Georg Cantor
Georg Cantor

Author: Joseph Warren Dauben

Publisher: Princeton University Press

Published: 1990

Total Pages: 422

ISBN-13: 9780691085838

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One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets. This revolution is the subject of Joseph Dauben's important studythe most thorough yet writtenof the philosopher and mathematician who was once called a "corrupter of youth" for an innovation that is now a vital component of elementary school curricula. Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradoxes in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by recurring attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory.

Labyrinth of Thought
Labyrinth of Thought

Author: Jose Ferreiros

Publisher: Springer Science & Business Media

Published: 2001-11-01

Total Pages: 472

ISBN-13: 9783764357498

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"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)

Notes on Set Theory
Notes on Set Theory

Author: Yiannis Moschovakis

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 280

ISBN-13: 1475741537

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What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.

The Human Being in Contemporary Philosophical Conceptions
The Human Being in Contemporary Philosophical Conceptions

Author: Nikolai Omelchenko

Publisher: Cambridge Scholars Publishing

Published: 2009-03-26

Total Pages: 355

ISBN-13: 1443808415

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This book is a collection of the selected proceedings of the 4th International Conference “Human Being in Contemporary Philosophical Conceptions,” which was held under the patronage of UNESCO at Volgograd State University (Russia) on May 28–31, 2007. In the letter to the organizers, Mr. Koïchiro Matsuura wrote: “I should like to congratulate you on this important initiative to promote philosophical reflection, which is one of the central objectives of UNESCO’s Intersectoral Strategy on Philosophy.” There is an interesting fact: the 19th World Congress of Philosophy in Moscow (1993) had no session on philosophical anthropology, the next Congress in Boston (1998) had one such session, the 21st Congress of Philosophy in Istanbul (2003) had already four sessions, and the 22nd World Congress of Philosophy in Seoul (2008) had six sessions on philosophical anthropology. Obviously, we may observe a new anthropological renaissance in contemporary thought. This book serves the philosophical anthropology becoming as well. Perhaps an idea of integral studies is the most attractive trend in the contemporary philosophy and science. The book presents an experience in integral philosophy of human being. Also, the development of philosophical anthropology is closely connected with practical tasks. Our political activities, welfare projects and educational programs can become really useful only when we are guided by knowledge of what human being is, what we are able to do, what are own needs, and what we must become. Philosophical anthropology could correctly define the research purposes of all human sciences. This volume includes various reflexions and styles of thinking. By this, all the papers demonstrate metaphysics of respect for human being. The contributors, scholars from the different countries, are open for free discussions and fresh ideas.