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The Outer Limits of Reason

What Science, Mathematics, and Logic Cannot Tell Us

Noson S. Yanofsky

Publication Year: 2013

An exploration of the scientific limits of knowledge that challenges our deep-seated beliefs about our universe, our rationality, and ourselves.

Published by: The MIT Press

Title Page, Copyright, Dedication

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pp. 2-7


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pp. vii-viii

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pp. ix-x

With understanding comes ambivalence. Once we know something, we often find it boring and trite. On the other hand, the mysterious and unknown fascinates us and holds our attention. That which we do not know or understand is what interests us, and what we cannot know intrigues us even more. This book explores topics that reason tells us we cannot...


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pp. xi-xiv

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1. Introduction

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pp. 1-14

A civilization can be measured by how much progress its science and technology have made. The more advanced their science and technology are, the more advanced their civilization is. Our civilization is deemed more advanced than what we call primitive societies because of all the technological progress we have made. In contrast, if an alien civilization...

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2. Language Paradoxes

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pp. 15-30

Rather than jumping headfirst into the limitations of reason, let us start by just getting our toes wet and examining the limitations of language. Language is a tool used to describe the world in which we live. However, don’t confuse the map with the territory! There is one major difference between the world we live in and language: whereas the real world is free...

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3. Philosophical Conundrums

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pp. 31-64

Long before modern scientists took up the task of investigating the limits of reason, philosophers were analyzing the complexities of our world and our knowledge of it. In this chapter I explore some of the ancient and contemporary philosophical aspects of reason’s limitations...

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4. Infinity Puzzles

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pp. 65-96

Since ancient times, people have contemplated the infinite and its properties. For most of that time, our thoughts on the infinite were mired in strange ideas that could not withstand the rigor of exact reasoning. With such confusion, the medievals would endlessly discuss inane questions, like “ How many angels can dance on the head of a pin? ” In the late...

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5. Computing Complexities

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pp. 97-134

Computers are paragons of reason. They are heartless machines that relentlessly obey the laws of logic. There is nothing emotional or wishy-washy about computers: they do exactly as they are told by following the dictates of logic. It is from the perspective of computers as engines of reason that we examine these machines and determine what tasks they can and cannot...

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6. Computing Impossibilities

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pp. 135-160

Computers can do many wonderful things. However, there are many tasks that they cannot perform. Computers cannot determine whether a painting is beautiful; they do not “ understand ” moral issues; and they cannot fall in love. Such “ human ” processes are beyond computation...

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7. Scientific Limitations

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pp. 161-234

Henri Poincaré (1854 – 1912) tells a morbid tale of a man walking down a street and getting killed because a roofer accidently drops a tile.1 Had the man been there a few seconds later or earlier, he might have lived for many years. Had the roofer not dropped the tile or done so a fraction of a second earlier or later, the man would have continued his stroll...

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8. Metascientific Perplexities

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pp. 235-296

In this section I explore different aspects of the philosophy of science. This large and fascinating branch of philosophy covers the nature of science and the way it progresses. Rather than attempting a detailed survey of the philosophy of science, I simply cherry-pick several topics at the core of the field and examine how they pertain to the limits of science...

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9. Mathematical Obstructions

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pp. 297-338

Mathematics is the epitome of pure reason. Much of science is based on mathematics and logic. In a sense, mathematics is the language of reason. It is the most successful of all human inventions. And yet, as we will see, it too has its limitations...

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10. Beyond Reason

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pp. 339-354

Every chapter of this book has discussed a different subject and its limitations. There are, however, other ways to categorize the myriad limitations we have found. Here I give another classification of four types of limitations on reason...


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pp. 355-378


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pp. 379-392


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pp. 393-404

E-ISBN-13: 9780262316774
E-ISBN-10: 0262316773
Print-ISBN-13: 9780262019354

Page Count: 328
Publication Year: 2013