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In 'Impossibility', John D. Barrow - one of our most elegant and accomplished science writers - argues convincingly that there are limits to human discovery, that there are things that are ultimately unknowable, undoable, or unreachable. Barrow first examines the limits of the human mind: our brain evolved to meet the demands of our immediate environment, and much that lies outside this small circle may also lie outside our understanding. He investigates practical impossibilities, such as those imposed by complexity, uncomputability, or the finiteness of time, space, and resources. Is the universe finite or infinite? Can information be transmitted faster than the speed of light? The book also examines deeper theoretical restrictions on our ability to know, including Gödel's theorem, which proved that there were things that could not be proved.

Science --- Limit (Logic) --- Gödel's theorem. --- Gèodel's theorem --- Sciences - General --- Physical Sciences & Mathematics --- Normal science --- Philosophy of science --- Logic --- Gödel's incompleteness theorem --- Undecidable theories --- Arithmetic --- Completeness theorem --- Incompleteness theorems --- Logic, Symbolic and mathematical --- Number theory --- Decidability (Mathematical logic) --- Philosophy. --- Philosophy --- Foundations --- Go ̈del's theorem. --- Limit (Logic). --- Science. --- Science - Philosophy --- Godel's theorem --- Gödel's theorem. --- Godel's theorem.

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Gödel's theorem. --- Teorema de Gödel --- Proposicions indecidibles --- Teoria de la decidibilidad --- Lògica matemàtica --- Teoria de nombres --- Decidibilitat (Lògica matemàtica) --- Gödel's incompleteness theorem --- Undecidable theories --- Arithmetic --- Completeness theorem --- Incompleteness theorems --- Logic, Symbolic and mathematical --- Number theory --- Decidability (Mathematical logic) --- Foundations --- Logic, Symbolic and mathematical. --- Intuitionistic mathematics. --- Constructive mathematics --- Mathematics --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism

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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.