The Myth of Completeness: Twelve Categories, Redundancy, and the Procedural Gap in Active Synthesis

Die Kantische Philosophie ist die Basis und der Ausgangspunkt der neueren deutschen Philosophie. Von ihr datiert sich die deutsche Philosophie.

— Hegel, G. W. F. Lectures on the History of Philosophy (Hegel, 1995)

When tracing the lineage of Western philosophy, three names stand out: Plato, Aristotle, and Immanuel Kant. If Plato established the foundations of metaphysics through the Theory of Forms and Aristotle built the architecture of rational inquiry with syllogistic logic, Kant integrated the fractured spirit of modernity into a critical synthesis and expanded the intellectual horizon of modern philosophy.

The late eighteenth century—the historical milieu of Kant’s critical philosophy—was an age of intense conflicts: continental rationalism versus British empiricism, religious faith versus scientific reason. His philosophy arose in response to a historical imperative to overcome these divides. In a world that felt fragmented, he aimed to restore the dignity of human reason and to mediate among conflicting values. In this spirit, the present essay honors Kant’s monumental achievement and calling. As Hegel notes in the Lectures on the History of Philosophy, it is hardly an overstatement to regard Kant as the starting point for both modern and contemporary philosophy.

However, the enormous scope and fundamental nature of the task he faced meant that some theses are presented at times dogmatically or programmatically, without a fully detailed argument. When setting limits to reason and charting a new path for metaphysics, Kant occasionally relied on bold intuitions; as a result, he left behind several points that require closer examination.

In particular, the claimed systematic completeness of the twelve categories presented in the Transcendental Logic warrants renewed examination. I consider whether this completeness results not from a logical necessity but from the architectonic demands of constructing a system. The four-by-three scheme—Quantity, Quality, Relation, and Modality—is so perfectly symmetrical that it appears less as the discovery of an a priori structure than as a product of theoretical design. Therefore, one might question whether the resulting table of categories—based on the logical forms of judgment and closely aligned with the Aristotelian tradition—truly reflects the necessary structure of human reason.

With this in mind, I disagree with Kant’s claim that the table of twelve categories is complete and uniquely necessary. I revisit the core argument of the Critique of Pure Reason at three key points: (1) the justification for, and completeness of, the twelvefold scheme; (2) redundancies among, and potential reductions of, specific categories; and (3) a procedural gap regarding the active synthesis of understanding (Verstand) that the Transcendental Deduction does not sufficiently explain.

Genuine philosophical dialogue involves critical reflection rather than blind acceptance. Confronting Kant’s arguments with my own full intellectual resources—even when that means challenging a master—is, I believe, the highest form of philosophical respect.

Critique of the Table of Categories

From Judgment-Forms to Categories: Unproven Completeness

In such a way there arise exactly as many pure concepts of the understanding, which apply to objects of intuition in general a priori, as there were logical functions of all possible judgments in the previous table: for the understanding is completely exhausted and its capacity entirely measured by these functions. Following Aristotle we will call these concepts categories, for our aim is basically identical with his although very distant from it in execution.

— Critique of Pure Reason, Cambridge pp. 211–212 (A80/B106) (Kant, 1998)

Kant derives the categories—the pure concepts of the understanding—from the forms of judgment in general logic (A70/B95) and systematizes them in the Metaphysical Deduction. He then contends, in the Transcendental Deduction, that by showing the categories to be conditions of the possibility of experience, their objective validity (quid iuris) is secured (A80/B106; A76–A83/B102–B109; B130–B169). However, these two-step procedures do not fully vindicate the twelvefold system.

To begin with, the "Metaphysical Deduction" claims to derive the categories from the logical table of judgments. Kant holds that the logical functions of judgment—e.g., universal, particular, and singular judgments—share a common root with the transcendental functions of the understanding that unify the manifold of intuition. Accordingly, to each form of judgment there corresponds a category (Unity, Plurality, Totality, etc.) (B105). For this claim to be persuasive, however, two premises would have to be established: first, that the table of judgments is complete and unique; and second, that the functions of formal logic stand in a one-to-one correspondence with the transcendental functions operative in cognition. Kant argues neither point with sufficient rigor. Hence, the elegant 4×3 symmetry seems to be a product of rational architectonic construction rather than a discovery. In the end, the "Metaphysical Deduction" leaves unanswered the question “Why must there be precisely these twelve?” and offers only a hypothetical list of candidate categories.

