The Architectonic Form of Kant's Copernican System
Human reason is by nature architectonic. That is to say, it regards all our knowledge as belonging to a possible system. [Kt1:502]
1. The Copernican Turn
The previous chapter provided not only concrete evidence that Kant's System is based on the principle of perspective [II.2-3], but also a general outline of its perspectival structure [II.4]. The task this sets for the interpreter is to establish in greater detail the extent to which the System actually does unfold according to this pattern. This will be undertaken primarily in Parts Two and Three. But before concluding Part One, it will be helpful to examine in more detail the logical structure of the relationships between the various parts of Kant's System, and how they fit together to compose what we have called Kant's 'Copernican Perspective'.
Kant rather boldly compares the contribution made to philosophy by Kt1 with that which Copernicus made to astronomy. Copernicus explained 'the movements of heavenly bodies' (i.e., of the planets, stars and sun) by denying 'that they all revolved round the spectator' (i.e., the earth), as they indeed appear to do, and suggesting instead that the earth and other planets revolve around the sun while the stars remain at rest. Likewise, Kant attempts to explain our knowledge of objects in general by denying 'that all our knowledge must conform to objects', as it indeed appears to do, and suggesting instead 'that objects must conform to our knowledge' [Kt1:xvi; cf. Kt65:83]. This metaphor, expressing the difference between appearance and reality in the theories of both Copernicus and Kant, suggests the following two models:
(a) Appearance (b) Reality
Figure III.1: The Two Aspects of a Copernican Revolution
These diagrams can be used to represent Kant's Copernican revolution simply by replacing 'earth' with 'subject' and 'sun' with 'object', and by stipulating that motion represents the active, determining factor in knowledge, while rest represents the passive factor. As a result, (a) would depict the ordinary person's (as such, quite legitimate) Empirical Perspective on the world, while (b) would depict the philosopher's special Transcendental Perspective.
The 'change in perspective' [Kt1:xxii] required by the philosopher's switch from (a) to (b) is the revolutionary 'touchstone' of Kant's entire System [see II.1], for it reveals that 'we can know a priori of things only what we ourselves put into them' [xviii]. The philosopher's primary attention, therefore, is directed away from the objects of knowledge and is focused instead on the subject (i.e., on humanity) and our mental activities. On this point, at least, there is widespread agreement among interpreters. Kant's Copernican revolution has been said to consist, for example, in claims such as these:
human knowledge can only be understood if we hypothesize the activities of the knower [C3:237];
the epistemological conditions for knowing natural entities are at the same time the ontological conditions for their existence as such [i.e., empirically] [Y2:977];
the universality and necessity of synthetic a priori propositions as established by ... critical argumentation are ... specifically relativized to the workings of the human intellect [R4:318; cf. 321];
the objects of human knowledge can only be legitimately [described] ... if they are 'considered' in relation to the human mind and its conceptual scheme.
Unfortunately, the agreement among Kant-scholars on general matters such as this does not carry over into matters of detailed interpretation or critical evaluation. Indeed, inasmuch as Kant never provides a thorough and consistent explanation of the logical relationships between the many constitutive 'elements' in his three Critiques"such as those in Kt1 concerning knowledge, which he discusses in the Transcendental Doctrine of Elements, there will probably never be widespread agreement concerning their intended meanings and relative importance. But in spite of the negative answer which the consensus of two centuries of interpretive scholarship has given to the question of the unity of Kant's System [cf. I.1], it seems incongruous to regard Kant as a 'megaphilosopher' and yet to confess that he failed in so basic a task. I shall therefore attempt in this chapter to reveal the architectonic unity of his entire System by providing an outline of its formal structure. My underlying goal will be to set the stage for an analysis of the content, and thus of the detailed arguments, of the three Critical systems [see Part Three]"one which could serve not only to facilitate more widespread agreement among interpreters, but also to help us understand why Kant believed his 'critical philosophy opens up the prospect of permanent peace among philosophers' [Kt33:416(288); see XII.3-4].
2. Kant's Logic and the Structure of His Three Critiques
Kant has often been accused, even in his own lifetime, of filling his philosophy with prefabricated divisions simply in order to support his architectonic plan. What such critics fail to understand is that this prefabrication is intimately bound up with the Copernican revolution in philosophy: rather than attempting to discover distinctions existing independently of the subject, the philosopher's task is to convert the mass of unorganized knowledge into an ordered System by examining the structure imposed on the world of experience by the subject. Or, as Kant himself puts it, such divisions, which are evident in other disciplines as well, such as in some natural scientists' reduction of matter to the four elements of 'earth, ... water, ... air, ... and salt', are the result of 'the influence of reason on the classifications we make' [Kt1:674]. Instead of pursuing the relationships between such classifications in order to discover an overall pattern (an architectonic unity), critics who ignore this point assume (as it were, a priori) that the precise number and order of these divisions is insignificant. (It is not surprising how often they complain in the next breath about Kant's lack of systematic unity!) The only way to correct this interpretive error is to establish precisely what relationship holds, according to Kant, between the patterns suggested by reason's architectonic structure and the organization of his System. Once this is done, a more detailed analysis of the types of patterns which reason 'prefabricates' for the human subject will provide us with an accurate model for interpreting Kant's System. But first it will be helpful to examine his conception of the nature and functions of logic in general.
Although Kant himself did not write anything like a Critique of logic, he lectured regularly on the subject"indeed 'often twice a year ... from 1755 to 1796' [H4:xvi; cf. J2:5]"so his logical methodology was repeatedly in the foreground of his thought. Moreover, towards the end of his life he did supervise one of his followers, Jäsche, in editing his lecture notes for publication. In his Preface Jäsche explains why Kant did not choose to set out his logical theory on his own:
His task of scientific foundation of the entire system of philosophy"the philosophy of what is realiter true and certain"that incomparably more important and more difficult task, which only he alone could carry out in his originality, did not permit him to think of working out a logic by his own hand. He could, however, very well leave this work to others who with insight and unbiased judgment could use his architectonic ideas for a truly well adapted and well ordered treatment of that science. [J2:7]
Jäsche's edition of Kant's Logic [Kt10] is indeed generally regarded as an authentic representation of Kant's own position.
The most important distinction in discussing Kant's logic is between formal or 'general' logic and material or 'transcendental' logic [see e.g., Kt22: 193-4; R11:1-25]. England describes this distinction with admirable clarity in E3:98: '"General logic" is concerned with forms of connection between concepts abstracted from experience, while transcendental logic is concerned with the source of their relation in the realm of fact.' This distinction is related to the distinction between the 'real use' and the 'logical use' of the understanding, which Kant was always careful to make, even in his early works. However, the real use of the understanding is the task of the faculty of judgment, which defines the empirical perspective in each of Kant's systems [see II.4]. For as we shall see in VII.3.A, judgment can give rise to empirical knowledge only when concepts work together with the content given from some intuition. The logic of Kant's System is transcendental because this content, which is always required by the real use of the understanding in judgment, arises out of the transcendental perspective in each system.
The question posed by general logic is: 'since the understanding is the source of rules, according to what rules does it proceed itself?' [Kt10:12(13-4)]. In order to answer this question, pure general logic 'abstracts from all content of the knowledge of understanding ... and deals with nothing but the mere form of thought'; consequently, it 'has nothing to do with empirical principles', such as those given in psychology [Kt1:78; s.a. Kt10:12(14-5), 45(50)]. For it 'teaches us nothing whatsoever regarding the content of knowledge, but lays down only the formal conditions of agreement with the understanding' [Kt1:86; s.a. Kt10:15(17)]. Since 'it has reason for its subject matter' [14(16)], it pays no attention to 'how representations arise' [33(38)]. Transcendental logic, on the other hand, derives its structure directly from general logic [R11:4]; thus it uses the abstract forms of general logic, but always refers them back to some extralogical content. By doing so, it can establish knowledge"the transcendental knowledge which can be gained by adopting the Copernican Perspective"whereas general logic on its own 'is not confined to any particular kind of knowledge made possible by the understanding' [Kt1:736]. 'Formal logic shows how to clarify concepts, transcendental logic how to construct objects' [H4:xix; cf. Kt10:63(65)].
General logic, therefore, is not regarded by Kant as a Critical system, for it 'is more than mere criticism' [Kt10:15(18)]. On the contrary, it is 'a separate, self-contained science grounded in itself' [J2:8; s.a. S14:474,496], 'a science of the necessary laws of thinking' [Kt10:13(15)]; indeed, it is 'the vestibule of the sciences' [Kt1:ix]. Rather than fulfilling a material function in Kant's System, as does transcendental logic, general logic serves as the systematic, architectonic form of the whole [cf. H4:xxii]. 'In this duality [between formal and transcendental logic] primacy, i.e., the status of being the point of departure, is given to the sphere of Formal Logic.... The two Logics are thus two aspects [viz., formal and material] of the same function [viz., thinking about judgment]' [R11:7; cf. H4:xvii]. Just as natural science is orderly because it is grounded in the principles established by transcendental logic [see VII.3.A], even though the latter is not actually a part of the former, so also is Kant's System grounded in and ordered by the separate system of general logic [cf. Kt10:13(15)]. Therefore it is general logic which, as mentioned in II.4, can be referred to as 'systeml', provided that in so doing it is regarded not as equal to, but as standing over and above, the three systems which constitute the material elements of Kant's Critical philosophy.
