“Philosophical cognition,” according to Kant, “is rational cognition from concepts” (KrV A713/B741). This passage occurs near the end of the first Critique in its Doctrine of Method, where Kant distinguishes the method appropriate to philosophy from that of mathematics. Both mathematics and philosophy deal with concepts, Kant explains, but only mathematics constructs concepts in a priori intuition, “and thus only mathematics has definitions” (KrV A729/B757). Because philosophical cognition, on the other hand, “confines itself solely to general concepts” without constructing them in a priori intuition, philosophy cannot, strictly speaking, give definitions (KrV A715/B743). In the strict sense, “to define properly means just to exhibit originally the exhaustive concept of a thing within its boundaries” (KrV A727/B755). What philosophy does instead of defining concepts, Kant says, is to explicate empirical concepts and to give expositions of a priori concepts. Kant’s reservations about philosophical definitions of empirical concepts concern the uncertain relationship between them and words (KrV A731/B759). But he articulates his reservations about defining a priori concepts differently:
For I can never be certain that the distinct representation of a (still confused) given concept has been exhaustively developed unless I know that it is adequate to its object. But since the concept of the latter, as it is given, can contain many obscure representations, which we pass by in our analysis though we always use them in application, the exhaustiveness of the analysis of my concept is always doubtful, and by many appropriate examples can only be made problematically but never apodictically certain. Instead of the expression “definition” I would rather use that of exposition, which is always cautious, and which the critic can accept as valid to a certain degree while yet retaining reservations about its exhaustiveness.
Immediately after saying this, however, Kant backtracks and allows that philosophy may, after all, arrive at definitions in the strict sense, but only via exposition: “philosophical definitions,” he now says, “come about only as expositions of given concepts” (KrV A730/B758) but he adds that “in philosophy the definition, as distinctness made precise, must conclude rather than begin the work” (KrV A731/B759).
These remarks from the Doctrine of Method seem to accord well with Kant’s procedure in the Transcendental Aesthetic, which is divided into sections providing what he calls expositions of the concepts of space and time, followed by sections presenting conclusions from these concepts, then an elucidation and general remarks. In the second edition, Kant distinguishes metaphysical and transcendental expositions of each concept,1 which he explains as follows:
I understand by exposition (exposition) the distinct (even if not complete) representation of that which belongs to a concept; but the exposition is metaphysical when it contains that which exhibits the concept as given a priori.
I understand by a transcendental exposition the explanation of a concept as a principle from which insight into the possibility of other synthetic a priori cognitions can be gained. For this aim it is required 1) that such cognitions actually flow from the given concept, and 2) that these cognitions are only possible under the presupposition of a given way of explaining this concept.
Here, too, Kant is careful not to claim that his expositions are exhaustive, which seems to rule out interpreting the conclusions that immediately follow these sections as offering definitions in the strict sense specified in the Doctrine of Method. These conclusions are the claims that together go by the name “transcendental idealism” and arguably amount to the key philosophical position defended by Kant in the first Critique: Namely, that space and time are merely the subjective forms of human intuition; and that they are not properties, relations, or objective determinations of things in themselves that would remain if one abstracted from all subjective conditions of our intuition.2
Normally Kant is interpreted as drawing these transcendental idealist conclusions on the basis of arguments contained in the Aesthetic – either in the expositions immediately preceding them or in the elucidation and remarks immediately after them. This interpretation is supported by a passage in the Antinomy chapter, where Kant writes:
We have sufficiently proved in the Transcendental Aesthetic that everything intuited in space or in time, hence all objects of an experience possible for us, are nothing but appearances, i.e., mere representations, which, as they are represented, as extended beings or series of alterations, have outside our thoughts no existence grounded in itself. This doctrine I call transcendental idealism.3
This passage likely refers specifically to the argument from geometry in the “general remarks” section that concludes the Aesthetic, because only in that argument does Kant use such strong language as to claim that transcendental idealism is not merely “a plausible hypothesis” but is “certain and indubitable.”4 The argument from geometry claims essentially that we know transcendental idealism is true on the grounds that we have certain knowledge of geometry, and that we could have certain knowledge of geometry only if we also knew that transcendental idealism is true.5 But setting aside whatever philosophical merits or demerits the argument from geometry may have, this argument does not fit the method Kant ascribes to the first Critique, both in the Prolegomena and in the first Critique itself.
