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They are supposed to be independently existing things, so that in this
case we just do not see how a priori concepts might relate to objects.31
Well, here (in section three of the Leitfaden) Kant is telling us that a
function of the understanding, the function of judging, is not arbitrarily
producing (constructing) representations of objects, as in geometry or
even in arithmetic, but at least unifying according to rules the presented
manifold of intuition, so that it can be analyzed into (empirical) concepts
and thought about in judgments.
Thus he writes:

Synthesis in general, as we shall subsequently see, is the mere effect of
imagination, a blind though indispensable function of the soul, without
which we would have no cognition at all, but of which we are seldom even
conscious. Yet to bring this synthesis to concepts is a function that pertains to the
understanding [my emphasis] and by means of which it first provides us
with cognition in the proper sense. (A78/B103)

What might it mean, to ˜˜bring synthesis to concepts™™? I suggest the
following. What is given to us in sensibility is given in a dispersed way “
spread out in space and in time, where similar things do not present
themselves to us at the same time but rather, need to be recalled in order
to be compared. Moreover, the variety and variability of what does
present itself is such that which pattern of regularity should be picked
out might be anybody™s guess. Even the way we synthesize or bind
together the manifold might itself be quite random, obeying here
some rule of habitual association, there some emotional connection,
and so on. So ordering the synthesis itself under systematic rules
so that the components of intuition can be thought under common
concepts in a regular fashion is the work of the understanding. The
understanding thus ˜˜brings synthesis to concepts.™™ It makes it the case
that synthesis does give rise to, opens the way for, conceptualization.

See above, p. 87. Cf. Correspondence, AAx , p. 131.

The analogy with the mathematical case is only partly helpful here.
Kant writes:

Now pure synthesis, universally represented, yields the pure concept of
the understanding. By this synthesis, however, I understand that which
rests on a ground of synthetic unity a priori: thus our counting (as is
especially noticeable in the case of larger numbers) is a synthesis in
accordance with concepts, since it takes place in accordance with a
common ground of unity (e.g. the decimal). Under this concept, there-
fore, the synthesis of the manifold becomes necessary. (A78/B104)

In counting, we add unit to unit, and then units of higher order
(a decade, a hundred, a thousand, and so on) that allow us to synthesize
(enumerate) larger and larger collections (of items, of portions of
a line . . . ). The idea is that similarly, in ordering empirical manifolds,
we make use of grounds of unity of these manifolds (say: whenever event
of type A occurs, then event of type B also occurs), which we think under
concepts or ˜˜represent universally™™ (in the case at hand, under the
concept of cause). We thus form chains of connections between these
manifolds, in an effort to unify them in one space and one time, in the
context of one and the same totality of experience. But of course,
whereas it is always possible to enumerate a collection of things or
parts of things once one has arbitrarily given oneself a unit for counting
or measuring, in contrast, actually finding repeated occurrences of
similar events depends on what experience presents to us. Because of
this difference, Kant distinguishes the former kind of synthesis, which he
calls ˜˜mathematical™™ synthesis, from the latter, which he calls ˜˜dynami-
cal,™™ and he accordingly distinguishes the corresponding categories by
dividing them along the same line (see B110; A178“9/B221“2).
Nevertheless, in the latter case just as in the former, a ˜˜ground of
unity™™ that has its source in the understanding is at work in our synthe-
sizing (combining, relating) the objects of our experience or their spatio-
temporal parts. This ground of unity, says Kant, is a pure concept of the
This reasoning leads to the core statement of all three sections of the
Leitfaden chapter:

The same function that gives unity to the different representations in
a judgment also gives unity to the mere synthesis of different representa-
tions in an intuition, which, expressed universally, is called the pure
concept of understanding. The same understanding, therefore, and

indeed by means of the very same actions through which it brings the
logical form of a judgment into concepts by means of the analytical unity,
also brings a transcendental content into its representations by means of
the synthetic unity of the manifold in intuition in general, on account of
which they are called pure concepts of the understanding that pertain
a priori to objects; this can never be accomplished by general logic.

