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in such a case, grounds the connection between antecedent and consequent
and thus the possibility of concluding from the antecedent™s being posited
that the consequent should also be posited.5

See Prolegomena, AAiv, p. 257. Cf. Attempt to Introduce the Concept of Negative Magnitudes in
Philosophy, AAii, pp. 202“4, in Theoretical Philosophy, 1755“1770.
See Metaphysics Herder, AAxxviii“1, p. 12; Negative Magnitudes, AAi, pp. 202“3. Note that
Kant™s hypothetical judgment thus differs from our material conditional: for the modus
ponens Kant mentions here has to be grounded on a connection, which Kant, like his
contemporaries, calls consequentia (in Latin) or Konsequenz (in German) between antecedent
and consequent (on this point see also the fifth section of this chapter). Kant™s question is: in
cases where the consequent in the hypothetical judgment is not conceptually contained in
the antecedent, and so the relation between antecedent and consequent is synthetic, what is
the nature of the connection? To my knowledge, the passage from Metaphysics Herder
characterizing causal connection in terms of a synthetic ratio ponens is the first mention we
find of the distinction between analytic and synthetic judgments which will become so
prominent in the critical period. It is interesting that it should occur in the context of
what will become, in Kant™s terms, ˜˜Hume™s problem,™™ and thus in considering a kind of
judgment which is not of the form ˜˜S is P™™ but ˜˜If S is P, then Q is R™™ (a hypothetical
judgment). Contrary to a widely held view and pace the characterization given in
the Introduction to the Critique of Pure Reason (A6“10/B10“14), Kant does not restrict the
distinction between analytic and synthetic judgments to categorical judgments. On the
relation between Kant™s hypothetical judgment and Kant™s understanding of the concept of
cause, see ch. 6, pp. 151“6; and ch. 7, pp. 188“90.

During the same period of the 1760s, Kant also becomes interested in
the difference between the method of metaphysics and the method of
mathematics. Metaphysics, he says, proceeds by analysis of confused and
obscure concepts. Mathematics, in contrast, proceeds by synthesis of clear,
simple concepts. In the same breath, Kant expresses skepticism with
respect to the Leibnizian project of solving metaphysical problems by
way of a universal combinatoric. This would be possible, Kant says, if we
were in a position to completely analyze our metaphysical concepts. But
they are far too complex and obscure for that to be possible.6
Note that the notions of analysis and synthesis by way of which Kant
contrasts the respective methods of metaphysics and mathematics are not
the same as the notions of analytic and synthetic connections at work in the
reflections on ratio ponens and tollens mentioned earlier. The latter describe
a relation of concepts in a (hypothetical) proposition. The former charac-
terize a method. Nevertheless, the two uses of the notions are of course
related. Just as mathematics proceeds by synthesis in that it proceeds by
combining concepts that were not contained in one another, similarly a
synthetic ratio ponens is a relation between antecedent and consequent that
does not rest on the fact that the concepts combined in the latter are
contained in the concepts combined in the former (as, for instance, in ˜˜if
God wills, then the world exists™™ or ˜˜if the wind blows from the West, then
rain clouds appear™™).7 Just as metaphysics proceeds by analysis in that it
proceeds by clarifying what is contained, or thought, in an initially obscure
concept, similarly an analytic ratio ponens is a relation between antecedent
and consequent that rests on the fact that the concepts combined in the
latter are contained in the concepts combined in the former. It is also worth
noting that in both cases, analysis and synthesis, and respectively analytic
and synthetic connection, are defined with respect to concepts. There is no
mention of the distinction between two kinds of representations (intuitions
and concepts) that will play such an important role in the critical period.
That distinction is introduced in the 1770 Inaugural Dissertation, On
the Form and Principles of the Sensible and Intelligible World.8 There Kant
maintains that all representations of spatiotemporal properties and rela-
tions of empirical objects depend on an original intuition of space, and

Inquiry Concerning the Distinctness of the Principles of Natural Theology and Morality, Being an
Answer to the Question Proposed for Consideration by the Berlin Royal Academy of Sciences for the
year 1763, AAii, pp. 276“91, especially p. 283; trans. in Theoretical Philosophy, 1755“1770.
Cf. Negative Magnitudes, AAii, pp. 202“3.
On the Form and Principles of the Sensible and the Intelligible World, AAii, pp. 385“419. trans. in
Theoretical Philosophy, 1755“1770 (henceforth: Inaugural Dissertation).

