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  1. Sunny Auyang, Nonlinear Dynamics: How Science Comprehends Chaos.
    Behaviors of chaotic systems are unpredictable. Chaotic systems are deterministic, their evolutions being governed by dynamical equations. Are the two statements contradictory? They are not, because the theory of chaos encompasses two levels of description. On a higher level, unpredictability appears as an emergent property of systems that are predictable on a lower level. In this talk, we examine the structure of dynamical theories to see how they employ multiple descriptive levels to explain chaos, bifurcation, and other complexities of nonlinear (...)
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  2. Noah Moss Brender (2013). Sense-Making and Symmetry-Breaking. Symposium: The Canadian Journal of Continental Philosophy 17 (2):246-270.
    From his earliest work forward, Merleau-Ponty attempted to develop a new ontology of nature that would avoid the antinomies of realism and idealism by showing that nature has its own endogenous sense which is prior to reflection. The key to this new ontology was the concept of form, which he appropriated from Gestalt psychology. However, Merleau-Ponty struggled to give a positive characterization of the phenomenon of form which would clarify its ontological status. Evan Thompson has recently taken up Merleau-Ponty’s ontology (...)
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  3. Carlos Castro (2010). On Nonlinear Quantum Mechanics, Noncommutative Phase Spaces, Fractal-Scale Calculus and Vacuum Energy. Foundations of Physics 40 (11):1712-1730.
    A (to our knowledge) novel Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson’s fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final formulation of (...)
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  4. Mohammed H. I. Dore & J. Barkley Rosser, Do Nonlinear Dynamics in Economics Amount to a Kuhnian Paradigm Shift?
    Much empirical analysis and econometric work recognizes that there are nonlinearities, regime shifts or structural breaks, asymmetric adjustment costs, irreversibilities and lagged dependencies. Hence, empirical work has already transcended neoclassical economics. Some progress has also been made in modeling endogenously generated cyclical growth and fluctuations. All this is inconsistent with neoclassical general equilibrium. Hence there is growing evidence of Kuhnian anomalies. It therefore follows that there is a Kuhnian crisis in economics and further research in nonlinear dynamics and complexity can (...)
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  5. Andrew A. Fingelkurts & Alexander A. Fingelkurts (2013). Dissipative Many-Body Model and a Nested Operational Architectonics of the Brain. Physics of Life Reviews 10:103-105.
    This paper briefly review a current trend in neuroscience aiming to combine neurophysiological and physical concepts in order to understand the emergence of spatio-temporal patterns within brain activity by which brain constructs knowledge from multiple streams of information. The authors further suggest that the meanings, which subjectively are experienced as thoughts or perceptions can best be described objectively as created and carried by large fields of neural activity within the operational architectonics of brain functioning.
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  6. GianCarlo Ghirardi (2002). Making Quantum Theory Compatible with Realism. Foundations of Science 7 (1-2):11-47.
    After a brief account of theway quantum theory deals with naturalprocesses, the crucial problem that such atheory meets, the measurement or, better, themacro-objectification problem is discussed.The embarrassing aspects of the occurrence ofentangled states involving macroscopic systemsare analyzed in details. The famous example ofSchroedinger's cat is presented and it ispointed out how the combined interplay of thesuperposition principle and the ensuingentanglement raises some serious difficultiesin working out a satisfactory quantum worldview, agreeing with our definiteperceptions. The orthodox solution to themacro-objectification problem, i.e. (...)
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  7. Giancarlo Ghirardi (1996). Quantum Dynamical Reduction and Reality: Replacing Probability Densities with Densities in Real Space. [REVIEW] Erkenntnis 45 (2-3):349 - 365.
    Consideration is given to recent attempts to solve the objectification problem of quantum mechanics by considering nonlinear and stochastic modifications of Schrödinger's evolution equation. Such theories agree with all predictions of standard quantum mechanics concerning microsystems but forbid the occurrence of superpositions of macroscopically different states. It is shown that the appropriate interpretation for such theories is obtained by replacing the probability densities of standard quantum mechanics with mass densities in real space. Criteria allowing a precise characterization of the idea (...)