Kant's first two Critiques both include a Doctrine of Elements (Elementarlehre) and a Doctrine of Method (Methodenlehre). Apparently the latter serves a formal role in relation to the former: it is appended in order to clarify the form according to which the content (the 'elements') of the system is patterned. Thus, after introducing this distinction in Kt1:29, Kant adds: 'Each of these chief divisions will have its subdivisions, but the grounds of these we are not yet in a position to explain.' This leads the reader to expect such an explanation in the Doctrine of Method. Yet in both cases [Kt1 and Kt4] Kant disappoints us, giving instead a rather haphazard treatment either of definitions of basic Critical concepts and explanations of their interrelationships, or of various implications of his Critical principles. What is still missing, then, is an account of why he prefers certain ways of dividing and ordering both his general exposition and his analysis of the particular topics with which he deals. In order to get a rough idea of just what sorts of divisions he preferred, we can begin by making a brief, a posteriori analysis of the Tables of Contents in each of his three Critiques. The logical basis of his preferences, however, can be determined only by comparing them with an a priori analysis of the actual architectonic structure of thought [see III.3].
Of the twenty-seven total divisions in the Table of Contents to Kt1 [see Table III.1], one is ninefold and two are sevenfold. 59% of all the divisions are either twofold (ten in all) or fourfold (six in all), and 30% are threefold (eight in all). The general structure of both Kt4 and Kt7 is, by contrast, much simpler [see Tables III.2,3]. Together they contain just thirteen divisions, two of which are ninefold, one fourfold, one threefold, and the remaining nine, twofold. Two points can be raised with respect to these statistics: (1) Kant's obvious preference, as indicated in Table III.4, for the divisions of two (47.5%), three (22.5%) and four (17.5%) might reflect a priority for such divisions in his conception of the very architectonic structure of reason; and (2) if so, he did not devote enough attention in his exposition to consistently revealing how these divisions determine reason's architectonic structure"that is, not enough for it to be as readily useful to the reader as it (apparently) was to him.
Our analysis of the Table of Contents in each of Kant's three Critiques reflects only a sampling of his preferred divisions. Nevertheless, it does provide a clue as to the type of divisions which will prove to be most important within the text itself"with one exception. Anyone undertaking even a cursory study of Kant's philosophy is likely to be astounded by his insistence on the uniqueness and completeness of his table of twelve categories, the form of which is repeated in several other twelvefold tables throughout his Critical works [see I.3]. A twelvefold division never occurs in the Table of Contents of any of the Critiques, probably because this number is explicitly used by Kant as a composite of other, more basic divisions which do occur (viz., two, three and four). In light of the great importance he attaches to his twelvefold divisions, we might find that, by examining the relationship between his use of twelvefold divisions and his use of divisions of two, three and four, our understanding of the formal structure of his architectonic can be greatly increased. For Kant's architectonic simply is the organization of divisions into patterns of interrelated wholes"and eventually, into an interrelated System.
Table III.1: Analysis of the Table of Contents to Kt1*
*The second edition of Kt1 has been used to prepare this table. In this and the following two tables, subdivisions are included only for sections given numbers or letters in the Table of Contents provided in the K2 edition; but the divisions using '§' are ignored.
Table III.2: Analysis of the Table of Contents to Kt4
Table III.3: Analysis of the Table of Contents to Kt7
Table III.4: Total Frequencies of Divisions
in Kant's Three Critiques
3. The Analytic and Synthetic Basis of Kant's Twelvefold Pattern
One of Kant's most pretentious claims about the value of his own philosophical System is that it is complete, whereas previous systems were incomplete precisely because they had not 'established a table of categories set out according to a solid principle' [Kt69:281-2]. The audacity of such claims is revealed in a 1783 letter to Schultz, in which Kant shares his idea that 'the table of categories ... contain[s] the material for a possibly significant invention', for an 'Artem characteristicam combinatoriam' [K2:10.329-30(Z1:109)] along the lines of Leibniz's attempt at constructing a 'universal algebra that would exhibit the relations among simple ideas.' For he confesses that he is 'unable to pursue' such a project, since it would 'require a mathematical mind'; he admits he has 'only been able to make out something hovering vaguely before me, obscured by fog, as it were.' Fortunately, Kant does offer various hints from time to time about just how such a project might proceed [see e.g., K2:10.344-5(Z1:112)]. By gathering his various hints and drawing them to their logical conclusions, I will attempt in this section to clear away some of the fog which has hindered both Kant and his interpreters from seeing clearly the structure of reason's architectonic form. In so doing, some of Kant's extravagent claims might turn out to look rather more plausible.
After presenting the reader of Kt7 with a typically contrived-looking table of twelve 'faculties of the soul' , Kant defends his questionable habit in an important, though much neglected, footnote [197n]. His initial answer to those critics who think it is 'somewhat suspicious that my divisions in pure philosophy almost always come out threefold' is that 'it is due to the nature of the case.' Fortunately, he then expands his answer by recapitulating the hints he has given elsewhere as to the nature of the patterns which arise out of the logical operations of analysis and synthesis. He explains that analytic operations (or 'divisions', as he calls them) are 'always twofold': they proceed by dividing a whole (e.g., a concept) into two equal and opposite parts, which can be represented by the logical symbols A and -A. Synthetic operations, on the other hand, 'must of necessity be trichotomous' in order 'to meet the requirements of synthetic unity in general, namely (1) a condition [or form], (2) a conditioned [or matter], (3) the concept arising from the union [or synthesis] of the conditioned with its condition': they proceed by integrating two equal and opposite parts into one whole, a process which can be represented by the logical symbols A, -A, and A + -A. (The condition and the conditioned are represented by A and -A rather than A and B, because on their own they constitute merely an analytic division between two aspects of 'conditioning', so they 'must be separated from one another by contradiction, not by mere contrariness' [Kt10:147(147)]. Analysis is twofold because it focuses only on determining the opposing parts, whereas synthesis is threefold because it aims at realizing the whole by combining the opposing parts; otherwise, the two operations are entirely reciprocal [see note III.10].) Unfortunately, Kant never explains how these simple correlations can be used to clarify the formal pattern of his architectonic plan. Nevertheless we can assume from this passage that he believed reason's architectonic structure to be integrally bound up in some way with the twofold nature of analytic operations and with the threefold nature of synthetic operations.
Commentators who attempt to explain Kant's preference for twelvefold patterns generally do so by discussing the relationship between the various parts of his original Table of Categories [Kt1:106; see e.g., W21:64-7]. This can be a valuable exercise, no doubt; but it is not the best way to discover the abstract structure which all such patterns are supposed to share. (Unfortunately, commentators rarely seem interested in pressing the matter this far anyway.) A better way would be to determine how analytic and synthetic operations, given Kant's abstract descriptions of their logical form, could be combined into a complete twelvefold formal 'mold' for a system. In this section I shall adopt the latter method.
Now the danger in using a logical apparatus to describe such a system is, as Kant points out in Kt11:390(217-8), that the symbolic expression may turn out to be more complex than the original argument, whereas 'the proper object [Zweck] of Logic is to bring everything to the simplest mode of cognition [Erkenntnissart]' [Kt14:56(89-90)]. One way of avoiding this danger will be to use geometrical figures in the way suggested in I.3. Furthermore, instead of using the traditional symbols A and -A to represent Kant's description of the positive and negative 'poles' of analytic and synthetic operations, I will drop the letter A and use the simpler symbols + and -, thus indicating that I will be abstracting completely from the content of such operations, and examining only their barest form, their 'positivity' or 'negativity'. Likewise, in place of the rather cumbersome A + -A, I shall use x to represent the synthesis of + and -. These simpler symbols must not, however, be confused with the mathematical symbols for addition, subtraction and variable quantity; for our purposes they will represent not mathematical operations but symbolic representations of the structural relationships between objects. I will begin by using these symbols to help clarify the structural differences between analytic and synthetic operations, after which I shall demonstrate how they can also clarify the abstract structure exhibited by Kant's favorite, twelvefold architectonic pattern.
The simplest analytic operation, as we have seen, is the division of a whole into two opposing parts, which I shall represent as + and -. I shall refer to this operation as (following Kant) 'analytic division', and to its product as 'an analytic relation'. All coherent thought is ultimately grounded in the first 'level' of analytic division, for it derives its validity directly from the basic law of noncontradiction (in this case expressed as + ≠ -). There are innumerable common examples of first-level analytic relations (1LARs), such as when we divide the concept of 'temperature' into 'hot' and 'cold', or that of 'the day' into 'daytime' and 'nighttime', or 'mankind' into 'male' and 'female', etc; yet such twofold division alone is not sufficient to reveal the complete structure of the analytic aspect of Kant's twelvefold pattern. For the Critical philosopher is concerned not just with thinking, but with thinking about processes such as thinking, suggesting, as it were, the need to apply the law of noncontradiction (often misleadingly called the law of 'contradiction') to itself.
