Practices and Principles in Cauchy’s Works

Abstract

In this chapter, we examine how, relative to the theme of rigor, principles and practices were articulated in Cauchy’s works. The age of Cauchy was a historical period in which scientific practices asserted an increasing degree of autonomy vis à vis philosophical reflections. If it is true, on the one hand, that the philosophers of the first half of the 19th century were less and less interested in the development of the sciences, with Auguste Comte as a notable exception, then it is also true that scholars—particularly mathematicians—increasingly insisted that they and they alone had the right to determine the content of their discipline and its standards of scientificality. The divorce between a particular scientific practice and general philosophical reflection, in a discipline whose foundations were quite uncertain at the time, gave rise to a blossoming of what might be termed local and spontaneous philosophies among the scholars and scientists who had dedicated themselves to this discipline. While these scholars’ philosophies were incomplete, approximate, and often anomalous, they nevertheless worked to the extent that they could justify current practices and thus mitigate existing theoretical shortcomings Thus, the principle of rigor in mathematics seems to be an excellent example of what we earlier referred to as local and spontaneous philosophies.