If A, Then B: How the World Discovered Logic

by Michael Shenefelt and Heidi White

Columbia Univeristy Press Publication date: June, 2013

The authors Michael Shenefelt and Heidi White

We all have a sense of logic—we rely on it every day—yet logic is also deeply mysterious. Where does our sense of logic come from? What is it really a sense of? And what drove people to start studying logic in the first place?

While logical principles seem timeless, placeless, and eternal, their discovery is a story of personal accidents, political tragedies, and broad social change. If A, Then B begins with logic's emergence twenty-three centuries ago and tracks its expansion as a discipline ever since.

Logic is more than the work of logicians alone. Its discoveries have survived only because logicians have also been able to find a willing audience, and audiences are a consequence of social forces affecting large numbers of people, quite apart from individual will. The story of logic is therefore more than a tale of individual abstraction; it is also a story of politics, economics, technology, and geography, because all these factors helped generate an audience for the discipline from the start.

Many great names have contributed to logic. Learn about the turbulent times of the enigmatic Aristotle, the ancient Stoic philosopher Chrysippus, the medieval theologian Peter Abelard, and the modern thinkers René Descartes, David Hume, Jeremy Bentham, George Boole, Augustus De Morgan, John Stuart Mill, Gottlob Frege, Bertrand Russell, and Alan Turing.

There are many kinds of logic today—including syllogistic, propositional, inductive, and symbolic. If A, Then B is the first book to situate the history of logic within the movements of a larger social world and to ground the discipline's principles in a compelling material narrative.

"This is a delightful book, both well written and highly informative."
(Kenneth G. Lucey, Teaching Philosophy, 2 June 2014)

"Michael Shenefelt and Heidi White's book is great fun for people who enjoy ideas. It is full of provocative claims about a variety of topics, but Shenefelt and White's positions are not just provocative. They are also perceptive and intriguing, and they are supported by often ingenious arguments."
(Phil Washburn, New York University )

“If A, then B provides a fascinating springboard for discussing how and why logic developed in various cultures....The book provides a new resource for those interested in studying aspects of the history of mathematics and logic.”
(Calvin Jongsma, Mathematical Association of America Reviews, 14 January 2015)

“This is a fascinating story of one of our most abstract yet foundational disciplines. The result is an insightful and wonderfully readable exploration of an essential part of human rationality at work. Highly recommended.”
(Lloyd Carr, Rivier University)