Brandom makes interesting connections between Hegel’s rather idiosyncratic discussion of Stoicism and Skepticism in the Phenomenology and the preceding discussion of Mastery. Stoicism and Skepticism for Hegel each in a different way reflect aspects of Mastery’s attitude that wants to claim total independence.
Hegel’s criticism of Stoicism in this context is rather different from my previously expressed issues with its foundationalism, claims of a completed system, and what the ancients called its dogmatism. My remarks probably apply more to the system of Zeno and Chrysippus, whereas Hegel’s apply more to the narrower ethical concerns of someone like Epictetus.
Zeno and Chrysippus are known only from references in other authors; none of their original works survive. Surviving references to early Stoic teaching often tend to be somewhat anonymous and generic. The details of the system are quite fascinating and worthy of study in their own right (see the collected fragments in Long and Sedley, The Hellenistic Philosophers; also Sambursky, Stoic Physics; Mates, Stoic Logic; and Nussbaum, Therapies of Desire).
Ancient Skepticism is also quite worthy of study in its own right. In addition to fragments, a number of works by the late author Sextus Empiricus survive. Ancient skeptics were mainly skeptical about theoretical developments. (The more extreme skepticism many modern authors have worried about in the third person seems to be a post-Cartesian development.)
Brandom says Hegel’s Stoics and Skeptics both refuse the experience of error that is crucial to the elicitation of conceptual content. On his reading, Hegel’s Stoic in, say, refusing to recognize physical pain, is both just being stubborn and refusing to address what turn out to be incompatible commitments, effectively denying the reality of the object in order to maintain the independence of consciousness at all cost. The Skeptic is just refusing to make any commitments at all, which is another attempt to maintain the independence of consciousness at all cost. Hegel’s point is that this attitude of wanting to maintain the total independence of consciousness from anything other is unsustainable.