. 5
( 9)


Principles, Kant characterizes the real in appearance as that “which
corresponds to [the sensation] in the object” (A edition) and that
“which is an object of the sensation” (B edition). I agree with Paton
that for Kant the real in appearance are the properties of matter as
determined by empirical science.21 Twice Kant gives as an example of
a degree of reality the moment of gravity, certainly a scienti¬c notion
(A168“9/B210“11). These properties may or may not resemble the
consciously represented sense qualities.22
The A edition proof from A167“9/B209“10 proceeds as follows:
1. Apprehension by means of sensation is instantaneous, i.e., it does
not take time.
2. Therefore, apprehension in sensation is not a successive synthesis
proceeding from the parts to the whole.
3. Therefore, the thing apprehended in sensation does not have exten-
sive magnitude.
4. That in empirical intuition which corresponds to sensation is
reality; that which corresponds to its absence is negation.
5. Every sensation is capable of diminishing gradually until it disap-
6. Therefore, between reality in appearance and negation there is a
continuum of sensations, such that between any two sensations
there is always a sensation; there is no smallest possible sensation.
7. Thus the real in appearance always has a magnitude which is not
21 See Kant™s Metaphysic of Experience, 2:137“8. I disagree, however, with Paton™s identi¬cation
of sensation with “the sensum considered as modi¬cation of the mind.”
22 Given the primary“secondary quality distinction, Kant believes that sense qualities do not
resemble the real properties in objects causing them. Moreover, MFNS presents a dynamical
theory of matter in which the ultimately real properties are fundamental forces of repulsion
and attraction.
Schematism, Analytic of Principles I
8. A magnitude which can only be apprehended as a unity, and in
which multiplicity can only be represented through approximation
to zero, is an intensive magnitude.
9. Therefore, every reality in appearance has intensive magnitude,
i.e., a degree.
This version begins with the premise that apprehension in sensation
is instantaneous. Although Kant does not defend it, it is plausible as
an account of the perception of something occupying space-time.
Either the senses are affected or they are not. In apprehension the
understanding “takes up” this sensory material into consciousness
and presents it as a sense quality. Thus it would seem to be an all-or-
nothing affair. Conclusions 2 and 3 follow from this and the Axioms
view that the synthesis required to represent extensive magnitudes
takes time because the whole is generated from the parts. Therefore
the instantaneous apprehension of sensation cannot take place by
means of such a synthesis. In consequence what is apprehended in
sensation cannot have extensive magnitude.
Premise 4 introduces the concepts of reality and negation by estab-
lishing the “fact” on which the Transcendental Deduction depends,
namely that we take sensations to represent real properties of objects
given in intuition. Reality is that in the object which corresponds
to the sensation; negation represents its correlate, the absence of a
property. The key to the argument is premise 5, the controversial
claim that every sensation can diminish gradually until it disappears.
Unfortunately Kant offers no support, and it is not obvious how to
defend it. Some commentators see it as based on Kant™s physics, which
explains the impenetrability of matter by intensive forces of repulsion
and attraction. This reading reverses the order of argument, however,
since the Principles provide necessary conditions for experience and
consequently are presupposed by empirical laws and theories. Kant
says this explicitly in both the MFNS and in a discussion of the pos-
sibility of empty space and time near the end of the Anticipations.
(We will look at this passage below.)
An alternative reading bases premise 5 on the phenomenology of
sensation and the notion of something ¬lling time. It is a fact that
at least some aspects of sense qualities can diminish gradually. The
brightness of light and the loudness of sound are two such aspects.
Premise 5 makes only the weak claim that it is possible for sensations
Schematism, Analytic of Principles I 153
to diminish gradually until they disappear. Admitting the slide from
sense qualities to sensations, this could be justi¬ed as a brute fact about
sensory consciousness. Based on these examples, one might argue that
the notion of something ¬lling time entails the possibility in principle
that it can diminish gradually to nothing. A problem with this defense
concerns a scope ambiguity. One reading would take the “possibility”
in a weak sense, so that it is possible for every sensation to diminish
gradually, although perhaps some in fact do not. Kant™s conclusion,
however, apparently requires the strong sense that every sensation
is such that it can diminish gradually. We shall return to this point
below. In any case, the phenomenological approach has the advantage
of not basing Kant™s view of sensation on a particular physical theory.
As we shall see, the B edition version supports this reading.
The rest of the proof follows from the analysis of intensive mag-
nitude. Statements 6 and 7 are conclusions from premise 5. In line 6
Kant states that both sensations and the “real in appearance” have a
magnitude such that they can diminish continually to nothing. He
then concludes in line 7 that the real in appearance has a non-extensive
magnitude. Premise 8 de¬nes intensive magnitudes as those appre-
hended only as unities, and in which the parts can be represented
only “through approximation to negation.” Kant then concludes that
every reality in appearance has some degree of intensity.
The gist of the argument is this: in order to represent objects ¬lling
time (and space), we must conceive of sensations and the real prop-
erties of objects as having some degree of intensity. This presupposes
a conceptual scheme that permits us to take sensations to correspond
to real properties of objects. On Kant™s view this is the function of
the schema of intensive measurement. It is the correspondence in
intensity that makes it possible for sensations to represent empirically
real objects.
The argument in the B edition is essentially the same, although
Kant uses the technical vocabulary of matter and form, and empha-
sizes the synthesis of the understanding in relating sensations to
objects. The proof is this:
1. Perception is empirical consciousness in which there is sensation.
2. As objects (Gegenst¨ nde) of perception, appearances are not pure
intuitions like space and time, but contain the matter for an object
in general.
Schematism, Analytic of Principles I
3. Through this matter something is represented as existing in space
and time.
4. This matter is the real of sensation, which is a merely subjective
representation by which one is aware of being affected.
5. This matter is related to an object in general (by a synthesis of
the understanding).
6. From empirical consciousness to pure consciousness a gradation
is possible in which the real disappears and a merely formal con-
sciousness of the spatiotemporal manifold remains.
7. Thus there is also possible a synthesis in representing the magni-
tude of sensation from 0 to any arbitrary magnitude.
8. Sensation is not in itself an objective representation, since neither
space nor time is found in it.
9. Therefore, it has no extensive magnitude.
10. But it does have a magnitude (such that through its apprehension,
empirical consciousness can grow in a certain time from 0 to a
given measure).
11. Therefore, it has an intensive magnitude.
12. Corresponding to this all objects of perception, insofar as it con-
tains sensation, must be ascribed an intensive magnitude, i.e., a
degree of in¬‚uence on sense (emphasis added).23
This version begins with the analysis of empirical consciousness.
Premises 1“4 are based on the Aesthetic and so should not be contro-
versial. Here Kant emphasizes that perceiving objects involves sensing
something ¬lling space-time, which he calls the matter of appearance.
This matter, which we consciously apprehend as sense qualities (the
real of sensation), makes possible our awareness of things existing in
space and time. Premise 5 restates this as the transcendental “fact”
that we relate this matter to an object in general. Since an object in
general is the judgmental notion of an object, Kant is here reminding
us that the understanding refers the matter to an object by means of
pure concepts.
At line 6 Kant introduces the notion of the gradual diminution in
the degree of reality through an analysis of empirical consciousness.
23 I emphasize “it” to indicate that I have altered Guyer and Wood™s translation. They take
the pronoun diese to refer to objects of perception rather than perception. But the verb for
“contain” is in the singular “ enth¨ lt “ rather than the plural; moreover, it makes no sense
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
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
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
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
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
Schematism, Analytic of Principles I
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
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
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
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
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“
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
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
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

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
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.

