Infinity: New Research Frontiers

by Heller, Michael; Woodin, W. Hugh

• ISBN13: 9781107003873
• ISBN10: 1107003873
• Edition: 1st
• Format: Hardcover
• Copyright: 2011-02-07
• Publisher: Cambridge Univ Pr

Summary

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 displaying 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.

Author Biography

Rev. Dr. Michael Heller is the Founder and Director of the Copernicus Center for Interdisciplinary Studies, Cracow. He is a Professor of Philosophy at the Pontifical University of John Paul II, Cracow, Poland; an Adjunct Member of the Vatican Observatory; and Ordinary Member of the Pontifical Academy of Sciences. Heller is the author of more than thirty books and nearly two hundred scientific papers. Dr. W. Hugh Woodin is a Professor of Mathematics and the Chair of the Mathematics Department at the University of California, Berkeley. Professor Woodin has published numerous articles and books and is the managing editor of the Journal of Mathematical Logic and editor of Mathematical Research Letters, Mathematical Logic Quarterly, and Electronic Research Announcements (American Mathematical Society).

Table of Contents

Contributors	p. ix
Preface	p. xi
Acknowledgments	p. xiii
Introduction	p. 1
Perspectives on Infinity from History
Infinity as a Transformative Concept in Science and Theology	p. 19
Perspectives on Infinity from Mathematics
The Mathematical Infinity	p. 55
Warning Signs of a Possible Collapse of Contemporary Mathematics	p. 76
Technical Perspectives on Infinity from Advanced Mathematics
The Realm of the Infinite	p. 89
A Potential Subtlety Concerning the Distinction between Determinism and Nondeterminism	p. 119
Concept Calculus: Much Better Than	p. 130
Perspectives on Infinity from Physics and Cosmology
Some Considerations on Infinity in Physics	p. 167
Cosmological Intimations of Infinity	p. 176
Infinity and the Nostalgia of the Stars	p. 193
Infinities in Cosmology	p. 218
Perspectives on Infinity from Philosophy and Theology
God and Infinity: Directions for Future Research	p. 233
Notes on the Concept of the Infinite in the History of Western Metaphysics	p. 255
God and Infinity: Theological Insights from Cantor's Mathematics	p. 275
A (Partially) Skeptical Response to Hart and Russell	p. 290
Index	p. 299
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