A double delayed hybrid stochastic prey-predator bioeconomic system with Lévy jumps is established and analyzed, where commercial harvesting on prey and environmental stochasticity on population dynamics are considered. Two discrete time delays are utilized to represent the maturation delay of prey and gestation delay of predator, respectively. For a deterministic system, positivity of solutions and uniform persistence of system are discussed. Some sufficient conditions associated with double time delays are derived to discuss asymptotic stability of interior equilibrium. For a (...) stochastic system, existence and uniqueness of a global positive solution are studied. By using the invariant measure theory and singular boundary theory of diffusion process, existence of stochastic Hopf bifurcation and stochastic stability are investigated. By constructing appropriate Lyapunov functions, asymptotic dynamic behavior of the proposed hybrid stochastic system with double time delays and Lévy jumps is discussed. Numerical simulations are provided to show consistency with theoretical analysis. (shrink)

Common wisdom holds that communication is impossible when messages are costless and communicators have totally opposed interests. This article demonstrates that such wisdom is false. Non-convergent dynamics can sustain partial information transfer even in a zero-sum signalling game. In particular, I investigate a signalling game in which messages are free, the state-act payoffs resemble rock–paper–scissors, and senders and receivers adjust their strategies according to the replicator dynamic. This system exhibits Hamiltonian chaos and trajectories do not converge to equilibria. This (...) persistent out-of-equilibrium behaviour results in messages that do not perfectly reveal the sender's private information, but do transfer information as quantified by the Kullback–Leibler divergence. This finding shows that adaptive dynamics can enable information transmission even though messages at equilibria are meaningless. This suggests a new explanation for the evolution or spontaneous emergence of meaning: non-convergent adaptive dynamics. (shrink)

Some problems rarely discussed in traditional philosophy of science are mentioned: The empirical sciences using mathematico-quantitative theoretical models are frequently confronted with several types of computational problems posing primarily methodological limitations on explanatory and prognostic matters. Such limitations may arise from the appearances of deterministic chaos and (too) high computational complexity in general. In many cases, however, scientists circumvent such limitations by utilizing reductional approximations or complexity reductions for intractable problem formulations, thus constructing new models which are computationally (...) tractable. Such activities are compared with reduction types (more) established in philosophy of science. (shrink)

Some problems rarely discussed in traditional philosophy of science are mentioned: The empirical sciences using mathematico-quantitative theoretical models are frequently confronted with several types of computational problems posing primarily methodological limitations on explanatory and prognostic matters. Such limitations may arise from the appearances of deterministic chaos and high computational complexity in general. In many cases, however, scientists circumvent such limitations by utilizing reductional approximations or complexity reductions for intractable problem formulations, thus constructing new models which are computationally tractable. (...) Such activities are compared with reduction types established in philosophy of science. (shrink)

John Earman's A Primer on Determinism treats the doctrine of Laplacian determinism by a careful look at a considerable variety of physical theories. This paper enriches Earman's discussion of chaos theory by considering in some detail the analysis of dripping faucets due to Robert Shaw. Shaw's analysis exhibits in a nice way some of the techniques used in chaos theory and gives a feel for research in this area. The paper concentrates on the tension between the determinism inherent (...) in any description involving differential equations and the in-practice unpredictability resulting from the extreme sensitivity to initial conditions of the non-linear differential equations characteristic of chaos theory. (shrink)

In a paper fifteen years ago about the meaning and the possibility of the beginning and end of time, our redoubtable session chair, John Earman, ended up like this:…[T]he answers to the questions posed at the outset lie somewhere in a thicket of problems growing out of the intersection of mathematics, physics, and metaphysics. This paper has only located the thicket and engaged in a little initial bush beating. This is not much progress, but knowing which bushes to beat is (...) a necessary first step.Some philosophers will be disappointed that the thicket is populated by so many problems of a technical and scientific nature. On the contrary, I am encouraged by this result because it shows that a long-standing philosophical problem has a nontrivial and, indeed, a surprisingly large content. Moreover, this result is a good illustration of the artificiality and danger of trying to separate philosophy from science. (Earman 1977, p. 131-2)These remarks are a kind of manifesto of an approach to philosophical questions about space and time dating from the late 1960’s. (shrink)

