PART THREE

 

THE TRANSCENDENTAL ELEMENTS

OF KANT'S SYSTEM

 

 

by Stephen Palmquist (stevepq@hkbu.edu.hk)

 

 

Reason's nature is such that it can never conceive anything except in­sofar as the latter is determined under given con­ditions. Conse­quent­ly, inasmuch as it can neither rest with the conditioned nor make the un­conditioned comprehensi­ble, nothing remains for it, when thirst for knowledge in­vites it to grasp the absolute totality of all conditions, but to turn back from objects to itself in order to investigate and determine the ultimate boundary of the capacity given it, instead of in­vestigating and determining the ultimate boundary of things. [Kt3:564-5]

Kant's System of Theoretical Perspectives

 

 

When one has thought according to a method and then expressed this method and distinctly stated the transition from one proposition to the next, then one has treated a cognition systematically. [Kt10:148(149)]

 

1. The Four Stages of Representation in General

 

      The task set before us here in Part Three is to fill the formal structure of Kant's architectonic, as outlined in III.3-4, with the content provided in the part of each Critique called the Transcendental Doctrine of Elements.[1] This will require us to put forward a more detailed interpretation of Kant's Critical philosophy, beginning in this chapter with his system of theoretical perspec­tives (as de­veloped mainly in Kt1). One of the risks of modulating from for­mal to transcen­dental logic in this way will be that of oversimplification-i.e., of making distinct what Kant (perhaps purposefully) left obscure, or vice versa. Conse­quently, I shall not pretend to have discovered texts in Kant's writings which match perfectly with each of the twelve formal components in Figure III.6, nor to have accounted adequately for all of his multitude of appar­ently techni­cal terms. Instead, I shall pick out those arguments which seem to constitute the essential elements of his system (and which must therefore, in the case of Kt1, be common to both editions [see note I.21]), in hopes of deter­mining the extent to which each can be correlated with one of the components given in Figure III.6. (The goal of such a procedure is to develop a schematic outline of systemt which can be used as a map to guide us through Kant's text, and which can therefore simplify the task of those who wish to reformulate Kant's arguments in contemporary terms [see I.1].) Such correlations are not always as straightforward as we might wish, so in some cases they must be advanced tentatively, as the best choice presented in the text. Nevertheless, I believe the correspondence between the elements Kant put forward and the twelvefold pattern described in III.3 is sufficiently close to establish my claim that he was working towards such an ideal pat­tern, but was unable to elabo­rate its structure precisely enough in his own mind to pass it on unambigu­ously to his reader [see Kt1:862-3].

 

      As suggested in III.4, the form of my interpretation of systemt will be as follows. Its four major 'stages' are concerned with the ana­lysis of the nature of sensibility [VII.2.A], understanding [VII.2.B], judgment [VII.3.A] and reason [VII.3.B]. Each stage has three 'steps', arranged in a synthetic pat­tern. Thus, I will interpret Kant's presentation of the 'conditions of knowing' in systemt as containing a total of twelve steps. Each step is itself estab­lished as necessary by means of a threefold (synthetic) argument. The various 'ele­ments' which operate in each step of Kant's overall argument (and which, taken together, constitute the 'Doctrine of Elements') can therefore be regarded as constituting a ninefold pattern in each stage. The formal structure of such 'second-level synthetic integration' is discussed in Pq18:4.1, but does not need to be described here. Instead, a very general, but also very important, ex­am­ple will be used to demonstrate the threefold structure of each step in Kant's presentation. Once this is done, we will discuss the general character of each of the four stages in systemt and their structural relationship. These two introductory tasks will prepare us for a detailed study of each stage.

 

      As we saw in VI.2, Kant's whole theory of the synthetic progression of the elements of knowledge is based on the assumption that the knowing sub­ject must 'represent' to itself an unknown thing in the form of a 'represen­tation'. The power to perform this function is attributed to the 'faculty' of representation. Two ambiguities concerning this claim, which could give rise to much confusion and hamper our understanding of almost every step in systemt, are discussed in Appendix VII.A.

 

      An examination of representation makes a good introduction to Kant's way of arguing not only because it reveals these typical ambiguities, but also because he uses the term in connection with almost every step in his theory [cf. Kt1:94,376-7]. Representation itself 'cannot be explained at all', since it 'would have to be explained again through another representation': human knowledge 'always presupposes representation' [Kt10:34(38)]. 'All representa­tions', he insists, 'can themselves become objects of other representations' [Kt1:A108]. So his entire discussion of the conditions of knowing can be re­garded as an account of the faculty of representation applying a series of con­ditions (+) to the object which is to be conditioned (-), so that the latter is represented in a more and more determinate form of representation (x), until all such steps eventually lead to the fully determined knowledge of the repre­sented object. The format chosen to summarize this most general function of knowing can therefore be adopted as the pattern for summarizing the steps in each of Kant's systems.[2] The synthetic structure of this basic argument can be depicted straightforwardly by using the following schema:

 

 

 

 

      Kant defines an 'organism' in Kt7:376 as 'an organized natural product in which every part is reciprocally both end and means.' Taking this comment, together with his subsequent claim that the interrelation­ships between the parts of an organism are 'founded upon ... the causality of an architectonic un­derstanding' [388-9], to apply not only to physi­cal organisms, but to rational systems as well (as he suggests in Kt1:xxii,xxxvii-xxxviii), can help us to understand the formal relationship between each of his twelve successive threefold arguments (or steps). Following the format given above, the first part of each step will specify the material given, i.e., the conditioned element (-), which is carried over from the conclusion of the previous step; the second part will specify the formal function, i.e., the condition (+), which is sup­plied by the subjective faculty involved;[3] and the third part will spe­cify the synthetic unity (x) of these, thus yielding a new level in the determina­tion of the ob­ject. The 'end' of each argument (i.e., the third part) is then presented to the 'means' (i.e., the second part) of the next step: that is, the object at this new level of determination serves as the material for the next step; and the process continues until the object is finally represented as fully determined. Such re­ciprocal development is what Kant means by 'the causality of an ar­chitectonic understanding'. Kant alludes to this synthetic pattern when he notes that a transcenden­tal argument is required whenever 'an a priori determi­nation is syn­the­tically added to the concept of a thing' [Kt1:286]. But even though the Critical philosopher is concerned primarily with the transcendental aspects of the elements defined by each argument, Kant often discusses their empirical aspects as well. I shall mention this empirical side of many of the arguments discussed, but concentrate mainly on their transcendental character (using 'transcendental' here in the broad sense in which all the conditions of know­ing, regardless of the stage in which they arise, are transcendental [see II.4, III.4 and IV.2].

 

      Two methodological clarifications must be made before we discuss the structural relationship between the four stages of systemt. The first is simply that its twelve progressive steps must be taken to determine only the transcendental-logical order of the elements which constitute experience, and not the empirical-temporal order in which they are experienced.[4] But the second is rather more complex: ignoring the fact that Kant is interested more in the formal conditions of knowing[5] than in actual experienced knowledge could lead an interpreter to confuse the synthetic method, which analyzes how em­pirical knowledge is possible [see Ap. IV and Kt2:276n], with actual 'syn­thetic a priori knowledge' as such. Inasmuch as we can discover the twelve condi­tions of knowing only through transcendental reflection on the way in which empirical knowledge arises, Kant's synthetic method in Kt1 can be thought of as an analysis of the elements of such knowledge, organized according to the (architectonic) form of their logical synthetic progression [see F1:114-6]. Once it is taken as given that we know something, any investi­ga­tion of that knowledge will be analytic; but such an investigation can be pre­sented in a synthetic form by theoretically putting all empirical knowledge in abeyance and asking what syntheses logically gave rise to the possibility for analysis.[6] Thus, although the series of arguments which constitutes the syn­thetic method will reveal at some point the content of some synthetic a priori knowledge, it will also reveal other types of knowledge [see Figure IV.2]; for the series itself is intended to trace all the conditions which, when regarded as syntheses from the Transcendental Perspec­tive, explain the possi­bil­ity of the empirical knowledge being analyzed.

 

      The first and second stages of systemt deal with the faculties of sensibil­ity and understanding. Kant describes the functions of these 'two sources of representation' [Kt1:327] in the Transcendental Aesthe­tic[7] and in the (Tran­scendental) Analytic of Concepts,[8] respectively. He defines sensibility as 'the capacity (receptivity) for receiving representations through the mode in which we are affected by objects' [Kt1:33; cf. 75 and Kt6:211n]. In other words, 'the senses' are 'the first foundation of all judgments' [Kt18:361(102)], so that the aim of the first stage is to discover how the material for knowl­edge (i.e., sen­sation) arises through the function of intuition. Special atten­tion is paid to the role of 'representations which are not empirical' [Kt1:A99]; thus the fac­ul­ty of sensibility adopts the transcendental perspective in sys­temt.[9] However, Kant defines understanding in a number of different ways. Indeed, he assigns to 'understanding' almost as wide a variety of possible meanings as he does to 'representation'. So it is important to determine which of his meanings ap­plies to the second stage of systemt and how the understanding in this sense is related to sensibility.

 

      'Understanding is, to use general terms, the faculty of knowledge' [Kt1: 137]. As such, it is 'the mind's power of producing representa­tions from it­self, the spontaneity of knowledge' [75]. Kant analyzes this general mean­ing in Kt66:138(19):

 

understanding (in the most general sense of the term) ... must include: 1) the power of apprehending given [representations] to produce intuition ..., 2) the power of abstracting what is common to several of these to produce a con­cept ..., and 3) the power of reflecting to produce knowledge of the object.

 

As we shall see, this threefold division of the general powers of the under­standing directly corresponds to the first three stages of systemt (i.e., to intu­itive sensibility, conceptual understanding and determin­ate judgment, respec­tively). But Kant later distinguishes this general type of understanding from sensibility by calling the former 'the higher cognitive power' and the latter 'the lower'. He then specifies that, as 'the higher cognitive power', the fac­ulty of understanding 'consists in understanding, judgment, and reason' [196-7 (68-9); s.a. Kt7i:201 and Kt39:476(182)]. And these three terms refer di­rectly to the second, third and fourth stages of knowing (i.e., to conceptual under­stand­ing, determinate judgment and inferential reason, respectively). In its most general sense, therefore, the understanding is equally well describable 'as a spontaneity of knowledge ..., as a power of thought, as a faculty of con­cepts, or again of judgments', as a 'faculty of rules' and as 'the lawgiver of nature' [Kt1:A126]; indeed, it is involved in some sense in every stage of knowing, so that, as Beck says in a note to Kt4:9, it is itself 'the faculty of empirical knowledge'.

 

      The terms sensibility, judgment, and reason all refer in their own right to stages in systemt, so the sense of 'understanding' we shall adopt-that is, as referring to the second stage-will be its narrow sense, according to which it refers to one aspect of the higher cognitive power in general. Kant uses the word in this sense when he says 'the understanding ... thinks only, and does not intuit' [Kt1:139]. But within this specific usage, the word 'understanding' is occasionally utilized even more specifically as a description of any one of the three functions which combine to make up the second stage [e.g., 134n]. Fully aware of its multifarious meaning, Kant observes that 'the proper task of a transcendental philosophy' is the 'dissection of the faculty of the under­standing itself, in order to investigate the possibility of concepts a priori' [90-1]. Rather than discussing every variation at this point, let us now examine the relationship between understanding and sensibility.

 

      As the second stage of knowing, understanding is always closely related to sensibility. In fact, Kant himself speculates that these 'two stems of hu­man knowledge' may 'spring from a common, but to us unknown, root' [Kt1:29]. Whereas sensibility provides the transcen­dental material for empiri­cal knowledge, understanding in the second stage provides 'the logical form of all judgments' by forming self-conscious thoughts which correspond to sensa­tions [Kt1:140e.a.; s.a. 143]. Understanding in this context is therefore al­ways conceptual understanding. Like sensibility, understanding is an abstract func­tion, in the sense that it is concerned not with concrete objects of real ex­peri­ence, but with one aspect of our knowledge of such objects in isolation from the other. The faculty of sensibility considers intuition in abstraction from the corresponding power, which I shall call 'conception' [see note VII.28], and is always 'passive, consisting in receptivity'; the faculty of un­derstand­ing, by contrast, considers conception in abstraction from intuition and is 'active and manifests power' [Kt66:140(21)]. This relation of passive to active, or matter to form, suggests the former can be correlated with - and the latter with + [see III.4].

 

      The third and fourth stages of systemt deal with the faculties of judgment and reason, and are presented in the Analytic of Principles and in the Di­alectic, respectively. Kant defines judgment as 'the mediate knowledge of an object, that is, the representation of a representation of it' [Kt1:93]: it is the empirical realization of the understanding in its concrete relation to sensi­bil­i­ty. Thus, the role of the third stage in clarifying how judgments are pos­sible can be depicted as a simple synthetic integration, as shown in Figure VII.1. 'The judgment indicates what use is to be made of the understand­ing.'[10] For, as Kant says in Kt7:407: 'understanding must wait for the subsump­­tion of        

Understanding (+)

 

 

Figure VII.1:

The 'Lower' Cognitive Powers as a 1LSR

 

the empirical intuition ... under the conception, to furnish the determination [of an empirical object] for the faculty of judgment.'

 

      Kant defines reason in a deceptively similar way, as 'the faculty of infer­ring, i.e., judging mediately' [Kt1:386; s.a. Kt14:59(93)]. Rational inference, or 'syllogism',[11] refers to the subjective function whereby certain universal conditions are determined to apply to an object of judgment which cannot be discovered through judgment alone [Kt1:360-1]. 'Concepts of understanding', he explains, 'first provide the material for making inferences' [366-7]; judg­ment, which now 'mediates between the other two faculties' [Kt7i:202], serves as the form (+) under which such conceptual material (-) is subsumed in order to be synthesized in an inference (x) [Kt1:360-1]. Thus, for Kant 'a syllogism shows in its conclusion something more than the activity of the understanding and judgment required by the premises, viz., a further particular activity belonging to reason' [K2:345(Z1:112)]. The synthetic relation be­tween these three higher stages is depicted in Figure VII.2. Kant summa­rizes the synthetic relation between these three faculties in Kt39:472(171): 'Under-

 

 

Figure VII.2:

The 'Higher' Cognitive Powers as a 1LSR

 

standing is the knowledge of the universal. Judgment is the ap­plication of the universal to the particular. Reason is the faculty of perceiv­ing the union of the universal with the particular.'

