David Hume's Critique of InfinityThis 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. |
Contents
TWOFOLD TASK OF HUMES CRITIQUE | 1 |
THE INKSPOT EXPERIMENT | 41 |
Against MindMediated Ideas of Infinite | 57 |
Lockes Category of Negative Ideas | 65 |
Kemp Smiths Analysis | 79 |
Hume on the Idea of a Vacuum and Complex | 92 |
Finite Divisibility of Extension into Sensible | 101 |
Adequate Ideas of Finite Divisibility | 110 |
Classical Mathematics and Humes | 197 |
Infinite Divisibility in Humes First Enquiry | 223 |
HUME AGAINST THE MATHEMATICIANS | 261 |
Mathematics and Science Without Infinity | 271 |
HUMES AESTHETIC PSYCHOLOGY | 305 |
Humes Philosophical Psychology and the Aesthetics | 315 |
Greatness Difficulty and Humes Aesthetics of | 325 |
Bibliography | 335 |
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Common terms and phrases
abstract general ideas addition of infinite adequate idea aesthetic argument against infinite assumption Bayle Bayle's trilemma Berkeley Berkeley's Cantor's complex idea conceivability concept of infinity conclusion Continuum Hypothesis contradiction criticism critique of infinity David Hume Descartes distance distinct divisibility of extension empiricism empiricist Enquiry Euclidean exact equality existence extended objects extension is infinitely finite extension finitist Fogelin geometry dilemma Hume's argument Hume's critique Hume's theory Hume's Treatise Ibid idea of extension idea of infinity ideas of space imagination infinite divisibility thesis infinite number infinitist infinity and infinite inkspot argument inkspot experiment ISBN 90 John Keill Kant Kant's Leibniz limitations mathematical points mathematicians mental images metaphysics metaphysics of space mind minima sensibilia natural belief philosophy of mathematics philosophy of mind physical points possibility problem reason reductio arguments reductio proofs refutation sense impressions sensible extensionless indivisibles set theory skeptical spatial extension sublime supposed theory of sensible transfinite trilemma vacuum Zeno's paradoxes