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Author: Jean van Heijenoort
Publisher: Harvard University Press
ISBN: 9780674324497
Category : Mathematics
Languages : en
Pages : 684
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Book Description
Gathered together here are the fundamental texts of the great classical period in modern logic. A complete translation of Gottlob Frege’s Begriffsschrift—which opened a great epoch in the history of logic by fully presenting propositional calculus and quantification theory—begins the volume, which concludes with papers by Herbrand and by Gödel.
Author: Jean van Heijenoort
Publisher: Harvard University Press
ISBN: 9780674324497
Category : Mathematics
Languages : en
Pages : 684
Get Book
Book Description
Gathered together here are the fundamental texts of the great classical period in modern logic. A complete translation of Gottlob Frege’s Begriffsschrift—which opened a great epoch in the history of logic by fully presenting propositional calculus and quantification theory—begins the volume, which concludes with papers by Herbrand and by Gödel.
Author: Jean van Heijenoort
Publisher: Harvard University Press
ISBN: 0674257243
Category : Philosophy
Languages : en
Pages : 684
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Book 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 König 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 Löwenheim’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 Gödel, 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: Jean van Heijenoort
Publisher:
ISBN:
Category :
Languages : en
Pages : 664
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Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: S.G. Shanker
Publisher: Routledge
ISBN: 1134947976
Category : Philosophy
Languages : en
Pages : 272
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Book Description
A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.
Author:
Publisher: Elsevier
ISBN: 0080930662
Category : Mathematics
Languages : en
Pages : 878
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Book Description
Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration Serves as a singular contribution to the intellectual history of the 20th century Contains the latest scholarly discoveries and interpretative insights
Author: Jean van Heijenoort
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 660
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Book Description
Author: Kurt Gödel
Publisher: Cambridge, Mass. : Harvard University Press
ISBN:
Category : Arithmetic
Languages : en
Pages : 138
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Book Description
This volume, a shortened edition of Mr. van Heijenoort's internationally acclaimed From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931 (HUP 1967), makes available in English the two most important works in the growth of modern mathematical logic. Heralded by Leibniz, modern logic had its beginnings in the work of Boole, DeMorgan, and Jevons, but the 1879 publication of Gottlob Frege's Begriffsschrift opened a great epoch in the history of logic with the full-form presentation of the propositional calculus and quantification theory. Frege and Gödel: Two Fundamental Texts in Mathematical Logic begins with this short book, which ushered in the classical age of mathematical logic by outlining the construction of a system of logical symbolism. The volume concludes with Gödel's famous incompleteness paper of 1931, which changed the development of logic and the foundations of mathematics by revealing the intrinsic limitations of formal systems, and brought to an end the classical phase. Mr. van Heijenoort has provided a new introduction which sets the Frege and Gödel pieces in perspective in the development of modern logic and points out difficulties in interpretation. Editorial comments, footnotes, and bibliographic information offer additional explanatory material.
Author: John Perry
Publisher: Oxford University Press
ISBN: 0192542087
Category : Philosophy
Languages : en
Pages : 161
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Book Description
John Perry offers a rethinking of Gottlob Frege's seminal contributions to philosophy of language. Frege's innovations provided the basis of modern logic, but his influence in other areas should not be understated. For instance, the view that he developed in "On Sense and Reference", the most studied essay in the philosophy of language, dominated twentieth-century work in the field and continues to be very influential. Perry explains and charts the development of Frege's views in this area, and argues that his doctrine of indirect reference directed philosophy of language on a long detour from which only now can we emerge. Perry advocates a move away from indirect reference and presents an alternative framework which does not require the abandoning of circumstances in the references of sentences.
Author: A. Orenstein
Publisher: Springer Science & Business Media
ISBN: 9780792359869
Category : Language Arts & Disciplines
Languages : en
Pages : 476
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Book Description
Quine is one of the twentieth century's most important and influential philosophers. The essays in this collection are by some of the leading figures in their fields and they touch on the most recent turnings in Quine's work. The book also features an essay by Quine himself, and his replies to each of the papers. Questions are raised concerning Quine's views on knowledge: observation, holism, truth, naturalized epistemology; about language: meaning, the indeterminacy of translation, conjecture; and about the philosophy of logic: ontology, singular terms, vagueness, identity, and intensional contexts. Given Quine's preeminent position, this book must be of interest to students of philosophy in general, Quine aficionados, and most particularly to those working in the areas of epistemology, ontology, philosophies of language, of logic, and of science.
