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intuition™™ in the passage from x38 of the Prolegomena quoted above,
which concerns the determination of the sensible form by concepts in
the construction of figures in space. It remains Fichant™s task, then, to
account for the fact that in the texts where Kant does make use of the
expression “ the footnote to x26 as well as On a Discovery “ Kant says that
the formal intuition precedes all concepts.

See Prolegomena, x38. Fichant, ˜˜˜L™Espace™,™™ p. 38, n. 34. The page reference in the citation
from Fichant is to KPJ. Cf. KCJ, p. 223.
Longuenesse, KCJ, n. 18, p. 222. Cf. Henry Allison, Kant™s Transcendental Idealism: An
Interpretation and Defense, rev. enlarged edn (New Haven: Yale University Press, 2004),
pp. 112“16.

Fichant thinks one should not give too much weight to the footnote to
the Transcendental Dialectic in which form of intuition and formal
intuition are expressly identified (B457). For, he says, Kant specifies in
this note that space, as a form of intuition or formal intuition, ˜˜is not an
object that can be intuited.™™ I suppose Fichant means that one cannot
therefore identify the formal intuition mentioned here with the space
˜˜represented as object (as is really required in geometry)™™ mentioned in
the footnote to x26. But in fact, what Kant says in the footnote to the
Transcendental Dialectic is that ˜˜space is merely the form of outer
intuition (formal intuition), but not a real object that can be outwardly
intuited [kein wirklicher Gegenstand, der ¨ußerlich angeschaut werden kann].™™
This is in agreement with the idea I am defending and Fichant is
opposing, that space, as one and infinite, is an ens imaginarium, a being
of imagination. That is to say, it is not empirically given but on the
contrary imagined, and as such, it is the condition for any intuition
of an object in space. The representation of space as one, and as infinite,
is a representation of the imagination. And indeed, what else could it
be? Is it not clear that it cannot be a perception? Nevertheless, it is the
condition for any situation and configuration of objects in space, and
once represented as a system of relations of the latter, it is the form of
phenomena. Only thus does space (as does time) acquire empirical
I will be quicker with the two further points I announced at the
beginning: space as ens imaginarium, and space as quantum infinitum.
For there the nature of our disagreement is for the most part clarified,
I think, by the two points I just discussed.

Space as ens imaginarium
In the extraordinary ˜˜table of nothing™™ which closes the Transcendental
Analytic, Kant defines ˜˜empty intuition, without an object,™™ as an ens
imaginarium (A292/B348), for which he gives as an example, space.
Michel Fichant suggests that this representation of space as imaginarium,
obtained when abstracting from any object given in it, should not be
associated with the exercise of imagination that Kant calls synthesis
It would be a mistake to interpret this description of space as an imagin-
ary being as if it made the pure intuition of space a product of an act of
transcendental imagination determining sensibility. As an originary and

given representation, this representation cannot be the product of spon-
taneity: in the characterization of space without an object as ens imaginar-
ium, the role of the imagination has to do with ˜˜without an object™™ and
not with space itself; in other words, what is an effect of the imagination
is the thought-experiment which expels things from space and so
discovers space itself as the ineliminable condition of all exercise of
the imagination.18

According to Fichant, in maintaining on the contrary that the ens
imaginarium mentioned at A292/B348 is the product of a synthesis of
the imagination, I am led to maintain also that the original quanta that
are space and time are subjected to the categories of quantity. This is not
what I take myself to be doing. But before considering this point (see
below), I would like to point out that Fichant himself cites, in a note to his
translation of Kant™s text on Kastner, a text from On a Discovery in which
the meaning given to the idea of ens imaginarium seems closer to my
interpretation than to his. There the ens imaginarium appears to be, not
the result of a process of abstraction “ which, strictly speaking, would fall
more under the authority of discursive understanding “ but rather, an
anticipation by imagination of the one space and the one time within
which all compositions and all Dichtungen (fictions) are generated:
Space and time are mere thought-entities [Gedankendinge] and beings of
imagination, not as if they were fictitiously manufactured [gedichtet] by
imagination, but because imagination must ground on them [my emphasis] all
its compositions and all its fictions.19

