first proposed by Elliott Sober (Sober, 1987, 2001), consists on a counterexample which involves corelations between bread prices in Britain (...)
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  5. Leszek Wroński (forthcoming). Reichenbach's Paradise. De Gruyter Open.
    Since its introduction by Hans Reichenbach, many philosophers have claimed to refute the idea – known as the common cause principle – that any surprising correlation between any two factors that do not directly influence one another is due to some common cause. For example, falsity of the principle is frequently inferred from falsifiability of Bell’s inequalities. The author demonstrates, however, that the situation is not so straightforward. There is more than one version of the principle formulated with the use (...)
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Chance and Determinism
  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. Marshall Abrams (2012). Mechanistic Probability. Synthese 187 (2):343-375.
    I describe a realist, ontologically objective interpretation of probability, "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 frequencies in the actual world. Though defined partly in terms of frequencies, FFF mechanistic probability avoids many drawbacks of well-known frequency theories and helps causally explain stable frequencies, which will usually be close to the values of mechanistic probabilities. I also argue that it's a virtue rather than (...)
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  3. A. Ahmed (2010). Out of the Closet. Analysis 71 (1):77-85.
  4. David Albert (2012). Physics and Chance. In. In Yemima Ben-Menahem & Meir Hemmo (eds.), Probability in Physics. Springer. 17--40.
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  5. David Albert (2010). Probability in the Everett Picture. In Simon Saunders, Jonathan Barrett, Adrian Kent & David Wallace (eds.), Many Worlds?: Everett, Quantum Theory, & Reality. Oup Oxford.
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  6. David Albert (2010). Review of Gerhard Ernst, Andreas Hüttemann (Eds.), Time, Chance, and Reduction: Philosophical Aspects of Statistical Mechanics. [REVIEW] Notre Dame Philosophical Reviews 2010 (9).
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  7. David Z. Albert (2000). Time and Chance. Harvard University Press.
    This book is an attempt to get to the bottom of an acute and perennial tension between our best scientific pictures of the fundamental physical structure of the ...
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  8. Frank Arntzenius (1997). Transition Chances and Causation. Pacific Philosophical Quarterly 78 (2):149–168.
    The general claims of this paper are as follows. As a result of chaotic dynamics we can usually not know what the deterministic causes of events are. There will, however, be invariant forwards transition chances from earlier types of events, which we typically call the causes, to later types of events, which we typically call the effects. There will be no invariant backwards transition chances between these types of events. This asymmetry has the same origin and explanation as the arrow (...)
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  9. Eftichios Bitsakis (1988). Quantum Statistical Determinism. Foundations of Physics 18 (3):331-355.
    This paper attempts to analyze the concept of quantum statistical determinism. This is done after we have clarified the epistemic difference between causality and determinism and discussed the content of classical forms of determinism—mechanical and dynamical. Quantum statistical determinism transcends the classical forms, for it expresses the multiple potentialities of quantum systems. The whole argument is consistent with a statistical interpretation of quantum mechanics.
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  10. Robert N. Brandon & Scott Carson (1996). The Indeterministic Character of Evolutionary Theory: No "No Hidden Variables Proof" but No Room for Determinism Either. Philosophy of Science 63 (3):315-337.
    In this paper we first briefly review Bell's (1964, 1966) Theorem to see how it invalidates any deterministic "hidden variable" account of the apparent indeterminacy of quantum mechanics (QM). Then we show that quantum uncertainty, at the level of DNA mutations, can "percolate" up to have major populational effects. Interesting as this point may be it does not show any autonomous indeterminism of the evolutionary process. In the next two sections we investigate drift and natural selection as the locus of (...)
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  11. Jeremy Butterfield (1987). Probability and Disturbing Measurement. Proceedings of the Aristotelian Society, Supplementary Volume 61:211--243.
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  12. P. Clark (1989). Determinism, Probability and Randomness in Classical Statistical Physics in Imre Lakatos and Theories of Scientific Change. Boston Studies in the Philosophy of Science 111:95-110.
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  13. Peter Clark (2006). Problems of Determinism: Prediction, Propensity and Probability. In Wenceslao J. González & Jesus Alcolea (eds.), Contemporary Perspectives in Philosophy and Methodology of Science. Netbiblio.
