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For Aristotle™s view, see Posterior Analytics ii, 19, 99b15“100b18, where Aristotle explains
that universals are deposited in our minds by the repeated perception of sensible indivi-
duals. Nothing could be further from Kant™s view of concept formation. On Cassirer™s
criticism of Mill, see Substanzbegriff und Funktionsbegriff, ch. 1.
See Substanzbegriff und Funktionsbegriff, chs. 2 and 3.


In the essay that accompanies his translation of Kant™s ˜˜Uber Kastners
Abhandlungen™™, Michel Fichant discusses some of the analyses I pro-
posed in my book (KPJ).2 His discussion of my view centers on the
nature of space as put forth in the Critique of Pure Reason. More speci-
fically, it centers on the distinction between ˜˜form of intuition™™ and

´ ´ ´
Michel Fichant, ˜˜˜L™Espace est represente comme une grandeur infinie donnee™. La radi-
´ ´
calite de l™Esthetique™™ [˜˜˜Space is represented as an infinite given magnitude™: the radicality
of the Aesthetic™™], Philosophie, no. 56 (1997), pp. 20“48 (henceforth ˜˜˜L™Espace™™™). This
article follows Fichant™s presentation (pp. 3“12, henceforth ˜˜Presentation™™) and translation
into French of Kant™s essay ˜˜Uber Kastners Abhandlungen™™ (˜˜On Kastner™s articles™™) AAxx,
¨ ¨
pp. 410“23 (pp. 12“20). Kastner was a mathematician whose three articles (˜˜What does
possible mean in Euclid™s geometry?™™; ˜˜On the mathematical concept of space™™; ˜˜On the
axioms of geometry™™) were published in Eberhard™s Philosophisches Magasin, as part of
Eberhard™s attempt to prove the superiority of the Leibnizian view over the Kantian view
of mathematics. Kant counters Eberhard by claiming that Kastner™s view is in fact in
complete agreement with his own. Kant™s essay on Kastner™s articles contains some of his
most illuminating remarks on space as a pure intuition, and its relation to geometry.
Michel Fichant™s article is an analysis of Kant™s view of space in contrast to that of Kant™s
Leibnizian predecessors. Fichant™s discussion of my thesis concerning the relation between
˜˜form of intuition™™ and ˜˜formal intuition™™ according to Kant is only a subsidiary discussion,
occupying a few pages in the main article: see pp. 35“8 and passim. I found his discussion
insightful and challenging, I am grateful to him for giving me this occasion to attempt a
clarification of my view. In this English version of my response, when citing Fichant™s
discussion I will give his own references to KPJ, and then give the corresponding page in
KCJ. In the cases where references to my book are my own, I will refer only to KCJ.


˜˜formal intuition™™ (introduced by Kant in x26 of the Transcendental
Deduction in the second edition of the Critique), and on the phrase in
the Transcendental Aesthetic according to which space is ˜˜represented
as an infinite given magnitude™™ (B40). Michel Fichant thinks that the
explanation I propose for Kant™s distinction leads me to intellectualize
the forms of sensibility expounded in the Transcendental Aesthetic and,
true to a tradition begun by Fichte and represented in France by
Lachieze-Rey among others, leads me, in effect, to deny that Kant grants
any independence to sensibility with respect to the understanding.3
This last reproach surprises me. Recognizing the irreducible charac-
ter of sensibility in the Kantian conception of knowledge is of central
importance to the argument of my book. More particularly, I try to
elucidate the consequences of the irreducibly receptive character of
our sensibility for Kant™s conception of the logical-discursive forms
themselves, that is, of the forms of spontaneity. In fact, Michel Fichant
takes pains to make clear that his criticism concerns only a ˜˜side issue™™ in
my book, and in no way challenges its central thesis.4 But if he is right,
then this means that the thesis I am defending with respect to space and
time is incompatible with the theses I defend in the rest of my book. So I
still need to answer the charge that I might be taking back with one hand
what I had granted with the other.
Michel Fichant is certainly right to say that we disagree on the parti-
cular issues at hand (Kant™s distinction between ˜˜form of intuition™™ and
˜˜formal intuition,™™ and the role of imagination in our representation of
space and time). Yet I do not think that the position he attributes to me is
the one I defend. I think our disagreement concerns four main issues:
(1) Kant™s view of the relation between the functions of the understand-
ing and the forms of sensibility; (2) Kant™s footnote to x26 of the
Transcendental Deduction, where he introduces the distinction between
forms of intuition and formal intuition; (3) the meaning of the expres-
sion ens imaginarium, which Kant uses to describe space and time; (4) the
relation between space as quantum and the category of quantity (quanti-
tas). In what follows I will try to clarify my position on each of these points
and explain what I believe to be the nature of our disagreement.

