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Exploring the Deduction of the Category of Totality from within the Analytic of the Sublime


Levi Haeck·

Ghent University, Belgium



I defend an interpretation of the first Critique’s category of totality based on Kant’s analysis of totality in the third Critique’s Analytic of the mathematical sublime. I show, firstly, that in the latter Kant delineates the category of totality — however general it may be — in relation to the essentially singular standpoint of the subject. Despite the fact that sublime and categorial totality have a significantly different scope and function, they do share such a singular baseline. Secondly, I argue that Kant’s note (in the first Critique’s metaphysical deduction) that deriving the category of totality requires a special act of the understanding can be seen as a ‘mark’ of that singular baseline. This way, my aesthetical ‘detour’ has the potential of revealing how the subjective aspects of object-constitution might be accounted for in the very system of the categories (of quantity) itself.

Key words

The mathematical sublime, totality, category, object, singularity.




My purpose is to show how an account of the mathematical sublime, as expounded by Kant in the third Critique, can give rise to a more focused take on Kant’s notion of totality (i.e., allness) in the first Critique’s metaphysical deduction of the categories.[1] It goes without saying that the categories of quantity have already been scrutinized profusely. More often than not, however, interpretations fail to delineate what totality — the third moment of the categories of quantity — exactly amounts to. To make sense of Kant’s metaphysical deduction of the category of totality, one must undoubtedly consider its derivation from (one or several of) the pure functions of judgment.[2] Yet the widespread debate as to from which function of judgment — the universal or the singular one — the category of totality must be derived, and how such a derivation should be understood, seems to stand unconnected to the question as to what categorial totality is. That Kant might envisage a specific kind of totality, is too often left implicit.

            In function of further disentangling this issue — an entire project indeed — I propose to make a start with the question what categorial totality could or should not be. In the spirit of Kant’s own stance towards negativity as a constitutive, hence positive philosophical force, I propose to accordingly delineate categorial totality.[3] To that end, I find inspiration in Kant’s account of the mathematical sublime as a form of totality that is, namely, by no means categorial.[4]

            Kant’s account of the mathematical sublime does two interesting things for my purposes. Firstly, it engages with a kind of totality that is indeed not categorial — with a kind of totality that is, in other words, supposedly not epistemologically relevant. Secondly, in said engagement Kant nonetheless presupposes some kind of ‘common ground’ between the mathematical sublime as a form of aesthetical totality on the one hand and categorial (epistemological) totality on the other hand. In that regard, I argue that the Analytic of the sublime can be read as subtly indicating points of convergence and divergence prevailing between the mathematical sublime and the category of totality, allowing to shed a new light on the latter. My analysis of the points of divergence is centered around Kant’s indications that the mathematical sublime must involve the idea of absolute totality, giving way to the qualification that categorial totality requires relativity and limitation. Then I move on to identify points of convergence, centered around Kant’s prominent yet underexplored claim that, in the end, “alle Größenschätzung der Gegenstände der Natur ist zuletzt ästhetisch (d. i. subjectiv und nicht objectiv bestimmt)” (KU, AA 05: 251.17-19). In what follows, I take this to imply that although categorial and sublime totality are significantly different, their origin is seemingly identical — both originate, namely, in the essentially singular position of a judging subject.

            From this, I move on to indicate how reading the Analytic of the sublime along these lines substantially contributes to the study of the metaphysical deduction of the category of totality. More precisely, I try to shed a light on Kant’s remark that deriving the category of totality requires ‘a special act of the understanding’ (KrV, B 111). This leads me to defend the claim that Kant’s system of transcendental logic is in fact marked by the singularity involved in categorial totality.



(I). The Sublime


(A). Reflecting and Determining Judgments


Studying the sublime is to engage with the power of judgment in its capacity as an autonomous faculty. This means, first of all, that one deals with the power of judgment as operating solely in accordance with its own a priori principle, namely the principle of purposiveness. This concerns what Kant calls the reflecting power of judgment, essentially tied to the subjective feelings of pleasure and displeasure. On this subjective basis, relations with other faculties can be maintained, evoking the aesthetical judgments of the beautiful and the sublime, treated by the first part of the third Critique (EEKU, AA 20: 248.13-250.18).

            Only when the power of judgment makes use of a priori principles proper to other faculties, operating schematically instead of technically, are we dealing with its determining capacity. Already in the first Critique, it is in fact the power of judgment that warrants the subsumption of specific intuitions under general concepts, respectively delivered by sensibility and the understanding. By way of this, the sensible given is determined by the discursive categories, bringing about the constitution of the object.

            More crucially, however, if the general or determining element is absent, there is still judgment at play. What remains, namely, is the power of judgment überhaupt. If only the specific is available to the power of judgment, the latter searches for something general that can be considered adequate with regard to the specific. This quest, stipulated in the third Critique as the reflecting judgment, is therefore to be called the proper, more basic power of judgment. In a sense, the structure of the reflecting judgment underlies the structure of the determining judgment — and not the other way around. The latter is, as it were, a dressed-up version of the former. According to Longuenesse, this asymmetrical relation between them is essential (Longuenesse 1998, pp. 162-66). In line with her, I contend that an account of the determining judgment must be guided by an account of the reflecting one.

            Moreover, I agree with De Vleeschauwer when he suggests that the mind — whether or not the general element is available to the power of judgment — is in fact not quite satisfied with the mere determination of the sensible given in function of constituting an object (De Vleeschauwer 1931, pp. 315-317). The mind, namely, also wonders about the meaning and significance of these given appearances themselves. Determining judgments only account for why certain appearances become constituted as objects, not for why these appearances are themselves given. And the faculty of the understanding, from which the determining categories flow, is not accommodated for tackling this concern. In function thereof, precisely the reflecting judgment, resorting to the principle of purposiveness, must be put in motion. If nature is approached by the principle of purposiveness, given appearances can be seen, for example, as necessarily belonging to the natural world as a whole.



(B). Sublimity and Purposiveness


The judgment of sublimity fully adheres to this principle of purposiveness. It entails the treatment of the sensible given insofar as it does not qualify for object-constitution or conceptual determination. Kant is adamant, already in the First Introduction to the third Critique, that sublimity has a purposiveness of its own: “Gleichwohl würde das Urtheil über das Erhabene in der Natur von der Eintheilung der Ästhetik der reflectirenden Urtheilskraft nicht auszuschließen sein, weil es auch eine subjective Zweckmäßigkeit ausdrückt, die nicht auf einem Begriffe vom Objecte beruht” (EEKU, AA 20: 250.15-18).

            The sublime involves, more precisely, the feeling of the “innern Zweckmäßigkeit in der Anlage der Gemüthskräfte” (EEKU, AA 20: 250.14). As for these Gemüthskräfte, the judgment of the sublime entails, moreover, that the given appearances of nature must serve a purposiveness with regard to our faculty of reason. This purposiveness is manifested by the reflecting capacity to represent a sublimity (eine Erhabenheit) in objects that is strictly speaking not to be represented in them. According to Kant, namely, the judgment of sublimity presupposes Geistesgefühl — the feeling of spirit (EEKU, AA 20: 250.33-34).