The formal structure of the second level of analytic division can be determined by applying another first-level opposition of + and - to each side of the original opposition. This can then be expressed symbolically by adding a second term (i.e., either + or -) to each of the two original terms, thus yielding the four complex 'components': ++, +-, -+ and --. Examples of such fourfold analytic relations are more complex and not quite as common as the twofold relations on the first level. But any attempt to interrelate the members of two sets of two opposing terms (2x2=4) can serve as an example. For instance, the two distinctions, universal-particular and affirmation-negation, can be used to label the corners of the traditional 'square of opposition' with the four components: universal affirmation, particular negation, universal negation and particular affirmation. In this, as in any second-level analytic relation (2LAR), the four components can be derived by asking two successive yes/no questions: (1) Is the proposition universal? and (2) Is it affirmative? In each case, a + value would be assigned for a 'yes' answer and a - for a 'no' answer. Putting the two resulting signs together for each possible combination of answers would then give rise to the four components listed above.
As I have demonstrated in Pq18:2.1, analytic divisions can be carried on to an indefinite number of levels. The formula for determining the number of possible components (=C) at each level (=n) is simply 2n=C, and the number of terms (=t) in each component will be the same as the level number (i.e., t=n). For our purposes, however, these higher levels can be ignored, since an understanding of the structure of second-level analytic division is all that is required for understanding the analytic aspect of Kant's twelvefold patterns.
The first two levels of analytic relations can be mapped onto simple geometrical figures. The basic form of a 1LAR can be mapped, for example, onto a (one-dimensional) line segment, with simple, one-term components denoting the relative position of its two poles:
Figure III.2: 1LAR, Mapped onto a Line Segment
NOTE: The double-headed arrow between the + and - signifies the fact that, as we shall see, one cannot determine in advance which 1LAR term has priority, or comes first in the developmental process.
Although my way of using this and the other maps in this chapter is ultimately arbitrary, I have defended my choices against some of the primary alternatives in Pq18. For instance, the relative position of the + and - in Figure III.2 is flexible; I have placed the - at the left and the + at the right because of the traditional association of the left with passivity and the right with activity, which Kant himself mentions in several places [see e.g., Kt52:380-1].
The basic form of a 2LAR can be mapped in a similar way onto a two-dimensional figure composed of two perpendicular line segments, with two-term components arranged so that the first term denotes the line segment in its relation to the other line segment, and the second term denotes the position of each pole on its own line segment. Associating the vertical axis with + and the horizontal axis with -, and assuming a clockwise progression from the 'pure' components (++ and --) to the 'mixed' components (+- and -+) yields the logical map given in Figure III.3. These four two-term components can serve to distinguish the structural relationships between each of the four poles in any 2LAR. For they symbolize the relationship of each pole not only to its opposite pole, but also to the pair of poles on the line segment ++
Figure III.3: 2LAR, Mapped onto a Cross
NOTE: The arrowheads point down and to the left in order to indicate the logical priority of the pure components in relation to the mixed components. This is due to the closer association of the pure components with the original 1LAR, as pictured by the two sides of the diagonal line in Figure III.4: 2LAR ++ and -- components simply duplicate the 1LAR + and - terms, respectively; the 2LAR -+ and +- components have a logically secondary status, because each is composed of two opposite 1LAR terms.
which opposes its own. Beyond this level, the rules for mapping analytic relations onto geometrical figures get more and more complex, and so also, less relevant to the present discussion [but see Pq18:2.3-4].
Kant makes extensive use of the first two levels of analytic division, both explicitly and implicitly; indeed, he occasionally even displays the resulting conceptual relations in tables which correspond directly to Figure III.3. His most important application of second-level analytic division is undoubtedly his division of the twelve categories into four classes. Yet because of his brief explanation of the formal structure of the resulting logical relation in the so-called 'Metaphysical Deduction of the Categories', many commentators agree that his theory 'is surely absurd' [W7:168]. However, once the fourfold structure of all 2LARs is properly understood, such a judgment seems grossly unfair. Kant himself does a somewhat better job of explaining the formal structure of his fourfold division of the categories in his discussion of the Principles of Pure Understanding [Kt1:187-294; see VII.3.A]. By using this as an example of how such division can actually be used to determine the relations between significant philosophical concepts, we can clarify not only the connection between 1LARs and 2LARs, but also the intelligibility of Kant's use of such formal operations.
Kant divides his four principles ('axioms', 'anticipations', 'analogies' and 'postulates') into two classes, the 'mathematical' and the 'dynamical' [Kt1: 199-200; s.a. 110]. Axioms and anticipations can be grouped together as mathematical because they both apply to 'the mere intuition of an appearance' (-), while analogies and postulates can be grouped together as dynamical because they both apply to 'its existence' (+) . Thus, the former pair 'allow of intuitive certainty', whereas the latter pair 'are capable only of a merely discursive certainty' . But the same principles can also be grouped according to a rather different 1LAR: axioms and analogies are both principles of extension (-) [202,A176-7], while anticipations and postulates are both principles of intension (+) [207,265-6]. If we now replace each first-position + in Figure III.3 with 'intensive' and each - with 'extensive', and replace each second-position + with 'thought' and each - with 'intuition', then we can plot both levels of Kant's analytic division of principles on the same diagram. The resulting 2LAR is represented by the four points of the cross in Figure III.4. The vertical and horizontal axes represent the 1LAR between intension and extension, respectively. And the 1LAR between intuition and discursive thought is represented by the relation between the end points of each axis, as well as by the two sides of the diagonal line which cuts across the first and third quadrants.
Now that we have examined some of the properties of the relations arising out of the first two levels of analytic division, and have demonstrated how the orderly (i.e., architectonic) structure of one of Kant's intricate theories can be revealed by mapping it onto the analytic model of the cross, we can proceed to examine the formal structure of synthetic operations. Synthetic opera-
Kant's Principles Mapped onto a 2LAR Cross
NOTE: This will always be the position of such a diagonal line, because the logical structure of all 2LARs, as set out in Figure III.3, precludes any polar relation between the contradictory pairs of components which border the first (++ and --) and third (+- and -+) quadrants.
tions differ from analytic operations in two important respects. First, the relationships between the components of an analytic operation are static (i.e., each component can be understood quite adequately as if it were distinct from the others), whereas those between the components of a synthetic operation are dynamic (i.e., each component can be understood only if it is viewed as part of a developmental process in which an integrated whole is being constructed). To reflect this difference I will refer to synthetic operations not as synthetic 'division', as Kant does in Kt7:197n and elsewhere, but as synthetic integration.
The dynamic character of synthetic integration is exemplified by Kant's openly synthetic method in the three Critiques [Kt1:19], which results in his exposition taking the form not so much of exhaustive argumentation designed to establish conclusive solutions to specific and isolated problems, as of a progressive unfolding of a connected whole through a large number of (in themselves) often inconclusive considerations. (This, incidentally, makes it especially dangerous to limit one's critical examination of Kant's philosophy to a detailed analysis of each argument [cf. I.1].) His general task is to perform 'a comprehensive self-examination of reason according to principles arising from its own nature' [B18:223; cf. Y2:973]. Thus he begins in the first Critique by putting forward a theory of 'knowledge' (a term that often has rather static connotations) which is really a theory of the conditions of the dynamic activity of 'knowing'. As Wolff rightly says in describing Kant's theory: 'Knowledge is an activity, not a state, of the mind. Judgment can be understood only if we first analyze judging' [W21:323]"i.e., only if we discern the synthetic functions which work together to compose a judgment. We shall examine the details of Kant's theory of knowledge in Chapter VII.
The second difference between analytic division and synthetic integration is that synthesis is based on a threefold rather than a twofold pattern. In his 1784 letter to Schultz [K2:10.344(Z1:112)], Kant explains that the third component in such relations 'does not arise out of [the] mere conjunction [of the first two components] but rather out of a synthesis', which 'always contains something more than the first and second alone or taken together, viz., the derivation of the second from the first.' A third symbol is therefore needed to represent the synthesis of the otherwise contradictory symbols, + and -; as mentioned above, x will be used as a symbol for the merging or integration of + and -. Thus a simple (first-level) synthetic integration consists of three one-term components: +, - and x. An appropriate geometrical model for this first-level synthetic relation (1LSR) is the triangle, whose three vertices can
Figure III.5: 1LSR, Mapped onto a Triangle
NOTE: The arrows pointing from the + and - components to the x signify the synthetic process, by which a mysterious 'third thing' draws together what is essential in both of two contradictory opposites.
be labelled with the three symbols of synthetic integration [see Figure III.5]; adding arrowheads to each side helps to suggest the dynamic relationship between the three components.
The threefold nature of synthetic integration was, of course, explicated most fully by Hegel, who used his famous 'thesis-antithesis-synthesis' triad as the structural basis of his entire philosophical System. As we have seen, Kant describes the structure of synthetic integration rather more narrowly with triads such as 'ground-grounded-whole' [see note III.10] or 'condition-conditioned-unity' [see Kt7:197n, q.a.]. Kant's terms will turn out to be particularly appropriate in Part Three when we apply the formal patterns developed in this section to the elements of his System.