an intuition of time, in which particular objects can be presented and
related to one another. These objects are themselves objects of particular
intuitions. All intuitions differ from concepts in that they are singular:
they are representations of individuals or, we might say in the case of
particular intuitions, they are the representational counterparts of
demonstratives. And they are immediate: they do not require the medi-
ation of other representations to relate to individual objects. Concepts,
in contrast, are general: they are representations of properties common
to several objects. And they are mediate or reflected: they relate to
individual objects only through the mediation of other representations,
i.e. intuitions. In saying that space and time are intuitions, Kant is saying
that they are representations of individual wholes (the representation of
one space in which all particular spaces and spatial positions are
included and related, and the representation of one time in which all
particular durations and temporal positions are included and related)
that are prior to, and a condition for, the acquisition of any concepts of
spatial and temporal properties and relations. And this in turn allows
him to distinguish two kinds of synthesis: the classically accepted synth-
esis of concepts; and the synthesis of intuitive representations of things,
and parts of things, individually represented in space and in time.9
The Dissertation thus has the resources for solving many of the pro-
blems that occupied Kant over the preceding twenty years. In particular,
because space and time are characterized not only as intuitions, but as
intuitions proper to our own sensibility or ability to receive representa-
tions from the way we are affected by things, their property of infinite
divisibility makes it the case that things as they appear to us can be
represented as susceptible to division ad infinitum. But from this, one
need not conclude that there are no ultimate components of the world as
a world of purely intelligible things, things independent of their repre-
sentation in our sensibility.10

In the Inaugural Dissertation, the distinguishing feature of intuitions, in contrast with
concepts, is their singularity: see Inaugural Dissertation, AAii, pp. 399, 402. Immediacy is
not explicitly mentioned. Moreover, the contrast between intuitions and concepts is not
firmly fixed: Kant also calls intuitions ˜˜singular concepts™™ (ibid., p. 397). In the Critique of
Pure Reason, Kant emphasizes not only the singularity, but also the immediacy of intui-
tions: see A19/B33. For a discussion of these two features of intuition in the critical period,
see Charles Parsons, ˜˜The Transcendental Aesthetic,™™ in Paul Guyer (ed.), The Cambridge
Companion to Kant (Cambridge: Cambridge University Press, 1992), p. 64. On the two
kinds of synthesis in the Inaugural Dissertation, see AAii, pp. 387“8.
Inaugural Dissertation, AAii, pp. 415“16.

Moreover, Kant asserts that in addition to space and time as forms of
our sensibility, i.e. original intuitions in which things given to our senses
are related to one another, we also have concepts ˜˜born from laws innate
to the mind™™ that apply universally to objects. Among such concepts, he
cites those of cause, substance, necessity, possibility, existence.11 It is our
use of such concepts that allows us to think the kinds of connections that
befuddled Kant in the 1760s. For instance, in applying the concept of
cause to objects, whether given to our senses or merely thought, we
come up with the kind of synthetic modus ponens Kant wondered about in
the essay on Negative Quantities and the related lectures on metaphysics.
However, in a well-known letter to Marcus Herz of February 1772,
Kant puts this last point into question: how can concepts that have their
origin in our minds be applied to objects that are given? This difficulty
concerns both our knowledge of the sensible world and our knowledge
of the intelligible world. For in both cases, things on the one hand, and
our concepts of them on the other hand, are supposed to be radically
independent of one another. Having thus radically divided them, how
can we hope to put them back together? In that same letter, Kant
announces that he has found a solution to this quandary, and that it
will take him no more than three months to lay it out.12 In fact, it took
him almost a decade. The result of that effort is the Critique of Pure
Reason, its metaphysical deduction of the categories and the two related
components in Kant™s solution to the problem laid out in the letter
to Herz: the transcendental deduction of the categories, and the proofs
of the principles of pure understanding (see Critique of Pure Reason,
Of these three components, the first “ the metaphysical deduction
of the categories, i.e. the establishment of their table according to a
systematic principle “ has always been the least popular with Kant™s
readers. In the final section of this chapter, I shall consider some of the
objections that have been raised against it, from the time the Critique
first appeared to more recent times. Whatever the fate of those objections,
it is important to keep in mind that the key terms and themes at work in
the metaphysical deduction “ the relation between logic and ontology,
the distinction between analysis and synthesis, between synthesis of
concepts and synthesis of intuitions “ are all part of Kant™s effort to

Ibid., p. 395.
Letter to Herz of February 21, 1772, AAxi, p. 132; ed. and trans. Arnulf Zweig,
Philosophical Correspondence 1759“1799 (Chicago: Chicago University Press, 1967), p. 73.

find the correct formulation for questions that have preoccupied him
since the earliest years of his philosophical development.

