Initially Skorupski follows the lead of the preface to the first edition of the Critique of Pure Reason in viewing "Critical Philosophy" as arising as kind of via media between dogmatism and scepticism. Interestingly, and of importance for subsequent discussion in Skorupski's book, the nature of the distinction between these three positions is presented as concerned with the "warrants for belief". In relation to this question Skorupski also identifies an important component of Critical Philosophy being its "descriptive" relation to common sense conceptions of cognition (thus implicitly following Strawson's distinction between "descriptive" and "revisionary" forms of metaphysics).
Due to thinking of Critical Philosophy in this way Skorupski identifies an immediate problem with there being such a thing as "critical metaphysics" since the critical attitude emerges as one that should be deflationary. This indicates again that Skorupski tends to follow a form of analytical view of critical procedure that sees it as being required to provide transcendental arguments in favour of established conceptions.
Whilst these elements of Skorupski's reading are inherited from previous analytical readings of Kant he does go on to provide an interesting independent reading of Kant's philosophy as a response to what is generally termed "transcendental realism" but which Skorupski identifies rather as "global realism". This notion of "global realism" is meant to capture in more general terms some sense of the pre-philosophical commitments that lead to "transcendental realism" and thus to capture in a way that is more intuitive for common sense what the clash between "transcendental realism" and "transcendental idealism" really amounts to.
Skorupski thus distinguishes "global realism" into two distinguishable claims. On the one hand there is "factualism" which involves the claim that asserting some proposition is equivalent to saying that a fact obtains and, on the other hand, there is "cognition independence" which is to state that facts are not dependent on cognition. Critical Philosophy is characterised, on Skorupski's view, by the statement that it is the combination of these two theses that renders knowledge impossible but it is also required, on this account, that the combination which is involved in global realism is not required for the claims of common cognition.
In order for the claims of global realism to be understood it is first necessary, however, to have some clarity about what could be meant by "facts" since both parts of the global realist view state a view about "facts". Skorupski follows the early modern tradition in philosophy here by distinguishing between nominal and substantial senses of fact taking the nominal sense as stating that a 'fact' is a true proposition and thus upholders of the nominal sense are Deflationists in the most general sense. It doesn't exactly follow from this as Skorupski seems to think that "no substantial notion of fact is being deployed" unless you think that there is a notion of fact that is credibly distinguishable from it which is what a full-blown Deflationist theory can deny.
The "substantial" notion of "fact" on Skorupski's view takes facts to be something different from propositions and he takes it to be the case that a "global realist" is committed to such a distinction which does seem to be required. It is due to this distinction being held that "factualism" can state a metaphysical view in the bold sense whereas the "factualist" statement would otherwise seem to assert a thin notion that best leads to Deflationism. Whilst the substantial notion of 'factualism' does not require commitment to a correspondence theory of truth, however, it is pretty clear it is not consistent with Deflationism but could, on Skorupski's view, fit any other theory of truth.
Cognition independence, by contrast to factualism, implies a clear form of cognitivism but not necessarily a realist commitment as factualism seems to indicate is naturally required. Cognition independence, in being in principle capable of being divorced from factualism might thus be thought to be the basis of Skorupski's cognitivism. Part of the point of commitment to cognition independence is also to ensure that Critical Philosophy is a form of descriptive rather than revisionary metaphysics.
Having set out this conception of "global realism" Skorupski begins his historical story of Critical Philosophy and opens it with his first pass at a characterisation of Kant's philosophy. After citing the passages from the preface to the second edition of the Critique of Pure Reason often used to maintain the claim about Kant's alleged "Copernican revolution" Skorupski uses them to point to Kant indicating a problem with a simple commitment to cognition independence. It follows from the claim that objects have to conform to our intuition that the cognition of objects is not, in the most manifestly "realist" sense, one that is "independent" of cognition. Further, if factualism is understood to require commitment to things-in-themselves being the basis of cognition then Kant also rejects factualism.
However, Skorupski obviously also has to accept that there is a sense in which Kant accepts cognition independence since the whole point of the Critical endeavour is to demonstrate the objectivity of cognition. In order to understand how Kant is able to make this move whilst apparently rejecting both parts of "global realism" Skorupski refers to the transcendental distinction between phenomena and noumena but also understands this distinction as based upon what he terms a "joint-product theory" characterised in the following way:
"the phenomenal facts are joint products of the forms of our sensibility and things as they really are, with the former structuring the input received from the latter" (11).
This claim that transcendental idealism is a "joint-product theory" is not strictly speaking one that is without some support in The Critique of Pure Reason but it would be fair to say that there are few Kantians who accept that it is what Kant is really claiming. In committing Kant to this theory Skorupski is automatically rejecting the more deflationary views of transcendental idealism such as are held by Henry Allison and Graham Bird. Whilst there are certainly problems with these forms of transcendental idealism it is hardly fair to simply reject them out of hand and starkly require that transcendental idealism be understood to have to be committed to the "joint-product theory".
It is because Skorupski takes Kant to be committed to the 'joint-product theory' that he thinks there is a need to restate Critical Philosophy in a way that need not require the distinction between phenomena and noumena although it is not at all obvious that the transcendental distinction requires the view of affection that Skorupski ties it to. So Skorupski wishes to state a form of Critical Philosophy that does not require the transcendental distinction because he relates this distinction to the 'joint-product theory' although the two are logically distinct.
After having described his first way of distancing himself from Kant Skorupski goes on to look at another side of Kant's view, the side that emphasises reason as something distinct from sensibility. This element of Kant's view requires, states Skorupski, a firm rejection of factualism for a different reason than the 'joint-product theory'. One of the grounds for the claim that this emphasis on reason does not require the 'joint-product theory' is then adduced in an interpretation of the 'fact of reason' claim Kant makes in the Critique of Practical Reason. Skorupski understands the 'fact of reason' to be mandated, as a view that requires not "knowledge" of our noumenal nature but rather a view of the basis of the claim that requirements of reason apply to us.
On this view of the "fact of reason" it is not that imperatives apply to us as due to something being true (some "fact") but rather that requirements of practical reason apply to us as part of the cognition independence of reason's requirements understood in some other sense. Skorupski is not here clear in what other sense cognition independence of reason is meant to be understood but he next goes on to look at Kant's claim concerning the spontaneity of reason. This claim is grasped as requiring that there are pure judgments that are not grounded on any further facts (thus do not commit Kant to a form of "noumenal factualism").
Skorupski's version of Kantian Critical Philosophy thus sees it as combining two moves that enable it to resist global realism. On the one hand Kant is thought to embrace the 'joint-product theory' as a way of allowing for theoretical cognitivism but at the cost of embracing here a form of noumenal factualism. However the cost of Kant's commitment to the latter can be mitigated by seeing a parallel emphasis in Kant's accounts of theoretical and practical reason on an autonomous quality of reason that does not require even a noumenal form of factualism. It is the latter that Skorupski's form of Critical Philosophy will rescue from the grip of the former.