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This volume commemorates the work of Alan Turing, who not only introduced the most persuasive and influential concept of a machine model of effective computability but also anticipated in his work contemporary debates about the extent and limitations of mechanistic explanations of nature. Turing's paper "On Computable Numbers, With an Application to the Entscheidungsproblem" appeared in 1937. It contained Turing's thesis that every "effective" computation can be programmed on a Turing machine. Furthermore it contained the unsolvability of both the halting problem and the decision problem for first-order logic, and it presented the invention of the universal Turing machine. The publication of this paper is acknowledged as a landmark of the computer age. Part I of this volume explores the historical aspect with essays on the background, on Turing's work, and subsequent developments. Part II contains an extensive series of essays on the influence and applications of these ideas in mathematics, philosophy, computer science, artificial intelligence, and physics. The book will interest a wide range of readers in these fields, in addition to historians of science and ideas.

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