Kant™s view of logic
The metaphysical deduction of the categories is expounded in chapter 1 of
the Transcendental Analytic in the Critique of Pure Reason, entitled ˜˜On
the Clue to the Discovery of All Pure Concepts of the Understanding™™
(A66/B92).13 This chapter is preceded by a fairly long introduction to
the Transcendental Analytic as a whole, where Kant explains what he
means by ˜˜logic.™™ This is worth noticing. For as we saw, one main issue in
his pre-critical investigations was that of the relation between logic and
ontology, and the capacity of logic to capture fundamental features of the
world. But now Kant puts forward a completely new distinction, that
between ˜˜general pure logic™™ (which he also sometimes calls ˜˜formal
logic™™, e.g. A131/B170) and ˜˜transcendental logic™™ (A50/B74“A57/B81).
In putting forward this distinction, Kant intends both to debunk
Leibnizian-Wolffian direct mapping of forms of thought upon forms of
being, and to redefine, on new grounds, the grip our intellect can have on
the structural features of the world. As we shall see, establishing a new
relation between logic and ontology is also what guides his ˜˜metaphysical
deduction of the categories,™™ namely his suggestion that a complete
and systematic table of a priori concepts of the understanding, whose
applicability to objects given in experience is impervious to empirical
verification or falsification, can be established according to the ˜˜leading
thread™™ of logical forms of judgment.
Kant™s primary tool for his twofold enterprise, first prying apart logic
and ontology, but then finding new grounds for the grip our intellect has
on the world, is the distinction between two kinds of access that we have
to reality: our being affected by it or being ˜˜receptive™™ to it, and our
thinking it or forming concepts of it. Each of these two kinds of access, he
says, depends on a specific capacity: our acquiring representations
by way of being affected depends on ˜˜receptivity™™ or sensibility, our
acquiring concepts depends on ˜˜spontaneity™™ or understanding. Kant

Here as elsewhere I am following the translation by Paul Guyer and Allen Wood. ˜˜Clue™™ is
their choice for translating Kant™s Leitfaden. It is certainly correct, but I prefer ˜˜leading
thread™™ which captures better what Kant is doing: following the lead of logical forms of
judgment to establish his table of the categories. In citations I will follow Guyer and Wood,
but in the main text I will adopt ˜˜leading thread.™™ The reader should be aware that both
words translate the German Leitfaden.

differentiates these capacities primarily by way of the contrast just men-
tioned, between receiving (through sensibility) and thinking (through
understanding). But they are also distinguished by the kinds of represen-
tations they offer, and by the ways in which they order and relate to one
another these representations. Sensibility offers intuitions (singular and
immediate representations), understanding offers concepts (general and
reflected representations). As beings endowed with sensibility or receptiv-
ity, we relate our intuitions to one another in one and the same intuition of
space and of time. As beings endowed with understanding, we relate
concepts to one another in judgments and inferences. These modes of
ordering representations are what Kant calls the ˜˜forms™™ of each capacity:
space and time are forms of sensibility, the logical forms of judgment are
forms of the understanding (cf. A19“21/B33“5; A50“2/B74“6).
These initial distinctions have important consequences for Kant™s char-
acterization of logic. Logic, he says, is ˜˜the science of the rules of the
understanding in general,™™ to be distinguished from aesthetic as ˜˜the
science of the rules of sensibility™™ (A52/B76). Characterizing logic in this
way is surprising for a contemporary reader. We are used to characteriz-
ing logic in a more objective way, as a science of the relations of implication
that hold between propositions. Learning logic is of course learning to
make use of these patterns of implication in the right way for deriving true
proposition from true proposition, or for detecting the flaw in a given
argument. But that is not what the proper object of logic is, or what logic is
about.14 Now, Kant™s more psychological characterization of logic is one
he shares with all early modern logicians, influenced by Antoine Arnauld
and Pierre Nicole™s Logic or the Art of Thinking, also known as the Port-
Royal Logic. However, as the very title of Arnauld™s and Nicole™s book
shows, even their logic is not just preoccupied with the way we happen to
think, but establishes norms for thinking well.15 But Kant is more explicit

