Philosophical aspects of chaos theory

In the past 25 years, scientists working in a variety of fields have developed mathematical models for natural phenomena with two features that seem highly incongruous: they consist of only a few simple equations, yet the solutions to these equations display extremely complex and even unpredictable behavior. The analysis of these models and the investigation of similar behavior in actual experimental settings has been termed the study of chaos. The new conceptual approaches and experimental techniques used in this research raise philosophical questions which challenge current notions about impossibility, determinism and understanding. These questions form the focus of my dissertation.;Chaotic systems are characterized by sensitive dependence on initial conditions, which means that even the smallest error in specifying the initial state of the system will grow rapidly enough to make the future state of the system impossible to predict. This impossibility is not due to any fundamental change in our theories, but it is also not due to mere practical difficulty. I contend that the limitation posed by chaos theory impels us to reassess the dichotomy between "impossibility in theory" and "impossibility in practice".;The unpredictability of chaotic systems presents a challenge to the doctrine of scientific determinism, especially where determinism is taken to include the total predictability of the physical universe. But even when considering determinism in the more limited sense proposed by John Earman, chaos theory raises serious doubts about the uniqueness of the world's course of development.;Chaos theory invites us to reconsider our notions of orderliness and intelligibility by providing scientific understanding which does not rely on exact prediction, reductive analysis or deductive rigor. The simplified mathematical systems studied offer instead a qualitative understanding of how unpredictability and ordered patterns arise.;One final philosophical issue is, Why did chaotic systems take so long to be investigated? Theoretical and experimental precursors took many decades to be fully developed. Computational limitations, institutionalized training which neglected nonlinear phenomena, and a social and cultural interest in the exploitation of predictable natural processes were all responsible for this "delay" in scientists' understanding of disorder in the natural world.