- Paperback: 672 pages
- Publisher: Harvard University Press; New edition edition (1 July 1990)
- Language English
- ISBN-10: 0674324498
- ISBN-13: 978-0674324497
- Product Dimensions: 25.1 x 16.5 x 4.4 cm
- Amazon Bestsellers Rank: 1,035,808 in Books (See Top 100 in Books)
- See Complete Table of Contents
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Review
It is difficult to describe this book without praising it...[From Frege to Godel] 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 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
Product Description
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 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 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.
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3 reviews
15 of 16 people found the following review helpful
Essential reference in the history of logic and computing
12 Dec 2002
Format:Paperback
The second part of my review title may shock some, but the excellent collection of papers that Van Heijenoort has edited (and in many cases translated!) is also an excellent reference in the history of computing. Everyone appreciates that mathematical logic gave rise to computer science; the papers in this collection from Hilbert, Herbrand, Gödel, and others will show why.
If your interest is instead the history of logic, all the classics in the range specified by the work's title are here, complete with their own ideosyncratic notation. van Heijenoort's wonderful introductions to each piece will interelate the works, provide references to other literature and situate everything in a wonderful intellectual climate.
Be warned, however, that the foundational papers in this still growing field continue for another 15 years or so; these are reprinted in Davis' (alas, out of print) anthology _The Undecidable_.
This collection will keep you busy and wet your appetite for a sequel!
3 of 3 people found the following review helpful
A classic
9 Jan 2007
Format:Paperback
This book contains translations of original articles from this period. In one case, Herbrand's theorem, there are extensive notes to repair a mistake; but most are simply presented as is, with short introductions that give some historical context. It is really wonderful to see the ideas develop. Fortunately, this book has recently been reprinted. Library copies are falling apart.
3 of 3 people found the following review helpful
Within the reach of determined general readers
20 Jan 2006
Format:Paperback
This excellent collection has introductions which help immensely. With only a math major from the 50's and no advanced degree I was still able to develop my own fairly rigorous single page synopsis of Godel's theorems.
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