¹ In this paper, I use the terms ‘cognition’ and ‘knowledge’ interchangeably -although I usually translate Kant's Erkenntnis with ‘cognition’. References to Kant's works, with the exception of the Critique of Pure Reason, refer to the volume and page of the German Academy of Sciences edition (Gesammelte Schriften, ed. Königliche Preuβische Akademie der Wissenschaften, later the Deutsche Akademie der Wissenschaften zu Berlin. 29 volumes. Berlin: Walter de Gruyter [and predecessors], 1902-.) References to the Critique of Pure Reason are cited according to the pagination of the first (A) and second (B) editions. Translations are my own (unless otherwise noted), but I consult the commonly used English translations.

² This characterization of the categories draws from Kant's account of the difference between intellectual, empirical, and arbitrary concepts in the Jäsche Logic (9:94).

³ Titles of any section of the Critique are given, often in abbreviated form, with the standard capitalization for titles; without such capitalization, the phrase instead refers to the general sort of argument or account in question. For example, Kant's reference to a ‘transcendental deduction of the concepts of space and time’ refers to no titled section of the book, and receives no capitals; the Transcendental Deduction of the Pure Concepts of the Understanding does.

⁴ Commentators tend to pass over Kant's remark about a transcendental deduction of space and time altogether; those who do address it tend to do so obliquely, or in footnotes - under the radar, as it were. And we find a wide range of views on the matter. Lorne Falkenstein says that this deduction is to be found in the Transcendental Aesthetic's Metaphysical Expositions of space and time; see Kant's Intuitionism: A Commentary on the Transcendental Aesthetic (Toronto: University of Toronto Press, 1995), pp. 394–5Google Scholar, n. 12. Daniel Warren is non-committal: he first implies that this deduction would be found in the Transcendental Aesthetic's Transcendental Expositions of space and time which follow the Metaphysical Expositions, maintaining that the objective validity of space and time cannot be addressed until after the Metaphysical Expositions; see ‘Kant and the Apriority of Space’, Philosophical Review, 107 (1998), 179–224CrossRefGoogle Scholar, p. 222, n. 57 and pp. 222–4. But in the final sentence of his paper, he seems to imply that this deduction might instead be achieved through the Transcendental Deduction of the categories (p. 224). Sadik AJ-Azm hints that the transcendental deduction of space and time requires the ‘synthetic approach’ of the Transcendental Deduction of the categories, and not the ‘analytical’ approach of the Aesthetic: ‘In this [synthetic approach] lies their transcendental justification’; see Kant's Theory of Time (New York: Philosophical Library, 1967), p. 35.Google Scholar

⁵ Karl Ameriks supposes that the transcendental deduction of space and time is the Aesthetic's Transcendental Exposition, and then goes on to treat Kant's remarks about ‘transcendental exposition’ as a guide to understanding the transcendental deduction of the categories; see ‘Kant's Transcendental Deduction as a Regressive Argument’, Kant Studien, 19 (1978), 273–87, pp. 274ff.Google Scholar

⁶ It is to be expected of a project as systematically driven as the Critique that our grasp of one part of the book should depend upon our grasp of another. Indeed, in so far as the Critique is truly a system, we should expect this to work in more than one direction: not only should an earlier part of the book provide a result that allows for a later argument to go through, at the same time the result of a later argument could mandate a return to an earlier part of the book so that we may see it in a newly corrected light. Much of the recent work on the relation between the Aesthetic and the Deduction is retrospective in this way, arguing that the Deduction reveals the Aesthetic to be a provisional text. See Longuenesse, Béatrice, Kant and the Capacity to Judge (Princeton: Princeton University Press, 1998)Google Scholar, esp. chapter 8; Waxman, Wayne, Kant's Model of the Mind (Oxford: Oxford University Press, 1991)Google Scholar, esp. chapter 2; and, looking further back, Sadik Al-Azm, Kant's Theory of Time, part II. For an example of recent commentary resisting this trend, see Lome Falkenstein, Kant's Intuitionism, especially chapters 1 and 2.