 

      Because the role of sensibility drops out in this fourth stage [Kt1:363; cf. R11:65], inferential reason, as we shall see, often tends to be employed spec­ulatively. This occurs when the understanding adopts sensibility's transcen­dental perspective, rather than the logical or empirical perspectives which properly belong to it; as Kant puts it in Kt1:345, 'employing the understand­ing transcendentally' is 'contrary to its vocation'. But in their proper employ­ment, the objects ultimately determined through inference 'serve only for the completion of reason's empirical perspective' [Kt1:593; cf. 714]-i.e., only to complete our systematic understanding of the nature of empirical objects. As we shall see in VIII.3.B and Appendix IX, the fourth stage in each of Kant's systems functions in this same way, revealing the ultimate ful­fill­ment or purpose of what might already seem to be complete at the end of stage three.

 

      The most comprehensive way of mapping the stages of systemt, how­ev­er, is not to isolate sets of three which form simple syntheses, but rather to include the relations between all four, in the form of a 2LAR.[12] By doing so, the four stages in systemt can be correlated on a one-to-one basis with the four perspectives mapped onto Figure IV.2. Each of these perspectives has as its task the defense of one type of synthetic a priori (and in this broader sense, transcenden­tal) condition for knowing, as shown in the following table:

 

Table VII.1: Basic Perspectival Relations in Systemt

 

Each of the conditions of knowing (i.e., 'transcendental forms') listed above serves as the formal element in its respective stage, so in each case it will ap­pear as the second step in that stage [see III.4 and Kt19:389-92]. The focal point in each stage, therefore, will be the task of determining rationally 'how an empty form ac­quires the content which fills it', rather than merely observ­ing empirically (as in a non-Copernican philoso­phy, such as Aristotle's) 'how a given content acquires its form' [G10:92n]. When that content fills the form, the empirical goal of the stage is reached, just as in the example of representa­tion, given above. This means each stage will start with a kind of transcenden­tal 'object' (or matter), proceed from there to a transcendental 'subject' (or form), and conclude with an empirical synthe­sis of the preceding two elements.

 

     One way of mapping these stages onto the cross is to regard them as aris­ing out of two 1LARs: between the axes, representing the re­ceptive (-) facul­ties of intuitive sensibility and determinate judgment and the sponta­neous (+) fac­ulties of conceptual understanding and inferential reason; and be­tween the end points of each axis, representing the abstract (-) faculties of sensibility and understanding and the concrete (+) faculties of judgment and reason. This gives us the model shown in Figure VII.3.

 

     We can now see that the synthetic relation mapped in Figure VII.1 at­tended only to the first term in the two-term components describing sensibil­ity and understanding. Likewise, Figure VII.2 made use only of the second term in the corresponding two-term components specified in Figure VII.3. More­over, the close affinity, as well as the marked distinction, Kant saw be­tween the Analytic of Concepts (conceptual understanding) and the Analytic of Principles (determinate judgment) [see note VII.8] is reflected by the fact that these two stages are represented in Figure VII.3 by the two secondary, or mixed components, while stages one and four are represented by the two pri­-

 

Figure VII.3: The Four Stages in Systemt

 

ma­ry, or pure components. (Kant's important distinction between the 'logi­cal' and 'real' employments of the understanding refers to the con­tradic­tory, i.e., +- vs. -+, relation between these two stages.)

 

      Keeping in mind this description of the formal relations between the four main stages of systemt will help us to steer a straight course through the rough waters of Kant's terminology. In VII.2 we will examine the six steps which constitute the first two stages of this system, the stages dealing with intuition and conception in abstraction from each other; and in VII.3 we will examine the third and fourth stages, which deal with our concrete judg­ment and reasoning concerning real objects of empirical knowledge. Once this arduous task is completed, we will be in a position in VII.4 to look back over our exposition in order to determine the extent to which the interpretive tools given in Parts One and Two have enabled us to discern order in the ac­tual content of systemt.

 

2. The Abstract Conditions of Knowing (-)

  A. Intuitive Sensibility (--)

 

      Kant's exceedingly broad understanding of terms such as 'represen­tation' and 'understanding' makes it necessary for him to introduce other terms to de­scribe both the objective and the subjective elements which operate at each particular step of systemt. Since we have already considered at length in Part Two several of the most important of these more specific terms, I will as­sume with only brief reminders that their meanings are already sufficiently understood. Two such terms come up in the first step of Kant's twelvefold progression.

 

      We saw in VI.2 that 'thing in itself' is a label for that aspect of an object of knowledge which transcends our modes of representation, and is therefore unknowable [s.a. Ap. V]. Since it does not have the status of a formal condi­tion of knowledge [see notes VI.12,17], it cannot be correlated with any of the components listed in Table III.5 (though we can label it with a neutral component, 0). When considered as determined only to the extent of being represented by a subject through an 'original' act of representation, the thing in itself can be called the 'transcendental object'.[13] This first representation of reality in the form of an undetermined object is entirely negative with re­spect to our knowledge, so it is appropriate that this material (-) step in the sensibility (--) stage is correlated with the purely negative component, ---.[14]

 

      Although he uses phrases such as 'original representation' and 'immedi­ate representation' only occasionally [e.g., Kt1:40,41], Kant seems to regard this condition as a necessary starting point. For he frequently uses 'original' in close proximity to 'representa­tion', usually when referring to the original (i.e., non-empirical [Kt1:72]) representations of space [40] and time [48], in contrast to the 'origi­nal apperception' in which the second stage cul­minates [see e.g., A107]. He also speaks in Kt1:A99-100 of the 'original re­ceptivity' through which the representations of sensibility become possible. Here 'origi­nal' indicates the bare fact that a thing must first of all be repre­sented as an object in order for us to know it empirically [33; s.a. W6:297]. Indeed, in­tu­i­tion itself is 'possible only if the subject's faculty of representa­tion is af­fected by that object' [Kt1:72], yet this 'transcendental object re­mains un­known to us' except, as we shall see, through the mediation of the 'forms of our sen­sible intuition' [63]. Moreover, in Kt10:64(71) he calls rep­resentation 'the first degree of cognition', thus suggesting its role as the first step in systemt. Using the method suggested in VII.1, we can now summarize step one as:

 

 

 

      The next step maintains that the transcendental object must be re­pre­sent­ed as an 'appearance' through the process Kant calls 'intuition'. Once again, the meaning of the third term of this argument was fully ex­plained in VI.2, where we referred to it, when viewed from the transcen­dental perspective of systemt (i.e., sensibility), as a 'transcendental appearance'; but the role of intuition as the 'form of appearances' [Kt1:223; s.a. 323-4] has yet to be explained. This process of intuition is neither an imaginative activity nor a ca­pacity for 'mystical insight' [R7:240-5], but the function whereby the undetermined object is inter­preted by the subject as a mass of unorganized representations called the 'manifold [Mannigfaltige]' (i.e., 'multiplicity' or 'vari­ety'). Once the original given, the transcendental object, is intuited [Kt1: A394], so that it has the formal (+) limits of sensibility (--) imposed upon it, it becomes a manifold of appearances (--+) and can serve as 'the data for a pos­si­ble experience' [A119,298]. 'Possible experience' is Kant's way of referring to immediate experience [see IV.1] as viewed from the theoretical standpoint. But another formal limit, as we shall see, must be imposed by the understand­ing in the second stage [A119] before the contents of this pos­sible experience can become 'data for a possible knowledge' [296]. Kant holds these formal limits to be 'concepts which are of two quite different kinds ..., namely, the concepts of space and time as forms of sensibility, and the cate­gories as con­cepts of understanding' [118]. The former, as given here in stage one, are the source of our immediate 'awareness of individual entities', while the latter, to be given in stage two, are the source of our awareness of their general nature, as mediated through thinking.[15]

 

      The manifold of appearances is sensible only when it appears in the con­text of space and/or time-i.e., only when these intuitive 'forms of sensibil­ity' [Kt1:522] are applied to it. (Since this is 'the only kind of intuition we pos­sess' [302], Kant calls a (transcendental) appearance 'the undetermined ob­ject of an empirical [or 'sensible'] intuition' [34].) Kant says: 'The faculty of sensible intuition is strictly only a receptivity, a capacity of being affected in a certain manner with representations, the relation of which to one another is a pure intui­tion of space and time' [522]. Thus time and space, the two pure forms of all human intuition, 'come before appearances and before all data of experience, and are indeed what make the latter at all possible.'[16]

 

      Kant proposes two ways in which this sensible intuition can be mani­fested in the human subject: through 'inner sense' (i.e., the soul) and through 'outer sense' (i.e., the body).[17] He proposes:

 

Space is nothing but the form of all appearances of outer sense. It is the subjective condition of sensibility [Kt1:42].

 

Time is nothing but the form of inner sense, that is, of the intuition of ourselves and of our inner state [49].

 

Time is the formal a priori condition of all appearances whatsoever [50].

 

This means all objects which appear to the inner sense-i.e., 'the sum of all representations' [220]-are intuited in the context of time, while both time and space are required for an object to appear to outer sense.[18] 'Time and space, taken together, are the pure forms of all sensible intuition, and so are what make a priori synthetic propositions possible' [55-6].

 

      Because the pure intuitions of time and space are not forms 'inher­ing in things in themselves as their intrinsic property' [Kt1:45], but exist 'only in us',[19] they cannot claim 'absolute reality'.[20] As Kant explains, 'these a pri­ori sources of knowledge, being merely conditions of our sensibility, just by this very fact determine their own limits, namely, that they apply to objects only in so far as objects are viewed as appearances, and do not present things as they are in themselves' [56; cf. A9:320]. This limiting function explains why such spatio-temporal intuition is the core element in the transcendental perspective of systemt. Pure spatio-temporal intuition fulfills the transcenden­tal function of enabling the representations of the first step, which could otherwise be regarded only in terms of the transcendental object, to be repre­sented as a manifold of appearances here in the second step. That is:

 

 

 

      This second condition not only determines the intuitive form of sensibil­ity, but also enables the matter provided by the transcendental object to be revealed in the appearances; for as Kant says, 'appearances contain in addition to intuition the matter for some object in general [i.e., for the transcendental ob­ject]' [Kt1:207]. The third condition of sensibility (--), therefore, must be to actualize these formal (+) and material (-) conditions in a synthetic unity (x); that is, the appear­ances, or sensible intuitions must actually be sensed, thus representing the manifold of appearances as a discrete sensation.[21] This pro­cess can be summarized as:

 

 

      Kant does not devote much attention to this third step in his argu­ment, perhaps because its conclusion is so obvious.[22] It is important to point out, however, that the sensations in this third step, as viewed here from the tran­scen­dental perspective, are not sensations as we actually experience them, but refer only to the level of determination of the object produced by the faculty of sensation in abstraction from the understanding. (Kant does sometimes view sensibility empirically, in an active sense-as, for example, when he says 'inner sense presents to me ...' [Kt1:321]. But when viewed transcen­den­tally, sen­sibility is the purely passive capacity for receiving objects, some of which will eventually help constitute knowledge.) This third step completes the sen­sibility stage of systemt and establishes sensation as 'the material of sen­sible knowledge'.[23] Of course, those sensations which are never concep­tualized in such a way as to produce possible knowledge will never be­com­e conscious [C1:1.352-5]. Inasmuch as unconscious sen­sations are not episte­mologically interesting, Kant ignores them and concen­trates instead on those destined to help make up empirical knowledge [Kt1:A111].

 

  B. Conceptual Understanding (+-)

 

      As mentioned in VII.1, the aim of the understanding in the second stage is to provide the abstract conceptual form for the abstract matter presented to it by sensibility. This does not mean 'All intuitional process is concep­tually controlled' [E3:89e.a.], but that in order to produce empirical knowl­edge, such material processes must submit to the formal 'control' of conceptual pro­cesses. In Kt1:A94 Kant lists three 'conditions for the possibility of expe­ri­ence', which must hold true in order for thoughts to arise out of a manifold of appearances : '(1) the synopsis of the manifold a priori through sense; (2) the synthesis of the manifold through imagination; finally (3) the unity of this synthesis through original apperception' [s.a. 104,A115]. He then re­minds us that the Aesthetic (i.e., the first stage) culminates in the first of these condi­tions, sensation [A94-5]. The second stage, as expounded in the Analytic of Concepts, now assumes the logical perspective (+-), which cul­minates in the formation of self-conscious thought; therefore, the other two conditions listed in Kt1:A94 should function as two of the steps in this sec­ond stage.

 

      Kant's account of the fourth step of systemt is somewhat muddled by his use of several terms in very similar ways with no clear explanation of their relationship. In particular, the terms 'imagination', 'perception' and 'appre­hension' are easily confused, because they all take part in the function of synthesis, which Kant regards as the 'first application' of the understanding to sensibility [Kt1:152], and which he defines as 'the act of putting different rep­resentations together, and of grasping what is manifold in them in one [act of] knowledge.... Synthesis of a manifold ... is what first gives rise to knowl­edge' [103]. 'The understanding does not', according to Kant, 'find in inner sense such a combination of the manifold, but produces it, in that it affects that sense.'[24] This 'synthetic influence of the understanding upon inner sense' is what Kant ordinarily refers to as 'the transcendental act of imagina­tion' [154]. In itself, apart from the illumination provided by the fifth and sixth condi­tions as they 'bring this synthesis to concepts', the imagination is 'a blind but indispensable function of the soul, without which we should have no knowl­edge whatsoever, but of which we are scarcely ever conscious' [103]; it sim­ply 'connects the manifold of sensible intuition' [164] in such a way as to form an inner image of the sensations involved.[25]

 

      This application of imagination to sensations results in a con­scious 'as­sociation of representations',[26] which Kant calls perception [Kt1:160,164]. Perception is the act in which appearances are 'combined with con­scious­ness' [A119-20] to produce 'objects of perception' [207]; it 'contains sensation' as its 'matter' [208-9]. Accordingly, a percep­tion can be described as a 'represen­tation accompanied by sensation' [147], as long as it is a 'sensation of which we are conscious' [272]. In short: 'Perception is ... a con­sciousness in which sensation is to be found' [207; cf. Kt22:217]. Since this conscious­ness, which forms sensations into perceptions, arises only through the syn­thesis of imagination, 'perception' can be thought of as a general de­scription of the whole process (i.e., the four steps) leading up to and includ­ing this synthesis. Kant suggests this when he describes the entire second stage as that in which 'our faculty of knowledge ... advan­ces from particular perceptions to universal concepts' [Kt1:118; cf. Kt7i:203n]. As the material (-) step in the second stage (+-), percep­tions can therefore be correlated with the +-- component in Figure III.6 [s.a. Table III.5].