Fichant, ˜˜˜L™Espace™,™™ p. 24, n. 11.
Ibid., p. 35, n. 30.

Understanding and sensibility
Michel Fichant thinks that my view is in some ways similar to that of
Cassirer, for whom ˜˜the functions of the understanding are the precon-
ditions for ˜sensibility™.™™5 Yet nowhere do I defend such a statement. On
the contrary, I expressly state that the radical distinction between sen-
sibility, endowed with forms specific to it, and the understanding, with its
logical forms or functions, is at the heart of Kant™s argument from one
end of the Critique to the other, and in particular in the sections that are
the main target of my investigation, the Transcendental Deduction of
the Categories and the System of Principles. Our real quarrel does not lie
here. Rather, it concerns the question whether I am right to maintain
that Kant™s presentation of space and time in the Transcendental
Aesthetic, while fully belonging in an aesthetic in Kant™s sense, that is,
in a science of the rules of sensibility or receptivity, is nevertheless seen in
a new light when the reference to the synthesis speciosa (i.e. the figurative
synthesis, or the transcendental synthesis of imagination), is introduced
into the argument of the Transcendental Deduction of the Categories.
In my account, it then appears that space and time, as described in the
Transcendental Aesthetic, certainly belong to sensibility, but to a sen-
sibility affected (and not generated, a point about which my position
differs from that of Fichte!) by spontaneity, that is, by the understanding.
In the Transcendental Aesthetic, Kant could not mention this ˜˜affection
by the understanding,™™ nor did he need to mention it. Indeed it appears
briefly only in the second edition, in an addition to the exposition of time
(B67“8). Kant did not need to mention it because what is important in
the Aesthetic is to show that space and time are originally intuitions
(˜˜singular and immediate representations™™) and not concepts (˜˜universal
and reflected representations™™), that they are sensible (a form or mode of
ordering according to which we receive ˜˜inner™™ and ˜˜outer™™ impres-
sions) and not intellectual (a function by which we produce concepts).
The further point that singular representations of space and time, sen-
sible though they may be, depend on a synthesis speciosa, that is, a trans-
cendental synthesis of imagination, is not important to the specific
argument of the Aesthetic. Nor could Kant have argued for this point,
had he wanted to. For at that stage in the Critique he had none of the tools
necessary for explaining the nature of the synthesis speciosa, since the

Ernst Cassirer, ˜˜Kant und die moderne Mathematik,™™ in Kantstudien, no. 12 (1907), p. 35.
Cited by Fichant, ˜˜˜L™Espace™,™™ p. 24, n. 11.

latter depends on a ˜˜transcendental unity of self-consciousness™™ whose
status is explained and justified only in the Transcendental Deduction of
the Categories. It is also in the latter that the distinction between form of
intuition and formal intuition, and along with this distinction, what I
have called a ˜˜re-reading™™ of the Transcendental Aesthetic, come into
play. Contrary to what Fichant seems to believe, according to me this
re-reading is neither a correction of the Aesthetic™s content, nor a rectifica-
tion of its place within the Critique. Rather, it is an added explanation: the
explanation of the relation of space and time to the unity of self-
consciousness, an explanation that can be provided only in the context
of the Transcendental Deduction of the Categories.
It is on this last point that there remains a significant disagreement
between Fichant and myself. Michel Fichant thinks I am wrong to
believe that the argument in the second part of the Transcendental
Deduction leads Kant to affirm that the forms of intuition or pure
intuitions, described in the Aesthetic “ whether we are talking about
space or about time “ are forms of a sensibility affected by the under-
standing. This is why he refuses the identification I am proposing
between ˜˜form of intuition™™ “ at least in one of its meanings, which, in
my view, is that of most of its occurrences in the Transcendental
Aesthetic “ and ˜˜formal intuition.™™