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, and determinism and the free will. In order to clarify these points a survey of the meaning variance of the concept(s) of deterministic chaos, or the various contexts in which it is applied, is given, and its actual epistemological implications are extracted. In summary, it turns out that the various concepts of deterministic chaos do not constitute a “new science”, or a “revolutionary” change of the “scientific world picture”. Instead, chaos research provides a sort of toolbox of methods which are certainly useful for a more detailed analysis and understanding of such dynamical systems which are, roughly speaking, endowed with the property of exponential sensitivity on initial conditions. Such a property, then, implies merely one, but quantitatively strong type of limitation of long-time computability and predictability, respectively. (shrink)

The general theme of this article is the actual practice of how definitions are justified and formulated in mathematics. The theoretical insights of this article are based on a case study of topological definitions of chaos. After introducing this case study, I identify the three kinds of justification which are important for topological definitions of chaos: natural-world-justification, condition-justification and redundancy-justification. To my knowledge, the latter two have not been identified before. I argue that these three kinds of justification (...) are widespread in mathematics. After that, I first discuss the state of the art in the literature about the justification of definitions in the light of actual mathematical practice. I then go on to criticize Lakatos’s account of proof-generated definitions—the main account in the literature on this issue—as being limited and also misguided: as for topological definitions of chaos, in nearly all mathematical fields various kinds of justification are found and are also reasonable. (shrink)

Deterministic Chaos: Some Interesting Points of View from the Philosophy of Science. A comparatively simple example is used to present some of the main features of deterministic chaos. From the point of view of the philosophy of science, three questions are dealt with: if the equations of motion of chaotic systems are falsifiable in a strict sense; whether experiments on chaotic systems are reproducible; to what extent the development of chaotic systems is predictable. It emerges that (...) in these respects chaotic systems, though being deterministic, behave essentially in the same way as stochastic (indeterministic) systems do. (shrink)

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 in Texas. The mathematical version of this property is known as sensitive dependence. However, it turns out that sensitive dependence is somewhat old news, so some of the implications flowing from it are perhaps not such “big news” after all. Still, chaos studies have highlighted these implications in fresh ways and led to thinking about other implications as well. -/- In addition to exhibiting sensitive dependence, chaotic systems possess two other properties: they are deterministic and nonlinear (Smith 2007). This entry discusses systems exhibiting these three properties and what their philosophical implications might be for theories and theoretical understanding, confirmation, explanation, realism, determinism, free will and consciousness, and human and divine action. (shrink)

Chaos theory not only stretched the concept of chaos well beyond its traditional semantic boundaries, but it also challenged fundamental tenets of physics and science in general. Hence, its present and potential impact on the Western worldview cannot be underestimated. I will illustrate the relevance of chaos theory in regard to modern Western thought by tracing the concept of order, which modern thinkers emphasised as chaos’ dichotomic counterpart. In particular, I will underline how the concern of (...) seventeenth-century natural philosophers with order and conservation oriented the production of their concept of nature. Moreover, I will match this resulting world of natural facts with both the classical construction of the cosmos , and the nineteenth-century physico-chemical structure of conservation laws. Furthermore, I will recall the challenges to the deterministic and determinable modern scientific framework. These challenges arose from within the hard sciences, and they were often understood as a temporary lack of knowledge. I will argue that scientists long failed to acknowledge results that were at odds with their expectations, which were deeply engrained in modern Western thought, and which even harked back to the classical theoretical framework. Finally, I will suggest a link between the cultural earthquake that shook Western societies during the ‘long sixties,’ and the questioning of scientific expectations, which chaos theory defied. (shrink)

An examination of determinism in the context of chaotic dynamics.