 

      An accurate summary of the complexities of this fourth condition would have to take into account Kant's variety of expression [see Ap. VII.E], which would be too cumbersome for our purposes. Instead, we need only express the essential function of this 'first principle of the human under­standing' [Kt1: 139; s.a. 152] in stage two:

 

 

No matter which terms we use to describe it, this fourth step serves, by means of a transcendental synthesis, to 'bring the manifold of intuition on the one side into connection with the condition of the necessary unity of pure apperception on the other' [Kt1:A124; s.a.164].

 

      Apperception, however, does not follow synthesis immediately in sys­temt (i.e., it does not function as the form to be imposed upon the percep­tions rep­resented in the material step); rather this function is fulfilled by the 'pure con­cepts of the understanding' (i.e., the 'categories') [see e.g., Kt1:A119], while apperception, as we shall see, acts as the synthetic condi­tion of stage two.[27] For 'our understanding ... can produce a priori unity of appercep­tion solely by means of the categories' [145e.a.]; indeed, such 'transcendental unity ... is thought in the categories' [151]. The categories, as 'the conditions of the nec­essary unity of apperception', and not apperception itself, can be re­garded therefore as doing for stage two what 'the formal condi­tions of space and time' do for stage one [A110e.a.; s.a. A111,136]. Whereas 'the categories contain, from the perspective of the understanding, the grounds of the possi­bility of all experience in general' [167], space and time contain the grounds for the same possibility, from the perspective of sensibili­ty. Since Kant believes 'All synthesis ... is subject to the categories' [161], he de­scribes the lat­ter as categories of synthesis, to which the object as given in step four, that is 'perception, must completely conform' [162], and which as such prepare the way for the unity of apperception in step six. 'Consequently, all possible perceptions ... must be subject to the categories' [164-5].

 

      Whereas the second condition of the first stage gave rise to objects of intuition (i.e., appearances), that of the second stage gives rise to objects of thought or conception (i.e., concepts). Kant defines thought rather loosely as 'knowledge by means of concepts' [Kt1:94], but more precisely as 'the act which relates given intuition to an object' [304]. In Kt1:A124 he explains that 'concepts ... are brought into play through the relation of the manifold to the unity of apperception', thus implying that they arise out of the applica­tion of categories to conscious perceptions here in step five. The connection between the concepts produced by this activity of 'categorial conception'[28] and the categories through which this task is achieved is frequently made ex­plicit, as when Kant refers to the categories as 'forms of thought' [e.g., 150, 289,305] (as opposed to space and time as 'forms of intui­tion'[29]), or as 'the pure form of the conceptual perspective on objects in general' [305]. As such, categories are 'concepts of objects in general' [K2:11.301(Z1:183); s.a. Kt1: 158], which suggests a correla­tion between the intuitive determination of the transcendental object in stage one and its conceptual manifestation in stage two [see Ap. VII.B]. Since the categories function as 'the law of the syn­thetic unity of all appearances' [A128], a concept produced by such conception 'is always, as regards its form, something universal which serves as a rule.'[30]

 

      Kant often stresses the necessary, reciprocal relationship between intu­ition and conception: 'Now there are two conditions under which alone the knowledge of an object is possible, first, intuition, through which it is given, though only as appearance; secondly, concept[ion], through which an object is thought corresponding to this intuition' [Kt1:125; see also Kt69:325; K2: 11.302(Z1:184)]. Just as intuitions are intelligible only when related to con­cepts, so also concepts are objectively valid only if they are related to in­tu­i­tions via perception [Kt1:272]. Even though in experience these two are al­ways combined, Kant believes that, by theoretically abstracting from the par­ticular content of all perceptions and examining their general content [A245], he can compile a complete list of all the a priori categories of pure under­stand­ing.[31] Moreover, as we saw in III.3, there is a sense in which the twelve categories correspond directly to the twelve steps in systemt-a corre­spon­dence which Kant himself begins to elaborate in Kt1:742-3 when he says quantities (--) can be 'exhibited a priori in intuition', while qualities (+-) can be known 'only through concepts'. In any case, our need to abstract from experience in order to arrive at the categories [Kt1:165] does not contradict the fact that they function in systemt as 'independent cognitive acts' [R11:89]. For as Wallace says: 'The pure or abstract categories have their home in logic' [W5:171]-i.e., in the logical perspective of systemt. So we can sum­marize the general function[32] of this formal (+) step in the logical perspec­tive (+-) of systemt as:

 

 

 

      Even though Kant establishes the categories by abstracting all sensibility from experience, he is careful to remind us that 'the categories, in themselves mere forms of thought, obtain objective reality' only when they are applied 'to objects which can be given us in intuition' [Kt1:150-1]. That is, since 'the categories are not in themselves knowledge, but are mere forms of thought for the making of knowledge from given intuitions', it follows that 'no synthetic proposition can be made from mere categories' [288-9]-in them­selves they define the formal character of the logical perspective in systemt. So, although in the second stage Kant occasionally exaggerates the cer­tainty of his choice of categories, he is careful to warn elsewhere that 'the pure cate­gory does not suffice for a synthetic a priori principle' [304]. Categories en­able us to know things 'only through their possible application to empirical intuition' [147]-a process which will not be fully explicated until the third stage.

 

      In the sixth step of systemt the faculty of 'transcendental apperception' synthesizes the material perceptions (-) with the formal concepts (+) devel­oped by the understanding: only through a 'synthesis according to concepts' can 'apperception demonstrate a priori its complete and necessary identity' [Kt1:A112]. Whereas categorial conception functions as the 'form of thought' (i.e., of stage two), the unity of apperception realizes the whole purpose of the understanding in the second stage, so it 'constitutes the form of all knowl­edge of objects; through it the manifold is thought as belonging to a single object' [A129e.a.]. Its function as the synthetic step in this formal stage of systemt leads Kant to characterize it as 'the radical faculty of all our knowl­edge' [A114]. Indeed, he goes so far as to say: 'The principle of apperception is the highest principle in the whole sphere of human knowledge' [135]; 'this faculty of apperception is the understanding itself' [134n; s.a. A119 and W21: 145].

 

      Kant defines transcendental apperception as a 'pure original un­changeable consciousness' [Kt1:A107], and as 'the thoroughgoing identity of the self in all possible representations' [A116]. As Paton suggests, its original character indicates that 'the unity of objects is deriva­tive' [P2:2.71]. Indeed, from the theoretical standpoint of systemt, 'the original synthetic unity of appercep­tion' [Kt1:135] is 'the source of all combination [i.e., synthesis]' [154e.a.] and so 'lies a priori at the foundation of empirical consciousness' [220; s.a. A116]. The cate­gories themselves are said to impose 'synthetic unity' on the objects of perception, thus converting what is varied and manifold into a more-or-less unified object (via the concept). But the object is not fully uni­fied until it is assimilated into one person's consciousness: 'it is only be­cause I ascribe all perceptions to one consciousness (original apperception) that I can say of all perceptions that I am conscious of them' [A122]. Apperception is therefore the synthetic condition for determining the ma­terial presented by the imagination's synthesis of the manifold, as well as the concepts pro­duced by the categories, to be elements in which I partici­pate (i.e., self-conscious thought).[33] Of course, imagination might be able to synthesize, and the categories to conceptualize, without ever arriving at the unity of apperception; but such a non-unified combination of the manifold would be ir­relevant to systemt, since it could not give rise to empirical knowledge.

 

      As Bird points out, Kant relates transcendental apperception 'both to the notions of a personal and a conceptual unity' [B20:115; s.a. 121,174,176]. The conceptual unity is determined by the categories in step five. Appercep­tion unifies the twelve categories (and so also the structure of tran­scendental logic itself [R11:10]) in a single, 'bare' or empty representation of the self [Kt1:A117n], thereby allowing all the abstract thoughts which arise in step five to be united in the I think. (In this analytic sense apperception can be regarded as 'the ground of the possibility of the categories' [A401], for its I think 'accompanies all categories as their vehicle' [406].) The personal unity of apperception, then, is 'the synthetic unity of appearances' which alone, Kant argues, enables the manifold of appearances to become known as 'one experience' [281]. For it is the unity 'to which everything that is to be­long to my knowledge ... has to conform' [220e.a.]. 'The synthetic unity of con­sciousness is, therefore, an objective condition ... under which every intu­ition must stand in order to become an object for me' [138]. In its most basic form, 'the consciousness of self' involved here is revealed in 'the simple rep­re­sentation "I"' [68]. Kant himself explains the nature and implications of the personal unity of apperception with unusual clarity:

 

pure apperception ... or, again, original apperception ... is that self-conscious­ness which, while generating the representation 'I think' ..., cannot it­self be accompanied by any further representation [132].

 

For through the 'I', as simple representation, nothing manifold is given; only in intuition, which is distinct from the 'I', can a manifold be given; and only through combination in one consciousness can it be thought [135].

 

      An important implication of the personal function of apperception is that in itself 'the representation "I am" ... does not so include any knowledge of that subject', because it 'is not an intuition, but a merely intellectual repre­senta­tion of the spontaneity of a thinking subject' [Kt1:277-8]. The 'I'-i.e., the concept of a conscious self-is supplied by a faculty of the understanding (viz., apperception) rather than by sensibility, so empirical knowledge of the self 'as it is in itself' is impossible [156]. For only that which can be intuited in time and space is empirically knowable: 'The determination of my exis­tence can take place only in conformity with the form of inner sense ... Accordingly I have no knowledge of myself as I am but merely as I appear to myself' [157-8]. Therefore, through the activity of 'the synthetic original unity of apperception, I am conscious of myself, not as I appear to myself, nor as I am in myself, but only that I am' [157].

 

      But Kant's immediate purpose in establishing the centrality of appercep­tion is not to explore its many implications for the concept of 'self'. For he treats this subject more thoroughly in the Paralogisms section of the Dialectic. Rather, his main reason for insisting at this midpoint of systemt that all the previous steps must be united in one person is to provide a firm basis for establishing empirical knowledge in the third stage [A110]. In much the same way that sensation actual­izes the transcendental function of sensibil­ity in the first stage, pure apperception actualizes the logical function of the understanding [134n] in the second stage (+-) by synthesizing the material (-) state of the object in step four (perceptions) with its formal (+) deter­mination in step five (concepts) in the form of a unified network of self-con­scious thought (x) here in step six.[34] So we can summarize the fulfill­ment of this final abstract condition for the possibility of experience as:

 

 

With this sixth step, the second stage of knowing is completed, thus bringing us to the midpoint of systemt.

 

      The first stage of knowing supplied the sensible material (--) for a possi­ble experience. The second stage has now informed us that 'the pure under­standing, by means of categories, is a formal and synthetic principle of all experience' [Kt1:A119]; as such it has supplied the intelligible form (+-) for a possible knowledge.[35] Kant summarizes his analysis of the first two stages of 'the act of knowing' in Kt7:238: 'a given object [step one], through the intervention of sense [steps two and three], sets the imagination at work in arranging the manifold [step four], and the imagination, in turn, [sets at work] the understanding in giving this arrangement the unity of concepts [steps five and six].' To complete systemt, these two epistemological building-blocks must be syn­thesized (-+) in judgment; and the resulting empirical knowledge must be grounded in the ultimate unity (++) of the rational ideas. In the next section, we shall follow Kant's argument through these two final stages.

 

3. The Concrete Conditions of Knowing (+)

  A. Determinate Judgment (-+)

 

      A source of possible confusion in interpreting the third and fourth stages of systemt is that Kant sometimes seems to suggest that empirical knowledge has already been actualized in the first two stages [e.g., Kt1:94,104; cf. W21: 159,227]. For example, he asserts: 'Intuitions and concepts consti­tute ... the ele­ments of all our knowledge' [Kt1:74]. But this does not mean the separate functions of intuition and conception as such are sufficient to constitute em­pirical knowledge, as some have assumed [see Ap. VII.H]. For he con­tin­ues: 'These two powers or capacities cannot exchange their functions. The under­standing can intuit nothing, the senses can think noth­ing. Only through their union can knowledge arise.'[36] Although there is, as mentioned above, a sense in which the first stage supplies us with possible experience and the second with possible knowledge, the essential Critical doc­trine is that actual empir­ical knowledge arises only in stage three, wherein the first two stages are combined from the empirical perspective of determinate judgment.[37]

 

      The synthetic role of the third stage[38] in relation to the first two implies that 'a third something is necessary' in order for an object to be judged. This third thing, Kant says, is the 'possibility of expe­rience' [Kt1:194-5]. By this he means that the intuition and conception of an object must be able to be synthesized in actual (determinate) experience. The object can then be said to 'exist', as long as 'the perception can, if need be, precede the concept' [272]. An object of thought can thus become empirically known as an object of judgment only if it is possible for that object to be given in intuition [146].

 

      On this basis we must qualify Kant's claim that thinking 'is the same as judging' [Kt2:304; s.a. Kt1:106] before his intended meaning can be rendered intelligible. Rather than regarding thought and judgment as strictly synony­mous terms, we should view judgment as thought which makes use (or at least can make use) of intuition. A clear understanding of their perspectival re­lationship will guard against the temptation to assume a strict 'identification of thinking and judging' [H4:xlvi; see Ap. VII.H]. For the two faculties refer to different levels in the determination of the object by the understand­ing: 'Now the only use which the understanding can make of these concepts [i.e., those arising out of the logical per­spective] is to judge by means of them'; so from the empirical perspec­tive, 'we can reduce all acts of under­stand­ing to judgments, and the understanding [in its broad sense] may therefore be repre­sented as a fac­ulty of judgment.'[39]

 

      Kant concisely summarizes the first two steps of this third stage in Kt1: 175: first, the schematism [176-86] 'will treat of the sensible conditions un­der which alone pure concepts of understanding can be employed' (-); and sec­ond, the principles [187-294] 'will deal with the synthetic judgments which under these conditions follow a priori from pure concepts of under­standing' (+). The third step, though neglected by Kant in this preview of the content of the third stage, is expounded just where we would expect to find it, in the third chapter of the Analytic of Principles [294-315]. By providing 'a sum­mary' of the theory through the distinction between 'phenomena' and 'noumena' [295], this chapter explicates how the actual judgment of objects establishes ob­jec­tively valid empirical knowledge (x). As we shall see, the new terminology introduced in this ninth step also points directly to the fourth stage.