            At the beginning of his exposition of the sublime (KU, AA 05: 244-247),[5] we learn that the beautiful is characterized by a concern for the form of the object in its limitation, while the sublime is (or can also be) characterized by a concern for the formlessness of the object as it is unlimited. [6] More crucially, the mathematical sublime entails unlimited formlessness that serves nonetheless to be thought as a totality (Totalität). Unlike the beautiful, the (mathematical) sublime is seen to be developed as a primarily quantitative issue, predicated on a conception of totality not involving limitation. Considering the sublime as a totality precisely by reference to the absence of limitation — namely, as constitutive for the kind of totality involved — is, according to Kant, to deal with totality as an idea of reason: “so daß das Schöne für die Darstellung eines unbestimmten Verstandesbegriffs, das Erhabene aber eines dergleichen Vernunftbegriffs genommen zu werden scheint” (KU, AA 05: 244.27-29). And whereas the judgment of beauty is often seen as a ‘predicate’ of the object contemplated, this cannot so easily be said of the judgment of the sublime. As already mentioned, Kant does not hesitate to contend that the objects we call sublime in fact only serve for the presentation of sublimity as a feeling of Geist. He therefore unforgivingly concludes: “[s]o kann der weite, durch Stürme empörte Ocean nicht erhaben genannt werden (KU, AA 05: 245.35-36). This potentially frustrating statement cannot be understood in isolation from Kant’s remark that the limitlessness represented in the object is nonetheless (doch) — in other words quite paradoxically — thought as a totality. Indeed, “denn das eigentliche Erhabene kann in keiner sinnlichen Form enthalten sein” (KU, AA 05: 245.31-32; italics added). To represent limitlessness in an object as a totality is something that simply denies the bounds of our sensibility. Technically speaking, this means that it is inappropriate to call empirical objects like seas sublime, no matter how unlimited their width may seem. An incredibly wide sea is never really unlimited. It is only potentially giving rise to a felt absence of limitation, in which case it is legitimately called sublime in the mathematical sense.

            As if to make up for the limitation proper to sensible presentations of objects, the reflecting mind is encouraged or tempted (angereizt) to leave sensibility behind and to occupy itself “mit Ideen, die höhere Zweckmäßigkeit enthalten” (KU, AA 05: 246.03-05). Kant nuances that the sublime entails, in that sense, the use — or perhaps rather misuse — of sensible intuitions “um eine von der Natur ganz unabhängige Zweckmäßigkeit in uns selbst fühlbar zu machen” (KU, AA 05: 246.24-25). So quite in line with its reflective rather than determinative origin, sublimity should not so much be considered as the predicate of an object, as it should be considered as entailing the subject’s attempt to feel its own supersensible nature. This means, as Zammito (Zammito 1992, p. 300) rightly pinpoints, that in seeking the supersensible in the sensible object of nature, sublimity fundamentally involves what Kant calls Subreption — namely the “Verwechselung einer Achtung für das Object statt der für die Idee der Menschheit in unserem Subjecte” (KU, AA 05: 257.22-23). By way of this ‘subreptive’ move, the sublime experience does the impossible: it makes our supersensible nature literally sensible or anschaulich (KU, AA 05: 257.26).

            For Kant, the judgment of sublimity in no way concerns aboutness regarding the object, this much is clear. What he is after, is to lay bare how judging objects aesthetically stands in relation to the feeling of the sublime (KU, AA 05: 247.04-05). The suggestion seems to be that to have a certain grasp of objects in a merely aesthetical way — i.e., a grasp of objects not configured to determining judgments of cognition — can give rise to acknowledging the presence in ourselves of yet another discursive power, a power, moreover, that explicitly transgresses any ‘sensible’ grasp. The sublime involves the annulment of what occasions it to begin with — indeed, the sublime experience must start from sensibility but move away from it at the same time. This dynamic, though seemingly paradoxical, is essential. It allows for setting the Kantian faculties up against each other so that their various features, possibilities, and limitations can be explored — without exclusion of the understanding.

            I propose, namely, that the judgment of the sublime points to a certain inadequacy not only of the determining functions of the faculty of the imagination, as Kant himself indicates (KU, AA 05: 258.15-16), but also of the determining functions of the faculty of the understanding. In what follows, I argue that a further delineation of the category of totality — as a central concept of the understanding — can emerge from a delineation of sublime totality. I argue, more precisely, that the category of totality is unfit for representing the constitution of overly vast objects insofar as they transgress the comprehensive powers of the imagination, and that this inadequacy clears the room for a totality bringing with it the feeling of sublimity. This juxtaposition of categorial and sublime totality proves, eventually, to disclose something about the nature of the former (and the epistemological significance of the latter).  



(II). Kant’s Multilayered Account of the Estimation of Totality


(A). Differentiating between Numerical and Aesthetical Estimation of Totality


In paradoxically beginning with as well as moving away from sensibility, the true face of the sublime is revealed. This peculiar dynamic lays the groundwork for Kant to characterize the mathematical sublime, in §25, as a totality that is absolutely great or schlechthin groß (KU, AA 05: 248.05). In that regard, Kant qualifies that “Groß sein […] und eine Größe sein, sind ganz verschiedene Begriffe (magnitudo und quantitas)” (KU, AA 05: 248.05-07). This distinction between Groß sein and eine Größe sein is of importance. To say that something is great (or small, or medium-sized, etc.) belongs, says Kant, to the power of judgment proper, as this predication does not consider how great something is. How great something is, namely, is a mathematical judgment of quantitas, which pertains to the faculty of the understanding. Groß sein concerns the merely subjective (be it universally communicable), non-mathematical judgment that something is great.

         Seemingly, Groß sein is synonymous with magnitudo, while eine Größe sein is synonymous with quantitas. In keeping with the first Critique, quantitas is concerned with the question how great something is. It is a comparative, numerical concept of the understanding. In the first Critique, however, the same comparative concept of quantitas is also explicitly differentiated from quantum (see KrV, B 202-203, B 205). Yet in the first Critique, quantum is presented as synonymous with eine Größe sein and not, as logic would dictate, with Groß sein. And in the Analytic of the mathematical sublime, the difference between quantum and quantitas is often left implicit.

            I propose to solve this initial problem by specifying the dichotomy between Groß sein and eine Größe sein in terms of a trichotomy. First of all, namely, Groß sein — or magnitudo — is not a concept of the understanding, whereas quantitas and quantum are. In the first Critique, quantum is defined as eine Größe involving “das Bewusstsein des mannigfaltigen Gleichartigen in der Anschauung überhaupt, so fern dadurch die Vorstellung eines Objects zuerst möglich wird” (KrV, B 203). Quantum, therefore, corresponds here with the category of totality (which is defined by Kant as “[…] die Vielheit, als Einheit betrachtet” (KrV, B 111). Cf. infra). Quantitas, on the other hand, is defined as die Größe that concerns “die Antwort auf die Frage: wie groß etwas sei” (KrV, B 205; italics added). Therefore, I suggest that what is called quantitas is nothing but quantum in comparison with another quantum insofar as the latter is considered as a measure (cf. infra).[7] Both can be seen as standing in opposition to Groß sein — to simply being great — which pertains to the power of judgment proper.

            Kant suggests that we must interpret the judgment of the sublime, involving that a certain totality be absolutely great (i.e., great without comparison), as a continuation of this merely subjective, non-categorial judgment. Both the judgment that something is simply great and the judgment that something is absolutely great escape the mathematical take on size, which involves a conceptual unit of measure (Maße) that enables numerical comparison (KU, AA 05: 249.28-33). Technically speaking, however, the latter modality of mathematical estimation is always at the horizon of the mind:  


Hier sieht man leicht: daß nichts in der Natur gegeben werden könne, so groß als es auch von uns beurtheilt werde, was nicht, in einem andern Verhältnisse betrachtet, bis zum Unendlich=Kleinen abgewürdigt werden könnte; und umgekehrt nichts so klein, was sich nicht in Vergleichung mit noch kleinern Maßstäben für unsere Einbildungskraft bis zu einer Weltgröße erweitern ließe. Die Teleskope haben uns die erstere, die Mikroskope die letztere Bemerkung zu machen reichlichen Stoff an die Hand gegeben (KU, AA 05: 250.13-20).