Examples of 1LSRs can be found in many of Kant's works, though he rarely explains exactly what makes them synthetic. Perhaps the best way to clarify Kant's descriptions of the threefold structure of 1LSRs is to use an example from everyday life, such as the 'man-woman-child' relationship. On their own, the concepts 'man' and 'woman' compose a 1LAR between the two anatomically distinct (i.e., mutually exclusive) sexes of the human race. (The + and - could be correlated with 'man' and 'woman' or with 'woman' and 'man', respectively, depending on which characteristics of men and women are used to make the correlation.) But when a man and woman join forces to produce a child, their relationship can be understood only in the dynamic terms of synthetic integration: the egg (the conditioned (-)) receives into itself a sperm (the condition (+)), both of which are transformed into an embryo (the unity (x)). This is a good example of synthetic integration because it implies what is true for synthetic operations in general, that on its own a synthetic relation is not rigidly structured or organized the way an analytic one tends to be. For a man and a woman can have more than one child, and their children may or may not have children of their own eventually. Note also that 'child' (x) is neither masculine nor feminine (neither + nor -), yet any given child is either male or female (just as the x in a 1LSR may become the + or - of another synthesis). Synthetic integration on higher levels does not necessarily follow a mathematical pattern, such as 3n=C. Although it may do so, a higher-level synthesis tends more often to be composed of a collection of 1SLRs, randomly strung together in a network of patterns, in which some synthetic components serve as the foundation for one or more new syntheses, while others prove to be dead ends. (For a detailed discussion, see Pq18:3.1-4.4.)
Unlike Hegel, Kant was not content to string together synthesis after synthesis in an intricate pattern of purely synthetic relations. His concern for architectonic neatness encouraged him to acknowledge both the real priority of synthesis and the logical priority of analysis. Thus he admits that 'analytic unity ... is possible only under the presupposition of a certain synthetic unity' [Kt1:133; s.a. 130]; but for this very reason he attempted to structure his systems by dividing each (according to the 2LAR pattern) into four simple synthetic (threefold) stages [see III.4 and VII.1]. The resulting 'compound synthetic integration' brings us to the very heart of Kant's conception of reason's architectonic unity. It should come as no surprise, then, to find that this operation involves the systematic interrelationships between twelve components (4x3=12). The preliminary table in Kt1:95, which I shall call the 'Table of Logical Functions' [see Ap. VII.F] turns out to be a 'clue' not just to the structure of the Table of Categories in Kt1:106, but also to the formal structure of each of his Critical systems in its entirety! It will be of utmost importance, therefore, to apply the symbolic apparatus we have developed for analytic and synthetic operations to this 'twelvefold compound relation' (12CR), and so also to plot the twelve components onto a diagram which can be used in Part Three as a model for each of Kant's systems. The model as presented in its abstract form in this section belongs to systeml; applying it to the three Critical systems should enable us to discern precisely where each element belongs in relation to all the others in a given system.
Applying a simple synthetic integration to each member of a 2LAR can be represented symbolically simply by appending a third term (either +, - or x) to each two-term component. In this way the synthesis which gives rise to each component in the analytic relation is explicitly represented. The twelve new components are listed on the following page [see Table III.5] in columns of synthetic relations and rows of analytic relations, beginning with the negative and proceeding to the positive.
This 12CR specifies the formal structure of many groups of concepts or
Table III.5: Derivation of 12CR from 2LAR and 1LSR
real objects which are related in a highly systematic manner. This can be exemplified by defining the components in Figure III.5 so that, with a slight rearrangement of the columns, it becomes a concise statement of the traditional 'four syllogistic figures' [see Table III.6]. (Kant discusses these in Kt14, where he argues that only the first figure is 'pure', the other three being 'mixed' [55-6(89-90)].) First, replace all the components in the - row with 'P"M', all those in the + row with 'S"M', and all those in the x row with 'SÆP'. (These letters are used in S14:84-86 to represent the subject-predicate relations composing the three steps in a syllogism.) Then, stipulate that the direction of the arrow between each pair of letters in the + and - rows is determined by the two-term analytic component labelling each column: the first term determines the - row and the second the + row; a - indicates that the arrow points to the right and a + indicates the arrow points to the left. As a result, we can see that this basic building-block of traditional formal logic exhibits precisely the same twelvefold pattern as Kant intends his Table of Categories and other twelvefold tables to exhibit.
Correlating Kant's various twelvefold tables with this formal description
Table III.6: The Four Syllogistic Figures as a 12CR
of 12CR can be a helpful tool for determining the extent to which he succeeds in organizing his thought according to a consistent pattern. His Table of Logical Functions in Kt1:95, for instance, can be directly correlated with the components in Table III.5, as follows:
Kant's Table of Logical Functions as a 12CR
In order to demonstrate the legitimacy of this table, Kant should have described more explicitly how quantity, quality, relation and modality are related according to a 2LAR. As we saw above, he provides enough information about the application of the categories as principles to enable us to describe in full the nature of their second-level relation [see Figure III.4]. Unfortunately, he makes little effort in Chapter I of the Analytic of Concepts to explain why just four functions of thought belong to this table, or how they are interrelated to form an exclusive whole. In the process of describing his formal 'clue' [see note III.17] he does, however, provide several paragraphs describing how the terms listed in each column in Table III.7 are related according to 1LSRs [Kt1:95-101,111-3]. His exposition could be used to assess, and perhaps even revise, the way I have correlated the symbols with his theory, or conversely, the apparatus provided here could be used to detect shortcomings in his exposition. (For example, in Kt1:322 Kant associates 'matter'"i.e., the conditioned"with the universal and 'form' with the particular. Since I have adopted the convention of associating matter with -, I have therefore labelled the row of categories corresponding to the 'conditioned' with a -, even though this means 'affirmation' and 'negation' correspond, paradoxically, to - and +, respectively.) But this is not the place to discuss the adequacy of Kant's Table of Logical Functions [see Ap. VII.F]. My purpose in this section has not been to determine the extent to which Kant accurately followed these architectonic patterns"that will be one of the central aims of Part Three"but rather to explicate just what those patterns are.
Finally then, in order to complete this task, I will construct a geometrical model which can serve as a standard map of a 12CR. Perhaps the best model would be a regular dodecahedron, since each component in Table III.5 could be mapped onto one of the vertices. However, in light of Kant's apparent preference for circular models [see I.3], a circle divided into twelve equal arcs will be more suitable. After constructing a circle around the cross in Figure III.3, we can place each synthetic component (i.e., each component containing an x) on its appropriate pole (as determined by its first two terms), with the other two components of the 1LSR positioned equidistantly in the preceding quadrant (once again assuming a clockwise development beginning with the negative). This results in the following comprehensive model of the architectonic form of systeml, based on the logical structure of a 12CR.
Figure III.6: The Crossed Circle as a Model of 12CR
The circle itself represents the dynamic connection"hence the arrowheads "between the twelve components which compose the progression of four sets of simple synthetic relations, whereas the axes of the cross represent the static connection between the four (logically) primary components which compose the second-level analytic relation. The distinction between the cross and the circle thus represents the distinction between the form of general logic and general logic itself (which is in turn the form of transcendental logic) [see III.2]. Just as general logic is synthetically constructed on the 2LAR framework, so also transcendental logic is synthetically constructed on the 12CR framework of general logic.
4. Formal Logic as a Pattern for Kant's Transcendental System
We saw in III.2 that Kant's conception of logic is based on a fundamental distinction between its formal (general) and material (transcendental) manifestations. Of all the distinctions in Kant's philosophy, this distinction between form and matter is one of the most pervasive, for it can be applied to virtually every aspect of his System. He says the concepts of form and matter 'underlie all other reflection, so inseparably are they bound up with every perspective of the understanding. The one [matter] signifies the determinable in general, the other [form] its determination' [Kt1:322t.b.; s.a. Kt19:389-90]. Mapping this fundamental distinction onto the various models developed in III.3 will not only help to clarify the different ways Kant most often uses it, but will also provide some helpful clues as to how the maps themselves can be used in interpreting Kant. Labelling the models is actually quite simple, since the terms 'form' and 'matter' can in each instance be substituted (rather arbitrarily) for the logical symbols + and -, respectively, so that 'matter-form-synthesis' can replace, when appropriate, the less familiar 'conditioned-condition-unity' as the principal description of a 1SLR. This yields the four diagrams given in Figure III.7.
