The “I think” of Descartes is perhaps the most famous example of what I have called a mentalist confusion of empirical and transcendental elements in subjectivity. Among other things, Descartes promoted an aggressive simplification of self/subject/mind into one simple foundational thing corresponding to a personal identity, while presenting this as a natural intuition. He also sharply privileged immediate presence to the mind. There are some very misleading passages in Kant and Hegel that appear to endorse a Cartesian “I think”, but Kant and Hegel’s own versions of “I think” were far more sophisticated, and fundamentally different. To begin with, Kantian unity of apperception and its analogues in Hegel are complex and shifting results and goals, not alleged foundational starting points.
Descartes is widely considered to have made nontrivial contributions to science and mathematics, although Leibniz argued that these were exaggerated. In any case, in philosophy I regard Descartes as mainly an arrogant pretender who really better fits the profile of an antiphilosopher. He simply refused to engage with the whole philosophical tradition, while replicating the Stoics’ dogmatic claim to possess a whole system of the world founded in certain knowledge. His abrupt dismissals of “dialectical subtlety” in favor of things allegedly simple and clear are mostly just bombastic rhetoric.
The famous hyperbolic doubt seems to me but a vast pretension, and a rhetorical ruse to clear the way for a foundationalist revindication of traditional values that was in most ways far less sophisticated than the arguments of medieval scholasticism. To claim to have doubted everything all at once is intellectually dishonest; we only doubt what it occurs to us to doubt. See my What and Why for a more reasonable alternative.
Descartes incoherently asserted both supernatural voluntarism (applied to God and man) and mechanistic determinism (applied to everything else). (See remarks on Descartes in Modernity, Again and Psyche, Subjectivity.)
Rereading Making It Explicit, I finally found a brief comment that better explains how Brandom somehow connects Descartes with some kind of revolution in normativity. It is pretty indirect. On p. 10, he says that Kant retrospectively read into Cartesian doubt an implicit requirement that we take responsibility for all our claims, and that we be prepared to justify them. This seems quite plausible, as a statement about Kant. Brandom offers his own account of the “notorious” failures of Descartes to adequately explain representation on pp. 6-7. In a nutshell, representation for Descartes is an unexplained explainer.
Thought for Aristotle and Hegel is in the first instance something shareable, determined by its publicly examinable inferential articulation. Cartesian thought, by contrast, is a private, interior affair. (See also Ego; Subject.)