What Kant appears to suggest, in other words, is that the mind will always consider the mathematical comparison of quanta in terms of size to be an option. Judging, then, that something is simply great or perhaps even absolutely great counts as a kind of suspension of this otherwise very present aspiration of the mind.  But although both suspend the mathematical take on the size of totalities, to say that something is great is not entirely the same as to say that something is absolutely great. A possible way of distinguishing between them is connected to the fact that the absolutely great functions as an idea belonging to the faculty of reason, whereas the simply great only flows from the power of judgment proper.

            Both of these estimations of size, however, are grounded in their opposition to quantitas. On the one hand, the judgment that x is simply great is grafted on the suspension of the otherwise inescapable condition that everything in intuition must be suitable for numerical comparison qua size. On the other hand, the judgment that x is absolutely great involves, furthermore, that x is not only great, but great “über alle Vergleichung” (KU, AA 05: 248.09-10). Contrary to Groß sein, namely, schlechthin Groß sein does not even qualify for comparison, hence for being considered as quantitas. This forces the power of judgment in question to escape the bounds of intuition altogether, installing a play between the power of judgment and the faculty of reason. Only this specific configuration is constitutive of the experience of the sublime, as “[n]ichts […] was Gegenstand der Sinnen sein kann, ist, auf diesen Fuß betrachtet, erhaben zu nennen” (KU, AA 05: 250.21-22).  

            Such a play, alliance, or plain cooperation between the power of judgment and the faculty of reason seems to obstruct the former’s possible alliance with the faculty of the understanding. Indeed, the power of judgment cannot at the same time be combined with concepts of the understanding — amounting to numerically comparative (or mathematical) estimation of size — and with ideas of reason, amounting to absolute estimation of size.

            In all of these cases, however, the faculty of the imagination plays an essential role. As for the sublime, Kant maintains that there is “[…] in unserer Einbildungskraft ein Bestreben zum Fortschritte ins Unendliche, in unserer Vernunft aber ein Anspruch auf absolute Totalität” (KU, AA 05: 250.22-24). This striving of the imagination, together with reason’s claim to absolute totality, is ratified precisely by the very inadequacy (Unangemessenheit) of the power of judgment for estimating the size of things of the sensible world (KU, AA 05: 250.25-26). This very inadequacy is due to the fact that the power of judgment is here considered as a reflecting judgment, hence a judgment without making use of concepts of the understanding. So, to Kant’s contention that the power of judgment is inadequate for estimating the size of quanta one must add the qualification that this is only so without the help of the understanding. This inadequacy, thus tied to the exclusion of the understanding, then prompts to “die Erweckung des Gefühls eines übersinnlichen Vermögens in uns” (AA 05: 250.26-27). The reflecting power of judgment resorts to this feeling, then, to accommodate for its own inadequacy.



(B). Connecting Numerical and Aesthetical Estimation of Totality — A Singular Baseline


Kant opens §26 (KU, AA 05: 251, and further) with a subtly different approach to the distinction between the two basic ways or types of estimating sizes, only one of which he deems to be required for the experience of sublimity. Now, as §25 already disclosed, in order to know how great something is, one must make use of the mathematical type of estimation. Numbers, relative to a standard of measurement, allow for mathematical comparison of totalities. Mathematical estimation of size is therefore conceptual, while aesthetical estimation occurs merely in intuition, or with the eye. In §26, however, Kant suggests that the former — transcendentally grounded in the first Critique’s category of totality — is somehow dependent on the latter. The distinction holding between them is, apparently, by no means hermetical.

            Kant maintains that any numerical estimation according to a unit or standard of measurement also requires the determination of a basic measure if it is to be objective. He seems to suggest, in that regard, that finding and using such a basic measure, by way of which the activity of measurement can take place, can never be accomplished by mathematical-numerical estimation in the latter’s purely logical capacity. Kant subtly states, namely, that any basic measure must be predicated on what can be captured immediately in one intuition:


Allein da die Größe des Maßes doch als bekannt angenommen werden muß, so würden, wenn diese nun wiederum nur durch Zahlen, deren Einheit ein anderes Maß sein müßte, mithin mathematisch geschätzt werden sollte, wir niemals ein erstes oder Grundmaß, mithin auch keinen bestimmten Begriff von einer gegebenen Größe haben können. Also mu[ß] die Schätzung der Größe des Grundmaßes bloß darin bestehen, daß man sie in einer Anschauung unmittelbar fassen und durch Einbildungskraft zur Darstellung der Zahlbegriffe brauchen kann (KU, AA 05: 251.10-17).


I take it, therefore, that mathematical estimation is to be distinguished from logical estimation, whereby the former is only partially grounded in the latter, since a basic measure delivered by the faculty of sensibility is required as well.[8]

            Herewith, Kant interestingly brings the two types of estimation, mathematical and aesthetical, together. Kant is adamant, furthermore, that “alle Größenschätzung der Gegenstände der Natur ist zuletzt ästhetisch (d. i. subjectiv und nicht objectiv bestimmt) (KU, AA 05: 251.17-19). Contrary to logical estimation, for which there is no greatest measure, as it is a merely theoretical construct of the understanding, the aesthetical estimation of totality is in that regard necessarily constrained by the singular position of a sensory subject. Therefore, one should in fact extract three types of estimation from the Analytic of the mathematical sublime: (i) logical estimation; (ii) aesthetical estimation; (iii) and mathematical estimation, whereby (iii) seems to be a combination of (i) and (ii).

            It is quite pertinent to note that for the mathematical estimation of size, considered in its purely logical capacity, there is “kein Größtes (denn die Macht der Zahlen geht ins Unendliche); aber für die ästhetische Größenschätzung giebt es allerdings ein Größtes” (KU, AA 05: 251.20-22). When the unlimited logical estimation of size transgresses the limits of an aesthetically basic measure, what ensues is the feeling of sublimity: “und von diesem sage ich: daß, wenn es als absolutes Maß, über das kein größeres subjectiv (dem beurtheilenden Subject) möglich sei, beurtheilt wird, es die Idee des Erhabenen bei sich führe” (KU, AA 05: 251.22-25).

            Despite the opposition between aesthetical and mathematical estimation — an opposition that is indeed constitutive of the feeling of sublimity — Kant does in fact also contend, quite strikingly for my purposes, that mathematical estimation must not be understood as fully distinct from the aesthetical one. If mathematical estimation is partly grounded in aesthetical estimation, like Kant does indeed suggest, I take this to mean that the former rests on the latter so as to make its numerical concepts objective. The singularity of the purely aesthetical estimation of size comes forward as a baseline for the estimation of both sublime and mathematical totality.  

