3 vols. London: Thomas Tegg.
10 Curley, Edwin. 1992. “‘I Durst Not Write So Boldly’ or How to Read Hobbes’ Theological-Political Treatise.” In Hobbes e Spinoza, edited by Daniela Bostrengi, 497–593. Naples: Bibliopolis
11 Detlefson, Karen. 2006. “Atomism, Monism, and Causation in the Natural Philosophy of Margaret Cavendish.” In Oxford Studies in Early Modern Philosophy, Vol. 3, edited by Daniel Garberand Steven Nadler, 199–240. Oxford: Oxford University Press.
12 Evans, Ernest1948. Adversus Praxean Liber. London: S.P.C.K.
13 Gorham, Geoffrey. 2013. “The Theological Foundations of Hobbesian Physics: A Defense of Corporeal God.” British Journal for the History of Philosophy 21: 240–61.
14 Gorham, Geoffrey. 2014a. “Mixing Bodily Fluids: Hobbes’s Stoic God.” Sophia: International Journal for the Philosophy of Religion 53: 33–49.
15 Gorham, Geoffrey. 2014b. “Hobbes on the Reality of Time.” Hobbes Studies 27: 80–103.
16 Herbert, Gary B.1977. “Hobbes’s Phenomenology of Space.” Journal of the History of Ideas 48: 709–17.
17 Hobbes, Thomas. 1839–1845a. The English Works of Thomas Hobbes, 11 vols., edited by Sir William Molesworth. London: John Bohn. Cited as EW.
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19 Hobbes, Thomas. 1976. Thomas White’s De Mundo Examined, edited by Harold W. Jones. London: Bradford University Press.
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3 Hobbesian Mathematics and the Dispute with Wallis
DOUGLAS JESSEPH
Mathematics plays a prominent role in Hobbes’s grand intellectual project. In the course of more than two decades he published over a dozen mathematical works, ranging from brief pamphlets to synoptic treatments of the subject.1 Quantity of output is no guarantee of its quality, however, and Hobbes’s mathematics is remembered primarily for his many failed attempts to square the circle and solve other famous mathematical problems. His long and humiliating controversy with John Wallis, Oxford’s Savilian Professor of Geometry, annihilated Hobbes’s mathematical reputation and has left the widely shared impression that there is nothing of value to be found in his many mathematical writings.2 My purpose here is not to defend Hobbes’s attempts to solve what we now know to be unsolvable problems, but rather to examine the philosophical and methodological basis upon which his mathematics was founded and the broader context in which it developed. Toward that end, this chapter is divided in two sections. The first is an overview of Hobbes’s materialistic philosophy of mathematics. The second investigates his controversy with Wallis.
3.1 The Hobbesian Philosophy of Mathematics
The significance that Hobbes attached to mathematics (and, more particularly, to geometry) is attested by a famous anecdote recorded by his friend John Aubrey. He reports that Hobbes was initiated into the study of mathematics by happening to come across Euclid’s proof of the Pythagorean Theorem (Euclid 1925):
He was … 40 yeares old before he looked upon geometry; which happened accidentally. Being in a gentleman’s library in ___, Euclid’s Elements lay open, and’twas the 47 El. libri. I. He read the proposition. “By G___,” sayd he, “this is impossible!” So he reads the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him