# The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us

Yanofsky, Noson S.
- ISBN:
- 9780262019354

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes. Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known. Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there. The MIT Press Editorial Reviews Publishers Weekly * 10/07/2013 Rather than write about what he knows, Yanofsky (Quantum Computing for Computer Scientists) prefers to explore the topic of what he doesn't know--or rather what we as humans cannot know. In this refreshingly original and ambitious philosophical inquiry, he attempts to map the limitations of human reason by examining the established conundrums, paradoxes, impossibilities within science and technology. Divided by subject area (including language, philosophy, science, mathematics, computing), each chapter lays out an array of paradoxes and unsolvable problems, clearly and concisely guiding readers into and around the worlds of reason. The examples range in complexity and some may be more familiar than others, such as his explanations of the Liar's Paradox, "this sentence is false." The more complicated contradictions, such as George Cantor's proof that an infinite set of numbers between 0 and 1 is vastly larger than an infinite set of natural numbers (1, 2, 3, 4 . . .), the author unpacks succinctly within the framework of modern life. He writes, "It would be foolhardy to cross a modern suspension bridge if you knew that the engineer did not believe in Cantor's work." Yanofsky takes on this mindboggling subject with confidence and impressive clarity. He eases the reader into the subject matter, ending each chapter with further readings. His book is a fascinating resource for anyone who seeks a better understanding of the world through the strangeness of its own limitations and a must-read for anyone studying information science. Illus. (Sept.) The New Scientist Yanofsky provides an entertaining and informative whirlwind trip through limits on reason in language, formal logic, mathematics -- and in science, the culmination of humankind's attempts to reason about the world. PsycCRITIQUES - Raymond S. Nickerson In my view, Outer Limits is an extraordinary, and extraordinarily interesting, book. It is a cornucopia of mind-bending ideas. Leonardo Reviews - Thomas Colin The scope of the material covered is so wide, and the writing so clear and intuitive, that all readers will learn something new and stimulating.