 While historians of mathematics have long emphasized the influence that Dedekind’s contributions to algebraic number theory had on the development of twentieth-century mathematics, the philosophical significance of these contributions has only started to be probed recently (with some early exceptions: Dugac 1976, Sinaceur 1979, Edwards 1980, 1983, Stein 1988). We should begin here by reviewing two related aspects: the roots of Dedekind’s number-theoretic investigations in the works of Gauss, Dirichlet, and Ernst Kummer; and the contrast between Dedekind’s approach and that of Leopold Kronecker.