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  8. N. Gisin (1983). Dissipative Quantum Dynamics for Systems Periodic in Time. Foundations of Physics 13 (7):643-654.
    A model of dissipative quantum dynamics (with a nonlinear friction term) is applied to systems periodic in time. The model is compared with the standard approaches based on the Floquet theorem. It is shown that for weak frictions the asymptotic states of the dynamics we propose are the periodic steady states which are usually postulated to be the states relevant for the statistical mechanics of time-periodic systems. A solution to the problem of nonuniqueness of the “quasienergies” is proposed. The implication (...)
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  9. Gordon G. Globus (2005). Nonlinear Dynamics at the Cutting Edge of Modernity: A Postmodern View. Philosophy, Psychiatry, and Psychology 12 (3):229-234.
  10. Stephen H. Kellert (2001). Extrascientific Uses of Physics: The Case of Nonlinear Dynamics and Legal Theory. Proceedings of the Philosophy of Science Association 2001 (3):S455-.
    This essay explores the metaphorical use of the area of nonlinear dynamics popularly known as "chaos theory," surveying its use in one particular field: legal theory. After sketching some of the mistakes encountered in these efforts, I outline the possibility of the fruitful use of nonlinear dynamics for thinking about our legal system. I then offer some general lessons to be drawn from these examples-both cautionary maxims and a limited defense of cross-disciplinary borrowing. I conclude with some reflections on the (...)
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  11. Julian Kiverstein & Michael Wheeler (eds.) (2012). Heidegger and Cognitive Science. Palgrave Macmillan.
  12. Helena Knyazeva (1999). Synergetics and the Images of Future. Futures 31 (3):281-290.
    The hope of finding new methods of predicting the course of historical processes could be connected with the recent developments of the theory of self-organisation, also called synergetics. It provides us with knowledge of constructive principles of co-evolution of complex social systems, co-evolution of countries and geopolitical regions being at different stages of development, integration of the East and the West, the North and the South. Due to the growth of population on the Earth in blow-up regime, the general and (...)
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  13. Matthew W. Parker (2009). Computing the Uncomputable; or, the Discrete Charm of Second-Order Simulacra. Synthese 169 (3):447 - 463.
    We examine a case in which non-computable behavior in a model is revealed by computer simulation. This is possible due to differing notions of computability for sets in a continuous space. The argument originally given for the validity of the simulation involves a simpler simulation of the simulation , still further simulations thereof, and a universality conjecture. There are difficulties with that argument, but there are other, heuristic arguments supporting the qualitative results. It is urged, using this example, that absolute (...)
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  14. Matthew W. Parker (2003). Undecidability in Rn: Riddled Basins, the KAM Tori, and the Stability of the Solar System. Philosophy of Science 70 (2):359-382.
    Some have suggested that certain classical physical systems have undecidable long-term behavior, without specifying an appropriate notion of decidability over the reals. We introduce such a notion, decidability in (or d- ) for any measure , which is particularly appropriate for physics and in some ways more intuitive than Ko's (1991) recursive approximability (r.a.). For Lebesgue measure , d- implies r.a. Sets with positive -measure that are sufficiently "riddled" with holes are never d- but are often r.a. This explicates Sommerer (...)
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  15. Matthew W. Parker (1998). Did Poincare Really Discover Chaos? [REVIEW] Studies in the History and Philosophy of Modern Physics 29 (4):575-588.
  16. Erik Rietveld (2012). Context-Switching and Responsiveness to Real Relevance. In Julian Kiverstein & Michael Wheeler (eds.), Heidegger and Cognitive Science. Palgrave Macmillan.
  17. Erik Rietveld (2008). The Skillful Body as a Concernful System of Possible Actions: Phenomena and Neurodynamics. Theory & Psychology 18 (3):341-361.
