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. 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. Hilbert, Russell, and Zermelo show various ways of overcoming these paradoxes and initiate, respectively, proof theory, the theory of types, and axiomatic set theory. The controversy between Hubert and Brouwer during the twenties is presented in papers of theirs and in others by Weyl, Bernays, Ackermann, and Kolmogorov.
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The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries. Frege Begriffsschrift , a formula language, modeled upon that of arithmetic, for pure thought 2. Peano The principles of arithmetic, presented by a new method 3. Dedekind a. Letter to Keferstein Burali-Forti and a.
A question on transfinite numbers and On well-ordered classes 4. Cantor Letter to Dedekind 5. Padoa Logical introduction to any deductive theory 6,Russell Letter to Frege 7. Letter to Russell 8. Hilbert On the foundations of logic and arithmetic 9. Zermelo Proof that every set can be well-ordered Richard The principles of mathematics and the problem of sets On the foundations of set theory and the continuum problem Russell a.
Mathematical logic as based on the theory of types A new proof of the possibility of a well-ordering Zermelo la. Investigations in the foundations of set theory I Whitehead and Russell Incomplete symbols: Descriptions Wiener A simplification of the logic of relations On possibilities in the calculus of relatives Skolem Logico-combinatorial investigations in the satisfiability or provability of mathematical propositions: A simplified proof of a theorem by L.
Post Introduction to a general theory of elementary propositions Fraenkel b. The notion "definite" and the independence of the axiom of choice Some remarks on axiomatized set theory 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 b, , and a. 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 On the building blocks of mathematical logic filbert On the infinite von Neumann An axiomatization of set theory Kolmogorov On the principle of excluded middle Finsler Formal proofs and undecidability Brouwer On the domains of definition of functions filbert The foundations of mathematics Weyl Comments on Hilbert's second lecture on the foundations of mathematics Bernays Appendix to Hilbert's lecture "The foundations of mathematics" Brouwer a.
Intuitionistic reflections on formalism Ackermann On filbert's construction of the real numbers Skolem On mathematical logic Herbrand Some metamathematical results on completeness and consistency, On formally undecidable propositions of Principia mathematica and related systems I, and On completeness and consistency Herbrand b. On the consistency of arithmetic References Index. Skip to main content. Search form Search. Login Join Give Shops. Halmos - Lester R. Ford Awards Merten M.
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From Frege to Gödel : A Source Book in Mathematical Logic, 1879-1931
From Frege to Gödel