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to say that objects contain sensation.
Schematism, Analytic of Principles I 155
Here the point is explicitly phenomenological: it is always possible
for the real of empirical consciousness to disappear gradually until
nothing remains but consciousness of the spatiotemporal manifold.
We can conceive of a sensation of color, for example, as fading until
the color disappears. From this Kant concludes at line 7 that it must be
possible for the understanding to perform a synthesis which produces
the magnitude of the sensation.
The remainder of the argument presents a revised version of the
¬rst edition proof. Here Kant argues that sensations lack extensive
magnitude because of their subjective nature, which he bases on the
view that sensations are inherently aspatial and atemporal. The latter
claim would follow from Kant™s distinction in the Aesthetic between
the form and the matter of intuition. In line 10 Kant claims that
sensation has some magnitude; he then concludes that its magnitude
must be intensive, and accordingly the real properties represented
through sensation must have intensive magnitude.
Another passage in the 1787 edition of the Critique yields addi-
tional evidence that Kant bases his view of sensation on a general
theory of consciousness. In the Paralogisms of Pure Reason in the
Dialectic, where Kant criticizes Mendelssohn™s proof that the soul is
immortal, he says this at B414“15: “For even consciousness always has
a degree, which can always be diminished;* consequently, so does the
faculty of being conscious of oneself, and likewise with all the other
faculties.”24 In the footnote indicated by the asterisk, he relates the
degree of consciousness to the degree of clarity and distinctness in a
representation:
Clarity is not, as the logicians say, the consciousness of a representation; for
a certain degree of consciousness . . . must be met with even in some obscure
representations . . . Rather a representation is clear if the consciousness in
it is suf¬cient for a consciousness of the difference between it and others.
To be sure, if this consciousness suf¬ces for a distinction, but not for a
consciousness of the difference, then the representation must still be called
obscure. So there are in¬nitely many degrees of consciousness down to its
vanishing.
Here the degree of consciousness is related to the degree to which
one can discriminate a representation from others. Since identity is