To say that space and time are ˜˜beings of imagination™™ is not to say that
they are fictions (Dichtungen) of imagination. It is to say, however, that
the imagination forms no imaginary representation without forming a
representation of space and time. But it is also to say that the ima-
gination generates no construction in pure intuition (˜˜composition™™,
Zusammensetzung) without laying as their ground (zum Grunde legen) the
intuition of space and time, represented as one space and one time. This
intuition is in itself a mere ˜˜being of imagination,™™ one that has, however,
empirical reality as the form of appearances.
Fichant might oppose to the interpretation I offer for the role of the
imagination in the representation of space and time (projecting space
and time as one whole rather than abstracting the representation of

Fichant, ˜˜˜L™Espace™,™™ p. 30, main text and n. 21.
AAviii, pp. 202“3, quoted by Fichant, ˜˜˜L™Espace™,™™ p. 19.

spaces and times from the representations of empirical objects) a passage
shortly preceding the one just cited, in which Kant speaks of ˜˜the abstract
space of geometry,™™ which he opposes to ˜˜the concrete space™™ of appear-
ances and describes as a ˜˜being of imagination [ein Wesen der
Einbildung].™™20 But I do not deny that a process of abstraction allows
one to isolate pure space and pure time. On the other hand, when Kant
says that what is thus isolated is a ˜˜being of imagination,™™ in my view he
can only mean that it is the imagination which makes space and time
present to us: although it does not produce them by a process of Dichten
or Zusammensetzen (as it does for imaginary representations and
geometrical figures), it grounds on them all its Dichtungen and
Zusammensetzungen. It is also worth noting that if one considers the
sentence in full, one finds in it a duality similar to that found in the
note to x26 of the Transcendental Deduction. For the sentence quoted
continues as follows: ˜˜for they [space and time] are the essential form of
our sensibility and of the receptivity of intuitions, by which objects are
generally given to us [ . . . ]™™21 In my view, space and time as ˜˜beings of
imagination,™™ on which the imagination ˜˜must ground all its composi-
tions and fictions,™™ are the formal intuitions of the note to x26 in the
Transcendental Deduction. Space and time as ˜˜the essential form of our
sensibility and of the receptivity of the intuitions™™ are the ˜˜first formal
ground of sensibility™™ from On a Discovery and the ˜˜form of intuition™™
from the footnote to x26. The two are of course inseparable: that the
forms of our sensibility or receptivity are space and time is what leads the
imagination to ˜˜ground on them [as formal intuitions] all its composi-
tions and fictions.™™
One of the arguments Fichant opposes to my thesis that space and
time, as pure intuitions (¼ formal intuitions), must be understood as the
product of synthesis speciosa, is that ˜˜while it is easily understood that all
figures are produced in space, one wonders what could possibly be the
˜figure™ of space itself.™™22 I explain this point in KCJ: the main reason I
retain the expression synthesis speciosa rather than figurative synthesis
(figurliche Synthesis in German) is that using the original Latin expression
emphasizes the semantic relation between this synthesis and the formae
seu sensibilium species, ˜˜forms or figures of things sensible,™™ that are,
according to the Inaugural Dissertation, space and time. In my view,

AAviii, p. 202.
Ibid., p. 203.
Fichant, ˜˜˜L™Espace™,™™ p. 36.

we must relate the synthesis speciosa primarily to these species, and only
secondarily to the construction of particular figures in space. It is also
these species that Kant calls ˜˜pure images of all magnitudes™™ just before
laying out the schemata of quantity (A142/B182). I am happy to grant
that this notion of ˜˜pure image™™ is itself enigmatic. But the enigma lies
with Kant. I did not invent it. And for my part I think that it has a
solution if one admits that the projection by the imagination of space
as one and time as one is the necessary condition for the representation
of all figures and durations, as well as the necessary condition of all
quantitative syntheses in space and in time.
This brings me to my fourth and last point: space as a quantum