This paper explores the possibility that chaos theory might be helpful in explaining free will. I will argue that chaos has little to offer if we construe its role as to resolve the apparent conflict between determinism and freedom. However, I contend that the fundamental problem of freedom is to find a way to preserve intuitions about rational action in a physical brain. New work on dynamic computation provides a framework for viewing free choice as a process that (...) is sensitive and unpredictable, while at the same time organized and intelligent. I conclude that this vision of a chaotic brain may make a modest contribution to an intuitively acceptable physicalist account of free will. (shrink)

Philosophical discourse traditionally distinguishes between ontology and epistemology and generally enforces this distinction by keeping the two subject areas separated. However, the relationship between the two areas is of central importance to physics and philosophy of physics. For instance, many measurement-related problems force us to consider both our knowledge of the states and observables of a system and its states and observables independent of such knowledge. This applies to quantum systems in particular. This contribution presents an example showing the importance (...) of distinguishing between ontic and epistemic levels of description even for classical systems. Corresponding conceptions of ontic and epistemic states and their evolution are introduced and discussed with respect to aspects of stability and information flow. These aspects show why the ontic/epistemic distinction is particularly important for systems exhibiting deterministic chaos. Moreover, this distinction provides some understanding of the relationships between determinism, causation, predictability, randomness, and stochasticity. (shrink)

Nonclarity around the understandingof the concept of chaos has caused someconfusion in the contemporary natural science.For instance, not making a clear distinctionbetween the deterministic and quantum chaos hasmade it impossible to evaluate the approach ofIlya Prigogine in an appropriate way. It isshown that Jean Bricmont has missed the targetin his critique of I. Prigogine's ideas, as thelatter has concentrated his interest on systemsconsisting of infinite (arbitrarily large)number of particles in incessant mutualimpact, the former on systems that have (...) afinite (not necessarily large, althoughsometimes very large) number of particles,which move freely of any mutual impact orparticipate only in transient interaction. Thedifference may sometimes be quite crucial. Itis also suggested that if we consider theirreversibility as the basic element ofdescription of physical world, the world oftrajectories and wave functions cannot beresearched apart from this real irreversibility. (shrink)

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

Laplacean determinism remains a popular theory among philosophers and scientists alike, in spite of the fact that the Copenhagen Interpretation of quantum mechanics, with which it is inconsistent, has been around for more than fifty years. There are a number of reasons for its continuing popularity. One, recently articulated by Honderich, is that there are too many possible interpretations of quantum mechanics, and the subject is too controversial even among physicists to be an adequate basis for overturning determinism. Nevertheless, quantum (...) mechanics is an enormously successful theory, considering the quantity and variety of its predictions which have been verified under conditions never dreamt of by its originators; and the Copenhagen Interpretation is the only widely accepted interpretation of it. Although a hidden variable theory consistent with the results of quantum mechanics is not impossible, one of its major advocates admits that it is highly speculative, and far from adequately developed. Yet such a theory would be needed to reconcile Laplacean determinism with quantum mechanics; most of the controversies alluded to by Honderich are irrelevant. (shrink)

Some irrational numbers are "random" in a sense which implies that no algorithm can compute their decimal expansions to an arbitrarily high degree of accuracy. This feature of (most) irrational numbers has been claimed to be at the heart of the deterministic, but chaotic, behavior exhibited by many nonlinear dynamical systems. In this paper, a number of now classical chaotic systems are shown to remain chaotic when their domains are restricted to the computable real numbers, providing counterexamples to the (...) above claim. More fundamentally, the randomness view of chaos is shown to be based upon a confusion between a chaotic function on a phase space and its numerical representation in Rn. (shrink)

