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. (shrink)

Die philosophische Methode ist im 17. und fruhen 18. Jahrhundert vom Vorbild der mathematischen Methode bestimmt. Die Arbeit zeigt, dass es sich dabei um unterschiedliche Methodenmodelle handelt. Diese fuhren dazu, dass sich bei Descartes, Leibniz und Wolff unter philosophischer Analysis sehr unterschiedliche Methodenansatze entwickeln. Sie bilden den historischen Hintergrund fur das analytische Programm und den Begriff der Aufklarung, was in der bisherigen Forschung oft ubersehen wurde. The philosophical method in the 17th and early 18th centuries was governed by the example (...) of the mathematical method. This work shows that there were however varying types of methods concerned. The result was that when subjected to philosophical analysis, in their works Descartes, Leibniz and Wolff developed very different approaches to their methods. These constitute the historical background for the analytical agenda and the concept of Enlightenment which has often been overlooked by researchers up to now. (shrink)

The series, founded in 1970, publishes works which either combine studies in the history of philosophy with a systematic approach or bring together systematic studies with reconstructions from the history of philosophy. Monographs are published in English as well as in German. The founding editors are Erhard Scheibe (editor until 1991), Günther Patzig (until 1999) and Wolfgang Wieland (until 2003). From 1990 to 2007, the series had been co-edited by Jürgen Mittelstraß.