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

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“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 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