Analytic of Principles II
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
existence of appearances cannot be “constructed,” that is, known a
priori (A179/B222). The fact that anything is given at all in intu-
ition, and when it exists, can be known only empirically. The second
implication concerns their demonstrability. Kant says that although
both types are a priori, they differ in “the manner of their evidence,
i.e., with regard to their intuitiveness” (A180/B223). Unlike extensive
Analytic of Principles II
and intensive properties, locations and relations in objective time
and possibility, actuality, and necessity are not intuitable features of
appearances. Now this distinction between the constitutive and reg-
ulative categories amounts to a distinction between principles estab-
lishing the mere intentionality of perception, and those establishing
the robust objectivity of the intuited objects. Although merely inten-
tional objects might present extensively and intensively intuitable
features, the order of their existence could not be distinguished from
their order of apprehension. The mark of real subject-independent
objects is objective spatiotemporal location.

2 . the fir st a na log y: t h e pri nci ple of subs ta nce
Kant intends the First Analogy to defend the belief in substances
as permanent things underlying changing states. Historically there
were many concepts of substance, but most philosophers subscribed
to the view that transitory states must belong to something perma-
nent. Since we are directly aware only of our own successive, ¬‚eeting
perceptions, Hume denied we could know any kind of permanent
entity, physical or mental. Although it does not become clear until the
Second Analogy, for Kant substance can only be physical; he rejects
Descartes™s dualistic concept of mind as a substantial entity.
Each relational category corresponds to a particular mode of time.
Kant correlates substance with duration or persistence, cause“effect
with succession, and causal interaction with simultaneity. Like the
other categories, the three relational concepts are interdependent,
because the three modes of time are also interdependent. Duration
(or persistence) is the fundamental mode, since all states last for some
time. Different states of affairs exist either successively or simultane-
ously. But determining the objective succession and coexistence of
states presupposes determining objective time intervals. As Melnick
points out, knowing only that one state precedes another does not
determine their exact locations in global time. Existing three min-
utes apart is a different order from existing three days apart. In the
two cases, the states will bear different relations to all other states
in time. Moreover, determining when a state begins or ends also
depends on measuring time intervals. To use Melnick™s example, if it
starts to rain at some time t, there must be some de¬nite time interval
Analytic of Principles II 167
before t during which it was not raining. Although we do not have
to determine how long before t it was not raining, we must be able
to determine some time interval before it started to rain. Otherwise
it would not be true that it began to rain at t.2 Thus the ability to
identify the beginnings, endings, and relations of states of affairs in
objective time presupposes being able to measure temporal intervals.
For Kant, this means that our notions of causal action and interaction
presuppose the concept of substance.
Kant offers two versions of the principle of substance. The A edition
states, “All appearances contain that which persists (substance) as the
object itself, and that which can change as its mere determination,
i.e., a way in which the object exists” (A182). The B edition says,
“In all change of appearances substance persists, and its quantum is
neither increased nor diminished in nature” (A182/B224). Although
the A version emphasizes permanence, the B version includes the
corollary principle of the conservation of substance. Both versions
claim that all changes in appearance must be thought as states of some
absolutely permanent substance. This principle is synthetic a priori
since it asserts that permanent things exist. Its deduction depends on
the assumption that we do in fact perceive states of affairs that endure
and that are related successively and simultaneously in time.
Kant offers two proofs for the principle. The ¬rst, which Melnick
calls the argument from time magnitude, occurs in the ¬rst paragraph,
at A182/B224“5. Kant elaborates on it up to the second proof at
A188/B231. These arguments raise three issues: ¬rst, whether substance
must be absolutely permanent; second, what counts as substances for
Kant; and third, how he defends the conservation principle.
The argument from time magnitude consists in the following steps:
1. Time is the substratum of all appearances; time itself cannot
1a. We do in fact perceive successive and simultaneous states in
2. Time itself cannot be perceived.
3. Therefore, there must be something in appearance that represents
time as the substratum of all change.