    For Merleau-Ponty,consciousness in skillful coping is a matter of prereflective ‘I can’ and not explicit ‘I think that.’ The body unifies many domain-specific capacities. There exists a direct link between the perceived possibilities for action in the situation (‘affordances’) and the organism’s capacities. From Merleau-Ponty’s descriptions it is clear that in a flow of skillful actions, the leading ‘I can’ may change from moment to moment without explicit deliberation. How these transitions occur, however, is less clear. Given that Merleau-Ponty suggested (...)
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  18. Barkley Rosser, Aspects of Dialectics and Nonlinear Dynamics.
    Three principles of dialectical analysis are examined in terms of nonlinear dynamics models. The three principles are the transformation of quantity into quality, the interpenetration of opposites, and the negation of the negation. The first two of these especially are interpreted within the frameworks of catastrophe, chaos, and emergent dynamics complexity theoretic models, with the concept of bifurcation playing a central role. Problems with this viewpoint are also discussed.
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  19. Barkley Rosser, Do Nonlinear Dynamics in Economics Amount to a Kuhnian Paradigm Shift?
    Much empirical analysis and econometric work recognizes that there are nonlinearities, regime shifts or structural breaks, asymmetric adjustment costs, irreversibilities and lagged dependencies. Hence, empirical work has already transcended neoclassical economics. Some progress has also been made in modeling endogenously generated cyclical growth and fluctuations. All this is inconsistent with neoclassical general equilibrium. Hence there is growing evidence of Kuhnian anomalies. It therefore follows that there is a Kuhnian crisis in economics and further research in nonlinear dynamics and complexity can (...)
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  20. Alexander Rueger & W. David Sharp (1996). Simple Theories of a Messy World: Truth and Explanatory Power in Nonlinear Dynamics. British Journal for the Philosophy of Science 47 (1):93-112.
    Philosophers like Duhem and Cartwright have argued that there is a tension between laws' abilities to explain and to represent. Abstract laws exemplify the first quality, phenomenological laws the second. This view has both metaphysical and methodological aspects: the world is too complex to be represented by simple theories; supplementing simple theories to make them represent reality blocks their confirmation. We argue that both aspects are incompatible with recent developments in nonlinear dynamics. Confirmation procedures and modelling strategies in nonlinear dynamics (...)
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  21. Jessica Wahman (2005). Determined by Chaos: The Nonlinear Dynamics of Free Will. Philosophy, Psychiatry, and Psychology 12 (3):235-237.
  22. Graham White (2000). Lewis, Causality, and Possible Worlds. Dialectica 54 (2):133–137.
    We show that, given standard assumptions about classical dynamical systems, Lewis' conception of possible worlds is incompatible with classical physics in that it would imply that all dynamical systems were integrable.
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  23. Jessica M. Wilson (2013). Nonlinearity and Metaphysical Emergence. In Stephen Mumford & Matthew Tugby (eds.), Metaphysics and Science.
    The nonlinearity of a composite system, whereby certain of its features (including powers and behaviors) cannot be seen as linear or other broadly additive combinations of features of the system's composing entities, has been frequently seen as a mark of metaphysical emergence, coupling the dependence of a composite system on an underlying system of composing entities with the composite system's ontological autonomy from its underlying system. But why think that nonlinearity is a mark of emergence, and moreover, of metaphysical rather (...)
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  24. Jeffrey Yoshimi (2007). Mathematizing Phenomenology. Phenomenology and the Cognitive Sciences 6 (3):271-291.
    Husserl is well known for his critique of the “mathematizing tendencies” of modern science, and is particularly emphatic that mathematics and phenomenology are distinct and in some sense incompatible. But Husserl himself uses mathematical methods in phenomenology. In the first half of the paper I give a detailed analysis of this tension, showing how those Husserlian doctrines which seem to speak against application of mathematics to phenomenology do not in fact do so. In the second half of the paper I (...)
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