On this point, see Gilbert Harman, ˜˜Internal critique: a logic is not a theory of reasoning
and a theory of reasoning is not a logic,™™ in Studies in Logic and Practical Reasoning, i (2002).
On the contrast between Kantian and Fregean logic with respect to this point (i.e. does
logic have anything to do with the way we think or even ought to think?), see John
MacFarlane, ˜˜Frege, Kant, and the logic in logicism,™™ Philosophical Review, no. 111
(2002), pp. 32“3.
Antoine Arnauld and Pierre Nicole, La Logique ou l™art de penser, ed. P. Clair and F. Girbal
(Paris: Librairie philosophique Vrin, 1981); trans. Jill Vance Buroker, Logic or the Art of
Thinking (Cambridge: Cambridge University Press, 1996). The full title contains, after the
subtitle (˜˜or the Art of Thinking™™) the further precision: ˜˜containing, in addition to the
common rules, several new observations proper to form judgment™™ (propres ` former le a

than they are about the normative character of logic: logic, he says, does
not concern the way we think but the way we ought to think. It ˜˜derives
nothing from psychology™™ (A54/B78).16 More precisely, logic so consid-
ered is what Kant calls ˜˜pure™™ logic, which he distinguishes from ˜˜applied™™
logic where one takes into account ˜˜the empirical conditions under which
our understanding is exercised, e.g. the influence of imagination, the laws
of memory, the power of habit, inclination, and so on™™ (A53/B77). Logic
properly speaking or ˜˜pure™™ logic has no need to take these psychological
factors into account. Rather, its job is to consider the patterns of com-
bination of concepts in judgments that are possible by virtue of the mere
form of concepts, i.e. their universality; and the patterns of inference
that are possible by virtue of the mere forms of judgments.
The idea of taking into account the ˜˜mere form™™ of concepts, judg-
ments, and inferences rests in turn on another distinction, that between
logic of the ˜˜general use™™ and logic of the ˜˜particular use™™ of the under-
standing. A logic of the particular use of the understanding is a science of
the rules the understanding must follow in drawing inferences in con-
nection with a particular content of knowledge “ each science, in this
way, has its particular ˜˜logic.™™17 But logic of the general use of the
understanding is a logic of the rules presupposed in all use of the under-
standing, whatever its particular domain of investigation.
Kant has thus identified ˜˜general pure™™ logic: a logic that, as ˜˜pure,™™
does not derive anything from psychology; and as ˜˜general,™™ defines the
most elementary rules of thought, rules that any use of the understand-
ing must follow. Now, that he also defines this logic as formal is where his
radical parting of ways with his Leibnizian-Wolffian rationalist prede-
cessors is most apparent. For the latter “ just as for the early Kant of the
1760s “ the most general principles of logic also defined the most general
structural features of being. But as we saw, ever since he distinguished
relations of concepts and relations of existence (in his metaphysical
essays of the early 1760s), Kant has not taken the identity of logical
and real connections for granted. This being so, forms of thought
are just this: forms of thought. And the question arises: just what is

Cf. also Logik, AAix, p. 14; ed. and trans. J. Michael Young, The Jasche Logic, in Lectures on
Logic (Cambridge: Cambridge University Press, 1992).
Kant was quite aware, for instance, that mathematical proof has rules of its own: see
A716“18/B744“6. Similarly, the mathematical science of nature has to combine the con-
structive methods of mathematics, the inductive methods of empirical inquiry, and the
deductive methods of syllogistic inference.

their relation to forms of being, or to the way things are? Logic, as
˜˜general and pure,™™ is thus only formal.18
On the other hand, the distinction between forms of sensibility and
forms of understanding helps delineate the domain for a logic that is just
as pure as formal logic, because it does not derive its rules from empirical-
psychological considerations of the kind described above, but that is not
as general as formal logic, in that the rules it considers are specified by
the content of thought they are relevant for. They are the rules for
combining representations given in sensibility, whatever the empirical
(sensory) content of these representations may be. Those rules are thus
not merely formal (concerning only the forms of thought in combining
concepts and judgment for arriving at valid inferences) but they concern
the way a content for thought is formed by ordering manifolds in intui-
tion (multiplicities of qualitatively determined spatial and temporal
parts). These rules are the rules of ˜˜transcendental™™ logic.
I now turn to Kant™s argument for his table of the logical forms of
judgment, in section one of the chapter on the ˜˜Leading Thread for the
Discovery of all Pure Concepts of the Understanding™™ (A67“9/B92“4),
and to the table itself, expounded in section two (A70“6/B95“101)

