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Summary Past global states of a deterministic system, together with the laws governing that system, entail the entire future history of the system. There is only one way that a deterministic system can evolve, given a prior state and deterministic laws. Prima facie, determinism excludes any non-trivial chance of that system evolving over time in any other way: it has chance 1 of evolving the way it in fact will evolve.   The dispute over deterministic chance, like that over free will and determinism, revolves around two issues: (i) how to make that prima facie case for the incompatibility of chance and determinism into a precise argument; and (ii) whether the resulting argument is successful.
Key works Incompatibilism about chance and determinism is rarely explicitly defended. (It is expressed forcefully by Lewis 1980.) Earman 1986 articulates the notion of determinism precisely, and also endorses the difficulty of making irreducible objective probability consistent with determinism (chapter VIII). The most notable recent attempt to defend incompatibilism is that of Schaffer 2007, who derives incompatibilism from considerations of the conceptual role of chance. A response along the same lines is Eagle 2011. A compatibilist approach relying on a more substantive Humean theory of chance is Frigg & Hoefer 2010. The recent compatibilist debate has focussed intensively on the status of probabilities in classical statistical mechanics, appearing as they do to be objective and nevertheless grounded in a deterministic theory. Clark 1987 and Loewer 2001 are prominent discussions of this issue; Ismael 2009 uses the basic framework of phase space to argue that some kind of objective probability, if not chance, is compatible with determinism. The prospects for quantum chances in deterministic versions of quantum theory, like the Everett interpretation, is explored by Greaves 2004.  The converse issue—can there be indeterminism without chance?—is addressed by Norton 2008.
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  1. added 2020-05-30
    God's Dice.Vasil Penchev - 2015 - In Actas: VIII Conference of the Spanish Society for Logic, Methodology, and Philosophy of Sciences (eds. J. Martínez, García-Carpintero, J. Díez, S. Oms),. Barcelona: Universitat de Barcelona. pp. 297-303.
    Einstein wrote his famous sentence "God does not play dice with the universe" in a letter to Max Born in 1920. All experiments have confirmed that quantum mechanics is neither wrong nor “incomplete”. One can says that God does play dice with the universe. Let quantum mechanics be granted as the rules generalizing all results of playing some imaginary God’s dice. If that is the case, one can ask how God’s dice should look like. God’s dice turns out to be (...)
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  2. added 2020-05-04
    The Structure of Space and Time, and Physical Indeterminacy.Hanoch Ben-Yami - manuscript
    I introduce a sequence which I call indefinite: a sequence every element of which has a successor but whose number of elements is bounded; this is no contradiction. I then consider the possibility of space and time being indefinitely divisible. This is theoretically possible and agrees with experience. If this is space and time’s structure, then even if the laws of nature are deterministic, the behaviour of physical systems will be probabilistic. This approach may also shed light on directionality in (...)
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  3. added 2020-04-28
    Everettian Theory as Pure Wave Mechanics Plus a No-Collapse Probability Postulate.Paul Tappenden - forthcoming - Synthese:1-28.
    Proposed derivations of the Born rule for Everettian theory are controversial. I argue that they are unnecessary but may provide justification for a simplified version of the Principal Principle. It’s also unnecessary to replace Everett’s idea that a subject splits in measurement contexts with the idea that subjects have linear histories which partition Many worlds? Everett, quantum theory, and reality, Oxford University Press, Oxford, pp 181–205, 2010; Wallace in The emergent multiverse, Oxford University Press, Oxford, 2012, Chapter 7; Wilson in (...)
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  4. added 2020-04-28
    Some Reflections on the Statistical Postulate: Typicality, Probability and Explanation Between Deterministic and Indeterministic Theories.Valia Allori - forthcoming - In Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature, (2020).
    A common way of characterizing Boltzmann’s explanation of thermodynamics in term of statistical mechanics is with reference to three ingredients: the dynamics, the past hypothesis, and the statistical postulate. In this paper I focus on the statistical postulate, and I have three aims. First, I wish to argue that regarding the statistical postulate as a probability postulate may be too strong: a postulate about typicality would be enough. Second, I wish to show that there is no need to postulate anything, (...)
