David Hume's critique of infinity / / by Dale Jacquette.

• Superior document: Brill's studies in intellectual history, volume 102
• VerfasserIn: Jacquette, Dale,
• Place / Publishing House: Leiden ;, Boston : : Brill,, 2001.
• Year of Publication: 2001
• Language: English
• Series: Brill's studies in intellectual history ; v. 102.
• Physical Description: 1 online resource (399 pages)

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.

Table of Contents

Preliminary Material -- INTRODUCTION: TWO-FOLD TASK OF HUME'S CRITIQUE -- 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 -- 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.