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Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy. From Dedekind to Godel: Essays on the Development of the Foundations of Mathematics illustrates the much greater variety of the actual developments in the foundations during the period covered. The viewpoints that serve this purpose included the foundational ideas of working mathematicians, such as Kronecker, Dedekind, Borel and the early Hilbert, and the development of notions like model and modelling, arbitrary function, completeness, and non-Archimedean structures. The philosophers discussed include not only the household names in logic, but also Husserl, Wittgenstein and Ramsay. Needless to say, such logically-oriented thinkers as Frege, Russell and Godel are not entirely neglected, either. Everybody interested in the philosophy and/or history of mathematics will find this book interesting, giving frequently novel insights.
Mathematics --- -Math --- Science --- Foundations --- Frege, Gottlob (1848-1925) --- Gödel, Kurt F., --- --Mathématique --- --Mathematics --- 4434 --- -Mathematical logic --- -510.6 Mathematical logic --- 510.6 --- 510.6 Mathematical logic --- Mathematical logic --- Math --- Philosophie --- Foundations. --- Logic --- Mathématiques --- Logique --- Philosophy --- History --- Histoire --- Frege, Gottlob, --- Mathématique --- Mathematics - Foundations --- Frege, Gottlob, 1848-1925 --- Gödel, Kurt F., 1906 --- -Mathematics --- -Philosophie --- Gödel, Kurt F., 1906-
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"Among the many expositions of Godel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzen gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Godel
Mathematical logic --- Philosophy of science --- Gödel's theorem --- Gödel's theorem. --- Incompleteness theorems. --- Gödel's theorem --- Incompleteness theorems --- Gödel's incompleteness theorem --- Undecidable theories --- Arithmetic --- Completeness theorem --- Logic, Symbolic and mathematical --- Number theory --- Decidability (Mathematical logic) --- Theorems, Incompleteness --- Constructive mathematics --- Proof theory --- Foundations --- Logique mathématique --- Gödel, Kurt F., 1906 --- -Logique mathématique --- Logique mathematique --- Theorie de la preuve --- -Gödel's theorem. --- -Gödel's theorem --- Gödel, Kurt F., 1906-
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Symbolism --- Psychoanalysis and philosophy --- SYMBOLISM --- Psychoanalysis - history --- Théorème --- Logique --- Gödel, Kurt F., 1906 --- -Frege, Gottlob, 1848-1925 --- Descartes, René, 1596-1650 --- Lacan, Jacques (1901-1981) --- Symbolisme --- Sémantique (philosophie) --- Psychanalyse --- Symbolique (psychanalyse) --- Psychanalyse et philosophie --- Symbolisme (psychologie) --- Psychanalyse et linguistique --- Psychoanalysis
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Theory of knowledge --- Depth psychology --- Semantics (Philosophy) --- Symbolism --- Psychoanalysis and philosophy --- Sémantique (Philosophie) --- Symbolisme --- Psychanalyse et philosophie --- SYMBOLISM --- Psychoanalysis --- Gödel, Kurt F., --- Théorème --- --Frege, Gottlob (1848-1925) --- Logique --- --Descartes, René, --- history --- 4434 --- Symbolism. --- Philosophy and psychoanalysis --- Philosophy --- Representation, Symbolic --- Symbolic representation --- Mythology --- Emblems --- Signs and symbols --- Symbolism (Psychology) --- Symbolisms --- Symbolisms (Psychology) --- history. --- Sémantique (Philosophie) --- Intension (Philosophy) --- Logical semantics --- Semantics (Logic) --- Semeiotics --- Significs --- Syntactics --- Unified science --- Language and languages --- Logic, Symbolic and mathematical --- Logical positivism --- Meaning (Psychology) --- Philosophy, Modern --- Semiotics --- Analysis (Philosophy) --- Definition (Philosophy) --- --Frege, Gottlob, --- Gödel, Kurt F., 1906 --- -Frege, Gottlob, 1848-1925 --- Descartes, René, 1596-1650
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