 

      Kant's seventh condition of knowing, 'the schematism of the pure under­standing' [Kt1:179], specifies just how the categories are applied 'to sensibil­ity in general' [A245]. The second stage has already shown that the categories stand in a necessary relation to sensibility, for the former arise out of the abstraction of all spatial and temporal con­tent from the latter [Kt1:161-2; cf. P2:2.67-8]. But in order for these categories, and the concepts they deter­mine, to be used validly in expe­rience, they must be grounded in something concrete once again [171]. Consequently, the third (synthetic) stage begins by positing something

 

which is homogeneous on the one hand with the category, and on the other hand with the appearance, and which thus makes the applica­tion of the former to the latter possible. This mediating repre­sentation must be pure, that is, void of all empirical content, and yet ... sensible. Such a representation is the transcendental schema [177].

 

Kant describes this first 'condition of judgment (the schema)' [304] as that in which the object is determined to be a 'manifold and an order of its parts' [861]. To fulfill this function, schematism must furnish abstract, self-conscious thought (step six) with the transcendental unity of one time.[40]

 

      Just as he believed the transition from the first to the second stage to have been accomplished by the transcendental imagination in the fourth step, so also Kant bases the transition from the second to the third stage on the work of this most mysterious of human powers here in the seventh step. He says, for instance, that a 'schema is in itself always a product of imagination' [Kt1:179]. As with the first application of imagination, he confesses he can­not explain how it works, because 'schematism ... is an art concealed in the depths of the human soul, whose real modes of activity nature is hardly likely ever to allow us to discover, and to open to our gaze' [180-1]. But he does warn that the schema 'has to be distinguished from the image', because, al­though it may be represented in an image, it is fundamentally the 'representa­tion of a universal procedure of imagination [viz., 'schematism'] in providing an image for a concept'.[41]

 

      Kant summarizes the fourfold, categorial division of the schemata rather concisely in Kt1:184-5, where he defines them as 'a priori determinations of time in accordance with rules', and relates them 'in the order of the categories to the time-series, the time-content, the time-order, and lastly to the scope of time in respect of all possible objects'. By limiting the categories in these four ways, the schemata, each of which is itself a 'sensible concept of an ob­ject in agreement with the category' [186], insure that the abstract concepts of stage two 'are altogether impossible, and can have no meaning, if no object is given for them' [178]. This means thoughts can never be more than sub­jec­tively valid if they do not correspond to a possible object of outer intu­ition; for as Paton says in P2:2.393, when an object is objectively valid, 'the matter of inner sense is derived from outer sense.' Thus, the seventh step in sys­temt, expressed as

 

 

is the material beginning (-) of the synthetic procedure of judgment (-+), whereby 'sensibility ... realises the understanding in the very process of restrict­ing it' [Kt1:187].

 

      Once schematism is shown to have secured the necessary relation be­tween sensibility and understanding, Kant turns his attention to what is often regard­ed as the most important part of systemt: 'the judgments which under­standing ... actually achieves a priori', which he calls 'principles' [Kt1:177]. Although he is not entirely consistent in his use of these terms, he ordinarily refers to the particular, empirical laws of the understanding as 'rules' and re­serves the word 'principle' for the transcendental laws of judgment to which all rules must conform.[42] 'Principles a priori', he explains, 'are so named not merely because they contain in themselves the grounds of other judgments, but also because they are not themselves grounded in higher and more univer­sal modes of knowledge' [188]. However, Kant is not interested at this point in every type of a priori principle. Inasmuch as the principles of mathematics, for example, 'are derived solely from intuition, not from the pure concept of understanding' [188], they do not qualify as principles of judgment. Similarly, the analytic principles of formal logic can be excluded, because, as we shall see, every principle of judgment must be synthetic.[43] But regardless of which type of principle is under consideration, the schema­tism requires that 'all prin­ci­ples ... have significance and validity only as prin­ciples of the em­pirical, not of the transcendental, perspective' [223], and that as such they will inevitably contain some non-pure elements [cf. IV.1 and C14:253]. For 'outside the field of possible experience there can be no syn­thetic a priori principles' [Kt1:304-5].

 

      The principles whose functions Kant discloses in step eight are the formal 'conditions of the unity of empirical knowledge in the synthesis of appear­ances'-i.e., in the synthesis of the third stage [see note VII.38]-which of course, 'can be thought only in the schema'.[44] Since they function as 'rules for the objective employment of the [categor­ies]' [Kt1:200], they can be com­pletely revealed under four headings, each corresponding to one cate­gory: the principles of quantity are 'axioms of intuition', of quality are 'antic­ipations of perception', of relation are 'analogies of experience', and of modal­ity are 'postulates of empirical thought in general'.[45] As we saw in III.3, Kant di­vides these four types of principles into two basic groups: math­emat­i­cal principles are those 'involved in the a priori determination of appear­ances ac­cording to the categories of quantity and quality', and dynamical prin­ciples are those correlated in a similar fashion to relation and modality [Kt1:200-1; see Figure III.4]. The former deal with the synthesis of various homogeneous aspects of an object and can be known with 'intuitive cer­tainty', while the latter deal with the synthesis of heterogeneous aspects and 'are capable only of a merely discursive certainty.'[46]

 

      A detailed account of the nature and role of each of the twelve principles which can be derived from the basic four is unnecessary here, since our pri­mary concern in this study is not with Kant's specific arguments [see I.1]. It will suffice instead merely to state each of the main synthetic a priori propo­sitions which Kant believes he has shown to be necessarily constitutive of all empirical objects. In the order of the categories, these principles are:

 

(1)  Axioms: 'All intuitions are extensive magnitudes' [Kt1:202].

 

(2)       Anticipations: 'In all appearances, the real that is an object of sensation has intensive magnitude, that is, a degree.'[47]

 

(3)  Analogies: 'Experience is possible only through the representation of a necessary connection of perceptions' [Kt1:218].

(a) Substance: 'In all change of appearances substance is permanent' [224].

(b) Causality: 'All alterations take place in conformity with the law of the connection of cause and effect' [232].

(c) Reciprocity: 'All substances, in so far as they can be perceiv­ed to coexist in space, are in thoroughgoing reciprocity' [256].

 

(4)  Postulates: (No general principle specified).

(a) Possibility: 'That which agrees with the formal conditions of experience ... is possible' [265].

(b) Actuality: 'That which is bound up with the material conditions of experi­ence ... is actual' [266].

(c)  Necessity: 'That which in its connection with the actual is determined in accordance with universal conditions of experience, is ... necessary' [266].

 

Kant omits any mention of the three derivative principles for the axioms and anticipations, as well as the general principle for the postulates, though Paton suggests these gaps can be filled easily enough [P2:2.64-5; but cf. M3:76-7]. In any case, Kant's neglect is not detrimental to the unity of the system it­self, since the function of step eight is clear whether or not its own architec­tonic structure as a 12CR is fully described.

 

      The key element supplied by the principles is the determination of an outer context into which the inner representation of the object as schematized (step seven) can be placed. Just as the form of time was reintroduced in step seven, so also the form of space is reintroduced here in step eight, so that at this point 'intuitions ... are in all cases outer intuitions'.[48] Establishing that, if the object is to be empirically knowable, it must be represented in terms of the formal conditions of quantity (extensive magnitude) and quality (intensive magnitude), and that it must stand in a possible, actual, and necessary relation to the subject, is, no doubt, an indispensable part of this task; but outweigh­ing all of these is the task of establishing that the object must be represented as a permanent substance which is both cause and effect in a reciprocally interdependent nexus of substances. It is for this reason that the analogies, whose purpose is to 'declare that all appearances lie, and must lie, in one nature' [Kt1:263], occupy well over half of the space Kant devotes to the proof of the principles.

 

      Taken together, the four principles provide 'the ground of experi­ence itself, and therefore precede it a priori' [Kt1:241]; for their application requires us to assume that our representations have a certain 'relation to an [empirical] object', through which they 'acquire objective meaning' [242]. As such, this eighth step provides the transcendental foundation for all scientific, empirical investigation (i.e., empirical investigation which aims at knowledge): 'We can extract clear concepts of [the principles] from experience, only because we have put them into experience, and because experience is thus itself brought about only by their means.'[49] This formal function (+) of the empirical perspective (-+) of systemt can be summarized accordingly:

 

 

      Kant's final task here in the third stage of his argument is to clarify the sense in which our time-schematized principles are actually employed in the production of empirical knowledge [cf. B20:152]. The synthesis of an ob­ject's inner determination in time (-) via schematism, and its outer determina­tion in space (+) via application of the prin­ciples, constitutes 'an empirical judg­ment' (x) [Kt1:246]-i.e., an item of empirical knowledge. (Since this is Kant's system of theoretical perspectives, he sometimes refers to this as 'theo­retical knowledge' [e.g., Kt7:195], a term we can treat as synonymous with 'empirical knowledge'.) The ninth condition of knowing is that such knowledge (x) arises only when an empirical object actually conforms to a person's determin­ate judgment (-+) that it is empirically real. This step can therefore be summarized quite simply as:

 

 

However, Kant is often less than clear about how this function actually oper­ates. He suggests at one point, for instance, that 'judgment is a peculiar tal­ent which can be practised only, and cannot be taught', and that 'the one great benefit of examples' is that they sharpen the judgment [172-3]. Fortunately, he does occasionally offer a more precise explanation of his intended meaning.

 

      Kant defines judgment as 'the faculty ... of distinguishing whether some­thing does or does not stand under a given rule' [Kt1:171]. From the empiri­cal perspective, all the judgments which result can be called 'rules' [304]; even the principles themselves are rules insofar as they are manifested in real judgments [Kt2:305]. But in its transcendental use as one of the twelve steps in systemt, 'judgment' refers to the act of using the principles to determine an objectively valid relation between two representations: Kant gives the exam­ple of combining the representations 'body' and 'heavy' in the judgment 'The body is heavy'. The word 'is' in such a proposition expresses the primary role of judgment, which is to bring 'given items of knowledge ... to the objective unity of apperception', and thus 'to distinguish the objective unity of [such] representations from the subjective' [Kt1:141-2]. This means the objects of knowledge are no longer regarded as being merely in the subject, as they were in the first two stages, but are now acknowledged also to have an independent reality of their own; for their representa­tions are 'combined in the object, no matter what the state of the subject may be'.[50]

 

      But this claim on behalf of judgment raises a problem which is not easi­ly solved: If representations exist only in the subject, and if the object (i.e., the thing) cannot be known it itself, then how can we know that two repre­sen­tations are actually united in the thing represented, or indeed, that they would always be so united for any subject? In hopes of reaching a convincing answer to this question here at the end of the third stage of his synthetic progression, Kant takes a new look at the first stage in light of what has now been revealed in the second and third. It is here that he introduces his now famous (or infamous) distinction between noumena and phenomena.

 

      The terms 'noumenon' and 'phenomenon' have been discussed at length in VI.3, where they were clearly differentiated from terms such as 'thing in itself' and 'appearance', which, as we saw in VII.2.A, relate mainly to the first stage of systemt. Kant's official introduction of the new 'object-terms' here in the third stage is intended to summarize the theory as it now stands by point­ing up the difference in the perspective from which the object is viewed in the first and third stages, and in so doing to prepare the way for the fourth and fi­nal stage of his theory. The clarification achieved by the new terms can be evinced by revising the foregoing account of steps eight and nine.

 

      The phenomenon, as we saw in VI.3, is the empirical object viewed from the empirical perspective (-+). We can now see that the phenomenon first comes to be determined as such through the formal, determining function of the principles (+) in step eight. We can therefore revise our summary of the eighth condition accordingly:

 

 

This modification stresses that the object, which is determined to be an object by the principles (and the objective reality of which is to be determined through judgment in step nine), is not a thing in itself, but only a phe­nome­non represented in outer sense as an object in space. A thorough inves­ti­gation of the function of the principles (especially that of substance, in which all the others are rooted) would be necessary before we could fully un­derstand just how Kant thinks they can fulfill their task of determining an ap­pearance to be a phenomenon [Kt2:304]. But such a detailed treatment would be an un­neces­sary digression from our general line of inquiry. Instead, as­suming that they do, in fact, succeed in their function, we will focus our at­tention on the main function of the phenomenon-noumenon distinction, which is to shed light on the ninth condition and its relation to the fourth stage.

 

      As we concluded towards the end of VI.3, our judgment of a thing to be 'objectively real' from the empirical perspective depends on the ex­tent to which we can validly represent it as a 'negative noumenon'. Just what this 'mark of independence' is, however, is not altogether clear. It has to do with abstracting the conditions (and the resulting material) of sensibility from the object just enough to judge whether it can be conceived to exist independently of the subject. Accordingly, in the process of realizing the goal of the empir­i­cal perspective (-+) in stage three, the synthetic (x) function of judgment also determines how the object, as a real item of empirical knowledge, will be presented to the fourth and final stage-i.e., its noumenal character is at this point judged to be either positive or negative. The former will give rise to a speculative perspective, and the latter to a hypothetical perspective, in stage four [see IV.3]. This revised form of the ninth step can be summarized as:

 

 

As such, judgment prepares the way for the fourth stage, where the object is re­leased from sensibility and treated, so far as is possible, as a noumenon. That is why Kant begins the Dialectic by reminding us 'truth or illusion is not in the object, in so far as it is intuited, but in the judgment about it' [Kt1:350].