The view of the Aesthetic as a provisional text is typically adopted on the basis of the Deduction's concluding argument regarding a spontaneous capacity of the mind ‘to determine sensibility a priori’ (§24 B152; cf. §26 B160n.) - a capacity expressed in what Kant refers to as ‘figurative synthesis’. As Longuenesse argues, the Aesthetic is provisional because Kant ultimately ‘wants to reveal in these forms [of intuition, i.e. space and time] the manifestation of an activity that only the Transcendental Deduction of the Categories can make explicit’ (Kant and the Capacity to Judge, pp. 211 and 213). In other words, the Aesthetic had to talk about things that it lacked the resources to account for; hence a ‘retrospective clarification’ of the Aesthetic is in order once those resources are in hand (Kant and the Capacity to judge, p. 217; see also Waxman, Kant's Model of the Mind, p. 80).

⁷ Could the Critique have been organized differently, so that the account of sensibility followed the account of the understanding? Kant addresses this question, briefly, in an unsent draft of a letter to J. H. Tieftrunk. There he says only that the order of exposition actually found in the Critique is certainly more ‘natural’ (13: 463), but does not maintain that it is required. But in the Critique itself, Kant suggests that the order of exposition – the Aesthetic first - is indeed required (A16/B30; see also Critique of Practical Reason, 5: 89–90).

⁸ By ‘hylomorphism thesis’, I refer to Kant's claim that a distinction can be drawn between the ‘matter’ and ‘form’ of intuition. In the Aesthetic, Kant goes on to explain their relation in the following way. Matter is dependent upon form: sensation cannot figure as matter for empirical intuition apart from the formal (spatio-temporal) conditions identified in the Aesthetic. Yet form is independent of matter, inasmuch as we can represent ‘pure space’ and ‘pure time’ at all.

⁹ This may be the place to mention an interpretative strategy of Lorne Falkenstein, who generally aims to take the Aesthetic on its own terms - resisting the trend to read the Aesthetic as a provisional text in light of the Transcendental Deduction's doctrine of figurative synthesis (on this general issue, see note 6 above; in Falkenstein's text see, e.g. p. 383, n. 31). Despite this, Falkenstein is prone to read the Critique backwards, relying on later developments in order to fill the gaps of the arguments he sees Kant as making (or needing to make) in the Aesthetic. For example, Falkenstein remarks that, at the end of the Aesthetic's Metaphysical Expositions, Kant has not yet ‘presented an argument that could demonstrate that space and time could not have originated from any sort of intellectual process whatsoever’ - instead he has only shown that ‘certain intellectual processes are inadequate to do this job’ (p. 242). In order to fill the gaps of what he takes to be Kant's argument, Falkenstein points to the Transcendental Analytic's putatively complete table of four types of synthesis (pp. 242–3); he then argues that ‘none of these four … types of synthesis could plausibly be supposed to originally generate a representation of space or time out of intuitions that are originally aspatiotemporal’ (p. 243). Whatever the philosophical insight of Falkenstein's account, it is distracting if our aim is to interpret the Aesthetic in a manner that is consonant with its own philosophical resources. (For another passage that raises similar concerns, see Kant's Intuitionism, p. 73.)

¹⁰ Practical cognition does not merely determine its object, but also makes it actual (Bix-x).

¹¹ The division into ‘metaphysical’ and ‘transcendental’ exposition is made explicit only in the second edition. I will be dealing with the second-edition text.

¹² See e.g. Allison, Henry, Kant's Transcendental Idealism, revised and enlarged edition (New Haven and London: Yale University Press, 2004), pp. 465–6, n.5).CrossRefGoogle Scholar

¹³ Kant, Falkenstein remarks, ‘needs simply to prove that our concepts of space and time are concepts of the form of intuition rather than the matter of intuition, of the objects of appearance, or of the functions of intellectual synthesis. As a matter of fact, this is what Kant does’ (Kant's Intuitionism, p. 150).

¹⁴ I dispute the details of Falkenstein's account on methodological grounds especially (see note 9 above).

¹⁵ As space and time are presented as concepts that admit of such exposition, they are, presumably, concepts that are ‘given a priori’. In the Jäsche Logic, Kant distinguishes between ‘given’ and ‘made’ concepts: the content of given concepts is revealed analytically, while the content of made concepts is established synthetically. Kant also refers to the ‘exposition (of appearances)’ as the explanation of the content of concepts made from empirical synthesis (§102, 9: 141).

¹⁶ On definition, and why philosophy cannot offer definition in the strict sense (while mathematics can) see A730/B758; and Jäsche Logic §§100–102, 9: 141. See also Kant's caveat that we should not expect to find definitions in the Critique: the work must provide a ‘complete enumeration of the fundamental concepts which comprise the pure cognition under consideration’, but it will not provide a ‘complete analysis of these concepts’ (A13/B27).