The Leading Thread: Kant™s view of judgment, and the table
of logical forms of judgment
In the Inaugural Dissertation, Kant distinguished what he called the
˜˜logical use™™ and the ˜˜real use™™ of the understanding. In the real use, he
said, concepts of things and of relations are given ˜˜by the very nature of
the understanding.™™19 In the logical use, ˜˜the concepts, no matter
whence they are given, are merely subordinated to each other, the
lower, namely, to the higher concepts (common characteristic marks)
and compared with one another in accordance with the principle of

Michael Wolff notes that Kant is not the first to make use of the expression ˜˜formal logic.™™
He cites Joachim Jungius™ Logica Hamburgensis (Hamburg, 1638) as an earlier source for
this expression. See Michael Wolff, Die Vollstandigkeit der Kantischen Urteilstafel. Mit einem
Essay ¨ ber Freges ˜˜Begriffsschrift™™ (Frankfurt-am-Main: Vittorio Klostermann, 1995),
p. 203n. He is right. Nevertheless, Kant™s emphasis on the idea that ˜˜general pure logic™™
is merely formal, as opposed to the various ˜˜logics of the special use of the understanding™™
(including transcendental logic) which are specified by the particular content of thought
they take into consideration, seems to be proper to him and certainly does not play
anywhere else the groundbreaking role it plays in Kant™s critical philosophy. On this
point, see again John MacFarlane, ˜˜Frege, Kant, and the logic in logicism,™™ pp. 44“57.
Inaugural Dissertation, section 2, x5, AAii, p. 393.

contradiction.™™20 The real use is what we saw Kant put into question in
the letter to Herz of February 1772: how could concepts that have their
origin in the laws of our understanding be applicable to objects inde-
pendent of our understanding?21 But the logical use remained
unscathed, and it is precisely what Kant describes again in section one
of the Leitfaden chapter under the title: ˜˜On the logical use of the under-
standing in general™™ (A67/B92). By ˜˜logical use of the understanding,™™ it
is thus clear we should not understand the use of understanding in logic “
whatever that might mean. Rather, it is the use we make of the under-
standing according to the rules of logic when we subsume sensible
intuitions under concepts and subordinate lower concepts to higher
concepts, in accordance with the principle of contradiction, thus forming
judgments and inferences. As we shall see, Kant argues that considering
precisely this ˜˜logical use of the understanding™™ gives him the clue or
leading thread (Leitfaden) he needs for a solution to the problem he
raised about its ˜˜real use.™™ For the very acts of judging by way of which
we subsume intuitions under concepts and subordinate lower concepts
to higher concepts also provide rules for ordering manifolds in intuition
and thus eventually for subsuming objects of sensible intuition under the
categories. Or so Kant will argue in section three of the Leitfaden chapter.
But before we reach that point, we need to consider the ˜˜logical use™™ in
more detail, to see how Kant thinks he can derive from it his table of the
logical forms of judgment.
The key term, in Kant™s exposition of the ˜˜logical use of the under-
standing,™™ is the term function:

All intuitions, as sensible, rest on affections, concepts therefore on func-
tions [Begriffe also auf Funktionen]. By a function, however, I understand
the unity of the action of ordering different representations under a
common one. (A68/B93)

The term ˜˜function™™ belongs to the vocabulary of biology and the
description of organisms. Kant talks of the ˜˜function™™ of mental capa-
cities as he would talk of the ˜˜function™™ of an organ. In this very general
sense, sensibility too has a ˜˜function.™™ Indeed, in the introduction to the
Transcendental Logic Kant writes:

AAx, p. 125.

The two capacities or abilities [Beide Vermogen oder Fahigkeiten] cannot
¨ ¨
exchange their functions. The understanding is not capable of intuiting
anything, and the senses are not capable of thinking anything. (A51/B76)

However, in the present context, Kant employs ˜˜function™™ in a more
restricted sense. Concepts, he says, rest on functions, as opposed to
intuitions which, as sensible, rest on affections. More precisely: because
intuitions rest on affections or depend on receptivity, concepts have to
rest on functions, namely they depend on our unifying representations
(intuitions) that are given in a dispersed, random order, in sensibility. In
this context, function is (as quoted above) the ˜˜unity of the action of
ordering different representations under a common representation.™™

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