 

      One of the main uses to which Kant puts his distinction between phe­nom­ena and noumena is to emphasize that the understanding can produce valid empirical knowledge only when it is applied within the phe­nomenal realm, the realm of 'possible experience' [see note VII.37]. The im­portance of this maxim for systemt can scarcely be overemphasized, since the 'possibility of experience' not only makes possible our ordinary a posteriori knowledge of the world, but also 'gives objective reality [in the transcendental sense-see note VII.3] to all our a priori modes of knowledge.'[51] This unify­ing function of experience was depicted in IV.4 by placing it in the center of the map of Kant's four main perspectives in Figure IV.2. For experi­ence itself (i.e., as immediate) is not one of the twelve conditions of know­ing; it is, as it were, the 'hub' around which all the formal conditions must revolve in order for us to know an object. We have seen that sensibility views the object transcen­den­tally as it appears (stage one), and un­derstanding views it as it is, either logically, in abstraction from sensibility (stage two), or empirically, in syn­thetic union with sensibility (stage three). Our only remaining task in inter­preting systemt, therefore, is to consider the fourth stage, in which Kant explains how reason views the object hypotheti­cally, as it may be.

 

  B. Inferential Reason (++)

 

      Both the subject-matter and the organization of Kant's Dialectic in Kt1 [349-732] tend to obscure rather than illuminate the nature of its role in pre­senting the fourth stage of systemt. For, although it occu­pies far more space than the sections which describe each of the other three stages [see Table VI.1], the Dialectic concentrates comparatively less than the others on ex­pounding the relevant steps in the synthetic progression of the formal condi­tions of knowing. Instead, that which is only a secondary task in the other sections-namely, the specification and discussion of various philosophical implications of the revolution­ary aspects of the theory-becomes Kant's pri­mary task in the Dialectic. This, of course, is a change Kant has to make in order to prove the inadequacy of traditional rational metaphysics. But as a result many commentators ignore the fact that the theory he affirms in place of traditional metaphysics is an integral part of systemt [but see E3:116 and IV.3]. They tend to detach the Dialectic from the rest of Kt1 as if it could do just as well standing on its own as a self-sufficient set of arguments. But, be­cause our interest here in Chapter VII is limited to the essential content of that portion of the Doctrine of Elements which evinces the architectonic form of Kant's theory of knowing, we shall ignore the main part of the Dialectic, Book II [Kt1:396-670], where Kant exposes and dispels the illusory 'dialecti­cal inferences' which uncritical human reason naturally tends to make;[52] we shall focus instead on Book I [349-96] and the Appendix [670-732], where Kant offers his own alternative to the former.

 

      The goal of reason in the fourth stage is to complete what remains in­complete in step nine-i.e., to determine, as far as is possible, the noumenal basis of phenomenal objects. Given the fact that stage three judges all ob­jects of knowledge to have some sort of noumenal character (i.e., either nega­tive or positive), the fourth stage is not just an optional extra, added to fulfill the re­quirements of the architectonic, or to pose some philosophically inter­esting points about the nature of human reason; on the contrary, it is the final set of conditions without which our empirical knowledge would risk losing its ob­jective reality. The function which fulfills this task Kant calls 'infer­ence'; and, as we might expect, it is itself the result of a three step pro­cess. Thus, here in the fourth stage we become conscious of existence 'mediately through inferences which connect something with perception' [Kt1:629]. (Con­cluding systemt with inferential reason is rather appropriate, since the German word for inference (Schluss) also means 'conclusion' or 'end' [but see note VII.11].) As Kant explains in Kt14:58(92), 'a distinct concept is possible only by means of a judgment, a complete concept only by means of an infer­ence.'

 

      The problem inherited by the fourth stage from the third is that 'no expe­rience [i.e., object of empirical knowledge] is unconditioned' [Kt1:383]; yet the very judgment which yields empirical knowledge de­pends on our ability to determine an object's participation in some sort of unconditioned (noumenal) reality. So the first task of reason in the fourth stage is to 'prescribe to the understanding [regarded as judgment (step nine)] its direction towards a certain unity ... in such a manner as to unite all the acts of the understanding, in re­spect of every [empiri­cal] object, into an absolute whole' [383]. The abstract representation involved in establishing the unifying 'direction' of rea­son in its relation to phenomenal objects is what Kant calls 'a schema' of reason [698]. Just as the schema of understanding (step seven) re­quires concepts (step six) to be applied only in the field of expe­rience, so also the schema of reason (step ten) requires ideas (see step eleven) to perform their unifying function only 'from reason's world-perspective' [726]-i.e., only in relation to real objects of judgment (step nine).

 

      The object as determined by the schematism of reason here in the tenth step acts as the material element (-) for the fourth stage (++); Kant calls it 'the unconditioned'.[53] The object as unconditioned is that 'to which reason leads in its inferences from experience, and in accordance with which it esti­mates and gauges the degree of its empirical employment, but which is never itself a member of the empirical synthesis' [Kt1:367-8]. The tenth condition of knowing can therefore be summarized as follows:

 

 

Kant asserts that this activity of finding 'for the conditioned knowledge obtained through the understanding the unconditioned whereby its unity is brought to completion' is 'a principle of pure reason [which] is obviously synthetic; the condition is analytically related to some condition but not to the unconditioned.'[54]

 

      Positing the object as unconditioned in step ten does not in itself estab­lish the ultimate unity of all empirical knowledge; for the unconditioned object 'can never come before us, since it cannot be given through any possible experience.'[55] As a result, reason must exert its unifying influence on the unconditioned in much the same way as the fa­culty of understanding does (by means of the categories) on the percep­tions of the second stage and as the fac­ulty of judgment does (by means of the principles) in the third stage [378,383,692-3]. This means the schematism of reason must construct its object 'in accordance with the conditions of the greatest possible unity of reason' [698]. Such unity is 'not the unity of a possible experience ..., which is that of under­standing' [363]; rather it is 'an a priori [read: 'analytic'-cf. 358 and IV.3] unity by means of concepts', imposed directly on the under­standing [359; cf. 392]. Reason in this step establishes itself as 'the faculty of princi­ples' [356]: 'Knowledge from principles is, therefore, that knowledge alone in which I apprehend the particular [an a posterio­ri fact] in the universal through [analytically related] concepts' [357].

 

      The 'pure concepts of reason' which produce this rational unity when applied to the unconditioned object are called 'transcendental ideas' [Kt1:378]. Kant explains that 'the idea is posited only as being the perspective from which alone [the unity of reason] ... can be further extended' [709]; it is the concept of an object which 'transcends the possibility of experience' [377]-i.e., 'a necessary concept of reason to which no corresponding object can be given in sense-experience' [383]. 'Just as the understanding unifies the mani­fold in the object by means of concepts, so also reason unifies the manifold of concepts by means of ideas ...'.[56] These 'concepts derived from pure rea­son', Kant insists, 'cannot be obtained by mere [i.e., empirical] reflection without inference.'[57] Hence 'it is a necessary maxim of reason to proceed al­ways in accordance with such ideas' [699]; for this procedure of using ideas to infer the systematic unity of reason [394] provides the form (+) of stage four (++), which, when applied to the object as unconditioned, brings us one step closer to the ultimate unification of empirical knowledge.[58] This eleventh step can be summarized as:

 

      Each member of Kant's favorite trio of metaphysical concepts (God, free­dom and immortality [see X.1-2]) is represented by one of the three primary ideas of reason: the Paralogism of Pure Reason [Kt1:A341-A405,399-432] assess­es the idea of the soul (including immortality); the An­tinomy of Pure Reason [432-595] assesses the idea of the world (includ­ing freedom); and the Ideal of Pure Reason [595-670] assesses the idea of God.[59] Each of these has a legitimate employment, but tends to be used to draw 'pseudo-rational' con­clusions [397]. As mentioned above, we shall omit from this chapter any de­tailed discussion of these ideas. The three chapters in Part Four correspond, in reverse order, to these three ideas. So it will suffice at this point to note that they can be used to construct either a legitimate or an illegitimate version of the twelfth and final condition of knowing. Both versions are concerned with re­alizing the object which is represented in an idea by actually reasoning as to its validity. The difference between them arises 'not [from] the idea in itself, but [from] its use only, [which] can be either transcendent or imma­nent' [671; cf. 697-8].

 

      The transcendent, or 'constitutive' use of the inferred ideas is employed by those who adopt the speculative perspective, and inevitably leads to meta­physical illusion [Kt1:352-4,537; see IV.3]. Speculative metaphysi­cians mis­takenly take the judgment of the negatively noumenal character of the ob­ject in step nine to be a positively noumenal judg­ment about the object as it is in itself. As a result, they naturally as­sume 'that there is an actual object corre­sponding to the idea' [510]. This 'objective employment of the pure concepts of reason is ... always transcendent' [383]; for it attempts to establish rational principles 'which profess to pass beyond' the 'limits of possible expe­rience' [Kt1:352]. The goal of such 'speculative' reasoning is 'the ascribing of objec­tive reality to an idea that [properly] serves merely as a rule' [537]. Establish­ing such objective reality in regard to a transcendent object would yield synthetic a priori knowledge of reality (i.e., of the positive noumenon) [see e.g., 386]. Such a 'representation of an indi­vidual existence as adequate to an idea' can be called 'an ideal' [Kt7:232]. Thus we can summarize this illu­sory version of step twelve as:

 

   

 

      Kant leaves no doubt that this use of the ideas invariably ends in failure: 'The cause of failure we must seek [not in the unconditioned object, but] in our idea itself. For so long as we obstinately persist in assuming that there is an actual object corresponding to the idea, the problem [of establishing objec­tive knowledge of the object] ... allows of no solution' [Kt1:510]. At the root of the problem raised by the speculative ideas lies a mistaken, transcendent use of the categories:

 

once we recognize these categories and their origin, merely as the form of thinking, we shall be convinced that they do not by themselves provide gen­uine knowledge, and that, when supplied with intuitions, they do not give us any supersensible theoretical knowledge, though they can be used for practi­cal ideas without stepping outside their proper sphere. [K2:11.38-9(Z1:142, alt.)]

 

      The solution to this problem, then, can be found only by adopting a hy­pothetical perspective, according to which the ideas are employed immanently in inference, as regulative principles [see IV.3 and V.4]. Kant explains in Kt10:86-7(94) that 'speculative cognitions ... [are] those from which no rules of behavior can be derived ... [They] are always theoretical, but conversely, not every cognition is speculative; viewed from another standpoint, it can at the same time be practical.' The hypothetical perspective, which, as we have seen, is the perspective in systemt which gives rise to the practical standpoint of systemp, requires that the unconditioned object represented in the form of an idea be 'viewed as if it were a real [object]' [Kt1:712; cf. 699] for the pur­poses of em­pirical inquiry and systematic unity. But this use of an idea is 'valid only in respect of our rational perspective on the world':[60] 'For the regulative law of systematic unity prescribes that we should study nature as if systematic and purposive unity, combined with the greatest possible mani­foldness, were everywhere to be met with, in infinitum' [728]. This activity differs from the speculative reifi­cation of the object inasmuch as it is per­formed only hypo­thetically, without assuming that objectively valid knowl­edge of transcendent reality can be established in this way.[61] All we can legitimately do is to 'ascribe [to an idea], from the [hypothetical] perspective of this unity, such properties as are analogous to the concepts employed by the understanding in the empirical perspective' [705-6; cf. D4:264-5]. (Exam­ples of how this might be done will be explored in Pq20 [cf. Ch. X].)

 

      This alternative perspective for step twelve accepts that an idea can be properly applied only when the object in step nine is judged to have a nega­tively noumenal character. For 'the idea instructs us only in regard to a cer­tain unattainable completeness, and so serves rather to limit the understanding than to extend it to new objects' [Kt1:620]. Since the idea is now confined within such negatively noumenal limits, its validity 'can be proved through experience' [830] by demonstrating in hypothetical inferences how 'an actual case' [387] (a posteriori) is subsumed (analytically) under the idea in question, even though 'the object of [the idea] can never be given empirically' [390]. Far from having a mere '"donkey's carrot" validity' [M2:248], Kant argues: 'The practical idea is ... always in the highest degree fruitful, and from the per­spective of our actual activities is indispensably necessary' [Kt1:385; s.a. 544-5]. The goal of hypothetical reasoning, as the synthetic step (x) in the fourth stage (++), is therefore to establish analytic a posteriori belief [cf. IV.3]. This legitimate version of the twelfth condition, then, is:

 

 

 

Once philosophers accept that each of their ideas must be regarded 'as an idea only and not as an entity', they will be able to replace the old (supposedly synthetic a priori) 'Logic of Illusion' with a new (analytic a posteriori) 'Logic of Regulative Principles' [R11:86]. For reason's entire pure en­deavor has 'its source exclusively in the practical interests of reason' [Kt1:825].

 

      Imposing the unity established by hypothetical reasoning in the fourth stage onto the empirical objects of the third stage secures the objective reality of all empirical knowledge. For in this final stage, we see how 'pure reason combines all its epistemological perspectives into a system' [Kt1:394]. Although the extent of an object's partici­pation in the thing in itself is still unknown, we have at this point established the conditions necessary for em­pirical knowledge to arise from the theoretical standpoint. For the determina­tion of the object has come full circle: that which began merely as a tran­scen­dental object is now treated as if it were subsumed under its unconditioned cause. The idea of the systematic whole, of which each object of knowledge is a condi­tioned part, provides the necessary context for objective theoreti­cal knowledge-a context which could not be provided by the unknowable thing in itself. The twelfth condition therefore concludes not only the fourth stage, but the entire system of theoretical perspectives. However, our interpretive task is not quite finished. Lest we lose sight of our main purpose in sift­ing through the many details of systemt, we must now summarize our findings and determine the extent to which they accord with the formal model developed in III.3.

 

4. An Analytic Summary and a Synthetic Model

 

      By asserting that all experience is dependent transcendentally on certain forms of knowing, even though knowing is itself dependent empirically on the reality of the things known [cf. Kt1:1], Kant maintained in systemt the a priori centrality of the human mind while at the same time upholding the per­spective of ordinary human beings. The foregoing interpretation of this system has followed the synthetic method of Kt1. But it may be helpful, now that the conditions which determine our knowledge have been fully explicated, to summarize systemt according to the analytic method, using the four reflec­tive perspectives discussed in IV.3 as an analytic framework. Listing sum­maries of each of the twelve steps in reverse order, as in the following four paragraphs, provides a concise, 'tabular' analysis of the elements of Kant's system. (In a 'tabular' method, Kant notes in Kt10:149(149), 'an already finished doctrinal edifice is presented in its entire context.') This will enable us to di­a­gram the relationships between each step [see Figure VII.4], and in so doing to reveal 'the unity of the manifold modes of knowl­edge under one idea'-viz., that of 'the form of a whole' [Kt1:860; cf. 673].

