Emulation, Reduction, and Emergence in Dynamical Systems (original) (raw)
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Reduction in Dynamical Systems: A Representational View
2010
ABSTRACT: According to the received view, reduction is a deductive relation between two formal theories. In this paper, I develop an alternative approach, according to which reduction is a representational relation between models, rather than a deductive relation between theories; more specifically, I maintain that this representational relation is the one of emulation. To support this thesis, I focus attention on mathematical dynamical systems and I argue that, as far as these systems are concerned, the emulation relation is sufficient for reduction. I then extend this representational view of reduction to the case of empirically interpreted dynamical systems, as well as to a treatment of partial, approximate, and asymptotic reduction.
A Representational Approach to Reduction in Dynamical Systems
Erkenntnis, 79(4):943-968, 2014
According to the received view, reduction is a deductive relation between two formal theories. In this paper, I develop an alternative approach, according to which reduction is a representational relation between models, rather than a deductive relation between theories; more specifically, I maintain that this representational relation is the one of emulation. To support this thesis, I focus attention on mathematical dynamical systems and I argue that, as far as these systems are concerned, the emulation relation is sufficient for reduction. I then extend this representational model-based view of reduction to the case of empirically interpreted dynamical systems, as well as to a treatment of partial, approximate, and asymptotic reduction.
Filosofia unisinos, 2019
Claims about reduction or emergence appear in cases in which there are different levels of facts that have between them some kind of ontological connection by which one of them is 'made up' from the other. In the case of reduction, it is supposed that the reduced level of facts is 'nothing over' the reducing level of facts. In the case of emergence, on the other hand, it is supposed that the emergent level is something 'new' with respect to the emergence base. In both reduction and emergence some kind of ontological priority of one level with respect to the other is involved, as well as some kind of explanatory asymmetry between them. In recent years a lot of work has been devoted to different notions of ontological priority, like grounding and dependence, that might be useful for the clarification of the more traditional questions about the nature of reduction and emergence. This work presents and discusses various attempts to make that clarification.
Reductionist and anti-reductionist perspectives on dynamics
Philosophical Psychology, 2002
In this paper reduction and its pragmatics are discussed in the light of the development in Computer Science of languages to describe processes. The design of higher-level description languages within Computer Science has had the aim of allowing for description of the dynamics of processes in the (physical) world on a higher level avoiding all (physical) details of these processes. The higher description levels developed have dramatically increased the complexity of applications that came within reach. The pragmatic attitude of a (scientific) practitioner in this area has become inherently anti-reductionist, but based on well-established reduction relations. The paper discusses how this perspective can be related to reduction in general, and to other domains where description of dynamics plays a main role, in particular, biological and cognitive domains.
More about Dynamical Reduction and the Enumeration Principle
1999
In view of the arguments put forward by Clifton and Monton [1999] in a recent preprint, we reconsider the alleged conflict of dynamical reduction models with the enumeration principle. We prove that our original analysis of such a problem is correct, that the GRW model does not meet any difficulty and that the reasoning of the above authors is inappropriate
Minati G., Abram R. M., Pessa E. (Eds.), Towards a Post-Bertalanffy Systemics, Springer International Publishing, Ch. 6, 2015
[This version is a preprint, DOI of published chapter http://dx.doi.org/10.1007/978-3-319-24391-7\_6.] Dynamical systems on monoids have been recently proposed as minimal mathematical models for the intuitive notion of deterministic dynamics. This paper shows that any dynamical system DS_L on a monoid L can be exhaustively decomposed into a family of mutually disconnected subsystems—the constituent systems of DS_L. In addition, constituent systems are themselves indecomposable, even though they may very well be complex. Finally, this work also makes clear how any dynamical system DS_L turns out to be identical to the sum of all its constituent systems. Constituent systems can thus be thought as the indecomposable, but possibly complex, building blocks to which the dynamics of an arbitrary complex system fully reduces. However, no further reduction of the constituents is possible, even if they are themselves complex.
Reduction Principle For Dynamical Systems
impulsive di#erential equations, Descartes Press, Koriyama, 1996. [16]P. W. Bates and K. Lu, A Hartman--Grobman theorem for Cahn--Hillard equations and phases--field equations, J. Dynam. Di#erential Equations 6 (1994), no. 1, 101--145. [17]N. N. Bogolyubov, On some statistical methods in mathematical physics, AN USSR, L'vov, 1945 (Russian). [18]N. N. Bogolyubov and Ju. A. Mitropol'ski, Asymptotic methods in the theory of nonlinear oscillations, Gordon and Breach, New York, 1962. [19]P. Bohl, Uber die Bewegung eines mechanischen Systems in der Nahe einer Gleichgewichtslage, J. Reine Angew. Math. 127 (1904), no. 3--4, 179--276. [20]M. A. Boudourides, Topological equivalence of monotone nonlinear nonautonomous di#erential equations, Portugal. Math. 41 (1982), no. 1--4, 287--294. [21]M. A. Boudourides, Hyperbolic Lipschitz homeomorphisms and flows, in Equadi# 82, Proceedings 82, Lecture Notes in Math., 1017, 1983, pp. 101--106. [22]R. Bowen, #--limit sets for Axiom A di#eomorphi...
The problem of reductionism from a system theoretical viewpoint
Journal for General Philosophy of Science - Zeitschrift für Allgemeine Wissenschaftstheorie, 1983
Inspite of the great success in many disciplines the program of reductionism has failed its genuine purpose. Systemtheory however has yielded a new concept of reducfionism which we call reductionism by correspondence and which may imply a new understanding of the mind-body problem. The crucial operations of reductionism by correspondence are called idealization, interpretation and classification. They are used to optimize the description of a system. Nevertheless they lead to certain deficiencies which cannot be avoided in principle. We are therefore driven to the assumption that natural systems can only be described as probabilistic systems. From this point of view nothing is said about the direction of the reduction.
Evolution, Explanation, Ethics and Aesthetics, 2016
A closer look at some proposed Gedanken-experiments on BECs promises to shed light on several aspects of reduction and emergence in physics. These include the relations between classical descriptions and different quantum treatments of macroscopic systems, and the emergence of new properties and even new objects as a result of spontaneous symmetry breaking.
Physics Reports, 2003
The report presents an exhaustive review of the recent attempt to overcome the difficulties that standard quantum mechanics meets in accounting for the measurement (or macro-objectification) problem, an attempt based on the consideration of nonlinear and stochastic modifications of the Schrödinger equation. The proposed new dynamics is characterized by the feature of not contradicting any known fact about microsystems and of accounting, on the basis of a unique, universal dynamical principle, for wavepacket reduction and for the classical behavior of macroscopic systems. We recall the motivations for the new approach and we briefly review the other proposals to circumvent the above mentioned difficulties which appeared in the literature. In this way we make clear the conceptual and historical context characterizing the new approach. After having reviewed the mathematical techniques (stochastic differential calculus) which are essential for the rigorous and precise formulation of the new dynamics, we discuss in great detail its implications and we stress its relevant conceptual achievements. The new proposal requires also to work out an appropriate interpretation; a procedure which leads us to a reconsideration of many important issues about the conceptual status of theories based on a genuinely Hilbert space description of natural processes. Attention is also paid to many problems which are naturally raised by the dynamical reduction program. In particular we discuss the possibility and the problems one meets in trying to develop an analogous formalism for the relativistic case. Finally we discuss the experimental implications of the new dynamics for various physical processes which should allow, in principle, to test it against quantum mechanics. The review covers the work which has been done in the last fifteen years by various scientists and the lively debate which has accompanied the elaboration of the new proposal.