This paper works to define the object of dialectical theory. To do so, it reconstruct the project of this theory as it unfolded in the early years of the Frankfurt School using protocols of discussions held in 1939 at the International Institute for Social Research in New York City, the importance of which has not yet been fully acknowledged. The paper claims that this project can be read in light of one of Marx's own statements which paradoxically suggest that one can choose either one of two paths to develop this project. It shows what leads Max Horkheimer to take one of these paths and Theodor W. Adorno to take the other. The paper then explains why, in the confrontation of their respective positions, Adorno's position asserts itself over Horkheimer's and shows how this confrontation allows us to sharpen our focus on the object of dialectical theory.