¹⁷ The Jäsche Logic uses the German Erörterung, whereas the Doctrine of Method uses the Latinate Exposition. However, the Jäsche Logic glosses Erörterung with the Latin exposition (9: 142), suggesting that remarks about exposition (Exposition) in the Doctrine of Method offer interpretative guidance regarding the expositions (Erörterungen) of space and time in the Aesthetic.

¹⁸ Here I am employing a somewhat limited notion of conceptual content - a notion of content that abstracts from questions about cognitive significance. In this respect, we can speak of the content of the concept phlogiston, even if this concept is not objectively valid or has no genuine cognitive significance. On this limited conception, the content of a concept can brought out by reflecting upon our usage of the concept, and taking note of the relevant entailment relations; it is still a further question to consider whether the concept in question has genuine cognitive significance or objective validity. A cognitively void concept could, in this restricted sense, still have content.

¹⁹ Since the Transcendental Expositions address an existence claim - namely that the concepts of space and time, as exposited in the Metaphysical Expositions, have a real referent - they can be thought of as the ‘synthetic’ complement to the mere concept analysis of the Metaphysical Expositions. While most commentators treat the Transcendental Expositions as an analytic ‘argument from geometry’, Lisa Shabel argues that this is mistaken; see ‘Kant's “Argument from Geometry”’, Journal of the History of Philosophy, 42 (2004), 195–215. Her view of the synthetic burden of the Transcendental Exposition differs significantly from my own, however. I assess this in note 33 below.CrossRefGoogle Scholar

²⁰ See note 9 above.

²¹ Warren, ‘Kant and the Apriority of Space’, §5.

²² Warren himself does not make much of the idea that the Metaphysical Expositions are concept analysis, and he remains somewhat non-committal about the repeated references to the concepts of space and time in the Aesthetic (‘Kant and the Apriority of Space’, pp. 219–20, n. 52).

²³ From a methodological perspective, the reconstructive approach that commentators have taken toward the Metaphysical Expositions is often problematic. Warren, for example, reconstructs only what he takes to be the ‘first apriority argument’; this leaves us wondering about its role in the account as a whole – how does it relate to the other three ‘a priority arguments’ that Warren suggests should be found in the Metaphysical Exposition? Why do we need four apriority arguments – is one not sufficient?

²⁴ Many commentators follow Henry Allison in seeing the division of labour in the Metaphysical Exposition in the following way: the first two moments provide two distinct arguments in favor of the apriority of the representation of space, while the second two moments provide two distinct arguments in favor of claim that space is an intuition rather than a concept (see Kant's Transcendental Idealism, pp. 99–112; for a recent endorsement of this view, see Shabel, ‘Kant's “Argument from Geometry”’, pp. 198–9). The moments do indeed seem to come in pairs, with the first pair arguably emphasizing the apriority theme, and the second pair arguably emphasizing the intuitionality theme. Nevertheless, emphasizing one issue over the other is not the same as disentangling the two and treating each in isolation from the other, so that distinct arguments for the apriority and intuition theses are advanced (or supplied by commentators). Take, for example, the second moment: even though it arguably emphasizes the apriority issue, it still has the intuition issue in play. For there Kant says that space is not to be regarded ‘as a determination dependent upon appearances’ (A24/B39). Inasmuch as the notion of ‘determination’ (Bestimmung) is generally associated with theories of judgement and hence with concepts, Kant seems to be working toward the claim that space is not a concept at the same time that he is working toward the claim that space is a priori.

At any rate, I am advocating a more holistic treatment of the Metaphysical Exposition than is standard. I have come to this interpretative position in large part because the text does not bear out the standard interpretative claim that there are four distinct, but interrelated, arguments. We find a far better characterization of what is actually there on the page of the Metaphysical Exposition in Kant's remarks regarding the analytic exposition of given concepts. In the Critique, he emphasizes that such exposition is merely ‘valid to a certain degree’ (A729/B757). And in the pre-Critical Prize Essay, Kant says that analytic exposition merely brings out what we ‘notice’ about the content of the concept - where these claims may be ‘elucidated’ but ‘can never be proven’ (2: 281). The Metaphysical Exposition better resembles a collective set of remarks offering gradual clarification and elucidation of the content of the concept of space, than it does a set of four apodictic demonstrations.

