Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century
This book provides the first comprehensive account of the relationship between philosophy of mathematics and the mathematical practice of the seventeenth century - the most eventful period of mathematical development in history. Starting with the Renaissance debates on the certainty of mathematics, the author leads the readers through the foundational issues raised by the emergence of new mathematical techniques including the influence of the Aristotelian conception of science in Cavalieri and Guldin. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical developments and philosophical reflection in seventeenth century mathematics.
- Hardback | 284 pages
- 160 x 236.2 x 25.4mm | 661.87g
- 19 Jun 1997
- Oxford University Press Inc
- New York, United States
- line figures
Mancosu's book succeeds admirably in explaining, clarifying and analysing the conceptual issues at stake in the material that it examines. Its author knows precisely when it is relevant to enter into the complexities of a mathematical derivation and when to bypass them. The material is fascinating, and in this treatment adds up to a lot more than just "sums in the past" * Times Literary Supplement * thoughtful and well-written * C.J.Scriba, MATH, Vol.939 *
Back cover copy
The seventeenth century saw more dramatic advances in mathematical theory and practice than any other era before or since. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, analytic geometry, the geometry of indivisibles, the arithmetic of infinites, and the calculus had been developed. Philosophy of mathematics and mathematical practice in the seventeenth century have often been studied independently of one another. In this groundbreaking work, Paolo Mancosu offers the first comprehensive account of the rich interaction between the two fields. Beginning with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes's Geometrie, the relationship between empiricist epistemology and infinitistic theorems in geometry, and the debates concerning the foundations of the Leibnizian calculus. In the process, Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth-century mathematics. Philosophers of mathematics and historians of philosophy and mathematics will welcome this much needed study.