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Defining chaos

Philosophy of Science 60 (1):43-66 (1993)

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  1. Emergence and Strange Attractors.David V. Newman - 1996 - Philosophy of Science 63 (2):245-61.
    Recent work in the Philosophy of Mind has suggested that alternatives to reduction are required in order to explain the relationship between psychology and biology or physics. Emergence has been proposed as one such alternative. In this paper, I propose a precise definition of emergence, and I argue that chaotic systems provide concrete examples of properties that meet this definition. In particular, I suggest that being in the basin of attraction of a strange attractor is an emergent property of any (...)
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  • Chaos and Qualia.David Newman - 2004 - Essays in Philosophy 5 (1):1-21.
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  • Structural Chaos.Conor Mayo-Wilson - 2015 - Philosophy of Science 82 (5):1236-1247.
    A dynamical system is called chaotic if small changes to its initial conditions can create large changes in its behavior. By analogy, we call a dynamical system structurally chaotic if small changes to the equations describing the evolution of the system produce large changes in its behavior. Although there are many definitions of “chaos,” there are few mathematically precise candidate definitions of “structural chaos.” I propose a definition, and I explain two new theorems that show that a set of models (...)
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  • The Domain Relativity of Evolutionary Contingency.Cory Lewis - 2018 - Biology and Philosophy 33 (3-4):25.
    A key issue in the philosophy of biology is evolutionary contingency, the degree to which evolutionary outcomes could have been different. Contingency is typically contrasted with evolutionary convergence, where different evolutionary pathways result in the same or similar outcomes. Convergences are given as evidence against the hypothesis that evolutionary outcomes are highly contingent. But the best available treatments of contingency do not, when read closely, produce the desired contrast with convergence. Rather, they produce a picture in which any degree of (...)
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  • On the Actual Impact of Deterministic Chaos.Theodor Leiber - 1997 - Synthese 113 (3):357-379.
    The notion of (deterministic) chaos is frequently used in an increasing number of scientific (as well as non-scientific) contexts, ranging from mathematics and the physics of dynamical systems to all sorts of complicated time evolutions, e.g., in chemistry, biology, physiology, economy, sociology, and even psychology. Despite (or just because of) these widespread applications, however, there seem to fluctuate around several misunderstandings about the actual impact of deterministic chaos on several problems of philosophical interest, e.g., on matters of prediction and computability, (...)
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  • Models, Confirmation, and Chaos.Jeffrey Koperski - 1998 - Philosophy of Science 65 (4):624-648.
    The use of idealized models in science is by now well-documented. Such models are typically constructed in a “top-down” fashion: starting with an intractable theory or law and working down toward the phenomenon. This view of model-building has motivated a family of confirmation schemes based on the convergence of prediction and observation. This paper considers how chaotic dynamics blocks the convergence view of confirmation and has forced experimentalists to take a different approach to model-building. A method known as “phase space (...)
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  • Regularity in Nonlinear Dynamical Systems.D. Lynn Holt & R. Glynn Holt - 1993 - British Journal for the Philosophy of Science 44 (4):711-727.
    Laws of nature have been traditionally thought to express regularities in the systems which they describe, and, via their expression of regularities, to allow us to explain and predict the behavior of these systems. Using the driven simple pendulum as a paradigm, we identify three senses that regularity might have in connection with nonlinear dynamical systems: periodicity, uniqueness, and perturbative stability. Such systems are always regular only in the second of these senses, and that sense is not robust enough to (...)
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  • Modely Chaotické Dynamiky a Problém Reprezentace Reálného Systému.Lukáš Hadwiger Zámečník - 2015 - Teorie Vědy / Theory of Science 37 (3):253-277.
    Příspěvek přináší základní matematické zakotvení pojmů „teorie chaosu". Představuje klíčové vlastnosti modelů chaotického chování dynamického systému s ohledem na explanační a prediktivní sílu modelů. Z pozice filosofie vědy podrobuje analýze především reprezentační aspekty modelů chaotické dynamiky systému. Nejzajímavějším aspektem těchto modelů je přísné omezení jejich reprezentační úlohy s ohledem na splnění podmínky hyperbolicity nutné pro platnost stínového lemma.
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  • Laplace’s Demon and the Adventures of His Apprentices.Roman Frigg, Seamus Bradley, Hailiang Du & Leonard A. Smith - 2014 - Philosophy of Science 81 (1):31-59.
    The sensitive dependence on initial conditions associated with nonlinear models imposes limitations on the models’ predictive power. We draw attention to an additional limitation than has been underappreciated, namely, structural model error. A model has SME if the model dynamics differ from the dynamics in the target system. If a nonlinear model has only the slightest SME, then its ability to generate decision-relevant predictions is compromised. Given a perfect model, we can take the effects of SDIC into account by substituting (...)
