From Frege to G�del A Source Book in Mathematical Logic, 1879-1931

ISBN-10: 0674324498

ISBN-13: 9780674324497

Edition: 1967

List price: $47.50
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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 Kouml;nig 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 Louml;wenheim'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 Gouml;del, 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.
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Book details

List price: $47.50
Copyright year: 1967
Publisher: Harvard University Press
Publication date: 1/15/2002
Binding: Paperback
Pages: 672
Size: 7.00" wide x 10.00" long x 1.25" tall
Weight: 2.2
Language: English

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
Kouml;nig (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 (l908a)
Investigations in the foundations of set theory I Whitehead and Russell (1910)
Incomplete symbols: Descriptions
Wiener (1914)
A simplification of the logic of relations
Louml;wenheim (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
Louml;wenheim 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
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 Schouml;nfinkel (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 Gouml;del (l930a)
The completeness of the axioms of the functional calculus of logic Gouml;del (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 consistencyHerbrand (1931b)
On the consistency of arithmetic
References
Index
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