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  14. Peter Clark (2001). Statistical Mechanics and the Propensity Interpretation of Probability. In Jean Bricmont & Others (eds.), Chance in Physics: Foundations and Perspectives. Springer. 271--81.
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  15. Peter Clark (1987). Determinism and Probability in Physics. Proceedings of the Aristotelian Society, Supplementary Volume 61:185--210.
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  16. Bob Coecke (1995). A Hidden Measurement Representation for Quantum Entities Described by Finite-Dimensional Complex Hilbert Spaces. Foundations of Physics 25 (8):1185-1208.
    It will be shown that the probability calculus of a quantum mechanical entity can be obtained in a deterministic framework, embedded in a real space, by introducing a lack of knowledge in the measurements on that entity. For all n ∃ ℕ we propose an explicit model in $\mathbb{R}^{n^2 } $ , which entails a representation for a quantum entity described by an n-dimensional complex Hilbert space þn, namely, the “þn,Euclidean hidden measurement representation.” This Euclidean hidden measurement representation is also (...)
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  17. Kevin Davey (2011). Thermodynamic Entropy and Its Relation to Probability in Classical Mechanics. Philosophy of Science 78 (5):955-975.
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  18. David Deutsch (1999). Quantum Theory of Probability and Decisions. Proceedings of the Royal Society of London:3129--37.
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  19. F. Dizadji-Bahmani (forthcoming). The Probability Problem in Everettian Quantum Mechanics Persists. British Journal for the Philosophy of Science:axt035.
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  20. Alon Drory (2012). Revising Statistical Mechanics: Probability, Typicality and Closure Time. In. In Yemima Ben-Menahem & Meir Hemmo (eds.), Probability in Physics. Springer. 115--134.
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  21. Detlef Dürr, Sheldon Goldstein & Nino Zanghí (1993). A Global Equilibrium as the Foundation of Quantum Randomness. Foundations of Physics 23 (5):721-738.
    We analyze the origin of quantum randomness within the framework of a completely deterministic theory of particle motion—Bohmian mechanics. We show that a universe governed by this mechanics evolves in such a way as to give rise to the appearance of randomness, with empirical distributions in agreement with the predictions of the quantum formalism. Crucial ingredients in our analysis are the concept of the effective wave function of a subsystem and that of a random system. The latter is a notion (...)
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  22. Antony Eagle (2011). Deterministic Chance. Noûs 45 (2):269 - 299.
    I sketch a new constraint on chance, which connects chance ascriptions closely with ascriptions of ability, and more specifically with 'CAN'-claims. This connection between chance and ability has some claim to be a platitude; moreover, it exposes the debate over deterministic chance to the extensive literature on (in)compatibilism about free will. The upshot is that a prima facie case for the tenability of deterministic chance can be made. But the main thrust of the paper is to draw attention to the (...)
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  23. 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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  24. 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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  25. John Earman (2004). Determinism: What We Have Learned and What We Still Don't Know. In Joseph K. Campbell (ed.), Freedom and Determinism. Cambridge Ma: Bradford Book/Mit Press. 21--46.
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  26. John Earman (1986). A Primer on Determinism. D. Reidel.
    Determinism is a perennial topic of philosophical discussion. Very little acquaintance with the philosophical literature is needed to reveal the Tower of ...
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  27. Ellery Eells & James H. Fetzer (eds.) (2010). The Place of Probability in Science. Springer.
    To clarify and illuminate the place of probability in science Ellery Eells and James H. Fetzer have brought together some of the most distinguished philosophers ...
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  28. Nina Emery (2013). Chance, Possibility, and Explanation. British Journal for the Philosophy of Science:axt041.
    I argue against the common and influential view that non-trivial chances arise only when the fundamental laws are indeterministic. The problem with this view, I claim, is not that it conflicts with some antecedently plausible metaphysics of chance or that it fails to capture our everyday use of ‘chance’ and related terms, but rather that it is unstable. Any reason for adopting the position that non-trivial chances arise only when the fundamental laws are indeterministic is also a reason for adopting (...)
