From Transformations: Studies in the History of Science and Technology
Isaac Newton on Mathematical Certainty and Method
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Summary
An analysis of Newton's mathematical work, from early discoveries to mature reflections, and a discussion of Newton's views on the role and nature of mathematics.
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. He examines the full range of Newton's works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton's understanding of method and his mathematical work then reveal themselves through Guicciardini's careful analysis of selected examples. Isaac Newton on Mathematical Certainty and Method uncovers what mathematics was for Newton, and what being a mathematician meant to him.
Hardcover
Out of Print ISBN: 9780262013178 448 pp.  7 in x 9 in 96 b&w illus., 9 tablesPaperback
$25.00 X ISBN: 9780262516488 448 pp.  7 in x 9 in 96 b&w illus., 9 tablesReviews

This wonderful book is at once deeply informed and surpassingly lucid. I can find nothing in it to criticize.
Katherine Dunlop
The Journal of the International Society for the History of Philosophy of Science

This book offers a detailed and welldocumented original view of Newton's conceptions, strengths and weaknesses, clearly and vividly exposed.
U. D'Ambrosio
Mathematical Reviews

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
Endorsements

Guicciardini's book is a major contribution to Newtonian studies, documenting in authoritative detail Newton's views on the nature of mathematics and the place of mathematics in natural philosophy. Examining the different stages in the development of Sir Isaac's thought, Guicciardini analyzes Newton's conceptions in relation to those of such famous seventeenthcentury philosophers as Descartes, Hobbes, and Leibniz. This penetrating study will be of interest to specialists in the history of exact science as well as to anyone interested in the intellectual context of seventeenthcentury science.
Craig Fraser
Institute for the History and Philosophy of Science and Technology, University of Toronto
Awards
 2011 Fernando Gil International Prize for the Philosophy of Science, presented by the Portuguese Foundation for Science and Technology and the Calouste Gulbenkian Foundation (http://fernandogil.org.pt/en/nominees/2011/winner/)