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Logicians --- Logiciens --- Biography --- Biographie --- Gödel, Kurt --- 160.1 --- -Logicians --- -#TELE:SISTA --- Philosophers --- Wezen en doel van de logica. Filosofie van de logica --- Godel, Kurt --- Gkentel, Kourt --- גדל --- Biography. --- 160.1 Wezen en doel van de logica. Filosofie van de logica --- Gödel, Kurt --- #TELE:SISTA --- Gödel, 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

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In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.

Gödel numbers. --- Logic, Symbolic and mathematical. --- Gödel, Kurt --- Gödel numbers --- Gödel's theorem. --- Logique symbolique er mathematique --- Gödel numbers --- Logic, Symbolic and mathematical --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Numbers, Gödel --- Number theory --- Gödel, Kurt. --- Gkentel, Kourt --- גדל --- Logique mathématique --- Gödel, Théorème de --- Incomplétude, Théorèmes d' --- Gödel's theorem --- Incompleteness theorems --- Logic, symbolic and mathematical --- Decidability (Mathematical logic) --- Gödel, Théorème de --- Gödel numbers. --- Gödel, Kurt Friedrich, --- Logique mathématique. --- Gödel, Théorème de. --- Incomplétude, Théorèmes d'. --- Arts and Humanities --- Philosophy --- Logique mathématique. --- Gödel, Théorème de. --- Incomplétude, Théorèmes d'. --- Gödel's theorem --- Gödel, Kurt