In the Critique of Pure Reason Kant appears to make incompatible claims regarding the unitary natures of what he takes to be our a priori representations of space and time. I argue that these representations are unitary independently of all synthesis and explain how this avoids problems encountered by other positions regarding the Transcendental Deduction and its relation to the Transcendental Aesthetic in that work. Central is the claim that these representations (1) contain, when characterized as intuitions and considered as (...) prior to any affections of sensibility, only an infinitude of merely possible finite spatial and temporal representations, and (2) are representations that are merely transcendental grounds for the possibilities for receiving or generating finite representations in sensibility that are determined (immediately, in the case of reception) by means of syntheses that accord with the categories. (shrink)

I argue for a new delimitation of what Kant means by ‘cognition [Erkenntnis]’, on the basis of the intermediate, transitional place that Kant gives to cognition in the ‘progression [Stufenleiter]’ of our representations and our consciousness of them. I show how cognition differs from mental acts lying earlier on this progression—such as sensing, intuiting, and perceiving—and also how cognition differs from acts lying later on this progression—such as explaining, having insight, and comprehending. I also argue that cognition should not be (...) confused with ‘knowledge [Wissen]’, insofar as knowledge represents the culmination of a separate orthogonal progression of acts of ‘holding-true’. Along the way, I show how having in focus the specific progression from representation, to consciousness, to cognition allows us to better appreciate the architectonic significance of the progression of Kant’s analysis in the first Critique, and also helps to illuminate the unity of Kant’s account of cognition itself across its variety of forms. (shrink)

Overview of the (non)conceptualism debate in Kant studies.

On one reading of Kant’s account of our original representations of space and time, they are, in part, products of the understanding or imagination. On another, they are brute, sensible givens, entirely independent of the understanding. In this article, while I agree with the latter interpretation, I argue for a version of it that does more justice to the insights of the former than others currently available. I claim that Kant’s Transcendental Deduction turns on the representations of space and time (...) as determinate, enduring particulars, whose unity is both given and a product of synthesis. (shrink)

I argue for a new delimitation of what Kant means by ‘cognition [Erkenntnis]’, on the basis of the intermediate, transitional place that Kant gives to cognition in the ‘progression [Stufenleiter]’ of our representations and our consciousness of them. I show how cognition differs from mental acts lying earlier on this progression—such as sensing, intuiting, and perceiving—and also how cognition differs from acts lying later on this progression—such as explaining, having insight, and comprehending. I also argue that cognition should not be (...) confused with ‘knowledge [Wissen]’, insofar as knowledge represents the culmination of a separate orthogonal progression of acts of ‘holding-true’. Along the way, I show how having in focus the specific progression from representation, to consciousness, to cognition (and beyond) allows us to better appreciate the architectonic significance of the progression of Kant’s analysis in the first Critique (and beyond), and also helps to illuminate the unity of Kant’s account of cognition itself across its variety of (empirical, mathematical, philosophical) forms. (shrink)

In this paper, I propose a novel interpretation of the role of the understanding in generating the unity of space and time. On the account I propose, we must distinguish between the unity that belongs to determinate spaces and times – which is a result of category-guided synthesis and which is Kant’s primary focus in §26 of the B-Deduction, including the famous B160–1n – and the unity that belongs to space and time themselves as all-encompassing structures. Non-conceptualist readers of Kant (...) have argued that this latter unity cannot be the product of categorial synthesis. While they are correct that this unity is not the product of any particular act of category-guided synthesis, I argue that conceptualists are right to nevertheless attribute this unity to the understanding. I argue that it is a result of what we can think of as the ‘original’ synthesis of understanding and sensibility themselves – it is a synthesis, moreover, in which the whole is logically prior to the parts. (shrink)

In this chapter I advance a moderately conceptualist interpretation of Kant’s account of the threefold synthesis in the A-Deduction. Often the first version of TD, the A-Deduction, is thought to be less conceptualist than the later B-version from 1787 (e.g. Heidegger 1991, 1995). Certainly, it seems that in the B-Deduction Kant puts more emphasis on the role of the understanding in determining the manifold of representations in intuition than he does in the A-Deduction. It also appears that in the A-Deduction (...) the seemingly pre-conceptual aspects of a priori synthesis, namely those of the synthesis of apprehension and the imagination, are more prominently featured than in the B-Deduction. And the fact that in the A-Deduction judgement does not appear to play any significant role reinforces the view that the A-Deduction is less strongly conceptualist. I believe that Kant is a conceptualist also in the A-Deduction (as much as in the B-Deduction) in the sense that all syntheses, which are expounded in the second section of the A-Deduction, must be seen as involving the categories or the understanding as the seat of the categories. However, despite some apparent strong modal claims regarding apperception in the A-Deduction, I argue that Kant is a moderate conceptualist in the sense that he allows for the real possibility that some representations are apprehended that are not subsumed or subsumable under the categories, or determined or determinable by the understanding as the seat of the categories. Not all representations must be synthesised and hence be conceptualised (by means of the categories), nor are all representations necessarily conceptualisable (by means of the categories). Often it is argued that the application of the categories must be seen as separate from or prior to conceptualisation (that is, employment of concepts in a judgement), so that the categories must be considered to apply to representations at least to the extent that the productive imagination or recognitive synthesis is involved, even if no empirical concepts are applied in an actual judgement. But it is difficult to see how categories can apply outside the context of an actual judgement in which ipso facto empirical concepts are employed, because, after all, categories are nothing but logical functions of judgement (e.g. B143). More in particular, I shall argue for the claims that (1) appearances to the contrary, all three levels of syntheses in the A-Deduction, including the synthesis of recognition, are interdependent and are not to be seen as operating singly or independently of each other, and hence of the categories; (2) ‘mere’ apprehension, or ‘mere’ intuition, is not dependent on the understanding and the application or possible application of the categories; and that (3) ‘mere’ apprehension does not even invoke a priori synthesis of apprehension and hence is as such fully lawless in terms of Kantian a priori laws. In this context, I also address Kant’s argument in the A-Deduction about the role of the imagination in the production of spatial objects and explain his apt use of the example of cinnabar to show that the kind of association that is at issue here concerns the possibility of knowledge, not the possibility of mere association, as is often assumed. (shrink)

