Georg Cantor: His Mathematics and Philosophy of the Infinite

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. Cover Page Half-title Page Title Page Copyright Page Dedication Page Contents Introduction 1. Preludes in Analysis 2. The Origins of Cantorian Set Theory: Trigonometric Series, Real Numbers, and Derived Sets 3. Denumerability and Dimension 4. Cantor's Early Theory of Point Sets 5. The Mathematics of Cantor's Grundlagen 6. Cantor's Philosophy of the Infinite 7. From the Grundlagen to the Beitrdge, 1883-1895 8. The Beitrdge, Part I: The Study of Simply-Ordered Sets 9. The Beitrdge, Part II: The Study of Well-Ordered Sets 10. The Foundations and Philosophy of Cantorian Set Theory 11. The Paradoxes and Problems of Post-Cantorian Set Theory 12. Epilogue: The Significance of Cantor's Personality Appendixes: Previously Unpublished Correspondence Notes Bibliography Index