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  • In What Sense is the Kolmogorov-Sinai Entropy a Measure for Chaotic Behaviour?—Bridging the Gap Between Dynamical Systems Theory and Communication Theory.Roman Frigg - 2004 - British Journal for the Philosophy of Science 55 (3):411-434.
    On an influential account, chaos is explained in terms of random behaviour; and random behaviour in turn is explained in terms of having positive Kolmogorov-Sinai entropy (KSE). Though intuitively plausible, the association of the KSE with random behaviour needs justification since the definition of the KSE does not make reference to any notion that is connected to randomness. I provide this justification for the case of Hamiltonian systems by proving that the KSE is equivalent to a generalized version of Shannon's (...)
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  • The Correspondence Principle and the Understanding of Decoherence.Sebastian Fortin & Olimpia Lombardi - 2019 - Foundations of Physics 49 (12):1372-1393.
    Although Bohr’s Correspondence Principle played a central role in the first days of quantum mechanics, its original version seems to have no present-day relevance. The purpose of this article is to show that the CP, with no need of being interpreted in terms of the quantum-to-classical limit, still plays a relevant role in the understanding of the relationships between the classical and the quantum domains. In particular, it will be argued that a generic version of the CP is very helpful (...)
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  • What Could Be Worse Than the Butterfly Effect?Robert C. Bishop - 2008 - Canadian Journal of Philosophy 38 (4):pp. 519-547.
    Some have argued that chaos, with its characteristic feature of sensitive dependence on initial conditions, should be sensitive to quantum events (Hobbs 1991; Kellert 1993). The upshot of these arguments is that classical chaos would then be indeterministic, but such a conclusion is dependent on which versions of quantum theory and solutions to the measurement problem are adopted (Bishop and Kronz 1999). In this essay, the relationship between quantum mechanics and sensitive dependence is placed in the general context of nonlinear (...)
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  • What Could Be Worse Than the Butterfly Effect?Robert C. Bishop - 2008 - Canadian Journal of Philosophy 38 (4):519-547.
    The discovery of sensitive dependence on initial conditions (SDIC) in nonlinear models runs counter to the textbook vision of CM, a vision guided by an almost exclusive focus on linear systems. Therefore, it is important to clearly distinguish between linear and nonlinear systems along with establishing some basic terminology (§I). The notions of SDIC and chaos also need clarification, since they play crucial roles in sensitive dependence (SD) arguments. This will require some discussion of Lyapunov exponents as well as the (...)
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  • Downward Causation in Fluid Convection.Robert C. Bishop - 2008 - Synthese 160 (2):229 - 248.
    Recent developments in nonlinear dynamics have found wide application in many areas of science from physics to neuroscience. Nonlinear phenomena such as feedback loops, inter-level relations, wholes constraining and modifying the behavior of their parts, and memory effects are interesting candidates for emergence and downward causation. Rayleigh–Bénard convection is an example of a nonlinear system that, I suggest, yields important insights for metaphysics and philosophy of science. In this paper I propose convection as a model for downward causation in classical (...)
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  • Anvil or Onion? Determinism as a Layered Concept.Robert C. Bishop - 2005 - Erkenntnis 63 (1):55 - 71.
    Kellert (In the Wake of Chars, University of Chicago press, Chicago, 1993) has argued that Laplacean determinism in classical physics is actually a layered concept, where various properties or layers composing this form of determinism can be peeled away. Here, I argue that a layered conception of determinism is inappropriate and that we should think in terms of different deterministic models applicable to different kinds of systems. The upshot of this analysis is that the notion of state is more closely (...)
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  • When Good Theories Make Bad Predictions.Vadim Batitsky & Zoltan Domotor - 2007 - Synthese 157 (1):79 - 103.
    Chaos-related obstructions to predictability have been used to challenge accounts of theory validation based on the agreement between theoretical predictions and experimental data. These challenges are incomplete in two respects: they do not show that chaotic regimes are unpredictable in principle and, as a result, that there is something conceptually wrong with idealized expectations of correct predictions from acceptable theories, and they do not explore whether chaos-induced predictive failures of deterministic models can be remedied by stochastic modeling. In this paper (...)
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  • Theories Between Theories: Asymptotic Limiting Intertheoretic Relations.Robert W. Batterman - 1995 - Synthese 103 (2):171 - 201.
    This paper addresses a relatively common scientific (as opposed to philosophical) conception of intertheoretic reduction between physical theories. This is the sense of reduction in which one (typically newer and more refined) theory is said to reduce to another (typically older and coarser) theory in the limit as some small parameter tends to zero. Three examples of such reductions are discussed: First, the reduction of Special Relativity (SR) to Newtonian Mechanics (NM) as (v/c)20; second, the reduction of wave optics to (...)
