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Allison thinks that in maintaining that the ˜˜affection of sensibility by
the understanding™™ is an affection of sensibility by the capacity to judge,
I am claiming that in synthesis speciosa, sensibility is affected by logical
functions of judgment rather than by the categories as full-fledged
concepts.27 But this is not exactly what I think. What I understand
Kant as saying is this: the unity of apperception, as a capacity to judge,
generates the representation of the unity and unicity of space and time,
as the condition for any specific act of judging at all, thus prior to any
specific synthesis according to the categories, let alone any subsumption
under the categories. This representation of unity (or, one might say, the
anticipation of an overall unity of appearances in one space and one
time), which is prior to any specific synthesis, was mentioned by Kant
without further explanation at the end of x15 of the Transcendental
Deduction. There he said that there is a unity which is not the category of
unity, but the higher unity that presides over all acts of judging. Applied
to the forms of intuition, we are now told, this unity generates the formal
unity of space and time within which any categorial synthesis at all
occurs. In my understanding, the formal intuitions thus generated are
the representations of space and time as ˜˜infinite given magnitudes™™
mentioned in the Transcendental Aesthetic, the ˜˜pure images of all
magnitudes™™ mentioned in the Schematism chapter, the entia imaginaria
mentioned in the table of nothing, and the ˜˜formal intuitions or forms of
intuition™™ mentioned in the Transcendental Dialectic as the original
intuitions in which the successive synthesis of appearances is achieved,
under the regulative idea of a world-whole.28



26
` ´ `
Cf. KCJ, pp. 222“3. See also my ˜˜Synthese et donation. Reponse a Michel Fichant,™™
Philosophie, no. 60 (1998), pp. 79“91, translated as ch. 3 in this volume.
27
Allison proposes that when Kant says, in the footnote to B160, that in the Transcendental
Aesthetic he has ˜˜ascribed the unity of space and time merely to sensibility, only in order to
note that it precedes any concept,™™ he means concepts of space and time, not the cate-
gories. He may be right on this point. But I do not think this can apply to the second
occurrence of ˜˜concepts™™ in the same footnote: ˜˜the unity of this a priori intuition belongs
to space and time, and not to the concept of the understanding.™™
28
The ˜˜infinite given magnitudes™™ of the Transcendental Aesthetic: A25/B39, A32/B48; the
˜˜pure images of all magnitudes™™ in the Schematism chapter: A142/B182; the entia imagi-
naria of the table of nothing: A292/B348; the ˜˜formal intuitions or forms of intuitions™™ of
the Transcendental Dialectic: A424/B457n.
KANT™S CATEGORIES 37

And this is why I described the second part of the Deduction as
making a more radical argument than is generally perceived. As I
understand him, Kant is claiming that the space and time represented
as one space and one time within which any object of experience is given,
are themselves, before any specific categorial activity (synthesis or ana-
lysis or subsumption under the categories) the product of the very same
unity of apperception that proceeds to generate syntheses according to
the categories and thus initiates the never-ending process of cognition.
So anything given in space and time, just by being given in space and
time, stands under the unity of apperception and thus the categories.
That this is the thrust of Kant™s argument seems to me to be confirmed
by what he says in xx21 and 26: the first part of the deduction considered
the categories as forms of thought. He states that we must now consider
the manner in which things are given. And he claims that he will show
that with, not in, the forms of intuition, a priori modes of ordering are
given (B161). Here at last Kant addresses the worry he expressed before
even beginning the Transcendental Deduction proper: it was relatively
easy, he said, to show that appearances must conform to forms of space
and time, because these forms just are forms according to which appear-
ances are given. The matter is quite different in the case of the
categories. For ˜˜appearances can certainly be given in intuition
independently of functions of the understanding™™ (A90/B123). Well,
this contrast loses much of its sting if space and time themselves, as
˜˜the manner in which things are given,™™ stand under the very same
unity of apperception that is the source of synthesis according to the
categories. This, I think, is the completion of the transcendental deduc-
tion Kant was announcing as early as x21.
A great deal more might be said in answer to Sedgwick™s and Allison™s
thoughtful comments. Within the limit of this response I will only men-
tion one last point. Both of them raise, only to withdraw it immediately,
the possibility that my reading of Kant™s argument might bring it into
some surprising proximity to later German Idealism. Allison makes, and
then withdraws, the suggestion that my view of the forms of intuition as
resulting from an ˜˜affection of sensibility by the understanding™™ might
bring Kant closer to Fichte™s view than either he or I would have
expected. Sedgwick makes, and then withdraws, the suggestion that
my talk of ˜˜generating™™ the categories might bring Kant closer than
either she or I would have thought to what she calls ˜˜Hegel™s attack on
the a priori.™™ I think this common pattern in their comments is due to the
fact that, in my reading, Kant™s notion of both ˜˜the a priori™™ and ˜˜the
REVISITING
38

