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

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 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 in papers
of theirs and in 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 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.