In the Prolegomena, Kant ascribes to the first Critique a synthetic or progressive method that “tries to develop cognition out of its original seeds without relying on any fact whatever” and that treats such facts as “having to be derived wholly in abstracto from concepts.”6 He contrasts this with the analytic or regressive method of the Prolegomena, which assumes that “some pure synthetic cognition a priori is actual and given, namely, pure mathematics and pure natural science,” and derives the conditions of its possibility from the fact that we have such a priori cognition (Prol 4:75). Since the argument from geometry assumes that synthetic a priori cognition of geometry is given as a fact, it fits the method Kant ascribes to the Prolegomena but not the method he ascribes here to the first Critique. In the first Critique’s Doctrine of Method, on the other hand, Kant does characterize the method of argument in the first Critique as relying on some given fact, but he describes that fact as “possible experience” and contrasts it with the “mathemata” or propositions demonstrated through the construction of concepts in mathematics (KrV A734–7/B762–5). What is distinctive to the method of argument appropriate to philosophy in contrast with mathematics, Kant says, is the following:
it certainly erects secure principles, but not directly from concepts, but rather always only indirectly through the relation of these concepts to something entirely contingent, namely possible experience; since if this (something as object of possible experience) is presupposed, then they are of course apodictically certain, but in themselves they cannot even be cognized a priori (directly) at all.
If this passage applies to Kant’s argument for transcendental idealism, which again is arguably the key philosophical position defended by Kant in the first Critique, then that argument cannot be contained entirely in the Aesthetic but must also go through Kant’s arguments concerning the conditions of possible experience in the Analytic, the chief of which is the Transcendental Deduction. While the first Critique does contain arguments for transcendental idealism that Kant consistently distinguishes from the type of argument that is distinctive to the first Critique, such as the argument from geometry, these arguments must be supplementary to Kant’s main argument for transcendental idealism.
Together, the remarks from the first Critique’s Doctrine of Method that I have assembled here suggest that Kant’s main argument for transcendental idealism has the following general form. The Metaphysical Expositions in the Aesthetic exhibit the concepts of space and time as given a priori, but the transcendental idealist conclusions that Kant states later in the Aesthetic follow only on the basis of arguments about the conditions of possible experience that are developed in the Analytic. Elsewhere, I have characterized the Metaphysical Expositions as issuing two promissory notes to be cashed in by arguments developed by Kant in the Analytic: Its first two numbered paragraphs claim that our representations of space and time are necessary conditions for determinate consciousness of appearances, while the last two numbered paragraphs claim that our representations of space and time are singular in the sense that we represent only one space-time (Rohlf 2013). In the same place, I claimed that in the Aesthetic Kant just asserts these promissory notes rather than arguing for them, but now I would rather say that the Metaphysical Expositions are one part phenomenology and one part promise of later arguments. Still, the phenomenological considerations adduced in the Metaphysical Expositions are not sufficient to establish transcendental idealism independently of Kant’s arguments about the conditions of possible experience in the Analytic that finally cash in promissory notes issued in the Aesthetic.
The remainder of this chapter focuses on what I take to be Kant’s argument for the second of these promissory notes issued in the Aesthetic – namely, that our representations of space and time are singular – which I claim is located in section 26 of the B-Deduction. To be clear, I am not claiming that section 26 is supposed to prove transcendental idealism on its own, but rather that it is one piece of an extended argument for transcendental idealism that begins in the Aesthetic and extends through the Analytic. Showing this will first require some discussion of the structure of the B-Deduction in the next section. I hope that what follows sheds light on both Kant’s main argument for transcendental idealism and the importance of the B-Deduction to that argument.
Paul Guyer has identified an argument in the B-Deduction that seems intended to provide independent support for transcendental idealism. According to Guyer, Kant argues in section 26 of the B-Deduction that “the unity of apperception or ‘original consciousness’ and with it the use of the categories are … the condition of the possibility of the unity of space and time themselves” (Guyer 2010: 146). But Guyer does not find this line of argument promising and concludes that, “[a]t the very least, some additional explanation of the relation between the unity of individual consciousness and the unity of space and time is needed here to convince us that apperception, as the former, has anything to do with the latter.”7 My intention in the next section is to provide some additional explanation for this relationship between apperception and the unity of space and time. But this explanation will depend on how one interprets what the Deduction is supposed to prove, and what is left to prove in its second part once the first part is completed.
