Philosophical Perspectives on Infinity [Paperback]

Graham Oppy (Author)

Book Description

ISBN-10: 0521108098 | ISBN-13: 978-0521108096 | Publication Date: January 29, 2009 | Edition: 1

This book is an exploration of philosophical questions about infinity. Graham Oppy examines how the infinite lurks everywhere, both in science and in our ordinary thoughts about the world. He also analyses the many puzzles and paradoxes that follow in the train of the infinite. Even simple notions, such as counting, adding and maximising present serious difficulties. Other topics examined include the nature of space and time, infinities in physical science, infinities in theories of probability and decision, the nature of part/whole relations, mathematical theories of the infinite, and infinite regression and principles of sufficient reason.

Editorial Reviews

Review

"I did encounter some new and provocative examples beyond the standard fare of Zeno's paradox and Hilbert's Hotel, and the meticulous framing of each conundrum and possible resolutions was fascinating and worth the effort." - MAA Review Bonnie Shulman, Bates College

"...read this book." Mathematical Reviews

Book Description

This book is an exploration of philosophical questions about infinity. Graham Oppy examines how the infinite lurks everywhere, both in science and in our ordinary thoughts about the world.

See all Editorial Reviews

Product Details

• Paperback: 336 pages
• Publisher: Cambridge University Press; 1 edition (January 29, 2009)
• Language: English
• ISBN-10: 0521108098
• ISBN-13: 978-0521108096
• Product Dimensions: 9 x 5.9 x 0.8 inches
• Shipping Weight: 1 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #606,432 in Books (See Top 100 in Books)

More About the Author

I am currently Associate Dean Research and Associate Dean Graduate Studies in the Faculty of Arts at Monash University. (I've been Associate Dean Research since 2004; I've taken on the Associate Dean Graduate Studies role in 2007 on a strictly one-year term.)

I was previously Head of the School of Philosophy and Bioethics at Monash (from 2001 through 2004).

I came to Monash in mid-1996 as a Senior Lecturer; I was promoted to Professor in 2005.

From 1993 to mid-1996, I was a Postdoctoral Fellow in the Philosophy Program in the Research School for the Social Sciences at the Australian National University in Canberra.

From mid-1990 through 1992, I was a Lecturer at the University of Wollongong (no, not Wolloomooloo).

Between 1987 and 1990, I was a graduate student in philosophy at Princeton University. My dissertation advisor was Gil Harman; my dissertation was about questions in the philosophy of language.

From 1979 through 1986, I was an undergraduate student at Melbourne University. I completed two degrees: a BA with a major in philosophy; and a B.Sc with a major in mathematics (and a minor in physics).

Skipping back a bit, I was born in Benalla (pop. 8000) in 1960; my family moved to Ballarat (pop. 80,000) in 1965, and were still living there when I started to attend Melbourne University in 1979.

My parents were Methodists; I ceased to be a religious believer when I was in my early teenage years.

Customer Reviews

Most Helpful Customer Reviews

2 of 2 people found the following review helpful:

5.0 out of 5 stars The other half of "Arguing About Gods", September 10, 2011

By 

A. Scott - See all my reviews
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This review is from: Philosophical Perspectives on Infinity (Paperback)

This book is the other half of Graham Oppy's "Arguing About Gods". They were originally supposed to be a mega-book titled "God and Infinity". It is good that Dr. Oppy separated them because both are heavy duty and may have been too much and too expensive if joined.

This book is a review of many of the puzzles surrounding infinity through the ages (for some reason, the other reviewer can not appreciate professor Oppy's goal of making this book definitive). While it covers some classical problems, it mostly focuses on those that have made their way into philosophical discussions involving mathematics and religion. The author's style is meticulous and concise. He carefully lays out his preliminary questions about different areas of mathematics, then dives right in. As someone who loves mathematics, physics, and philosophy, I really enjoyed this book.

4 of 14 people found the following review helpful:

3.0 out of 5 stars Re-arguments of questions mathematicians and physicists settled long ago, February 27, 2007

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
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This review is from: Philosophical Perspectives on Infinity (Hardcover)

There is no question that the concept of infinity is a difficult one. It is compounded by the fact that there are different levels of infinity, broadly split into the categories of countable and uncountable. It is also possible for two different infinite sets to have the same number of elements and yet one is completely contained in the other. For example, it is possible to match up the set of counting numbers {1, 2, 3, ...} with the set of even numbers {2, 4, 6, ...} by matching each number in the first with its double in the second. Clearly, the second set is completely contained in the first.
Mathematicians work constantly with the concept of infinity. The first year of undergraduate mathematics involves limits, summing infinite series and infinitesimals. Getting to this point has not been an easy journey, the finest mathematicians struggled with summing some series and it took years to successfully resolve the problems.
Oppy covers most of this ground and it is unfortunate that he doesn't seem to grasp some of the basic ways in which mathematicians deal with infinity. For example, on page 100 there is the statement: "Similarly, in topology, we have it that a one-dimensional line can be composed of nothing but zero-dimensional points. Yet how can one put together things that are all zero-dimensional and end up with something that is one-dimensional?" This is a supposed paradox that was settled by the mathematical community long ago.
Oppy also brings up the classic paradox of Zeno involving Achilles and the tortoise. This is a classic example of the sum of an infinite series being finite and even advanced precalculus students can determine the precise point where Achilles will pass the tortoise. He also brings up the famous "Olbers' paradox", which was raised by Heinrich Olbers in 1823. Olbers argued that the universe could not be statically infinite because otherwise the combined starlight would prevent the sky from ever getting dark. While there are still some arguments that take place on the edges, the overall expansion of the universe and the corresponding redshift easily explains why it is possible for the universe to be infinite and the sky dark at night.
Oppy spends a great deal of time on this problem, concluding that "It is not true that we can explain the darkness of the night sky by adverting to any of these versions of the claim that, even though there are stars in any direction we choose to look, there is a reason why we fail to see some of those stars." Unfortunately, while Oppy uses the term cosmology on a regular basis, he does not seem to be up on the current model of the universe.
Mathematicians long ago reached a comfort level when dealing with infinities. So much so that even first year college math students are expected to work with them without difficulty. While he certainly mentions a lot of mathematics and how it is used, Oppy seems not to have achieved this basic level.