 

      Stage four. The hypothetical perspective (++) is concerned with viewing an experience (a posteriori) as if it is contained (analytical­ly) in a regu­la­tive idea of an unconditioned object. Practical belief (x), the legitimate goal of reason's unifying influence on expe­rience, arises as a result of such hypo­theti­cal reasoning. (Speculative reason­ing, the illegitimate alternative to                  

                    STAGE          STAGE          STAGE          STAGE

                   ONE (--)       TWO (+-)    THREE (-+)    FOUR (++)

 

Figure VII.4: Schematic Analysis* of Systemt

hy­pothe­t­ical reasoning, is believed by speculative metaphysicians to yield syn­thetic a priori knowledge through a direct apprehension of the uncondi­tioned object, by means of a constitutive idea.) The idea (+), which is the formal aspect of infer­ring reason, provides a way of seeing the empirical world as a rational unified whole; such unity is inferred to exist on the basis of an idea of the whole. The material aspect (-) is the object as unconditioned (and thus, as such, unknown), which itself arises out of the application of the schema­tism of reason to items of empirical knowledge. In this way reason guides and limits the understanding (stage two) in its formation of judgments (stage three).

 

      Stage three. The empirical perspective (-+) is concerned with the real objects (synthetic) presented to us in experience (a posteriori). Empirical knowledge of an object (x) is attained by judging its nega­tively noumenal (i.e., independently permanent) character. (Speculative reasoning requires the ob­ject to be viewed here as a positive noumenon.) Such a judgment is 'ob­jec­tive­ly valid' in virtue of its conformity to the principles of pure under­stand­ing, through which the object first comes to be determined as a phe­nomenon (+) in space and time. The principles are applicable only to objects which have been schematized-i.e., only to those categorized appearances which have been synthesized according to the imagination's inner determina­tion of time. The schematized object (-) can therefore be analyzed into its conceptual (stage two) and its intuitive (stage one) components.

 

      Stage two. The logical perspective (+-) is concerned with the concep­tual form (analytic) of an object as abstracted completely from experience (a priori). Self-conscious thought (x) arises out of the imposition of the bare 'I' (pure apperception) onto the various concepts a person forms on the basis of his or her experience. These concepts (+) are formed through categorial con­ception, in which pure categories are applied to conscious perceptions (-). The latter, in turn, are produced as a result of the imagination's transcendental synthesis of the sensations presented to it by sensibility (stage one).

 

     Stage one. The transcendental perspective (--) concerns that which must hold true of an intuited object (synthetic) before it can be processed (a priori) by the synthetic functions of the understanding in stages two and three. The object at this point is therefore merely a sensation (x), which is to say, it is a manifold of appearances (+) received by the senses. An appearance is an object represented to the inner and/or outer sense through the function of pure spatio-temporal intuition. If it is an appearance of something real, it will be related in this way to the transcendental object. The transcendental object (-) is the general and totally undetermined original representation of the thing in itself. And the thing in itself (0) is the unrepresented and thus unknowable form of an object of experience, considered apart from the conditions which enable us to experience it. We can have no knowledge of it, because there is no perspec­tive from which we can view it as such.

 

      Having now analytically summarized and diagrammed the interpreta­tion of systemt put forward in VII.2-3, we can assess the extent to which it corre­sponds to the ideal, architectonic model constructed in III.3. The legitimacy of distinguishing between the four main stages in systemt, and of relating them according to the 2LAR pattern, seems to me to be beyond doubt. The account of their relationships in III.4, IV.3 and VII.1 has, I hope, demon­strated this with sufficient force. Since the first two terms in the compo­nents appended to each of the summaries of the twelve steps refer solely to one of these stages, any doubt about my interpretation or about the appropri­ateness of the component attached to any particular condition must arise out of the way I have correlated the steps within each stage-i.e., out of the way the third term in each component is assigned. Now I freely admit there is plenty of room for debate concerning the way I have applied the matter-form-synthesis pat­tern [see III.4] to the details of Kant's text. The scarcity of tex­tual evidence for the third step in some of the stages (especially stage one) could be used to argue that there should really be only two steps in each stage, yielding a total of eight (though this would create quite a problem as to how the synthetic (threefold) character of Kant's method in Kt1 should be un­derstood). Alterna­tively, one could argue that 'form' should in each case pre­cede 'matter', or that 'synthesis' should precede both (in which case the com­ponents would be correlated in different ways, but the whole would exhibit the same 4x3=12 pat­tern). Or again, one could question whether such a clear-cut, 'sausage-factory' approach to systemt does not misrepresent Kant's inten­tions: perhaps he in­ten­tionally presented the 'elements' of each stage as blur­ring into each other, without ever wanting to suggest any clear distinctions (though this would seem to contradict his emphasis on architectonic neat­ness).

 

      The most such objections would require is relatively minor rear­range­ments in the interpretation of systemt as I have presented it. One might remain un­convinced, for example, by my arguments for associating the tran­scendental object with sensibility rather than understanding, or for associating the imag­ination with the latter instead of the former. To all such suggested revisions I would be open, provided the proponent of such a change is able to collect suf­ficient textual evidence for the alternative interpretation and is able to explain how the texts I have used can be adapted to fit the alternative inter­pretation.

 

      To simplify the task of checking whether or not each element in my in­terpretation is accurately described by the logical component assigned to it, I will review briefly what the terms in each component represent. The first term in each three-term component signifies that the element in question functions in a receptive (-) or a spontaneous (+) stage: for this purpose, the stages directly involving the elements of sensibility are receptive, while those which do not are spontaneous. The second term in each component signifies that the element in question functions in an abstract (-) or concrete (+) stage: the perspectives concerned with isolating the fundamental constituents of empirical knowledge contain abstract elements, whereas those requiring these constituents to be combined in empirical knowledge contain concrete ele­ments. The third term in each component represents the material (-), formal (+) or synthetic (x) function of the condition within its particular stage: the material condition determines the bare necessities for an object to be viewed from a given perspective; the formal condition determines the limits which define each perspective; and the synthetic condition fulfills the purpose of its per­spective by uniting the material and formal conditions.

 

      The schematic representation of systemt in Figure VII.4 might give the impression of being rather too rigid to represent accurately Kant's intentions. For this reason we can supplement that analytic flowchart with a synthetic model, using 'the circle of experience' [Kt1:8; cf. I.3 and Figure III.6] to re­flect the fact that in the text of Kt1 the twelve steps tend to flow into each other in one continuous motion. Representing the function of each step by a curved arrow and labelling the inside of each curve with its corresponding roman numeral gives rise to the following model:

 

 

Figure VII.5: Kant's Circle of Experience

 

The four perspectives now correspond to the four quadrants delineated by the axes of a cross, rather than to their end points, as in Figure IV.2. The outside of the diagram is labelled with Kant's terms for the state of the determination of the object between each func­tion.[62]

 

      The first and last points of the arc in Figure VII.5 are sepa­rated by a gap (thus converting the circle to one cycle of a spiral) for several reasons. First, this gap can represent Kant's contention that the ori­ginal presupposi­tion of the thing in itself is not definitely confirmed to be an empirically known ob­ject through hypothetical reasoning, but only to be a regulative idea of what it might be if it could be repre­sented in itself as an object. As such, the gap suggests that, although systemt is theoretically complete (i.e., it has suc­ceed­ed in describing, from the theoretical standpoint, the nature and possi­bil­ity of empirical knowledge), it is teleologically incomplete (i.e., it fails to provide an adequate basis for the reality of the objects to which its ideas refer). Thus the gap shows that systemt points beyond itself to some other stand­point, from which ideas of 'totality' (especially Kant's three favorite metaphysical ideas [see X.1-2]) can be more firmly grounded. In addition, this gap provides a way of representing the differences between the hypothetical and speculative perspectives. The latter could be represented by a slightly dif­ferent kind of arc, which bends outward (towards 'ultimate reality') rather than in­ward (towards immediate experience [cf. Figure IV.2 and IX.2]). Such a spiral would accord well with Kant's own metaphorical description of speculative reasoning as an at­tempt to rise 'to dizzy heights where [reason] finds itself entirely cut off from all possible action in conformity with experience' [Kt1:717]. Whereas from the speculative perspective knowledge of reality is regarded as ever tran­scend­ing our experience of the thing in itself, from the hypotheti­cal perspec­tive the thing in itself is regarded as transcendent, and knowledge of reality is regarded as legitimate only when it is directed towards experience.

 

      These two ways of positioning the gap in Figure VII.5 can also help to clar­i­fy a possible ambiguity in labelling Kant's System 'Copernican': Copernicus' astronomy takes humanity out of the center of the universe, yet Kant's emphasis on the subject seems to do just the opposite. However, Kant gives this impression only because of his bad habit of occasionally exaggerat­ing various claims. For his theory of the subject is, in fact, intended to con­vey the notion that it is the subject's representational determinations which sepa­rate the thing in itself from the objects of our knowledge. And this role, far from contradicting Copernicus' principles, establishes their philosophical equiva­lents as valid [see III.1]. For just as the sun does not revolve around the earth, but vise versa, so also the subject does not look directly out upon the thing in itself revolving around it (as philosophers formerly assumed), but looks only inward, towards the 'earth' of experience, while the transcendent 'grav­itational fire' of the thing in itself mysteriously holds everything together.

 

      Numerous ways of interrelating various combinations of steps could be discussed at this point (indeed, almost ad infinitum!)-e.g., by connecting the twelve points in Figure VII.5 with three squares or with four triangles [see Pq18:6.3-4]. (The formal similarities revealed in the former case [see e.g., note VII.55] can also be seen in Figure VII.4 by reading down each column rather than following the arrows across.) One such possibility would be to relate the four main categories to the four main stages in systemt [cf. Figures III.4 and VII.3]. Thus quan­tity might have some special association with sensibility, quality with under­standing, relation with judgment, and modality with reason.[63] Similarly, the twelvefold progression of systemt could be correlated with the twelvefold structure of the categories, or likewise of the principles, both of which can be regarded as representing the twelve points of the diagram in Figure VII.5, as viewed from the perspective of a single point. In other words, each category could be depicted as arising, in turn, out of the influence of one of the twelve elements on the fifth element. But to elaborate the implications of such pro­pos­als in sufficient detail would be to stray too far from our overall goal.

 

      The theory put forward and defended in this chapter, especially as repre­sented graphically in Figure VII.5, relates to the preparatory consider­ations dealt with in Parts One and Two in several ways. First, the four perspectives examined in Chapter IV, especially as represented graphically in Figure IV.2, delineate the basic perspectival structure of systemt. Likewise, the special object-terms examined in Chapter VI, especially as represented graphically in Figure VI.1, turned out to constitute a cross-section of the whole system: we can now see that these terms relate only to stages one and three (i.e., to what is different about an object if it is regarded on the one hand only as intuited, or on the other hand as intuited and conceptualized, but without considering conceptual understanding (stage two) or inferential reason (stage four) on their own). Finally, systemt has been shown to contain a step-by-step argument which corresponds with a surprising degree of accuracy to the architectonic structure of formal logic, especially as represented graphically in Figure III.6. These correlations are sufficient to establish the principle of perspective [Chapter II] and its representation in models [I.3] as valuable tools, not only for the interpretation of Kant's Critical philosophy, but also for philosophical think­ing in general. Nevertheless, in order to appreciate more fully the extent of their usefulness, and thus of their applicability to the three ideas of reason [see Part Four], we must also apply them to the other two systems which, together with systemt, establish the Transcendental elements of Kant's System of Perspectives.

 


 [1] Kant's use of the term 'elements' here implies an analogy between his philoso­phy   and the geometry developed in Euclid's Elements. (Lambert suggests this kind of an analogy in his 1766 letter to Kant [K2:10.63-4(Z1:52-3].) Moreover, just as the Elements section in Kt1 begins with an exposition on how to view Euclid's Elements in its proper perspective, so also it continues by doing the same with three other classical traditions. The Analytic of Concepts develops a doctrine of categories which enables us to view Aristotle's classic book, Categories, in its proper perspective. The Analytic of Principles develops a doctrine of principles which enables us to view Newton's classic book, Principia, in its proper perspec­tive. And the Dialectic develops a doctrine of ideas which enables us to view the corresponding classical theory of Plato (as expressed in his Dialogues) in its proper perspective. The first Critique is an attempt to show that each of these clas­sical theories has a proper role to play in a complete system of theoretical philos­ophy, but that the validity of each can be established only by limiting each to a specific perspective [see XI.2]. Without a clear recognition of Kant's Critical attitude towards his tradition (an attitude which always includes both nega­tive and positive aspects), the significance of this modern classic cannot be fully under­stood.

 

 [2] In B27:45-6 Buchdahl uses arrows in a similar way to summarize the 'movement'   of steps in Kant's argument [39]. He stresses that it is 'of the utmost importance to present Kant's arguments in such summary fa­shion, to avoid getting lost in the usual style of endless distinctions heaped upon distinctions [54].

 

 [3] It is important to note that, from the transcendental perspective, Kant considers  something to be 'objective' if it is grounded a priori in the subject, and 'subjec­tive' if it is grounded a posteriori in the object (i.e., in the world of appear­ances) [see Kt1:139-40]. Only from the empirical perspective does 'objective' re­fer to a grounding in outer objects and 'subjective' to inner states. Kuehn makes a similar point in K14:158, and goes a step further: 'Something that is subjective in a tran­scendental sense ... may very well be objective in an empirical sense (e.g., space and time). Moreover, "subjective" and "objective" have different meanings, de­pending on whether they are used in theoretical or practical contexts.' See also C6:154n.

 

 [4] Kt1:91; Kt2:304; cf. E3:111 and P2:1.77-80,548. The empirical ele­ments Kant does introduce in connection with many of his transcendental considerations must therefore be regarded as simultaneous elements into which one and the same expe­rience could be analyzed. That is, from the empirical perspective intuitions (for example) do not necessarily come before empirical concepts; on the contrary, they could just as well arise together.

