The Evolution of Logic

by W. D. Hart

• ISBN13: 9780521747721
• ISBN10: 0521747724
• Format: Paperback
• Copyright: 2010-08-23
• Publisher: Cambridge University Press

Summary

The Evolution of Logic examines the relations between logic and philosophy over the last 150 years. Logic underwent a major renaissance beginning in the nineteenth century. Cantor almost tamed the infinite, and Frege aimed to undercut Kant by reducing mathematics to logic. These achievements were threatened by the paradoxes, like Russell's. This ferment generated excellent philosophy (and mathematics) by excellent philosophers (and mathematicians) up to World War II. This book provides a selective, critical history of the collaboration between logic and philosophy during this period. After World War II, mathematical logic became a recognized subdiscipline in mathematics departments, and consequently but unfortunately philosophers have lost touch with its monuments. This book aims to make four of them (consistency and independence of the continuum hypothesis, Post's problem, and Morley's theorem) more accessible to philosophers, making available the tools necessary for modern scholars of philosophy to renew a productive dialogue between logic and philosophy.

Author Biography

W. D. Hart is currently a Professor of Philosophy at the University of Illinois at Chicago, where he chaired the philosophy department for twelve years. He has also taught at the University of Michigan, University College London, and the University of New Mexico. He is the author of The Engines of the Soul, now available in paperback (Cambridge, 2009), and the editor of The Philosophy of Mathematics and has published more than seventy articles and reviews in academic journals.

Table of Contents

Preface	p. ix
Cantor's Paradise	p. 1
Die Urwahrheiten	p. 31
Expeditions: Which Sets Exist?	p. 59
The Universe and Everything	p. 89
Truth Eludes Proof	p. 123
Accommodating Cantor	p. 152
Or Not	p. 175
The Critique of Pure Reason	p. 205
The Ways of the World	p. 235
The Zoology of Reality	p. 268
Bibliography	p. 281
Index	p. 291
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