David Hume's Critique of Infinity

Erscheinungsjahr 2000
ISBN: 978-90-04-11649-8
Verlag: Brill

Buch, Englisch, Band 102, 390 Seiten, Format (B × H): 171 mm x 244 mm, Gewicht: 880 g

Reihe: Brill's Studies in Intellectual History

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.

Zielgruppe

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.

Autoren/Hrsg.

Jacquette, Dale

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Geschichtswissenschaft Geschichtliche Themen Kultur- und Ideengeschichte
• Geisteswissenschaften Philosophie Geschichte der Westlichen Philosophie Westliche Philosophie: 19. Jahrhundert
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik

Inhaltsverzeichnis

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

Über Autor(innen)

Jacquette, Dale
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).

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).