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Author: Joseph Warren Dauben Publisher: Princeton University Press ISBN: 9780691085838 Category : Biography & Autobiography Languages : en Pages : 422
Book Description
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.
Author: Joseph Warren Dauben Publisher: Princeton University Press ISBN: 9780691085838 Category : Biography & Autobiography Languages : en Pages : 422
Book Description
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.
Author: Joseph Warren Dauben Publisher: Princeton University Press ISBN: 0691214204 Category : Science Languages : en Pages : 422
Book Description
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.
Author: Georg Cantor Publisher: Franklin Classics Trade Press ISBN: 9780344921582 Category : Languages : en Pages : 100
Book Description
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author: Mary Tiles Publisher: Courier Corporation ISBN: 0486138550 Category : Mathematics Languages : en Pages : 258
Book Description
DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div
Author: Jose Ferreiros Publisher: Springer Science & Business Media ISBN: 9783764357498 Category : Mathematics Languages : en Pages : 472
Book Description
"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)
Author: Michael Hallett Publisher: Oxford University Press ISBN: 9780198532835 Category : Mathematics Languages : en Pages : 372
Book Description
Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.
Author: Kenneth Binmore Publisher: Springer Nature ISBN: 3030653870 Category : Philosophy Languages : en Pages : 209
Book Description
How would Plato have responded if his student Aristotle had ever challenged his idea that our senses perceive nothing more than the shadows cast upon a wall by a true world of perfect ideals? What would Charles Darwin have said to Karl Marx about his claim that dialectical materialism is a scientific theory of evolution? How would Jean-Paul Sartre have reacted to Simone de Beauvoir’s claim that the Marquis de Sade was a philosopher worthy of serious attention? This light-hearted book proposes answers to such questions by imagining dialogues between thirty-three pairs of philosophical sages who were alive at the same time. Sometime famous sages get a much rougher handling than usual, as when Adam Smith beards Immanuel Kant in his Konigsberg den. Sometimes neglected or maligned sages get a chance to say what they really believed, as when Epicurus explains that he wasn’t epicurean. Sometimes the dialogues are about the origins of modern concepts, as when Blaise Pascal and Pierre de Fermat discuss their invention of probability, or when John Nash and John von Neumann discuss the creation of game theory. Even in these scientific cases, the intention is that the protagonists come across as fallible human beings like the rest of us, rather than the intellectual paragons of philosophical textbooks.
Author: Loren Graham Publisher: Harvard University Press ISBN: 0674032934 Category : History Languages : en Pages : 252
Book Description
In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.
Author: Joseph Warren Dauben
Author: Joseph Warren Dauben
Author: Joseph Warren Dauben
Author: Georg Cantor
Author: Georg Cantor
Author: Amir D. Aczel
Author: Mary Tiles
Author: Jose Ferreiros
Author: Michael Hallett
Author: Kenneth Binmore
Author: Loren Graham