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Informationen zum Autor Jean van Heijenoort, well known in the fields of mathematical logic and foundations of mathematics, is Professor of Philosophy at Brandeis University and has taught at New York and Columbia Universities. Klappentext Gathered together in this book are the fundamental texts of the great classical period in modern logic. A complete translation of Gottlob Frege's "Begriffsschrift--which opened a great epoch in the history of logic by fully presenting propositional calculus and quantification theory--begins the volume. The texts that follow depict the emergence of set theory and foundations of mathematics, two new fields on the borders of logic, mathematics, and philosophy. Essays trace the trends that led to "Principia mathematica, the appearance of modern paradoxes, and topics including proof theory, the theory of types, axiomatic set theory, and Lowenheim's theorem. The volume concludes with papers by Herbrand and by Godel, including the latter's famous incompleteness paper. Zusammenfassung Gathered together here are the fundamental texts of the great classical period in modern logic. A complete translation of Gottlob Frege’s Begriffsschrift—which opened a great epoch in the history of logic by fully presenting propositional calculus and quantification theory—begins the volume, which concludes with papers by Herbrand and by Gödel. Inhaltsverzeichnis 1. Frege (1879). Begriffsschrift! a formula language! modeled upon that of arithmetic! for pure thought 2. Peano (1889). The principles of arithmetic! presented by a new method 3.Dedekind (1890a). Letter to Keferstein Burali-Forti (1897 and 1897a). A question on transfinite numbers and On well-ordered classes 4.Cantor (1899). Letter to Dedekind 5.Padoa (1900). Logical introduction to any deductive theory 6!Russell (1902). Letter to Frege 7.Frege (1902). Letter to Russell 8.Hilbert (1904). On the foundations of logic and arithmetic 9.Zermelo (1904). Proof that every set can be well-ordered 10.Richard (1905). The principles of mathematics and the problem of sets 11.Konig (1905a). On the foundations of set theory and the continuum problem 12.Russell (1908a). Mathematical logic as based on the theory of types 13.Zermelo (1908). A new proof of the possibility of a well-ordering 14.Zermelo (l908a). Investigations in the foundations of set theory I Whitehead and Russell (1910). Incomplete symbols: Descriptions 15.Wiener (1914). A simplification of the logic of relations 16.Lowenheim (1915). On possibilities in the calculus of relatives 17.Skolem (1920). Logico-combinatorial investigations in the satisfiability or provability of mathematical propositions: A simplified proof of a theorem by L. Lowenheim and generalizations of the 18.theorem 19.Post (1921). Introduction to a general theory of elementary propositions 20.Fraenkel (1922b). The notion "definite" and the independence of the axiom of choice 21.Skolem (1922). Some remarks on axiomatized set theory 22.Skolem (1923). The foundations of elementary arithmetic established by means of the recursive mode of thought! without the use of apparent variables ranging over infinite domains 23.Brouwer (1923b! 1954! and 1954a). On the significance of the principle of excluded middle in mathematics! especially in function theory! Addenda and corrigenda! and Further addenda and corrigenda von Neumann (1923). On the introduction of transfinite numbers Schonfinkel (1924). On the building blocks of mathematical logic filbert (1925). On the infinite von Neumann (1925). An axiomatization of set theory Kolmogorov (1925). On the principle of excluded middle Finsler (1926). Formal proofs and undecidability Brouwer (1927). On the domains of definition of functions filbert (1927). The foundations of mathematics Weyl (1927). Comments on Hilbert's second lecture on the foundations of mathematics Bernays (1927). Appendix to Hil...
