From Frege to Gödel

The outstanding quality of the translations and introductions still make this source book the most important reference for the history of mathematical logic. -- Paolo Mancosu, University of California, Berkeley Meticulously edited, with excellent translations and helpful introductory notes, From Frege to Godel is an indispensable volume for anyone interested in the development of modern logic and its philosophical impact. -- Warren Goldfarb, Harvard University If there is one book that every philosopher interested in the history of logic should own, not to mention all the philosophers who pretend they know something about the history of logic, From Frege to Godel is that book. -- Hilary Putnam, Harvard University From Frege to Godel lays out before our eyes the turbulent panorama in which modern logic came to be. -- W. D. Hart, University of Illinois at Chicago From Frege to Godel is the single most important collection of original papers from the development of mathematical logic-an invaluable source for all students of the subject. -- Michael Friedman, University of Indiana A Bible for historians of logic and computer science, this invaluable collection will profit anyone interested in the interplay between mathematics and philosophy in the early decades of the twentieth century. It provides a unique and comprehensive way to appreciate how modern mathematical logic unfolded in the hands of its greatest founding practitioners. -- Juliet Floyd, Boston University Year in, year out, I recommend this book enthusiastically to students and colleagues for sources in the history and philosophy of modern logic and the foundations of mathematics; I use my own copy so much, it is falling apart. -- Solomon Feferman, Stanford University For more than three decades this outstanding collection has been the authoritative source of basic texts in mathematical logic in the English language; it remains without peer to this day. -- Michael Detlefson, University of Notre Dame Jean van Heijenoort's Source Book in Mathematical Logic offers a judicious selection of articles, lectures and correspondence on mathematical logic and the foundations of mathematics, covering the whole of the single most fertile period in the history of logic, namely from 1879 (the year of Frege's epochmaking discovery/invention of modern mathematical logic) to 1931 (the year of Godel's epoch-ending incompleteness theorem). All the translations are impeccable. Each piece is introduced by an expository article and additionally furnished with a battery of supplementary technical, historical, and philosophical comments in the form of additional footnotes. The collection as a whole allows one to relive each of the crucial steps in this formative period in the history of logic, from Frege's introduction of the Begriffsschrift, to the discovery of Russell's paradox (including Frege's heroic and heart-breaking letter of congratulation to Russell(, the development of axiomatic set theory, the program of Russell and Whitehead's Principia Mathematica, Brouwer's intuitionism, Hilbert's proof theory, to the limitative theorems of Skolem and Godel, to mention only a few of the highlights. Anyone with a serious interest in the history or philosophy of logic will want to own this volume. -- James Conant, University of Chicago

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.

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 König 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 Löwenheim’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 Gödel, 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.