From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931 by Jean van Heijenoort (PDF)

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 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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A great historical piece on modern logic. Each paper, starting with Frege, is introduced with an historical background relative to the modern development of mathematical logic and the ideas at the core of the paper itself. Bits of correspondence such as Russell’s letter to Frege on the paradox found within Frege’s publication is a great insight inside the mathematical community at the time. It was a joy to read Hilbert and Von Neumann, and if reading what was on the mind of these two intellectual giants sparks an interest in you, this is a valuable addition to your library. One thing to note, is that the notation and symbols used on many of these papers are often archaic and not very intuitive. This is not meant to be an introduction to logic, rather, it is a time machine which shows the evolution of thinking on the matter of mathematical logic.

⭐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.

⭐Book in bad condition

⭐As promised!

⭐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!

⭐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.

⭐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.

⭐Meines Wissens ist dieses Buch konkurenzlos. Wer sich für die Entstehung und die Probleme der formalen Logik interessiert, darf sich glücklich schätzen, diese z.T. nur schwierig herbeizuschaffenden originalen Texte in englischer Übersetzung in einem umfangreichen Band versammelt zu finden. Positiv zu erwähnen ist auch die umfangreiche Bibliografie der einzelnen Autoren, denn eine wirklich objektive Auswahl der wichtigsten Grundlagentexte, liegt wohl jenseits des Möglichen. So eine Auswahl von originalen Quelltexten würde ich mir auch für andere Themen, wie z.B. die Quantenmechanik wünschen.

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