Sound Bite
The idea of infinity stands at the intersection of mathematics and philosophy. As da Vinci said, "Arithmetic is a computational science in its calculations, but it is of no avail in dealing with continuous quantity." The End of Infinity reviews the philosophical history of infinity, mathematics, numbers, and logic to demonstrate that the modern conception of infinity involves a logical and metaphysical contradiction that argues for a return to Aristotle's conception of potential infinity.
About the Author
Anthony C. Patton has worked with the U.S. Air Force, the Department of Defense, and the Department of State, serving in eight foreign countries.
He earned an MBA with high honors at Thunderbird-School of Global Management and a BA from Augsburg College with a double major in mathematics and philosophy, magna cum laude. He lives with his wife and three sons in Southern California. This is his third nonfiction work published by Algora.
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About the Book
The way we think about infinity shapes the way we think about other subjects. The author says, "My heart fluttered the first time I heard the paradoxical claim of a 19th-century mathematician who said infinity was real, that there was more than...
The way we think about infinity shapes the way we think about other subjects. The author says, "My heart fluttered the first time I heard the paradoxical claim of a 19th-century mathematician who said infinity was real, that there was more than one type of infinity, and that not all infinities were the same size! It was either one of the most absurd or one of the most important theories in intellectual history."
The chapters that follow investigate the issue from a variety of perspectives. This book focuses mainly on the philosophy of infinity; it does not require an extensive understanding of mathematics, although relevant terms and concepts are introduced and explained. From the late 19th to the early 20th century, great thinkers like Cantor, Frege, and Russell attempted to provide a new foundation for mathematics by replacing the intuitions of Kant with logic, rigorous definitions, and axiomatic set theory. One of the results of their work was a new conception of infinity, which included the surprising claims that infinite sets exist, that there are different types of infinite sets, and that not all infinite sets are the same size.
However, the great logician Gödel proved that all axiomatic systems, like set theory, are necessarily incomplete and therefore cannot not provide a solid foundation for mathematics, evidenced by the fact that there are known mathematical truths that cannot be proven or disproven with set theory. Despite this setback, set theory continues to dominate modern mathematics, with limited attempts to reconsider its validity - until now.
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More . . .
An article based on The End of Infinity was selected for publication in Online Mathematics, a peer-reviewed journal. Click to read it!
An article based on The End of Infinity was selected for publication in Online Mathematics, a peer-reviewed journal. Click to read it!
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Pages 200
Year: 2018
LC Classification: BD411 .P38 2018
Dewey code: 111/.6-dc23
BISAC: PHI011000 PHILOSOPHY / Logic
BISAC: MAT016000 MATHEMATICS / Infinity
BISAC: MAT028000 MATHEMATICS / Set Theory
Soft Cover
ISBN: 978-1-62894-339-9
Price: USD 22.95
Hard Cover
ISBN: 978-1-62894-340-5
Price: USD 32.95
eBook
ISBN: 978-1-62894-341-2
Price: USD 22.95
Mobi - for Amazon's Kindle
ISBN: 978-1-62894-341-2
Price: USD 22.95
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