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Gödel, Kurt, - 1906-1978

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Gödel, Kurt --- Gödel's theorem --- Mathematical logic --- Axioms --- Gödel, kurt (1906-1978) --- Godel's theorem

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Kurt Gödel (1906-1978) fut sans doute l'un des plus grands logiciens de l'histoire. Son théorème d'incomplétude, publié en 1931, est peut-être la proposition mathématique la plus significative du XXe siècle. Il a bouleversé les fondements des mathématiques et fait l'objet de commentaires philosophiques sans fin comme d'exploitations abusives sans nombre. Gödel ne publiera que peu pendant la cinquantaine d'années qui suivront. Mais il laissera des milliers de pages de notes philosophiques inédites. On connaissait déjà les excentricités de la vie de Gödel, qui, craignant d'être empoisonné, mourra quasiment d'inanition. Ses notes, décryptées et étudiées ici pour la première fois en français, révèlent une pensée encore plus surprenante. Elles montrent que Gödel croyait aux anges comme au diable - parmi bien d'autres étrangetés. Il tente au cours des années de constituer ces idées bizarres en système logiquement cohérent, dont l'analyse éclaire d'un jour nouveau ses découvertes mathématiques. Cette apparente " folie " d'un esprit génial pose de redoutables questions sur la nature même de la pensée logique. L'auteur de cet essai les aborde sans hésiter à y impliquer sa propre subjectivité, sous formes de courtes fictions fantasmées. Un livre aussi inquiétant que stimulant.

Logicians --- Logic, Symbolic and mathematical. --- Science --- Logiciens --- Logique symbolique et mathématique --- Sciences --- Biography. --- Philosophy --- Biographie --- Philosophie --- Gödel, Kurt. --- Gödel, Kurt, --- Logique symbolique et mathématique --- Gödel, Kurt. --- Gödel, Kurt, - 1906-1978

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Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this book is divided into three parts. Part I contains a general essay on Husserl's conception of science and logic, an essay of mathematics and transcendental phenomenology, and an essay on phenomenology and modern pure geometry. Part II is focused on Kurt Godel's interest in phenomenology. It explores Godel's ideas and also some work of Quine, Penelope Maddy and Roger Penrose. Part III deals with elementary, constructive areas of mathematics. These are areas of mathematics that are closer to their origins in simple cognitive activities and in everyday experience. This part of the book contains essays on intuitionism, Hermann Weyl, the notion of constructive proof, Poincaré and Frege.

Mathématiques intuititionnistes --- Constructive mathematics. --- Intuitionistic mathematics. --- Logic, Symbolic and mathematical. --- Mathematics --- Phenomenology. --- Philosophy. --- Phenomenology --- Logic, Symbolic and mathematical --- Intuitionistic mathematics --- Mathématiques --- Phénoménologie --- Logique symbolique et mathématique --- Philosophy --- Philosophie --- Constructive mathematics --- Philosophy, Modern --- Logic of mathematics --- Mathematics, Logic of --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Mathematics, Constructive --- Logique mathématique --- Phénoménologie --- Arts and Humanities --- Logique mathématique --- Logique --- Mathématiques --- Gödel, Kurt (1906-1978) --- Gödel, Kurt (1906-1978)

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This volume commemorates the life, work, and foundational views of Kurt Godel (1906-1978), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances, and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology, and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Godel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Godel's fundamental work in mathematics, logic, philosophy, and other disciplines for future generations of researchers

Gödel, Théorème de --- Gödel, Kurt --- Godel's theorem --- Mathematics/ Logic --- Godel, Kurt --- Gödel's theorem. --- Gödel's incompleteness theorem --- Undecidable theories --- Incompleteness theorems --- Decidability (Mathematical logic) --- Gödel's theorem --- Gödel, Théorème de --- Gödel, Kurt --- Mathematics --- 510.2 --- 510.6 --- 510.6 Mathematical logic --- Mathematical logic --- 510.2 Foundations of mathematics --- Foundations of mathematics --- Logic of mathematics --- Mathematics, Logic of --- Arithmetic --- Completeness theorem --- Logic, Symbolic and mathematical --- Number theory --- Philosophy --- Foundations --- Gödel, Kurt. --- Gkentel, Kourt --- גדל --- Mathématiques --- Philosophie --- Gödel's theorem. --- Philosophy. --- Mathematical Sciences --- General and Others --- Mathematics - Philosophy --- Gödel, Kurt (1906-1978) --- Mathématiques --- Godel's theorem. --- Godel, Kurt.