The Evolution of Logic

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Cambridge University Press, 23.08.2010
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.
 

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Inhalt

Cantors Paradise
1
Die Urwahrheiten
31
Which Sets Exist?
59
The Universe and Everything
89
Truth Eludes Proof
123
Accommodating Cantor
152
Or Not
175
The Critique of Pure Reason
205
The Ways of the World
235
The Zoology of Reality
268
Bibliography
281
Index
291
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Über den Autor (2010)

W. D. Hart is currently a Professor of Philosophy at the University of Illinois at Chicago, where he chaired the Philosophy department for 12 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 University Press, 2009), and the editor of The Philosophy of Mathematics, and has published more than seventy articles and reviews in academic journals.

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