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  5. added 2020-03-05
    Objectivity and the Method of Arbitrary Functions.Chloé de Canson - forthcoming - British Journal for the Philosophy of Science:axaa001.
    There is widespread excitement in the literature about the method of arbitrary functions: many take it to show that it is from the dynamics of systems that the objectivity of probabilities emerge. In this paper, I differentiate three ways in which a probability function might be objective, and I argue that the method of arbitrary functions cannot help us show that dynamics objectivise probabilities in any of these senses.
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  6. added 2019-10-08
    Two Kinds of High-Level Probability.Meir Hemmo & Orly Shenker - 2019 - The Monist 102 (4):458-477.
    According to influential views the probabilities in classical statistical mechanics and other special sciences are objective chances, although the underlying mechanical theory is deterministic, since the deterministic low level is inadmissible or unavailable from the high level. Here two intuitions pull in opposite directions: One intuition is that if the world is deterministic, probability can only express subjective ignorance. The other intuition is that probability of high-level phenomena, especially thermodynamic ones, is dictated by the state of affairs in the world. (...)
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  7. added 2019-09-13
    The Only Probability Is Verbal Probability.George Masterton - 2014 - Metaphysica 15 (1).
    In 1977 van Fraassen showed convincingly, and in detail, how one can give a dissentive answer to the question `[a]re there necessities in nature?'. In this paper I follow his lead and show in a similar fashion and detail, how it is possible to give a dissentive answer to: Are there probabilities in nature? This is achieved by giving a partial analysis—with the aid of Kaplanian pragmatics—of objective chance in terms of that credence that is reasonable where prevailing laws and (...)
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  8. added 2019-09-13
    Chance in the Everett Interpretation.Simon Saunders - 2010 - In Simon Saunders, Jonathan Barrett, Adrian Kent & David Wallace (eds.), Many Worlds?: Everett, Quantum Theory & Reality. Oxford University Press.
    According to the Everett interpretation, branching structure and ratios of norms of branch amplitudes are the objective correlates of chance events and chances; that is, 'chance' and 'chancing', like 'red' and 'colour', pick out objective features of reality, albeit not what they seemed. Once properly identified, questions about how and in what sense chances can be observed can be treated as straightforward dynamical questions. On that basis, given the unitary dynamics of quantum theory, it follows that relative and never absolute (...)
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  9. added 2019-06-21
    Randomness and Reality.Geoffrey Hellman - 1978 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:79-97.
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  10. added 2019-03-26
    Time's Arrow in a Quantum Universe: On the Status of Statistical Mechanical Probabilities.Eddy Keming Chen - forthcoming - In Valia Allori (ed.), Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature. World Scientific.
    In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two (...)
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  11. added 2019-03-26
    Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature.Valia Allori (ed.) - forthcoming - World Scientific.
    The book explores several open questions in the philosophy of statistical mechanics. Each chapter is written by a leading expert in the field. Here is a list of some questions that are addressed in the book: 1) Boltzmann showed how the phenomenological gas laws of thermodynamics can be derived from statistical mechanics. Since classical mechanics is a deterministic theory there are no probabilities in it. Since statistical mechanics is based on classical mechanics, all the probabilities statistical mechanics talks about cannot (...)
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  12. added 2019-03-26
    Probability in Two Deterministic Universes.Mateus Araújo - 2019 - Foundations of Physics 49 (3):202-231.
    How can probabilities make sense in a deterministic many-worlds theory? We address two facets of this problem: why should rational agents assign subjective probabilities to branching events, and why should branching events happen with relative frequencies matching their objective probabilities. To address the first question, we generalise the Deutsch–Wallace theorem to a wide class of many-world theories, and show that the subjective probabilities are given by a norm that depends on the dynamics of the theory: the 2-norm in the usual (...)
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  13. added 2019-02-06
    Chance, Determinism, and Unsettledness.Antony Eagle - 2019 - Philosophical Studies 176 (3):781-802.