I indicated above how the introduction of the term function at the
beginning of section one already foreshadowed the argument of section
three: the very same ˜˜unity of the act™™ that accounts for the unity of
concepts of judgments also accounts for there being just those forms of
unity in our intuitions that make them liable to being reflected under
concepts in judgment. The concepts that reflect those forms of unity in
intuition are the categories. But they do not just reflect those forms of
intuitive unity. As the mathematical analogue made clear (cf. A78/B104
cited above), they originally guide them. So for instance, as we just saw,
the concept of magnitude is that concept that guides the operation of
finding (homogeneous) units (say, points, or apples) or as the case may
be, units of measurement (say, a meter) and adding them to one another
in enumerating a collection or in measuring a line. The end result of this
operation is the determination of a magnitude, whether discrete (the
number of a collection) or continuous (the measurement of a line) as
when we say that the number of pears on the table is seven or the
measurement of the line is 4 meters. Here we reflect the successive
synthesis of homogeneous units under the concept of a determinate
magnitude (7 units, 4 meters). Similarly, the concept of cause (the con-
cept of some event™s being such as to be adequately or ˜˜in itself™™ reflected
under the antecedent of a hypothetical judgment with respect to another
event, adequately or ˜˜in itself™™ reflected under the consequent) guides
the search for some event that might always precede another in the
temporal order of experience. Once such a constant correlation is
found, we say that event of type A is the cause of event of type B. In
other words, the sequence is now reflected under the concept of a
determinate causal connection.32

In the chapter on the Schematism of the Pure Concepts of the Understanding, Kant
maintains that the schema of the concept of cause is ˜˜the real upon which, when it is
posited, something else always follows™™ (A144/B183). This means that it is by apprehend-
ing the regular repetition of a sequence of events or states of affairs (˜˜the real upon which,

The two aspects in our use of categories are explicitly mentioned in x10.
Kant says, on the one hand, that categories ˜˜give unity to [the] pure synth-
esis™™ (A79/B104). He says, on the other hand, that the pure concepts of the
understanding are ˜˜the pure synthesis generally represented ™™ (A78/B104; see
also A79/B105 quoted earlier, where both aspects are present in one and
the same sentence: ˜˜the same function . . . gives unity which expressed gene-
rally, is the pure concept of the understanding™™). These two points are fully
explained only in book two of the Transcendental Analytic, ˜˜The Analytic
of Principles.™™ There Kant explains that categories, insofar as they deter-
mine rules for synthesis of sensible intuitions, have schemata (ch. 1 of book
two, A137/B176). Being able to pick out instances of such schemata allows
us to subsume our intuitions under the categories (ch. 2 of book two, A148/
B187“A235/B287). Only in those chapters does Kant give a detailed
account of the way in which each category both determines and reflects a
specific rule (a schema) for the synthesis of intuitions.
As far as the metaphysical deduction is concerned, Kant is content with
making the general case that:
In such a way there arise [entspringen] exactly as many pure concepts of
the understanding which apply to objects of intuition a priori, as there
were logical functions of all possible judgments in the previous table: for
the understanding is completely exhausted, and its capacity entirely
measured by these functions. (A80/B106)

Kant does not mean that every time we make use of a particular logical
function/form of judgment, we thereby make use of the corresponding
category. True, absent a sensible manifold to synthesize, all that remains
of the categories are logical functions of judgment. But the logical func-
tions of judgment are not, on their own as it were, categories. They
become categories (categories ˜˜arise,™™ entspringen, as Kant says in the text

whenever posited, something else follows™™) that we recognize in experience the presence
of a causal connection. But conversely, we look for such constant conjunctions because we
do have a concept of cause as the concept of something that might be thought under the
antecedent of a hypothetical judgment, with respect to something else that might be
thought under the consequent. Of course Kant™s point is also that we can always be
mistaken about what we so identify. Some repeated sequence is warranted as a true causal
connection only if it can be thought under a causal law, and this involves the application of
mathematical constructions that allow us to anticipate the continuous succession and
correlation of events in space and in time. However, here I am anticipating developments
of Kant™s argument that go way beyond the metaphysical deduction properly speaking.
See my ˜˜Kant on causality: what was he trying to prove?™™ in Christia Mercer and Eileen
O™Neill (eds.), Early Modern Philosophy: Mind, Matter and Metaphysics (Oxford: Oxford
University Press, 2005); reprinted as ch. 6 in this volume.

