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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...

In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work. Jesseph challenges the prevailing view that Berkeley's mathematical writings are peripheral to his philosophy and argues that mathematics is in fact central to his thought, developing out of his critique of abstraction. Jesseph's argument situates Berkeley's ideas within the larger historical and intellectual context of the Scientific Revolution.

Jesseph begins with...

The essays offer a unified and comprehensive view of 17th century mathematical and metaphysical disputes overstatus of infinitesimals, particularly the question whether they were real or mere fictions. Leibniz's development of the calculus and his understanding of its metaphysical foundation are taken as both a point of departure and a frame of reference for the 17th century discussions of infinitesimals, that involved Hobbes, Wallis, Newton, Bernoulli, Hermann, and Nieuwentijt. Although the calculus was undoubtedly successful in mathematical practice, it remained controversial because its...

The A to Z of Descartes and Cartesian Philosophy includes many entries on Descartes's writings, concepts, and findings. Since it is historical, there are other entries on those who supported him, those who criticized him, those who corrected him, and those who together formed one of the major movements in philosophy, Cartesianism. To better understand the period, the authors drew up a brief chronology, and to see how Descartes and Cartesianism fit into the general picture, they have written an introduction and a biography. Since everything cannot be summed up in one volume, a bibliography...