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Axiomatic Set Theory
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L’« Homme » ou la « structure », la « philosophie du sujet » ou la « philosophie du concept » : ces oppositions balisées dans le cadre de la « querelle de l’humanisme » ont la dent dure. Elles contribuent à surdéterminer la manière dont nous héritons, aujourd’hui encore, de la vie intellectuelle des années soixante. Ce livre se situe délibérément après cette querelle : à rebours des polémiques convenues et des dialogues de sourds, il propose une reconstruction dialogique du problème de la pratique et de son primat supposé sur la théorie, comme enjeu commun à trois auteurs réputés incompatibles : Althusser, Foucault et Sartre. Privilégiant le caractère intempestif des thèses à la systématicité des œuvres, l’ouvrage suit le fil conducteur des rapports entre pratique et structure, prenant la forme d’une « théorie des ensembles pratiques ». Le dialogue ainsi reconstruit accorde une importance toute particulière à la critique par Althusser des philosophies de la praxis constituante – parmi lesquelles la Critique de la raison dialectique de Sartre occupe une place majeure – au profit d’une analyse structurale des pratiques constituées. Ce geste althussérien a un coût, qui consiste à écarter l’ancrage historique et empirique des pratiques au profit d’une théorie de l’histoire comme « procès sans sujet ». Foucault et Sartre se démarquent nettement du traitement althussérien de l’intelligibilité des pratiques. Il s’agit pour eux de sonder l’intelligibilité des pratiques à même le concret : celui des archives de pratiques passées chez Foucault, celui de la dialectique comme logique de l’action en cours chez Sartre. Contre l’idée galvaudée d’un Sartre vieillissant parmi ses contemporains, s’ouvre alors la possibilité d’un véritable dialogue entre Foucault, Sartre, et les sciences sociales sur la question d’une histoire politique de la vérité, qui contribue à remanier en profondeur les rapports entre théorie et pratique.
Philosophy --- History --- philosophie politique --- pratique --- structure --- philosophie française du XXe siècle --- théorie des ensembles pratiques --- critique de la raison dialectique --- praxis --- querelle de l’humanisme
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This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume 1 includes formal proof techniques, a section on applications of compactness (including nonstandard analysis), a generous dose of computability and its relation to the incompleteness phenomenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen theorem.
Mathematische Logik --- MENGENLEHRE (MATHEMATIK) --- LEHRBÜCHER (DOKUMENTENTYP) --- MATHEMATICAL LOGIC --- logique mathématique --- THÉORIE DES ENSEMBLES (MATHÉMATIQUES) --- SET THEORY (MATHEMATICS) --- TEXTBOOKS (DOCUMENT TYPE) --- MANUELS POUR L'ENSEIGNEMENT (TYPE DE DOCUMENT) --- Mathematische Logik. --- MENGENLEHRE (MATHEMATIK). --- LEHRBÜCHER (DOKUMENTENTYP). --- MATHEMATICAL LOGIC. --- logique mathématique. --- THÉORIE DES ENSEMBLES (MATHÉMATIQUES). --- SET THEORY (MATHEMATICS). --- TEXTBOOKS (DOCUMENT TYPE). --- MANUELS POUR L'ENSEIGNEMENT (TYPE DE DOCUMENT). --- Logique mathématique. --- Logic, Symbolic and mathematical. --- Set theory. --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Logic, Symbolic and mathematical --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Logic, symbolic and mathematical
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Provability, Computability and Reflection
Set theory. --- Descriptive set theory. --- Set theory --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- Descriptive set theory --- Théorie des ensembles. --- Théorie des ensembles --- Théorie descriptive des ensembles --- ELSEVIER-B EPUB-LIV-FT
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Provability, Computability and Reflection