Quantum and quantitas
According to Michel Fichant, in maintaining that space and time are
products of the synthesis speciosa of imagination, I am committed to
maintaining also that space and time, as original quanta (magnitudes)
are represented under the categories of quantitas, quantity. According to
him, this amounts to ˜˜subordinating the Aesthetic to the Logic.™™23 Now the
distinction between quantum and quantitas is one that I discuss at length,
and I insist there on the fact that the representation of space and time, as
quanta, precedes and conditions the generation of schemata and the
application of categories of quantity.24 About Kant™s distinction between
quantum and quantitas, and the two notions of infinity (the actual infinity
of metaphysical space, presupposed by geometry, where the whole pre-
cedes the parts rather than being the product of a synthesis of parts; and
the potential infinity, or indefiniteness, of any successively synthesized
series of units), I believe we are in complete agreement. But I think “ and
here we certainly disagree “ that according to Kant, representing space
(or time) as quantum infinitum datum, infinite given magnitude, is already
the effect of ˜˜the affection of inner sense by the understanding,™™
although this affection precedes all concepts, indeed precedes all sche-
matization guided by the logical-discursive functions that lead to concept

Ibid., p. 29, n. 21.
On the distinction between quantum and quantitas, see KCJ, pp. 263“71. A quantum is an
entity that is represented as one entity, and represented in such a way that quantitative
determinations can be applied to it. The quantitative determination of a quantum is its
quantitas. For a further discussion of these issues, see ch. 2 in this volume, pp. 43“52.

What, in the end, is our disagreement about? It is about the extent to
which, according to Kant, our intuitions and concepts respectively
depend on the passive and the active aspects of our representational
capacities. Kant™s thesis, as I understand it, is that a merely passive
subject would not have available to her the spatiotemporal unity (˜˜repre-
sented as an infinite given magnitude™™) in which to organize her intui-
tions. I think this thesis is the foundation of the solution Kant proposes to
the problem of the transcendental deduction of the categories: although
the unity of space and time in which appearances are given is not a unity
determined by the categories, the synthesis speciosa or ˜˜effect of the under-
standing on sensibility™™ which generates this unity is also what generates
the particular syntheses by virtue of which appearances become suscep-
tible to being reflected under concepts in accordance with the logical
forms of judgment, and consequently reflected under categories. In the
end, our disagreement cannot be resolved through a consideration
of the Transcendental Aesthetic alone. It calls for a consideration of
the argument in the course of which, and for the benefit of which the
distinction under discussion comes into play: the argument of the
Transcendental Deduction of the Categories.
I do not want to conclude this discussion without noting the many
points of agreement between Michel Fichant and myself. Here are just a
few of those points, listed in the order in which they appear in Fichant™s
article: the novelty of the Kantian theory of modalities and its relation to
Kant™s view of the forms of intuition (Fichant, p. 9; Longuenesse,
pp. 187“8); the novelty of the Kantian treatment of the category of
reality and its relation to the critique of the idea of a whole of reality “
totum realitatis “ in the Transcendental Ideal, in the Critique of Pure Reason
(Fichant, p. 15; Longuenesse, pp. 341“53); the relation between ˜˜mat-
ter™™ and ˜˜form™™ of sensibility and the concepts of matter and form as they
are analyzed in the appendix to the Transcendental Analytic, On the
Amphiboly of Concepts of Reflection (Fichant, p. 23; Longuenesse,
pp. 197“200); the primacy of form over matter of sensibility (ibid.); the
distinction between quantitas and quantum, and the twofold meaning of
the German term Große, translated in French by grandeur (and in English
by magnitude) (Fichant, p. 26; Longuenesse, pp. 298“307); the fact that
space, as the ˜˜pure image of all magnitudes,™™ is a quantum and not a
quantitas, and that as a quantum it precedes the application of any cat-
egory of quantitas (Fichant, p. 34; Longuenesse, pp. 301“4); the import-
ance, to clarify this point, of Kant™s text on Kastner™s articles, a point only
briefly mentioned in my book (p. 303) and on which Fichant™s essay

brings unprecedented light.25 I have learnt a great deal from Fichant™s
meticulous analysis of Kant™s interpretation/appropriation of Kastner™s
articles. I do not believe I have resolved our disagreement, but I hope to
have helped identify and clarify its grounds.