just cited) only when the understanding™s capacity to judge is applied to
sensible manifolds, thus synthesizing them (combining them in intui-
tion) for analysis (into concepts) for synthesis (of concepts in judgments).
And even then, there remains a difference between the category™s guid-
ing the synthesis of manifolds, and the manifolds™ being correctly
subsumed under the relevant category. For instance, it may be the case
that the understanding™s effort to identify what might fall under the
antecedent and what might fall under the consequent of a hypothetical
judgment, leads it to recognize the fact that whenever the sun shines on
the stone, the stone gets warm. This by itself does not warrant the claim
that there is an objective connection (a causal connection) between the
light of the sun and the warmth of the stone. Only some representation
of the overall unity of connections of events in the world can give us at
least a provisional, revisable warrant that this connection is the right one
to draw.33
Kant is not yet explaining how his metaphysical deduction of the
categories might put us on the way to resolving the problem left open
after the 1770 Inaugural Dissertation: how do concepts that have their
source in the understanding apply to objects that are given? All we have
here is an exposition as a system ˜˜from a common principle, namely the
capacity to judge™™ (A80“1/B106) of the table of the categories, and an
explanation of the role they perform in synthesizing manifolds so that
the latter can be reflected under concepts combined in judgments. To
respond to the problem he set himself, Kant will need to argue that those
combining activities are necessary conditions for any object at all to
become an object of cognition for us. And as I suggested earlier, only
the later argument will provide a full justification of the table of logical
forms itself: it is a table making manifest just those functions of judging
that are necessary for any empirical concept at all to be formed by us,
and thus for any empirical object to be recognized under a concept.
This confirms again that the ˜˜leading thread™™ from logical forms to
categories is precisely no more (but no less) than a ˜˜leading thread.™™ Its
actual relevance will be proved only when the argument of the
Transcendental Deduction is expounded and in turn, opens the way to
the Schematism and System of Principles.

On this example, see Prolegomena, AAiv, pp. 312“13. See also the related discussion above,
ch. 2, pp. 58“62.

The impact of Kant™s metaphysical deduction of the categories
The history of Kant™s metaphysical deduction of the categories is not a
happy one. Kant™s idea that a table of logical functions of judgments
might serve as a leading thread for a table of the categories was very early
on an object of suspicion, on three main grounds. First, Kant™s careless
statement that he ˜˜found in the labors of the logicians,™™ namely in the
logic textbooks of the time, everything he needed to establish his table of
the logical forms of judgment raises the obvious objection that the latter
is itself lacking in systematic justification.34 This in turn casts doubt on
Kant™s claim that unlike Aristotle™s ˜˜rhapsodic™™ list (A81“2/B106“7), his
table of the categories is systematically justified. Second, even if one does
endorse Kant™s table of the logical forms of judgment, this does not
necessarily make it an adequate warrant for his table of the categories.
And finally, once the Aristotelian model of subject“predicate logic was
challenged by post-Fregean truth-functional, extensional logic, it
seemed that the whole Kantian enterprise of establishing a table of
categories according to the leading thread of forms pertaining to the
old logic seemed definitively doomed.
An early and vigorous expression of the first charge mentioned above
was Hegel™s. In the Science of Logic, Hegel writes:
Kantian philosophy . . . borrows the categories, as so-called root notions
for transcendental logic, from subjective logic in which they were
adopted empirically. Since it admits this fact, it is hard to see why
transcendental logic chooses to borrow from such a science instead of
directly resorting to experience.35

Note, however, that it is not Kant™s table of logical forms per se that
Hegel objects to. Rather, it is the way the table is justified (or rather, not
justified) and the random, empirical way in which the categories them-
selves are therefore listed. Nevertheless, in the first section of his
Subjective Logic, Hegel too expounds four titles and for each title,
three divisions of judgment that exactly map the titles and divisions of