given™™ is more complex than is generally supposed. This complexity was
certainly grasped by the German Idealists better than it has been in more
recent readings of Kant, even while they (especially Hegel) chastised
Kant for remaining adamant in distinguishing receptivity (passivity) and
spontaneity (activity) in our cognitive capacities. As for me, my view is
that Kant was right to insist on this distinction, and I do not think
anything in my reading of the Critique leads to loosening it in any
way.29 I do think, however, that one of the benefits of my interpretation
is its making clearer how Kant could remain true to this distinction while
radically challenging what we have come to call, after Sellars, ˜˜the Myth
of the Given.™™30
I have tried to show that this challenge, and Kant™s elucidation of the
reason-giving activity by way of which we relate our representations to
objects, was made possible by two extraordinary moves. The first is
Kant™s invention of the notion of a form of intuition “ namely a form,
or forms, for ordering and individuating what is empirically given. The
second is his unprecedented use of a quite traditional logic of concept
combination, into which he introduces the reference to an x of judgment
that ultimately stands for the intuited individual™s thought under con-
cepts combined in judgment. Both inventions are essential to the argu-
ment of the Metaphysical and Transcendental Deductions of the
Categories. But the full measure of their pay-off can be gleamed not
there, but rather in the next section of the Critique: the System of
Principles of the Pure Understanding, where Kant expounds his con-
ception of mathematics and its application to the science of nature, the
meaning and use of the traditional metaphysical concepts of substance,
causality, and universal interaction, and the meaning and use of the
modal categories “ possibility, actuality, necessity.31




29
On this point, see my ˜˜Point of view of man or knowledge of God: Kant and Hegel on
concept, judgment and reason,™™ in Sedgwick, Kant and German Idealism.
30
Cf. Wilfrid Sellars, ˜˜Empiricism and the philosophy of mind,™™ in Herbert Feigl and
Michael Scriven (eds.), Minnesota Studies in the Philosophy of Science, i (Minneapolis:
University of Minnesota Press, 1956), pp. 253“329; repr. with an introduction by
Richard Rorty and a study guide by Robert Brandom (Cambridge, Mass.: Harvard
University Press, 1997); John McDowell, Mind and World (Cambridge, Mass.: Harvard
University Press, 1994; 2nd edn 1996).
31
On the relation of space and time to the relational categories, see in this volume chs. 6
and 7.
2


SYNTHESIS, LOGICAL FORMS, AND
THE OBJECTS OF OUR
ORDINARY EXPERIENCE




Michael Friedman has offered a rich and stimulating discussion of my book,
KCJ. While giving a characteristically generous and clear-sighted account of
my views, he maintains that on the whole I fail to do justice to what is most
revolutionary about Kant™s natural philosophy, and instead attribute to
Kant a pre-Newtonian, Aristotelian philosophy of nature. The reason for
this distortion, according to Friedman, is that I put excessive weight on
Kant™s claim to have derived his categories from a set of logical forms of
judgment which he inherited, with some adjustments, from a traditional
Aristotelian logic. In taking Kant at his word on this point, I wrongly
attribute to him a traditional view of concepts and concept formation that
was shared by early modern empiricists and rationalists alike, but that Kant™s
lasting contribution is precisely to have rejected. And I fail to give their full
import to Kant™s remarkable insights into the newly discovered applications
of mathematical concepts and methods to the science of nature. According
to Friedman™s assessment, then, at worst my book ends up hurling back
Kant™s philosophy into the dark ages of Aristotelianism. At best, it reveals in
Kant a tension between Aristotelianism and Newtonianism that more
enlightened minds are now better able to identify and pry apart.1

1
´
See Michael Friedman, ˜˜Logical forms and the order of nature: comments on Beatrice
Longuenesse™s Kant and the Capacity to Judge,™™ Archiv fu Geschichte der Philosophie, vol. 82
¨r
(2000), pp. 202“15.

