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From Frege to Goedel: A Source Book in Mathematical Logic, 1879-1931 (Source Books in the History of the Sciences)
 
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From Frege to Goedel: A Source Book in Mathematical Logic, 1879-1931 (Source Books in the History of the Sciences) [ペーパーバック]

Jean van Heijenoort

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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 Knig 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 Lwenheim'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 Gdel, 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.

レビュー

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 Gdel is an indispensable volume for anyone interested in the development of modern logic and its philosophical impact. (Warren Goldfarb, Harvard University)

It is difficult to describe this book without praising it...[From Frege to Gdel] 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)

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 Gdel is that book. (Hilary Putnam, Harvard University)

From Frege to Gdel 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 Gdel 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 Gdel'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 Gdel, 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)

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Amazon.com: 5つ星のうち 4.8  4 件のカスタマーレビュー
18 人中、17人の方が、「このレビューが参考になった」と投票しています。
5つ星のうち 5.0 Essential reference in the history of logic and computing 2002/12/13
投稿者 Keith Douglas - (Amazon.com)
形式:ペーパーバック
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!
5 人中、5人の方が、「このレビューが参考になった」と投票しています。
5つ星のうち 5.0 A classic 2007/1/10
投稿者 William F. Scott - (Amazon.com)
形式:ペーパーバック
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.
5 人中、5人の方が、「このレビューが参考になった」と投票しています。
5つ星のうち 5.0 Within the reach of determined general readers 2006/1/20
投稿者 Maltese Falcon - (Amazon.com)
形式:ペーパーバック
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.
5つ星のうち 4.0 Eye-opening! 2014/9/15
投稿者 Loren Cobb - (Amazon.com)
形式:ペーパーバック|Amazonで購入
As a universal principle in mathematics, it helps the understanding of any topic to go back to the original papers. Reading these, one learns what the original problems were. These are often quite different from the way the topics are presented by modern specialists. This book is no exception: I learned a lot from it. Most particularly, my appreciation for Gottlob Frege has risen dramatically.
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