    A previously unrecognised argument against deterministic chance is introduced. The argument rests on the twin ideas that determined outcomes are settled, while chancy outcomes are unsettled, thus making cases of determined but chancy outcomes impossible. Closer attention to tacit assumptions about settledness makes available some principled lines of resistance to the argument for compatibilists about chance and determinism. Yet the costs of maintaining compatibilism may be higher with respect to this argument than with respect to existing incompatibilist arguments.
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  14. added 2019-01-30
    Czy możemy wykazać istnienie zjawisk całkowicie przypadkowych?Marek Kuś - 2018 - Philosophical Problems in Science 65:111-143.
    I show how classical and quantum physics approach the problem of randomness and probability. Contrary to popular opinions, neither we can prove that classical mechanics is a deterministic theory, nor that quantum mechanics is a nondeterministic one. In other words it is not possible to show that randomness in classical mechanics has a purely epistemic character and that of quantum mechanics an ontic one. Nevertheless, recent developments of quantum theory and increasing experimental possibilities to check its predictions call for returning (...)
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  15. added 2018-06-28
    Gott Würfelt Nicht. Einsteins Immer Noch Aktuelle Kritik der Quantenmechanik.Gregor Schiemann - 2005 - In J. Renn (ed.), Albert Einstein. Ingenieur des Universums. 100 Autoren für Einstein.
    Kaum eine Äußerung Einsteins ist so bekannt wie sein Wort, dass Gott nicht würfelt. In ähnlicher Weise, wie Einstein dies unerläutert gelassen hat, ist seine gesamte Position zur Quantenmechanik, auf die es sich bezieht, von Uneindeutigkeiten nicht frei geblieben. Für seine Würfelmetapher ergibt sich ein Spielraum von gegensätzlichen Sichtweisen. Sie lässt sich zum einen mit jüngeren Forschungsresultaten verbinden und weist zum anderen auf rückschrittliche Elemente in Einsteins Denken hin. Ich wende mich zuerst diesen Elementen zu und betrachte dann eine dazu (...)
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  16. added 2018-06-26
    Causation, Realism, Determinism, and Probability in the Science and Philosophy of Max Born.Thomas Bunce - unknown
    In this thesis I will examine the philosophy of the physicist Max Born. As well as his scientific work, Born wrote on a number of philosophical topics: causation, realism, determinism, and probability. They appear as an interest throughout his career, but he particularly concentrates on them from the 1940s onwards. Born is a significant figure in the development of quantum mechanics whose philosophical work has been left largely unexamined. It is the aim of this thesis to elucidate and to critically (...)
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  17. added 2018-06-26
    Chance.Darrell Patrick Rowbottom - 2018 - Vocabulary for the Study of Religion.
    This entry explains that a chance is a kind of probability in the world, introduces a number of ways to understand probabilities in the world, and discusses how the existence of chances bears on the issue of determinism.
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  18. added 2018-06-21
    Did the Universe Have a Chance?C. D. McCoy - 2019 - Philosophy of Science 86 (5):1262-1272.
    In a world awash in statistical patterns, should we conclude that the universe’s evolution or genesis is somehow subject to chance? I draw attention to alternatives that must be acknowledged if we are to have an adequate assessment of what chance the universe might have had.
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  19. added 2018-06-15
    No Chances in a Deterministic World.C. D. McCoy - manuscript
    Several philosophers have developed accounts to dissolve the apparent conflict between deterministic laws of nature and objective chances. These philosophers advocate the compatibility of determinism and chance. I argue that determinism and chance are incompatible and criticize the various notions of “deterministic chance” supplied by the compatibilists. Many of the compatibilists are strongly motivated by scientific theories where objective probabilities are combined with deterministic laws, the most salient of which is classical statistical mechanics. I show that, properly interpreted, statistical mechanics (...)
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  20. added 2018-06-05
    Probability.Antony Eagle - 2016 - In Paul Humphreys (ed.), The Oxford Handbook of Philosophy of Science. USA: Oxford University Press. pp. 417-439.
