Grassmann’s epistemology: multiplication and constructivism

Abstract

Grassmann’s epistemological insights have attracted less attention than his mathemati cal results.Mathematicians have considered himas a precursor ofmodernmathematical theories – vector algebra, exterior algebra, Clifford algebra, and geometric algebrapaying attention to the development of mathematical results rather than to the philosophical differences between Grassmann’s own project and modern mathematical reconstructions [Cartan 1907; Hestenes 1985]. Historians of mathematics have analyzed the reception and influence of Grassmann (see for example the papers collected in[Schubring 1996a]), and philosophers’ attention has been driven especially to the Introduction to the 1844 edition of Ausdehnungslehre, or to a comparison with other philosophers.2.

This work was completed with the support of ANR Chaire d’Excellence “Ideals of Proof,” Université de Nancy, Université de Paris 7 Diderot (France), but had its origin in my dissertation discussed at the University of Genova (Italy) in 2003.