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From Frege to Godel
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Table of Contents

1. Frege (1879). Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought 2. Peano (1889). The principles of arithmetic, presented by a new method 3.Dedekind (1890a). Letter to Keferstein Burali-Forti (1897 and 1897a). A question on transfinite numbers and On well-ordered classes 4.Cantor (1899). Letter to Dedekind 5.Padoa (1900). Logical introduction to any deductive theory 6,Russell (1902). Letter to Frege 7.Frege (1902). Letter to Russell 8.Hilbert (1904). On the foundations of logic and arithmetic 9.Zermelo (1904). Proof that every set can be well-ordered 10.Richard (1905). The principles of mathematics and the problem of sets 11.Konig (1905a). On the foundations of set theory and the continuum problem 12.Russell (1908a). Mathematical logic as based on the theory of types 13.Zermelo (1908). A new proof of the possibility of a well-ordering 14.Zermelo (l908a). Investigations in the foundations of set theory I Whitehead and Russell (1910). Incomplete symbols: Descriptions 15.Wiener (1914). A simplification of the logic of relations 16.Lowenheim (1915). On possibilities in the calculus of relatives 17.Skolem (1920). Logico-combinatorial investigations in the satisfiability or provability of mathematical propositions: A simplified proof of a theorem by L. Lowenheim and generalizations of the 18.theorem 19.Post (1921). Introduction to a general theory of elementary propositions 20.Fraenkel (1922b). The notion "definite" and the independence of the axiom of choice 21.Skolem (1922). Some remarks on axiomatized set theory 22.Skolem (1923). The foundations of elementary arithmetic established by means of the recursive mode of thought, without the use of apparent variables ranging over infinite domains 23.Brouwer (1923b, 1954, and 1954a). On the significance of the principle of excluded middle in mathematics, especially in function theory, Addenda and corrigenda, and Further addenda and corrigenda von Neumann (1923). On the introduction of transfinite numbers Schonfinkel (1924). On the building blocks of mathematical logic filbert (1925). On the infinite von Neumann (1925). An axiomatization of set theory Kolmogorov (1925). On the principle of excluded middle Finsler (1926). Formal proofs and undecidability Brouwer (1927). On the domains of definition of functions filbert (1927). The foundations of mathematics Weyl (1927). Comments on Hilbert's second lecture on the foundations of mathematics Bernays (1927). Appendix to Hilbert's lecture "The foundations of mathematics" Brouwer (1927a). Intuitionistic reflections on formalism Ackermann (1928). On filbert's construction of the real numbers Skolem (1928). On mathematical logic Herbrand (1930). Investigations in proof theory: The properties of true propositions Godel (l930a). The completeness of the axioms of the functional calculus of logic Godel (1930b, 1931, and l931a). Some metamathematical results on completeness and consistency, On formally undecidable propositions of Principia mathematica and related systems I, and On completeness and consistency Herbrand (1931b). On the consistency of arithmetic References Index

Promotional Information

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

About the Author

Jean van Heijenoort, well known in the fields of mathematical logic and foundations of mathematics, is Professor of Philosophy at Brandeis University and has taught at New York and Columbia Universities.

Reviews

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 Goedel 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 Goedel] 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 Goedel is that book. -- Hilary Putnam, Harvard University
From Frege to Goedel 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 Goedel 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 Goedel'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 Goedel, 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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