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  29. Gerhard Ernst & Andreas Hüttemann (eds.) (2010). Time, Chance and Reduction: Philosophical Aspects of Statistical Mechanics. Cambridge University Press.
    Statistical mechanics attempts to explain the behaviour of macroscopic physical systems in terms of the mechanical properties of their constituents. Although it is one of the fundamental theories of physics, it has received little attention from philosophers of science. Nevertheless, it raises philosophical questions of fundamental importance on the nature of time, chance and reduction. Most philosophical issues in this domain relate to the question of the reduction of thermodynamics to statistical mechanics. This book addresses issues inherent in this reduction: (...)
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  30. James H. Fetzer (1983). Probability and Objectivity in Deterministic and Indeterministic Situations. Synthese 57 (3):367--86.
    This paper pursues the question, To what extent does the propensity approach to probability contribute to plausible solutions to various anomalies which occur in quantum mechanics? The position I shall defend is that of the three interpretations — the frequency, the subjective, and the propensity — only the third accommodates the possibility, in principle, of providing a realistic interpretation of ontic indeterminism. If these considerations are correct, then they lend support to Popper's contention that the propensity construction tends to remove (...)
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  31. Peter D. Finch (1982). Classical Probability and the Quantum Mechanical Trace Formulation for Expectations. Foundations of Physics 12 (4):327-345.
    The trace formulation of quantum mechanical expectations is derived in a classical deterministic setting by averaging over an assembly of states. Interference of probabilities is discussed and its usual Hilbert space formulation is questioned. Nevertheless, it is shown that the observable predictions of quantum statics remain unchanged in the framework developed here.
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  32. Roman Frigg, Chance and Determinism.
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  33. Roman Frigg (2008). Chance in Boltzmannian Statistical Mechanics. Philosophy of Science 75 (5):670-681.
    In two recent papers Barry Loewer ( 2001 , 2004 ) has suggested to interpret probabilities in statistical mechanics as chances in David Lewis’s ( 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. †To contact the author, please write to: Roman Frigg, Department of Philosophy, Logic and Scientific Method, London School of Economics, Houghton Street, (...)
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  34. Roman Frigg & Carl Hoefer (2010). Determinism and Chance From a Humean Perspective. In Friedrich Stadler, Dennis Dieks, Wenceslao González, Hartmann J., Uebel Stephan, Weber Thomas & Marcel (eds.), The Present Situation in the Philosophy of Science. Springer. 351--72.
    On the face of it ‘deterministic chance’ is an oxymoron: either an event is chancy or deterministic, but not both. Nevertheless, the world is rife with events that seem to be exactly that: chancy and deterministic at once. Simple gambling devices like coins and dice are cases in point. On the one hand they are governed by deterministic laws – the laws of classical mechanics – and hence given the initial condition of, say, a coin toss it is determined whether (...)
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  35. Philippe Gagnon (2009). Les Limites du Vivant Sont-Elles Riches D’Une Leçon? Contribution à L’Étude du Déterminisme Morphique. Eikasia. Revista de Filosofía 27 (August):155-186.
    Freedom is first apprehended as the pursuit of an activity which implies the choice to defend a thesis among other possible ones. This translation of the problem of freedom in an articulate language presupposes a complex nervous system and sensory apparatuses which we take for granted. In this study, I try to explore the undergrounds of the problem of freedom along with the suggestion that the notion of coding could enable one to bridge nature and the mind. When organisms invent, (...)
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  36. Stuart S. Glennan (1997). Probable Causes and the Distinction Between Subjective and Objective Chance. Noûs 31 (4):496-519.
    In this paper I present both a critical appraisal of Humphreys' probabilistic theory of causality and a sketch of an alternative view of the relationship between the notions of probability and of cause. Though I do not doubt that determinism is false, I claim that the examples used to motivate Humphreys' theory typically refer to subjective rather than objective chance. Additionally, I argue on a number of grounds that Humphreys' suggestion that linear regression models be used as a canonical form (...)
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  37. Bruce Glymour (2001). Selection, Indeterminism, and Evolutionary Theory. Philosophy of Science 68 (4):518-535.
