David Hume's Critique of Infinity

Jacquette (philosophy, Pennsylvania State U.) critically examines David Hume's philosophy of mathematics, focusing on his objections to the concept of infinity. He considers Hume's critique of infinity in historical context as a product of Enlightenment theories of knowledge and assesses the prospects of his strict finitism in light of contemporary mathematics, science, and philosophy. The first part focuses on minima sensibilia , mind-mediated ideas of infinite divisibility, and Hume's inkspot metaphysics of space. In the second section he presents refutations of infinite divisibility, discussing Hume's reductio arguments, antithesis in Kant's second antinomy, classical mathematics and Hume's refutation of infinite divisibility, and infinite divisibility in Hume's first Enquiry . An afterword discusses Hume's aesthetic psychology of distance, greatness, and the sublime. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Dale Jacquette, Ph.D. (1983) in Philosophy, Brown University, is Professor of Philosophy at The Pennsylvania State University. He has written numerous books and articles on logic, metaphysics, philosophy of mind, and aesthetics, and has recently published Wittgenstein’s Thought in Transition (Purdue University Press, 1998).