            Some scholars, however, might refuse to accept this subtle intertwinement. Allison, for example, puts much more weight on the qualification that “the reflecting judgment that something is simply great does not serve for a logical, that is, mathematically determinate, estimation of magnitude, but only for an aesthetic one” (Allison 2004, p. 312). Although this is not wrong per se, Allison does give the impression that subjective estimation, that is to say estimation with the eye, can in no way (partially) underly, or even be seen as plainly relevant for mathematical estimation. All the while Allison admits, in relation to mathematical estimation, that “the basic unit of measure must itself be determined merely aesthetically” (Allison 2004, p. 316), yet is hereby not lead to acknowledge that between aesthetical and mathematical estimation a connection should nonetheless be presupposed. His account stubbornly adheres to the hermetical distinction between the two types of estimation. I would say that such is only superficially valuable. More specifically, my analysis clarifies that a hermetical distinction, if any, must rather be presupposed to hold between (i) mathematical estimation in its purely logical capacity and (ii) aesthetical estimation, with (iii) mathematical estimation standing in between. Unfortunately, Allison seems to equate (i) and (iii). Allison specifies, moreover, that “the demand for totality” proper to the sublime comes with “an additional requirement for which the understanding has no need, namely, comprehension in one intuition (…)” (Allison 2004, p. 230). Here, Allison sharply disconnects estimation of totality on the level of the understanding from any aesthetical, singular grasp of the object whatsoever. I take this to be the result of his un-attentive equation of (i) and (iii). To lay bare the epistemological relevance of Kant’s account of the sublime is of course not Allison’s objective. Perhaps his otherwise lucid account is thus not damaged by sidelining Kant’s suggestion that mathematical estimation is, in a way, reliant on aesthetical estimation. Nonetheless Allison’s account does block the way to conceive of mathematical estimation of size and, in a second move, categorial totality, as partially reliant on the singular position of a subject’s sensory, comprehensive capacities.  



(C). The Singularity of the Imagination


Now, to further substantiate and elaborate on my hypothesis that mathematical estimation of totality, if it is to be objective, must share such a subjective ‘baseline’ with aesthetical estimation, I must also address the role of the power of the imagination. In that regard, Kant adds quite lucidly: “Die Einbildungskraft schreitet in der Zusammensetzung, die zur Größenvorstellung erforderlich ist, von selbst, ohne daß ihr etwas hinderlich wäre, ins Unendliche fort; der Verstand aber leitet sie durch Zahlbegriffe, wozu jene das Schema hergeben muß” (KU, AA 05: 253.28-31).

            Now, Kant adds that if the imagination — proper to the subjective determination of estimation just discussed — is not guided by the understanding, therefore not providing a schema, and thus advances to infinity without hindrance, the mind listens to the voice of reason in itself (KU, AA 05: 254.09). As a matter of fact, the imagination’s unhindered advancement to infinity is theoretically close to the idea of absoluteness. This theoretical kinship between infinity and absoluteness is due to our faculty of reason: “Das gegebene Unendliche aber dennoch ohne Widerspruch auch nur denken zu können, dazu wird ein Vermögen, das selbst übersinnlich ist, im menschlichen Gemüthe erfordert” (KU, AA 05: 254.35-37). Indeed, in the first Critique Kant contends that, as to infinity, “die successive Synthesis der Einheit in Durchmessung eines Quantum niemals vollendet sein kann” (KrV, B 460). Precisely because the categorial synthesis of infinity into an object cannot be completed, infinity can only be considered as an absolute totality thought by reason.[9]

            Interestingly enough, due to its logical capacity, mathematical estimation (see KU, AA 05: 254.10) is, much like the imagination’s apprehensive powers, capable of proceeding infinitely as well. However, in line with its need for a subjective basic measure, mathematical estimation of totality seems in turn to be without objective value if not related to the comprehension carried out by imagination:


Anschaulich ein Quantum in die Einbildungskraft aufzunehmen, um es zum Maße oder als Einheit zur Größenschätzung durch Zahlen brauchen zu können, dazu gehören zwei Handlungen dieses Vermögens: Auffassung (apprehensio) und Zusammenfassung (comprehensio aesthetica). Mit der Auffassung hat es keine Noth: denn damit kann es ins   Unendliche gehen; aber die Zusammenfassung wird immer schwerer, je weiter die Auffassung fortrückt, und gelangt bald zu ihrem Maximum, nämlich dem ästhetisch=größten Grundmaße der Größenschätzung. […] so verliert sie auf einer Seite eben so viel, als sie auf der andern gewinnt, und in der Zusammenfassung ist ein Größtes, über welches sie nicht hinauskommen kann (KU, AA 05: 251.32-252.09).


Whereas in §25 the singular baseline of mathematical estimation was explained in terms of aesthetical estimation, it is now explained in terms of the faculty of the imagination. When the imagination’s subjective, intuitive attempts at comprehension perish under the understanding’s conceptual stride towards infinite numerical progression, both loose something: the imagination obviously finds itself obliged to pull comprehension back into apprehension, giving way to the feeling of sublimity, while the understanding hereby loses its relation to the object of intuition. Namely, the infinite progression of numerical measures is one thing; its imaginative schematization in relation to the singularity of sensible intuitions so as to generate a unified, hence totalized object, is another.

            In a sense, the sublime is due to the imagination’s natural advancement to infinity as much as to its failure to comprehend this self-produced infinity as a totality without the aid of another (discursive) faculty. Therefore, Kant maintains that although nature is called sublime when the intuition of its appearances prompts to the idea of infinity, he qualifies that such cannot take place except “durch die Unangemessenheit selbst der größten Bestrebung unserer Einbildungskraft in der Größenschätzung eines Gegenstandes” (KU, AA 05: 255.16-18). If the imagination is tied to numerical concepts of the understanding, the estimation of the size of an object can be successful. This ‘successful’ estimation then makes a resort to reason redundant. This informs us that only the annulment of the imagination’s alliance with the understanding can yield an alliance with the faculty of reason, thus installing the experience of the sublime.[10] In this regard, Vandenabeele specifies the experience of the sublime as a ‘limit experience’ (Vandenabeele 2015, p. 85). This is crucial, but I want to add that the experience of the sublime comes forward, more specifically, as necessarily accompanied by the acknowledgement of the limitations of our faculties, namely of sensibility, the understanding, and between them the power of the imagination. The sublime experience rests on the feeling of the limitations and inadequacies of these faculties, immediately heralding a role for the faculty reason, and its accompaniment by yet another feeling — the feeling of Geist (EEKU, AA 20: 250.33-34). The limitlessness that accompanies the sublime owes, in other words, much to the fact that it is at the same time grounded in an experience of limit.



(III). Sublime and Categorial Totality


(A). From Mathematical Estimation to the Category of Totality


But let us take things a bit further. I read Kant’s account of sublime totality not only as revelatory with regard to the understanding’s mathematical estimation of totality. It could also reveal something about the category of totality itself. What kind of totality is the first Critique’s metaphysical deduction concerned with? What transcendental procedure might be presupposed to underly the derivation of this category? These problems, so I propose, are close to Kant’s account of the singular baseline of mathematical estimation of size just discussed. Let me first reiterate a key point with regard to the imagination: “Anschaulich ein Quantum in die Einbildungskraft aufzunehmen, um es zum Maße oder als Einheit zur Größenschätzung durch Zahlen brauchen zu können, dazu gehören zwei Handlungen dieses Vermögens: Auffassung (apprehensio) und Zusammenfassung (comprehensio aesthetica) (KU, AA 05: 251.32-35).

