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Squaring the Circle

The War between Hobbes and Wallis

In 1655, the philosopher Thomas Hobbes claimed he had solved the centuries-old problem of "squaring of the circle" (constructing a square equal in area to a given circle). With a scathing rebuttal to Hobbes’s claims, the mathematician John Wallis began one of the longest and most intense intellectual disputes of all time. Squaring the Circle is a detailed account of this controversy, from the core mathematics to the broader philosophical, political, and religious issues at stake.

Hobbes believed that by recasting geometry in a materialist mold, he could solve any geometric problem and thereby demonstrate the power of his materialist metaphysics. Wallis, a prominent Presbyterian divine as well as an eminent mathematician, refuted Hobbes’s geometry as a means of discrediting his philosophy, which Wallis saw as a dangerous mix of atheism and pernicious political theory.

Hobbes and Wallis’s "battle of the books" illuminates the intimate relationship between science and crucial seventeenth-century debates over the limits of sovereign power and the existence of God.

Table of Contents

List of Abbreviations
Chapter One: The Mathematical Career of the Monster of Malmesbury
Chapter Two: The Reform of Mathematics and of the Universities
Ideological Origins of the Dispute
Chapter Three: De Corpore and the Mathematics of Materialism
Chapter Four: Disputed Foundations
Hobbes vs. Wallis on the Philosophy of Mathematics
Chapter Five: The "Modern Analytics" and the Nature of Demonstration
Chapter Six: The Demise of Hobbesian Geometry
Chapter Seven: The Religion, Rhetoric, and Politics of Mr. Hobbes and Dr. Wallis
Chapter Eight: Persistence in Error
Why Was Hobbes So Resolutely Wrong?
Appendix: Selections from Hobbes’s Mathematical Writings

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