These four maps provide both a summary of III.3 and a transition to Parts Two and Three. For it is only when these patterns in general logic are used as forms for patterning the material discussed by the transcendental logician that the unique 'Copernican' Perspective of Kant's System comes into full view. From the Perspective of general logic, the four sets of three moments or 'steps' in a 12CR can be seen to fulfill parallel functions within their respective analytic quadrants, or 'stages': they are related to each other as matter, form and synthesis. However, when Kant applies this twelvefold pattern to the interpretation of experience in general, and so views it from the Perspective of transcendental logic, he is regarding all the steps as 'formal conditions' imposed by the subject on the object which awaits its conditioning. (Hence, - precedes + in Kant's version of synthetic integration.) In this Copernican sense, therefore, it is accurate to characterize the mind as 'a native faculty of forms' [W5:154] and Kt1, or any other system constructed according to this pattern, as a 'theory of form' [P8]. This is a legitimate description of the elements proposed in each of Kant's systems, when 'form' is understood
(d) Compound (Analysis and Synthesis)
Figure III.7: The Form-Matter Distinction
in the context of transcendental logic, even though our investigation of their relations has revealed that they are not all formal after all, when 'form' is understood in the context of general logic. But in any case, there is no justification for England's claim that Kant views 'epistemology as a species of [general] logic' [E3:7], or that his transcendental logic 'is, in fact, ultimately subversive of the traditional [general] logic' : the two are fully complementary, with the latter serving as the pattern for the former.
Figure III.6 specifies the architectonic form of each of the three systems in Kant's Critical philosophy. Their content will be revealed in Part Three when we examine how these general forms are applied to experience as transcendental forms. If the patterns discussed in III.3 accurately reflect Kant's understanding of reason's architectonic structure, then we should expect to find within the pages of all three Critiques, as well as Kant's other systematic works, numerous theories which give content to this formal mold. For one of the gravest errors in interpreting Kant is to suppose that because Kt1 is 'Kant's principal work' all 'his other writings are ... superfluous, or may at least be considered as commentaries' [see note I.1]. To guard against this error, and at the same time to prepare for interpreting the content of Kant's System, it will therefore be helpful to conclude Part One by investigating how Kant's architectonic can be used to determine the logical relationships between his major philosophical writings. This will provide us with a context without which the details of the System developed in these works would threaten to overwhelm us.
As we saw in II.4, one of the basic architectonic divisions in Kant's System is that between the three Critiques [cf. Figure II.1]. In Kt7:171-9, 195-7 Kant clearly explains the relation between these works in terms of a 1LSR. He begins by distinguishing between 'two parts' in the proper 'division of philosophy': 'a theoretical, as Philosophy of Nature, and a practical, as Philosophy of Morals' . But he then points out that by this division 'a great gulf is fixed' between our empirical knowledge (or 'natural concept') and our moral activity (or 'concept of freedom') [175-6,195]. The purpose of Kt7, then, is to 'effect a transition' between Kt1 and Kt4, between the Critical examination of nature and of freedom, 'just as in its logical employment [i.e., from the theoretical standpoint in systemt] it [i.e., judgment] makes possible the transition from understanding to reason' [179,196; cf. Figure III.10]. The distinct standpoints which, as we saw in II.4, these three books adopt, correspond directly to the three questions which Kant says specify all reason's 'interests': 'What can I know?' (theoretical), 'What ought I to do?' (practical), and 'What may I hope?' (judicial) [Kt1:832-3]. All three Critiques employ a 'synthetic method' [see Ap. IV] to determine the transcendental conditions which can answer these questions concerning the various standpoints we can adopt to reflect upon human experience: Kt1 sets forth the foundation for empirical knowledge (i.e., 'nature'); Kt4 sets forth the foundation for moral action (i.e., 'freedom'); and Kt7 sets forth the foundation for purposive judgments (the 'transition' between nature and freedom). Taken together, the three Critiques constitute what we could call the Transcendental (or Critical) 'wing' of Kant's System of Perspectives, while the subject matters to which the standpoints refer constitute the Empirical 'wing'.
Unfortunately, the other major systematic works in which Kant adopts his three main standpoints are not as easy to classify as are the three Critiques themselves. The problem is that he does not usually explain how these other books work together with the Critiques to compose a single, integrated System. Fortunately, there are two exceptions, which together give us a much-needed clue as to how to classify the works whose position in the System is rather less clear. First, Kant leaves no doubt that Kt6 is the fulfillment of his long-standing plan to write a 'Metaphysics of Morals' to serve as the doctrinal correlate to Kt4 [see e.g., Kt1:xliii; Kt5:388; Kt7:170; K2: 10.93,382-3(Z1:59,119)]. However, in the same texts he also usually claims that a 'Metaphysics of Nature' is required to serve as the doctrinal correlate to Kt1 [s.a. Kt1:Axxi]. Yet he never published a book by this title. For reasons that will become clear below, I cannot agree with those commentators who claim that Kt9, which was left uncompleted at his death, was destined to be his Metaphysics of Nature. Instead, I believe Kt3 is the best candidate to fill this role in Kant's System. Although Kant explicitly distinguishes between Kt3 and the proposed Metaphysics of Nature in K2:382-3(Z1:119), he does say it is an 'application of it' which is intended to provide 'some concrete examples'. And although he says in Kt3:478 that the book is not 'properly' considered to be a part of 'transcendental philosophy', or to be the explication of a 'general metaphysics', he does refer to it as a 'metaphysics of corporeal nature' which does an 'indispensable service', thus suggesting its close affinity to the book he originally intended to write. Moreover, as Kant grew older he seems to have changed his mind about Kt3, coming to regard it as at least a partial fulfillment of his original plan. For he states unambiguously in Kt6:205(3; tr. Hastie) that Kt6 (which itself consists largely of examples and applications) 'forms a counterpart to [Kt3]'!
The second exception to the ambiguity over the placement of the works complementing the three Critiques is that Kt2 is clearly described by Kant as a simplified version of systemt, only adopting the 'analytic method' instead of the synthetic method of Kt1 [Kt2:263; cf. Kt1:395n]. Unfortunately, Kant never explains so directly the relationship between Kt4 and Kt5. Nevertheless, he does describe Kt5 in such a way as to suggest a direct correlation between the Kt1-Kt2 relationship and the Kt4-Kt5 relationship. Just as Kt2 provides the 'prolegomena' to any future metaphysics of nature, so also Kt5 provides the 'foundation' for any future metaphysics of morals [Kt5:391; cf. V4:114]. Moreover, Kt5, like Kt2, adopts the same standpoint as the Critique to which it corresponds, but is written in a more popular style. Kt5 starts from 'common rational knowledge of morals' , just as Kt2 'start[s] from the fact that ... synthetical but purely rational knowledge actually exists' [Kt2:276]. Kant even says that the first two sections of Kt5 'proceed analytically' [Kt5:392,445]; the third section proceeds synthetically only because it is a preview of Kt4. The fact that Kt5 was actually written three years before Kt4 does not preclude the possibility of regarding the former as the logical sequel to the latter. In Kt4:8 Kant does say that Kt4 'presupposes' Kt5, but he adds that it does so only in the sense that it provides some 'preliminary acquaintance' with some of the key concepts; 'otherwise it is an independent work.' Kant could just as well have written Kt2 before Kt1 for the same reason. Therefore, although the Kt1-Kt2 relationship is not identical in every respect to the Kt4-Kt5 relationship, there is ample justification for viewing the two pairs as fulfilling parallel roles in Kant's System.
If my placement of Kt3 and Kt5 in Kant's System is correct, then as far as the theoretical and practical standpoints are concerned, Kant has consistently followed an architectonic plan by writing one book from each of three Perspectives to develop the implications of each standpoint. From the above discussion we can see that the relationship between each set of three books, when considered together with the experiential subject matter which first defines each standpoint, forms a 2LAR, as depicted in Figure III.8. Proceeding analytically from the Empirical Perspective (thus reversing the arrows on the model in Figure III.3), we find that the first task in the elaboration of these two systems
is to adopt the Transcendental Perspective in order to criticize reason's interpretation of the field of human experience under consideration. Next, the results of this Critique are expressed in a simpler form, by using the Logical Perspective's analytic method. This can then serve as the foundation for constructing the full-fledged metaphysics proper to the standpoint in question [see Kt1:878]. Such explicitly metaphysical works serve to complete the circuit of philosophical explanation by shedding new light, from the Metaphysical Perspective, directly upon the details which arise out of our experience.
The remaining question, then, is whether or not an equivalent pair of books exists to complement Kt7 and its judicial standpoint. Our answer to this question should, I maintain, be affirmative. First of all, a proper interpretation of Kant's book on religion [Kt8], as we shall see in X.3, requires us to recognize that Kant wrote it not from the practical standpoint, as is so often assumed, but from the judicial standpoint. In fact, I will argue in Pq20 that Kt8 deserves to be regarded as itself a kind of 'system of religion', which is in several respects more important to the overall System than Kt7. Not only does the text of Kt8 contain many clearer and more obvious architectonic parallels to the first two Critiques than does Kt7, but it also provides a more suitable answer to the question 'What may I hope?' than the answer provided in Kt7, because it fits in more naturally with the general theocentric orientation of the entire System. That is why Kant says that in writing Kt8 'I have tried to complete the third part of my plan.' Furthermore, Kant's claim in Kt8:14(12), that in order to understand Kt8 'only common morality is needed, without meddling with the [Critiques]', is at least similar to his claims that Kt2 and Kt5 are simplified or popularized versions of their corresponding Critiques, even though they adopt the same standpoint. Hence, although I will argue elsewhere [see note III.23] that Kt8 adopts the synthetic method (whereas the method adopted in Kt7 appears to be more analytic than synthetic [see note IX.5]), there is a close enough parallel here to group Kt8 along with Kt2 and Kt5 as systematic sequels to the three Critiques.
