Berkeley and Mathematics

Abstract This chapter investigates Berkeley’s approach to mathematics. The first section connects Berkeley’s philosophical understanding of mathematics to his anti-abstractionist epistemology. Where a long tradition had taken mathematics to be concerned with abstract ideas, Berkeley sought to show that mathematics did not depend upon the supposition of abstract ideas. The second section deals with Berkeley’s account of geometry and outlines a significant change in his approach to the subject. In his early writings, Berkeley was prepared to abandon traditional geometry in favor of a radical doctrine of sensible minima, but in the Principles of Human Knowledge and later works, he accommodates essentially all of Euclidean geometry within the constraints of his epistemology. The third section examines Berkeley’s highly nominalistic approach to arithmetic and algebra, arguing that his doctrine is in many respects a predecessor of the formalist philosophy of mathematics. The fourth section studies Berkeley’s approach to the calculus, particularly his critique of the Newtonian calculus of fluxions in his 1734 work The Analyst.