Infinity: New Research Frontiers

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Michael Heller, W. Hugh Woodin
Cambridge University Press, Feb 7, 2011 - Mathematics
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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.
 

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Contents

Introduction
1
Infinity as a Transformative Concept in Science and Theology
19
The Mathematical Infinity
55
Warning Signs of a Possible Collapse of Contemporary Mathematics
76
Technical Perspectives on Infinity from Advanced
87
A Potential Subtlety Concerning the Distinction between
119
Much Better Than
130
Some Considerations on Infinity in Physics
167
Infinity and the Nostalgia of the Stars
193
Infinities in Cosmology
218
Perspectives on Infinity from Philosophy and Theology
231
Notes on the Concept of the Infinite in the History of Western
255
Theological Insights from Cantors Mathematics
275
A Partially Skeptical Response to Hart and Russell
290
Index
299
Copyright

Cosmological Intimations of Infinity
176

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About the author (2011)

Revd 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).

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