    I argue that results from foraging theory give us good reason to think some evolutionary phenomena are indeterministic and hence that evolutionary theory must be probabilistic. Foraging theory implies that random search is sometimes selectively advantageous, and experimental work suggests that it is employed by a variety of organisms. There are reasons to think such search will sometimes be genuinely indeterministic. If it is, then individual reproductive success will also be indeterministic, and so too will frequency change in populations of (...)
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  38. Clark Glymour (1971). Determinism, Ignorance, and Quantum Mechanics. Journal of Philosophy 68 (21):744-751.
    is every bit as intelligible and philosophically respectable as many other doctrines currently in favor, e.g., the doctrine that mental events are identical with brain events; the attempt to give a linguistic construal of this latter doctrine meets many of the same sorts of difficulties encountered above (see Hempel, op. cit.). Secondly, I think that evidence for universal determinism may not, as a matter of fact, be so hard to come by as one might imagine. It is a striking fact (...)
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  39. Luke Glynn (2010). Deterministic Chance. British Journal for the Philosophy of Science 61 (1):51–80.
    I argue that there are non-trivial objective chances (that is, objective chances other than 0 and 1) even in deterministic worlds. The argument is straightforward. I observe that there are probabilistic special scientific laws even in deterministic worlds. These laws project non-trivial probabilities for the events that they concern. And these probabilities play the chance role and so should be regarded as chances as opposed, for example, to epistemic probabilities or credences. The supposition of non-trivial deterministic chances might seem to (...)
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  40. Sheldon Goldstein (2012). Typicality and Notions of Probability in Physics. In. In Yemima Ben-Menahem & Meir Hemmo (eds.), Probability in Physics. Springer. 59--71.
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  41. Leslie Graves, Barbara L. Horan & Alex Rosenberg (1999). Is Indeterminism the Source of the Statistical Character of Evolutionary Theory? Philosophy of Science 66 (1):140-157.
    We argue that Brandon and Carson's (1996) "The Indeterministic Character of Evolutionary Theory" fails to identify any indeterminism that would require evolutionary theory to be a statistical or probabilistic theory. Specifically, we argue that (1) their demonstration of a mechanism by which quantum indeterminism might "percolate up" to the biological level is irrelevant; (2) their argument that natural selection is indeterministic because it is inextricably connected with drift fails to join the issue with determinism; and (3) their view that experimental (...)
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  42. Hilary Greaves (2004). Understanding Deutsch's Probability in a Deterministic Universe. Studies in History and Philosophy of Modern Physics 35 (3):423-456.
    Difficulties over probability have often been considered fatal to the Everett interpretation of quantum mechanics. Here I argue that the Everettian can have everything she needs from `probability' without recourse to indeterminism, ignorance, primitive identity over time or subjective uncertainty: all she needs is a particular *rationality principle*. The decision-theoretic approach recently developed by Deutsch and Wallace claims to provide just such a principle. But, according to Wallace, decision theory is itself applicable only if the correct attitude to a future (...)
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  43. Amit Hagar, Thou Shalt Not Commute!
    For many among the scientifically informed public, and even among physicists, Heisenberg's uncertainty principle epitomizes quantum mechanics. Nevertheless, more than 86 years after its inception, there is no consensus over the interpretation, scope, and validity of this principle. The aim of this chapter is to offer one such interpretation, the traces of which may be found already in Heisenberg's letters to Pauli from 1926, and in Dirac's anticipation of Heisenberg's uncertainty relations from 1927, that stems form the hypothesis of finite (...)
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  44. Amit Hagar & Giuseppe Sergioli (forthcoming). Counting Steps: A Finitist Interpretation of Objective Probability in Physics. Epistemologia.
    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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  45. Alan Hajek, Chance.
    Much is asked of the concept of chance. It has been thought to play various roles, some in tension with or even incompatible with others. Chance has been characterized negatively, as the absence of causation; yet also positively—the ancient Greek τυχη´ reifies it—as a cause of events that are not governed by laws of nature, or as a feature of the laws themselves. Chance events have been understood epistemically as those whose causes are unknown; yet also objectively as a distinct (...)
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