    Rather than entailing that a particular outcome will occur, many scientific theories only entail that an outcome will occur with a certain probability. Because scientific evidence inevitably falls short of conclusive proof, when choosing between different theories it is standard to make reference to how probable the various options are in light of the evidence. A full understanding of probability in science needs to address both the role of probabilities in theories, or chances, as well as the role of probabilistic (...)
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  21. added 2018-05-31
    A Subjectivist’s Guide to Deterministic Chance.J. Dmitri Gallow - forthcoming - Synthese.
    I present an account of deterministic chance which builds upon the physico-mathematical approach to theorizing about deterministic chance known as 'the method of arbitrary functions'. This approach promisingly yields deterministic probabilities which align with what we take the chances to be---it tells us that there is approximately a 1/2 probability of a spun roulette wheel stopping on black, and approximately a 1/2 probability of a flipped coin landing heads up---but it requires some probabilistic materials to work with. I contend that (...)
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  22. added 2018-02-18
    Time and Chance.Jos Uffink - 2002 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 33 (3):555-563.
  23. added 2018-02-16
    Determinism and Chance.Barry Loewer - 2001 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (4):609-620.
    It is generally thought that objective chances for particular events different from 1 and 0 and determinism are incompatible. However, there are important scientific theories whose laws are deterministic but which also assign non-trivial probabilities to events. The most important of these is statistical mechanics whose probabilities are essential to the explanations of thermodynamic phenomena. These probabilities are often construed as 'ignorance' probabilities representing our lack of knowledge concerning the microstate. I argue that this construal is incompatible with the role (...)
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  24. added 2018-01-15
    Chance, Determinism and the Classical Theory of Probability.Anubav Vasudevan - 2018 - Studies in History and Philosophy of Science Part A 67:32-43.
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  25. added 2017-12-28
    Случайности. Историческа типология.Vassil Vidinsky - 2017 - Sofia: Sofia University Press.
    В настоящата книга се изследва идеята за случайността през нейното историческо и концептуално развитие и са отделени пет основни и типични понятия. Анализът тръгва от класическите примери – Платон, Аристотел, Кант и Хегел – и стига до съвременния контекст на случайността, който е представен през теорията на вероятностите и теорията на сложността. Някои от изведените понятия са формализирани и имат по-логически, математически или пък информационен характер, а други са по-скоро физически или субектни, но всички те са представени в една обща (...)
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  26. added 2017-08-31
    Zufall und naturgesetzliche Notwendigkeit.Alfred Gierer - 1998 - In O. Marquard G. V. Graevenitz (ed.), Kontingenz, Poetik und Hermeneutik XVII. Muenchen Germany: Wilhelm Fink Verlag. pp. 123-139.
    Die Reflexion der Grundlagen der Wissenschaft mit ihren eigenen Mitteln, wie die gedankliche Vermessung des Messprozesses, die in die Begründung der Quantenphysik eingeht, und die logische Analyse der Logik im Rahmen der mathematischen Entscheidungstheorie zeigt schließlich prinzipielle Grenzen des möglichen Wissens auf. Eine Theorie des Leib-Seele-Zusammenhangs läuft auf das Bewusstsein von Bewusstsein hinaus und ist damit von dem gleichen Typ des Selbstbezugs, der auf prinzipielle Grenzen der Erkenntnis verweist. Die moderne Naturwissenschaft ist offen für damit verbundene philosophische Fragestellungen, und das (...)
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  27. added 2017-08-08
    Are Objective Chances Compatible with Determinism?Seamus Bradley - 2017 - Philosophy Compass 12 (8):e12430.
    We review the question of whether objective chances are compatible with determinism. We first outline what we mean by chance and what we mean by determinism. We then look at the alleged incompatibility between those concepts. Finally, we look at some ways that one might attempt to overcome the incompatibility.
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  28. added 2017-03-13
    Determinism and Probability in Physics.Peter Clark & Jeremy Butterfield - 1987 - Proceedings of the Aristotelian Society, Supplementary Volumes( 61:185-243.