A manifold that is contained in an intuition that I call mine is represented as belonging to the necessary unity of self-consciousness through the synthesis of the understanding, and this takes place by means of the category. This indicates, therefore, that the empirical consciousness of a given manifold of one intuition stands under a pure a priori self-consciousness, just as empirical intuitions stand under a pure sensible one, which likewise holds a priori.

— Critique of Pure Reason, Cambridge pp. 253 (B144–B145) (Kant, 1998)

The "Transcendental Deduction" argues that all experience necessarily presupposes a rule-governed synthesis, and that these rules are none other than the categories in general. For the manifold of intuition to be unified in a single consciousness as “mine,” a synthetic unity of self-consciousness—the transcendental unity of apperception—is required (B144–B145), and that unity is possible only through the categories. Hence, the categories are conditions of the possibility of objects of experience as such. What the Transcendental Deduction secures, however, is only the general thesis that the categories are indispensable for the possibility of experience; it does not establish the uniqueness or completeness of any determinate twelvefold list. Put differently, it vindicates the transcendental necessity of the categories while remaining silent on why the list should have precisely this number and architectonic arrangement—an unresolved quid facti.

In sum, Kant’s elaborate argumentative edifice successfully grounds the necessity of categories in general, yet the completeness and uniqueness of the twelvefold inventory itself remain unproven.

Reassessing the Table: Infinite Judgment, Limitation, and Redundancy

In a transcendental logic infinite judgments must also be distinguished from affirmative ones, [...] If I had said of the soul that it is not mortal, then I would at least have avoided an error by means of a negative judgment. Now by means of the proposition "The soul is not mortal" I have certainly made an actual affirmation as far as logical form is concerned, for I have placed the soul within the unlimited domain of undying beings.

— Critique of Pure Reason, Cambridge pp. 206–207 (A72–A74/B97–B99) (Kant, 1998)

The insufficiency of the justification for the table of categories becomes clear when one turns to the individual entries. In particular, Limitation—one of the categories of Quality—fails to be cleanly distinguished from Negation. Kant maintains that an infinite judgment locates the object within an unrestricted field of possible beings. That is, an infinite judgment of the form “$a$ is non $R$,” with respect to a predicate $R$, is read as membership in the complement class: $a \in \neg R$. Yet the force of this construal shifts with the choice of formal notation. If the corresponding negative judgment is taken as the Negation of the entire predication, we obtain $\neg(a \in R)$, which does not, by itself, positively place $a$ in the domain of possible beings. In the end, the hazy boundary between negative and infinite judgments is reduced to the scope of Negation: is it restricted to the predicate, or does it range over the whole proposition?

For the combination of the first and second in order to bring forth the third concept requires a special act of the understanding, which is not identical with that act performed in the first and second. Thus the concept of a number (which belongs to the category of allness) is not always possible wherever the concepts of multitude and of unity are (e.g., in the representation of the infinite);

— Critique of Pure Reason, Cambridge pp. 214–215 (B110–B112) (Kant, 1998)

In the Critique of Pure Reason, Kant concedes that the third category in each group can be obtained by combining the first two, which seems to suggest a kind of reducibility at the level of formal logic. He nonetheless maintains that because this combination rests on a special act of the understanding, the third category is not derivative but primitive. However, he offers no adequate account of what this “special act” amounts to.

To secure the independent standing of the third categories, he typically cites Totality. The concept of Totality, he claims, does not arise automatically wherever Unity and Plurality are given; Infinity is proposed as the paradigmatic case, allegedly irreducible to a mere conjunction of the one and the many. This is unconvincing. As the Transcendental Aesthetic shows, infinity can be represented through a successive synthesis—namely, the iterative addition of units (B50). Kant’s assertion that the concept of the infinite is independent of the union of unity and plurality thus conflicts with his own theory of Transcendental Aesthetics. Moreover, the category of Limitation can be reduced not only to a combination of Reality and Negation but even to a mere difference in formal expression, and Kant provides no distinctive argument in favor of Limitation as an individual category.

In reply to the formal-logical objection, one might insist that Kant’s doctrine of the categories mirrors not logical form but the a priori structure of human cognition, and hence resists reduction to formal logic. However, even at the epistemic level, the line between Limitation and Negation remains blurry. When we issue a negative judgment, our cognition does not automatically posit the object within some determinate positive domain of possible being. In judging “This is not a desk,” we simply deny the proposition “This is a desk”; we do not, in the same cognitive act, positively represent “some possible being other than a desk.” Such placement of the object within a positive domain of possible beings can be achieved by further inference, but that is the product of reflective thought rather than an original form of cognition.