What then about the final gap in the System? Does Kant provide us with a metaphysics written from the judicial standpoint? At first sight, this question seems to demand an unreservedly negative answer, in light of Kant's statement in 1790, at the close of the Preface to Kt7:
With this [i.e., Kt7], then, I bring my entire critical undertaking to a close.... It is obvious that no separate division of Doctrine [i.e., no Metaphysics] is reserved for the faculty of judgment, seeing that with judgment Critique takes the place of Theory; but, following the division of philosophy into theoretical and practical ..., the whole ground will be covered by the Metaphysics of Nature and of Morals. [170; s.a. Kt7i:205,207,242]
Nevertheless, Kant does give some hints, even in Kt7, that some third type of metaphysics might some day be possible. Just after saying there will be no metaphysics corresponding to Kt7 as 'a separate constituent part' of his System, he adds that such a system might be 'some day worked out under the general name of Metaphysic' (as opposed to the more specific names, Metaphysics of Nature and Metaphysics of Morals), and that if this were to happen, 'this edifice' would require Kt7 as 'the critical examination of its ground' . This seems to be Kant's first glimpse of the possibility of, as it were, a 'Grand Unified Theory' of metaphysics. But did he himself ever change his belief that such a project was unnecessary, if not impossible? Did he ever attempt to construct such a system himself?
There will probably never be a fully conclusive answer to these questions, since Kant died before completing the work he claimed would be the final and ultimate work of his entire System. Commentators vary greatly on their interpretation of just what kind of book Kt9 was to be; but I will argue at length in Pq20 that Kt9 is Kant's attempt at establishing the grand unification of metaphysics in general, as hinted in Kt7:168. That Kant intended Kt9 to be a constitutive part of his System is evident in his 1798 letter to Kiesewetter [K2:12.256(Z1:252)], where he says that with Kt9 'the task of the critical philosophy will be completed and a gap that now stands open will be filled.' Vleeschauwer accurately explains how Kant could view Kt9 in this way even though he had previously stated that Kt7 completes the final gap in his System: although the three Critiques establish 'an absolutely complete system of philosophy, in so far as form is concerned', a work such as Kt9 was still necessary in order to complete the System 'from the point of view of its content' [V4:178]"i.e., the doctrinal content which Kant associated with metaphysics [s.a. W17:175,198]. In Pq20 I will take this idea even further and argue not only that in Kt9 Kant attempts to unify Nature and Morals, but that he does so by constructing a Metaphysics of Religious Experience which forms the heart of what I call his 'Critical Mysticism' [see X.4]. This is significant because it implies a close connection between Kt8 and Kt9"just the sort of connection we would expect if these two works were intended to be related in the way Kt2 is related to Kt3, or Kt5 to Kt6.
Perhaps the major obstacle to this interpretation of Kt9 is the common assumption that this work was to be entitled Transition from the Metaphysical Foundations of Natural Science to Physics [see e.g., E2:ix], a belief which has led some to regard Kt9 as the long-awaited Metaphysics of Nature and thus as filling a gap in Kant's theoretical works. For instance, the latter view is expressed by Wallace when he says Kt9 was intended to become Kant's elaboration of 'the grand consummation of his system"the application of his abstract principles to construct a philosophy of nature' [W5:83]. In opposition to this view, I believe that when Kant told Kiesewetter in 1798 that he was then working on a 'transition ...', which 'must not be left out of the system' [K2:12.256 (Z1:252)], he was referring not to the title of Kt9, but to one of the several tasks Kt9 was to fulfill. From the text of Kt9 itself, it seems much more likely that Kant was experimenting with titles such as The Ideal of the Physical and at the same time Morally-Practical Reason United under One Sense Object, a title which would obviously place Kt9 beyond (or between) the theoretical and practical standpoints, and hence, firmly rooted in the judicial standpoint, as its doctrinal expression of the Metaphysical Perspective. Had his mental capacities held up for a few more years, Kant may well have completed his task in a way which would have supported even more explicitly the interpretation suggested here.
The above explanations of the role of Kt3, Kt5, Kt8 and Kt9 in Kant's System are inevitably somewhat conjectural (especially in the case of Kt9); nevertheless, they are sufficiently well-founded to merit a tentative acceptance, especially once we see how they can be used to construct a complete model of the overall structure of Kant's main writings. For the above interpretation suggests that the pattern which determines the structural relationship between the major works in Kant's System is a 12CR of a sort slightly different from that depicted in Figure III.6: it is a synthesis of three 2LARs (3x4=12). Each component of the basic 1LSR defined by the three standpoints is itself composed of a 2LAR corresponding to the one in Figure III.8. The structural form of the pattern which binds all the resulting components into a synthetic whole is determined by systeml, which Kant elaborates most completely in Kt10. Kt10 can therefore be regarded as one of Kant's major systematic works, and placed appropriately at the center of the model which combines Kant's ten major writings into one complete picture, as in Figure III.9. Comparing this model with the diagrams given in Figure III.7 reveals the following correlations: systemt, with its standpoint rooted in empirical knowledge, serves as the matter of the System; systemp, with its standpoint rooted in moral action, serves as its form; and systemj, with its standpoint rooted in purposive (i.e., aesthetic, teleological, religious, etc.) experience, serves as the synthesis of systemt and systemp. The interrelationships between all these books, as depicted by the arrows, give rise to more than just the sum of the parts; they constitute a complete formal description of the architectonic structure of Kant's System of Perspectives.
Not only is Kant's System as a whole structured according to this architectonic pattern, but in addition, as I have hinted at several points, each system is itself structured in this way. In Part Three we will investigate the extent to which each Critical system progresses synthetically according to the form of a 12CR, and analytically according to the four stages into which these twelve steps are categorized. By filling only a few minor gaps in Kant's exposition of these stages, we shall find not only that each is concerned primarily with a threefold synthesis of elements, but also that each of the twelve resulting steps can itself be established by a threefold argument (though it is sometimes admittedly obscure, and occasionally left undeveloped by Kant). Each of these arguments, as we shall see, essentially involves a synthetic movement from one form of the object to the next by means of an activity or 'formal condition' of the subject.
Without delving too deeply into Kt1, for instance, we can find a major fourfold division in the Doctrine of Elements, which corresponds to the structure of a 2LAR: viz., the fourfold division between the faculties of sensibility, understanding, judgment and reason, which is reflected in the Table of Contents by the sections generally known as the Aesthetic, the Analytic of Concepts, the Analytic of Principles and the Dialectic. This architectonic pattern is suggested in the opening sentence of the paragraph crucially placed at the end of the Doctrine of Elements, where Kant summarizes the stages through which his theory of knowledge passes: 'Thus all human knowledge [i.e., all judgment] begins with intuitions, proceeds from thence to concepts,
Kant's Ten Major Systematic Works as a 12CR
and ends [i.e., once judgment has taken place] with ideas' [Kt1:730]. He goes on to refer to these as the 'three elements' of knowledge which a person 'possesses a priori'; but when the reality of which they are elements (i.e., judgment) is considered in its necessary relation to these elements, the total number turns out to be four. This is consistent with Kant's practise of listing understanding, judgment and reason as the three 'cognitive faculties' [see note II.23 and Figure VII.2] and so also with his claim that logic 'deals with concepts, judgments and inferences' [Kt1:169]"intuitions being pre-logical and inferences being the operation through which ideas are produced. All four types of representation produced by the four stages in systemt are listed even more clearly (though not in order) in Kt7:248: '... a pure concept of understanding, ... an intuition of sense; ... a concept of reason, ... a concept of judgment ...' These four faculties and their respective modes of representation can be mapped directly onto the 2LAR cross given in Figure III.3, as follows:
Figure III.10: The Four Primary Faculties in Systemt
Moreover, the same four stages lie behind the organization of the Doctrine of Elements in Kt4 (where the first stage is given not by intuition but by freedom), as well as that in Kt10 (where the first stage is excluded, since formal logic always abstracts from all particular content).
Before interpreting in Part Three the arguments within these various stages of Kant's three Critical systems, it will be necessary to examine in Part Two Kant's basic epistemological assumptions. In particular, three issues relating to the underpinnings of Kant's System must be addressed: (1) What is the precise nature of the four perspectives (the transcendental, logical, empirical and hypothetical) which operate in each of the three systems? (2) What is the justification for Kant's overall Transcendental Perspective? and (3) In just what way do these perspectives alter the way in which the object of inquiry, must be viewed at different points in a given system? In Part Two one chapter will be devoted to answering each of these questions in turn. Thus, having now sufficiently outlined in Part One the general structure of Kant's System, let us turn our attention to its epistemological underpinnings; for this will fully prepare us to interpret in Part Three the transcendental elements of the System.
