Philosophy of Mathematics and Mathematical Practice in the Seventeenth CenturyOxford University Press, 1996 - 275 pàgines 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. |
Continguts
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 |
249 | |
267 | |
Altres edicions - Mostra-ho tot
Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century Paolo Mancosu Previsualització limitada - 1999 |
Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century Paolo Mancosu Previsualització limitada - 1996 |
Frases i termes més freqüents
algebraic analysis apagogical Archimedes Aristotelian Aristotle arithmetic Arnauld Barrow Bernoulli Biancani Bolzano causal Cavalieri center of gravity chapter circle circumference claim Clavius Clüver concept conclude cone considered construction curves cylinder debate definition Descartes differential direct proofs discussion equal equation Euclid Euclid's Elements example finite Fontenelle formal cause foundational Galileo Gassendi Géométrie geometry given Gottignies Guldin Hobbes hyperbolic solid infinitely long solid infinitely small infinitesimal infinity issue Leibniz Leibnizian calculus magnitudes material cause mathematical practice mathematicians Mersenne method of indivisibles modus tollens motion nature Nieuwentijt objections Pappus paradox Pereyra perfect demonstration philosophy of mathematics Piccolomini plane figures Posterior Analytics principles problem Proclus proof by exhaustion proofs by contradiction proposition proved qu'il quadratrix quadrature Quaestio quantities ratio reason reductio reductio ad absurdum right angles Rolle's segments seventeenth century square straight line superposition tangent theorem theory things Torricelli Torricelli's result triangle truth Varignon Wallis