From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931

✍ Scribed by Jean Van Heijenoort (editor)

• Publisher: iUniverse
• Year: 1999
• Tongue: English
• Leaves: 671
• Category: Library

✦ Synopsis

“Collected here in one volume are some thirty-six high quality translations into English of the most important foreign-language works in mathematical logic, as well as articles and letters by Whitehead, Russell, Norbert Weiner and Post…This book 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

“An invaluable work of reference and study. The selection of contents could hardly be bettered; those of the papers which were not originally in English have been admirably translated; and the editing of the book is impeccable in every way.”

-New Scientist

“This is an excellent selection of classical contributions to symbolic logic. The bringing together in English of so many important papers is in itself a major contribution… this book will long remain a standard work, essential to the study of symbolic logic.”

-Library Journal

✦ Table of Contents

Contents
Frege (1879). Begriffsschrift, a formula language, modeled upon that
of arithmetic, for pure thought
Peano (1889). The principles of arithmetic, presented by a new method
Dedekind (1890a). Letter to Keferstein
Burali-Forti (1897 and 1897a). A question on transfinite numbers and
On well-ordered classes
Cantor (1899). Letter to Dedekind
Padoa (1900). Logical introduction to any deductive theory
Russell (1902). Letter to Frege
Frege (1902). Letter to Russell
Hilbert (1904). On the foundations of logic and arithmetic
Zermelo (1904). Proof that every set can be well-ordered
Richard (1905). The principles of mathematics and the problem of
sets
Konig (1905a). On the foundations of set theory and the continuum
problem
Russell (1908a). Mathematical logic as based on the theory of types
Zermelo (1908). A new proof of the possibility of a well-ordering
Zermelo (1908a). Investigations in the foundations of set theory I
Whitehead and Russell (1910). Incomplete symbols: Descriptions
Wiener (1914). A simplification of the logic of relations
Lowenheim (1915). On possibilities in the calculus of relatives
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 theorem
Post (1921). Introduction to a general theory of elementary
propositions
Fraenkel (1922b). The notion "definite" and the independence of the
axiom of choice
Skolem (1922). Some remarks on axiomatized set theory
IX
X CONTENT8
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
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
Hilbert (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
Hilbert (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 Hilbert's construction of the real numbers
Skolem (1928). On mathematical logic
Herbrand (1930). Investigations in proof theory: The properties of
true propositions
Godel (1930a). The completeness of the axioms of the functional
calculus of logic
Godel (1930b, 1931, and 1931a). 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