Inspired by my thread of medieval universities, this is a similar question, but in a different direction: Assume thay the Roman Empire never loses any serious territory to the Arabs unified under Islam, though the Caliphate still takes out the Sassanids, and does its thing in Asia. In this scenario, the general corpus of Greek Philosophy is never as broadly disseminated throughout the Islamic world, and the Arabs don’t have much of an argument that they’re the just as much heirs of Greco-Roman Antiquity as the Byzantines are. I’m sure there would be some cross-cultural pollination, but not nearly as much as we got, historically.
So, how might philosophy in the Islamic world develop?