The domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics. A few examples are in meteorology, ecological dynamics, and social and economic dynamics. These new ideas have profound implications for our understanding and practice in domains involving complexity, predictability and determinism, equilibrium, control, planning, individuality, responsibility and (...) so on. Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of their complexity. The book will focus specifically on the philosophical concepts, principles, judgments and problems distinctly raised by work in the domain of complex nonlinear dynamical systems, especially in recent years. -Comprehensive coverage of all main theories in the philosophy of Complex Systems -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields are also included. (shrink)

The "usual story" regarding molecular chemistry is that it is roughly an application of quantum mechanics. That is to say, quantum mechanics supplies everything necessary and sufficient, both ontologically and epistemologically, to reduce molecular chemistry to quantum mechanics. This is a reductive story, to be sure, but a key explanatory element of molecular chemistry, namely molecular structure, is absent from the quantum realm. On the other hand, typical characterizations of emergence, such as the unpredictability or inexplicability of molecular structure based (...) on quantum mechanics, do not characterize the relationship between molecular chemistry and quantum mechanics well either. A different scheme for characterizing reduction and emergence is proposed that accommodates the relationship between quantum mechanics and molecular chemistry and some initial objections to the scheme are considered. (shrink)

Though most contemporary philosophers and scientists accept a physicalist view of mind, the recent surge of interest in the problem of consciousness has put the mind /body problem back into play. The physicalists' lack of success in dispelling the air of residual mystery that surrounds the question of how consciousness might be physically explained has led to a proliferation of options. Some offer alternative formulations of physicalism, but others forgo physicalism in favour of views that are more dualistic or that (...) bring in mentalistic features at the ground- floor level of reality as in pan-proto-psychism. My aim here is to give an overview of the recent philosophic discussion to serve as a map in locating issues and options. I will not offer a comprehensive survey of the debate or mark every important variant to be found in the recent literature. I will mark the principal features of the philosophic landscape that one might use as general orientation points in navigating the terrain. I will focus in particular on three central and interrelated ideas: those of emergence, reduction, and nonreductive physicalism. The third of these, which has emerged as more or less the majority view among current philosophers of mind, combines a pluralist view about the diversity of what needs to be explained by science with an underlying metaphysical commitment to the physical as the ultimate basis of all that is real. The view has been challenged from both left and right, on one side from dualists and on the other from hard core reductive materialists. Despite their differences, those critics agree in finding nonreductive physicalism an unacceptable and perhaps even incoherent position. They agree as well in treating reducibility as the essential criterion for physicality; they differ only about whether the criterion can be met. Reductive physicalists argue that it can, and dualists deny it. (shrink)

The fundamental problem on which Ilya Prigogine and the Brussels–Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of time (...) was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels–Austin Group, is to consider the observed direction of time to be a basic physical phenomenon due to the dynamics of physical systems. This essay focuses mainly on recent developments in the Brussels–Austin Group after the mid-1980s. The fundamental concerns are the same as in their earlier approaches (subdynamics, similarity transformations), but the contemporary approach utilizes rigged Hilbert space (whereas the older approaches used Hilbert space). While the emphasis on nonequilibrium statistical mechanics remains the same, their more recent approach addresses the physical features of large Poincare systems, nonlinear dynamics and the mathematical tools necessary to analyze them. (shrink)

This paper examines the relationship between physical theories of causation and theories of difference-making. It is plausible to think that such theories are compatible with one another as they are aimed at different targets: the former, an empirical account of actual causal relations; the latter, an account that will capture the truth of most of our ordinary causal claims. The question then becomes: what is the relationship between physical causation and difference-making? Is one kind of causal fact more fundamental than (...) the other? This paper defends causal foundationalism: the view that facts about difference-making are dependent on the obtaining of facts about physical causation. However, the paper's main goal is to clarify the structure of the debate. At the end of the paper, it is shown how settling the issue about the relationship between physical theories of causation and theories of difference-making has more than mere intrinsic interest in unifying the very different pursuits that have been undertaken in the philosophy of causation. It can help to break a stalemate that has arisen in the current debate about mental causation. (shrink)

The causal argument for physicalism is anayzed and it's key premise--the causal closure of physics--is found wanting. Therefore, a hidden premise must be added to the argument to gain its conclusion, but the hidden premise is indistinguishable from the conclusion of the causal argument. Therefore, it begs the question on physicalism.

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 (...) mechanics, far more robust and less speculative than the examples typically provided in the philosophy of mind literature. Although the physics of Rayleigh–Bénard convection is quite complicated, this model provides a much more realistic and concrete example for examining various assumptions and arguments found in emergence and philosophy of mind debates. After reviewing some key concepts of nonlinear dynamics, complex systems and the basic physics of Rayleigh–Bénard convection, I begin that examination here by (1) assessing a recently proposed definition for emergence and downward causation, (2) discussing some typical objections to downward causation and (3) comparing this model with Sperry’s examples. (shrink)

The context of an operational description is given by the distinction between what we consider as relevant and what as irrelevant for a particular experiment or observation. A rigorous description of a context in terms of a mathematically formulated context-independent fundamental theory is possible by the restriction of the domain of the basic theory and the introduction of a new coarser topology. Such a new topology is never given by first principles, but depends in a crucial way on the abstractions (...) made by the cognitive apparatus or the pattern recognition devices used by the experimentalist. A consistent mathematical formulation of a higher-level theory requires the closure of the restriction of the basic theory in the new contextual topology. The validity domain of the so constructed higher-level theory intersects nontrivially with the validity domain of the basic theory: neither domain is contained in the other. Therefore, higher-level theories cannot be totally ordered and theory reduction is not transitive. The emergence of qualitatively new properties is a necessary consequence of such a formulation of theory reduction (which does not correspond to the traditional one). Emergent properties are not manifest on the level of the basic theory, but they can be derived rigorously by imposing new, contextually selected topologies upon context-independent first principles. Most intertheoretical relations are mathematically describable as singular asymptotic expansions which do not converge in the topology of the primary theory, or by choosing one of the infinitely many possible, physically inequivalent representations of the primary theory (Gelfand–Naimark–Segal-construction of algebraic quantum mechanics). As examples we discuss the emergence of shadows, inductors, capacitors and resistors from Maxwell’s electrodynamics, the emergence of order parameters in statistical mechanics, the emergence of mass as a classical observable in Galilei-relativistic theories, the emergence of the shape of molecules in quantum mechanics, the emergence of temperature and other classical observables in algebraic quantum mechanics. (shrink)

Along with exploring some of the necessary conditions for the chemistry of our world given what we know about quantum mechanics, I will also discuss a different reductionist challenge than is usually considered in debates on the relationship of chemistry to physics. Contrary to popular belief, classical physics does not have a reductive relationship to quantum mechanics and some of the reasons why reduction fails between classical and quantum physics are the same as for why reduction fails between chemistry and (...) quantum physics. However, a neoreductionist can accept that classical physics has some amount of autonomy from quantum mechanics, but still try to maintain that classical+quantum physics taken as a whole reduces chemistry to physics. I will explore some of the obstacles lying in the neoreductionist’s path with respect to quantum chemistry and thereby hope to shed more light on the conditions necessary for the chemistry of our world. (shrink)

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 (...) dynamics and is investigated in detail, revealing further limitations and quali…cations on these sensitive dependence arguments. (shrink)