24 I thank Falkenstein for drawing my attention to this passage.
Schematism, Analytic of Principles I
156
a feature of all representation, this account is independent of any
particular physical theory. Unfortunately even this view may not be
suf¬cient to secure Kant™s claim that all sensations must be subject
to a continuum of degrees of intensity. To see why, let us look at the
notion of intensive magnitude.
We can understand the concept of intensive magnitude by com-
paring measuring procedures for intensive properties such as temper-
ature with those for extensive properties such as length or mass.25 We
shall see that extensive and intensive properties differ in two related
ways. First, they are subject to different types of empirical measuring
procedures. Second, as a result, their magnitudes are represented on
scales having different mathematical structures. Let us ¬rst examine
the procedures for measuring length, an extensive property.
Although there are various ways to interpret the notion of an exten-
sive magnitude, as we saw above Kant takes additivity to be essential.
In measuring length, some unit measure is applied successively to the
object; the resulting magnitude is the product of the unit and the
number of times it is applied. Thus a key characteristic of extensive
magnitudes is that they are additive. Combining a length x with a
length y produces a length z where “x + y = z” is a valid arithmetical
formula. In terms of measurement theory, extensive properties are
those measured on ratio scales. For ratio scales the choice of unit is
arbitrary, but the origin or zero point is ¬xed. So zero feet is always
equivalent to zero meters, or zero length expressed in any unit. Ratio
scales are related by a transformation function known as a similarity
transformation, or multiplication by a positive constant. Thus we can
convert a length given in meters into a length given in feet by mul-
tiplying by 3.28 (1 meter = 39.37 inches). It is characteristic of ratio
scales that the empirical measuring operations determine equality of
ratios. So the ratio of two lengths l1 /l2 is invariant regardless of the
unit being used: let l1 = 1 meter and l2 = 2 meters; the ratio 1/2 is
preserved in the equivalent measurement in feet, where l1 = 3.28 feet
and l2 = 6.56 feet.
By contrast, intensive magnitudes are measured differently, because
they are not additive. Consider that combining a quart of water at
25 This discussion is taken from my article, “Descartes on Sensible Qualities,” 593“7. There
I argue that Descartes rejects sensible qualities as real physical properties precisely because
they are intensive magnitudes.
Schematism, Analytic of Principles I 157
72—¦ F with another quart of water at 72—¦ F does not produce two quarts
of water at 144—¦ F. Intensive properties like temperature are measured
on interval scales rather than ratio scales. The Fahrenheit and Celsius
scales for temperature are constructed by selecting two ¬xed points,
and dividing the range between them into a certain number of inter-
vals, which is also arbitrarily selected. Both Fahrenheit and Celsius
scales use the ice point of water and the temperature of steam over
boiling water as ¬xed points, but they assign them different values:
the Fahrenheit values are 32—¦ and 212—¦ , the Celsius values 0—¦ and 100—¦ .
Consequently they divide the range between these points into differ-
ent numbers of intervals. Thus interval scales have both an arbitrary
zero point and choice of unit, although the units are uniform as they
are for ratio scales. But measurements on such scales are not additive
because there is no empirical procedure for combining the properties
these scales measure. Moreover, although ratios of temperatures are
not invariant, the ratios of intervals or differences of temperatures are
invariant. Consider the following assignments:
Fahrenheit temperatures Celsius temperatures
=
F1 C1
50 10
=
F2 C2
68 20
=
F3 C3
86 30
Notice that while the ratio F1 /F2 is not preserved by C1 /C2 , since
50/68 = 10/20, the ratio of intervals F1 ’ F2 /F2 ’ F3 is preserved by
the ratio C1 ’ C2 /C2 ’ C3 since
50 ’ 68 10 ’ 20
=
68 ’ 86 20 ’ 30
’18 ’10
=
’18 ’10
1=1
Interval scales are related by a transformation function j, known as
a linear transformation, so that to convert a reading from one scale
to another, one uses an equation of the form φ(x) = ax + b, with
a > 0. To convert a reading in degrees Fahrenheit (x) to degrees
Celsius [j(x)], we use the transformation: C = 5/9F ’ 160/9. To sum
up, then, here are the salient differences between ratio and interval
scales:
Schematism, Analytic of Principles I
158
Scale type Basic empirical operations Mathematical group structure
Interval Determination of equality of Linear or af¬ne group:
φ(x) = ax + b, a > 0.
intervals or differences
Zero point and unit arbitrary;
no addition operation.
Ratio Determination of equality of ratios Similarity group:
φ(x) = ax, a > 0.
Zero point ¬xed; unit arbitrary;
addition operation.
Although Kant was probably unaware of the mathematical group
structures of these scales as represented here, he certainly was aware
that intensive magnitudes are not additive. He also recognizes that
measuring procedures for such properties involve comparison. Now
as we can see, this is a fair description of the process of measurement
using an interval scale, since degrees of intensity are constructed by
making relative comparisons from one or more ¬xed points. One
difference between Kant™s conception and the example of temperature
concerns the zero point. Clearly Kant assumes that there is a non-
arbitrary zero point for intensive magnitudes, namely the absence of
the property or the sensation. In fact the notion of an absolute zero for
temperature in terms of the minimum volume of a gas was developed
during the eighteenth century, although the current value (’273.15
±.02—¦ C) was not established until the middle of the nineteenth
century.26
This analysis clari¬es the relation between the pure concepts of
quality and their schemata. Recall that the logical concepts express the
forms of af¬rmative, negative, and “in¬nite” judgments. As applied
to objects, af¬rmation corresponds to reality understood as the pres-
ence of some property represented in sensation (the “real” expressed
by a predicate). Negation then corresponds to the absence of a prop-
erty, and in¬nite judgments to the idea of drawing limitations. The
concept of intensive magnitude incorporates all three interdependent
categories. For Kant thinks of a determinate degree of intensity as a
limitation on reality constructed by comparison with negation, the
absence of the property.