Guyer holds (and I agree) that “the goal of the Deduction is to prove that the categories necessarily apply to all our intuitions” (Guyer 2010: 121–2). But Guyer interprets Kant’s transition from the first to the second parts of the B-Deduction as a move from an abstract to a concrete characterization of the categories as necessary conditions of apperception (Guyer 2010: 142–4). In doing so, Guyer rejects Dieter Henrich’s view that the first part shows the categories to be necessary for some or one intuition, while the second part argues that they apply to all intuitions (Henrich 1982). There are indeed problems with Henrich’s view, as Guyer and others have noted.8 But in its place, Guyer develops an interpretation that seems to leave too little for the second part of the Deduction to do. The first part of the Deduction, as Guyer interprets it, appears to provide an abstract account that achieves the goal of the entire Deduction, while the second part is left simply to draw certain implications from the first part along with the concrete point that our intuition is spatio-temporal. For my purposes here, the important point is that the line of argument in section 26 that Guyer finds incoherent or insufficiently explained tries to do more than this, and taking it seriously requires giving a different account of the relation between the first and second parts of the Deduction.
I do not have room to go into details about Henrich’s account here, but I think he must be more or less right that the transition from the first to the second part of the B-Deduction is not only a move from abstract to concrete (although it is that too), but also moves from arguing that the categories are necessary for some intuition(s) to arguing that they are necessary for all intuitions, as Kant’s language in section 20 suggests. If the goal of the entire Deduction is (as Guyer also holds) to prove that the categories are necessary for all intuitions, then on such a reading only the second part of the Deduction will finally achieve this goal. The difficulty, however, in maintaining such a view is, of course, to explain which intuitions the first part of the Deduction has not yet shown the categories to be necessary for, and why not.
To explain this, I would like to invoke a well-known article by Lewis White Beck, which suggests that Kant’s way of artificially isolating sensibility and understanding from one another prior to this point in the text created some ambiguities and misleading impressions that must be removed when Kant finally sets out in the second part of the Deduction to address the way these faculties function together to generate experience. For Beck, this led Kant to write specifically about experience and intuition in two different senses. What Beck calls “L-experience” refers to the raw material of sensible impressions without the conceptual and interpretive activities of the mind, while “K-experience” refers to knowledge or cognition of objects. And what Beck calls the “inspectional conception of intuition” refers to the raw material of sensible impressions, while the “functional conception of intuition” refers to the unified presentation of an object as phenomenologically present (Beck 2002: 86–7). We can simplify Beck’s point by mapping these two distinctions onto one another, since there is really one main ambiguity infecting Kant’s language here: namely, between (1) sensible data that has not yet been processed by the understanding in any way, which I will call data1 and (2) sensible data that has been processed in some way by the understanding, which I will call data2.
Before unpacking this, let me assert that I think the B-Deduction is not finished after section 20 because Kant takes himself to have established by that point only that data2 must conform to the categories, but he has not yet established this with respect to data1. There might be data1 that do not conform to the categories, for all the first part of the Deduction proves. Indeed, there might be sensory data (data1) that our understanding cannot process into self-conscious experience. The aim of section 26 is then to rule this out and to show that even all data1 must conform to the categories. So, to switch back to the language of intuition, only the second part of the Deduction establishes that all intuitions must conform to the categories. The first part establishes this with respect to some intuitions (namely, data2), but not all of them (not data1).
To begin unpacking this, let me follow Beck and many others in looking back to section 13 (which Kant himself does at the end of section 20) for insight into what remains to be achieved in the second part of the Deduction.9 In section 13, Kant starts explaining what the entire Deduction is supposed to do, and he presents a counterfactual that the Deduction is charged with showing not to be a real possibility, even if it may be logically possible. The counterfactual, in Kant’s words, is that
appearances could after all be so constituted that the understanding would not find them in accord with the conditions of its unity, and everything would then lie in such confusion that, e.g., in the succession of appearances nothing would offer itself that would furnish a rule of synthesis and thus correspond to the concept of cause and effect, so that this concept would therefore be entirely empty, nugatory, and without significance.
Henry Allison calls this counterfactual scenario “the Kantian specter” (Allison 2004: 160). The worry expressed by Kant here, according to Allison, “is that the deliverances of sensibility might not correspond to the a priori rules of thought. Accordingly, the Kantian specter is one of cognitive emptiness rather than of global skepticism” (Allison 2004: 160). So, for Allison, Kant is not worried simply that we might be self-conscious while some deliverances of sensibility escape our notice because they do not conform to the conditions of self-consciousness. Rather, Kant’s aim in the Deduction is to rule out the possibility that we might not be able to generate self-consciousness at all.