            At first glance, it seems that the process of apprehending and comprehending quanta so as to estimate their size is the only epistemological issue Kant is concerned with in the Analytic of the sublime. Arguably, however, this imaginative process is as much applicable to estimating quanta by intuitively taking them up, as it is applicable to categorially constituting them. Kant continues, namely, that “[…] die Zusammenfassung wird immer schwerer, je weiter die Auffassung fortrückt, und gelangt bald zu ihrem Maximum, nämlich dem ästhetisch=größten Grundmaße der Größenschätzung (KU, AA 05: 252.01-03). It seems that the subjective requirement of comprehension, on which the understanding must predicate itself so as to make mathematical estimation possible, is equally applicable to the constitution of these quanta themselves. So I agree with Crowther when he argues that the process of apprehension and comprehension “must also apply to our attempts to grasp the phenomenal totality of any object in a single whole of intuition”, in spite of the fact that Kant only discusses said process “in relation to the attempt to present infinity as an absolute measure” (Crowther 1989, p. 10).    

            The power of the imagination is, in either case, incapable of attaining categorial (conceptual, discursive) totality by itself. Only upon combining its powers with the understanding is the comprehension produced by the imagination able to give rise to categorial totality, hence to the conceptual determination of intuitions as objective totalities. As mentioned already, however, maintaining the opposite is equally accurate. In discussing the estimation of size, the Analytic of the sublime suggests that this joint act of comprehension — namely in reference both to the understanding and to the imagination — can never be completely ‘taken over’ by the understanding. As the imagination is itself grafted on a purely aesthetical estimation of objects, it cannot keep matching basic measures with the ever-progressing numerical concepts of the understanding. In attempting to comprehend ever vaster objects, the imagination fails to meet the needs of the understanding. As a consequence, the imagination and the understanding are eventually seen to be disconnected, making space for the imagination to engage in a play with the faculty of reason instead. In categorially constituting empirical objects as totalities, the understanding must somehow be accompanied by the imagination. What happens, namely, when imaginative comprehension inevitably reaches its subjective limit in the ever-progressing (logical-numerical) estimation of vast objects? Seemingly, what the understanding loses in this procedure, is exactly its capacity to constitute those overly large quanta as totalities, that is to say, as objects.

            Judging that something is a quantum or totality, says Kant, “läßt sich aus dem Dinge selbst ohne alle Vergleichung mit andern erkennen: wenn nämlich Vielheit des Gleichartigen zusammen Eines ausmacht” (KU, AA 05: 248.17-19). In the first Critique, Kant says something similar, describing the category of totality as “nichts anders als die Vielheit, als Einheit betrachtet” (KrV, B 111). If this act of ‘con-stitution’ fails, the feeling of the mathematical sublime ensues. The claims at absolute totality pertaining to the judgment of the sublime entail, namely, that it is precisely not the case that a certain homogenous plurality (“Vielheit des Gleichartigen”) can be synthesized as one object (“zusammen Eines ausmacht”) (KU, AA 05: 248.17-18). In sublime totality, the unity involved is merely thought — it is not concerned with a synthesis of the plurality involved. In fact, it completely sets aside said plurality, necessarily overcoming it. In case of objects judged and felt to be absolutely large, namely, the imagination fails to comprehend the very plurality involved. But this failure must be credited to the category of totality as well — it is, so to speak, equally inappropriate to do the job. The felt inadequacy of the imagination to present vast quanta as totalities, giving way to the experience of the sublime, also informs us (be it partially) about the nature of the understanding. In the feeling of the sublime, what is veritably lost is not merely the possibility of mathematical estimation of quanta, but — so I argue — also the very legitimacy and suitability of the category of totality itself.

            The Analytic of the sublime reveals that the aspirations of the understanding are extensively influenced by its inevitable collaboration with the imagination and that it too involves a limit-experience. Kant’s account of the mathematical sublime can thus be read as establishing a more fine-grained analysis of categorial totality. Exploring the intricate interdependency between the numerical concepts of the understanding and the imagination, in juxtaposition with the purposive play between the imagination and reason, serves to be a valuable avenue of research, not only for explaining the latter pair, which is of course its established function in the Analytic of the sublime, but also for delineating the former.

            Both categorial totality and sublime totality are, each in their own specific way, grafted on the imagination and the power of judgment. With regard to categorial totality, both the understanding’s and the imagination’s tendency towards infinity, be it numerically for the understanding and apprehensively for the imagination, must be constrained and limited. Quite crucially, “the constraint is the possibility” (Van de Vijver & Noé 2011). Quite surreptitiously, however, in a violent harmony with reason the power of judgment sees in the imagination’s tendency towards infinity a way to escape said limitation, suggesting the potentiality of a totality that is absolutely great. These insights can now be applied to a more systematic and specific aspect of the category of totality: its metaphysical deduction.



(B). Kant’s transcendental logic of the categories


The categories that flow from the faculty of the understanding are entirely inherent to it. This means that they cannot be derived from anything else than the understanding. At the same time, these categories are related a priori to that with which they stand in complete opposition, namely the manifold of intuition, provided by the faculty of sensibility. The categories relate to the manifold of intuition, more precisely, by synthesizing it into the unity of an object (KrV, B 102-103). Without the categories, the manifold of intuition cannot attest to the unity proper to the object, cannot be anything else than a manifold. Therefore, the unity of categorial synthesis must be fully ‘distinct from’ or ‘external to’ the manifold provided by intuition.

            The externality of the categories is guaranteed by their being derived from the functions (or forms) of judgment. These functions are themselves only formally directed at unity. Because of this, the categories are also formal, non-intuitive or discursive in nature (KrV, B 93). But one must keep in mind that the categories are nonetheless synthetical — directed at intuitions.[11]

            From this peculiar, yet properly transcendental dynamic follows a rather dazzling problem. One wonders, namely, what it means for a formal, discursive, and general system, like the one of the categories, to be developed with constant eyes to its ‘material’, sensible, and essentially singular counterpart. In what follows, I suggest — on the basis of my reading of the Analytic of the mathematical sublime — that the otherwise general system of categories manages to inscribe, in the system itself, an anticipation of this singular counterpart (quite apart from but not unrelated to the fact, of course, that the categories do require schematization, carried out not by the faculty of the understanding but by the power of the imagination).[12] I develop the idea, more precisely, that Kant’s compelling insertion of the special act of the understanding into the system of categories, at least on the level of quantity, counts as a transcendental ‘mark’ of said anticipation.



(C). The Special Act of the Understanding


While spinning out the basic elements of the metaphysical deduction of the categories in the first Critique, Kant adds that every third category depends on a specific ‘combination’ of the first two categories of its group. For the categories of quantity, this means — as mentioned already — that the category of totality is “nichts anders als die Vielheit, als Einheit betrachtet” (KrV, B 111). That is, the category of totality is the result of a specific combination of the first two categories of quantity: unity on the one hand, and plurality on the other. Kant, seemingly anticipating potential objections to this rather unorthodox feature of his logic, adds that “Man denke aber ja nicht, dass darum die dritte Categorie ein bloß abgeleiteter, und kein Stammbegriff des reinen Verstandes sei” (KrV, B 111). Kant qualifies, namely, that ‘deriving’ each third category requires a “besonderen Actus des Verstandes” (KrV, B 111) or special act of the understanding, thus conferring them with an originality of their own. With regard to the category of totality (Allheit), Kant illustrates this important point by giving the example that “[…] der Begriff einer Zahl (die zur Kategorie der Allheit gehört) [ist] nicht immer möglich, wo die Begriffe der Menge und der Einheit sind (z. B. in der Vorstellung des Unendlichen)” (KrV, B 111). However, with these very brief lines, Kant’s explanation of the special act of the understanding comes to an end. No more clarification appears to be offered in the metaphysical deduction of the categories. Yet by taking at hand the Analytic of the sublime, the significance of this quite underexplored clause can be further interpreted. My analysis is twofold.