This paper aims at a logico-mathematical analysis of the concept of chaos from the point of view of a constructivist philosophy of physics. The idea of an internal logic of chaos theory is meant as an alternative to a realist conception of chaos. A brief historical overview of the theory of dynamical systems is provided in order to situate the philosophical problem in the context of probability theory. A finitary probabilistic account of chaos amounts to the (...) theory of measurement in the line of a quantum-theoretical foundational perspective and the paper concludes on the non-classical internal logic of chaos theory. Finally, deterministic chaos points to a philosophy which asserts that chaotic systems are no less measurable than other physical systems where predictable and non–predictable phenomena intermingle in a constructive theory of measurement. (shrink)

The paper attempts to reconcile two very different approaches to the concept of causation. In the original form, it is the opposition found in Laplace between his doctrine of constant and variable causes on the one hand and his mechanistic determinism on the other. This tension was described clearly only by Maxwell who stressed the contrast between the statistical and the dynamical method (calling the latter also the historical or strictly kinetic method). A similar dichotomy surfaces in the work of (...) Wesley Salmon who distinguished statistical from aleatory causation. Acknowledging that we seem to have conflicting intuitions about causality and explanation, I argue that assigning probabilistic laws a fundamental role in scientific explanation does not conflict with the assumption of Laplacian determinism. This is due to the fact that in most systems of interest, we confront a complex interaction of multiple causal factors and an extreme sensitivity to small variations of initial conditions. (shrink)

Recent articles by Michael Heller, Carl Helrich, Peter Hodgson, Jeffrey Koperski, and Nicholas Saunders present a challenge to much current thinking on God, divine action, and cosmology. In the process, they also reveal underlying assumptions and current problems, especially in the debate over physics and divine action. In particular, three issues come up that need to be addressed further. First, what is the status of determinism, and what can physics contribute? Second, what kind of divine action are we talking about? (...) Third, what is the relationship between God and time, and how does this affect claims about the personhood of God? While these essays present necessary critiques and interesting, positive proposals, they also reveal unresolved tensions that need to be addressed. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Chaos and LiteratureCarl Matheson and Evan KirchhoffIChaos theory was the intellectual darling of pop-science writers of the late 1980s. 1 In their eyes, it would provide a new paradigm by which to describe the world, one that liberated scientists from clockwork determinism—or, alternatively, from incomprehensible randomness. In an introductory textbook of the period, Robert Devaney called chaos theory “the third great scientific revolution of the 20th century, (...) along with relativity and quantum mechanics.” Similar attitudes propagated into philosophy; for example, Stephen Kellert argued that an acceptance of chaos theory would involve a reconfiguration of scientific methodology. 2It was in the domain of literary theory, however, that chaos found its most enthusiastic reception in the humanities, and the enthusiasm lives on. Many literary theorists display no hesitation in touting the supposedly revolutionary implications of chaos science. Katherine Hayles, the chief among them, argues that because the concept of order has undergone a “radical reevaluation” in recent decades, “textuality is conceived in new ways within critical theory and literature, and new kinds of phenomena are coming to the fore within an emerging field known as the science of chaos” (CO, p. 1). She infers that the new “paradigm of orderly disorder” (CB, p. xiii) represented by chaos theory signifies a conceptual revolution in modern culture as a whole. 3 She attempts to establish a parallel between chaos theory and various poststructuralist philosophical positions, including those of Derrida and Foucault, claiming that this new paradigm “may well prove to be as important to the second half of the century as the field concept was to [End Page 28] the first half” (CB, p. xiii), and that chaos may soon be “on a par with evolution, relativity, and quantum mechanics in its impact on the culture” (CO, p. 4). Other theorists make claims for the interpretive power of chaos; according to William Demastes, “chaos theory can help in comprehending several paths that the theatre has followed since the inception of postmodernism” (p. 242). 4 By a conservative estimate, over fifty papers have been published which link chaos theory to literature or literary theory. Clearly, the idea that chaos theory has application outside of science is not restricted to one or two over-eager humanists.In this essay, we wish to address some of the claims which concern the relationship between chaos science and the study of literature. Three such claims are:a. There are significant similarities between the science of chaos, contemporary literary theory, and/or philosophy.b. We can trace a common etiology for chaos theory and poststructuralist criticism. The two are so intimately related that they are really different formulations of a common claim, as filtered through two different fields.c. The science of chaos can help us interpret and understand specific literary works, and perhaps contemporary literature in general.However, before assessing the relationship between chaos and literature, we will briefly introduce chaos theory itself and demonstrate that even a minimal understanding is sufficient to undercut the supposed revolutionary significance of chaos theory. 5IIChaotic systems are deterministic: an exact description of a system at any given time, together with the laws of nature that apply to it, will entail the entire future behavior of the system. In this sense, chaotic systems form a subclass of classical systems (and are to be distinguished from quantum systems, which are indeterministic). However, chaotic systems differ from the systems studied throughout most of the history of science in two major ways. First, the differential equations used to model them are nonlinear, while the history of mathematical physics is largely devoted to a treatment of linear differential equations. Technical issues aside, the ramifications of nonlinearity are: (i) equations which are impossible to solve using the general strategies designed for [End Page 29] linear equations; and consequently (ii) the need for solutions by methods of numerical approximation, generally performed on a computer. Second, chaotic systems exhibit a feature known as “sensitive dependence”—or, more colorfully, as “the butterfly effect,” a figure of speech intended to evoke the worry that our long-term forecasts of the weather can be hopelessly disrupted by the atmospheric fluctuations due to a single butterfly... (shrink)

