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Approaching Infinity (Englisch) Taschenbuch – 14. März 2016

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Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters.

The book addresses the need for a theory of infinity, and reviews both old and new theories of infinity. It discussing the purposes of studying infinity and the troubles with traditional approaches to the problem, and concludes by offering a solution to some existing paradoxes.

Über den Autor und weitere Mitwirkende

Michael Huemer received a B.A. from UC Berkeley and a Ph.D. from Rutgers University. He is presently a full professor at the University of Colorado, where he has taught since 1998. He has published three single-author scholarly books, one edited anthology, and more than fifty academic articles in epistemology, ethics, political philosophy, and metaphysics. His articles have appeared in such journals as the Philosophical Review, Mind, the Journal of Philosophy, Ethics, and others. Michael's first book, Skepticism and the Veil of Perception, significantly advanced the theory of Phenomenal Conservatism in epistemology, which is now considered one of the leading theories of justified belief and is the focus of the recent anthology, Seemings and Justification (Oxford, 2013). His second book, Ethical Intuitionism, is one of the leading contemporary defenses of ethical intuitionism and of moral realism more generally. It has been assigned as course reading by two colleagues at my own university, in addition to philosophers at the University of Massachusetts at Amherst, Lafayette College, Huron University College, Syracuse University, and Princeton University. It was the subject of a book symposium in Philosophy and Phenomenological Research. Michael's most recent book, The Problem of Political Authority, was published in 2013.

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19 von 20 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Huemer Makes Everything Fascinating 7. Mai 2016
Von Bryan Caplan - Veröffentlicht auf Amazon.com
Format: Taschenbuch Verifizierter Kauf
Huemer is my favorite philosopher. While I have little intrinsic interest in infinity, I can't imagine a better book on the topic. I devoured the whole thing this weekend. Huemer begins by cataloging six forms of "infinite regress" and seventeen puzzles about infinity. He then carefully reviews and critiques earlier theories of infinity, from ancient Greek philosophy to modern set theory. (If you suffered through set theory in Ph.D. microeconomics, you'll especially enjoy the latter discussion). Finally, he presents his own theory of infinity, beginning with the key distinction between logical impossibility and metaphysical impossibility. Then he uses it to distinguish "virtuous" from "vicious" infinite regresses, and solve his seventeen puzzles.

My favorite part of the book: Huemer's reply to the "anti-foundational" view that our beliefs can be justified through an infinite series of reasons rather than resting on foundational premises.

I doubt I'll ever read another book steeped in the philosophy of mathematics. But Huemer is such a singular intellect I'm grateful to read his thoughts about anything. If you're going to read one book about infinity, choose Approaching Infinity.
2 von 2 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen To infinity and beyond! 26. Dezember 2016
Von Amazon Customer - Veröffentlicht auf Amazon.com
Format: Taschenbuch
This is a wonderful book. Huemer writes very clearly and makes difficult ideas comprehensible. He has a lovely writing style which is almost conversational at times. Huemer's presentation of the various paradoxes of the infinite in the opening part of the book is incredibly engaging and fun. Those readers who are approaching these fascinating questions for the first time will not feel excluded, and they are sure to experience many of those 'wow' moments we all crave. Topics relevant to his discussion are presented in a logical order and he does an excellent job of covering the orthodox theories which he finds inadequate. Even if you ultimately reject Huemer's own theory, you will find lots of interesting ideas here to ponder.

My main concern is that Huemer's theory is based on an epistemological position called rationalism. In a nutshell, it says that some substantive knowledge of reality is gained via intuition; not all knowledge is rooted in sensory experience. Huemer admits that this is very controversial in philosophy, and any empiricists who read this book will reject his theory. Perhaps the book could have had a subtitle indicating that Huemer's approach assumes the truth of rationalism. To be fair to him, he does include a short section summarising his reasons for rejecting empiricism, and he references other works where the arguments are developed in more detail. However, any empiricist who remains unconvinced by this material may be left wondering whether they should even bother reading the second half of the book.
1 von 4 Kunden fanden die folgende Rezension hilfreich
1.0 von 5 Sternen his new theory of infinite amounts to use some of his favourite pet metaphysical principles 27. Dezember 2016
Von Amazon Customer - Veröffentlicht auf Amazon.com
Format: Taschenbuch
I agree with the previous reviewer, the book looks amateurish. The author seems unable to conceive curved space without embedding it in higher dimension spaces. His treatment of straight lines is very silly. Also, it seems that Set Theory should be rejected because (among other reasons), empty sets are not collections of anything. In my opinion, his new theory of infinite amounts to use some of his favourite pet metaphysical principles. If this strategy had been followed in science, we wouldn't have general relativity or quantum mechanics. By the way, he tells physicists the correct interpretation of General Relativity or the correct interpretation of imaginary numbers. This is not a good book about infinity, but you will definitely find INFINITE EGO here.
5 von 11 Kunden fanden die folgende Rezension hilfreich
1.0 von 5 Sternen Amateurish twaddle that is filled with errors. There are far better books around. 17. Dezember 2016
Von Samantha K. - Veröffentlicht auf Amazon.com
Format: Taschenbuch
Huemer, a philosopher with little or no training in mathematics, doesn't really understand his subject matter and hasn't bothered learning. He confuses countable and uncountable infinities, misunderstands the mathematical interpretation of Zeno's paradoxes, and messes up Cantor's diagonal proof of the uncountability of the reals. His discussion of the infinity of space is at the level of a Bill Nye kids' show, filled with big words that he either invented or doesn't quite understand.

There is no reason to drudge through this amateurish twaddle when there are so many excellent books on infinity out there, e.g. Gamow's "One, Two, Three... Infinity", D. F. Wallace's "Everything and More: A Compact History of Infinity" and, for the advanced, Heller and Woodin's "Infinity: New Research Frontiers". Give these a shot if you want to learn something about infinity, and leave Huemer's book on the shelf.
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