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Le présent volume regroupe les textes de conférences données lors de la rencontre « Logique mathémathique, Informatique et Philosophie », organisé en avril 2003 à l’université Paris 1 Panthéon-Sorbonne sous la direction de Jean-Baptiste Joinet. Ce colloque réunissait les principaux acteurs du collectif interdisciplinaire « Logique et Interaction : vers une Géométrie de la Cognition » (LIGC) et divers universitaires d’autres horizons. La première partie, intitulée La logique à la croisée des chemins, rassemble des réflexions sur les évolutions récentes de la logique et les aspects fondamentaux de la mathématisation des champs scientifiques spécifiques (physique, biologie). Ces contributions (J.-Y. Girard, J.-B. Joinet et G. Longo, T. Paul) visent à dégager un nouveau statut épistémologique pour la logique et les mathématiques, et à tirer les leçons philosophiques de ces évolutions quant à la rationalité scientifique et l’intelligibilité de la nature. Dans la seconde partie, intitulée Questions sémantiques : réalisme, règles et vérité, les contributeurs (S. Tronçon, P. Dehornoy, G. Dowek, P. Livet, D. Bonnay) revisitent les grandes notions sémantiques traditionnelles sous l’angle des évolutions récentes de la logique dans son dialogue avec l’informatique fondamentale.
Philosophy --- logique mathématique --- temps --- sciences de la nature --- mécanique quantique
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Philosophy --- Philosophy & Religion --- Logic --- 510.6 --- Logique mathématique --- 510.6 Mathematical logic --- Mathematical logic
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Logic, Methodology and Philosophy of Science VII
Science --- Mathematical logic --- Logic, Symbolic and mathematical --- Philosophy --- Methodology --- Logique mathématique --- Philosophie des sciences
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Provability, Computability and Reflection
Mathematical logic --- Logique mathématique --- Intuitionnisme --- Logic, Symbolic and mathematical --- Intuition --- Logique mathématique. --- Logique symbolique et mathématique --- Congresses --- Congrès --- EPUB-LIV-FT ELSEVIER-B --- Logic, Symbolic and mathematical -- Periodicals. --- Logic, Symbolic and mathematical. --- 510.24 --- 510.24 Intuitionism--(mathematical aspects) --- Intuitionism--(mathematical aspects) --- Logique mathematique --- Theorie de la preuve --- Intuitionistic mathematics
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Semantics (Philosophy) --- Sémantique (Philosophie) --- Congresses --- Congrès --- Sémantique (philosophie) --- -801.56 --- Syntaxis. Semantiek --- 801.56 Syntaxis. Semantiek --- Sémantique (Philosophie) --- Congrès --- 801.56 --- Language and languages --- Logique mathématique
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Provability, Computability and Reflection
Logic, Symbolic and mathematical --- 510.6 --- 510.6 Mathematical logic --- Mathematical logic --- Logique symbolique et mathématique --- Congresses --- Congrès --- ELSEVIER-B EPUB-LIV-FT --- Logique mathématique
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Provability, Computability and Reflection
Logic, Symbolic and mathematical --- Mathematics --- Math --- Science --- Logique symbolique et mathématique --- Congresses --- Congrès --- ELSEVIER-B EPUB-LIV-FT --- Congresses. --- Logique mathématique --- Logic, Symbolic and mathematical - Congresses
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Logic Colloquium '80
Mathematical logic --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Logique mathématique
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Degrees of unsolvability
Mathematical logic --- Récursivité, Théorie de la --- Logique mathématique. --- Logic, Symbolic and mathematical --- Recursion theory --- Recursive functions. --- Logic, Symbolic and mathematical. --- Récursivité, Théorie de la --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Functions, Recursive --- Algorithms --- Arithmetic --- Number theory --- Decidability (Mathematical logic) --- Foundations --- Logique mathematique --- Calculabilite
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Kurt Gödel (1906-1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Gödel's centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Gödel's writings are among the topics covered. Several chapters discuss his intellectual development and his relation to predecessors and contemporaries such as Hilbert, Carnap, and Herbrand. Others consider his views on justification in set theory in light of more recent work and contemporary echoes of his incompleteness theorems and the concept of constructible sets.
Théorie de la démonstration --- Logique mathématique --- Mathématiques --- Philosophie --- Gödel, Kurt, --- Logic, symbolic and mathematical --- Logic, Symbolic and mathematical. --- Théorie de la démonstration. --- Logique mathématique. --- Philosophie. --- Logic, Symbolic and mathematical --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Mathematics. --- Math --- Science --- Gödel, Kurt --- Mathematical Sciences --- General and Others
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