Classical and quantal physics are fundamentally different in the way that each deals with complexity. We examine both the algorithmic and the computational aspects of this difference. Any comprehensive deterministic theory must contain a certain ineffectiveness in producing long-term predictions of the future, whereas a probabilistic theory is not so handicapped. The relevance of these considerations to chaos is discussed.

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

On reconnait en Castoriadis l'un des principaux penseurs politiques alternatifs contemporains, toujours actuel. Mais on connaît sans doute moins le lien étroit qui existe entre ses analyses politiques et ses prises de position philosophiques. Or, elles s'éclairent réciproquement. Le refus de subordonner la raison pratique à la raison théorique permet à Castoriadis de penser l'idée de création. Sa rupture avec Marx, auquel il reproche son ontologie déterministe, l'amène à repenser l'émancipation politique et sociale à partir de la notion d'imaginaire créateur. (...) Pour bien comprendre cette notion, il faut la confronter avec les conceptions de l'imagination défendues notamment par la phénoménologie, particulièrement Sartre et Husserl. Elle débouche sur le concept de chaos, dont il ressort que l'action humaine repose sur un désordre pour une part irréductible, ce qui explique qu'on ne puisse fonder celle-ci, pas plus que la démocratie, en référence à une légitimité indiscutable. Cherchant à tisser un lien entre la pensée, l'oeuvre et la vie d'un homme engagé dans son temps, ce livre trace un parcours à travers les thèmes centraux de la pensée philosophique et politique de Castoriadis, qu'il met en rapport avec d'autres approches contemporaines : Maurice Merleau-Ponty, Claude Lefort, Richard Rorty, Vincent Descombes, ou encore Michel Foucault à propos de l'éthique du sujet. Un chapitre est également consacré à la place de l'exil dans la vie et la pensée de Castoriadis. (shrink)

From the beginning of chaos research until today, the unpredictability of chaos has been a central theme. It is widely believed and claimed by philosophers, mathematicians and physicists alike that chaos has a new implication for unpredictability, meaning that chaotic systems are unpredictable in a way that other deterministic systems are not. Hence, one might expect that the question ‘What are the new implications of chaos for unpredictability?’ has already been answered in a satisfactory way. (...) However, this is not the case. I will critically evaluate the existing answers and argue that they do not fit the bill. Then I will approach this question by showing that chaos can be defined via mixing, which has never before been explicitly argued for. Based on this insight, I will propose that the sought-after new implication of chaos for unpredictability is the following: for predicting any event, all sufficiently past events are approximately probabilistically irrelevant. (shrink)

The movement from fate to faith -- Freeing God -- Lucky? -- Fate, chaos, and faith -- The movement from magic to mystery -- Abracadabra, hocus-pocus -- God is in control (?) -- Unsolved mysteries -- The movement from destiny to desire -- God's activity -- God told me to -- God's dream and our purpose.