 

 [5] As pointed out in III.4, these conditions are formal from the Perspective of tran­scendental logic, even though they combine to make up the content of Kant's System when viewed from the Perspective of general logic.

 

 [6] E5:40; B6:35. Critics such as Bennett, who either reinterpret Kant's theories as 'analytic but untrivial' [B17:83], or else reject them as trivial or false, tend to be unaware that Kant himself would have regarded large portions of systemt as ana­lytic (in method) when viewed from the empirical perspective. Since Bennett starts from the presupposition that every question must be analyzed from the em­pirical perspective, in terms of 'abilities' [71], it is not surprising that he finds only falsities and analytic truths in Kant's system.

 

 [7]   The word 'aesthetic' comes from the Greek 'asqhtikV', meaning 'of or for sense-perception' [L4:1.42].

 

 [8] Kant groups this section together with the Analytic of Principles under the first division of the Transcendental Logic, which he entitles the Transcendental Analytic [see Table III.1], because both sections deal with 'the principles without which no object can be thought' [Kt1:87]. This unfortunately obscures its equally important relationship to each of the other stages. Indeed, as should become clear in VII.2-3, the first and second stages and the third and fourth stages are in some respects more closely related than the second and third. Kant acknowledges this in Kt1:169 by explaining that the Aesthetic and the Analytic of Concepts deal with 'elementary concepts' while the Analytic of Principles and the Dialectic deal with 'their employment', and that his 'division by numbered paragraphs' can therefore be discontinued at the end of the Analytic of Concepts.

 

 [9] See II.4, VI.1 and note IV.23. Another way of making clear the sense in which sensibility assumes the transcendental perspective while judgment (as we shall see) assumes the empirical is to note that in this use the terms relate primarily to the subject's perspective on the object, whereas the broad use [see II.4 and IV.2] refers to Kant's general emphasis on the subject (in which case all four stages are transcendental). In the Aesthetic Kant refers to objects as being ideal and 'in us', while in the Analytic of Principles he refers to these same objects as being real and 'outside us' [see VI.2]. The reason for this apparent discrepancy is that the former way of looking at objects is transcendental [see e.g., Kt1:45,61-2] and the latter, empiri­cal. Moreover, the titles of the four principles themselves clearly indicate their empirical orientation (referring, as they do, to intuition, perception, experience and empirical thought).

 

[10] Kt7i:476. This picture of judgment accords with Rotenstreich's account in R10:10   of 'the fundamental paradox of knowledge: by one and the same activity [viz., judgment] the distance between the subject [via understanding] and object [via sensibility] is both established and bridged.' Likewise, the distinction com­monly made between 'sense', 'meaning' and 'reference' is highly suggestive of Kant's distinction between the faculties of sensibility, understanding and judg­ment.

 

[11] The important role of inference in defining the fourth stage of systemt is un­fortu­nately obscured by the difficulty of translating 'Schluss' and related words consis­tently. For example, when 'Schluss' is translated as 'conclusion' [see e.g., Kt10: 114-36(120-39)], or 'Vernunftschluss' as 'syllogism' (admittedly legitimate ren­derings in themselves), the reader is left unaware (aside from occasional notes by translators) of the fact that both terms literally refer to the function of infer­ence. As a result, the parallel relationship between inference and its counterparts in the previous stages (viz., judgment, conception and intuition) can easily go unnoticed [e.g., Kt1:378]. For the sake of clarity, therefore, I shall henceforth al­ter the translation of Kant's use of such terms whenever appropriate.

 

[12] Kant does this, though not in an entirely clear way, in K2:10.471-2(Z1:125) and K2:11.300-1(Z1:182). A model of this 2LAR has already been given in Figure III.10; but the following discussion specifies the derivation of this division more precisely than in III.4.

 

[13] Kant's doctrine of the transcendental object was thoroughly examined in VI.2. The reasons for placing the transcendental object here in the first stage rather than in the second stage are discussed in Appendix VII.B.

 

[14] See Kt1:347. As Allison rightly says, 'unconceptualized representa­tions' are for      Kant the 'materials for knowledge' [A11:25; cf. K2:17.616-7]. Thus sensibil­ity, the home of such representations, is the material (--) stage in systemt [see note VII.23].

 

[15] E5:18,37. Walsh notes that intuition 'can be described as awareness of partic­u­lars only proleptically, since strictly it is not a species of acquaintance' [W9:15]. That is, an intuition provides such an awareness only when it comes under some concept. Thus, although Kant sometimes re­fers to space and time as 'concepts', his official view is that spatial and temporal relations 'lie entirely outside the con­cepts of understand­ing, strictly regarded' [Kt1:159]. For an excellent discussion of Kant's theory of intuition, see A7:68-72,75-92. The important point to re­member is that intuitions always convey singular representations immediately, whereas concepts convey common representations mediately [see e.g., Kt1:136n,298, 377; Kt10:91(96); Kt69:325].

 

[16] Kt1:323; s.a. 208 and Kt19:399; Kt69:266; cf. P2:1.112. Kant also regards cer­tain mathematical (especially geometrical) judgments as dependent on pure intuition [Kt1:16-7,A24,40-1,64-6,749-50]. Some problems concerning this assumption are discussed in Appendix VII.C.

 

[17] Kant explains: '"I", as thinking, am an object of inner sense, and am called "soul".   That which is an object of the outer senses is called "body"' [Kt1:400; s.a. 50,69]. Soul and body, then, are not two essen­tially separate realities, but two manifestations of one and the same human sensibility. (In Kt69:270 Kant makes a similar point about the 'twofold self, the I as subject and the I as object', which arises in the second stage; he stresses that this self is a unity, not 'a double per­sonality'.) When the perspectival character of Kant's theory is recognized, we can see that such statements do not support the traditional assumption that, as Walsh puts it [W9:192], Kant 'worked generally within Cartesian assumptions about the relations of mind and body.' On the contrary, Kant explicitly criticizes Descartes' assumptions in Kt1:A341-405.

 

[18] Kt1:182; s.a. Kt6:214 and Kt19:396-405. Some ambiguities relating to Kant's use of the term 'inner sense' are discussed in Appendix VII.D.

 

[19] Kt1:59. This, of course, applies only from the transcendental per­spective (stage one), in which case it implies that 'thinking in spatial [and temporal] terms ... is a purely human way of thinking, determined by the nature of human ex­peri­ence' [M6:136]. Kant points out that 'other thinking beings' might be able to in­tuit space (and time) in a way dif­ferent from the way humans do [Kt1:43]. To deny the subjective necessity of the inner forms of representation would be, for Kant, tan­tamount to claiming we can attain a wholly perspectiveless knowledge which somehow exists outside the boundaries of time and space (and the cate­gories). (Yet this would require a perspective from which we could view the whole space-time continuum at a single glance.) From the empirical perspective (stage three), outer appearances are distinct from us in the sense that they are objects which are out­side of our inner sense [cf. VI.2 and B20:51]. Similarly, although the intu­itions of time and space logically precede the appearance transcendentally, they are chrono­logically simultaneous with it empirically.

 

[20] Kt1:52. Thus, Kant's doctrine of pure spatio-temporal intuition, which re­gards space and time as 'the relations in which our sensa are given' [P2:1.103], re­vises the then popular notion of 'absolute space', so that pure space is now 'nothing at all belonging to the existence of things', but 'merely to the determina­tion of concepts' [Kt3:563].

 

[21] Kt1:74; s.a. Kt19:96. It is impossible to imagine how something could ap­pear without being sensed, because we experience appearances and sensations si­multa­neously. (The alternative would be to say 'sensations are elements of ap­pearances' [as in G7:513]; yet this is absurd, since it would require a sensation of some­thing which has not yet appeared!) When we recall that these distinctions are logi­cal and not necessarily chro­nological [see VII.1], we can nevertheless regard the third (synthetic) function in stage one as that of representing appearances as sensa­tions.

 

[22] Another reason may be that he regards the investigation of actual sensations as an empirical task. His transcendental task in this first stage, by contrast, is to discover the formal conditions which must pertain in order for any sensations to arise.

 

[23] Kt1:74; cf. 270,286,323. Kotzin wrongly takes Kant's classification of sen­sa­tion    as the 'material' element in knowledge to refer to its place within the first stage, rather than to the role of the first stage itself in systemt as a whole [see note VII.14]. She says 'sensation is the determinable, material factor in empirical intu­ition', which 'remains in our account when we are considering the sensible, intu­itive side of empirical cognition and when Space and Time, as formal factors, are not taken into account' [K10:114-5e.a.]. But she fails to explain on the one hand how sensations would be possible outside the context of space and time, and on the other how her understanding of sensation differs from what the present inter­pretation regards as the material element in the first stage (viz., the transcendental object).

 

[24] Kt1:155. Wolff points out that 'the assertion that a synthetic unity of repre­sen­tations cannot be given, but must be produced by the mind ... is so basic to Kant's philosophy that he never attempts to prove it', except by elaborating its implica­tions for systemt [W21:69n]. This assumption is indeed an integral part of Kant's Copernican revolution.

 

[25] Heidegger believes the imagination's role as mediator between sensi­bility and understanding makes it the 'common root' mysteriously uniting these two facul­ties [H11:144-8; cf. Kt1:29]. This is supported by Kant's view of the imagination as an 'original' faculty [A94], intimately connected with both sensibility and un­der­standing [see W21:77 and Ap. VII.D-E], yet also, as we shall see in VII.3.A, playing an important role in stage three.

 

[26] Kt1:A121. In A113 Kant explains: 'The ground of the possibility of the as­socia­tion of the manifold, so far as it lies in the object, is named the affinity of the manifold.' It is this affinity, and not (as Walsh suggests [W9:116]) the syn­thesis which brings it to light, which can be described as 'connectibility'. Moreover, affinity is directly dependent on apperception (step six) [Kt1:A122], and is there­fore the basis of the 'objective deduction' [see Ap. VII.G].

 

[27] Kant does seem to suggest at certain points that apperception follows synthe­sis    immediately [see e.g., Kt1:A94,A124]. Moreover, his overall exposition in both editions of the Deduction is misleading, because he discusses apperception and synthesis before discussing the role of the categories [cf. A98-111,129-42 and A111-30,143-69]. But this analytic procedure is to be expected from a deduc­tion: in order to deduce the necessity of the categories, Kant argues for the neces­sity of the material step (synthesis of imagination) and of the synthetic step (pure apper­ception), then shows how the categories are required as the formal step which leads from the former to the latter [see e.g., A119]. Allison attests to the 'analytical' character of much of Kant's argument in the Deduction [A12:9], and emphasizes the same three steps we have chosen as the key to stage two: 'the transcendental synthesis of the imagination and its relationship to apperception and the cate­gories constitutes the real nerve of the Deduction' [10]. The close rela­tion­ship be­tween the categories and apperception leads Wolff to proclaim that 'the categories ... are the unity of apperception' [W21:178]. But, as we shall see, such an identifi­cation is not strictly accurate.

 

[28] Because of its affinity with 'intuition', I have been using 'conception' as a tech­nical term referring to the power of forming concepts, even though this word appears only nine times in Kt1 [see Pq10:67], and never in connec­tion with 'intui­tion' [but see K2:11.302(Z1:184)]. In this sense 'categorial con­ception' refers to the operation of the catego­ries, which, as Kant says, 'contain ... the logi­cal func­tion for bringing the manifold under a concept' [Kt1:A245]. Other, less compre­hen­sive terms could just as well have been used to name this power, such as 'thinking' (which pro­duces thought), 'conceptu­alizing' (which produces concepts) or 'categoriza­tion' (which uses categories to make concepts).

 

       My interpretation of categorial conception contradicts Paton's claim in P2:2.82 that 'the lack of homogeneity between appearance and category indicates that the [direct] subsumption ... of appearances under the categories is impossi­ble.' I would argue that this is precisely what Kant has in mind when he refers to the ac­tivity of 'thinking'. He brings up this 'lack of homogeneity' in the third stage of his argument [see VII.3.A] in order to show it is impossible to produce empirical knowledge by means of such direct subsumption alone.

 

       The word 'concept' in contexts such as this can denote either an empirical or a pure concept. Allison defines 'a concept (analytic universal)' in A11:35 as 'a set of marks (themselves concepts), which are thought together in an "analytic unity," and which can serve as a ground for the recognition of objects. These marks col­lectively constitute the intension of a concept.' Because Kant largely ignores the role of empirical concepts, most commentators follow suit [e.g., E5: 133]. Schrader does mention that they 'are not derivable from the categories but must conform to them' [S6:142-3]. And Pippin devotes a great deal of atten­tion to the subject [P8:103-23,143-50]; but the maze of problems he raises is of little help in determining how Kant understood such issues.

 

[29] E.g., Kt1:305. Although the pure intuitions of space and time are sometimes called 'concepts' [e.g., 37,46; cf. A7:72], and although the term also has empiri­cal [Kt1:A111,A125] and other applications [367,377,434], Kant uses it most often in its strict logical sense to designate an object 'not of intuition and sensi­bility but of pure a priori thought ..., apart from all conditions of sensibility' [120].

 

[30] Kt1:A106. Wolff regards this definition as the essential tenet of the entire Analytic [W21:viii], and devotes much of his commentary to expounding its im­plica­tions [s.e. 121-31]. At one point he lists the 'three characteristics of rule-governed activities' as: (1) they 'can legitimately be said to proceed correctly or in­correctly'; (2) 'the order of the steps of the activity is not haphazard'; and (3) they are characterized by their 'coherence' [122-3]. Whereas empirical concepts are 'first-order' rules, pure concepts are 'second-order' rules [124-5]. Raschke dis­tin­guishes between rules and laws by saying the former provide general guidelines which are not universal or necessary, while the latter are obligatory [R3:18-24].

