The Art of Logic in an Illogical World

by Eugenia Cheng

Overview

How both logical and emotional reasoning can help us live better in our post-truth world

In a world where fake news stories change election outcomes, has rationality become futile? In The Art of Logic in an Illogical World, Eugenia Cheng throws a lifeline to readers drowning in the illogic of contemporary life. Cheng is a mathematician, so she knows how to make an airtight argument. But even for her, logic sometimes falls prey to emotion, which is why she still fears flying and eats more cookies than she should. If a mathematician can't be logical, what are we to do? In this book, Cheng reveals the inner workings and limitations of logic, and explains why alogic — for example, emotion — is vital to how we think and communicate. Cheng shows us how to use logic and alogic together to navigate a world awash in bigotry, mansplaining, and manipulative memes. Insightful, useful, and funny, this essential book is for anyone who wants to think more clearly.

Product Details

ISBN-13:	9781541672482
Publisher:	Basic Books
Publication date:	09/11/2018
Pages:	320
Sales rank:	537,714
Product dimensions:	5.50(w) x 8.30(h) x 1.30(d)

About the Author

Eugenia Cheng is the scientist in residence at the School of the Art Institute of Chicago and an honorary fellow at the University of Sheffield. She is the author of How to Bake Pi, Beyond Infinity, and The Art of Logic in an Illogical World. She lives in Chicago, Illinois.

Table of Contents

Introduction ix

Part I The Power of Logic

1 Why logic? 3

2 What logic is 22

3 The directionality of logic 42

4 Opposites and falsehoods 58

5 Blame and responsibility 81

6 Relationships 101

7 How to be right 115

Part II The Limits of Logic

8 Truth and humans 129

9 Paradoxes 147

10 Where logic can't help us 165

Part III Beyond Logic

11 Axioms 183

12 Fine lines and gray areas 191

13 Analogies 208

14 Equivalence 235

15 Emotions 262

16 Intelligence and rationality 278

Acknowledgments 299

Index 301

Editorial Reviews

06/11/2018
Mathematician Cheng (Beyond Infinity) considers how the principles of math can be used to help define one’s personal ethos and bridge the gap between differing points of view. She explores real-life ethical and philosophical problems, like white privilege, “arbitrary standards” in education, and racially-motivated police brutality, through the lens of data-driven logical precepts and mathematical techniques. These include proofs, Venn diagrams, truth tables, flow charts, fractal trees, and more. Using these methods, Cheng argues, can help people avoid mistakes in logical thinking and recognize fallacies. However, she posits that there is more to having a constructive conversation than logic alone, stating that “we should look to engaging people’s emotions to convince them of logical arguments.” Discussing thorny issues, she says, requires a sense of “nuance,” rather than the “false promise of black and white clarity,” and a more intuitive and feelings-based approach. Cheng is largely successful in making mathematical principles and formulas accessible to a lay audience, though the occasional statement—such as “it is the contrapositive of the converse so is equivalent to the converse”—will be challenging for those unfamiliar with math jargon. Cheng’s suggestion to combine the persuasive powers of logic with emotional appeal to find common ground is original and pragmatic, particularly in these divisive times. Agent: George Lucas, InkWell Management. (Sept.)

Publishers Weekly

"It's a shame that not everyone can read this book, but Cheng claims it is incumbent on those of us who can to use compassion and logic to argue productively with those who can't. In this way, advanced mathematics could make a meaningful contribution to creating a better society as well as happier conversations and relationships. There is a sense in which this book is proof it can."—Guardian


"Following in the tradition of George Boole, Lewis Carroll and John Venn, who provided algebraic or diagrammatic aids to logical calculation, Eugenia Cheng enhances her reputation as a popular mathematics writer with this perceptive analysis of logic and its limitations."—Times Higher Education


"Cheng's book covers the basics of logic, argumentation, and emotion through humor and an excellent use of illustrations like ice cream, sexism, and Gödel's Incompleteness Theorem."—MAA Reviews


"Entertaining... a very welcome primer in logical thinking."—Kirkus Reviews


"Cheng's suggestion to combine the persuasive powers of logic with emotional appeal to find common ground is original and pragmatic, particularly in these divisive times."—Publishers Weekly


"With humor, grace, and a natural gift for making explanations seem fun, Eugenia Cheng has done it again. This is a book to savor, to consult, and to buy for all your friends. You'll think more clearly after reading this book, something that is unfortunately in short supply these days. I am buying several copies to send to heads of state."—Daniel J. Levitin, Ph.D., New York Times bestselling author of This Is Your Brain on Music and The Organized Mind


"This book is empowering! Eugenia Cheng makes logic alive and relevant with prose that is accessible, clear and engaging. In this masterpiece, you will learn how the power of logic can clarify some of the most pressing issues that confront us, as individuals and a society."—Stephon Alexander, author of The Jazz of Physics and professor of physics, Brown University

From the Publisher

2018-06-27
Logic helps people build bridges to understanding. But what if people don't want those bridges? Aha, says this entertaining guide: There's a meta-problem for you….In our current landscape of the postfactual, the loudest bellower is king. Enter Cheng (Beyond Infinity: An Expedition to the Outer Limits of Mathematics, 2017, etc.), the scientist in residence at the Art Institute of Chicago—now there's a good idea—and possessor of a formidable, mathematically inclined mind. Though the author aims to teach math, science, and formal logic as she progresses, she really means to help readers construct better arguments, which may turn out to be a world-saving proposition. There is a built-in advantage to using logic, she writes, in that it provides a framework for discovering what is true, and "one of the main reasons to have a clear framework for accessing truth is to be able to agree about things." The notion of agreement will come into play late in the book, when Cheng analyzes the best kinds of arguments, which allow us to understand another person's point of view. Until that point, there are theorems, axioms, and proofs to go through, for mathematically based logic hinges on such things as the union of sets (the place where two circles meet in a Venn diagram) and the proper application of analogy to any particular problem. The author isn't exactly playful, but she pitches a few paradoxes as she moves along—one of them being the fact that, since logic doesn't actually correspond to what we know as the real world, we have to "forget the pesky details that prevent things from behaving logically." In other words, we have to think abstractly, which poses plenty of other challenges.Though full of pauses, second glances, and head-scratches, this is a very welcome primer in logical thinking.

Kirkus Reviews

11/01/2018
At the heart of mathematics is the proof{amp}mdash;a logical argument from an agreed-upon set of axioms to reach some conclusion. In the real world few things are that simple. In her latest work, mathematician Cheng (Beyond Infinity), using current areas of disagreement from political to social, explains how logical arguments should be constructed and why they frequently fail. These include some cases in which a statement does not necessarily follow logically from the one before but still manages to fail in a different way. For example, people may have similar yet different or unspoken sets of basic assumptions. Other disagreements may arise from unclear generalizations, false equivalencies, or faulty analogies. In clear and easy-to-read prose, Cheng walks readers through simple logic, the limitations of the law of the excluded middle, handling gray areas, and even a little about logical paradoxes. VERDICT This well-written, accessible book offers insight into other people's positions and may even help us find the flaws in our own reasoning.{amp}mdash;Harold D. Shane, Mathematics Emeritus, Baruch Coll. Lib., CUNY

Library Journal

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