Mathematical logic --- Bernays, P. --- Bernays, Paul, --- Bernays, Paul --- Axiomatic set theory --- Théorie axiomatique des ensembles --- ELSEVIER-B EPUB-LIV-FT --- Axiomatic set theory. --- #WWIS:ALTO --- 510.22 --- 510.22 Set theory. Set theoretic approach. Theory of order types, of ordinal and cardinal numbers --- Set theory. Set theoretic approach. Theory of order types, of ordinal and cardinal numbers --- Axioms --- Logic, Symbolic and mathematical --- Set theory --- Théorie des ensembles --- Bernays, Paul, - 1888-1977
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Les notions d'ordre, de classement, de rangement sont présentés dans de multiples activités et situations humaines. La formalisation mathématique de ces notions a permis d'abord le grand développement de la théorie des treillis, puis celui de structures ordonnées plus générales, notamment celles relevant des mathématiques discrètes. Les buts principaux de cet ouvrage qui comble un vide sont donc de: - donner les concepts et résultats fondamentaux sur les ensembles ordonnés finis, - présenter leurs usages dans des domaines variés (de la RO ou l’IA à la micro-économie), - signaler un certain nombre de résultats et de recherches en cours. Le lecteur sera ainsi à même de trouver tout ce qu'il a besoin de connaître sur ces structures sans devoir le rechercher dans de multiples revues relevant de disciplines variées.
Ordered sets. --- Computer science --- Knowledge representation (Information theory) --- Operations research. --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Mathematics. --- Representation of knowledge (Information theory) --- Artificial intelligence --- Information theory --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Sets, Ordered --- Set theory --- Mathematics --- Algebra. --- Order, Lattices, Ordered Algebraic Structures. --- Game Theory, Economics, Social and Behav. Sciences. --- Operations Research, Management Science. --- Math --- Science --- Mathematical analysis --- Ordered algebraic structures. --- Game theory. --- Management science. --- Games, Theory of --- Theory of games --- Mathematical models --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra --- Ensembles ordonnés --- Théorie des ensembles
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Provability, Computability and Reflection
Mathematical logic --- Mathematics --- Set theory. --- Philosophy. --- Set theory --- #WWIS:ALTO --- 510.22 --- Logic of mathematics --- Mathematics, Logic of --- 510.22 Set theory. Set theoretic approach. Theory of order types, of ordinal and cardinal numbers --- Set theory. Set theoretic approach. Theory of order types, of ordinal and cardinal numbers --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Philosophy --- Théorie des ensembles. --- Logic, Symbolic and mathematical -- Periodicals. --- Logic, Symbolic and mathematical. --- Mathematics -- Philosophy. --- Théorie des ensembles --- Mathématiques --- Philosophie --- EPUB-LIV-FT ELSEVIER-B
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In 1965 Lotfi Zadeh, a professor of electrical engineering at the University of California in Berkeley, published the first of his papers on his new Fuzzy Set Theory. Since the 1980s this mathematical theory of "unsharp amounts" has been applied in many different fields with great success. The word "fuzzy" has also become very well-known among non-scientists thanks to extensive advertising campaigns for fuzzy-controlled household appliances and to their prominent presence in the media, first in Japan and then in other countries. On the other hand, the story of how Fuzzy Set Theory and its earliest applications originated remains largely unknown. In this book, the history of Fuzzy Set Theory and the ways it was first used are incorporated into the history of 20th century science and technology. Influences from philosophy, system theory and cybernetics stemming from the earliest part of the 20th century are considered alongside those of communication and control theory from mid-century. Today, Fuzzy Set Theory is the core discipline of "soft computing," and provides new impetus for research in the field of Artificial Intelligence.