2 See Melnick, Kant™s Analogies of Experience, 60“1.
Analytic of Principles II
4. The substratum of everything real is substance; everything that
belongs to existence can be thought only as a determination of
5. Therefore, there must be real substance in appearance; all perceiv-
able changes must be alterations of real substance. Moreover, the
quantity of substance cannot increase or diminish. (A182/B224“5)
Allison calls steps 1“3 the “backdrop thesis,” since they express Kant™s
view of time perception underlying all the Analogies. Let us now
examine each step of the argument.
1. Time is the substratum of all appearances; time itself cannot change.
Here Kant restates the Aesthetic view that time is the universal form of
all appearances. The difference between the term ˜substratum™ and the
term ˜substance™ is crucial. By a substratum Kant means a foundation
or underlying structure. His point is that we can perceive succession
and simultaneity only in time. But the Aesthetic also proves that there
is only one time. Thus all appearances must be related to one another
in the same unchanging, global time.
1a. We do in fact perceive successive and simultaneous states in time.
This is the premise establishing the “fact” from which the princi-
ple follows. It is not stated explicitly but is presupposed in Kant™s
statements at A181/B225 that “succession and simultaneity can be
represented” and “all change or simultaneity can be perceived” only
in time.
2. Time itself cannot be perceived. It is an axiom of Kant™s theory
that neither empty space nor empty time is an object of perception.
Only appearances in space and time are perceivable. But the absolute
times of states are not given in the appearances. First, time is qual-
itatively homogeneous and so the nature of time provides no basis
for distinguishing one moment or interval from another. Second, the
qualities we sense are independent of their times (and places): they
do not come “stamped” with objective temporal locations, and none
can be inferred from them alone.
3. Therefore, there must be something in appearance that represents
time as the substratum of all change. Since time itself cannot be per-
ceived, something else must represent the underlying substratum
against which to judge successive and coexisting states. The only
other thing given in intuition is appearances. Therefore there must
Analytic of Principles II 169
be some feature of appearances functioning as the basis for ordering
transitory states in time.
4. The substratum of everything real is substance; everything that
belongs to existence can be thought only as a determination of substance.
Here Kant connects substance with the substratum of change, but
his claim involves two different notions of substance.3 The correla-
tion between the pure concept of substance and the subject-predicate
form of judgment retains the traditional idea of substance as the sub-
ject which is not itself predicable of anything else. This substance,
which Bennett dubs “substance1 ,” must endure only relative to its
changing predicates. Another conception, Bennett™s “substance2 ,” is
of something absolutely permanent.4 This is Kant™s schematized con-
cept of substance: “the proposition that substance persists is tautolog-
ical” (A184/B227). This premise maintains that the only candidate in
appearances to represent the persistence of time is the enduring sub-
ject of changing states, the “substratum of everything real.” It involves
two claims: ¬rst, that the only thing that can serve in appearance as the
substratum of change is the subject of changing states (substance1 ),
which, second, must be absolutely permanent (substance2 ) to repre-
sent the persistence of time.
5. Therefore, there must be real substance in appearance; all perceivable
changes must be alterations of real substance. Finally Kant draws the syn-
thetic a priori conclusion that permanent substances must exist as the
subjects of the changes we perceive in appearances. At A187/B230“1
he clari¬es the terms ˜change™ (Wechsel ) and ˜alteration™ (Ver¨ nderung):
“Arising and perishing are not alterations of that which arises or per-
ishes. Alteration is a way of existing that succeeds another way of
existing of the very same object. Hence everything that is altered is
lasting, and only its state changes.” That is, a change consists in
a coming-to-be or ceasing-to-be of some state. The subject of this
change undergoes an alteration, but does not itself change. Thus the
conclusion asserts that all changing states perceived in appearances
must be alterations of some permanent substance.
On this reading the debatable claims are evident. The backdrop
thesis (steps 1“3) is uncontroversial, since premises 1 and 2 are based

3 4
See Allison, Kant™s Transcendental Idealism, 212“15. See Bennett, Kant™s Analytic, 182.
Analytic of Principles II
on the Aesthetic. Now one might question step 1a, depending on
what counts as a “state” in time. Certainly Kant cannot presuppose
that the changing states we perceive must be fully objective in the
sense of apprehension-independent states of affairs, since this is what
he intends to prove. But he does not need that claim. Even Hume
admits that “perceptions of the mind” occur successively. Taking these
as states, it follows that in inner sense, we do perceive a succession of
changing states. So the skeptic who admits steps 1, 1a, and 2, must
also accept conclusion 3.
This puts the burden on steps 4 and 5, where Kant identi¬es the
substratum of real changes with substance. Here I follow Melnick,
who offers the most plausible account of step 4.5 First, we must
note something not expressed here, namely the empirical criterion of
substance. In the Second Analogy Kant says this criterion is action:
“Where there is action, consequently activity and force, there is also
substance” (A204/B250). Later, in the Amphiboly of the Concepts of
Re¬‚ection, Kant remarks: “We know substance in space only through
forces that are ef¬cacious in it” (A265/B321). In other words, the
empirical basis for determining time intervals are actions of things
we take to be enduring entities. Examples of such actions are the
motion of the hands of a clock, the motion of the Earth around the
Sun, and the decay of a radioactive particle. Steps 4 and 5 claim that
only if an action is taken to be of something persisting through a
change can we use it as a basis for measuring the time interval.
To defend this, Melnick describes a case in which an object used
in measurement fails to persist through an interval. Imagine we are
measuring an interval from t1 to t2 by the motion of the hands of
a clock. Suppose at t1 the hands read 4:00, and at t2 the hands read
4:05. But further suppose that the substance of the clock (call it A)
goes out of existence at some point t between t1 and t2 , and that
its replacement (call it B) comes into existence at some later time t
before t2 . Thus we have the following situation:
t1 - - - - - - -A- - - - - - - t t =======B=======t2
Now measuring the interval t1 “t2 requires measuring the component
interval t “t . But we cannot do this by reference to the hands of
5 See Kant™s Analogies of Experience, 62“6.
Analytic of Principles II 171
the clock. Let the reading at t be 4:02:25, and the reading at t be
4:02:27. Although we are tempted to say the interval t “t is 2 seconds,
we cannot do so, since the readings of the clocks are signi¬cant only
insofar as they record the mechanical actions of the two clocks. In
this case their signi¬cance is lost, since the time interval t “t “is
not marked off by the mechanical process” (66). In other words, the
action used to measure a temporal interval must be the action of
something existing continuously through the interval. Thus Kant™s
stated conclusion appears justi¬ed.
On the other hand, Melnick thinks Kant is wrong to claim that
substances must be absolutely permanent. He should conclude only
that the things serving as substrata for time measurement cannot go
out of existence during the intervals being measured. On Melnick™s
view, if some substance had to be employed for all measurements, then
that substance would have to be absolutely permanent. But that con-
dition does not obtain, since we use many different kinds of physical
processes for different cases. Near the end of the First Analogy, Kant
defends his claim about absolute permanence based on the “unity of
time”: “The arising of some [substances] and the perishing of others
would itself remove the sole condition of the empirical unity of time,
and the appearances would then be related to two different times,
in which existence ¬‚owed side by side, which is absurd” (A188“9/
B231“2). Kant thinks that if substances were not absolutely perma-
nent, and time-determinations were based on actions of different
substances, then con¬‚icting measurements might result, disrupting
the coherence of temporal ordering in global time (the “empirical
unity of time”). Melnick agrees that measurements of the same inter-
val based on two different substrates could differ. But he argues that
the problem arises only when both substrata are employed at the same
time.6 As long as only one substratum is used to measure any par-
ticular temporal interval, the use of different physical processes for
different intervals need not disrupt the unity of time.
Kant™s second proof that substance exists is the argument from
empirical veri¬ability, that the absolute coming into being or perish-
ing of something is not a possible object of perception:

6 Kant™s Analogies of Experience, 67“9.
Analytic of Principles II
If you assume that something simply began to be, then you would have to
have a point of time in which it did not exist. But what would you attach this
to, if not to that which already exists? For an empty time that would precede is
not an object of perception; but if you connect this origination to things that
existed antecedently and which endure until that which arises, then the latter
would be only a determination of the former, as that which persists. It is just
the same with perishing: for this presupposes the empirical representation
of a time at which there is no longer an appearance. (A188/B231)
As Melnick explains, Kant is arguing that it is impossible to iden-
tify the absolute beginning or ceasing of a state of affairs unless one
attaches it to an enduring substance.7 He describes the situation in
which we want to determine that something S came into existence at
a certain time t. To do so we must show that S did not exist before
t, say at t . But if S is not connected to anything enduring before t,
then to verify that S did not exist before t requires showing that for all
possible locations, S did not exist at any location at t . But this is not
a possible perception, and so the claim is not veri¬able. By contrast,
if S is a state of some enduring thing x, then it is possible to verify
that S did not exist at t , since we can verify that x was not S at t .
To illustrate, he describes the creation of an electron pair (electron“
positron) from a photon. This is the creation of an electron because
there are no laws connecting the existence of this electron at t with the
existence of an electron at any other place before t. But there are laws
connecting the electron being here at t with another phenomenon
at an earlier time and a certain place, in this case with the actions of
photons. Melnick points out that for Kant, being governed by spatial
laws is essential to states of substance; this foreshadows the argument
in the Refutation of Idealism that substances must be spatial. In fact,
Kant added this marginal note to the A edition text: “Here the proof
must be so conducted that it applies only to substances as phenomena
of outer sense, consequently from space, which exists at all time along
with its determination.”8 We examine the Refutation below.
By now the reader is no doubt wondering what counts as a sub-
stance for Kant. Assuming substances must be physical, it is not
obvious what they would be. First, they could not be macro-objects
7 Kant™s Analogies of Experience, 71“7.
8 Cited in CPR, 299. Original source given as Erdmann, Nachtr¨ ge zu Kants Kritik der reinen
Vernunft, 32; Academy edition of Kant™s gesammelte Schriften, 23:30.
Analytic of Principles II 173
such as trees, tables, and chairs, since these objects pass in and out
of existence. Melnick™s example of electron creation also shows that
even sub-atomic particles of matter could not qualify as substances if
they can be created or destroyed. In MFNS, Kant argues that matter
must be composed of absolutely permanent centers of force. Accord-
ingly, these centers would count as substances, and the particles and
objects they give rise to would count as their states. In any case, only
theoretical physics can decide the nature of substance.
Finally, we should consider Kant™s corollary, that the quantity
of substance is conserved. Kant offers no argument for it here. A
marginal note in the A edition, however, speci¬es that substance can
be conceived only in terms of quantity: “Now everything that can
be distinguished from that which changes in experience is quantity
(gr¨sse), and this can only be assessed through the magnitude of the
merely relative effect in the case of equal external relations (Relatio-
nen) and therefore applies only to bodies.”9 Allison points out that
at A848/B876 Kant de¬nes matter as “impenetrable lifeless exten-
sion,” that is, a mere occupier of space. So the corollary hinges on the
idea that the only conceivable property of substance is its quantity.
Unfortunately Kant does not explain why this must be so.10

3. the se cond a na logy: t h e pri nc iple of caus a li t y
The Second Analogy argues for the general principle that every event
has a cause. Although commentators agree that Kant is responding
to Hume™s attack on belief in causal connections, they disagree about
whether he also intends to guarantee the existence of empirical laws.
Despite a majority opinion against this view, Melnick and Friedman
present compelling reasons in its favor. We shall examine this issue
after analyzing the argument and some objections to it.
The A edition principle states: “Everything that happens (begins to
be) presupposes something which it follows in accordance with a rule”
(A188). The B edition version says, “All alterations occur in accordance

9 Allison™s discussion of this topic is found at Kant™s Transcendental Idealism, 210“12. The
marginal note is cited in CPR, 299. Original source given as Erdmann, 32; Ak. 23:30“1.
10 For Kant™s conception of matter in the MFNS, see Allison, Kant™s Transcendental Idealism,
210“12, Brittan, Kant™s Theory of Science, chapter 6, and Friedman, Kant™s and the Exact
Sciences, 38“9.
Analytic of Principles II
with the law of the connection of cause and effect” (A188/B232).
Whereas the B edition mentions only the general causal principle,
the A edition refers to a rule, which, it appears, could only be an
empirical law. As we have seen, the relational categories function
to determine the position of states of affairs in objective time. The
Second Analogy ties the concept of cause“effect to our experience of
succession. Kant will argue that the perception of states as objectively
successive presupposes that events are caused.
First we need to clarify the notions of an event and a cause. For
Kant an event is a change of state, which, as the First Analogy argues,
can only be the state of a substance. Thus an event is a coming to
be in something of a state that did not already obtain. In general
an event E consists in a succession of states of an object from S1
to S2 (hereafter ˜S1 “S2 ™). Events are objective happenings: they have
a determinate position in global time. Examples of events are the
freezing or melting of water, the radioactive decay of a particle, and a
stationary billiard ball beginning to move. Note also that the change of
representations in a subject would be an event, albeit a “mental event.”
Kant uses the example of a ship moving downstream at A192/B237,
but according to the law of inertia, only accelerations, not uniform
motions, are changes of state. Kant in fact recognizes this in a footnote
at A207/B252: “Hence if a body is moved uniformly, then it does
not alter its state (of motion) at all, although it does if its motion
increases or diminishes.” Now this analysis of an event makes no
reference to causal connections or rule-governed succession. Thus
Arthur O. Lovejoy is wrong to claim that for Kant the causal principle
is analytic since an event is de¬ned as “a phenomenon that follows
another phenomenon according to a rule.”11 To the contrary: Kant
clearly recognizes the synthetic a priori nature of the causal principle.
A second confusion concerns the relation between events and their
causes. Philosophers often take the successive states S1 “S2 composing
the event to be respectively the cause and the effect. As Melnick shows,
however, this is not Kant™s view, and it is generally not true of events
as we understand them.12 Consider the freezing of water: clearly the
state of being liquid is not the cause of the water becoming solid.
The event consists in the change S1 “S2 , but the cause is some other
11 See Lovejoy, “On Kant™s Reply to Hume,” 295.
12 Kant™s Analogies of Experience, 100“1.
Analytic of Principles II 175
event or condition, such as lowering the temperature. Kant conceives
of the cause as a condition that brings about the change according
to a rule: “there must therefore lie in that which in general precedes
an occurrence the condition for a rule, in accordance with which this
occurrence always and necessarily follows” (A193/B238“9). In sum,
the event is the effect, and the cause is some other event.
The ¬rst statement of the proof occurs at B233“4; Kant then elab-
orates the argument several times. Here are the main steps, not in
their order of presentation:
1. All apprehension is successive. (A189/B234; A192/B237)
2. I perceive events, and thus can distinguish an objective succession
of states in time from a merely subjective succession of apprehen-
sions. (B233; A190/B235“6; A192/B237)
3. Perceiving an objective succession of states requires the imagina-
tion to connect and order perceptions in global time. (B233)
4. The “backdrop thesis”: the objective position of states in global
time cannot be determined by mere perception, since: (a) time
itself cannot be perceived; (b) the manifold given in intuition is
not “stamped” with its objective time position; and (c) the order
of apprehension does not yield objective time positions. (B233“4;
5. Therefore, the only alternative is to think the succession of states as
necessarily determined or irreversible. (A188/B234; A192“3/B237“
6. The concept required to think the irreversibility of states is cause-
effect, that is, the concept of a condition upon which something
else follows necessarily according to a rule. (A193/B238)
7. Therefore, event perception presupposes that all events are caused.
8. Corollary: the subjective sequence of apprehension is “bound to”
or derived from the objective order of the states. (A192/B237“8)
Kant wants to derive the principle that all events are caused from
the fact that we perceive events or objective successions in time. Like
the First Analogy, the proof depends on the backdrop thesis, that the
objective times of appearances are not given in “mere perception,”
but must be thought. Judging that a succession of states is necessary
means thinking it as irreversible. Kant believes that cause“effect is the
a priori concept required to think successions as irreversible. From this
Analytic of Principles II
he concludes that all events are governed by causal laws. Let us now
examine each step in turn.
1. All apprehension is successive. This follows from the Aesthetic
analysis of time as the form of inner sense.
2. I perceive events, and can thus distinguish an objective succession
of states in time from a merely subjective succession of apprehensions.
Kant™s argument is based on the fact that we distinguish between a
mere succession of perceptions and the perception of a succession.
As the example of perceiving a house shows (A190/B235), that two
states are perceived successively does not entail that they exist suc-
cessively. Now we must consider whether a skeptic like Hume could
object to this premise. Allison maintains that Hume cannot reject this
premise since “event awareness is presupposed by his own well-known
account of how we come to form the belief that future sequences of
events will resemble past sequences.”13 Moreover, Hume™s theory that
impressions precede their corresponding ideas evidently requires him
to distinguish between objective and subjective successions.
3. Perceiving an objective succession of states requires the imagination
to connect and order perceptions in global time. Recognizing an event
requires one to perceive (judge) the component states as having a
determinate order in global time. Now commentators disagree over
what Kant is claiming about this temporal ordering. Allison believes
Kant is arguing only that we must be able to determine the relative
order of states in time.14 By contrast, Melnick takes Kant to argue
that it must be possible to locate an event in relation to all other
events in global time. In support, he cites passages such as A177/B219,
where Kant describes the principles as rules “in accordance with which
the existence of each [appearance] can be determined with regard to
the unity of all time.”15 Melnick™s reading offers a more coherent
interpretation of Kant, one reinforced by the Postulates of Empirical
Thought, as well as the First Analogy.
4. The “backdrop thesis:” the objective position of states in global
time cannot be determined by mere perception. In discussing the First
Analogy we accepted this view, that neither the data of intuition nor
the mere order of apprehension can determine the objective times

