The Architectonic Form of Kant's Copernican System

 

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

 

 

 

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.[1]

 

      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,[2] 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.[3] (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.[4] 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.[5] 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;[6] 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).[7] 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.'[8] 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' [196], 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.'[9] 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.[10] 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'.[11] 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.[12] 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'[13] 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':[14] ++, +-, -+ 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[15]

 

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.[16] 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',[17] 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' (+) [199]. Thus, the former pair 'allow of in­tuitive certainty', whereas the latter pair 'are capable only of a merely discursive certainty' [201]. 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-

 

  

 

Figure III.4:

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.[18]

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.[19] 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.[20] 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 th