Page references to Longuenesse are in KPJ. Corresponding pages in KCJ are respectively:
pp. 148“9 (modality), pp. 298“310 (reality), pp. 156“7 (matter and form in the
Amphiboly), pp. 263“71 (quantitas and quantum), pp. 266“8 (space as a quantum), p. 268
(reference to Kant on Kastner).



In chapter 1 of the Transcendental Analytic, in the Critique of Pure Reason,
Kant establishes a table of the categories, or pure concepts of the under-
standing, according to the ˜˜leading thread™™ of a table of the logical forms
of judgment. He proclaims that this achievement takes after and improves
upon Aristotle™s own endeavor in offering a list of categories, which
Aristotle took to define the most general kinds of being. Kant claims that
his table is superior to Aristotle™s list in that it is grounded on a systematic
principle.1 This principle is also what will eventually ground, in the
Transcendental Deduction, the a priori justification of the objective valid-
ity of the categories: a justification of the claim that all objects (as long as
they are objects of a possible experience) do fall under those categories.
Kant™s self-proclaimed achievement is the second main step in his effort
to answer the question: ˜˜how are synthetic a priori judgments possible™™?
The first step was the argument offered in the Transcendental Aesthetic,
to the effect that space and time are a priori forms of intuition. As such,
Kant argued, they make possible judgments (propositions) whose claim to
truth is justified a priori by the universal features of our intuitions. Such

What allows Kant to make a claim to the completeness and systematic unity of the table of
categories is the demonstration that the latter have their origin in the understanding as a
˜˜capacity to judge.™™ This point will be expounded and analyzed in the third section of this


propositions are thus both synthetic and a priori. They are synthetic in
that their truth does not rest on the mere analysis of the subject-concept of
the proposition. They are a priori in that their justification does not
depend on experience but on a priori features of our intuitions that
make possible any and all experience. However, space and time, as forms
of intuition, do not suffice on their own to account for the content of any
judgment at all, much less for our forming or entertaining such judgments.
Kant™s second step in answering the question, ˜˜how are synthetic a priori
judgments possible?™™ consists in showing that conceptual contents for
judgments about objects of experience are provided only if categories
guide the ordering of our representations of those objects so that we can
form concepts of them and combine those concepts in judgments.
The two aspects of Kant™s view (we have a priori forms of intuition, we
have a priori concepts whose table can be systematically established accord-
ing to one and the same principle) gradually took shape during three
decades of Kant™s painstaking reflections on issues of natural philosophy
and ontology. His questions about natural philosophy include for instance
the following: how can we reconcile the idea that the reality of the world
must be reducible to some ultimate components, and the idea that space is
infinitely divisible? Are there any real interactions between physical things,
and if so, what is the nature of those interactions? Such questions call upon
the resources of an ontology, where Kant struggles with questions such as:
what is the nature of space and time? How does the reality of space and
time relate to the reality of things? Do we have any warrant for asserting
the universal validity of the causal principle? Is the causal principle just a
variation on the principle of sufficient reason and if so, what is the warrant
for the latter principle?
Kant™s argument for his table of the categories (what he calls, in the
second edition of the Critique of Pure Reason, the ˜˜metaphysical deduc-
tion of the categories™™ [B159]) is one element in his answer to these
questions, as far as the contribution of pure concepts of the understand-
ing is concerned. Further elements will be the transcendental deduction
of the categories, in which Kant argues that the categories whose table he
has set up do have objective validity; and the system of principles of pure
understanding, where Kant shows, for each and every one of the cate-
gories, how it conditions any representation of an object of experience
and is thus legitimately predicated of such objects. From these proofs it
follows, as Kant maintains in the concluding chapter of the Analytic of
Principles, that ˜˜the proud name of an ontology, which presumes to
offer synthetic a priori cognitions of things in general in a systematic