39
REVISITING
40

The questions Friedman raises are insightful and challenging.
However, my impression is that his assessment of my position suffers
from the relatively scarce attention he devotes to my views about the role
of synthesis in Kant™s Transcendental Analytic. I insist throughout the
book that this notion “ not that of the ˜˜logical use of the understanding™™
according to the logical forms of judgment “ carries the weight of Kant™s
conception of mathematics and its application in natural science. As early
as ch. 1 (˜˜Synthesis and judgment™™) I explain that Kant™s argument in the
metaphysical and transcendental deductions of the categories is built on
the consideration of two quite different, but related and complementary,
aspects of the understanding™s employment or use: its ˜˜logical use™™
according to the logical forms of judgment; and its use in ˜˜pure syn-
thesis,™™ that is, in the a priori ordering of manifolds in space and time,
the work of pure (productive) imagination. And I show how Kant™s
critical notion of synthesis is gradually developed in connection with
his epistemological insights into the concepts and methods of mathe-
matics. It ought to come as no surprise, then, if in neglecting what I say
about synthesis and focusing his discussion almost entirely on what I say
of the relationship between Kant™s categories and the logical forms of
judgment, Friedman should find my interpretation difficult to reconcile
with Kant™s avowed Newtonianism.
Still, I think Friedman is correct in stressing the disagreements
between our respective readings of Kant™s argument in the
Transcendental Analytic of the Critique of Pure Reason. In what follows I
shall try to clarify the grounds of this disagreement on each of the points
raised by Friedman.


Bottom up or top down?
Friedman sees me as defending an essentially ˜˜bottom-up™™ interpreta-
tion of the relation between Kant™s pure concepts of the understanding
and experience. In other words, he thinks I maintain that Kant™s cate-
gories are derived from experience by an inductive method relying on
procedures of comparison and abstraction performed upon what is
given to our senses. To this supposedly ˜˜bottom-up™™ view of Kant™s
categories and their application in natural science, he opposes his own
˜˜top-down™™ view, according to which the modern mathematical science
of nature relies on the instantiation of strictly a priori synthetic princi-
ples: Kant™s ˜˜Principles of the Pure Understanding,™™ expounded in the
Transcendental Analytic of the Critique of Pure Reason.
SYNTHESIS AND LOGICAL FORMS 41

But actually, I do not defend a ˜˜bottom-up™™ interpretation of Kant™s
categories, their acquisition, and their use. On the contrary, I insist that
according to Kant, categories are a priori concepts that originate in the
understanding alone: this is precisely what their agreement with a table
of logical functions of judgment is supposed to show. And I agree with
Friedman that according to Kant the modern mathematical science of
nature rests on the instantiation, in connection with the empirical con-
cept of matter, of the synthetic a priori principles which predicate the
categories of all appearances. But Kant™s question in the Critique of Pure
Reason is: how is such application of pure concepts of the understanding
possible, that is, what makes it legitimate to presuppose that the cate-
gories are universally true of objects given to our senses? In answering
this question, Kant lays out two main aspects of the human intellect and
its use: what he calls the ˜˜logical use of the understanding™™; and what he
calls the ˜˜transcendental synthesis of imagination™™ which is, he says, the
˜˜first application of the understanding (and the one that grounds all
others™™ (B152)). The relationship between the ˜˜logical use of the under-
standing™™ and the transcendental synthesis of imagination is at the core
of Kant™s metaphysical deduction of the categories, namely his laying out
of their complete table according to the leading thread provided by a few
elementary logical functions of judgment.
In its logical use, says Kant, the understanding orders various repre-
sentations “ intuitions or concepts “ under a common representation (a
generic concept). The forms according to which such ordering takes
place (the logical forms of judgment), then, are not only forms according
to which concepts are combined (subordinated to one another) in judg-
ments. They are forms (modes of combination of concepts) that guide
the very acquisition of concepts from the sensible given in the first place:
empirical concepts are formed for use in judgment (A68/B93). In KCJ
I argue that this aspect of the logical use of the understanding is also
what Kant calls, in the Critique of the Power of Judgment, ˜˜reflection™™ (the
˜˜bottom-up™™ process of forming empirical concepts from the represen-
tation of particular objects). And I examine in great detail the ways in
which each logical form of judgment guides this reflective process of
concept formation. In doing this, I rely on the important appendix to the
Transcendental Analytic, the Amphiboly of Concepts of Reflection
(A260/B316“A290/B346).
Now, immediately after expounding the ˜˜logical use of the under-
standing™™ and the table of logical forms according to which it is exer-
cised, Kant goes on to argue that for this logical, reflective use of the
REVISITING
42