Accordingly, Kant’s distinction of the categories of Negation and Limitation conflicts with his own claim that the categories faithfully reflect the actual structure of human cognition (A85–A87/B117–B120). The impression, instead, is that the formal-logical status of the infinite judgment has been left deliberately indeterminate.

Active Synthesis Beyond the Unity of Apperception

Kant’s "Transcendental Deduction" undertakes to establish the categories’ objective validity—their quid iuris (A128). However, this expansive argument, while formally vindicating the right to employ the categories, never reaches a procedural elucidation of the active synthesis by which the manifold of intuition is combined into a single, unified object (A99–100/B130–131). For an empirical object to be cognized as one, an active synthesizing deed of the subject is required (A104–110 / B136–138); Kant nowhere specifies how that deed is to be executed. So long as this lacuna remains, the Transcendental Deduction proclaims that combination occurs without disclosing the grounds that render such a combination possible.

The point becomes still clearer when one turns to the table of categories derived in the Metaphysical Deduction. That table does not explain the active operation of the understanding. A classification obtained from the forms of judgment yields only a formal taxonomy of thought; it leaves undetermined which judgment-form the understanding applies to a given intuition, and under what conditions and procedures. Even where the Transcendental Deduction derives the validity of the categories from the unity of pure apperception, merely naming the categories “functions of unity” does not supply the concrete methods or rules by which active synthesis proceeds.

Kant introduces the infinite judgment as a third form of judgment, coordinate with affirmation and negation. Negative judgment restricts a concept’s extension by denying the predicate, but it does so without incurring any ontological commitment (A72–73/B97–98). If, as he contends, cognition is constituted not by external things but by an immanent a priori structure, then determinate criteria or rules are needed. These criteria should indicate when the subject ought to employ an infinite judgment rather than a straightforward negative one. To institute a third form, despite the charge of formal-logical redundancy, is to owe a transcendental justification—namely, that it mirrors the architecture of cognition more faithfully. Although Kant concentrated on elucidating the conditions of possibility of that a priori structure, his position would be more compelling were it accompanied by a systematic account of the rules and procedures that govern active synthesis.

Conclusion

This paper follows Kant’s epistemological project and, along three axes, re-examines the central arguments of the Critique of Pure Reason. The celebrated “Copernican turn” was a bold attempt to ground the universality and necessity of cognition in the subject’s a priori forms; yet within this framework, several structural difficulties come to light.

First, despite its elegant $4\times3$ symmetry, the twelvefold system of categories lacks a secure basis for uniqueness and completeness. The Metaphysical Deduction purports to derive the categories from the table of judgments. Still, neither the completeness of that table nor the one-to-one correspondence between the functions of formal logic and the transcendental functions of cognition is adequately demonstrated. The Transcendental Deduction vindicates the necessity of the categories in general, yet it does not explain why the list should have precisely this number and arrangement—an unresolved quid facti.

Second, at least within Quality, the category of Limitation appears reducible to a combination of Reality and Negation. The restriction of the scope of cognition that Kant seeks to capture via the infinite judgment can, in formal logical notation, be rendered as a mere shift in the scope of negation. This invites reconsideration of whether Limitation must retain independent standing, even in a transcendental sense.

Third, while the Transcendental Deduction defends the right (quid iuris) to employ the categories, it does not sufficiently describe how the active synthesis that unifies the manifold into an object is actually carried out. A gap remains between declaring that the “I think” furnishes the ground of unity and articulating the concrete rules and procedures by which that unity is effected.

Even so, Kant’s epistemological project was a remarkable—and, in a sense, unavoidable—effort to re-found the authority of reason between dogmatism and skepticism. His work encourages German Idealism and reshaped the terrain of thought from Neo-Kantianism to phenomenology and analytic philosophy. We may well criticize Kant; to philosophize without him is hard. The live controversial points he left are themselves part of the reason his philosophy continues to be respected.

References

• Kant (1998): Kant, I. (1998). Critique of Pure Reason (P. Guyer & A. W. Wood, Trans. & Eds.). Cambridge University Press. (Original work published 1781/1787)
• Hegel (1995): Hegel, G. W. F. (1995). Lectures on the History of Philosophy (E. S. Haldane & F. H. Simson, Trans.). University of Nebraska Press. (Original work published 1892–1896)