Fuzzy sets. --- Set theory. --- Ensembles flous --- Théorie des ensembles --- Fuzzy sets --- Set theory --- Algebra --- Applied Mathematics --- Civil Engineering --- Engineering & Applied Sciences --- Mathematics --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Sets, Fuzzy --- Computer science. --- Artificial intelligence. --- Computer-aided engineering. --- Applied mathematics. --- Engineering mathematics. --- Computer Science. --- Computer-Aided Engineering (CAD, CAE) and Design. --- Appl.Mathematics/Computational Methods of Engineering. --- Artificial Intelligence (incl. Robotics). --- Logic, Symbolic and mathematical --- Fuzzy mathematics --- Computer aided design. --- Mathematical and Computational Engineering. --- Artificial Intelligence. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Engineering --- Engineering analysis --- Mathematical analysis --- CAD (Computer-aided design) --- Computer-assisted design --- Computer-aided engineering --- Design --- CAE --- Data processing
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Provability, Computability and Reflection
Mathematical logic --- Algebraic logic --- Logique algébrique --- Algebra, Boolean --- Boole, Algèbre de --- Cylindric algebras --- Algèbres cylindriques. --- Set theory. --- Cardinal numbers. --- Arithmetic, Cardinal --- Cardinal arithmetic --- Cardinals (Numbers) --- Numbers, Cardinal --- Set theory --- Transfinite numbers --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- 510.22 --- 510.22 Set theory. Set theoretic approach. Theory of order types, of ordinal and cardinal numbers --- Set theory. Set theoretic approach. Theory of order types, of ordinal and cardinal numbers --- 510.64 --- 510.64 Non-classical, formal systems of logic. Modal logic. Multiple-value logics. Syllogistics. Inductive logic. Probabilistic logic --- Non-classical, formal systems of logic. Modal logic. Multiple-value logics. Syllogistics. Inductive logic. Probabilistic logic --- Recursion theory --- 510.6 --- 510.6 Mathematical logic --- Congresses --- Axiomatic set theory --- Axioms --- Congresses. --- Proof theory --- Logique algébrique --- Théorie de la preuve --- ELSEVIER-B EPUB-LIV-FT --- Cardinal numbers --- Théorie des ensembles --- Nombres cardinaux --- Théorie de la récursivité --- Congrès --- Théorie axiomatique des ensembles --- Axiomatic set theory. --- Logique mathématique. --- Récursivité, Théorie de la. --- Recursion theory - Congresses --- Numbers, cardinals --- Théorie des ensembles --- Logic, Symbolic and mathematical -- Periodicals. --- Logic, Symbolic and mathematical. --- Recursion theory - Congresses. --- Recursion theory -- Congresses. --- Physical Sciences & Mathematics --- Mathematical Theory --- Algebraic logic. --- Proof theory.
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Provability, Computability and Reflection
Mathematical logic --- Recursion theory --- Théorie de la récursivité --- Congresses --- Congrès --- ELSEVIER-B EPUB-LIV-FT --- Congresses. --- Recursive Functions --- Logic, Symbolic and mathematical --- Proof theory. --- Mathematics --- Abstract structures --- Inductive definability. --- 510.6 --- 510.67 --- Logique mathématique --- Récursivité, Théorie de la --- Mathématiques --- 510.67 Theory of models --- Theory of models --- 510.6 Mathematical logic --- Logique mathématique. --- Récursivité, Théorie de la. --- Induction (mathématiques) --- Logic, Symbolic and mathematical. --- Recursion theory. --- Induction (Logic) --- Recursive functions. --- Induction (Mathematics) --- Proof theory --- Théorie de la preuve --- Recursive functions --- Fonctions récursives --- Induction (Mathématiques) --- Mathematical induction --- Functions, Recursive --- Algorithms --- Arithmetic --- Number theory --- Decidability (Mathematical logic) --- Foundations --- 510.22 --- 510.22 Set theory. Set theoretic approach. Theory of order types, of ordinal and cardinal numbers --- Set theory. Set theoretic approach. Theory of order types, of ordinal and cardinal numbers --- Logique mathematique --- Theorie de la preuve --- Théorie des modèles --- Set theory --- Théorie des ensembles --- Cardinal numbers. --- Nombres cardinaux --- Logique mathématique --- Philosophy --- Philosophy & Religion --- Logic
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