 A10:52. Allison continues: 'But considering objects in this relation is precisely what is meant by considering them as appearances; while considering them apart from this relation is what is meant by regarding them as things in themselves.' He then explains that this 'simply is the Copernican revolution in philosophy' .
 Kt1:31-732. This is one of many examples of Kant's use of the word 'transcendental' in the broadest sense discussed in II.4, in which case it does not refer to one of his four technical perspectives [see IV.3], but acts almost as a synonym for 'subjective' [Kt1:397] or, as we shall see in IV.2, for a similarly broad sense of 'a priori'; so it here describes the status of the whole content of the system elaborated in Kt1. (Another good example is when Kant later says: 'Transcendental philosophy is the system of Ideas in an absolute whole: God, the world, and the being in the world which is gifted with free will' [Kt9:21.80(V3:1026)].) The Transcendental Doctrine of Elements, therefore, includes within it reflections concerned not only with the transcendental perspective, but with the logical, empirical and hypothetical perspectives as well. The Critical philosophy can be called 'Transcendental Philosophy' in this broad sense because the perspective with which it begins, and in the light of which every subsequent perspective must be viewed, is the transcendental [see II.4].
 See e.g., W21:191n. Yovel, after rightly describing 'architectonic' as a teleological term referring to 'goal-oriented activity' [Y3:14], explicitly denies that reason's architectonic presents itself in a fixed form [24-5]. Instead, he thinks the subjective character of the Copernican Perspective requires reason's architectonic structure to be different for every individual knowing subject! Swing, by contrast, begins by clarifying the importance of Kant's distinction between formal and material (i.e., transcendental) logic [S21:vii; see below], and then offers a detailed analysis of how Kant derived his various logical distinctions. Unfortunately, he still fails to give a clear explanation of the overall structure of the logical patterns Kant had in mind. And this leads him to assert that 'Kant's Table of Categories is far from complete' .
 See e.g., Kt19:393. Kant says in K2:11.35(Z1:139) that the logical is a relation 'having to do with the manner of representation', whereas the real is a relation 'in the object itself'. In A7 Allison does a good job of explaining the importance of this distinction in Kant's philosophy.
 R11:2; s.a. Kt1:171-2. Rotenstreich points out that Maimon, a contemporary of Kant, 'argues that there holds a relation of mutual interdependence between the forms of Formal Logic and those of Transcendental Logic: the forms of Transcendental Logic presuppose, for their possibility, the forms of Formal Logic; while the latter presuppose, for their actuality, the forms of Transcendental Logic' [R11:16]. Kant would support the same position.
 Many of Kant's other books are divided along similar lines, as is exemplified by his other primary systematic works: Kt2 and Kt5 are divided into three parts, while Kt3 and Kt8 are divided into four parts [s.a. Kt6:413]. (That he had in mind a specific architectonic pattern when he made such divisions is suggested in Kt3: 473-6, where Kant explicitly relates the four sections of Kt3 to the fourfold division of the categories.) Furthermore, Kt9 is divided into twelve parts, a number the significance of which will become evident in III.3.
 That Kant was well aware of the special status of the number twelve is clearly indicated by his discussion of the 'mystique of numbers' in Kt66:194-6, where he focuses attention on the supposed 'mystical significance' of the number twelve (e.g., in the zodiac), and asks 'what interest have we in making this a privileged number?' Unfortunately, instead of answering this question by referring to its role in the structure of architectonic logic, he passes off the issue as one of the 'puerilities [into which] man sinks...when he lets sensibility lead him by its guiding rope!' As I have demonstrated in Pq12 and Pq13, however, Kant had more than a passing interest in mysticism, though he was always reluctant to admit it publicly. That relationship between this interest and his overall purpose in constructing a philosophical System will be explained more fully in Pq20 [s.a. X.4].
 The latter quote is added by Zweig in Z1:109n. Kant makes a similar suggestion in a 1791 letter to Beck [K2:278(Z1:179-80)], where he suggests that his 'new way of presenting abstract concepts may itself yield something analogous to Leibniz's universalis characteristica combinatoria. For the table of categories and the table of ideas...are after all enumerated and as well defined in regard to all possible uses that reason can make of them as mathematics could ask, so that we can see to what extent they at least clarify if not extend our knowledge.'
 Many of Kant's divisions are indeed threefold. However, their importance can be over-stressed, as when Caird lets his Hegelianism determine his interpretation to the extent that he uses the triadic pattern as the ultimate key to interpreting the entire Critical philosophy [s.e. C1:1.148,424-5]. Moreover, as is evident not only from our analysis of the structure of the three Critiques, but also from Kant's own comments in the remainder of the footnote [Kt7:197n], twofold and fourfold patterns play just as vital a role in the architectonic as do threefold patterns. This will become even more clear in the remainder of this section.
Kt1:110,386-7,695; s.e. Kt10:147-8(148). In Kt19:388n we find Kant already suggesting that 'synthesis is either qualitative, a progression within a series of subordinates from the ground to the grounded, or quantitative, a progression within a series of co-ordinates from a given point through its complements to the whole.' Likewise, 'analysis' can proceed either 'from the grounded to the ground' or 'from a whole to its possible or mediate parts'.
Kant himself often distinguishes between the'positive'and'negative'ways of viewing a given concept. No doubt the most obvious example is his distinction between the positive and negative 'noumenon' in Kt1:307. But there are many others as well, such as: Kt39:442(104),452(127),453(131),465-6(156-7),484 (195); Kt65:49; Kt66:passim. Moreover, he occasionally uses the '+' and '-' signs to refer to this distinction [see note III.12].
Kant himself uses the sema thematical symbols (usually with the letter A, but often specifying both + and - values) in this logical sense on a number of occasions [see Kt1:488; Kt6:384; Kt8:22-3n(18n); Kt10:104(109-10),147(148); Kt16:172-7; Kt66:230]. His most important discussion of their use in such contexts comes in Kt16, where he discusses the 'polarity' between 'positive and negative' in numerous different ways, including its application to magnetic and electrified bodies [185-6(47)]. He begins by distinguishing between 'logical opposition' and 'real opposition', noting that in the former, as in mathematics, an object qualified as + or - is positive or negative in an absolute sense, whereas in the latter, as Wallace explains, 'two statements are equally positive, and only distinguished as positive and negative when brought into relation with each other' [W5:125; s.a. 126-30 and Kt1:328-9,488]. Whereas a logical opposition always requires both a negative and a positive component, in a 'real opposition both predicates are positive' [Kt16:172(46)]: 'Disgust is as positive as appetite; it is positive displeasure' [196(48)]. Goldmann refers to this essay, with its emphasis on the positive (or 'actual') status of real oppositions, as 'one of the earliest expressions of what was to become with Hegel the theory of dialectical contradictions' [G10:72].
Throughout this and subsequent chapters such symbols will be used to represent 'real' oppositions, from which all differences in the content of the real have been abstracted. As such, they actually refer to a capacity for relations of a certain type to hold between real objects, objects which in themselves are neither + nor -. For this reason I refer to these in Pq18:1.3 as 'forms of relation'.
 I use the word 'level' to refer to different degrees of complexity within a given type of logical operation. Thus, as will become evident shortly, my use of 'level' is analogous to the use of the word 'power' in algebra, where numbers of vastly different sizes can operate according to the same rule as long as the base number remains the same and only the power (cf. the 'level') changes.
 In Pq4:277 I called these components 'variables', and added a footnote suggesting that a better name would be 'expressions' (which was the term I used in some earlier drafts of this book). However, the misleading connotations of these two titles are avoided by the word 'component', which refers more precisely to a primary (self-sufficient) part of an analytic or synthetic relation. The word 'term', incidentally, is used to denote any individual '+', '-' or 'x' which is used to construct one component in an analytic or synthetic relation on any level.
 The purpose of this and other such maps is to make it easier to 'orient' ourselves in a given 'logical space', much as a compass enables us to orient ourselves in physical space by fixing the positions of four interrelated poles. In his 1768 essay, 'Concerning the Ultimate Foundation of the Differentiation of Regions of Space', Kant distinguishes the 'horizontal surface', which enables us to differentiate between objects which are 'above and below', from the two 'vertical surfaces', which enable us to differentiate between the 'right and left half' and between the 'front and back sides' of an object [Kt52:379]. Later, in Kt20:134-6(294-6), he offers an analogy between 'geographical', 'mathematical' and 'logical' orientation much like the one suggested here [see I.3].
 See e.g., Kt4:39-40; Kt6:413. Kant usually arranges such tables in the shape of a cross, but with the first and fourth components on the vertical axis and the second and third on the horizontal axis. As I explain in Pq18:2.2, this sets up two pairs of 'contradictory' oppositions (viz., ++ vs. -- and +- vs. -+) whereas the model I have chosen to use assumes 'polar' opposition (viz., ++ vs. +- and -- vs. -+). This difference of position is relatively insignificant, however, since the order he assigns to the four analytic components is always identical to the order specified by a clockwise reading of Figure III.3.
