Oxford University Press (1996)
The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting 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' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics.
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|Call number||QA8.4.M36 1996|
|ISBN(s)||0195132440 9780195132441 9780195084634|
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Citations of this work BETA
The Classical Model of Science: A Millennia-Old Model of Scientific Rationality.Willem R. de Jong & Arianna Betti - 2010 - Synthese 174 (2):185-203.
Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes From Berkeley to Russell and Beyond. [REVIEW]Mikhail G. Katz & David Sherry - 2013 - Erkenntnis 78 (3):571-625.
On the Relationship Between Plane and Solid Geometry.Andrew Arana & Paolo Mancosu - 2012 - Review of Symbolic Logic 5 (2):294-353.
Measuring the Size of Infinite Collections of Natural Numbers: Was Cantor's Theory of Infinite Number Inevitable?Paolo Mancosu - 2009 - Review of Symbolic Logic 2 (4):612-646.
Ten Misconceptions From the History of Analysis and Their Debunking.Piotr Błaszczyk, Mikhail G. Katz & David Sherry - 2013 - Foundations of Science 18 (1):43-74.
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