Exploring the Deduction of the Category of Totality
from within the Analytic of the Sublime
Levi Haeck·
Ghent University, Belgium
Abstract
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.
Introduction
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 Critique — but also to fundamentally underly
the metaphysical deduction of the category of totality, be it under the guise
of a special act.[14]
Conclusion
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.
Bibliography
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. https://doi.org/10.1515/kant-2018-3002.
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), https://plato.stanford.edu/archives/win2019/entries/kant- 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. https://doi.org/10.1017/CBO9780511804656
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. https://doi.org/10.1017/CBO9780511498220.001
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. https://doi.org/10.1515/kant.2005.96.3.312
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. https://doi.org/10.1017/S1369415414000302
Vandenabeele, B. (2015), The Sublime in
Schopenhauer’s Philosophy, Palgrave Macmillan,
London. http://hdl.handle.net/1854/LU-3235223
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.
