Mathematics and the Image of Reason

by Tiles,Mary

• ISBN13: 9780415033183
• ISBN10: 0415033187
• Format: Hardcover
• Copyright: 1991-06-18
• Publisher: Routledge

Summary

As science has become more heavily mathematical and as computers continue to infiltrate life in affluent societies, the philosopher's concern with mathematics has, paradoxically, dwindled. It has come to be tacitly presumed that mathematics is nothing but logic. Concentrating on three key figures in the philosophy of mathematics--Frege, Russell, and Hilbert--Mary Tiles seeks to dispel the misconception that scientific rationality and the character of reason is merely pure logic --and therefore inherently at odds with imagination. Tiles argues against those who see mathematics as uncreative and irrelevant to our postmodern, post-structuralist age. Mary Tiles writes in a lively, refreshingly non-technical style and succeeds in combining the highest degree of rigor with imagination and insight to provide a valuable book for students of the philosophy of logic and mathematics, epistemology, as well as for philosophically minded mathematicians and computer scientists.

Table of Contents

Acknowledgements	p. xi
Introduction	p. 1
Axiomatization, Rigour and Reason	p. 7
Axiomatization, Rigour and Reason	p. 7
Frege: Arithmetic as Logic	p. 33
Russell: Mathematics as Logic	p. 59
Hilbert: Mathematics as a Formula-Game?	p. 89
Ideal Elements and Rational Ideals	p. 129
Glossary of Symbols	p. 175
Further Reading	p. 176
Bibliography	p. 178
Index	p. 184
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