Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

By Paolo Mancosu | Go to book overview

1

Philosophy of Mathematics and
Mathematical Practice in the
Early Seventeenth Century

In the last forty years one of the most active areas of research in the history and philosophy of science has been the study of the Galilean revolution in physics. In particular, scholars have focused their attention on the relationship between the emergence of Galilean science and the scientific developments of the Middle Ages. Already Duhem at the beginning of the century in his ten-volume work Le Système du Monde had uncovered the existence of a vital scientific thought in the medieval period. In the English-speaking world, the work that has done most to bring about awareness of the deep links between medieval and seventeenth-century science has been Crombie Augustine to Galileo ( 1952). In this justly celebrated book, Crombie defends a strong version of the continuity thesis. In the preface to the second edition ( 1958), he describes his effort as follows: "Especially I have tried to bring out, what I believe to be the most striking result of recent scholarship, the essential continuity of the Western scientific tradition from the Greek times to the seventeenth century and, therefore, to our own day." In his Robert Grosseteste and the Origins of Experimental Science, 1100-1700 ( 1953), Crombie singled out Grosseteste's commentary on Aristotle Posterior Analytics as representative of a new conception of scientific methodology.

The other scholars who have argued extensively for the continuity thesis are J. H. Randall in his 1961 work The school of Padua and the Emergence of Modern Science and W. Wallace in Galileo and his Sources: the Heritage of the Collegio Romano in Galileo's Theory of Science ( 1984). Consider, for example, Randall's thesis: Randall argues at length that Galileo's conception of science was ultimately dependent on Zabarella's notion of regressus,1 which in turn could be traced back to the medical commentaries on Galen's writings, such as that of Pietro d'Abano. Finally, it is an easy step to show that the latter commentaries rely heavily on distinctions made by Aristotle in the Posterior Analytics. Randall could thus conclude that

Zabarella's version of the Aristotelian logic, though interpreted and colored in terms of each of the three great theories of knowledge inherited and reconstructed by the seventeenth-century thinkers, and though receiving in practice

-8-

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Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century
Table of contents

Table of contents

  • Title Page iii
  • Preface vii
  • Contents *
  • Introduction 3
  • 1 - Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century 8
  • 2 - Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity 34
  • 3 - Descartes' Géométrie 65
  • 4 - The Problem of Continuity 92
  • 5 - Paradoxes of the Infinite 118
  • 6 - Leibniz's Differential Calculus and Its Opponents 150
  • Appendix 178
  • Notes 213
  • References 249
  • Index 267
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