13 14 See Allison, Kant™s Transcendental Idealism, 229.
Kant™s Transcendental Idealism, 228.
15 Melnick, Kant™s Analogies of Experience, 85“8.
Analytic of Principles II 177
of the intuited states. Lovejoy objects, however, that it is possible to
perceive the succession of states constituting an event. Citing Kant™s
example of the ship ¬‚oating downstream, Lovejoy says, “I can, in the
language of common sense, see the ship move.” From this he concludes
that the principle of causality (he says suf¬cient reason) is not required
to distinguish between objective successions and coexisting states.16
Lovejoy is right, of course, that one can perceive successive states of
an object (this is consistent with premise 2). But it does not follow
from mere perception that these are states of the same substance, or
that we can locate the states in global time. Consider the ship case:
what guarantees that the substance of the ship upstream is the same
substance as the ship downstream? It will turn out that one function
of causal laws is precisely to justify assumptions about the identity of
the objects whose states are being perceived. The discussion of time
determination above also shows that mere perception is not suf¬cient
to locate successive states in global time. Thus Lovejoy™s example does
not refute Kant™s argument.
5. Therefore, the only alternative is to think the succession of states as
necessarily determined or irreversible. This is the famous “irreversibil-
ity thesis,” about which there is much confusion. What Kant actually
says is that in order to determine the objective relation of the appear-
ances, “the relation between the two states must be thought in such
a way that it is thereby necessarily determined which of them must
be placed before and which after rather than vice versa” (A188/B234,
my italics). And at A192“3/B237“8 he distinguishes event perception
from the successive perception of coexisting states: “if in the case of
an appearance that contains a happening I call the preceding state
of perception A and the following one B, then B can only follow A
in apprehension, but the perception A cannot follow but only pre-
cede B” (my italics). By contrast, in the successive apprehension of
coexisting states, the order of perceptions has no necessity: “In the
previous example of a house . . . there was therefore no determi-
nate order that made it necessary when I had to begin in the appre-
hension in order to combine the manifold empirically” (A193/B238).
Thus what characterizes event perception is the irreversibility of the
perceptions; as Strawson puts it, perceptions of coexisting states have

16 See Lovejoy, “On Kant™s Reply to Hume,” 297“8.
Analytic of Principles II
“order-indifference.”17 The question arises whether Kant is attribut-
ing irreversibility to the states perceived or to our apprehensions of
them, since the term “perception” is ambiguous. As I emphasized
above, however, irreversibility must be attributed originally to the
appearances. In consequence (I list this as a corollary in step 8), we
must think the order of apprehension as “bound to” the order of the
states perceived. Here, then, Kant identi¬es the feature characterizing
event perception as the thought that the sequence S1 “S2 constitut-
ing the event is irreversible. As both Melnick and Allison emphasize,
Kant is not arguing that irreversibility in apprehension is a datum
from which we infer the irreversibility of states of appearances.18
A second issue concerns whether Kant™s claim that one must think
the succession as necessary is analytic. Several commentators argue
that given that one perceives an event E constituted by S1 “S2 , it is
logically necessary that the states occur in the order S1 “S2 . If they
occurred in the order S2 “S1 , by de¬nition one would perceive a dif-
ferent event.19 But as James Van Cleve has shown, this objection
commits two fallacies.20 First is a scope error: Kant is arguing that the
necessity attaches unconditionally to the existence of the event rather
than to the consequent of a conditional. That is, event perception
is characterized by the thought “Necessarily S1 is followed by S2 ,”
rather than “If I perceive E, necessarily S1 is followed by S2 ,” which
is analytic. A related error is construing the necessity here as logical
rather than real. Clearly the sequence S1 “S2 has a real necessity, which
Kant attributes to the necessity of causal laws. Kant is offering a tran-
scendental deduction to show that the real necessity of metaphysical
principles is grounded in their “epistemic” status.
6. The concept required to think the irreversibility of states is cause“
effect, that is, the concept of a condition upon which something else follows
necessarily according to a rule. Finally, Kant connects the idea of irre-
versibility to causal laws. As we saw earlier, the event being perceived
is the effect, and the cause is some condition that initiates the change