While I concede that Allison’s interpretation might fit this passage in section 13, I do not think it fits what Kant actually says and does in the second half of the Deduction. In section 21 and section 26, Kant repeatedly says that the goal of the second part of the Deduction is to show that the categories apply to all the deliverances of sensibility.10 Allison may be right that Kant is not trying to refute global skepticism with this argument, since we already know from the first part of the Deduction that any sensible data of which we can become conscious – in my terminology, data2 – must conform to the categories. But that’s different from showing that we can become conscious of all sensible data, including all data1, so that in principle none is left out of the unified whole of experience that our understanding makes possible. So, contrary to Allison, Kant is not trying to show that our experience is veridical. He’s trying to show that it is, or at least in principle can be, complete – that there is nothing in nature of which we cannot in principle become aware. For a transcendental idealist, of course, this is not a claim about things in themselves. The claim is not that all of reality in itself can in principle appear to us, since such a claim would be obviously transcendent. Rather, the touchstone of nature for Kant is sensibility: that is, appearances, not things in themselves. So, on my view, the claim that Kant wants to establish in the second part of the Deduction is that our understanding makes out of all sensory data that we can ever encounter (all data1 and data2) a single, unified whole of experience, which Kant identifies with nature (considered formally, not in respect of its material content). The first part of the Deduction aims to show that the categories are conditions of self-consciousness; and the second part aims to show that they ground the fundamental laws of nature, which requires ruling out the possibility (articulated in section 13) that some sensible data1 might not conform to the categories.
How, then, does Kant attempt to establish this claim in the second part of the Deduction? In section 21 Kant says that he intends to show “from the way in which the empirical intuition is given in sensibility that its unity can be none other than the one the category prescribes.”11 Kant refers us to section 26 for his argument. Here is the key text:
We have forms of outer as well as inner sensible intuition a priori in the representations of space and time, and the synthesis of the apprehension of the manifold of appearance must always be in agreement with the latter, since it can only occur in accordance with this form. But space and time are represented a priori not merely as forms of sensible intuition, but also as intuitions themselves (which contain a manifold), and thus with the determination of the unity of this manifold in them (see the Transcendental Aesthetic).12 Thus even unity of the synthesis of the manifold, outside or within us, hence also a combination with which everything that is to be represented as determined in space or time must agree, is already given a priori, along with (not in) these intuitions, as condition of the synthesis of all apprehension. But this synthetic unity can be none other than that of the combination of the manifold of a given intuition in general in an original consciousness, in agreement with the categories, only applied to our sensible intuition. Consequently all synthesis, through which even perception itself becomes possible, stands under the categories, and since experience is cognition through connected perceptions, the categories are conditions of the possibility of experience, and are thus also valid a priori of all objects of experience.13
This passage is extremely dense. According to Béatrice Longuenesse, it amounts to:
a revisiting, in light of the argument of part one, of “the manner in which things are given,” namely the forms of intuition, space and time, that were expounded in the Transcendental Aesthetic. Kant’s point is that space and time themselves, which have been described in the Transcendental Aesthetic as forms of intuition and pure intuitions, are now revealed to be the product of the “affection of sensibility by the understanding,” namely by the unity of apperception as a capacity to judge. And so, by the mere fact of being given in space and time, all appearances are such that they are a priori in accordance with the categories, and thus eventually subsumable under them.
In particular, Longuenesse reads Kant to be claiming here that “the unity, unicity (there is only one space and one time), and infinity of time and space” are “the product of synthesis speciosa, the transcendental synthesis of imagination,” while “the qualitative features of spatiality and temporality depend on our sensibility, which thus provides ‘first formal grounds’ of the ordering of sensations that yields appearances” (Longuenesse 2005: 34–5). As I understand her interpretation, Longuenesse is not attributing to Kant the view that the transcendental synthesis of imagination produces conscious perception of the whole of space and time as actually infinite, but rather as limitless, because representing boundaries to space or time would undermine the conditions of self-consciousness. In other words, the result of the transcendental synthesis of imagination is that everything of which we ever can become conscious – in my terminology, all data1 and data2 – is represented as occurring in a single time, unlimited in both future and past; and as related in and to a single space that likewise is unlimited in all its dimensions. As Longuenesse puts it, the unity, unicity, and infinity of time and space “are features we imagine or anticipate and thus project as preconditions of the unity of experience.”14
Now one could accept that the unity, unicity, and infinity of space and time are conditions of self-conscious experience without accepting Longuenesse’s view that they are products of the transcendental synthesis of imagination. Again, for Longuenesse the transcendental synthesis of imagination produces the pure intuitions of time and space, and these features of them, which are conditions of experience. This transcendental synthesis in some sense precedes the empirical synthesis of apprehension, which is the ongoing process of generating specific unities of sensible data within the single space-time, and which occurs in accordance with or is a specification of the transcendental synthesis. In her words: “the unity of apperception, as a capacity to judge, generates the representation of the unity and unicity of space and time, as the condition for any specific act of judging at all, thus prior to any specific synthesis according to the categories, let alone any subsumption under the categories.”15 But Allison and Guyer both reject this view, while accepting that for Kant it is a condition of experience that space and time have the features that Longuenesse attributes to the transcendental synthesis of imagination. Allison denies not only that the transcendental synthesis of imagination plays this role, but also that it is distinct from the empirical synthesis of apprehension in the way Longuenesse claims it is. He writes the following about Kant’s example later in section 26 of the perception of a house:
Kant’s point here is that the perception of a house, which tokens a three-dimensional object, is conditioned by the determination of the space it is perceived to occupy. It is not, however, a matter of two distinct syntheses: an a priori or transcendental synthesis that determines the space and an empirical one that determines the contours and extent of what is perceived in it. It is rather that these are related as the formal and material aspects of one synthesis. The transcendental synthesis of the imagination is the form of the empirical synthesis of apprehension in the sense that the apprehension or perception of a house is governed by the conditions of the determination of the space it is perceived to occupy.
