David Hume's Critique of Infinity
Series: Brill's Studies in Intellectual History; 102;
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Product details:
- Publisher BRILL
- Date of Publication 14 November 2000
- ISBN 9789004116498
- Binding Hardback
- No. of pages390 pages
- Size 235x155 mm
- Weight 764 g
- Language English 0
Categories
Short description:
This new study of David Hume?s philosophy of mathematics critically examines his objections to the concept of infinity, and his alternative phenomenalist theory of space and time as constituted by minima sensibilia or sensible extensionless indivisibles.
MoreLong 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.
MoreTable 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
David Hume's Critique of Infinity
55 576 HUF
51 130 HUF