17 See Strawson, The Bounds of Sense, 133.
18 See Melnick, Kant™s Analogies of Experience, 82“3, and Allison, Kant™s Transcendental Idealism,
19 Among those raising this objection are Strawson, The Bounds of Sense, 137, Wolff, Kant™s
Theory of Mental Activity, 268, and Bennett, Kant™s Analytic, 221.
20 See Van Cleve, “Four Recent Interpretations of Kant™s Second Analogy,” 82“3.
Analytic of Principles II 179
from S1 to S2 . It is essential to causality that the relation between cause
and effect be rule-governed: “This connection must therefore consist
in the order of the manifold of appearance in accordance with which
the apprehension of one thing (that which happens) follows that of
the other (which precedes) in accordance with a rule” (A193/B238).21
As Melnick explains, Kant sees causal laws as rules for ordering
states, based on features of appearances.22 Since the sequence is irre-
versible, the law must be asymmetrical: Kant says that being rule-
governed entails “that I cannot reverse the series and place that which
happens prior to that which it follows” (A198/B243). But causal laws
are complex, and it is an oversimpli¬cation to represent them in the
form, “Whenever C occurs, E occurs.” For in addition to describing
the cause and the effect, they must take into account other relevant
factors called boundary conditions. For example, it is not the case
that water invariably freezes at a temperature of 32—¦ Fahrenheit; other
factors come into play, including the volume and shape of the liquid
mass and the pressure acting on it. Thus the rules relating cause to
effect must always refer to the circumstances in which the event takes
place. To cite Melnick™s more elaborate example, an automobile can
be rust-free (P1 ) at t, and corroded (P2 ) at t . How we order these states
depends on the circumstances. The event could be the change P1 “P2
if oxidation occurs; or it could consist of P2 “P1 if the automobile is
repainted. Causal laws, then, take the form, “Given circumstances B,
whenever event C occurs, S1 will be followed by S2 .”
Whether step 6 is acceptable, then, depends on whether order-
ing successive states requires us to think them as governed by causal
laws. Given the backdrop thesis, the conclusion that this objective
ordering depends on features of appearances appears undeniable. But
as Melnick points out, nothing about appearances determines their
order “except in terms of some rule that orders the appearances on
the basis of these features.”23 As we saw above, ordering the states as
non-coexistent means that the rule must be asymmetrical: given the
circumstances, S1 is followed by S2 and not vice versa. Thus Kant
can reasonably conclude that perceiving states as necessarily succes-
sive requires thinking them as subject to causal laws. Causal laws

21 Additional passages occur at A193/B238“9, A195/B240, and A201/B247.
22 23 Kant™s Analogies of Experience, 89.
Kant™s Analogies of Experience, 89“90.
Analytic of Principles II
function as rules for ordering states as successive based on features of
the states.24
7. Therefore, the perception of events in time presupposes that all events
are caused. Kant™s conclusion is the general principle that all events are
caused. This follows from steps 5 and 6, for if it is true that we must
think of the states making up an event as necessarily successive, and
if causal laws are required to order states in this way, then all events
must be subject to causal laws.
As I mentioned, commentators question whether Kant also intends
to prove the existence of particular empirical laws. On the above
interpretation, the causal principle must be true because we must
think of events as governed by empirical laws. Friedman defends
this reading in discussing Kant™s view of empirical laws.25 Friedman
argues that for Kant, causality is a rule-governed relation between two
events, such that given the cause, the succession of states constituting
the effect follows necessarily. Moreover, the universality of a rule
entails that it applies to types of events (e.g., lowering temperature
with the freezing of water).26 Thus he agrees with Melnick that Kant
justi¬es the causal principle by showing that all events are governed
by empirical laws; in other words, “the universal causal principle
must assert the existence of particular causal laws.”27 Now as Melnick
explains, this does not guarantee that we can discover these causal
laws. The Second Analogy argues only that there must be causal
laws governing changes of state, not that we must know them. For
one thing, we may need the repetition of types of events to discover
causal laws, but the Second Analogy does not imply anything about
the frequency of types of events.28
Friedman also argues that Kant does not construe particular causal
laws as inductive generalizations. Of course empirical laws are more
speci¬c than the causal principle because they employ empirical con-
cepts (e.g., matter as the movable in space). Although “empirical laws
can only obtain and be found by means of experience” (A216/B263),
it does not follow that they are a posteriori. Throughout the Analytic,

24 See Melnick, Kant™s Analogies of Experience, 89“90.
25 See “Causal Laws,” especially 165“75.
26 See “Causal Laws,” 192n4 and 193n6. Obviously the general causal principle does not specify
the kind of rule Kant is arguing for.
27 28 See Melnick, Kant™s Analogies of Experience, 91“3.
“Causal Laws,” 171.
Analytic of Principles II 181
Kant emphasizes the necessity of causal connections. At A91/B124 he
says the concept of causality requires that the effect follow from the
necessarily and in accordance with an absolutely universal rule . . . thus
to the synthesis of cause and effect there attaches a dignity that can never
be expressed empirically, namely that the effect does not merely come along
with the cause, but is posited through it and follows from it.
And at A159/B198 he says laws of nature “carry with them an expres-
sion of necessity, thus at least the presumption of determination by
grounds that are a priori and valid prior to all experience.” For Kant,
empirical laws have a mixed necessity, which Friedman describes as
“a priori in a derivative sense.”29 Although empirical laws are not
deducible from the principle of causality, that principle makes possi-
ble particular causal laws.30 Friedman describes the three-stage pro-
cedure for deriving the law of gravitation from Kepler™s laws, which
subsumes both the latter and the theory of gravitation under the
necessary transcendental principles. Melnick™s and Friedman™s analy-
ses should put to rest doubts that Kant intends to demonstrate the
existence of particular causal laws.
8. Corollary: the subjective order of apprehension is “bound to” or
derived from the objective order of the states. Finally we come to Kant™s
claim concerning the order of apprehension in event perception. As
I see it, this is not a premise, but an implication of the conclusion.
One could interpret it to mean that to represent states as necessarily
successive, our apprehensions of those states must also be necessarily
successive. But a careful reading shows that Kant never says this: he
claims only that the subjective order is “bound to” or “derived from”
the objective order. A better construal is based on a causal theory of
perception, according to which our apprehensions are mental events
themselves subject to the principle of causality. Thus the order of our
apprehensions a“b of an event A“B is determined by the location
of the event A“B in time. Whether the subjective order reproduces
the objective order depends on the circumstances. Under ordinary
circumstances, such that the way a depends on A does not differ from

