David Hume's Critique of Infinity

Description

This new study of David Hume's philosophy of mathematics critically examines his objections to the concept of infinity. Although infinity raises some of the most challenging paradoxes for Hume's empiricism, there have been few detailed and no fully comprehensive systematic discussions of Hume's critique. In a series of eight interrelated arguments, Hume maintains that we cannot experience and therefore can have no adequate idea of infinity or of the infinite divisibility of extension. He proposes to replace the notion of infinity with an alternative phenomenalist theory of space and time as constituted by minima sensibilia or sensible extensionless indivisibles. The present work considers Hume's critique of infinity in historical context as a product of Enlightenment theory of knowledge, and assesses the prospects of his strict finitism in light of contemporary mathematics, science, and philosophy. PREFACE ACKNOWLEDGMENTS INTRODUCTION TWO-FOLD TASK OF HUME'S CRITIQUE PART ONE. THE INKSPOT EXPERIMENT CHAPTER 1. MINIMA SENSIBILIA CHAPTER 2. AGAINST MIND-MEDIATED IDEAS OF INFINITE DIVISIBILITY CHAPTER 3. HUME'S INKSPOT METAPHYSICS OF SPACE: FINITE DIVISIBILITY OF EXTENSION INTO SENSIBLE EXTENSIONLESS INDIVISIBLES PART TWO. REFUTATIONS OF INFINITE DIVISIBILITY CHAPTER 4. HUME'S 'REDUCTIO' ARGUMENTS CHAPTER 5. ANTITHESIS IN KANT'S SECOND ANTINOMY CHAPTER 6. CLASSICAL MATHEMATICS AND HUME'S REFUTATION OF INFINITE DIVISIBILITY CHAPTER 7. INFINITE DIVISIBILITY IN HUME'S FIRST ENQUIRY CONCLUSION. HUME AGAINST THE MATHEMATICIANS AFTERWORD. HUME'S AESTHETIC PSYCHOLOGY OF DISTANCE, GREATNESS, AND THE SUBLIME BIBLIOGRAPHY INDEX