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 systems. (shrink)

Chaos, once considered antithetical to scientific law and order, is presently the subject of a vigorous and progressive scientific research program. "Chaos" as it is used in current scientific literature is a technical term: it refers to stochastic behavior generated by deterministic systems. This behavior has appeared in models of a wide range of phenomena including atmospheric patterns, population dynamics, celestial motion, heartbeat rhythms, turbulent fluids, chemical reactions and social structures. In general, chaos arises in the (...) nonlinear dynamics of complex systems. Grebogi, Ott and Yorke reflect the sentiment of the scientific community when they state that chaotic nonlinear dynamics has "fundamental implications." This dissertation explores these results in a philosophic context. ;The research is organized as follows: The Context of Science. Scientific results are achieved in and make sense in the practical context of research which includes both experiment and theory. Drawing on the work of Dyke, Galison, Garfinkel and Hacking, a philosophic context is described which more accurately reflects the significance of scientific results than do the contexts of discovery and justification. Models. Chaos theory is constituted by a family of numerical models. In this chapter, Giere's account of modeling is extended to both bio-medical and numerical models. Chaos in Scientific Models. This is a rather lengthy primer of chaos theory that is, although technically accurate, accessible to nonspecialists. It constitutes a road map for the primary literature on chaos. Chaos and Prediction. Chaos theory shows a limit of our science, namely, chaotic systems are deterministic yet unpredictable in the long run. The chapter includes a discussion of scientific determinism following Popper and, it concludes by providing evidence against the laplacian claim that deterministic systems are predictable. Chaos and Complexity. This shows what contribution chaos theory makes toward answering the challenge of organized complexity articulated by Weaver. It discusses attempts to characterize complexity and shows how the results of chaos theory can help. I draw on the work of Abraham, Arecchi, Atlan, Chaitin, Eckmann, Peacocke, Rosen, Ruelle, and others. Chaos theory provides a thoroughly nonvitalistic framework for understanding dynamical complexity in organic, as well as inorganic, systems. (shrink)

Like relativity and quantum theory chaos research is another prominent concept of 20th century physics that has triggered deep and far-reaching discussions in the philosophy of science. In this volume outstanding scientists discuss the fundamental problems of the concepts of law and of prediction. They present their views in their contributions to this volume, but they also are exposed to criticism in transcriptions of recordings made during discussions and in comments on their views also published in this book. Although (...) all authors assume familiarity with some background in physics they also address the philosophers of science and even a general audience interested in modern science's contribution to a deeper understanding of reality. (shrink)

The fact that there exist in nature thoroughly deterministic systems whose future behavior cannot be predicted, no matter how advanced or fined-tune our cognitive and technical abilities turn out to be, has been well established over the last decades or so, essentially in the light of two different theoretical frameworks, namely chaos theory and (some deterministic interpretation of) quantum mechanics. The prime objective of this paper is to show that there actually exists an alternative strategy to ground (...) the divorce between determinism and predictability, a way that is older than—and conceptually independent from—chaos theory and quantum mechanics, and which has not received much attention in the recent philosophical literature about determinism. This forgotten strategy—embedded in the doctrine called “emergent evolutionism”—is nonetheless far from being a mere historical curiosity that should only draw the attention of philosophers out of their concern for comprehensiveness. It has been indeed recently revived in the works of respected scientists. (shrink)