29 “Causal Laws,” 174.
30 Friedman sketches how the law of universal gravitation is “grounded” in the MFNS in section
IV of “Causal Laws,” 175“80, and Kant and the Exact Sciences, 165“210.
Analytic of Principles II
the way b depends on B, the order of apprehension would repro-
duce the order of the states.31 Moreover, since this is only a corollary
of the causal principle, there is no circularity in basing this claim on a
causal theory of perception. Demonstrating the truth of the principle
of causality a fortiori justi¬es a causal theory of perception and this
corollary claim.
Throughout the Second Analogy, Kant claims that only transcen-
dental idealism, and not transcendental realism, can account for
the distinction between objective and subjective temporal orders.
Although this does not play a role in the proof, it does bolster the
case for transcendental idealism. Kant explains the inadequacy of
transcendental realism thus:
If appearances were things in themselves, then no human being would be
able to assess from the succession of representations how the manifold is
combined in the object. For we have to do only with our representations;
how things in themselves may be . . . is entirely beyond our cognitive
sphere. (A190/B235)
For the transcendental realist, all representations are empirical and
provide no basis for distinguishing the subjective order of apprehen-
sion from the objective order of events. Only by taking appearances to
be constituted by the act of judging, can we recognize features essen-
tial to experience of objects: “If we investigate what new characteristic
is given to our representations by the relation to an object, and what
is the dignity that they thereby receive, we ¬nd that it does nothing
beyond making the combination of representations necessary in a
certain way, and subjecting them to a rule” (A197/B242“3).32
One last question concerns the simultaneity of cause and effect.
At A202“3/B247“9 Kant denies that the cause necessarily precedes
the effect, or that the necessary succession obtains between cause and
effect. Kant™s examples of the stove heating a room and the lead ball
creating a depression in the pillow illustrate that “The majority of
ef¬cient causes in nature are simultaneous with their effects, and the
temporal sequence of the latter is occasioned only by the fact that the

31 Van Cleve calls this condition “perceptual isomorphism” in “Four Recent Interpretations of
Kant™s Second Analogy,” 81“2.
32 See also A191/B236, A196“7/B241“2, and A199“200/B244“5.
Analytic of Principles II 183
cause cannot achieve its entire effect in one instant” (A203/B248). As
we have seen, causal laws imply not that causes must precede their
effects, but that given the cause, the succession of states constituting
the effect is necessary. Now one relation that must obtain between
cause and effect is that the effect could not precede its cause: “For if I
lay the ball on the pillow the dent follows its previously smooth shape;
but if (for whatever reason) the pillow has a dent, a leaden ball does
not follow it” (A203/B248“9). In Kant™s view, the actual temporal
relations between cause and effect will depend on the nature of the

4. the third a nalog y: th e prin ci pl e
of c au sa l in te racti on
In the Third Analogy, Kant argues that our ability to determine
that states of distinct substances coexist presupposes laws of causal
interaction. This completes his analysis of the necessary conditions
for determining objective time relations of appearances. As Melnick
points out, however, the Second and Third Analogies are actually
two sides of the same coin. This is not surprising since, according
to Newton™s third law of motion, every causal action also involves
an interaction. Melnick argues that Kant™s distinction between the
schemata of causality (succession) and that of mutual interaction
(coexistence) is mistaken. By generalizing the notion of causal law
to include dynamical interactions, Kant can combine the two argu-
ments. Thus the weakness is in the detail rather than the substance
of the arguments.33
As usual, Kant presents two versions of the Third Analogy prin-
ciple, which the B edition labels the “Principle of simultaneity,
according to the law of interaction, or community.” The A edition
version states, “All substances, insofar as they are simultaneous, stand
in thoroughgoing community (i.e., interaction with one another)”
(A211). The B edition reads: “All substances, insofar as they can be
perceived in space as simultaneous, are in thoroughgoing interaction”
(B256). Since substances are absolutely permanent, simultaneity must

33 Here I follow Melnick in Kant™s Analogies of Experience, 94“7 and 102“10.
Analytic of Principles II
be a feature of their states. The point, then, is to show that judging
states of (distinct) substances to be simultaneous requires that they
fall under laws of dynamical interaction.
The of¬cial argument is given at B257“8, and closely parallels the
argument of the Second Analogy. The main steps are these:
1. Things (states) are simultaneous when their perceptions are recip-
rocal or reversible. For example, perceptions of coexisting states of
the moon and the earth can occur in any order.
2. Simultaneity is the existence of the manifold at the same time.
3. The backdrop thesis: objective simultaneity is not given in intu-
4. Therefore, the understanding must think the perceived states as
simultaneous and thereby as reversible in perception.
5. The concept required to do this is mutual dynamical interaction.
6. Therefore, the perception of simultaneous states presupposes laws
of dynamical interaction.
The problem is how to distinguish causal actions determining
objective successions from the dynamical interactions correlated with
objective simultaneity. Melnick thinks this is not serious, since it is
possible to unify the arguments of the Second and Third Analo-
gies. The Second Analogy principle applies to successive states of
one substance, the Third Analogy to simultaneous states of distinct
substances. Melnick shows that determining a succession of states of
distinct substances requires both causal action and mutual interac-
tion. Had Kant generalized his approach, the two arguments could
be combined as follows:34
1. We can determine the objective times of events or states of affairs
only relative to other events or states of affairs, and presupposing
that the position of an event can be determined relatively to all
other events.
2. Objective time-determinations are not given in perception.
3. Therefore temporal determinability must be based on features of
4. Features of appearances can be used to locate events and states of
affairs only by presupposing rules licensing such inferences.
34 I paraphrase Melnick at Kant™s Analogies of Experience, 95“7.
Analytic of Principles II 185
5. Rules licensing inferences from features of appearances to their
temporal locations are laws describing real connections, both asym-
metrical and mutual, among substances.
6. Therefore, the objective determination of states as successive
or simultaneous requires the application of causal laws or rules
describing necessary connections among states of affairs.
Melnick defends his view by analyzing the impact motion of billiard
balls described by laws of collision. Consider an impact law L that
describes the motions of bodies following a collision as a function of
the magnitude and direction of force, their elasticity, the coef¬cient
of friction, and so on. Melnick argues that such a law can be used
to determine both successive and simultaneous states of the balls.35
Suppose a billiard ball a simultaneously strikes two billiard balls at
rest, b and c. If we are interested only in the positions of b and
c relative to each other, but not with respect to a, we can use L to
determine the simultaneous positions of b and c after the collision. By
the same token, we can use L to determine that b is at p before c is at p
following the collision. In neither case are the positions of the two balls
a function of each other, nor does any mutual interaction between
them play a role. Thus where there is a causal interaction involving
a change of state(s) brought about by an initiating condition, the
same law can be used to determine both the objective succession and
coexistence of states, in the same and distinct substances.
Melnick concludes that although Kant wrongly correlates causal-
ity with succession and interaction with simultaneity, he is right that
objective time-determination requires us to apply causal laws of action
and interaction to the things whose states they are.36 In the absence of
dynamical interactions among substances, we could not make objec-
tive temporal claims about their states, since we could not determine
whether the two states are objectively successive or simultaneous. In
concluding, Kant claims that “There are therefore certain laws, and
indeed a priori, which ¬rst make a nature possible” (A216/B263). By
“nature” he means the necessary unity of all appearances in one space-
time. “Thus together [the Analogies] say: All appearances lie in one
nature, and must lie therein, since without this a priori unity no unity
35 See Melnick, Kant™s Analogies of Experience, 102“10 for the full discussion.
36 Melnick, Kant™s Analogies of Experience, 109.
Analytic of Principles II
of experience, thus also no determination of the objects in it, would
be possible” (A216/B263).