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  29. added 2017-03-02
    The Universe Had One Chance.Heather Demarest - 2016 - Philosophy of Science 83 (2):248-264.
    In a deterministically evolving world, the usefulness of nontrivial probabilities can seem mysterious. I use the ‘Mentaculus’ machinery developed by David Albert and Barry Loewer to show how all probabilities in such a world can be derived from a single, initial chance event. I go on to argue that this is the only genuine chance event. Perhaps surprisingly, we have good evidence of its existence and nature. I argue that the existence of this chance event justifies our epistemic reliance on (...)
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  30. added 2017-02-14
    Deterministic Causation of Probabilities.Daniel M. Hausman - 1998 - Communication and Cognition. Monographies 31 (4):365-390.
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  31. added 2017-02-14
    Opinions and Chances.Simon Blackburn - 1980 - In D. H. Mellor (ed.), Prospects for Pragmatism. Cambridge University Press. pp. 175--96.
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  32. added 2017-02-14
    The Statistical Processes of Evolutionary Theory.A. W. F. Edwards - 1963 - The Eugenics Review 54 (4):217.
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  33. added 2017-02-11
    Probabilities All the Way Down.Adam LaCaze - 2006 - Metascience 15 (3):547-551.
  34. added 2017-02-09
    Objective Probabilities in Number Theory.J. Ellenberg & E. Sober - 2011 - Philosophia Mathematica 19 (3):308-322.
    Philosophers have explored objective interpretations of probability mainly by considering empirical probability statements. Because of this focus, it is widely believed that the logical interpretation and the actual-frequency interpretation are unsatisfactory and the hypothetical-frequency interpretation is not much better. Probabilistic assertions in pure mathematics present a new challenge. Mathematicians prove theorems in number theory that assign probabilities. The most natural interpretation of these probabilities is that they describe actual frequencies in finite sets and limits of actual frequencies in infinite sets. (...)
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  35. added 2017-02-08
    A Dilemma for Objective Chance.Phil Dowe - 2003 - In Jr Kyburg & Mariam Thalos (eds.), Probability is the Very Guide of Life: The Philosophical Uses of Chance. Open Court. pp. 153--64.
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  36. added 2017-02-08
    Objectivism Without Objective Probabilities.Ruth Weintraub - 1990 - Theoria 56 (1-2):23-41.
    After defending the pluralistic approach to the interpretation of probability statements, I argue that the correctness of objective probability statements is not to be explained in terms of objective probabilities attached to propositions. Such an explanation will enable us to uphold an intuitively appealing connection between probability and action only in indeterministic contexts, whereas the objectivity of probability statements doesn’t depend on the truth of indeterminism. I show how objective probability statements can be interpreted without ascribing objective probabilities to propositions. (...)
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  37. added 2017-02-07
    What Could Be Objective About Probabilities?Tim Maudlin - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):275-291.
  38. added 2017-02-07
    Probability as Typicality.Sérgio B. Volchan - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (4):801-814.
  39. added 2017-01-31
    Chance, Possibility, and Explanation.N. Emery - 2015 - British Journal for the Philosophy of Science 66 (1):95-120.
    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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  40. added 2017-01-29
    Is Nature Deterministic? A Branching Perspective on Epr Phenomena.Tomasz Placek - 2000
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  41. added 2017-01-29
    The Chances of Evolution: An Analysis of the Roles of Chance in Microevolution and Macroevolution.Roberta Lynn Millstein - 1997 - Dissertation, University of Minnesota
    Evolutionary theory is thoroughly probabilistic, due to such elements as random mutation, random drift, and stochastic models of speciation and extinction. This uncontroversial claim raises a number of contentious issues: Is evolutionary theory probabilistic in any general sense, or only in a variety of particular, distinct senses? Are these processes inherently probabilistic, or does the use of probabilities simply provide a convenient way to camouflage a multitude of unknown causes? Does chance play an explanatory role in evolutionary theory, and if (...)
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  42. added 2017-01-29
    Inquiries in the Philosophy of Probability: Randomness and Independence.Paul William Humphreys - 1976 - Dissertation, Stanford University
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  43. added 2017-01-26
    Can the World Be Shown to Be Indeterministic After All?Christian Wuthrich - 2010 - In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford University Press. pp. 365--389.
