From Dedekind To Godel

Author : Jaakko Hintikka
Publisher : Springer Science & Business Media
ISBN 13 : 9401584788
Total Pages : 585 pages
Book Rating : 4.84/5 ( download)

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Download or read book From Dedekind to Gödel written by Jaakko Hintikka and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy. From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics illustrates the much greater variety of the actual developments in the foundations during the period covered. The viewpoints that serve this purpose included the foundational ideas of working mathematicians, such as Kronecker, Dedekind, Borel and the early Hilbert, and the development of notions like model and modelling, arbitrary function, completeness, and non-Archimedean structures. The philosophers discussed include not only the household names in logic, but also Husserl, Wittgenstein and Ramsey. Needless to say, such logically-oriented thinkers as Frege, Russell and Gödel are not entirely neglected, either. Audience: Everybody interested in the philosophy and/or history of mathematics will find this book interesting, giving frequently novel insights.

Author : Jaakko Hintikka
Publisher : Springer
ISBN 13 : 9789401584791
Total Pages : 490 pages
Book Rating : 4.96/5 ( download)

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Download or read book From Dedekind to Godel written by Jaakko Hintikka and published by Springer. This book was released on 2014-01-15 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy. From Dedekind to Godel: Essays on the Development of the Foundations of Mathematics illustrates the much greater variety of the actual developments in the foundations during the period covered. The viewpoints that serve this purpose included the foundational ideas of working mathematicians, such as Kronecker, Dedekind, Borel and the early Hilbert, and the development of notions like model and modelling, arbitrary function, completeness, and non-Archimedean structures. The philosophers discussed include not only the household names in logic, but also Husserl, Wittgenstein and Ramsey. Needless to say, such logically-oriented thinkers as Frege, Russell and Godel are not entirely neglected, either. Audience Everybody interested in the philosophy and/or history of mathematics will find this book interesting, giving frequently novel insights.

Author : Jean van Heijenoort
Publisher : Harvard University Press
ISBN 13 : 9780674324497
Total Pages : 684 pages
Book Rating : 4.98/5 ( download)

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Download or read book From Frege to Gödel written by Jean van Heijenoort and published by Harvard University Press. This book was released on 1967 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Peter Smith
Publisher : Cambridge University Press
ISBN 13 : 0521857848
Total Pages : 376 pages
Book Rating : 4.40/5 ( download)

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Download or read book An Introduction to Gödel's Theorems written by Peter Smith and published by Cambridge University Press. This book was released on 2007-07-26 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Peter Smith examines Gödel's Theorems, how they were established and why they matter.

Author : Jean van Heijenoort
Publisher : Harvard University Press
ISBN 13 : 0674257243
Total Pages : 684 pages
Book Rating : 4.45/5 ( download)

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Download or read book From Frege to Gödel written by Jean van Heijenoort and published by Harvard University Press. This book was released on 2002-01-15 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Kurt Gödel
Publisher :
ISBN 13 : 0195039726
Total Pages : 426 pages
Book Rating : 4.26/5 ( download)

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Download or read book Publications 1929-1936 written by Kurt Gödel and published by . This book was released on 1986 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : M. Beatrice Fazi
Publisher : Rowman & Littlefield
ISBN 13 : 1786606097
Total Pages : 249 pages
Book Rating : 4.99/5 ( download)

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Download or read book Contingent Computation written by M. Beatrice Fazi and published by Rowman & Littlefield. This book was released on 2018-11-15 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Contingent Computation, M. Beatrice Fazi offers a new theoretical perspective through which we can engage philosophically with computing. The book proves that aesthetics is a viable mode of investigating contemporary computational systems. It does so by advancing an original conception of computational aesthetics that does not just concern art made by or with computers, but rather the modes of being and becoming of computational processes. Contingent Computation mobilises the philosophies of Gilles Deleuze and Alfred North Whitehead in order to address aesthetics as an ontological study of the generative potential of reality. Through a novel philosophical reading of Gödel’s incompleteness theorems and of Turing’s notion of incomputability, Fazi finds this potential at the formal heart of computational systems, and argues that computation is a process of determining indeterminacy. This indeterminacy, which is central to computational systems, does not contradict their functionality. Instead, it drives their very operation, albeit in a manner that might not always fit with the instrumental, representational and cognitivist purposes that we have assigned to computing.

Author : Hao Wang
Publisher : MIT Press
ISBN 13 : 9780262730877
Total Pages : 366 pages
Book Rating : 4.71/5 ( download)

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Download or read book Reflections on Kurt Gödel written by Hao Wang and published by MIT Press. This book was released on 1990-03-14 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Newton/Descartes. Einstein/Gödel. The seventeenth century had its scientific and philosophical geniuses. Why shouldn't ours have them as well? Kurt Gödel was indisputably one of the greatest thinkers of our time, and in this first extended treatment of his life and work, Hao Wang, who was in close contact with Gödel in his last years, brings out the full subtlety of Gödel's ideas and their connection with grand themes in the history of mathematics and philosophy. The subjects he covers include the completeness of elementary logic, the limits of formalization, the problem of evidence, the concept of set, the philosophy of mathematics, time, and relativity theory, metaphysics and religion, as well as general ideas on philosophy as a worldview. Wang, whose reflections on his colleague also serve to clarify his own philosophical thoughts, distinguishes his ideas from those of Gödel's and on points of agreement develops Gödel's views further. The book provides a generous array of information on and interpretation of the two main phases of Gödel's career - the years between 1924 and 1939 at the University of Vienna, which were marked by intense mathematical creativity, and the period from 1940 to his death in 1978, during which he was affiliated with the Institute for Advanced Studies in Princeton, a time in which Gödel's interests steadily shifted from questions of logic to metaphysics. And it also examines Gödel's relations with the Vienna Circle, his philosophical differences with Carnap and Wittgenstein, the intimate and mutually fruitful friendship with Einstein, and the periodic bouts of depression for which Gödel was hospitalized a number of times over the course of his life. A Bradford Book.

Author : Kurt Gödel
Publisher : Oxford University Press
ISBN 13 : 9780198500735
Total Pages : 692 pages
Book Rating : 4.34/5 ( download)

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Download or read book Kurt Gödel: Collected Works: Volume IV written by Kurt Gödel and published by Oxford University Press. This book was released on 1986 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kurt Gödel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gödel's writings. The first three volumes, already published, consist of the papers and essays of Gödel. The final two volumes of the set deal with Gödel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.

Author : Sebastian Sunday Grève
Publisher : Springer
ISBN 13 : 1137472545
Total Pages : 519 pages
Book Rating : 4.40/5 ( download)

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Download or read book Wittgenstein and the Creativity of Language written by Sebastian Sunday Grève and published by Springer. This book was released on 2016-01-26 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first to focus on a particular complex of questions that have troubled Wittgenstein scholarship since its very beginnings. The authors re-examine Wittgenstein’s fundamental insights into the workings of human linguistic behaviour, its creative extensions and its philosophical capabilities, as well as his creative use of language. It offers insight into a variety of topics including painting, politics, literature, poetry, literary theory, mathematics, philosophy of language, aesthetics and philosophical methodology.