Horkheimer and Adorno deferred foundational questions by prioritizing materialist social theory.

Evidence

With their cautious attitude towards questions concerning the basis for Critical Theory, and the emphasis they gave to the role of determinate negation and to merely expressing what was the case, Horkheimer and Adorno had pleaded for the main emphasis to be put on a materialist theory of society. But if work on the materialist theory of society was not progressing, should the problem of the foundations of Critical Theory not inevitably move to the fore, and did Marcuse’s book not deserve to be discussed from this point of view? It ought to have been so. — Rolf Wiggershaus, The Frankfurt School, 529