 

[31] These categories 'are nothing but the condition of thought in a possible expe­ri­ence, just as space and time are the condi­tions of intuition for that same experi­ence' [Kt1:A111]. They comprise 'all original pure concepts of synthesis that the understanding contains within itself a priori' [106], and through which 'appear­ances have a necessary relation to the understand­ing' [A119]. Paton de­scribes them as 'the ultimate predicates which universally and necessarily apply to every thing so far as it is a thing' [P2:1.257]. But the categories are not just highly general and all-encompassing empirical concepts: when functioning as the formal condition for all conception, they cannot themselves be empirical. Hence Kant describes their status further as 'concepts which prescribe laws a priori to appear­ances, and therefore to nature, the sum of all appearances ... [These] laws do not exist in the appearance but only relatively to [the subject], so far as it has under­standing.... [They] instruct us in regard to experience in general, and as to what it is that can be known as an object of experience' [Kt1:163-5]. Like space and time, these natural laws must therefore 'lie in ourselves', for 'the understanding does not draw its laws (a priori) from nature, but prescribes them to nature' [Kt2:320].

 

[32] The details of Kant's choice of categories will be examined in more detail in VII.3.A, where we will discuss their application to appear­ances in the form of principles [see also III.3]. Some of the many specific problems and ambiguities raised by Kant's discussion of the categories are discussed in Appendix VII.F.

 

[33] Kant refers to this 'transcendental consciousness' [Kt1:A117n] as the 'abiding and unchanging' faculty of 'pure apperception' [A123] in order to distinguish it from 'empirical apperception'. The latter refers to one's actual awareness of the 'always changing' mani­fold of one's own perceptions [A107]. Although Kant sometimes seems to equate it with inner sense [e.g., A107], they should technical­ly be dis­tinguished [cf. P2:1.399-400]. Inner sense as such de­notes the unorga­nized manifold of transcendental appearances which present themselves to a person's inner intuition [but cf. Ap. VII.D]; empirical apper­cep­tion refers to one's consciousness of these perceptions as they are synthesized in thought. Hence, they denote the same object, but viewed either from the tran­scendental or the empirical perspectives of systemt.

 

[34] Although the function of the fourth step in relation to the third is the synthe­sis of imagination, it nevertheless plays a material role in the second stage. For the purpose of synthesizing the sensations presented by the third step is to bring them to a level of determination (viz., as perceptions) which can be used by the un­derstanding as the matter for its conceptual synthesis. Recognizing the material status of the fourth condition can help us to understand why 'Combination [or syn­thesis] serves the same func­tion [in the arguments of the Deduction in B] as the transcendental object [the ma­terial step in the first stage] did in A' [G11:200]. And this, in turn, helps us explain why the second edition is an improvement on the first, since the transcendental object belongs primarily to stage one.

 

[35] Allison equates 'possible experience' and 'possible knowledge' in A12:5. But the two should be kept distinct, as referring to the goals of the first and second stages, respectively.

 

[36] Kt1:75; s.a. 314 and P2:2.21n,27n. The word 'understanding' in this context        must be interpreted narrowly, since Kant also portrays the understanding (in its broadest sense [see VII.1]), as involved with pure intuitions as well.

 

[37] This, no doubt, is why Kant stresses in Kt1:244 that 'Understanding is required for all experience and for its possibility', even though he elsewhere talks loosely as if sensibility on its own can be called 'possible experience' [199]. Evidently, sensibility can only properly be referred to in this way when its necessary connec­tion with the understanding is taken into account. The same holds, of course, for understanding as 'possible knowledge' in its connection with sensibili­ty. Both phrases look forward to the development of empirical knowledge, which includes 'all synthetic unity of perceptions' [226; cf. K3:52].

 

[38] This application of synthesis should be distinguished from the synthesis of imag­i­nation in step four, from the synthesis in synthetic (as opposed to analytic) judgments, and from the synthetic method in general [see III.3 and IV.2]. The lu­cidity of interpretations such as Wolff's, which emphasize the role of synthesis, could be substantially increased by recognizing the differences between these types of synthesis [cf. W21:180,201 and H4:xxii-cxv].

 

[39] Kt1:93-4. Pippin suggests that this association between concepts and judg­ments is the 'clue' Kant intends the Metaphysical Deduction to provide [P8:94,97]. Although I believe the nature of Kant's clue goes beyond this [cf. note III.17], Pippin's view does point up Kant's mis­placement of this section, inasmuch as the transition it hints at is not between the first and second stages, but between the second and third.

 

[40] Kt1:178; cf. P2:2.40. Kant's reasons for singling out time are relatively clear. In the second stage both space and time were abstracted from the appear­ance. But the goal towards which the third stage works is the empirical knowledge of outer ob­jects; so Kant re-introduces time as its first component in order to establish the inner framework into which all objectively real objects must fit.

 

[41] Kt1:179-80e.a. Kant says the schema of a sensible concept may be accompa­nied by an image; but 'the schema of a pure concept of under­standing can never be brought into any image whatsoever' [181]. As an example of the latter he says the schema of 'the concept of a triangle in general' is beyond any particular sensi­ble image: 'The schema of the triangle can exist nowhere but in thought' [180]. Thus Allison explains that, 'unlike the image, the schema is not something extra­neous to the concept, but is really the concept itself qua realized in intuition' [A7:89; cf. P8:140]. Heidegger draws a helpful distinction along these lines be­tween an 'image' and a 'schema-image' [H11:97-108], and explains that the unify­ing pro­cedure of the latter 'is never apprehended in itself', but only 'in the exercise of its regulative function' [101].

 

[42] Cf. Kt1:195-7,355-9, and note VII.30; s.a. P2:1.495. In Kt1:187-8 Kant says 'the   pure understanding ... is itself the source of principles', and the natural laws, or rules of experience, 'stand under higher prin­ciples of understanding.' In Kt1:359 he gives a slightly different account of their relationship: 'Understanding ... se­cures the unity of appearances by means of rules, and reason ... secures the unity of the rules of understanding under principles.' (As we shall see, this reflects the par­allel between the third and fourth stages.) Bennett express­es the role of princi­ples more simply [B17:61]: they define 'what our intuitions must be like in order to be intellectually manageable.' In so doing, 'principles ... proceed from con­cepts to intuition, not from intuition to concepts' [Kt1:199].

 

[43] P2:1.220. 'The principle of [non]contradiction', Kant says, 'must therefore be recognised as being the universal and completely sufficient principle of all analytic knowledge; but beyond the sphere of analytic knowledge it has, as a sufficient criterion of truth, no authority and no field of application' [Kt1:191].

 

[44] Kt1:223. Because the categories as applied in the principles are always schema­tized (i.e., restricted by the schema), the principles can be called 'schematized cat­egories' [P2:2.19n,182], though Kant himself never uses this phrase. Ewing gives a good summary of the relationship between pure categories, schemata and schematized categories in E5:134-5.

 

[45] Kt1:200. Although Kant sometimes speaks loosely as if the principles them­selves   were axioms, anticipations, etc. [cf. 760-1 and P2:2.124n], they are strictly speaking the ultimate principles which make possible these specific types of principles [cf. note VII.46].

 

[46] Kt1:200-1. Kant explains: 'It is through these principles of pure understand­ing       that the special principles of mathematics and dynamics become possible. I have named them ... on account rather of their appli­cation than of their content' [202]. Thus, they are not themselves prin­ciples of mathematics and dynamics, but are the bases of these sciences.

 

[47] Kt1:207. Whereas axioms determine that objects will have characteristics di­rectly related to their appearance in time and space, anticipations determine 'that an object is more than the space which it occupies and the time through which it lasts' [P2:2.139].

 

[48] Kt1:291. Kant is perhaps not clear enough in his explanation of the role of space         in the chapter on the principles. Nevertheless, it is this reintroduction of space which makes the chapter a suitable place for him to insert his second-edition revi­sion of the Refutation of Idealism [274-9], where the necessity of outer ob­jects in space is firmly established (from the empirical perspective). The role of the prin­ciples in determining how it is that empirical objects (viewed from the empirical perspective) stand out from the subject as independent realities in the outer world of space and time could be referred to, albeit rather fancifully, as 'extuition'. Along these lines, we could add, in a Heideggerian vein, that it is only because the principles enable a representation to be e-jected from the subject that it can become an ob-ject (i.e., can stand opposite the subject) [cf. H11:35-6].

 

[49] Kt1:241. This Copernican assumption [cf. III.1] helps explain why Kant's spe­cial type of 'transcendental argument' [see V.3, Ap. V and note IV.26] can insure that the principles 'are not only true a priori, but are indeed the source of all truth (that is, of the agree­ment of our knowledge with objects)' [296]. Kant's as­sump­tion here is not that we all decide to prescribe certain a priori principles to our experience, but that human knowledge necessarily presupposes such princi­ples, regardless of a person's conscious recognition of them.

 

[50] Kt1:142; s.a. P2:1.571; cf. Kt7:20. Bird notes that something objectively real         'can be conceived independently of any particular experience, but not inde­pen­dently of every experience' [B20:145].

 

[51] Kt1:195; cf. P2:2.88-9,93-6. As Kant says in Kt1:303: 'the Transcendental Ana­lytic leads to this important conclusion, that the most the understanding can achieve a priori is to anticipate the form of a possible experience in general.'

 

[52] Kt1:353-4,397. Rotenstreich disagrees with Kant's emphasis on rea­son's nat­ural      tendency towards illusion, and regards it as a result of the historical influence of rationalism on Kant [R11:66-7]. 'That there is no necessity' in committing such errors, he explains, 'is clearly shown by Kant himself in his attempt to re­place traditional systems of metaphysics by regulative concepts' [70]. Although this is a good point, I would suggest in Kant's defense that by calling these illu­sions 'natu­ral' he may not mean that reason unavoidably succumbs to them, but only that the source of errors is such that they will always, as it were, tempt reason to fall for them when it asks questions about ultimate reality. Such temptation is unavoidable because of the opposition between sensibility (--) and reason (++), as the first and last stages of systemt: if we are not careful in using our reason, we will naturally tend to forget the sensible ground upon which alone it is able to stand.

 

[53] Kt1:379. Kant's notion of 'the maximum' [693] is roughly equivalent to that of the unconditioned. Thus he says 'the idea of [the maximum of] reason is an analo­gon of a schema of sensibility; but with this difference, that the application of the concepts of understanding to the schema of reason does not yield knowl­edge ..., but only a principle for the systematic unity of the entire conceptual per­spective' [693e.a.]-i.e., only an 'idea' (in its technical sense, described below). The implications of this limitation of knowledge will be examined shortly.

 

[54] Kt1:364; cf. 358. This does not contradict my proposal in IV.3 that hypo­thetical     reflection yields analytic a posteriori knowledge (or belief); for Kant is here de­scribing the role of the tenth step in his overall system of conditions (all of which proceed synthetically), and so is best understood as referring to the syn­thetic method which must be employed to advance from step nine to step eleven. As applied to inferences in general, Kant refers to the synthetic method as 'a parte priori' (ascending from conditioned to unconditioned) and the analytic method as 'a parte posteriori' (descending from unconditioned to conditioned) [389].

 

[55] Kt1:511. This characteristic of the unconditioned object is also true of the tran­scendental object, the synthesis of imagination, and the schematism of under­standing, all of which arise in the first step of their respective stages in systemt.

 

[56] Kt1:672; s.a. 368,595-6,670. 'An idea is nothing else than the concept of a perfection which has not yet been met with in experience'; but it is not 'for that rea­son impossible' [Kt39:444(109)].

 

[57] Kt1:366, alt. Kemp Smith, incidentally, paraphrases the latter quote as '[can] be obtained ... only by inference', which could be taken wrongly to imply that infer­ence is itself the only element in the fourth stage.

 

[58] Dister points out a similarity between the schema's influence on the un­der­stand­ing and the idea's influence on reason [D4:262-3]. But a more direct paral­­lelism exists between the influence of the categories (+-+) on the manifold of ap­pear­ances (--+) and that of the ideas (+++) on the phenomenon (-++), both being the influence of a stage's formal step on the formal step in the preceding stage (as symbolized by the change from + to - in the first term of each of the corresponding logical components). Kant alludes to this parallelism in Kt1:368: 'just as we have entitled the pure concepts of understanding categories, so we shall give a new name to the concepts of pure reason, calling them transcendental ideas.' In order to make this parallelism clear the summary of step eleven regards ideas as both functions and products: just as conception uses the categories to form concepts, inference uses the ideas (or we might say 'ideation') to form ideas.

 

[59] Kt1:391-2. Kant says the 'transcendental ideas ... follow the guiding thread of the categories' [392]; however, they are actually arranged in three groups of four (rather than four groups of three) because they are based on the synthetic relation between the three analogies, each of which is expounded in terms of a 2LAR [397]. The only exception to the fourfold structure of the analy­sis of each is Kant's treatment of the Ideal of Pure Reason [595-670], which I shall discuss briefly in X.2 and in more detail in Pq20.

 

[60] Kt1:726. The phrase emphasized by Kant indicates he is thinking here of the hy­pothetical perspective, which looks towards the world, as opposed to the speculative perspective, which looks beyond the world.

 

[61] Rotenstreich is correct in stating: 'Dialectic in Kant mainly means the reifica­tion of ideas, the trend of reason towards hypostatic assumptions' [R11:63]. However, he unfortunately fails to distinguish sufficiently between this and the hypothetical 'acting as if' which Kant puts in its place. Only from the latter per­spec­tive are objects properly regarded as 'the ever-unattainable goal of investiga­tion' [W5:182]. As I hope to demonstrate in Pq21 [s.a. XI.4], Kant's hypothetical perspective is much more relevant to modern conceptions of science and scientific inquiry than most interpreters recognize.

 

[62] Kant sometimes hints at something like this sort of diagram (at least as an 'archetype' [see I.3]), as when he refers to 'ascending' from the conditioned (step nine) to the unconditioned (step ten) by the synthetic method [e.g., Kt1:394]. Likewise, he says in Kt7:410 that to move 'downwards' from God to nature 'is a priori', while to 'move from below upwards' is 'a posteriori'-a metaphor which is consistent with my placement of the two a priori perspectives on the downward arc, and the two a posteriori perspectives on the upward arc.

 

[63] Schrader seems to be hinting as some such associations when he says in S6:139 that 'the categories of quantity and quality are constitutive of the space-time mani­fold as such [just as intuitions and concepts are constitutive of judg­ments], while the relational categories are constitutive of objects in space and time [i.e., phenomena].'

 

 

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