Guyer, too, prefers to emphasize the second part of section 26 where this example of the perception of a house occurs (KrV B162), which he reads as suggesting an alternative to the account of the first part that I quoted earlier (KrV B160–1). According to this account, Guyer writes, “the categories are necessary not for the representation of the unity of space and time as such but rather for the representation, or judgment, of determinate objects of any kind in space and time” (Guyer 2010:147). To be fair, Longuenesse (whom Guyer is not addressing in his article) also does not believe the categories are necessary for representing the unity of space and time as such. She reads B160–1 as saying that apperception is necessary for representing the unity of space and time as such, and that apperception is distinct from and prior to any use of the categories.16 But presumably, Guyer would agree with Allison that, at least according to the account Guyer favors at B162, both the transcendental and empirical syntheses proceed according to the categories, and that the empirical synthesis does not presuppose the completion of the transcendental synthesis in the way Longuenesse believes it does.
I think Longuenesse’s account is closer to the truth. To see why, let us return once more to section 13 and to my earlier disagreements with Guyer and Allison about what the second part of the Deduction is supposed to show. If it is supposed to show, as I claimed, that the categories ground the laws of nature, because our understanding makes a single, unified whole of experience out of all sensible data that we can ever encounter (all data1 and data2) – which had not yet been shown by the first part of the Deduction – then clearly the argument would fall well short of this goal on Guyer’s and Allison’s interpretation of section 26. Their interpretation might explain how (again to use Kant’s example) we represent the unity of the space in which we perceive a house, or any other individual perceptions. But it does not even attempt to account for the a priori representation of the whole of space and time as unified, or (to use the language of the Aesthetic) that it is an infinite given magnitude. So Longuenesse is right to attribute such an account to Kant at B160–1 and to distinguish the transcendental synthesis of the imagination from the empirical synthesis that it conditions. Indeed, and here is my main point in this section, Kant’s overall argument in the B-Deduction, interpreted as I have argued it should be, simply could not work and would not even make sense as an argument unless it involves the claim that apperception produces the unity and singularity of our representations of space and time. In other words, the B-Deduction could succeed only by cashing in the second promissory note from the Aesthetic that I identified in the previous section.
Does the B-Deduction succeed or does it merely reassert the second promissory note from the Aesthetic, namely that our representations of space and time are unified and singular, and pass on to the Principles the task of finally proving this claim? I cannot hope to settle this question here. But in this final section let me defend an interpretation of how the claim I take Kant to be making in section 26 is different from and presupposed by some other claims he argues for in the Principles.
I propose that we interpret Kant as claiming at B160–1 that possessing formal intuitions of time and space is a condition of being able to assign specific time-determinations to our representations, which in turn is a condition of self-consciousness. Kant emphasizes from the first part of the Deduction through the Analogies that it is a condition of self-consciousness that we can assign specific time-determinations to our representations: for example, A represents something happening at T1, B at T2, and so on. But assigning specific time-determinations to our representations requires that we have a way of measuring time, a single standard by reference to which we can assign specific time-determinations to our representations. Even if our sensations, thoughts, and other representations originally occur in or are received in some temporal order, becoming conscious of that or indeed of any temporal order among representations requires that we use some sort of standard for measuring temporal relations. As Kant writes at the very beginning of the Deduction in section 15, “we can represent nothing as combined in the object without having previously combined it ourselves,” and “all combination … is an action of the understanding” (KrV B130). Representing temporal relations is a form of combination and requires some internal, subjective measure for assigning specific time-determinations to particular representations. I propose that the single, unified, and boundless intuition of time plays this role of acting as the abstract standard for measuring particular temporal relations. That is the sense in which, contrary to the interpretation of section 26 shared by Guyer and Allison, the empirical synthesis of apprehension is conditioned by a distinct and completed transcendental synthesis of the imagination. This transcendental synthesis produces the internal standard for measuring time in general (namely, the formal intuition of time), which is presupposed by all assigning of specific time-determinations to particular representations in the empirical synthesis of apprehension.