Cf. Prolegomena, AAiv, pp. 323“4.
G. W. F. Hegel, Wissenschaft der Logik, ii: Die subjective Logik, in Gesammelte Werke, Deutsche
Forschungsgemeinschaft, ed. Rhein-Westfal. Akad. d.Wiss. (Hamburg: F. Meiner,
1968“), vol. xii, pp. 253“4; Science of Logic, trans. A. V. Miller (Atlantic Highlands, NJ:
Humanities Press International, 1989), p. 613. What Hegel means here by ˜˜subjective
logic™™ is what Kant called ˜˜pure general logic,™™ namely the logic of concepts, judgments,
and syllogistic inferences. But unlike Kant™s ˜˜pure general logic,™™ Hegel™s subjective logic
is definitely not ˜˜merely formal.™™ More on this shortly.

Kant™s table, although Hegel starts with the title of quality rather than
quantity. Moreover, the names of each title are changed, although the
names of the divisions remain the same. Kant™s title of ˜˜quality™™ becomes
˜˜judgment of determinate-being™™ (Urteil des Daseins), with the three
divisions of positive, negative, and infinite judgment. ˜˜Quantity™™
becomes ˜˜judgment of reflection™™ with the three titles of singular, parti-
cular, and universal. ˜˜Relation™™ becomes ˜˜judgment of necessity™™ (sic!)
with the three titles of categorical, hypothetical, and disjunctive. And
finally ˜˜modality™™ becomes ˜˜judgment of the concept™™ with the three
divisions of assertoric, problematic, and apodeictic.36 Of course, the
change in nomenclature signals fundamental differences between
Hegel™s and Kant™s understanding of the four titles and their twelve
divisions. The most important of those differences is that for Hegel the
four titles and three divisions within each title do not list mere forms of
judgment, but forms with a content, where content and form are
mutually determining. So for instance, the content of ˜˜judgments of
determinate-being™™ (affirmative, negative, infinite) is the immediate,
sensory qualities of things as they present themselves in experience.
The content of ˜˜judgments of reflection™™ (singular, particular, universal)
is what Hegel calls ˜˜determinations of reflection,™™ namely general repre-
sentations, or representations of common properties as they emerge for
an understanding that compares, reflects, abstracts. The content of
˜˜judgments of necessity™™ (categorical, hypothetical, disjunctive) is the
relation between essential and accidental determinations of things.
And finally the content of ˜˜judgments of the concept™™ (assertoric,
problematic, apodeictic) is the normative evaluation of the adequacy of
a thing to what it ought to be, or its concept. So certainly Hegel™s
interpretation of each title radically transforms its Kantian ancestor.
Nevertheless, the fact that despite his criticism of Kant™s empirical
derivation, Hegel maintains the structure of Kant™s divisions, indicates
that his intention is not to criticize the classifications themselves, but rather
to denounce the cavalier way in which Kant asks us to accept them as well
as Kant™s shallow separation between form and content of judgment.37
Nor is Hegel™s intention to challenge the relation between categories
and functions of judgment. In the Science of Logic, categories of quantity
and quality are expounded in part one (Being) of book one (The

See Die subjective Logik, pp. 59“90; trans. pp. 623“63.
On this point see my ˜˜Hegel, Lecteur de Kant sur le jugement,™™ in Philosophie, no. 36
(1992), pp. 62“7.

