Online research in philosophy

This paper considers definitions of classical dynamical chaos that focus primarily on notions of predictability and computability, sometimes called algorithmic complexity definitions of chaos. I argue that accounts of this type are seriously flawed. They focus on a likely consequence of chaos, namely, randomness in behavior which gets characterized in terms of the unpredictability or uncomputability of final given initial states. In doing so, however, they can overlook the definitive feature of dynamical chaos--the fact that the underlying motion generating the behavior exhibits extreme trajectory instability. I formulate a simple criterion of adequacy for any definition of chaos and show how such accounts fail to satisfy it.

Chaos theory is beginning to find applications in the field of medicine. The theory of chaos should be introduced to students to help them as they make the transition from learning the scientific literature to actually applying this newly acquired knowledge in clinical situations. Chaos theory will give the students a powerful conceptual framework from which they can better understand the limits of predictability in clinical situations. Failure to understand the limits of predictability in chaotic natural systems will invariably lead to frustration in both patients and physicians.

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. Introduction Dynamical Systems and Unpredictability 2.1 Dynamical systems 2.2 Natural invariant measures 2.3 Unpredictability Chaos 3.1 Defining chaos 3.2 Defining chaos via mixing Criticism of Answers in the Literature 4.1 Asymptotic unpredictability? 4.2 Unpredictability due to rapid or exponential divergence? 4.3 Macro-predictability and Micro-unpredictability? A General New Implication of Chaos for Unpredictability 5.1 Approximate probabilistic irrelevance 5.2 Sufficiently past events are approximately probabilistically irrelevant for predictions Conclusion CiteULike Connotea Del.icio.us What's this?

This article uses an autobiography as an object of research, to both illustrate some principles of chaos theory in analytic practice, and give those ideas a personal and social context, thereby producing a unique but explanation-rich history of chaos theory and recent intellectual history of transdisciplinarity and social research in the West. The ideas from Chaos Theory it uses and illustrates include: three-body analysis (Poincaré); fractals (Mandelbrot); fuzzy logic (Zadeh); and the butterfly effect (Lorenz).

A recent noninterventionist account of divine agency has been proposed that marries the probabilistic nature of quantum mechanics to the instability of chaos theory. On this account, God is able to bring about observable effects in the macroscopic world by determining the outcome quantum events. When this determination occurs in the presence of chaos, the ability to influence large systems is multiplied. This paper argues that although the proposal is highly intuitive, current research in dynamics shows that it is far less plausible than previously thought. Chaos coupled to quantum mechanics proves to be a shaky foundation for models of divine agency.

The ubiquity of chaos in classical mechanics (CM), as opposed to the situation in standard quantum mechanics (QM), might be taken as speaking against QM being the fundamental theory of physical phenomena. Bohmian mechanics (BM), as a formulation of quantum theory, may clarify both the existence of chaos in the quantum domain and the nature of the classical limit. Two interesting possibilities are (i) that CM and classical chaos are included in and underwritten by quantum mechanics (BM) or (ii) that BM and CM simply possess a common region of (noninclusive) overlap. In the latter case, neither CM nor QM alone would be sufficient, even in principle, to account for all of the physical phenomena we encounter. In this talk I shall summarize and discuss the implications of some recent work on chaos and on the classical limit within the framework of BM.

In his recent book, Explaining Chaos, Peter Smith presents a new problem in the foundations of chaos theory. Specifically, he argues that the standard ways of justifying idealizations in mathematical models fail when it comes to the infinite intricacy found in strange attractors. I argue that Smith's analysis undermines much of the explanatory power of chaos theory. A better approach is developed by drawing analogies from the models found in continuum mechanics.

The scientific study of chaotic dynamics, popularly known as chaos theory, has been described by several writers as a revolution in the sense of Kuhn. I provide a definition of chaos theory and offer a brief description of this field of research. I then take up the question of whether or not chaos theory should be described as "revolutionary," in light of the fact that no well-developed science of nonlinear dynamics preceded it. In some respects, chaos theory may be fruitfully described as an "immature science," and the semantic view of theories helps to bring out some of its important features. Many aspects of this emerging field make it most appropriate to consider it a new style of scientific reasoning, analogous to statistical thinking as interpreted by Ian Hacking.

Can physics explain the difference between past and future? The laws of physics seem to be time-symmetric. If they allow a process with one temporal orientation, they allow it in reverse. Yet many ordinary pro– cesses seem to be irreversible. Ilya Prigogine calls this the time paradox, and argues that the solution lies in chaos theory, and related methods pioneered by himself and his Brussells colleagues—a radical alternative, he thinks, to a tradition dating from Boltzmann.

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.