Infinity: New Research Frontiers 1st Edition by Michael Heller (PDF)

Description

“The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.” – David Hilbert 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.

User’s Reviews

Editorial Reviews: Review “On the whole, 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.” Linguistic and Philosophical Investigations Book Description A dozen world-renowned researchers explore the concept of infinity through the prism of mathematics and beyond. About the Author 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). Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Excellent!Thank you!tjd

⭐It’s a math book. I don’t want to read 3 chapters about god and the religious ramifications of infinity just to getto some actual set theory. Chapter 4 which was written by Dr. Wooden explains large cardinals in a very relaxed and understandable manner.

⭐W. Hugh Woodin and Michael Heller guarantee good quality.

⭐A good exposition on Infinity. It is one of my favorites of books on infinity and a good read for a non mathematical reader.

⭐It’s a little mature but interesting and very describing about the ups and downs of the infinite and eternity of life.

⭐It was excellent, The book covered so many different aspects of Infinity Research- great chapter contributors. Learned a lot. L.S.

⭐I was looking forward to reading this book and it was the first one I started in the last batch that I bought. However, I’m disappointed. It isn’t obvious what level the book is pitched at. The book is composed of 14 different articles in 4 sections from 13 different researchers. The topics are all based on Infinity but each section considers the concept from different schools of thought: mathematics, physics, and theology.Some articles, or parts of articles, are great while others are merely good. Unfortunately there are a couple of articles that really don’t belong. The book is published by Cambridge Academic which should suggest that the articles are at a research level, that isn’t quite the case. I’d say about 75% is fairly readable from a lay perspective and definitely readable by a keen/willing reader. The remaining 25% is either too mathematically abstruse or too frustrating to read; one article seems to use made up words that are closer to random unpronounceable strings than actual words (phonologically illegal). If you Google these words then it turns out some of them are ‘real’ but almost no explanation is given of them and I’d wager that a very narrow subset of professional researchers worldwide will know them.As a concise volume of information for reference to topics on Infinity then this might be the book to have. That said, I still think it could have been better formed. Ultimately, there is a lot of good information in there but it could have been presented in a more coherent way. Part of the problem is that it is composed of several research articles that hang together by a common theme but don’t really inter-related in a coherent enough way that you’d ideally want from a popular science/maths book. No doubt it was the intention to aim at the former rather than the latter but I think there is a lot of value in releasing a modern book about infinity that engages with cutting edge research, and that’s what this book almost is.For me the highlights were articles 2, 3, 10, 11 & 13.Some of the concepts covered: historical perspective, countability, cardinal/ordinal infinity, Absolute Infinity, how to understand (envisage) what infinity is, the relation of physical and mathematical infinity, the reality of physical infinities, relation of God and Infinity.

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