understanding to take place, synthesis must have occurred. By synthesis,
he means the combination of sensible manifolds in intuition. This com-
bination has a ˜˜pure™™ aspect: for any empirical manifold to be synthe-
sized, the forms of space and time in which intuited manifolds are given
and ordered must themselves be combined in such ways that the mani-
folds in them can be reflected under concepts according to logical forms
of judgment. Categories, says Kant, are just the pure concepts that guide
these syntheses or combinations: they are concepts of the unity of syn-
thesis of the spatiotemporal manifolds. As such, they guide the synthesis
of manifolds in very much the same way in which, for instance, a concept
of number guides the enumeration of a collection (A78/B104).
So considered (as ˜˜concepts of the necessary unity of synthesis™™),
categories are quite different in kind from the generic concepts formed
by comparison and abstraction. In KCJ I explain in detail how Kant™s
discovery of the categories under this aspect is related to his under-
standing of mathematical concepts as opposed to concepts of natural
kinds acquired by empirical inductive processes. However, I also main-
tain that the categories, which, as ˜˜pure concepts of the unity of synth-
esis™™ guide synthesis and, as such, are necessarily at work before any
analysis or reflection takes place, are themselves reflected as ˜˜clear™™
concepts only after empirical concepts have been formed under their
guidance. Indeed, Kant is quite explicit about this twofold status of the
categories when he describes his method of investigation at the begin-
ning of the Transcendental Analytic:

We shall follow the pure concepts all the way to their initial germs and
foundations in the human understanding, in which they lie prepared [in
denen sie vorbereitet liegen], until finally they are developed under the spur
of experience and are presented by this same understanding, freed from
the empirical conditions that attach to them, in their purity. (A66/B91)

In my view, the ˜˜initial germs and foundations™™ of the categories are the
logical functions of judgment as a priori forms of discursive thought;
their ˜˜development under the spur of experience™™ is their emergence as
concepts of the unity of synthesis (namely, a priori rules for the unity of
synthesis, guiding it toward analysis according to the logical forms of
judgment); their ˜˜presentation, freed from the empirical conditions™™ is
their reflection as clear concepts under which appearances are sub-
sumed, for instance when we form causal judgments or when we apply
concepts of extensive or intensive magnitudes to objects of experience.
According to such an account, then, when Newtonian science appears in
SYNTHESIS AND LOGICAL FORMS 43

the history of human knowledge, it inherits this long process of develop-
ment and clarification of the pure concepts of the understanding. Does
this make my account of the categories a ˜˜bottom-up™™ account rather than
a ˜˜top-down™™ one? I do not think so, for the following two reasons.
First, in my account, the categories are a priori concepts that guide
˜˜from the top down™™ the syntheses of sensible intuitions so that our
representations are related to objects susceptible to being conceptua-
lized by means of reflection, and thereby related to other concepts in
judgments. The top-down procedure thus precedes and makes possible
the bottom-up. The role of categories as logical functions of judgment
governing reflection capable of yielding concepts of objects presupposes
their role as synthesis determiners (concepts of the unity of synthesis).
Second, this is why we can be confident that when Newton presup-
poses “ as he does, according to Kant “ the truth of the synthetic a priori
principles instantiated in the laws of motion of the Principia, he is war-
ranted in doing so: the categories, and thus the principles that predicate
them of appearances, are indeed true of the objects of perceptual
experience, the middle-sized objects of the modern mathematical
science of nature. This being said, it remains the task of empirical science
to determine which specific combinations and connections of appear-
ances instantiate the pure principles of the understanding. The answer
to this question can be given only by considering any empirically
discovered combination and connection in the context of the totality
of (endlessly revisable) experience.
In order further to substantiate this view, let me now consider the two
cases Friedman discusses more particularly: quantity and causality.