26 I do not know whether Kant was familiar with the notion of absolute zero for temperature.
Schematism, Analytic of Principles I 159
One question that naturally arises concerns which aspects of sense
qualities have intensive magnitudes. Kant assumes that all qualities
have intensity, but he does not specify whether this is true of all of
their aspects. For example, color can be analyzed in terms of hue,
saturation, and brightness. Now the brightness of a color can vary in
intensity, and so can its saturation, the degree to which it is free
from admixture with white. But it is not so clear whether Kant
thinks this is the way to describe hue. Hues of colors “ red, blue,
green, and so on “ can be located on a continuum; red, for exam-
ple, shades from the orange side to the purple side. In this sense we
could designate degrees of redness, although this scale would have a
maximum point (where red is pure) and two minimal points, unlike
brightness and saturation. An examination of sound, taste, and odor
shows that there is no general pattern exhibited by the aspects of all
sense qualities. It may be that all Kant needs for his argument is that
each type of sense quality have some aspect that admits of degrees of
intensity.
We should also note that Kant does not claim that we “directly”
perceive the real properties of objects causing our sensations. In the
Postulates of Empirical Thought he uses the example of magnetic
forces: “Thus we cognize the existence of a magnetic matter penetrat-
ing all bodies from the perception of attracted iron ¬lings, although
an immediate perception of this matter is impossible for us given
the constitution of our organs” (A226/B273). Presumably the same
is true of fundamental forces of repulsion and attraction: he postu-
lates the force of repulsion to explain the impenetrability of bodies,
which is sensed through the feeling of solidity. Kant understands the
real properties of objects as those investigated by scienti¬c theories,
based on evidence given directly or indirectly in perception. What
we directly sense is in part a function of the nature of our sense
organs. Kant maintains, however, that no theoretical claim can be
empirically meaningful unless it is testable by reference to empirical
intuition.
Now we can address the relation between apprehension and the
synthesis involved in measuring intensive properties. Paton, for exam-
ple, thinks the idea of a continuous change from its absence to
any determinate degree of sensation applies to the apprehension of
Schematism, Analytic of Principles I
160
qualities: “I think Kant does believe that when we open our eyes
and look at a red colour, we pass from complete absence of colour
through various degrees up to that particular shade of red.”27 But as
Guyer points out, this contradicts the doctrine that all sensation is
instantaneous.28 Paton™s reading confuses what happens in apprehen-
sion with what happens in measuring degrees of intensity. Recall that
an intensive magnitude “can only be apprehended as a unity, and in
which multiplicity can only be represented through approximation
to negation = 0” (A168/B210). Now Kant says explicitly:
Apprehension, merely by means of sensation, ¬lls only an instant (if I do
not take into consideration the succession of many sensations). As some-
thing in the appearance, the apprehension of which is not a successive synthesis,
proceeding from the parts to the whole representation, it therefore has no
extensive magnitude. (A167/B209, emphasis added)
And at A168/B210: “the real in appearance always has a magnitude,
which is not, however, encountered in apprehension, as this takes place by
means of the mere sensation in an instant” (emphasis added). These
two passages clearly separate the mere, instantaneous apprehension of
sensation from the representation of its degree of intensity. In appre-
hension we instantaneously take up the sensation as a whole. By
contrast, awareness of the degree of intensity, either through compar-
ison or some measuring procedure, requires a synthesis in which the
whole is divided into parts. The difference between this synthesis and
that involved in extensive measurement is not the temporality of the
process “ all synthesis takes time “ but rather the part-whole relation,
since the degrees of the perceived quality or property are determined
relative to one or more ¬xed points. Kant apparently thinks it possible
simply to apprehend sense qualities without recognizing their degree
of intensity.29 Now he does say of the apprehension of sensation that
“the empirical consciousness can grow in a certain time from noth-
ing = 0 to its given measure” (B208, italics added). The fact that
intensities can vary in apprehension does not mean apprehension is