Form of intuition and formal intuition
Michel Fichant asserts that ˜˜no textual evidence™™ supports the identity
I suggest that Kant intends to maintain between the form of intuition (or
pure intuition) of the Transcendental Aesthetic, and the formal intuition
of the Transcendental Deduction of the Categories.6 And yet he himself
cites (although relegating them to a footnote) two texts, quoted in my
book, in which Kant ˜˜expressly identifies form of intuition and formal
intuition.™™7 So much for ˜˜no textual evidence.™™ But this is not what is
essential for my purpose. What is essential lies in x26 of the
Transcendental Deduction and its footnote, which lend support to my
interpretation of the two instances of ˜˜express identification™™ acknowl-
edged by Fichant. Here is the passage from x26, and its footnote:

Fichant, ˜˜˜L™Espace™,™™ p. 35.
Ibid., p. 37, n. 32; cf. KCJ, pp. 221“2. The texts cited are B457, and On a Discovery, AAviii,
pp. 222“3.

But space and time are represented a priori not merely as forms of
sensible intuition, but also as intuitions themselves (which contain a
manifold), and thus with the determination of the unity of this manifold
in them (see the Transcendental Aesthetic).*
*Space, represented as object (as is really required in geometry), con-
tains more than the mere form of intuition, namely the comprehension of
the manifold given in accordance with the form of sensibility in an
intuitive representation, so that the form of intuition merely gives the
manifold, but the formal intuition gives unity of the representation. In
the Aesthetic I ascribed this unity merely to sensibility, only in order to
note that it precedes all concepts, though to be sure it presupposes a
synthesis, which does not belong to the senses but through which all
concepts of space and time first become possible. For since through it (as
the understanding determines the sensibility) space or time are first
given as intuitions, the unity of this a priori intuition belongs to space
and time, and not to the concept of the understanding. (B160 and

As we can see, Kant expressly states here that the same unity of
intuition that he had attributed, in the Transcendental Aesthetic, to
sensibility alone because it is anterior to all concepts must now be held
to suppose a synthesis by which ˜˜space and time are first given as intui-
tions.™™ Michel Fichant probably thinks that the unity in question here is
the unity of particular figures in space, resulting from the construction
of geometrical concepts.8 But the text, it seems to me, does not allow this
interpretation, since it expressly states that the unity in question pre-
cedes all concepts. What is in question here is space as one whole, and
time as one whole, within which all particular figures and durations are
delineated. How can space and time as a whole nevertheless result from
an ˜˜affection of sensibility by the understanding?™™ In my view, this is
because the understanding in question is none other than the ˜˜trans-
cendental unity of apperception,™™ which, Kant explains in the

Cf. ˜˜Presentation,™™ p. 11, where Fichant cites the following sentence from Kant™s essay on
Kastner™s articles: ˜˜Objectively given space is always finite™™ (AAxx, p. 420, cf. Fichant™s
translation, p. 18). Fichant concludes this sentence in his own way, writing: ˜˜since it is only
attained by the construction which subordinates it to the concept in order to make of it a
formal intuition.™™ Yet Kant does not use the term ˜˜formal intuition™™ in this text. Kant opposes
the finite space resulting from construction under concepts to the infinite space of the
metaphysician, which the geometrician must presuppose. This space, he says, is a ˜˜pure
form of the subject™s sensible mode of representation as a priori intuition.™™ We must therefore
ask ourselves which of the two descriptions of space (finite space constructed under concepts
or the infinite space presupposed by this construction) corresponds to what is described, in
the note to x26, as a ˜˜formal intuition,™™ which, Kant specifies, ˜˜precedes all concepts.™™

