Since you're criticizing an article based on my own chosen excerpts of it, it would be irresponsible of me not to give fuller quotes so that Dunlop can respond:

Subsequent advances in mathematics and physics appeared to discredit Kant's view of intuition. They showed that no geometry can be known a priori to apply to physical space. In their light, Kant's view appeared to rest on a confusion between pure geometry, which is known a priori but empty, and its applications. While conceding that Kant confuses pure and applied geometry, P. F. Strawson tries to preserve the interest of his view. Strawson seeks to explain how the application of geometry can be independent of experience. Kant holds that the applicability of geometrical concepts to all objects represented in empirical intuition (ordinary sense-perception) is proved by our ability to represent objects falling under them in pure intuition. Strawson interprets Kant's “pure intuition” as the capacity to give ourselves “pictures” in imagination. He takes Kant to argue that because all use of geometrical concepts involves picturing, what holds of all pictures we can give ourselves must hold of all objects represented through sensibility.

A preliminary goal of this paper is to defend Strawson's view that Kant intends to explain our ability to formulate the criteria (marks) by which we recognize instances of a concept. [...] Strawson is also right that on Kant's view, concepts acquire content of this kind (criteria of application) through an exercise of the imagination. But Strawson misunderstands the imaginative activity through which concepts are defined. He regards it as an application of concepts, to pictures, which is a priori in the sense that it mediates all use of the concepts in sense-experience. But I argue (in §3) that for Kant, it is a priori in the stronger sense that it is required even to possess the concepts. Kant holds that mathematical concepts are formed by defining them. Since we cannot possess them without grasping definitions, which assure the universal applicability of the concepts, no experience (even that of inspecting pictures) can provide any further guarantee of their applicability. I explain why, according to Kant, experience is not needed either to formulate or to ascribe the marks included in mathematical concepts.

Strawson points us toward a key element of Kant's theory of geometry, but it does not fit the place he gives it in Kant's catalogue of kinds of representation. I sketch a way of reconciling Strawson's interpretation of “pure intuition” (on which it represents objects as we imagine, or are prepared to picture, them) with Kant's view that it proves the applicability of concepts independently of experience. Pure intuition can be taken, in the spirit of Strawson's interpretation, to represent procedures for constructing objects that fall under the concepts. I argue that on Kant's view, the representation of such procedures indeed yields a priori knowledge of the applicability of concepts. But because these procedures must be represented as general, and intuition represents particulars, it would be wrong to understand pure intuition as the representation of these procedures. I explain that on Kant's view, procedures for constructing objects are represented as “schemata”, which are distinct from concepts and intuitions.

My main objection to Strawson is that he overlooks the implications of Kant's view of definition. Kant uses the definition of geometrical concepts to illustrate the sensible faculty's role in cognition. He thinks it is distinctive of mathematical concepts that they are formed by defining them. [...] If Kant's theory of geometry is defunct, we should join Strawson's effort to detach from it insights that can claim to last. So to defend the relevance of Kant's theory (even for interpreting the Critique), I must deal with the objections that lead Strawson to minimize its role. If Kant's view that mathematical concepts have schemata rested merely on an inability to conceive them more abstractly, he could still be charged with confusing pure and applied geometry. But Kant holds that outside of mathematics, concepts can be formed independently of the constraints imposed by sensibility. Since we can form (but not give schemata to) concepts that do not accord with (Euclidean) geometry, the formation of geometrical concepts involves a kind of choice (as I explain in §6).

Kant's view of geometry thus has an affinity, overlooked by Strawson, with “conventionalist” views. Yet this choice is not arbitrary for Kant in the way it is on later views. Kant holds that the choice of concepts intended for mathematical use is informed by cognition of their applicability (as I explain in §7). Specifically, we voluntarily restrict the understanding to forming only those concepts whose schemata we can represent (which entails that objects answering to them can be represented in accordance with the conditions on our perception). By choosing to form only applicable concepts, we license ourselves to ascribe their marks independently of experience: in particular, without regard to our experience of how concrete material objects fall short of geometry's specifications. So our prerogatives to fix criteria for the application of mathematical concepts, and stipulate their satisfaction, ultimately rest on a more fundamental ability to perceptually represent objects that answer to the concepts.

The criticism has been made that philosophers waste too much time on historical exegesis; but I found surprisingly very little historical work in Noûs, and even this Kant stuff is surprisingly relevant to some of the contemporary issues we ourselves have been debating recently -- concerning the relationship between imagined or constructed 'mathematical reality' and the empirical world, the dependence of logical truth upon thought, etc.