doctrine . . . must give way to the more modest one of a mere analytic of
the pure understanding™™ (A247/B303). In other words, where the ontology
of Aristotelian inspiration defended by Kant™s immediate predecessors
in German school-philosophy purported to expound, by a priori argu-
ments, universal features of things as they are in themselves, Kant™s
more modest goal is to argue that our understanding is so constituted
that it could not come up with any objective representation of things as
they present themselves in experience, unless it made use of the con-
cepts expounded in his table of the categories.
It would be futile to try to summarize even briefly the stages through
which Kant™s view progressed before reaching its mature formulation in
the Critique of Pure Reason. Nevertheless, it will be useful for a proper
understanding of the reversal Kant imposes on the ambitions of tradi-
tional ontology to recall a few of the early formulations of the problems he
tries to address in the metaphysical deduction of the categories.

Historical background
In the 1755 New Elucidation of the First Principles of Metaphysical
Cognition, Kant offered a ˜˜proof™™ of the principle of sufficient reason
(or rather, as he defined it, of the principle of determining reason)
understood inseparably as a logical and an ontological principle, as
were also the principle of identity and the principle of contradiction.2
From this general ˜˜proof™™ he then derived a proof of the principle of
determining reason of every contingent existence (i.e. of every existing
thing that might as well have existed as not existed). He also derived a
proof of the ˜˜principle of succession™™ (there is a sufficient reason for any
change of state of a substance) and a ˜˜principle of coexistence™™ (the
relations between finite substances do not result from their mere coex-
istence, but must have been instituted by a special act of God).3 Although
these proofs differed from those provided by Christian Wolff and his
followers, they nevertheless had the same general inspiration. They
rested on a similar assumption that logical principles (defining the rela-
tions between concepts or propositions) are also ontological principles

See Principiorum primorum cognitionis metaphysicae nova dilucidatio, AAi, pp. 388“94, ed. and
trans. David Walford and Ralf Meerbote, A New Elucidation of the First Principles of
Metaphysical Cognition, in Theoretical Philosophy, 1755“1770 (Cambridge: Cambridge
University Press, 1992). On Kant™s pre-critical defense of the principle of sufficient reason,
see ch. 5 of this book.
AAi, pp. 396“8, 410“16.

(defining the relations between existing things and states of affairs), and
that one can derive the latter from the former.
In his lectures on metaphysics from the early 1760s, as well as in the
published works of the same period, Kant expresses doubts on precisely
this point. In the 1763 Attempt to Introduce the Concept of Negative Magnitudes
into Philosophy, he distinguishes between logical relations and real rela-
tions. And he formulates the question that he will later describe, in the
preface to the Prolegomena, as ˜˜Hume™s problem™™: how are we to under-
stand a relation where ˜˜if something is posited, something else also is
posited™™?4 It is important to note that the question is formulated in the
vocabulary of the school logic in which Kant was trained. The relation
between something™s ˜˜being posited™™ and something else™s ˜˜being posited™™
is just the logical relation of modus ponens, according to which if the
antecedent of a hypothetical judgment is posited, then the consequent
should also be posited. In his Lectures on Metaphysics of the 1760s, Kant
notes that the logical ratio ponens or tollens is analytic, but the real ratio
ponens or tollens is synthetic: empirical. By this he means that in an
empirical hypothetical judgment, the relation between the antecedent
and consequent of the judgment is synthetic: the consequent is not
conceptually contained in the antecedent. Kant™s question follows: what,

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