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Isaac Newton on Mathematical Certainty and Method

by Niccolo Guicciardini The MIT Press
Pub Date:
Pbk 448 pages
AU$29.99 NZ$33.03
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Historians of mathematics have devoted considerable attention to Isaac Newton’s work on algebra, series, fluxions, quadratures, and geometry. In Isaac Newton on Mathematical Certainty and Method, Niccolò Guicciardini examines a critical aspect of Newton’s work that has not been tightly connected to Newton’s actual practice: his philosophy of mathematics.

Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes’s Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. Guicciardini shows how Newton carefully positioned himself against two giants in the “common” and “new” analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity's legitimate heir, thereby distancing himself from the moderns.

Guicciardini reconstructs Newton’s own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. Isaac Newton on Mathematical Certainty and Method uncovers what mathematics was for Newton, and what being a mathematician meant to him.

This book will become a classic. I recommend it very highly to any reader with interests in the history of mathematics, the history of science, or the philosophical issues emerging from mathematical and scientific practice.

'Paolo Mancosu, American Scientist
Niccolò Guicciardini is Professor of the History of Science at the University of Bergamo, Italy. He is the author of The Development of Newtonian Calculus in Britain, 1700-1800 and Reading the Principia: The Debate on Newton’s Mathematical Methods for Natural Philosophy from 1687 to 1736. He is the recipient of the Sarton Medal for 2011-12 awarded by the University of Ghent, Belgium.