arguments of the Metaphysical Deduction and the Transcendental
Deduction of the Categories, is the source of a synthesis of what is
given in sensibility prior to any analysis (and thus prior to any concept).
To describe this, I have used the expression ˜˜pre-discursive understand-
ing,™™ and I have proposed the idea that our ˜˜capacity to judge™™ (Vermogen
zu urteilen, to be distinguished from the power of judgment, or
Urteilskraft), determining our sensibility (the expression is Kant™s: see
the text quoted above), generates the representation in imagination of
one, undivided space and one, undivided time, within which all spatial
or temporal extension is to be delineated.
I cannot restate here the whole exposition and defense of the point I
make in KCJ. I would like simply to emphasize this: my interpretation
has the advantage of taking into account not only all of Kant™s formula-
tions in the footnote cited above but also the function of this text in the
general structure of Kant™s argument in the Transcendental Deduction.
In the main text to which the footnote is appended, Kant expressly states
that what he now intends to do is to consider ˜˜whatever comes before our
senses,™™ in order to comprehend how appearances can fall under the
laws of the understanding. The interpretation I am proposing for Kant™s
answer to this question differs both from Heidegger™s response, assert-
ing that imagination is the ˜˜common root™™ of sensibility and the under-
standing, and from Cassirer™s response, intellectualizing sensibility.
What I am proposing is that by ˜˜affecting sensibility,™™ spontaneity, or
the mere ˜˜capacity to judge,™™ even before producing the least concept
and thus the least judgment, promotes space and time, originally the
mere forms of manifoldness (Mannigfaltigkeit, which translates the Latin
multitudo), to forms of the unity of the manifold within which schemata
for the categories can be delineated and the subsumption of appearances
under the categories or ˜˜universal representations of pure synthesis™™ is
thus made possible.
Fichant thinks that I ˜˜entirely make up™™ the idea of a ˜˜mere poten-
tiality of form,™™ as one of the meanings of the expression ˜˜form of
intuition.™™9 In KCJ I acknowledge that the expression ˜˜potentiality of
form™™ is my coinage, and I explain why I offer it. I relate it back to the
theme of epigenesis, which is not at all made up by me.10 In any case, the
fact that the term ˜˜form of intuition™™ has several meanings seems to me

Fichant, ˜˜˜L™Espace™,™™ p. 36.
See Longuenesse, KCJ, pp. 221“2, n. 17. Epigenesis is discussed in this volume, ch. 1,
pp. 26“9, and ch. 2, pp. 42“3.

to be uncontroversial. In his 1790 discussion with Eberhard, Kant dis-
tinguishes the ˜˜mere formal ground™™ of sensibility, i.e. the form of space
(and we may suppose, the form of time as well) as the form proper to the
mere capacity to receive impressions, from the ˜˜form of external objects
in general™™ or formal intuition, generated when sensible impressions
provoke the activity (the term is Kant™s) of the mind and thus ˜˜the
original acquisition™™ of the representation of space as pure intuition.
Kant specifies, as he did in x26 of the Transcendental Deduction, that the
original acquisition of this intuition ˜˜precedes by far the determined
concept of things which are adequate to this form.™™11 I do not agree
with Fichant when he claims that the formal intuition of the footnote to
x26, unlike that of the response to Eberhard, is a product of a ˜˜derivative
acquisition™™ in which ˜˜the pure concepts of the understanding play a
part.™™12 Kant, as we just saw in the text quoted above, explicitly states the
opposite: the formal intuition of x26 ˜˜precedes all concepts.™™
The lesson I take from On a Discovery is thus the following: the ˜˜first
formal ground of sensibility™™ is what I have called ˜˜mere potentiality of
form™™ (which Kant also calls simply ˜˜form™™: I will return to this point in a
moment). The ˜˜formal intuition™™ or ˜˜pure intuition™™ or ˜˜form of external
objects™™ (appearances) is in my view the form of intuition or pure intui-
tion of the Transcendental Aesthetic, the formal intuition of the
Transcendental Deduction, and the ˜˜form of intuition or formal intui-
tion™™ of the note to the Transcendental Dialectic cited above. I would not
say that ˜˜all distinctions between the three terms are erased™™ in the
interpretation I propose. In fact I devote several pages to elucidating
the meaning and function of their distinction.13 However, it is true that
in my view, these different terms serve primarily to distinguish different
aspects under which one and the same referent is considered: this
referent is the space presupposed by geometry and whose nature meta-
physicians endeavor to explain (as Kant says in his remarks on Kastner)¨
rather than the figures in space that the geometrician constructs, or the
position and spatial figures in space of the empirical objects studied by
the natural sciences, both of which presuppose the formal intuition of
space as one space in which geometrical figures are constructed and
empirical objects are located and related to each other.

