When dichotomous connotations have already been applied to a distinction in some communicative context, it can be tricky to simultaneously clarify the transcendence of the dichotomy and the preservation of the underlying distinction, but the general solution is not far to find — just ensure that the underlying distinction is expressed in terms of some finite relation, rather than A versus not-A. Then we have Hegelian determinate negation or Aristotelian difference between the terms, rather than classical negation. So in effect, the solution lies in recognizing that the previous understanding of the distinction in terms of dichotomy was wrong in the first place. More positively, Hegel eliminates dichotomies by putting determinate relations, coherence, and mediation first in the order of explanation, before all particular terms.
Hegel famously wanted to move beyond the subject-object dichotomy he saw as typical of early modernity. In practical terms, Kant’s most famous concern to avoid “dogmatic” assumptions about direct possession of epistemic objects had seemed to accentuate the separation of subject and object, by focusing on the distinction between appearance and reality. But both Kant and Hegel wanted to assert the possibility of knowledge in a strong sense, while avoiding what Kant called dogmatism. They also had considerable common ground in a shared rejection of naive early modern notions of subjects and objects and their relations.
Kant had begun — seemingly unwittingly — to recover some neglected Aristotelian insights in these areas, and Hegel made this an explicit theme. Thus they both already questioned the dichotomous interpretation of subject-object relations. Kant had also already highlighted the inevitable involvement of concepts in experience. For Kant, there is no direct epistemic access to real-world objects, or things in themselves (or to our own subjectivity). All knowledge proceeds by way of concepts, but he retains the concept of objects (and subjects) as a sort of placeholders for new distinctions between appearance and reality that can always be wrapped around current concepts in a new iteration.
The Hegelian Absolute — or that which transcends the subject-object dichotomy — is just a handle for perspectives that put processes, relations, coherence, and mediation before any preconceived notion of the conceptual content of particular terms. I think Hegel saw this sort of structure as common to Aristotelian substance or “what it was to have been” a thing and Kantian subjectivity or synthesis of apperception. Working in the Hegelian Absolute does not require epistemic super powers or specious Cartesian certainty, just a sustained honest effort that is still implicitly defeasible. Hegel intends the Absolute to be a kind of Aristotelian achievable perfection, not a kind of omniscience or theological perfection that could never be legitimately claimed by a rational animal. (See Substance Also Subject.)
In approaching these matters in A Spirit of Trust, Brandom characteristically focuses not directly on higher-order abstractions, but on their implications for what we do with ordinary concepts in ordinary experience. Like Aristotle and Hegel but following a distinct strategy of his own, Brandom avoids the impasse of a supposed transition from psychological to “metaphysical” terms, or from ordinary experience to something that would seemingly have to be like the mind of God, by clarifying what we implicitly mean by concepts in the first place.
With Aristotle, Hegel, and Frege and in contradistinction to the empiricist tradition, Brandom understands concepts and apperception in a nonpsychological, nonrepresentational, normative-pragmatic, inferential-semantic way. Through the discovery of counterfactually robust relations, concepts evolve toward increasing universality. Through the experience of error, synthesis of apperception comes to recognize that not only its commitments but also its concepts are always in principle provisional, subject to reformulation when faced with a new case. Through both of these combined with the additional cross-checks provided by mutual recognition, synthesis moves toward increasing objectivity and what might be called contact with reality. Through Brandom’s “expansive” model of responsibility, the last remaining obstacle to a full resolution of subject-object separation — the lack of a normative interpretation of unintended consequences of actions — is removed.
Neither “subjects” nor “objects” as such are very prominent in an account of this sort. It is much more a story about processes, relations, coherence, and mediation. Aristotle, Hegel, and Brandom each develop their own ways of working that start in the middle, as it were, and do not need reified subjects and objects to begin with. This, again, is just what the Hegelian Absolute is — a name for the sort of perspective that emphasizes the in-principle provisional character of all finite concepts, as contrasted with the more directly practical sort of perspective that provisionally works with the current basis as a source of reasons for particular sayings and doings.