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

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Jul 31, 2023

Noson Yanofsky, a professor at Brooklyn College and author of The Outer Limits of Reason, explores the boundaries of knowledge and understanding. He dives into what science and math reveal about the limits of reason, discussing paradoxes and problems computers can't solve. With intriguing examples, he illustrates how small changes can lead to significant consequences, highlighting our intuition's failings, especially in complex systems and quantum mechanics. Yanofsky uncovers patterns in the limitations of reasoning, bridging philosophy with scientific discoveries.

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INSIGHT

Evolving Definition of Reason

Reason encompasses science, math, logic, computers, and physics but is hard to define precisely.
Its definition evolves over time as new knowledge and ideas reshape what is considered reasonable.

INSIGHT

Objectivity and Debate in Reason

Reason aims to produce objective knowledge verifiable by anyone at any time.
Yet, what counts as reasonable or scientific can be debated, like with string theory or negative numbers historically.

INSIGHT

Paradoxes Reveal Reason's Limits

Many limitations of reason show up as paradoxes or self-referential paradoxes.
These patterns reveal errors in assumptions, showing where reason reaches its boundaries.

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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.

Noson S. Yanofsky is Professor in the Department of Computer and Information Science at Brooklyn College and The Graduate Center of the City University of New York. He is a coauthor of Quantum Computing for Computer Scientists.

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