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First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.
This book—the culmination of forty years of friendship between J. Hillis Miller and Jacques Derrida, during which Miller also closely followed all Derrida’s writings and seminars—is “for Derrida” in two senses. It is “for him,” dedicated to his memory. The chapters also speak, in acts of reading, as advocates for Derrida’s work. They focus especially on Derrida’s late work, including passages from the last, as yet unpublished, seminars. The chapters are “partial to Derrida,” on his side, taking his part, gratefully submitting themselves to the demand made by Derrida’s writings to be read—slowly, carefully, faithfully, with close attention to semantic detail. The chapters do not progress forward to tell a sequential story. They are, rather, a series of perspectives on the heterogeneity of Derrida’s work, or forays into that heterogeneity. The chief goal has been, to borrow a phrase from Wallace Stevens, “plainly to propound” what Derrida says. The book aims, above all, to render Derrida’s writings justice. It should be remembered, however, that, according to Derrida himself, every rendering of justice is also a transformative interpretation. A book like this one is not a substitute for reading Derrida for oneself. It is to be hoped that it will encourage readers to do just that.
This well-known book by the famed logician consists of three treatises: A General Method in Proofs of Undecidability, Undecidability and Essential Undecidability in Mathematics, and Undecidability of the Elementary Theory of Groups. 1953 edition.
Limits of Computation: An Introduction to the Undecidable and the Intractable offers a gentle introduction to the theory of computational complexity. It explains the difficulties of computation, addressing problems that have no algorithm at all and problems that cannot be solved efficiently. The book enables readers to understand:What does it mean
Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life.This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences.
Programming Legend Charles Petzold unlocks the secrets of the extraordinary and prescient 1936 paper by Alan M. Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be computable, creating the field of computability theory in the process, a foundation of present-day computer programming. The book expands Turing’s original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing’s statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others. Interwoven into the narrative are the highlights of Turing’s own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of "gross indecency," and his early death by apparent suicide at the age of 41.
The revolutions that Gregory Chaitin brought within the fields of science are well known. From his discovery of algorithmic information complexity to his work on Gödel's theorem, he has contributed deeply and expansively to such diverse fields. This book attempts to bring together a collection of articles written by his colleagues, collaborators and friends to celebrate his work in a festschrift. It encompasses various aspects of the scientific work that Chaitin has accomplished over the years. Topics range from philosophy to biology, from foundations of mathematics to physics, from logic to computer science, and all other areas Chaitin has worked on. It also includes sketches of his personality with the help of biographical accounts in some unconventional articles that will provide a rare glimpse into the personal life and nature of Chaitin. Compared to the other books that exist along a similar vein, this book stands out primarily due to its highly interdisciplinary nature and its scope that will attract readers into Chaitin's world
"A valuable collection both for original source material as well as historical formulations of current problems." — The Review of Metaphysics "Much more than a mere collection of papers. A valuable addition to the literature." — Mathematics of Computation An anthology of fundamental papers on undecidability and unsolvability by major figures in the field , this classic reference is ideally suited as a text for graduate and undergraduate courses in logic, philosophy, and foundations of mathematics. It is also appropriate for self-study. The text opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by Godel, Church, Turing, and Post single out the class of recursive functions as computable by finite algorithms. Additional papers by Church, Turing, and Post cover unsolvable problems from the theory of abstract computing machines, mathematical logic, and algebra, and material by Kleene and Post includes initiation of the classification theory of unsolvable problems. Supplementary items include corrections, emendations, and added commentaries by Godel, Church, and Kleene for this volume's original publication, along with a helpful commentary by the editor.
Badiou is widely considered to be France's most important and exciting contemporary thinker. Much of Badiou's earlier work (including Being and Event) can only be fully understood with a clear grasp of Theory of the Subject, one of his most important works.
For more than forty years Jacques Derrida has attempted to unsettle and disturb the presumptions underlying many of our most fundamental philosophical, political, and ethical conventions. In The Philosophy of Derrida, Mark Dooley examines Derrida's large body of work to provide an overview of his core philosophical ideas and a balanced appraisal of their lasting impact. One of the author's primary aims is to make accessible Derrida's writings by discussing them in a vernacular that renders them less opaque and nebulous. Derrida's unusual writing style, which mixes literary and philosophical vocabularies, is shown to have hindered their interpretation and translation. Dooley situates Derrida squarely in the tradition of historicist, hermeneutic and linguistic thought, and Derrida's objectives and those of "deconstruction" are rendered considerably more convincing. While Derrida's works are ostensibly diverse, Dooley reveals an underlying cohesion to his writings. From his early work on Husserl, Hegel and de Saussure, to his most recent writings on justice, hospitality and cosmopolitanism, Derrida is shown to have been grappling with the vexed question of national, cultural and personal identity and asking to what extent the notion of a "pure" identity has any real efficacy. Viewed from this perspective Derrida appears less as a wanton iconoclast, for whom deconstruction equals destruction, but as a sincere and sensitive writer who encourages us to shed light on out historical constructions so as to reveal that there is much about ourselves that we do not know.