This article examines Hobbes’s conception of mathematical method, situating his methodological writings in the context of disputed mathematical issues of the seventeenth century. After a brief exposition of the Hobbesian philosophy of mathematics, it investigates Hobbes’s attempts to resolve three important mathematical controversies of the seventeenth century: the debates over the status of analytic geometry, disputes over the nature of ratios, and the problem of the “angle of contact” between a curve and tangent. In the course of these investigations, Hobbes’s (...) account of mathematics and its method is contrasted with the those of Descartes, Isaac Barrow, John Wallis, and Christopher Clavius. (shrink)

Why would someone concerned with heresy, who defined it as private opinion that flew in the face of doctrine sanctioned by the public person, harbor such a detailed interest in heterodoxy? Hobbes's religious beliefs ultimately remain a mystery, as perhaps they were meant to: the private views of someone concerned to conform outwardly to what his church required of him, and thereby avoid to heresy, while maintaining intellectual autonomy. The hazard of Hobbes's particular catechism is that he and his supporters (...) could never avoid the suspicion of insincerity. His preparedness to believe whatever the prince demanded of him smacked of heresy in the more usual sense, despite elaborate biblical exegesis designed to prove his orthdoxy. Undoubtedly he realized it even as he wrote the last lines of Leviathan, expressing the hope that "I cannot think it will be condemned at this time, either by the Publique Judge of Doctrine, or by any that desires the continuance of Publique Peace/7 Indicating an intention to return to science, he continued, "I hope the Novelty will as much please, as in the Doctrine of this Artificiall Body it useth to offend" (Lev, Rev. and Conclusion, 491). (shrink)