This argument can be applied to space as well, using Kant’s point at B154 that we can represent time only by drawing a line in space. If we need a pure intuition for measuring time, and yet we can represent such a measure for time only by making reference to space, then it follows that we need a pure intuition of space, too, that is singular, unified, and boundless for all the same reasons. But I do not have room to develop the application of this argument to space here and will focus my remaining remarks on its application to time.
To be clear, I am not claiming that Kant regards the formal intuition of time as a specific metric for measuring temporal relations, such as a second or a centiday. At no point in Kant’s argument – not in the Deduction, the Schematism, the Axioms of Intuition, etc. – does he descend to the level of specific metrics for measuring temporal relations, except by way of example.17 Rather, I am claiming that Kant regards the formal intuition of time as a condition of assigning schemata to categories in the Schematism chapter, which in turn is a condition of deploying schematized categories to assign specific time-determinations to empirical representations, as discussed in the Principles section. What the formal intuition of time supplies that makes possible these more specific forms of time determination is the bare representation of unity as applied to time. This exquisitely abstract point is emphasized by Kant at KrV B160: “space and time are represented a priori not merely as forms of sensible intuition, but also as intuitions themselves (which contain a manifold), and thus with the determination of the unity of this manifold in them.” In the footnote to this sentence he adds that “the form of intuition merely gives the manifold, but the formal intuition gives unity of the representation.” Thus, all the work being done here is accomplished by adding unity to the form of time, which results not just in the representation of some unified time but of Time (that is, all of time) as a unity, or again it results in representing the singularity and unicity (as Longuenesse says) of time. The claim is that we need to represent time abstractly as a singular whole before (logically speaking) we can carve it up into aspects (schematism) or assign particular times to empirical representations. That is why, Kant says, that the representation of unity in the formal intuition of time is a “condition of the synthesis of all apprehension,” in which specific time-determinations are assigned to our representations (KrV 161).
A critic of my interpretation might object that Kant assigns to the mathematical principles – namely, the Axioms of Intuition and Anticipations of Perception – something like the task I am imputing to the Deduction at B160–1. This critic may concede that Kant vaguely waves his hand in this direction in section 26 but maintain that B160–1 does no more than issue (or, if my interpretation of the Aesthetic from the first section of this chapter is granted, reassert) a promissory note that he finally argues for at length only in the Principles. The mathematical principles in particular, as Kant later summarizes, aim to show of appearances that “both their intuition and the real in their perception could be generated in accordance with rules of a mathematical synthesis, hence how in both cases numerical magnitudes and, with them, the determination of the appearance as magnitude, could be used” (KrV A178/B221). Focusing only on the Axioms of Intuition, Kant’s task there is to argue that the categories of quantity guarantee both that the concept of number arises and that every intuition is measurable by numerical concepts. So, according to this objection, Kant must regard the standard for measuring time as fixed not by apperception in the Deduction but rather in the Axioms by the categories of quantity, whose schema, he says, “is number, which is a representation that summarizes the successive addition of one (homogeneous) unit to another. Thus, number is nothing other than the unity of the synthesis of the manifold of a homogeneous intuition in general.”18
To this objection I reply, first, by appealing to another passage from section 15:
Combination is the representation of the synthetic unity of the manifold. The representation of this unity cannot, therefore, arise from the combination; rather, by being added to the representation of the manifold, it first makes the concept of combination possible. This unity, which precedes all concepts of combination a priori, is not the former category of unity (section 10); for all categories are grounded on logical functions in judgments, but in these combination, thus the unity of given concepts, is already thought. The category therefore already presupposes combination. We must therefore seek this unity (as qualitative, section 12) someplace higher, namely in that which itself contains the ground of the unity of different concepts in judgments, and hence of the possibility of the understanding, even in its logical use.
