From Frege to Gödel: a source book in mathematical logic, 1879-1931

Abstract

The fundamental texts of the great classical period modern logic, some of them never before available 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 1879 of Gottlob Frege's Begriffsschrift that opened a great epoch the history of logic by presenting, full-fledged form, the propositional calculus and quantification theory. Frege's book, translated 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 Konig 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 Lowenheim's theorem, and heand 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 papers of theirs and others by Weyl, Bernays, Ackermann, and Kolmogorov. The volume concludes with papers by Herbrand and by Godel, 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 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 perspective, explains its importance, and points out difficulties interpretation. Editorial comments and footnotes are interpolated where needed, and an extensive bibliography is included.

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