27 See Kant™s Metaphysic of Experience, 2:142n2.
28 See Kant and the Claims of Knowledge, 205. Guyer connects the intensity of sensation with the
schema of ¬lling time, but he does not distinguish between apprehension and the synthesis
required to conceive of intensive magnitude.
29 An analogous case is the indeterminate intuition of spatial extent Kant recognizes at A426“
8n/B454“6n.
Schematism, Analytic of Principles I 161
not instantaneous, but rather that we can become aware that a sound
is becoming louder, for example, through the “succession of many
sensations” mentioned at A167/B209. Thus I see no inconsistency
between the views that sensations are apprehended instantaneously
and that the synthesis required for measurement takes time.
It remains to consider whether Kant™s argument depends on unwar-
ranted assumptions about the causes of sensation, and whether, even
granting his assumptions, his conclusion follows. I argued above that
his proof is independent of his dynamical theory. But we have seen
that he conceives of sensations as effects on sense organs caused by
interactions with external bodies. It is not clear, however, that the
causal assumption plays a role in the proof. The A edition version
does not explicitly appeal to a causal connection between sensa-
tions and real properties of objects; the B edition version mentions
it only in the conclusion. I agree with Paton that the only relation
the Anticipations argument presupposes between sensations and real
properties is an intentional or representative relation, namely that
we take sensations to represent real properties of objects. Once Kant
defends the principle of causality in the Second Analogy, he can
then conclude that they must be caused by contact with external
bodies.
I think, however, that Kant cannot escape the objection that his
premises do not entail that every sensation must admit of a continuum
of intensity. The premises claim merely that it is possible for sensation
to diminish gradually, whereas the latter claims that sensations and
real properties do admit of degrees of intensity. As Falkenstein points
out, the argument does not rule out the possibilities that sensations
(and hence real properties) have a unit value “ either they are present
or they are not “ or admit of degrees that consist in discontinuous
quantum states. Such a quality could be present at, for example, 50%
or 60% of intensity, but not at intermediate states.30 Even granting
that consciousness admits of degrees of clarity, it does not follow that
sensations must admit of continuous degrees of intensity.

30 Both B´atrice Longuenesse and Jonathan Bennett recognize that Kant could have what I
e
called the weaker conception of possibility such that any sensation could vary continuously
in principle, although in fact some sensations might not do so. See Longuenesse, Kant and
the Capacity of Judge, 314“15, and Bennett, Kant™s Analytic, 172.
Schematism, Analytic of Principles I
162

5. s um ma ry
In the Schematism, Kant describes the transcendental schemata “
sensible conditions “ required to apply pure concepts of the under-
standing to objects of intuition. A schema is a procedure by which the
productive imagination constructs temporal features of objects. Thus
it provides the sensible content that turns a syntactic concept into a
real concept of an object. The Axioms of Intuition and the Anticipa-
tions of Perception are synthetic a priori principles of the understand-
ing expressing the mathematical categories of quantity and quality.
The Axioms specify that spatiotemporal objects must have extensively
measurable properties; the Anticipations require that the real proper-
ties of objects must be intensively measurable. These transcendental
deductions thus justify synthetic a priori cognition of appearances,
while explaining why such knowledge does not apply to things in
themselves.
ch ap t e r 7

The Analytic of Principles II




This chapter examines three of Kant™s most important arguments,
those responding to skepticism. From the Greeks up to Hume, skep-
tics attacked metaphysical claims about reality, especially regarding
substance, causal connections, and the external world. Kant replies
to these attacks in the Analogies of Experience and the Postulates of
Empirical Thought, where he defends pure principles based on the
relational and modal categories. According to Kant™s proofs, these
regulative principles supply the elements required to turn mere intu-
itions into perceptions of objects in the “weighty” sense, as subject-
independent entities in uni¬ed space and time. The Analogies argue
that the principles of substance and causal connection are necessary to
locate events in objective time. The Postulates of Empirical Thought,
which include the Refutation of Idealism, demonstrate the principles
enabling subjects to judge the real possibility, actuality, and necessity
of states of affairs. Here I ¬rst explain Kant™s arguments for these prin-
ciples, and then comment on Kant™s success in answering skepticism.

