David Hume's critique of infinity

Author(s)

• Jacquette, Dale

Bibliographic Information

David Hume's critique of infinity

by Dale Jacquette

（Brill's studies in intellectual history, v. 102）

Brill, 2001

Note

Includes bibliographical references (p. [335]-351) and index

Description and Table of Contents

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.

Table of Contents

Preface Acknowledgments INTRODUCTION: TWO-FOLD TASK OF HUME'S CRITIQUE Hume's Strict Finitism Dialectical Structure of Hume's Critique Historical-Philosophical Context Bayle's Trilemma for the Divisiblity of Extension Legacy and Influence of Berkeley on Hume's Metaphysics of Space and Philosophy of Mathematics PART I. THE INKSPOT EXPERIMENT 1. Minima Sensibilia 2. Against Mind-Mediated Ideas of Infinite Divisibility 3. Hume's Inkspot Metaphysics of Space: Finite Divisibility of Extension into Sensible Extensionless Indivisibles PART II. REFUTATIONS OF INFINITE DIVISIBILITY 4. Hume's Reductio Arguments 5. Antithesis in Kant's Second Antinomy 6. Classical Mathematics and Hume's Refutation of Infinite Divisibility 7. Infinite Divisibility in Hume's First Enquiry CONCLUSION: HUME AGAINST THE MATHEMATICIANS On the Experiential Origin of Ideas Mathematics and Science Without Infinity Hume's Finitism and Cantor's Transfinite Cardinals Resilience of Hume's Critique AFTERWORD: HUME'S AESTHETIC PSYCHOLOGY OF DISTANCE, GREATNESS, AND THE SUBLIME Concepts of the Sublime Infinity, Greatness, and the Sublime Hume's Philosophical Psychology and the Aesthetics of Greatness and the Sublime Aesthetics of Great Distance in Space and Time Greatness, Difficulty, and Hume's Aesthetics of the Sublime Bibliography Index

by "Nielsen BookData"

• NCID: BA50099954
• ISBN:
  • 9004116494
• LCCN: 00045414
• Country Code: ne
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Leiden
• Pages/Volumes: xvi, 384 p.
• Size: 25 cm
• Classification:
  • LCC : B1499.I67
  • DC21 : 192
• Subject Headings:
  • LCSH : Hume, David, 1711-1776 -- Contributions in concept of the infinite
  • LCSH : Infinite -- History -- 18th century
• Parent Bibliography ID:
  • BA0144067X