In his argument for the possibility of knowledge of spatial objects, in the Transcendental Deduction of the B-version of the Critique of Pure Reason, Kant makes a crucial distinction between space as “form of intuition” and space as “formal intuition.” The traditional interpretation regards the distinction between the two notions as reflecting a distinction between indeterminate space and determinations of space by the understanding, respectively. By contrast, a recent influential reading has argued that the two notions can be fused into (...) one and that space as such is first generated by the understanding through an act of synthesis of the imagination. Against this reading, this article argues that a key characteristic of space as a form of intuition is its nonconceptual unity, which defines the properties of space and is as such necessarily independent of determination by the understanding through the transcendental synthesis of the imagination. The conceptual unity that the understanding prescribes to the manifold in intuition, by means of the categories, defines the formal intuition. Furthermore, this article argues that it is the sui generis, nonconceptual unity of space, when takenas a unity for the understanding by means of conceptual determination, that first enables geometric knowledge and knowledge of spatially located particulars. (shrink)

Logic diagrams have been increasingly studied and applied for a few decades, not only in logic, but also in many other fields of science. The history of logic diagrams is an important subject, as many current systems and applications of logic diagrams are based on historical predecessors. While traditional histories of logic diagrams cite pioneers such as Leibniz, Euler, Venn, and Peirce, it is not widely known that Kant and the early Kantians in Germany and England played a crucial role (...) in popularising Euler(-type) diagrams. In this paper, the role of the Kantians in the late eighteenth and early nineteenth centuries will be analysed in more detail. It shows that diagrams (or intuition in general) were a highly contentious topic that depend on the philosophical attitude and went beyond logic to touch on issues of physics, metaphysics, linguistics and, above all, mathematics. (shrink)

Prolegomena §38 is intended to elucidate the claim that the understanding legislates a priori laws to nature. Kant cites various laws of geometry as examples and discusses a derivation of the inverse-square law from such laws. I address 4 key interpretive questions about this cryptic text that have not yet received satisfying answers: How exactly are Kant's examples of laws supposed to elucidate the Legislation Thesis? What is Kant's view of the epistemic status of the inverse-square law and, relatedly, of (...) the legitimacy of the geometric derivation of that law? Whose account of laws, the understanding, and space is Kant critiquing in the passage? What positive account of the relationship between laws, the understanding, and space is Kant offering in the passage? My answer to depends crucially on my answers to –. As I interpret Kant, he holds that a wide range of a priori laws—including geometric laws, the inverse-square law, and the universal laws discussed in the Analytic of Principles—are ‘grounded’ in categorial syntheses rather than the intrinsic nature of the space given to us in pure intuition. (shrink)

In his 1763 Prize Essay, Kant is thought to endorse a version of formalism on which mathematical concepts need not apply to extramental objects. Against this reading, I argue that the Prize Essay has sufficient resources to explain how the objective reference of mathematical concepts is secured. This account of mathematical concepts’ objective reference employs material from Wolffian philosophy. On my reading, Kant's 1763 view still falls short of his Critical view in that it does not explain the universal, unconditional (...) applicability of mathematical concepts. (shrink)

Recent work on Kant’s conception of space has largely put to rest the view that Kant is hostile to actual infinity. Far from limiting our cognition to quantities that are finite or merely potentially infinite, Kant characterizes the ground of all spatial representation as an actually infinite magnitude. I advance this reevaluation a step further by arguing that Kant judges some actual infinities to be greater than others: he claims, for instance, that an infinity of miles is strictly smaller than (...) an infinity of earth-diameters. This inequality follows from Kant’s mereological conception of magnitudes (quanta): the part is (analytically) less than the whole, and an infinity of miles is equal to only a part of an infinity of earth-diameters. This inequality does not, however, imply that Kant’s infinities have transfinite and unequal sizes (quantitates). Because Kant’s conception of size (quantitas) is based on the Eudoxian theory of proportions, infinite magnitudes (quanta) cannot be assigned exact sizes. Infinite magnitudes are immeasurable, but some are greater than others. (shrink)

The article proposes an interpretation of Kant’s notions of form of, and formal intuition of space to explain and justify the claim that representing space as object requires a synthesis. This involves identifying the transcendental conditions of the analytic unity of consciousness of this formal intuition and distinguishing between it and its content. On this reading which builds upon recent proposals, footnote B160–1n. involves no revision of the Transcendental Aesthetic: space is essentially characterized by non-conceptual features. The article also addresses (...) worries about the infinite magnitude and the unicity of space, by considering the characteristics and requirements of geometric constructions. (shrink)