1 . th e a na logies of e x pe ri e nce
The Analogies argue that the a priori concepts of substance and
causality are required to order appearances in one time.1 Although
the text contains a distinct proof for each category, the introduction
argues for a general principle emphasizing the notion of objective
time-determination. The A edition principle states: “As regards their
existence, all appearances stand a priori under rules of the determina-
tion of their relation to each other in one time” (A176/B218). The B
1 This discussion is heavily indebted to Melnick™s Kant™s Analogies of Experience.

163
Analytic of Principles II
164
edition version reads: “Experience is possible only through the rep-
resentation of a necessary connection of perceptions” (A176/B218).
Despite their differences, both versions claim that a consistent order-
ing of states of affairs in global time requires thinking appearances by
the relational categories.
As with the previous principles, Kant added a new proof to
the beginning of the B edition. The brief A edition argument at
A177/B220 proceeds by claiming that “original apperception is related
to inner sense.” This means that we can become aware that our rep-
resentations exist in one uni¬ed time. Since performing the t.u.a.
requires synthesis, and synthesis requires an a priori ground, the rules
for ordering representations in one time must be a priori. Therefore,
“all empirical time-determinations must stand under rules of general
time-determination,” namely the Analogies.
Unfortunately this does not explain why the intuitions being
ordered in time must be of subject-independent objects. Kant
addresses this defect in the B edition by emphasizing the notion
of objective time-determination. The key is the contrast between a
merely subjective order of representations in apprehension and the
objective order of events in time. At B218 Kant de¬nes experience as
empirical cognition of objects through perception, which we know
requires a synthesis in one consciousness. At B219 Kant states that in
apprehension representations occur in a contingent, subjective order,
which can be distinguished from the objective order of the perceived
states in uni¬ed time. This latter order can be thought only by means
of a priori rules expressing necessary temporal features of objective
states. Insofar as they unify appearances in one time, these synthetic a
priori principles ground our judgments of subject-independent states
of affairs.
Some common experiences illustrate the distinction between the
subjective order of apprehension and the objective order of events.
The simplest case involves successive perceptions of coexisting states
of affairs. In the Second Analogy at A191/B235 Kant uses the example
of perceiving a house. Although the parts of the house coexist, our
perceptions of them occur successively, the order contingent on where
we begin. But this does not prevent us from recognizing that the parts
exist simultaneously. A more subtle case occurs when we see lightning
at a distance and hear thunder a few moments later. Knowing that
Analytic of Principles II 165
light travels faster than sound, we can recognize that the lightning and
thunder actually occur simultaneously, although we apprehend them
successively. Finally, it is even possible to apprehend states of affairs
in an order opposite to that in which they exist. Suppose one ¬rst sees
a cat moving nearby, and then observes some distant astronomical
event, such as a nova. Given the time it takes light to travel to the
Earth, we can judge that the nova actually occurred long before the
cat moved. Clearly we do in fact distinguish the objective order of
events from their order in apprehension.
Kant™s strategy is to show that locating states in objective time
presupposes the principles of the Analogies. Put simply, an objective
time-determination is a way of conceiving the order of appearances in
global time, in terms of three modes: persistence (or duration), suc-
cession, and simultaneity. “Hence three rules of all temporal relations
of appearances, in accordance with which the existence of each can
be determined with regard to the unity of all time, precede all experi-
ence and ¬rst make it possible” (A177/B219). The “modes of time” are
actually properties of appearances rather than time itself. Although
global time persists, it cannot be either successive or simultaneous.
Distinct parts of time exist successively, and only states can exist
simultaneously. Thus all states of affairs have some objective dura-
tion, and distinct states exist successively or simultaneously. Objective
time-determination involves measuring temporal intervals, as well as
determining the orders of states of affairs.
Kant next emphasizes the regulative role of the principles. As we
saw in chapters 4 and 6, Kant characterizes quantitative and quali-
tative categories and principles as “mathematical” or “constitutive,”
and relational and modal categories and principles as “dynamical” or
“regulative.” Whereas mathematical categories are required to repre-
sent distinct individuals and their properties, dynamical categories
relate these representations to one another in time and to the sub-
ject (A178/B220“1). This has two important implications. First, the

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