 An initial, rough answer to that question is already contained in our discussion so far: Dedekind’s approach is set-theoretic and infinitary, while Kronecker’s is constructivist and finitary. However, that leaves us with a deeper issue: What exactly is it that a set-theoretic and infinitary methodology allows us to accomplish that Kronecker’s doesn’t, and vice versa? The specific strength of a Kroneckerian approach is often summed up thus: It provides us with computational, algorithmic information (Edwards 1980, 1990, Avigad 2008). But what is the characteristic virtue of a Dedekindian approach? Here an informative and articulate answer is harder to find, especially one that is philosophically satisfying.