Infinity: New Research Frontiers

doi:10.1017/CBO9780511976889

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.

'… Infinity: New Research Frontiers is an excellent collection from some first-rate philosophers. The importance of the contributors along with the high quality of their pieces make this a volume worth reading.'

Source: Linguistic and Philosophical Investigations

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Contents

Frontmatter
pp i-vi
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Contents
pp vii-viii
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Contributors
pp ix-x
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Preface
pp xi-xii
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Acknowledgments
pp xiii-xiv
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Introduction
pp 1-16
- By Rudy Rucker, San José State University (California), United States
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I - Perspectives on Infinity from History
pp 17-18
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1 - Infinity as a Transformative Concept in Science and Theology
pp 19-52
- By Wolfgang Achtner, Justus Liebig University; Johann Wolfgang Goethe University, Germany
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II - Perspectives on Infinity from Mathematics
pp 53-54
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2 - The Mathematical Infinity
pp 55-75
- By Enrico Bombieri, Institute for Advanced Study (New Jersey), United States
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3 - Warning Signs of a Possible Collapse of Contemporary Mathematics
pp 76-86
- By Edward Nelson, Princeton University (New Jersey), United States
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III - Technical Perspectives on Infinity from Advanced Mathematics
pp 87-88
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4 - The Realm of the Infinite
pp 89-118
- By W. Hugh Woodin, University of California, Berkeley
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5 - A Potential Subtlety Concerning the Distinction between Determinism and Nondeterminism
pp 119-129
- By W. Hugh Woodin, University of California, Berkeley
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6 - Concept Calculus: Much Better Than
pp 130-164
- By Harvey M. Friedman, The Ohio State University, United States
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IV - Perspectives on Infinity from Physics and Cosmology
pp 165-166
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7 - Some Considerations on Infinity in Physics
pp 167-175
- By Carlo Rovelli, University of the Mediterranean; National Center for Scientific Research (CNRS)-Luminy, France
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8 - Cosmological Intimations of Infinity
pp 176-192
- By Anthony Aguirre, University of California, United States
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9 - Infinity and the Nostalgia of the Stars
pp 193-217
- By Marco Bersanelli, University of Milan, Italy
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10 - Infinities in Cosmology
pp 218-230
- By Michael Heller, Copernicus Center for Interdisciplinary Studies; The Pontifical University of John Paul II, Poland
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V - Perspectives on Infinity from Philosophy and Theology
pp 231-232
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11 - God and Infinity: Directions for Future Research
pp 233-254
- By Graham Oppy, Monash University at Clayton, Australia
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12 - Notes on the Concept of the Infinite in the History of Western Metaphysics
pp 255-274
- By David Bentley Hart, Providence College (Rhode Island), United States
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13 - God and Infinity: Theological Insights from Cantor's Mathematics
pp 275-289
- By Robert John Russell, The Center for Theology and the Natural Sciences, United States
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14 - A (Partially) Skeptical Response to Hart and Russell
pp 290-298
- By Denys A. Turner, Yale Divinity School, United States
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Index
pp 299-311
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New Research Frontiers

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