Quantity
Friedman focuses his discussion on the issue of the respective primacy of
continuous and discrete magnitudes in Kant™s treatment of the cate-
gories of quantity. He contends that I give undue privilege to the latter
over the former, whereas in Kant™s treatment, continuous magnitudes
are primary. Number itself is ˜˜conceived in terms of the addition of line
segments with an arbitrarily chosen unit, say, rather than in the Fregean
style in terms of the extensions of concepts.™™2 In failing to perceive this
primacy, says Friedman, I remain insufficiently aware of the relationship


2
Ibid., p. 206.
REVISITING
44

between Kant™s critical philosophy and the modern mathematical
science of nature.
Let me first recall the three main questions Kant addresses, concern-
ing the categories in general: (1) what is thought in them, as ˜˜pure
concepts of the understanding™™? (2) How do they relate to sensible
intuition? (3) How does the account of their relation to sensible intuition
justify the synthetic a priori judgments that state their universal applic-
ability to appearances? With respect to the categories of quantity (unity,
plurality, totality), if we follow the metaphysical deduction of the cate-
gories, Kant™s answer to the first question is that they are pure concepts
of just those syntheses necessary so that particulars are subsumed under
concepts in singular, particular, and universal judgments.3
Kant™s account of number occurs in the course of his answer to the
second question: how do categories relate to sensible intuition? Number,
says Kant, is the schema of quantity, namely a ˜˜representation that gathers
together the successive addition of unit to (homogeneous) unit [eine
Vorstellung, die die sukzessive Addition von Einem zu Einem (gleichartigen)
zusammenfaßt]™™ (A142/B182). I argue that ˜˜homogeneous™™ should be
understood as ˜˜of the same kind,™™ i.e. ˜˜falling under the same concept.™™4
In relating number to the pure concept of quantity and the latter to the
logical quantity of judgments, I maintain that Kant thus appears strikingly
close to Frege™s view that numbers are properties of concepts, namely that
they attach to collections of individuals falling under the same concept.5
Now, Friedman urges that I ˜˜slide without any real argument™™ from
this notion of number as attaching to sets of objects thought under a
concept (the proto-Fregean notion of number), to number as assigning
to individual objects particular sizes or magnitudes (the pre-Fregean,
Euclidean notion of number, where number is defined in relation to the
measurement of line segments in space). I find the charge surprising: in
fact I take pains to explain the transition from the first to the second use
of number in some detail, and then conclude that according to Kant,
˜˜when we measure a line by adding units of measurement, what we do is
in effect recognize in the line a plurality of elements thought under the
same concept: ˜segment equal to segment s™.™™6 In my view, the notion of

3
In KCJ I defend the view that the correspondence between logical forms and categories
is: singular judgment/unity, particular/plurality, universal/totality. Friedman challenges
this view. I discuss this point below, pp. 45“6.
4
KCJ, p. 250.
5
KCJ, p. 257.
6
KCJ, p. 265.
SYNTHESIS AND LOGICAL FORMS 45

number as attaching to arbitrarily chosen units of measurement is thus
to be understood in the light of the notion of number attaching to
extensions of concepts, which itself is referred back to our capacity to
form judgments determined as to their logical quantity (that is, to our
capacity to subsume individuals under concepts, and thus to represent
them as homogeneous units). This does not mean that measuring a line
segment, a surface, or a volume, is forming a discursive judgment in
which a generic concept is subordinated to another. All it means is that
the capacity to recognize homogeneous units, susceptible to being gone
through and synthesized as units of measurement, depends on the
discursive capacity to judge according to the logical form of quantity.
Of course, the discursive capacity is not the only faculty in play here.
Number, as the schema of quantity, or as a ˜˜representation that gathers
together the addition of unit to (homogeneous) unit™™ also depends on
the intuitive capacity to ˜˜go through and keep together™™ collections of
(homogeneous) units through time, and thus on our pure intuition of
time (our capacity to keep track of our representations in one time).

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