²⁵ Speaking roughly, we might say that one rhapsodic blotch is ‘bigger than’ another, or ‘to the left of’ another, or even positioned at a certain relative distance from another (e.g. ‘blotch a stands at a distance of half the width of blotch a to blotch b’). But to be precise we should not refer to these as spatial properties, but rather as properties analogous to spatial properties; this is because rhapsodic blotches are not in space at all.

²⁶ My interpretation here does not draw upon anything other than the fundamental distinction Kant draws between intuition and concept as modes of representation; this distinction is already in place from the beginning of the Aesthetic (§1 A19/B33).

²⁷ A judgement is a representation (‘the representation of a representation’, A68/B93).

²⁸ The fourth moment turns on the point that we cannot conceive of a concept's containing an ‘infinite multitude’ of concepts within its intension. But this is not a self-evident claim, even though Kant treats it as one. For it is not hard to imagine a theory of concepts that would not find any incoherence in this idea. Such a theory might say of the concept book that the predicate is not a member of parliament belongs to its intension; and so does the predicate is not the number 2, along with much else. Such a theory could countenance the possibility of a concept's containing infinitely many representations within its intension. Kant, however, seems to be considering the nature of concepts, at least with respect to their intension, quite differently. He is evidently supposing that certain considerations of relevance factor into what we can plausibly take the intension of a concept to be – a great many negative predicates will simply not be relevant. Unfortunately, Kant does not argue the point; and the incoherence of a concept's containing infinitely many predicates in its intension is not self-evident.

²⁹ In §26 of the Transcendental Deduction, Kant says that it is through figurative synthesis that ‘all concepts of space and time first become possible’ (B161n.). Kant's remark indicates that we should not expect the Aesthetic to provide an account of how we acquire the concepts of space and time, since such an account would need to draw upon resources that presumably only become available in the Deduction. Cf. ‘Über eine Entdeckung’ (8: 221–3), where Kant indicates that not only are the categories ‘originally acquired’ but also the pure intuitions of space and time. The issue of original acquisition is central to Waxman, Kant's Model of the Mind (pp. 44–7, and chapter 3), and also figures prominently in Longuenesse, Kant and the Capacity to Judge (chapter 8, esp. p. 222; and pp. 252ff.).

³⁰ Some clarification of this claim that the concept of space refers to ‘all of the following: a pure intuition, a unique particular, and a mode of representing’ is in order, as an anonymous referee has suggested. It makes sense to say that (e.g.) there are distances between various conceivable points in space;if we take space to be either a pure intuition or a unique particular. But is it not rather strained to suppose that there are distances between various conceivable points in space considered as ‘a certain capacity for representing’ or a ‘mode of representing’? However, there is no need to attribute distances between various conceivable points to the capacity for a priori intuition. Rather, there would only be such distances in any representation of space, i.e. in any representation that results from the exercise of this capacity. The capacity in question is constitutionally connected to the representation of space as pure intuition. More generally, saying that the concept of space refers to a capacity for intuition entails that spatial properties apply to things as they are represented through the exercise of this capacity.

³¹ Kant does not refer to an account of the ‘legitimacy’ of these concepts – that is my term; but he does, of course, refer to the account of their objective validity, through their transcendental deduction. The account of the legitimacy of the concepts of space and time differs from the account of their objective validity in the following way: the account of their legitimacy just shows that these concepts have a real referent (space and time as pure intuitions), while the account of their objective validity addresses their necessary applicability to objects that can only be given in experience. For more on this, see §§6–7 below.

³² The importance of this point will be brought out below.

³³ In denying that the Transcendental Exposition offers a regressive ‘argument from geometry’, Shabel suggests that its task is ‘synthetic’ (see pp. 195–6 and passim). Although I agree that the argumentative burden of the Transcendental Exposition is ‘synthetic’, I find serious problems with her account.

