From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931 (Source Books in the History of the Sciences)

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 Löwenheim's theorem. The volume concludes with papers by Herbrand and by Gödel, including the latter's famous incompleteness paper. "There can be no doubt that the book is a valuable contribution to the logical literature and that it will certainly spread the knowledge of mathematical logic and its history in the nineteenth and twentieth centuries." --Andrzej Mostowski, Synthese "It is difficult to describe this book without praising it...[From Frege to Gödel] is, in effect, the record of an important chapter in the history of thought. No serious student of logic or foundations of mathematics will want to be without it." --Review of Metaphysics The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for the first time. Modern logic, heralded by Leibniz, may be said to have been initiated by Boole, De Morgan, and Jevons, but it was the publication in 1879 of Gottlob Frege's Begriffsschrift that opened a great epoch in the history of logic by presenting, in full-fledged form, the propositional calculus and quantification theory. Frege's book, translated in its entirety, begins the present volume. The emergence of two new fields, set theory and foundations of mathematics, on the borders of logic, mathematics, and philosophy, is depicted by the texts that follow. Peano and Dedekind illustrate the trend that led to Principia Mathematica. Burali-Forti, Cantor, Russell, Richard, and Kouml;nig mark the appearance of the modern paradoxes. Hilbert, Russell, and Zermelo show various ways of overcoming these paradoxes and initiate, respectively, proof theory, the theory of types, and axiomatic set theory. Skolem generalizes Louml;wenheim's theorem, and he and Fraenkel amend Zermelo's axiomatization of set theory, while von Neumann offers a somewhat different system. The controversy between Hubert and Brouwer during the twenties is presented in papers of theirs and in others by Weyl, Bernays, Ackermann, and Kolmogorov. The volume concludes with papers by Herbrand and by Gouml;del, including the latter's famous incompleteness paper. Of the forty-five contributions here collected all but five are presented in extenso. Those not originally written in English have been translated with exemplary care and exactness; the translators are themselves mathematical logicians as well as skilled interpreters of sometimes obscure texts. Each paper is introduced by a note that sets it in perspective, explains its importance, and points out difficulties in interpretation. Editorial comments and footnotes are interpolated where needed, and an extensive bibliography is included. - Publisher