            First, it is crucial to note that whereas infinity delineated sublime totality positively in the Analytic of the sublime, it does so negatively for categorial totality in the metaphysical deduction. Indeed, although infinity does imply a combination of the categories of unity and plurality, it does so without requiring a special act of the understanding. Therefore, Kant concludes that infinity cannot belong to the category of totality. But the reverse applies as well: whereas Kant puts forward number (Zahl) as ‘belonging’ to categorial totality (namely, as requiring a special act to combine unity and plurality), he treats it negatively in delineating the scope of sublime totality (cf. supra). There appears to be some kind of symmetrical opposition between sublime and categorial totality in terms of the inclusion and exclusion of number and infinity.

            Now, quite essentially, this means that if the category of totality would nevertheless have to include infinity — that is, would not require a special act of the understanding — it would not be a category anymore, but an idea of reason. In that case, it would, namely, not only have a heterogenous relationship with sensibility — which is a necessary feature of both categories and ideas — but it would also cease to be valid for sensibility. It would, thus, cease to be synthetical. Or put differently: if the category of totality would include infinity, it would not qualify for schematization by the power of imagination. This, as we saw, is due to the imagination’s inadequacy to intuitively comprehend infinity, motivating the power of judgment to transgress sensibility whatsoever, thus engendering a play with reason instead of the understanding. In that sense, the exclusion of infinity from the category of totality is contingent on the limited comprehensive capacities of the imagination, an insight that is a direct consequence of my reading of the Analytic of the mathematical sublime. By spelling out more thoroughly the connection between the imagination and infinity, the Analytic of the sublime appears to be offering a more elaborate explanation of the necessity of something like a special act of the understanding for deriving the category of totality.[13]

            Secondly, I interpret the Analytic of the sublime to be an attempt to interweave this exclusion of infinity (and absolute totality) from the category of totality to the hypothesis, argued for in the second part of this paper, that objective estimation of totality is always accompanied by subjective determination. I argued, namely, that even numerical estimation of totality presupposes the subject’s capacity for comprehension, and that this should also hold for the constitution of the object as a totality. The latter could imply that the special act of the understanding not only accounts for the heterogeneous yet a priori valid relation between the category of totality and the faculty of sensibility in view of the former’s schematization. It could also mean that the special act of the understanding counts as an a priori anticipation, on behalf of the understanding, of the essential singularity proper to this schematization. On that exegetical line of thinking, the Analytic of the sublime contributes substantially to the idea that the derivation of the category of totality, while concerned with a formal and discursive account of the determination of quantum, could indeed autonomously prelude its relation to intuition. This allows to interpret the faculty of the understanding, insofar as it delivers the necessary conditions of possibility of the object in terms of totality, to call for a special act precisely because it must be able to account a priori for the singularity involved in relating itself to intuitions, thus even before schematization is in order.

            I am not suggesting that the first Critique does not already testify profusely to the inclusion of said singularity into the activities of the understanding. That it does, goes without saying, for instance in its groundbreaking account of objectivity as heterogeneously (i.e., intuitively and discursively) constituted. Testifying to this is the following, all-encompassing  statement of Kant’s in the Transcendental Dialectic: “Nicht dadurch, daß ich bloß denke, erkenne ich irgend ein Object, sondern nur dadurch, daß ich eine gegebene Anschauung in Absicht auf die Einheit des Bewußtseins, darin alles Denken besteht, bestimme, kann ich irgend einen Gegenstand erkennen” (KrV, B 406). However, in the metaphysical deduction of the categories, the possibility that the system of categories might itself be anticipating singularity, remains implicit. The Analytic of the sublime does seem to make plausible, however, that the subject’s singular ‘range’ is already at the heart of Kant’s exposition of the categories, the pure concepts of the understanding otherwise counting as completely general. Or, to say it with Pierobon, one must consider that “[l]’organisation architectonique de l’entendement témoigne de ce qu’il est fondamentalement orienté vers l’expérience sensible, même en son usage logique où justement abstraction en est faite (Pierobon 2005, p. 315; italics added).

            Thus, the Analytic of the sublime is not only relevant for delineating categorial totality, but hereby also for investigating the procedure of object-constitution (insofar as the category of totality is involved), connecting the often-fragmented insights of the first Critique. In this respect, the third Critique pinpoints better than the first what is at stake in the latter’s metaphysical deduction. In a slightly speculative exegetical vein, it allows for establishing a connection between the previous citation (i.e., KrV, B 406) and the following: “Nicht das Bewußtstein des bestimmenden, sondern nur das des bestimmbaren Selbst, d. i. meiner inneren Anschauung (so fern ihr Mannigfaltiges der allgemeinen Bedingung der Einheit der Apperception im Denken gemäß verbunden werden kann), ist das Object (KrV, B 407). From my reading of the Analytic of the sublime, this much overlooked contention of Kant’s, suggesting that the object is the determinable self, namely that object-constitution always involves subject-constitution, can be seen not only to complete — as it obviously does in the first Critiquebut also to fundamentally underly the metaphysical deduction of the category of totality, be it under the guise of a special act.[14]





By virtue of the fact that the Analytic of the sublime largely bypasses the faculty of the understanding, that is, largely treats it negatively, a sharper delineation of the latter’s category of totality could be achieved. What the category of totality consists of, is tied to the conditions of possibility of the object. Insofar as totality cannot be an object, the reflective power of judgment is free to engage in a play with reason instead of the understanding, so installing the feeling of sublimity. More specifically, I highlighted the relative and limited countenance of categorial totality in opposition to the absolute and infinite countenance of sublime totality.

            On that basis, I moved on to stipulate that in the Analytic of the sublime, mathematical estimation of totality is revealed not only to be grounded in conceptuality, but also that in order to obtain its rightful objectivity, it must be grafted on imaginative, subjective determination — in other words, that it must also be singularly grounded. Furthermore, I considered the singular aspects of object-constitution to be accounted for by the understanding in the very system of the categories of quantity itself. My reading of the Analytic of the sublime lead me to interpret the special act of the understanding — insofar as it is required to derive the category of totality — as essentially tied to the limited comprehensive powers of the imagination and the determination of the subject.

            This way, my aesthetical detour contributes to the study of Kant’s epistemology by proposing that the category of totality is not only to be necessarily complemented by imaginative subjective determination in order to qualify for object-constitution, but that this category could be understood as fundamentally marked by it itself.



Allison, H. (2004), Kant’s Transcendental Idealism: Revised and Enlarged Edition, Yale           University Press, New Haven.

Borboa, S. de J. S. (2018), “On Kant’s Derivation of the Categories”, Kant-Studien, no. 4,         pp. 511–536.

Crowther, P. (1989), The Kantian Sublime: From Morality to Art, Oxford University Press,       Oxford.

De Vleeschauwer, H. J. (1931), Immanuel Kant, N.V. Standaard-Boekhandel, Antwerpen.

Ginsborg, H. (2016), The Role of Taste in Kant’s Theory of Cognition. Routledge, New York.

Ginsborg, H. (2019), “Kant’s Aesthetics and Teleology”, The Stanford Encyclopedia of Philosophy (Winter 2019),      aesthetics/.