Shabel explains the relation between the Metaphysical Exposition and the Transcendental Exposition in the following way: the Metaphysical Exposition issues a ‘background claim that space is a pure intuition’, leading Kant to ask, in the Transcendental Exposition, ‘how does our representation of space manage to afford us those cognitions that are the unique domain of the science of geometry? His question is not whether it does so, but how’ (p. 203). While I acknowledge that Kant's overarching question in the Critique is of the latter sort, it must be recognized that the Transcendental Aesthetic does not possess the explanatory resources to provide any account of how synthetic a priori judging is possible, or even how some particular species of it is possible (e.g. geometry). In the Critique, Kant proceeds with the general question about the possibility of synthetic a priori judging (B19–22); he does not attempt to address – piecemeal – separate questions about the possibility of pure mathematics, of pure natural science, and of metaphysics (as he does in the Prolegomena). The general question about the possibility of synthetic a priori cognition, or judging, only begins to be addressed in the Transcendental Deduction, since the account of its possibility rests on the establishment of the principle of the synthetic unity of apperception. In short: the Aesthetic's Transcendental Exposition does not possess the explanatory resources to address the question that Shabel attributes to it - i.e. a question about how the science of geometry is possible.

Moreover, Shabel does not give adequate attention to the difference in modality between the conclusions of the Metaphysical Exposition versus the Transcendental Exposition. On Shabel's view, Kant ‘takes himself already to have shown that space is a pure intuition’ in the Metaphysical Exposition (p. 202) – she sees this as a concrete result on which Kant then builds a ‘philosophical bridge … to his transcendental idealism’ (p. 196), with Kant's philosophy of mathematics serving as the relevant bridge. However, we should consider the contrast between the Metaphysical Exposition's claim that ‘the original representation of space is a priori intuition’ (B40, my emphasis on the copula), and the Transcendental Exposition claims that space ‘must originally be intuition’ (B41). On my reading, this difference can be explained: the Metaphysical Exposition is analytic, laying bare merely what we actually think in a given concept, whereas the Transcendental Exposition is synthetic, showing that there really is something to which this concept refers – space as pure intuition. The Transcendental Exposition shows that space must really be as exposited in the Metaphysical Exposition.

³⁴ The Transcendental Exposition of time relies, in a similar fashion, on what Kant refers to as the ‘general theory of motion [allgemeine Bewegungslehre]’ (B49). Kant makes a point here of not invoking the empirical concept of matter, conceiving of alteration and motion in the abstract (B48).

³⁵ Kant's appeal to geometry in the Transcendental Exposition is all the more striking, given that it is arguably emphasized in the second edition (1787) version, which appeared after these remarks on the Critique's methodology in the 1783 Prolegomena. For it is only in the second edition version that Kant explicitly divides the exposition into ‘metaphysical’ and ‘transcendental’ phases; simply marking that division would, it seems, draw extra attention to the Transcendental Exposition's appeal to geometry. (In the first edition, a version of the second edition's Transcendental Exposition is sandwiched in between what later became the second and third moments of the exposition of space; see A24.)

³⁶ Critique of Judgement, Introduction §IV (5:180); see also Critique of Pure Reason §26 (B165).

³⁷ This interpretation of the methodological stricture might also account for the Critique's reliance on pure general logic in the presentation of the table of categories (A70–83/B95–109). While it lies well beyond the bounds of this paper to examine the role of pure general logic in the argument of the Critique, it might prove instructive to acknowledge that the same methodological difficulty seems to arise there, too. And the resolution of the apparent methodological difficulty would run along parallel lines: just as geometry is a science of space, concerned with the ‘sensible’ faculty of pure general reason, so pure general logic is concerned with the ‘intellectual’ faculty of pure general reason. Kant can appeal to both, without flouting the restriction to take nothing as given except reason itself. (Presumably, the same point could be made with regard to the Transcendental Exposition of time's appeal to the ‘general theory of motion’ (B49), as well.)

³⁸ In this passage from the Prolegomena, Kant runs together two issues that are kept distinct in the Critique. In the Transcendental Aesthetic's deduction of the concept of space, Kant draws the inference that the concept of space is necessarily applicable to objects of our cognition. The problem of the necessary applicability of mathematics to appearances is a different (but related) issue. For the former addresses the applicability of a concept to appearances, while the latter addresses the applicability of a body of cognition to appearances. The account of how mathematics is necessarily applicable to appearances depends upon the result of the transcendental deduction of the categories; in the Critique, this account is provided only later, in the Analytic of Principles – it is the point of the Axioms of Intuition and the Anticipations of Perception.

³⁹ For the parallel passage regarding the concept of time, see A34–5/B51–2.

⁴⁰ I am grateful to two anonymous referees for this journal, whose comments and criticisms greatly improved this paper. Thanks to Sasha Newton and Sebastian Rand for comments on an earlier version of this paper. Special thanks are due, as ever, to Markos Valaris for much discussion and for helpful comments throughout.