Frege et la géométrie projective : La Dissertation inaugurale de 1873 / Frege and projective geometry : The 1873 inaugural dissertation

Abstract

SUMMARY. — Like all of Frege's other writings that appeared before his Begriffsschrift, in 1879, Frege's first work, the 1873 Inauguralschrift, does not deal with either logic or arithmetic. Its subject is complex projective geometry. Here I examine the work's essential elements, without too much emphasis on its purely technical details. It is more interesting to identify Frege's viewpoints that did not vary after 1873, as well as the ones that did change after 1873. I end this paper by examining the Fregean conception of the extension of traditional geometry to projective geometry. We shall see the reality of the influences that Frege was subject to at the time - especially Kant's, Gauss's, and von Staudt's - and tie Frege's work of 1873 to his later great works, in particular the Begriffsschrift, the Grundlagen der Arithmetik, and the Grundgesetze der Arithmetik.