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  • Chaos, Quantization, and the Correspondence Principle.Robert W. Batterman - 1991 - Synthese 89 (2):189 - 227.
  • Chaos and Algorithmic Complexity.Robert W. Batterman & Homer White - 1996 - Foundations of Physics 26 (3):307-336.
    Our aim is to discover whether the notion of algorithmic orbit-complexity can serve to define “chaos” in a dynamical system. We begin with a mostly expository discussion of algorithmic complexity and certain results of Brudno, Pesin, and Ruelle (BRP theorems) which relate the degree of exponential instability of a dynamical system to the average algorithmic complexity of its orbits. When one speaks of predicting the behavior of a dynamical system, one usually has in mind one or more variables in the (...)
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  • Numerical Instability and Dynamical Systems.Vincent Ardourel & Julie Jebeile - 2021 - European Journal for Philosophy of Science 11 (2):1-21.
    In philosophical studies regarding mathematical models of dynamical systems, instability due to sensitive dependence on initial conditions, on the one side, and instability due to sensitive dependence on model structure, on the other, have by now been extensively discussed. Yet there is a third kind of instability, which by contrast has thus far been rather overlooked, that is also a challenge for model predictions about dynamical systems. This is the numerical instability due to the employment of numerical methods involving a (...)
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  • Chaos.Robert Bishop - 2015 - Stanford Encyclopedia of Philosophy.
    The big news about chaos is supposed to be that the smallest of changes in a system can result in very large differences in that system's behavior. The so-called butterfly effect has become one of the most popular images of chaos. The idea is that the flapping of a butterfly's wings in Argentina could cause a tornado in Texas three weeks later. By contrast, in an identical copy of the world sans the Argentinian butterfly, no such storm would have arisen (...)
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  • Prediction and Novel Facts in the Methodology of Scientific Research Programs.Wenceslao J. Gonzalez - 2015 - In Philosophico-Methodological Analysis of Prediction and its Role in Economics. Springer Verlag. pp. 103-124.
    In the methodology of scientific research programs (MSRP) there are important features on the problem of prediction, especially regarding novel facts. In his approach, Imre Lakatos proposed three different levels on prediction: aim, process, and assessment. Chapter 5 pays attention to the characterization of prediction in the methodology of research programs. Thus, it takes into account several features: (1) its pragmatic characterization, (2) the logical perspective as a proposition, (3) the epistemological component, (4) its role in the appraisal of research (...)
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  • Complexity and Information.Panu Raatikainen - 1998 - ”, Reports From the Department of Philosophy, University of Helsinki, 2.
    \Complexity" is a catchword of certain extremely popular and rapidly developing interdisciplinary new sciences, often called accordingly the sciences of complexity1. It is often closely associated with another notably popular but ambiguous word, \information" information, in turn, may be justly called the central new concept in the whole 20th century science. Moreover, the notion of information is regularly coupled with a key concept of thermodynamics, viz. entropy. And like this was not enough, it is quite usual to add one more, (...)
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  • Chance and Time.Amit Hagar - 2004 - Dissertation, UBC
    One of the recurrent problems in the foundations of physics is to explain why we rarely observe certain phenomena that are allowed by our theories and laws. In thermodynamics, for example, the spontaneous approach towards equilibrium is ubiquitous yet the time-reversal-invariant laws that presumably govern thermal behaviour in the microscopic level equally allow spontaneous departure from equilibrium to occur. Why are the former processes frequently observed while the latter are almost never reported? Another example comes from quantum mechanics where the (...)
     
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  • Stability in Cosmology, From Einstein to Inflation.C. D. McCoy - 2020 - In Claus Beisbart, Tilman Sauer & Christian Wüthrich (eds.), Thinking About Space and Time. Cham: Birkhäuser. pp. 71-89.
    I investigate the role of stability in cosmology through two episodes from the recent history of cosmology: Einstein’s static universe and Eddington’s demonstration of its instability, and the flatness problem of the hot big bang model and its claimed solution by inflationary theory. These episodes illustrate differing reactions to instability in cosmological models, both positive ones and negative ones. To provide some context to these reactions, I also situate them in relation to perspectives on stability from dynamical systems theory and (...)
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  • The Reasonable Effectiveness of Mathematics in the Natural Sciences.Nicolas Fillion - unknown
    One of the most unsettling problems in the history of philosophy examines how mathematics can be used to adequately represent the world. An influential thesis, stated by Eugene Wigner in his paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," claims that "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Contrary to this view, this thesis delineates and implements (...)
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