The deterministic economic system will also produce chaotic dynamic behaviour, so economic chaos is getting more and more attention, and the research of economic chaos forecasting methods has become an important topic at present. The traditional economic chaos forecasting models are mostly based on large samples, but in actual production activities, there are a large number of small-sample economic chaos problems, and there is still no effective solution. This paper proposes a combined forecasting model based (...) on the traditional economic chaos forecasting method. First of all, through the decision tree classification, priority selection of features, rough prediction is achieved. Secondly, we use BP neural network to make secondary prediction. Because the initial weight is randomly selected, it is easy to fall into the defect of local minimum. This paper optimizes the BP neural network. Finally, the decision tree model and the BP neural network model optimized by the improved genetic algorithm are combined, and the combined model is optimized by the improved GA. This method can take advantage of many prediction models and combine the prediction information of multiple different prediction models to effectively improve the fitting ability of the model and improve the prediction accuracy. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 12.3 (2005) 235-237 [Access article in PDF] Determined by Chaos: The Nonlinear Dynamics of Free Will Jessica Wahman Keywords free will, chaos theory, determinism, materialism In "antidepressants and the Chaotic Brain: Implications for the Respectful Treatment of Selves," Douglas Heinrichs provides an intriguing justification of individuated and longer term therapy for depressive clients. He does not reject medication as a therapeutic strategy, nor (...) does he question the materialist basis of the traditional medical model. Rather, he offers a physically deterministic account of depression that is at the same time compatible with a sense of human agency and individuality. Heinrichs suggests that human physiology and its psychiatric disorders are better accounted for by the nonlinear dynamics of chaos theory than by the traditional account of neurotransmitter production and reuptake. Because the latter, microscopic, explanation suggests a direct cause-and-effect relationship between synaptic activity and subjective affect, it cannot account for the wide variation of responses to the same medications, nor can it satisfy the client's fears that her drug-induced well-being is not fully hers to control. Chaos theory, he asserts, can provide a better explanation by treating the human organism as a complex holistic system whose patterns resemble a topographical map of probability more than they do a unidirectional vector model of cause to effect. Like the weather, human affect and behavior are physically determined but difficult to predict, and so careful attention to both the individual history of the client and the uniqueness of responses to medication are a necessary part of any successful therapeutic program.Connected to this theory of nonlinear physiology is Heinrichs's account of autonomy and agency under this rubric. He notes that a psychology based on chaos theory is not only compatible with the notion of free will, it can better explain why the successful use of medication actually increases freedom and autonomy instead of limiting it. It is here that I wish to focus my comments, because his interpretation of free will may give us, to borrow a phrase from Daniel Dennett, a "variet[y] of free will worth wanting" (1984, title page). Free will, in this case, is not a metaphysical ability to act above and beyond our material causes, but is instead a property of the material system itself, namely when that system feels itself capable of greater psychic mobility around the topographical map of probabilistic patterns.According to this model, our ability to reason, plan, and act on the decisions we make is itself a [End Page 235] part of our chaotically determined neurologic system. When we are healthy, we are able to reason in our best interests and act on those reasons. This is modeled as an ability for the organism to metaphorically "move about" the map of its own possibilities, and more important, to both enter and escape certain states, known as chaotic attractors, into which it is likely to be drawn. "Where" we wind up, psychologically speaking, at any point in time is determined by our own system, and so we may say that in such a case we are autonomous and our choices are made freely. Depression, on the other hand, can be compared to a deep groove in the map, a chaotic attractor that is hard to escape, and so the system quite literally becomes "stuck in a rut." This is subjectively experienced as the tendency for thought processes and activities to fall into negative and self-defeating patterns despite the best efforts of the client to escape these habits. So long as the organism does not have a sense of being "trapped" in an attractor (whether a depressive or, for example, manic or compulsive state), then that organism may be said to be free. Medication and the therapy that accompanies it, so far as it facilitates our ability to escape deep chaotic attractors, promotes our own freedom of will. If a car cannot spin its way out of a ditch, does the tow truck hinder or promote its freedom by hauling it back onto solid pavement where it may again... (shrink)

