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 Konig 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 Lowenheim's theorem, and heand 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 Godel, 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.
Author(s): Jean van Heijenoort
Series: Source Books in the History of the Sciences
Publisher: Harvard University Press
Year: 1967
Language: English
Pages: 673
Tags: Математика;История математики;
Van Heijenoort, Jean.From Frege to Godel_A source book in mathematical logic, 1879-1931(ser.Source Books in the History of the Sciences)(HUP,1967)(ISBN 9780674324503)(600dpi)(773p) 4......Page 4
Copyright iv......Page 5
Contents ix......Page 10
General Editor’s Preface v ......Page 6
Preface vi ......Page 7
Frege (1879). Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought 1 ......Page 13
Peano (1889). The principles of arithmetic, presented by a new method 83 ......Page 95
Dedekind (1890a). Letter to Keferstein 98 ......Page 110
Burali-Forti (1897 and 1897a). A question on transfinite numbers and On well-ordered classes 104 ......Page 116
Cantor (1899). Letter to Dedekind 113 ......Page 125
Padoa (1900). Logical introduction to any deductive theory 118 ......Page 130
Russell (1902). Letter to Frege 124 ......Page 136
Frege (1902). Letter to Russell 126 ......Page 138
Hilbert (1904). On the foundations of logic and arithmetic 129 ......Page 141
Zermelo (1904). Proof that every set can be well-ordered 139 ......Page 151
Richard (1905). The principles of mathematics and the problem of sets 142 ......Page 154
Konig (1905a). On the foundations of set theory and the continuum problem 145 ......Page 157
Russell (1908a). Mathematical logic as based on the theory of types 150 ......Page 162
Zermelo (1908). A new proof of the possibility of a well-ordering 183 ......Page 195
Zermelo (1908a). Investigations in the foundations of set theory I 199 ......Page 211
Whitehead and Russell (1910). Incomplete symbols: Descriptions 216 ......Page 228
Wiener (1914). A simplification of the logic of relations 224 ......Page 236
Lowenheim (1915). On possibilities in the calculus of relatives 228 ......Page 240
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 252 ......Page 264
Post (1921). Introduction to a general theory of elementary propositions 264 ......Page 276
Fraenkel (1922b). The notion “definite” and the independence of the axiom of choice 284 ......Page 296
Skolem (1922). Some remarks on axiomatized set theory 290 ......Page 302
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 302 ......Page 314
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 334 ......Page 346
von Neumann (1923). On the introduction of transfinite numbers 346 ......Page 358
Schonfinkel (1924). On the building blocks of mathematical logic 355 ......Page 367
Hilbert (1925). On the infinite 367 ......Page 379
von Neumann (1925). An axiomatization of set theory 393 ......Page 405
Kolmogorov (1925). On the principle of excluded middle 414 ......Page 426
Finsler (1926). Formal proofs and undecidability 438 ......Page 450
Brouwer (1927). On the domains of definition of functions 446 ......Page 458
Hilbert (1927). The foundations of mathematics 464 ......Page 476
Weyl (1927). Comments on Hilbert’s second lecture on the foundations of mathematics 480 ......Page 492
Bernays (1927). Appendix to Hilbert’s lecture “The foundations of mathematics’’ 485 ......Page 497
Brouwer (1927a). Intuitionistic reflections on formalism 490 ......Page 502
Ackermann (1928). On Hilbert’s construction of the real numbers 493 ......Page 505
Skolem (1928). On mathematical logic 508 ......Page 520
Herbrand (1930). Investigations in proof theory: The properties of true propositions 525 ......Page 537
Godel (1930a). The completeness of the axioms of the functional calculus of logic 582 ......Page 594
Godel (1930b, 1931, and 1931a). Some metamathematical results on completeness and consistency, On formally undecidable propositions of Principia mathematica anS related systems I, and On completeness and consistency 592 ......Page 604
Herbrand (1931b). On the consistency of arithmetic 618 ......Page 630
References 629 ......Page 641
Index 657 ......Page 669
cover......Page 1