    This essay considers and evaluates recent results and arguments from classical chaotic systems theory and non-relativistic quantum mechanics that pertain to the question of whether our world is deterministic or indeterministic. While the classical results are inconclusive, quantum mechanics is often assumed to establish indeterminism insofar as the measurement process involves an ineliminable stochastic element, even though the dynamics between two measurements is considered fully deterministic. While this latter claim concerning the Schrödinger evolution must be qualified, the former fully depends (...)
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  44. added 2017-01-26
    On the Character of Statistical-Mechanical Probabilities'.D. Albert - 1997 - Philosophy of Science 64.
  45. added 2017-01-25
    Physical Determinism.R. G. Swinburne - 1969 - Royal Institute of Philosophy Lectures 3:155-168.
    The object of this paper is to examine what evidence we can have for or against the truth of determinism, a doctrine often set forward by the proposition ‘every event has a cause’. I understand in this context by the cause of an event a set of prior conditions jointly sufficient for the occurrence of the event. Since the determinist is concerned with all physical states and not merely with changes of states, which are most naturally termed events, we may (...)
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  46. added 2017-01-22
    Probability as a Theoretical Concept in Physics.Lorenz Kruger - 1986 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1986:273 - 287.
    This paper intends to explore the prospects of a realistic view of scientific explanation, according to which the objects and structures occurring in the explanation must have real referents. Theories involving probability either lose their explanatory function or become counter-examples to this view, if real referents of probabilistic notions do not exist. It is argued that such referents can be found for statistical mechanics and quantum mechanics: the overall structure of mass phenomena that renders them capable of irreversible developments and (...)
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  47. added 2017-01-22
    Randomness.Henry E. Kyburg - 1972 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1972:137 - 149.
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  48. added 2017-01-20
    Observational Equivalence of Deterministic and Indeterministic Descriptions and the Role of Different Observations.Charlotte Werndl - 2012 - In Stephan Hartmann, Samir Okasha & Herman De Regt (eds.), Proceedings of the Second Conference of the European Philosophy of Science Association. Springer. pp. 427-439.
    Recently some results have been presented which show that certain kinds of deterministic descriptions and indeterministic descriptions are observationally equivalent (Werndl 2009a, 2010). This paper focuses on some philosophical questions prompted by these results. More specifically, first, I will discuss the philosophical comments made by mathematicians about observational equivalence, in particular Ornstein and Weiss (1991). Their comments are vague, and I will argue that, according to a reasonable interpretation, they are misguided. Second, the results on observational equivalence raise the question (...)
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  49. added 2017-01-20
    Are Deterministic Descriptions and Indeterministic Descriptions Observationally Equivalent?Charlotte Werndl - 2009 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40 (3):232-242.
    The central question of this paper is: are deterministic and indeterministic descriptions observationally equivalent in the sense that they give the same predictions? I tackle this question for measure-theoretic deterministic systems and stochastic processes, both of which are ubiquitous in science. I first show that for many measure-theoretic deterministic systems there is a stochastic process which is observationally equivalent to the deterministic system. Conversely, I show that for all stochastic processes there is a measure-theoretic deterministic system which is observationally equivalent (...)
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  50. added 2017-01-20
    Deterministic Versus Indeterministic Descriptions: Not That Different After All?Charlotte Werndl - 2009 - In Alexander Hieke & Hannes Leitgeb (eds.), Reduction, Abstraction, Analysis. Ontos. pp. 63-78.
    The guiding question of this paper is: how similar are deterministic descriptions and indeterministic descriptions from a predictive viewpoint? The deterministic and indeterministic descriptions of concern in this paper are measure-theoretic deterministic systems and stochastic processes, respectively. I will explain intuitively some mathematical results which show that measure-theoretic deterministic systems and stochastic processes give more often the same predictions than one might perhaps have expected, and hence that from a predictive viewpoint these descriptions are quite similar.
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