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Mathematics --- Logic, Symbolic and mathematical --- Philosophy --- Gödel, Kurt --- Gkentel, Kourt --- גדל --- philosophy

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The collected works of Kurt Gödel is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy.

Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Gödel, Kurt

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Kurt Gödel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently 'undecidable.' His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Gödel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the text will appeal to mathematicians, philosophers, and computer scientists.

Gödel's theorem. --- Gödel's theorem. --- Gödel, Kurt. --- Gödel's incompleteness theorem --- Undecidable theories --- Arithmetic --- Completeness theorem --- Incompleteness theorems --- Logic, Symbolic and mathematical --- Number theory --- Decidability (Mathematical logic) --- Foundations --- Gkentel, Kourt --- גדל

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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.

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This volume tackles Gödel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained. The author analyses the historical and systematic aspects of that project, and then evaluates it, with an emphasis on the second stage. The book is organised around Gödel's use of Leibniz, Husserl and Brouwer. Far from considering past philosophers irrelevant to actual systematic concerns, Gödel embraced the use of historical authors to frame his own philosophical perspective. The philosophies of Leibniz and Husserl define his project, while Brouwer's intuitionism is its principal foil: the close affinities between phenomenology and intuitionism set the bar for Gödel's attempt to go far beyond intuitionism. The four central essays are `Monads and sets', `On the philosophical development of Kurt Gödel', `Gödel and intuitionism', and `Construction and constitution in mathematics'. The first analyses and criticises Gödel's attempt to justify, by an argument from analogy with the monadology, the reflection principle in set theory. It also provides further support for Gödel's idea that the monadology needs to be reconstructed phenomenologically, by showing that the unsupplemented monadology is not able to found mathematics directly. The second studies Gödel's reading of Husserl, its relation to Leibniz' monadology, and its influence on his publishe d writings. The third discusses how on various occasions Brouwer's intuitionism actually inspired Gödel's work, in particular the Dialectica Interpretation. The fourth addresses the question whether classical mathematics admits of the phenomenological foundation that Gödel envisaged, and concludes that it does not. The remaining essays provide further context.  The essays collected here were written and published over the last decade. Notes have been added to record further thoughts, changes of mind, connections between the essays, and updates of references.

Philosophy. --- Phenomenology. --- Mathematical Logic and Foundations. --- Philosophy of Science. --- Philosophy (General). --- Science --- Logic, Symbolic and mathematical. --- Phénoménologie --- Sciences --- Logique symbolique et mathématique --- Philosophie --- Science_xPhilosophy. --- Philosophy & Religion --- Philosophy --- Mathematics --- Gödel, Kurt --- Logic of mathematics --- Mathematics, Logic of --- Gkentel, Kourt --- גדל --- Philosophy and science. --- Mathematical logic. --- Phenomenology . --- Normal science --- Philosophy of science --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Philosophy, Modern --- Science and philosophy