. The question of whether or not our universe is deterministic remains of interest to both scientists and theologians. In this essay I argue that this question can be solved only by metaphysical decision and that no scientific evidence for either determinism or indeterminism will ever be conclusive. No finite being, no matter how powerful its cognitive abilities, will ever be able to establish the deterministic nature of the universe. The only being that would be capable of doing (...) so would be one that is at once transcendent and immanent. Such a being is compatible with the God of the Christian tradition, which yields that a deterministic worldview is compatible with a deterministic worldview. A more important point is that because science is never able to establish the determinism of our universe, it can never definitely rule out divine action except on metaphysical grounds. (shrink)

[Time, the fundamental dimension of our existence, has fascinated artists, philosophers, and scientists of every culture and every century. All of us can remember a moment as a child when time became a personal reality, when we realized what a "year" was, or asked ourselves when "now" happened. Common sense says time moves forward, never backward, from cradle to grave. Nevertheless, Einstein said that time is an illusion. Nature's laws, as he and Newton defined them, describe a timeless, deterministic (...) universe within which we can make predictions with complete certainty. In effect, these great physicists contended that time is reversible and thus meaningless. (shrink)

Determinism and unpredictability are compatible since deterministic flows can produce, if sensitive to initial conditions, unpredictable behaviors. Within this perspective, the notion of scenario to chaos transition offers a new form of predictability for the behavior of sensitive to initial condition systems under the variation of a control parameter. In this paper I first shed light on the genesis of this notion, based on a dynamical systems approach and on considerations of structural stability. I then suggest a link (...) to the figure of epigenetic landscape, partially inspired by a dynamical systems perspective, and offering a theoretical framework to apprehend developmental noise. (shrink)

Various processes are often classified as both deterministic and random or chaotic. The main difficulty in analysing the randomness of such processes is the apparent tension between the notions of randomness and determinism: what type of randomness could exist in a deterministic process? Ergodic theory seems to offer a particularly promising theoretical tool for tackling this problem by positing a hierarchy, the so-called ‘ergodic hierarchy’, which is commonly assumed to provide a hierarchy of increasing degrees of randomness. However, (...) that notion of randomness requires clarification. The mathematical definition of EH does not make explicit appeal to randomness; nor does the usual way of presenting EH involve a specification of the notion of randomness that is supposed to underlie the hierarchy. In this paper we argue that EH is best understood as a hierarchy of random behaviour if randomness is explicated in terms of unpredictability. We then show that, contrary to common wisdom, EH is useful in characterising the behaviour of Hamiltonian dynamical systems. (shrink)

: Lately, a new language for the understanding of the complexity of life (organism, ecosystem, and social system) has been developed. Chaos, fractals, dissipative structures, self-organization, and complex adaptive systems are some of its key concepts. On this view, reality is not the deterministic structure that Newton envisaged, but rather, a partially unknown or at least unpredictable world of multiple possibilities. As the horizon of our knowledge of natural realities expands, the emergent comprehensive perspective requires a radical reconstruction (...) of both the concrete structure upon which human life is materially built and the symbolic structure that reason has schemed. (shrink)

Lately, a new language for the understanding of the complexity of life has been developed. Chaos, fractals, dissipative structures, self-organization, and complex adaptive systems are some of its key concepts. On this view, reality is not the deterministic structure that Newton envisaged, but rather, a partially unknown or at least unpredictable world of multiple possibilities. As the horizon of our knowledge of natural realities expands, the emergent comprehensive perspective requires a radical reconstruction of both the concrete structure upon (...) which human life is materially built and the symbolic structure that reason has schemed. (shrink)

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 systems.. (shrink)