 Kt1:91-116. The often misunderstood purpose of this section (i.e., of Chapter I of the Analytic of Concepts in Kt1) is explicitly to reveal the a priori 'clue' as to how the categories can be discovered, not to prove Kant's choices are all necessarily correct. The latter is the task of the Analytic of Principles. The clue Kant gives in the former chapter is that the number and ordering of the categories must be determined a priori, not a posteriori in the manner of Aristotle's list of categories [106-7]. Kant makes it quite clear that it is the formal structure of any table of categories which interests him [see e.g., 110] when he excuses himself for not including 'the definitions of the categories' by stating: 'The divisions are provided; all that is required is to fill them' [108-9]. Ellington defends the apriority of Kant's method for choosing the categories in E2:148-9n against several critics who mistakenly charge Kant with collecting them in a 'haphazard' a posteriori way. Moreover, he argues in detail that Kant's table is in fact both correct and complete [150-73; s.a. Ap. VII.F].
 Of course, the same 2LAR components could be mapped onto the same figure according to different rules, or onto an altogether different figure exemplifying the same structure [see Pq18:2.1-4]. For our purposes there is no need to explore more than one paradigm in great detail, so a single example of an alternative form will suffice. But regardless of how we arrange the model, we must keep in mind that every 2LAR arises out of two opposing 1LARs"a connection Kant himself often explicates. In Kt6:398, for example, he maps two sets of 1LARs onto opposite sides of a rectangle's exterior, and maps the four resulting 2LAR components onto the corresponding interior vertices, thus producing the following model:
Kant uses a similar model in Kt6:240(26), but Hastie unfortunately replaces Kant's diagram with a table (an error Ladd rectifies in his translation of Kt6). Likewise, Kant uses a rectangle in Kt66:290(156) to map the relations between four types of human temperament ('Sanguine', 'Melancholy', Phlegmatic' and 'Choleric'), though in this case he does not specify the two 1LARs which give rise to such a 2LAR. That Kant was not entirely aware of the architectonic structure of such distinctions is evidenced by the fact that he occasionally describes them incorrectly. In Kt66:330, for instance, he lists the 'four conceivable combinations of power with freedom and law', when in fact such a combination of three 1LARs always gives rise to a third-level analytic relation, which contains eight components (23=8). Kant's difficulties in coping with the architectonic which he loved so much may explain why he confesses in Kt6:218n: 'The Deduction of the division of a system, i.e. the proof that the division is complete and final...is one of the most difficult conditions which the architect of a system has to fulfill.'
 Instead, he normally gives only hints. In Kt3:523, for example, he describes the 'quality of matter' by distinguishing between the 'attractive force' (-), the 'repulsive force' (+) and 'the limitation of the first force by the second' (x). Even in planning his lectures he often made use of such 1LSRs: in Kt36:312-3(256-7), for instance, he announces a three-part lecture series in which the third part will consider 'the interaction of both of the...forces' discussed in parts one and two.
 Seee.g.,Kt1:189-97.AristotlepointsoutasimilardistinctioninA15:1112bwhen he says what is 'last in the order of discovery [i.e., analysis], is the first in the chain of causes [i.e., synthesis].' He adds: 'what comes last in the analysis comes first in the [synthetic] process as a result of which the subject investigated is brought into being.' As we will see in III.4 and elsewhere, Kant also acknowledges this reciprocal relationship between analysis and synthesis by, for example, adopting a synthetic method in Kt1 and then an analytic method to describe the same system in Kt2.
 Thesamemodelcould also be produced by plotting the four analytic components counterclockwise around the circle and viewing each set of synthetic components as analytic abstractions from the preceding analytic component. To do so would be to follow the analytic (or regressive) method [cf.VI.4 and Ap.VI], which is also dynamic, insofar as it still depends on simple synthetic integration for its structure [cf. H4:xl]. When this logical method is used to pattern our thinking, Kant says, it 'serves to make clear concepts distinct' [Kt10:63(69)].
InF5:294-5Förster,whounfortunately fails tomentionthislattertext,discusses the ambiguities surrounding the place of Kt3 in Kant's System. He provides an impressive list of interpreters who have debated the issue  and points out that 'to the present day there is no agreement as to whether the concept of motion in [Kt3] is a transcendental or a metaphysical concept' . Aside from Kant's clear statement in Kt3:478 that Kt3 is not 'properly' transcendental, the very title of this book indicates that he at least intends its content to be not transcendental (not the 'Foundations of the Metaphysics of Natural Science'), but metaphysical (the 'Metaphysical Foundations of Natural Science'). Unfortunately, Förster seems to assume that if we deny a transcendental status to Kt3, then it can have no place in Kant's System. But this ignores the fact that Kant's System extends beyond the three Critiques to metaphysics itself [see X.1]!
 Kt7 also has a theocentric emphasis [see IX.3.B],though it becomes explicit only in a lengthy Appendix [Kt7:416-85]. The importance of the theocentric orientation of Kant's System will be discussed briefly in Chapter X, and demonstrated more thoroughly in Pq20.
 K2:11.414(Z1:205). Indeed, when Kant lists his three questions of pure philosophy in this 1793 letter to Stäudlin, he adds '(philosophy of religion)' after the third question to specify it as the third 'field [i.e., standpoint] of pure philosophy' [s.a. Kt10:25(29); Kt1:833]. As Webb puts it, Kant makes a 'threefold division of the interests of human reason into the scientific, the moral, and the religious' [W13:2].Kant hints at such a correlation of religion with systemj asearlyas 1764, when, in an essay on aesthetics, he refers to 'the doctrines of religion'as the true complement to metaphysics and morals [Kt57:246n(63n)].
This suggestion is unfortunately not considered by Despland, who has trouble fitting Kt8 into Kant's System, even though he recognizes that it provides Kant's most suitable answer to the question 'What may I hope?' [D3:158; cf. note III.24]. He argues quite correctly that Kt8 is not 'a fourth Critique', nor does it 'find a place...among the doctrinal works' "i.e., the works written from the Metaphysical Perspective [e.g., Kt3 and Kt6]"but he fails to see any other alternative. Gregor, by contrast, posits a rough parallel between Kt3, Kt6 and Kt8, on the grounds that one of the Critiques 'must precede' each of these works [G17:xxvii]. Although this is correct as far as it goes, she unfortunately connects Kt8 with Kt4 rather than with Kt7, fails to distinguish between the ways in which Kt4 and Kt5 must precede Kt6, and neglects mentioning Kt2 altogether.
 Förster defends such an interpretation when he says Kt9 is the only book in which 'Kant succeeds in uniting theoretical and practical reason into one system, namely in the new concept of transcendental philosophy as Selbstesetzungslehre, or the system of the ideas of reason' [F5:302]. Unfortunately, he neglects the principle of perspective and portrays Kant as giving up in Kt9 his mature, Critical view of the nature of philosophy as synthetic and returning to his earlier view of philosophy as analytic [298-9]. Förster quotes from Kt9:22.130: 'Metaphysics analyzes given concepts; transcendental philosophy contains principles of synthetic a priori judgments and their possibility.' Yet this marks no change whatsoever in Kant's mature view! Kant consistently regards transcendental Critique (the 'metaphysics of metaphysics', so to speak) as a synthetic task which paves the way for the analytic task of constructing particular metaphysical judgments [e.g., Kt17:286; Kt2:270-1; s.a. B28:142]. Whenever Kant says metaphysics contains synthetic a priori judgments, he is referring either to the 'intention' of (false) speculative metaphysics [e.g., Kt1:18] or to the Transcendental foundation of (true) analytic metaphysics [Kt2:273-4]. The fact that Kant plays down the synthetic in favor of the analytic in Kt9 is therefore evidence not of a change in his concept of the nature of philosophy, but of a perspectival change from the Transcendental to the Metaphysical Perspective in his System [see Figure III.8].
Since each of Kant's other works [Kt11-Kt66] can also be regarded as presupposing one of the three basic standpoints specified in Figure III.9, I have organized them in this way in the Bibliography.
 The fact that Kant does not give each of these sections an equal status [see Table III.1] is surprising, to say the least, since he openly correlates each with a distinct faculty of knowledge. It must be taken as an example of his incomplete application of his architectonic plan [see note VII.8].
 Kant himself calls attention to this 'analogy' between the structure of Kt1 and that of Kt4 in Kt4:89-91, and hopes we 'will get a certain enjoyment out of such comparisons, for they correctly occasion the expectation of bringing some day into one view the unity of the entire pure rational faculty (both theoretical and practical) and of being able to derive everything from one principle' [90-91; cf. 16]"perhaps another early allusion to Kt9. Likewise, as Kant stresses throughout the Introduction to Kt7, the third (judicial) system in his System cannot be fully understood without a clear recognition of its architectonic parallels with its two predecessors. Enhancing the potential for recognizing such parallels has been one of the chief goals of this chapter.
 Kt10:91(96). The four sections of Kt3 and, as I shall demonstrate in Pq20, those of Kt8, follow a similar pattern. Likewise, Humphrey discerns four 'major divisions' in Kt69 [H22:17-8].