Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Capa
Oxford University Press, 1999 - 275 páginas
The seventeenth century saw dramatic advances in mathematical theory and practice than any 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. Although many technical studies have been devoted to these innovations, Paolo Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. 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' 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.
 

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Índice

Philosophy of Mathematics and Mathematical Practice in the Early
8
Cavalieris Geometry of Indivisibles and Guldins Centers of Gravity
34
Descartes Geometrie
65
The Problem of Continuity
92
Paradoxes of the Infinite
118
Leibnizs Differential Calculus and Its Opponents
150
Giuseppe Biancanis De Mathematicarum Natura
178
Notes
213
References
249
Index
267
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Acerca do autor (1999)

Paolo Mancosu is at University of California at Berkeley.

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