Geometry and Politics: Mathematics in the Thought of Thomas Hobbes

Abstract

It is a commonplace of intellectual history that the 17th century's explosive development of mathematized science offered a seductive example in other spheres of thought. The successes of this Revolution seemed to rest on conceptual foundations and to use methods whose adoption promised similar triumphs wherever tried. The physicists' isolation, in thought and experiment, of categories amenable to quantification-mass, velocity, acceleration, force-had allowed the derivation of rigorous laws (Galileo's account of free fall, Newton's of universal gravitation); why should not other areas of study achieve so much? The clarity of ideas, the certainty of inference, characteristic of mathematical thinking became beacons. The geometrical manner of presenting a subject, stemming from Euclid's Elements and adopted by Galileo and Newton alike-the step-by-step deduction of results from explicit definitions and axioms-gave a model to those who would organize and expound their own realms to best advantage (Spinoza's Ethics is perhaps the most striking example). Few thinkers felt more deeply the lure of the new science and its mathematical mystique than the great British philosopher Thomas Hobbes, the author of Leviathan. Though his primary concerns-politics, morals, the law-might seem far from physical science in subject and spirit, Hobbes came to believe that mathematical categories and methods might be brought to bear even here, and might bring understanding and agreement where confusion and discord notoriously prevailed. Like all of us he was shaped as much by his personal history as by the spirit of his age. The son of a disreputable clergyman, he made his way up the social scale by attaching himself, aged nineteen (1608), to a noble family as tutor, only to find his employer in shaky financial straits; his ensuing sense of insecurity may have been an impulse toward the certainties of mathematics and science'. Moreover his career had for background a painftil and protracted time of social strife: the Puritan Rebellion, the Long Parliament (1640-53), civil war, the beheading of a king (Charles I, 1649), the ascendancy of Cromwell, the eventual restoration of the monarchy (1660). The royalist philosopher found it prudent to spend eleven of these turbulent years (1640-51) in exile in Paris.* In his eyes the conflicts tearing his homeland seemed to typify the worst of social ills, and to give practical urgency to a rational reconstruction of political life. Meanwhile his European travels brought personal encounters with some of the makers of the Scientific Revolution. In Florence he sought out Galileo, then (1636) an old man; what passed between them is not known, but Hobbes