Hobbesian Mathematics and the Dispute with Wallis

Abstract

This chapter provides an overview of Thomas Hobbes's materialistic philosophy of mathematics. Hobbes's mathematical ontology rejects the seventeenth century's received view of the subject and his proposed first principles departed quite significantly from the tradition. Hobbes's understanding of geometry as a generalized science of material bodies puts him at odds with the traditional notion that the objects of geometrical investigation are radically distinct from the realm of material things. Hobbes's methodology holds that demonstrative knowledge must be based on definitions that identify the causes of things. Hobbes was quite hostile to the algebraic methods characteristic of Descartes's analytic geometry, and he found fault with some presentations of the “method of indivisibles” that is an important precursor to the calculus. Hobbes approved of Bonaventura Cavalieri's method while dismissing John Wallis's approach as incoherent. The chapter investigates Hobbes's controversy with Wallis. Any discussion of Hobbes's mathematics takes place against the background of his controversy with Wallis.