Infinity : new research frontiers /
Heller, Michał.
Woodin, W. H.(W. Hugh)
Cambridge : Cambridge University Press,
2011.
"'The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.' David Hilbert (1862-1943). This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen world-renowned researchers in the fields of mathematics, physics, cosmology, philosophy, and theology offer a rich intellectual exchange among various current viewpoints, rather than a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: Can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity"--Provided by publisher.
"'The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.' David Hilbert (1862-1943). This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen world-renowned researchers in the fields of mathematics, physics, cosmology, philosophy, and theology offer a rich intellectual exchange among various current viewpoints, rather than a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: Can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity"--Provided by publisher.
Includes bibliographical references and index.
Introduction / Rudy Rucker -- Part I. Perspectives on infinity from history : 1. Infinity as a transformative concept in science and theology / Wolfgang Achtner -- Part II. Perspectives on infinity from mathematics : 2. The mathematical infinity / Enrico Bombieri ; 3. Warning signs of a possible collapse of contemporary mathematics / Edward Nelson -- Part III. Technical perspectives on infinity from advanced mathematics : 4. The realm of the infinite / W. Hugh Woodin ; 5. A potential subtlety concerning the distinction between determinism and nondeterminism / W. Hugh Woodin ; 6. Concept calculus : much better than / Harvey M. Friedman -- Part IV. Perspectives on infinity from physics and cosmology : 7. Some considerations on infinity in physics / Carlo Rovelli ; 8. Cosmological intimations of infinity / Anthony Aguirre ; 9. Infinity and the nostalgia of the stars/ Marco Bersanelli ; 10. Infinities in cosmology / Michael Heller -- Part V. Perspectives on infinity from philosophy and theology : 11. God and infinity : directions for future research / Graham Oppy ; 12. Notes on the concept of the infinite in the history of Western metaphysics / David Bentley Hart ; 13. God and infinity : theological insights from Cantor's mathematics / Robert J. Russell ; 14. A partially skeptical response to Hart and Russell / Denys A. Turner.
Infinite
Mathematics