Kant, I. (1900a), “Gesammelte Schriften (Vol. 1–22)”, Preußische Akademie der            Wissenschaften, Berlin.

Kant, I. (1900b), Kritik der reinen Vernunft (B. Erdmann, coord.), De Gruyter, Berlin.

Kant, I. (2000), Critique of the Power of Judgment (P. Guyer & E. Matthews, Trans.),    Cambridge University Press, Cambridge.  

Kukla, R. (2006), “Introduction: Placing the Aesthetic in Kant’s Critical Epistemology”, en       R.             Kukla (coord.), Aesthetics and Cognition in Kant’s Critical           Philosophy, Cambridge             University Press, Cambridge, pp. 1–32.   

Longuenesse, B. (1998), Kant and the Capacity to Judge: Sensibility and Discursivity in            the Transcendental Analytic of the Critique of Pure Reason, Princeton           University       Press,             Princeton.

Longuenesse, B. (2005), Kant on the Human Standpoint, Cambridge University Press,   Cambridge.    

Pierobon, F. (2005), “Quelques Remarques Sur la Conception Kantienne du Jugement    Singulier”, Kant-Studien, no. 3, pp. 312–335.

Pillow, K. (2000), Sublime Understanding: Aesthetic Reflection in Kant and Hegel, MIT           Press,             Cambridge.

Smith, S. D. (2015), “Kant’s Mathematical Sublime and the Role of the Infinite: Reply to          Crowther”, Kantian Review, no. 1, pp. 99–120.

Vandenabeele, B. (2015), The Sublime in Schopenhauer’s Philosophy, Palgrave Macmillan, London.

Van de Vijver, G., & Noé, E. (2011), “The Constraint Is the Possibility: A Dynamical    Perspective on Kant’s Theory of Objectivity”, Idealistic Studies, no. 1-2, pp.        95-112.  

Zammito, J. (1992), The Genesis of Kant’s Critique of Judgment, The University of        Chicago Press, Chicago.

Zuckert, R. (2019), “Kant’s Account of the Sublime as Critique”, Kant Yearbook, no. 1,                         pp. 101–­­120.


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· PhD Researcher at Ghent University as a fellow of the FWO Flanders. E-mail: [email protected]


[1] This paper joins the established scholarly project set to investigate the epistemological relevance of the first part of the third Critique, allowing for, in the words of Kukla, a ‘retrospective re-reading’ of the first Critique (Kukla 2006, p. 23). See, for instance, Longuenesse (Longuenesse 1998; 2005), Ginsborg (Ginsborg 1990; 2019) and Kukla (Kukla 2006). From these endeavors, however, the sublime is often remarkably absent. The spirit of this paper is in that sense perhaps closest to Pillow, who contends that the sublime is tied to “the uncanny Other ‘outside’ our conceptual grasp” and that it thereby, nonetheless, “advances our sense-making pursuits even while eschewing unified, conceptual determination” (Pillow 2000, p. 2). I also agree with Zuckert when she argues that the sublime, “as an experience of human cognitive limitations, [seems] pertinent to Kant’s theoretical project of critique, namely his attempt to delimit the scope of human knowledge” (Zuckert 2019, p. 102).

[2] In the metaphysical deduction of the first Critique Kant derives the twelve pure categories of the understanding — which account for the constitution of the object — from the twelve forms of judgment. This derivation is at the heart of his transcendental idealism, as it aims to show the a priori character and pure origin of the categories, i.e., that they cannot be derived from experience, but instead must be derived from the general laws of thinking. Apart from that, the metaphysical deduction describes the basic features of the system of the categories, considering how the categories relate to each other in each group (see KrV, B 91-116).

[3] See, e.g., the first Critique’s Table of Nothing (KrV, B 346-9) as an exposition of what does not count as an object, hereby at the same time disclosing what does.

[4] One may wonder if this choice is really best suited for the methodology of negatively delineating categorial totality. Another, perhaps more obvious strategy to achieve such a negative delineation would be to compare categorial totality, developed as a pure concept of the understanding, not with the mathematical sublime, but with totality as an idea of reason — this is De Vleeschauwer’s interesting yet volatile suggestion (De Vleeschauwer 1931, p. 59). In this regard, it is important to note that such a strategy is grafted on the assumption that the faculty of pure reason is — supposedly quite unlike the understanding — detached from the faculty of sensibility. Contrary to the understanding, namely, reason has a less limited or even un-limited extension. In that sense, totality as an idea of reason could indeed serve to negatively delineate totality as a category of the understanding, whereby the latter could be distinguished from the former by reference to its necessary relation with sensible intuitions — necessary, namely, in function of constituting objects. Such a methodological choice would, however, have a much harder time pinpointing how discursive faculties can (and must) relate to sensibility. Indeed, so does the third Critique suggest that, apart from a determining (e.g., categorial) relation of totality to sensible intuitions, there can also be a reflecting (e.g., sublime) one. This means that the different notions of totality can be delineated not only by asking whether they must be related to sensibility, but also how they are related to it. In function thereof, investigating categorial totality by looking at the mathematical sublime promises to yield much more specific insights than would a mere investigation of totality as an idea of reason. As for the mathematical sublime, we will see that the totality at play here is intricately connected to sensibility and imagination as much as the category of totality is (as for the latter, see the first Critique’s Transcendental Deduction (KrV, A 95-130/B 116-169) and the chapter on the Schematism (KrV, B 176-187)). In both cases, however, the intricate connection is seemingly established in a highly unique and different manner. As a consequence, such a juxtaposition allows for a more focused delineation. To delineate categorial totality by comparing it with totality as an idea of reason would, by contrast, not bring us as far, since in the latter case it seems that there is no intricate relation to sensibility to begin with — but this is only an assumption, not unworthy of further investigation. Fortunately, however, as the experience of the sublime cannot be understood without at the same time explaining the role of reason in it (cf. infra), the idea of totality must in either case be addressed by my analysis. To delineate categorial totality by way of a comparison with sublime totality is therefore still to compare it with the idea of totality. Thus, my methodology by no means sidelines the faculty of reason.

[5] As it is my aim to further disentangle the notion of totality, be it preliminarily, I concentrate here on the mathematical sublime, although the dynamical sublime (treaded by §§28-29) should not necessarily count as irrelevant.

[6] Quite contrary to the Guyer-Matthews translation, Kant himself writes that “das Erhabene ist dagegen auch an einem formlosen Gegenstande zu finden […]” (KU, AA 05: 246.24-25; italics added). In this text, however, I deal with the sublime in this specific capacity of formlessness nevertheless thought as a totality.

[7] Guyer and Matthews (2000) have chosen to translate eine Größe sein with ‘to be a magnitude’ and to translate Groß sein with ‘to be great’, leaving behind the concept of quantitas and attributing the English translation of magnitudo to the latter’s opposite. In the English language, this makes sense, but it does complicate things a bit. To avoid any misunderstandings, I have chosen not to use the English term ‘magnitude’ in this text.


[8] See KU, AA 05 251.09, 254.17, where Kant mentions logische Größenschätzung. However, only rarely does Kant distinguish between logische and mathematische Größenschätzung consistently and explicitly. One must infer from the context which one is at play. But in the end, logische Größenschätzung is seemingly nothing but mathematische Größenschätzung as conceived in isolation from imagination and sensibility.

