Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Capa
Oxford University Press, 1996 - 275 páginas
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.
 

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Índice

1 Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century
8
2 Cavalieris Geometry of Indivisibles and Guldins Centers of Gravity
34
3 Descartes Géométrie
65
4 The Problem of Continuity
92
5 Paradoxes of the Infinite
118
6 Leibnizs Differential Calculus and Its Opponents
150
Giuseppe Biancanis De Mathematicarum Natura
178
Notes
213
References
249
Index
267
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Paolo Mancosu is at University of California at Berkeley.

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