David Hume's Critique of Infinity
Biographical note
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).
Readership
Students (advanced undergraduate and graduate), professional scholars, and other readers interested in David Hume, philosophy, metaphysics, epistemology, philosophy of mathematics, philosophy of science, history of philosophy, history of mathematics, history of science, Enlightenment studies, history of ideas, history of technology, and intellectual background of contemporary Western civilization.
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
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
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