This passage distinguishes the role of apperception from that of all categories and specifically the quantitative category of unity, which Kant says presupposes apperception. Second, in the Axioms, Kant invokes the categories of quantity to explain “empirical consciousness … of a determinate space or time,” not the generation of pure, formal intuitions as standards for measuring space or time in general (KrV B202). Thus, the task of the Axioms aligns with the interpretation shared by Guyer and Allison of B162–3 but not with the claims of B160–1 as I have interpreted them. Third, it is consistent with my interpretation of the abstract claim of B160–1 that Kant would follow it up with examples (at B162–3) at a lower level of abstraction that track arguments about specific categories that he develops only later in the Principles. But the actual argument of the Axioms is an application of, and thus depends on, the abstract claim of B160–1. The Axioms argue that apprehending an intuition as a unified whole presupposes an act of synthesis, and now we learn that the categories of quantity are involved in composing a unified intuition out of the manifold of sensory data. Apparently, Kant means that we fix a unit by means of the category of unity, successively add units of data to one another by means of the category of plurality, and finally arrive at a whole intuition by means of the category of totality. As the quoted passage from section 15 says, however, the first step of this argument in the Axioms presupposes a higher unity that obviously refers to apperception; and since the argument goes on to invoke successive synthesis, it also presupposes the application of apperception to the form of time. Thus, Kant’s argument in the Axioms depends on and cannot replace his claim at B160–1 that we have a pure, formal intuition of time.
Moreover, we find further evidence in favor of my interpretation of B160–1, its importance in the Deduction, and the dependence of Kant’s argument in the Principles on it, by considering the relationship between the mathematical principles and the Analogies of Experience, which Kant calls dynamical principles. He writes, “[i]n the application of the pure concepts of the understanding to possible experience the use of their synthesis is either mathematical or dynamical: for it pertains partly merely to the intuition, partly to the existence of an appearance in general” (KrV A160/B199). In other words, the mathematical principles describe how perception of intuitions is generated; and, on this basis, the dynamical principles describe how we relate these intuitions to existing objects understood as appearances. This distinction maps onto the one Kant draws in section 24 of the B-Deduction between two levels of cognitive processing: What he there calls the figurative synthesis (i.e., the empirical synthesis of apprehension)19 turns out to involve using the categories of quantity and quality to generate perception of intuitions, as described by the Axioms and Anticipations; and the intellectual synthesis turns out to use categories of relation to generate self-conscious experience of objects (as appearances) distinct from these intuitions of them, as described by the Analogies.20 Kant argues in the Axioms and Anticipations, in effect, that the output of the figurative synthesis is unified, empirical intuitions (and sensations) with both extensive and intensive magnitude, and that the way these are generated guarantees that they can be measured mathematically. But from the Deduction we remember that the figurative synthesis by itself is not sufficient for self-consciousness, which also requires the next level of cognitive processing. At this level, the intellectual synthesis, we interpret the output of the figurative synthesis as perceptions of existing objects that are distinct from our intuitions of them. This is Kant’s concern in the first part of the B-Deduction, especially sections 16–19: Namely, to argue that becoming conscious of the identity of the self in all of our representations requires interpreting them as representations of objects distinct from us that interact in accordance with constant laws.
In the Deduction, Kant describes these laws generally as the categories, without naming particular (sets of) categories or distinguishing between categories that are operative at one level of processing and those that are operative at the other level. This distinction is made only later in the Principles. But Kant is often criticized for giving the misleading impression in the Deduction that all of the categories are operative at both levels of processing, as if his strategy for averting the counterfactual or specter articulated in section 13 was to argue that intuitions are generated in the figurative synthesis in accordance with the very same categories that we use to think them in the intellectual synthesis. Allison, for example, concludes that the Deduction is “at best only partly successful” because only its second part averts the specter of section 13 and this part turns out to apply only to the mathematical categories, as we learn later in the Principles; thus, since the first part of the Deduction turns out to concern the relational categories and does not avert the specter of section 13 as it applies to them, on Allison’s view Kant fails to prove in the Deduction itself that all of the categories are objectively valid conditions of experience, and leaves it to the Analogies to prove this of the relational categories (Allison 2004:200).
