The Search for Certainty: A Philosophical Account of Foundations of Mathematics

Paperback | July 5, 2004

byMarcus Giaquinto

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Marcus Giaquinto traces the story of the search for firm foundations for mathematics. The nineteenth century saw a movement to make higher mathematics rigorous; this seemed to be on the brink of success when it was thrown into confusion by the discovery of the class paradoxes. That initiated aperiod of intense research into the foundations of mathematics, and with it the birth of mathematical logic and a new, sharper debate in the philosophy of mathematics. The Search for Certainty focuses mainly on two major twentieth-century programmes: Russell's logicism and Hilbert's finitism. Giaquinto examines their philosophical underpinnings and their outcomes, asking how successful they were, and how successful they could be, in placing mathematics on a soundfooting. He sets these questions in the context of a clear, non-technical exposition and assessment of the most important discoveries in mathematical logic, above all Godel's underivability theorems.More than six decades after those discoveries Giaquinto asks what our present perspective should be on the question of certainty in mathematics. Taking recent developments into account, he gives reasons for a surprisingly positive response.

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Marcus Giaquinto traces the story of the search for firm foundations for mathematics. The nineteenth century saw a movement to make higher mathematics rigorous; this seemed to be on the brink of success when it was thrown into confusion by the discovery of the class paradoxes. That initiated aperiod of intense research into the foundat...

Marcus Giaquinto is in the Department of Philosophy, University College London.

other books by Marcus Giaquinto

Visual Thinking in Mathematics
Visual Thinking in Mathematics

Hardcover|Jul 13 2007

$146.75 online$192.00list price(save 23%)
Format:PaperbackDimensions:300 pages, 9.21 × 6.14 × 0.68 inPublished:July 5, 2004Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198752458

ISBN - 13:9780198752455

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Table of Contents

1. Setting2. The Class Paradoxes and Early Responses3. The Language Paradoxes and Principia Mathematica4. Axiomatic Set Theory and Hilbert's Programme5. Godel's Underivability Theorems6. AftermathBibliography, Index

Editorial Reviews

`Review from previous edition Giaquinto has provided a careful and judicious discussion and analysis of these matters, supplying needed technical background for readers who are not mathematicians ... Readers of this book will be well prepared to follow the current literature on foundations ofmathematics.'Martin Davis, American Scientist