[9] Yet on Crowther’s “austere reading” the role of the infinite would be redundant here (Crowther 1989, pp. 104-106). On Crowther’s account, reason would not require additional theoretical support from the imagination’s stride to infinity in order to develop totality. Here, Crowther maintains quite unproblematically that reason is able to attain totality without the imagination’s help. However, he also argues that this involves “comprehension of the phenomenal totality of any given magnitude in a single whole of intuition—that is, irrespective of whether or not it is to be used as a measure in the estimation of magnitude” (Crowther 1989, p. 101). This is flawed because in the Analytic of the sublime Kant intends to connect reason’s idea of totality to the sensible dynamics of the imagination (e.g., in the latter’s stride to infinity); and more importantly, because Crowther confuses the concept of totality as a concept of the understanding with totality as an idea of reason, as Allison rightly remarks (Allison 2004, p. 397). In this regard, agreeing with Crowther would be a step back in attempting to analyze the notion of totality. I do however completely agree with Crowther when he contends, quite in line with my aim, and pace Allison, that “while Kant discusses this process [of apprehension and comprehension] only in relation to the attempt to present infinity as an absolute measure, it must also apply in relation to our attempts to grasp the phenomenal totality of any object in a single whole of intuition” (Crowther 1989, p. 102). I want to stress, however, that this still requires a thorough differentiation of (i) totality conceived by the understanding from (i) totality conceived by reason. 

[10] In that sense, I fully agree with Smith when he contends that “[a] sense of the infinite only comes through an imaginative release (after an initial tension) […]” (Smith 2015, p. 115).

[11] Despite this ‘directedness’, the transcendental logic of the categories is seen as solely general in nature because it solely rests on the general functions of judgment. To say that the categories are general is yet another way to say that they are unlike intuitions. Intuitions are, namely, not general but singular. Kant makes clear that knowledge ‘is’ either intuition or concept, adding that the former relates to the object directly and is therefore singular (einzeln) while the latter relates to the object indirectly through marks or characteristics (vermittelst Merkmals) that can hold for different objects in general (KrV, B 377).

[12] In the Schematism chapter, Kant tries to show how the faculty of the understanding and the faculty of sensibility could be reconciled, given the fact that their representations (Vorstellungen) are completely heterogeneous. At that point in the Critique, it is still unclear how categories can be ‘applied to’ (angewandt auf) intuitions, although it is clear (from their transcendental deduction) that they must. He seeks, thus, for a third power that can ‘mediate’ between the two faculties: “Nun ist klar, dass es ein Drittes geben müsse, was einerseits mit der Categorie, anderseits mit der Erscheinung in Gleichartigkeit stehen muss, und die Anwendung der ersteren auf die letzte möglich macht. Diese vermittelnde Vorstellung muss rein (ohne alles Empirische), und doch einerseits intellectuell, anderseits sinnlich sein. Eine solche ist das transscendentale Schema” (KrV, B 177). Only the power of the imagination, says Kant, can vouch for such representations. In this paper, however, I make the claim that the system of categories, which pertains to the faculty of the understanding alone (and not to the power of the imagination), is itself anticipatory of said relation to sensibility, i.e., of its schematization. How my claim here — that the system of the categories itself anticipates schematization — could relate to the still necessary procedure of schematizing these categories surely requires more in-depth textual analysis of the first Critique’s Analytic of concepts and principles.  

[13] See Borboa, who argues that this special act of the understanding functions as the central principle of Kant’s deduction of every third category (Borboa 2018). His approach finds inspiration in Kant’s discussions with Johann Schultz on the necessity to include these third categories in the Table. In the first Critique, Kant states that the combination of every first category with the second of its group should give way to the third (KrV, B 110). In his letter to Schultz from February 17th, 1784, I take it that Kant defends this triadic dynamic as inseparable from the essentially transcendental instead of merely general (or formal) nature of the derivation (Br, AA 10: 366-367). Borboa’s main contribution, in attempting to find a principle for this transcendental derivation, consists in the suggestion that it must be every third form of judgment that combines the first two categories in generating the third category. For the categories of quantity, this means that the singular judgment combines the category of unity (as derived from the universal judgment) with the category of plurality (as derived from the particular judgment) to generate the category of totality. From a formal logical perspective — i.e., the presumed ‘default mode’ of the faculty of the understanding — such a derivation must count as a special act indeed. Yet the fact that this special act is nonetheless carried out by the understanding — which proceeds only in a general, discursive manner — might nonetheless indicate the latter’s potential to systematically anticipate its own singular — i.e., non-general — capacities. Quite fundamentally, this would mean that my exploration of categorial totality from within the Analytic of the sublime — extensively drawing on the power of the imagination and sensibility — is far from incompatible with accounts that focus, on the other hand, on the specificity of the logic behind the functions of judgment and the categories they are related to. But Borboa’s suggestion is particularly interesting because it is potentially on par with my hypothesis (cf. supra) that mathematical estimation (and constitution) of quanta can be dissected into (i) a moment of logical estimation, (ii) a moment of aesthetical estimation, and (iii) a moment of ‘proper’ mathematical estimation, whereby (iii) requires a combination of (i) and (ii). I propose that here too a singular moment — namely, (ii) — is connected to a universal moment — namely, (i) — in relation to a certain totality — namely, (iii). But these issues require further research.

[14] It could be argued (although I cannot substantiate it here) that my interpretation of the special act of the understanding (i.e., as a mark of the singularity pertaining to the category of totality) might also hold for the other classes of categories. The special act is required, according to Kant, to derive all third categories: the category of limitation must be considered as reality combined with negation; community, as the reciprocal causality of substances; necessity, as existence given by possibility. This paper does not purport to defend that the special act entails a mark of singularity in all of these derivations. It only tries to substantiate that this might be the case for the category of totality. In itself, this should not be a problem, since Kant does not give the impression that the special act must be of identical nature in all of its instances. Kant only states that the understanding must posit a special act in order to derive the third categories, highlighting that the latter involve a ‘constraint’ pertaining to the transcendental rather than merely formal logical countenance of their derivation. Regarding the third category of quality, however, it occurs to me that the special act might very well testify to singularity. As Borboa has it, to acquire the category of limitation (in an infinite judgment), it does not suffice to have a mere combination of reality (in an affirmative judgment) with negation (in a negating judgment). Indeed, something can be positively affirmed of a subject (e.g., that it involves pleasure) and something else can be negated of that same subject (e.g., that it is a vice, by opposing virtue), but then “the positive and negative determinations are not combined so as to oppose each other and yield a limitation” (Borboa 2018, p. 524). By stating, however, in an infinite judgment, that the soul is non-mortal (nichtsterblich), a certain negation (a negative predicate) is itself positively affirmed of a subject. Kant interestingly adds that, hereby, an infinite space of possible predicates is opened up — “dem übrigen Raum ihres Umfangs” (KrV, B 97). Judging that the soul is nichtsterblich gives a negative direction to positively delineating this subject according to other predicates. This direction can then be further articulated by adding that the soul is also, e.g., timeless or spaceless, etc. In that sense, subsuming a subject under a negative predicate has positive effects that are as yet undetermined, merely encircling a field of determinability for the subject. Crucially, however, it appears to me that the conceivability of such an undetermined predicative space calls for assuming a singular position within this predicative space. The category of limitation arguably indicates, namely, that one can only gradually determine a subject in terms of predicates, and that this positive endeavor can only be put in motion by negatively giving direction to a certain infinite realm, explored step-by-step. But this interpretation is evidently in need of further investigation.


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