Objective Logic); those of relation and modality are expounded in part
two (The Doctrine of Essence) of book one. Logical forms of judgment
and syllogistic inference are expounded in section one of book two (The
Subjective Logic or the Doctrine of the Concept). If we accept, as I
suggest we should, that book two expounds the activities of thinking
that have governed the revelation of the categorical features expounded
in parts one and two of book one, then Hegel™s view of the relation
between categories and forms of judgment is similar to Kant™s at least
in one respect: there is a fundamental relation (in need of clarification)
between the structural features of the acts of judging and the structural
features of objects. The difference between Hegel™s view and Kant™s view
is that Hegel takes this relation to be a fact about being itself, and the
structures thus revealed to be those of being itself, whereas Kant takes
the relation between judging and structures of being to be a fact about
the way human beings relate to being, and the structures thus revealed
to be those of being as it appears to human beings.
Hegel™s grandiose reinterpretation of Kant™s titles of judgments did
not have any immediate posterity, and his speculative philosophy was
soon superseded by the rise of naturalism in nineteenth-century philo-
sophy.38 When Hermann Cohen, reacting against both the excesses of
German Idealism and the rampant naturalism of his time, undertook to
revive the Kantian transcendental project, he declared that his goal was
to ˜˜ground anew the Kantian theory of the a priori™™ (˜˜die Kantische
Aprioritatslehre erneut zu begrunden™™).39 By this he meant that, against
¨ ¨
the vagaries of Kant™s German Idealist successors, he intended to lay out
what truly grounds Kant™s theory of the categories and a priori princi-
ples. According to Cohen, Kant™s purpose in the Critique of Pure Reason is
to expound the presuppositions of the mathematical science of nature
founded by Galileo and Newton. The leading thread for Kant™s pure
concepts of the understanding or categories (expounded in book one of
the Transcendental Analytic) is really Kant™s discovery of the principles
of pure understanding (expounded in book two), and the leading thread
for the latter are Newton™s principles of motion in the Principia
Mathematica Philosophiae Naturalis. Thus the true order of discovery of
the Transcendental Analytic leads from the Principles of Pure
Understanding (book two), to the Categories (book one). This does not

On this point, see Hans D. Sluga, Gottlob Frege (London: Routledge and Kegan Paul, 1980),
pp. 8“35.
Cohen, Kants Theorie der Erfahrung, p. ix.

make the logical forms of judgment irrelevant, in Cohen™s eyes. For the
latter formulate the most universal patterns or models of thought
derived from the unity of consciousness, which for Cohen is nothing
other than the epistemic unity of all principles of experience, where
experience means scientific knowledge of nature expounded in
Newtonian science. So it is quite legitimate to assert that the categories
depend on these universal patterns. But the systematic unity of the
categories and of the logical forms can be discovered only by paying
attention to the unity of the principles of the possibility of experience, i.e.
of the Newtonian science of nature.40
Cohen follows up on his interpretative program by showing how
Kant™s systematic correlation between logical forms of judgment and
categories can be understood in the light of the distinction he offers in
the Prolegomena between judgments of perception and judgments of
experience. Cohen then proceeds to explain and justify Kant™s selection
of logical forms by relating each of them to the corresponding category
and to its role in the constitution of experience. In other words, he
implements the very reversal in the order of exposition that he argues
is faithful to Kant™s true method of discovery: moving from the a priori
principles that may ground judgments of experience, to the categories
present in the formulation of these principles, to the logical forms of
Cohen™s achievement is impressive. But it is all too easy to object that
his reducing Kant™s unity of consciousness to the unity of the principles
of scientific knowledge, and his reducing Kant™s project to uncovering
the a priori principles of Newtonian science, amount to a very biased
reading of Kant™s Critique of Pure Reason. In fairness to Cohen, his
interpretation of Kant™s critical philosophy did not stop there. In Kants
¨ndung der Ethik,42 he considered Kant™s view of reason and its
role in morality. And this in turn led him to give greater consideration,
in the second and third editions of Kants Theorie der Erfahrung, to Kant™s
theory of the ideas of pure reason and to the bridge between knowledge
and morality.43 Nevertheless, as far as the metaphysical deduction of
the categories is concerned, his interpretation remained essentially

Cohen, Kants Theorie der Erfahrung, p. 229.
Ibid., pp. 245“8.
Hermann Cohen, Kants Begrundung der Ethik (Berlin, 1877; 2nd edn 1910).
See Kants Theorie der Erfahrung, preface to the second edition, p. xiv.

That interpretation found its most vigorous challenge in Heidegger™s
reading of Kant™s first Critique. Heidegger urges that Kant did not intend
his Critique of Pure Reason primarily to clarify the conceptual presuppositions
of natural science. Rather, Kant™s goal was to question the nature and
possibility of metaphysics. According to Heidegger, this means laying out
the ontological knowledge (knowledge of being as such) that is presupposed
in all ontic knowledge (knowledge of particular entities). Kant™s doctrine of
the categories is precisely Kant™s ˜˜refoundation™™ of metaphysics, or his effort

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