Hegel argues that Kant has inappropriately exceptionalised his four cosmological antinomies as such antinomies can be multiplied

Science of Logic Reading Group: Not Adding Up from Roughtheory.org by N Pepperell

Hegel starts by recognising Kant’s importance for dissolving an older metaphysics, and thus opening the path to a new philosophy. This recognition is promptly tempered by Hegel’s observation that Kant’s approach is “imperfect” in both its methods and its results. Hegel treats Kant’s antinomies as possessing a rational core that needs to be extracted from its form of presentation. His concern, as always with Kant, is that the approach is intrinsically dogmatic - that it presupposes that cognition possesses characteristics that have not been established (and, specifically, that it presupposes what it claims to prove) - and that the approach restricts reason, predeciding that it “should not soar beyond sensuous perception and should take the world of appearance, the phenomenal world, as it is” (407, 428). In the process of demonstrating these arguments, this remark also casts some light on Hegel understands his own method.
Hegel begins by suggesting that Kant has inappropriately exceptionalised his four cosmological antinomies, not recognising that such antinomies can be found at the heart of any Notion. Hegel argues “as many antinomies could be constructed as there are Notions” (408). Kant compounds this mistake by not locating the antinomies he does identify in the Notions themselves, but rather in a concrete, “applied” form in which such antinomies cannot be explored in their purity, but rather become intrinsically caught up in other determinations extrinsic to the Notion (409). Further, although Kant on one level recognises that these antinomies are not simply illusions, but contradictions that reason necessarily confronts, his attempt to resolve these contradictions contravenes this insight by treating the contradiction as fundamentally something subjective, something residing in the “transcendental ideality of the world of perception” (410).
These problems can only be overcome, Hegel argues, by grasping the antinomies as “two opposed determinations which belong necessarily to one and the same Notion” (410). Such an approach recognises the validity of each determination - but only as sublated within their Notion. By contrast, Kant’s approach is one-sided - it attempts to take up each determination in isolation from the other - to assert the validity of each dogmatically. Hegel’s description of Kant’s method here is not kind:

…this simple categorical, or strictly speaking assertoric statement is wrapped up in a false, twisted scaffolding of reasoning which is intended to produce a semblance of proof and to conceal and disguise the merely assertoric character of the statement… (411)

Hegel proceeds to illustrate his point by examining how the antinomy of continuity and discreteness arises in Kant’s argument relating to the infinite divisibility of matter. Much of the subsequent discussion consists of an argument that the way in which Kant frames his discussion of this problem, already assumes what it sets out to prove, and is therefore a tautological statement, rather than the proof it purports to be. Hegel wields an interesting and somewhat expansive concept of tautology here.
Hegel begins with Kant’s statement that every composite substance in the world is comprised of the simple (the atom) (412). Hegel notes that, by substance in the world, Kant intends substances as sensuously perceived, and that this substance is taken to be indifferent to the existence of the antinomy itself. Hegel argues that the very definition of a composite is that of something externally put together from things other than itself. The “other” of the composite, however, is the simple. Therefore it is tautological to say the composite consists of the simple - we know nothing more by this statement, than we already knew by simply examining the term “composite” (413). In Hegel’s (sarcastic) words:

To ask of what something consists is to ask for an indication of something else, the compounding of which constitutes the said something. If ink is said to consist simply of ink, the meaning of the inquiry after the something else of which it consists has been missed and the question is not answered but only repeated. (413)