On a Discovery, AAviii, pp. 222“3. Cf. KCJ, p. 252.
Fichant, ˜˜˜L™Espace™,™™ p. 37, n. 32.
Ibid., p. 35; Longuenesse, KCJ, pp. 216“19. The three terms in question are ˜˜form of
intuition,™™ ˜˜pure intuition,™™ and ˜˜formal intuition.™™

I would not say either that I ˜˜reject any intrinsic difference between
form of intuition and formal intuition.™™14 It is true that I think the
expression ˜˜form of intuition™™ in one of its uses, and the expression
˜˜formal intuition™™ have the same referent, although Kant uses one
expression or the other depending on the context. But in addition, I
do maintain a difference not only relative to the aspect and context in
which one and the same referent is considered, but even in referent,
between form of intuition as ˜˜first formal ground™™ of sensibility, and
formal intuition. This is because in my interpretation, the form of intui-
tion as ˜˜first formal ground of sensibility™™ (in On a Discovery) is different
from the form of intuition as the form of appearances, i.e. (I maintain)
formal intuition.15
Michel Fichant thinks he can draw an argument against my position
from x38 of the Prolegomena, where Kant explains:
That which determines space to assume the form of a circle, or the
figures of a cone and a sphere is the understanding, so far as it contains
the ground of the unity of their constructions. The mere universal form
of intuition, called space, must therefore be the substratum of all intui-
tions determinable to particular objects; and in it, of course, the condi-
tion of possibility and of the variety of these intuitions lies. But the unity
of the objects is entirely determined by the understanding.

Fichant comments in a footnote:
This text invalidates one of the arguments by which Beatrice
Longuenesse rejects any intrinsic difference between form of intuition
and formal intuition: form being by definition the determination with
respect to the matter which is the determinable, attempting to determine
by concept the forms of intuition in order to make them into formal
intuitions would be to ˜˜misinterpret the very notion of form (which
would in that case, paradox of paradoxes, be characterized as that

˜˜˜L™Espace™,™™ p. 38, n. 34.
The ˜˜first formal ground of sensibility™™ of On a Discovery seems to me to be the same as what
Kant calls ˜˜subjective condition regarding form™™ in the Transcendental Aesthetic (cf. A48/
B65) or form of ˜˜synopsis™™ (cf. A94“5). This ˜˜form™™ or ˜˜first formal ground™™ is a form for
the ˜˜matter™™ that are sensations. The ˜˜form of intuition™™ as ˜˜formal intuition™™ is a form for
the ˜˜matter™™ that are appearances. The two meanings of the term ˜˜matter™™ (sensation and
appearances), and the two meanings of ˜˜form™™ can be found, it seems to me, in this passage
of the Amphiboly of Concepts of Reflection, in the Critique of Pure Reason: ˜˜the form of
intuition (as a subjective constitution of sensibility [form (i)]) precedes all matter (the
sensations), thus space and time [form (ii)] precede all appearances and all data of appear-
ances™™ (A267/B323).

which is undetermined!)™™ (op.cit., p. 248). If anyone has produced a
misinterpretation, it would be, as the text of the Prolegomena shows,
Kant himself, yet another paradox!16

I have just explained why I do not take myself to ˜˜reject any intrinsic
difference™™ between form of intuition and formal intuition, as Fichant
supposes I do. I now would like to clarify just what it is I denounce as a
˜˜misinterpretation.™™ I do not say or think that it would be a misinterpre-
tation to believe that the form of intuition can be determined by
concepts. What I do say is that in considering the relation between ˜˜form
of intuition™™ and ˜˜formal intuition,™™ it would be paradoxical to interpret
the term ˜˜form™™ in ˜˜form of intuition™™ as meaning ˜˜undetermined,™™ and
˜˜formal intuition™™ as that which is ˜˜determined™™ (by concepts). In making
this remark, I am opposing a thesis defended by Henry Allison,
mentioned in a footnote.17 But I should have been more precise. This
is what I mean to say: form is always form for a matter, which it deter-
mines or orders. The form of intuition as ˜˜first formal ground of intui-
tion™™ is the form for a matter, sensations. When unified under the
transcendental unity of apperception, before any concept, the form of
intuition is again the form for a matter, the appearance or ˜˜indetermi-
nate object of empirical intuition™™; this form, considered independently
of any matter, is ˜˜pure intuition™™ or ˜˜formal intuition™™ (the space ˜˜that is
needed in geometry™™). Pure intuition is determined by concepts when
figures are constructed in space, when spatial configurations and posi-
tions of empirical objects are schematized and recognized, and when the
mathematical constructions of concepts are applied in a mathematical
science of nature. Space and time are then forms for a matter, phenom-
ena, objects of empirical intuition determined by concepts.
It is worth noticing that Kant does not use the expression ˜˜formal

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