But my interpretation of B160–1 explains why Kant thought the Deduction does prove the objective validity of all the categories. On my reading, the Axioms and Anticipations aim to show that our categories of relation can get a grip on all possible perception of intuitions because they are measurable magnitudes. In short, if I can measure the size of one intuition, then I can compare, correlate, relate it to other intuitions of the same or different size. If I can measure the intensity of a sensation, then I can compare it to the intensity of another sensation that I receive from the same object or different objects and draw inferences about the properties of objects through their influence on me.21 Thus, in the Axioms and Anticipations, Kant is not only providing support for the science of applied mathematics but also explaining how he averts the specter from section 13: We know a priori that the categories of relation can get a grip on all possible perception of intuitions because they are generated by the categories of quantity and quality in such a way that they are mathematically measurable. We ourselves must carry out such (perhaps implicit) measurements in order to make empirical judgments about existing objects that are related to but distinct from both our perceptions and one another. But for my purposes here, the key point is that this argument, linking the justification for the objective validity of the categories of relation to that of quantity and quality, depends on B160–1 having already established the unity and singularity of our representation(s) of time (and space), for two reasons. The first reason is again the abstract point that assigning time-determinations to representations presupposes a standard for measuring time. But, second, in order to draw inferences about the properties of objects from their influence on me, I must assume a single (space-)time in which all of my actual and possible representations can be related both to one another and to independently existing objects. It would not suffice to presuppose only the unity of the (space-)time in which I perceive the determinate object at hand, as Guyer and Allison would have it, because I am drawing inferences about objects whose locations in (space-)time may be different from those of my representations of them and which I do not know prior to drawing these inferences. For example, the feeling of warmth on my skin now was caused by light emitted from the surface of the sun more than eight minutes ago at a distance of around 150 million kilometers from the earth. Before inferring from this feeling of warmth to its cause, I do not know at what location in (space-)time to place it, and drawing such an inference requires me to assume that all objects that can influence me exist in a single (space-)time together with all of my representations of them.
So, I conclude that Kant’s argument in the Principles cannot establish, but rather depends on his claim in section 26 of the B-Deduction, that our representations of time and space are unified and singular. Earlier I argued that the success of the B-Deduction depends on this claim, which also cashes in a promissory note in Kant’s extended argument for transcendental idealism. Although I have not argued that the B-Deduction succeeds or defended transcendental idealism, I have tried to show that these arguments are linked in a deeper way than is typically noticed and to develop a plausible interpretation of the crucial claim on which both depend.
1 The first edition also calls them “expositions” (KrV A27) even though it does not draw this distinction.
2 KrV A26/B42, KrV A32–4/B49–50. These conclusions are restated and discussed throughout the rest of the Aesthetic.
3 KrV A490–1/B518–19. Kant goes on to develop a separate, indirect proof of transcendental idealism (KrV A506/B534).
4 KrV A46/B63. In the second edition, Kant suggests that the argument from geometry simply elaborates on the material in the Transcendental Exposition, which was also present in the first edition but not under that heading (KrV B64). The second edition also adds three new considerations “[f]or the confirmation of this theory” (KrV B66ff.), but the Antinomy passage quoted cannot refer to these since it was present in the first edition and they were not.
5 See KrV A48–9/B66.
6 Prol 4:274, 4:279. See Prol 4:263, 4:274–6, and Prol 4:279.
10 See KrV B144–5, B159–61, and B163–5.
11 KrV B144–5. I take this use of “intuition” to be a reference to data1, saying that the unity even of data that has not yet been processed by the understanding can be none other than what the category prescribes.
12 Kant’s note:
Space, represented as object (as is really required in geometry), contains more than the mere form of intuition, namely comprehension of the manifold given in accordance with the form of sensibility in an intuitive representation, so that the form of intuition merely gives the manifold, but the formal intuition gives unity of the representation. In the Aesthetic I ascribed this unity merely to sensibility, only in order to note that it precedes all concepts, though to be sure it presupposes a synthesis, which does not belong to the senses but through which all concepts of space and time first become possible. For since through it (as the understanding determines the sensibility) space or time are first given as intuitions, the unity of this a priori intuition belongs to space and time, and not to the concept of the understanding. (section 24)
13 KrV B160–1. Here I take “perception” to be used in the technical sense of data1, while “experience” refers to data2.
14 Longuenesse 2005:34. This addresses Guyer’s worry that if apperception were a condition of the unity of space and time themselves, then we would not represent the scope of space and time as extending beyond the scope of our own unified consciousness. See Guyer 2010:146–7.
17 See, for example, his reference to the decimal or base ten numeral system at KrV A78/B104.
18 KrV A142–3/B182. The passage continues: “because I generate time itself in the apprehension of the intuition.” I understand this clause to mean that I generate empirical consciousness of time in the empirical synthesis of apprehension.
19 The figurative synthesis seems to include both the transcendental synthesis of the imagination and the empirical synthesis of apprehension, or both are figurative syntheses. I have been arguing that these should be regarded as distinct syntheses and refer here only to the latter.
20 KrV B151–2. See also KrV A158/B197.
21 See KrV A143/B182–3.