5 . t he post ul ates of e mpi ri ca l thou g h t
Up to this point the Principles describe conditions that constrain
the content of our experience of objects. By contrast, the Postulates
govern the mode in which the subject holds objective judgments, as
to their real possibility, actuality, or necessity. At A219/B266 Kant says
the modal categories are peculiar insofar as “they do not augment the
concept to which they are ascribed in the least, but rather express only
the relation to the faculty of cognition.” Rather than contributing
to the concept of an object, the modal categories relate objects “to
the understanding and its empirical use, to the empirical power of
judgment, and to reason.” In other words, the modal categories are
required to create a coherent system of knowledge.
The categories of modality are schematized versions of the logical
concepts of modality discussed in the Metaphysical Deduction. In
chapter 4 we saw that the latter concern the illocutionary or assertive
force of judgments: logical possibility expresses the mode in which
the subject merely considers a proposition; logical actuality expresses
assertion; and logical necessity expresses the assertion of a proposition
as following from other propositions. In the Postulates, Kant claims
our ability to judge states of affairs as really possible or impossible,
actual or non-actual, and necessary or contingent, requires us to think
appearances under these modal concepts.
Kant™s discussion does not so much justify as explain the application
of the Postulates. The interesting argument here is the Refutation of
Idealism, which Kant added to the B edition, along with a long foot-
note in the B edition Preface at Bxxxix“xli. As previously mentioned,
this argument responds to Descartes™s view that self-knowledge is
more certain than knowledge of external objects. Kant inserted this
proof, one of his key arguments against skepticism, in the middle
of his analysis of actuality. In spite of its location, the argument is
signi¬cant enough to stand on its own. Here I shall discuss Kant™s
general claims about the modal categories. The next section examines
the Refutation.
Analytic of Principles II 187
Judgments about real possibilities are governed by the postulate
that objects conform to the formal conditions of experience in gen-
eral, that is, to conditions of synthesis required for empirical cognition
(A220/B267). These conditions include both the forms of intuition,
and the categories defended previously. Hence for a state to be a
possible object of experience, it must ¬rst be located in the global
space-time of human intuition. Moreover, it must be both exten-
sively and intensively measurable (Axioms and Anticipations), and
governed by the principles of substance and causality (Analogies).
Clearly these are stronger constraints than the mere notion of logical
possibility expressed in the principle of non-contradiction. Kant says
the impossibility of a ¬gure enclosed between two straight lines “rests
not on the concept in itself, but on its construction in space” (A220“
1/B268). Given our form of spatial intuition, such a plane ¬gure is
not a possible object of experience. Similarly, invented concepts not
derived from the formal conditions of experience have no a priori
Because assertions about the actual make stronger claims, they
depend on not only formal but also material conditions of experi-
ence, namely sensation. At A225/B270 Kant says this does not require
“immediate perception of the object itself” but rather “its connection
with some actual perception in accordance with the analogies of expe-
rience.” That is, one can assert the existence of a state of affairs that
is not immediately perceived, as long as it is connected by laws with
what is given in intuition. This permits us to assert the existence of
theoretical or unobserved entities such as electrons, dinosaurs, and
so on. Kant uses the example of a magnetic ¬eld: “Thus we cognize
the existence of a magnetic matter penetrating all bodies from the
perception of attracted iron ¬lings, although an immediate percep-
tion of this matter is impossible for us given the constitution of our
organs” (A226/B274). And in the Antinomies he says:

That there may be inhabitants in the moon, although no one has ever
perceived them, must certainly be admitted. This, however, only means that
in the possible advance of experience we may encounter them. For everything
is real which stands in connection with a perception in accordance with the
laws of empirical advance. (A493/B521)
Analytic of Principles II
This postulate also provides a criterion for distinguishing between
dreams and waking experience, since dream states are not integrated
into experience by causal laws.
Finally, the concept of empirical necessity applies only to states per-
ceived as following from other states according to causal laws. As Kant
puts it at A226/B280, real necessity is neither logical necessity, nor
the formal necessity of a valid inference (Kant™s logical form of neces-
sity), nor absolute metaphysical necessity. Instead it is a hypothetical
or material necessity of a state of affairs, given certain conditions,
according to a universal law. Consequently, real necessity attaches
not to substances, but only to their states: “Hence we cognize only
the necessity of effects in nature, the causes of which are given to
us . . . and even in this it does not hold of the existence of things,
as substances, since these can never be regarded as empirical effects,
or as something that happens and arises” (A227/B280). No substance
exists necessarily; as the Second Analogy shows, empirical necessity
attaches only to states of substances.
Finally Kant explains why he calls the modal principles postulates.
Although ˜postulate™ sometimes means a proposition assumed with-
out justi¬cation, this is not Kant™s de¬nition. As pure principles of the
understanding, the Postulates express “the synthesis through which we
¬rst give ourselves an object and generate its concept” (A234/B287).
Here Kant is thinking of propositions describing the construction
of ¬gures in space. These mathematical postulates cannot be proved
“since the procedure that it demands is precisely that through which
we ¬rst generate the concept of such a ¬gure.” Similarly, the Pos-
tulates of Empirical Thought cannot be proved since they do not
add content to the concept of an object, but only indicate how it
“is combined with the cognitive power” (A235/B287). In expressing a
priori conditions for judging real states of affairs, the Postulates make
it possible to construct a coherent system of empirical cognition.

6 . th e ref utati on of i de al i s m
Kant inserts the Refutation in the discussion of actuality, since he
intends to show that we must have actual knowledge of the exter-
nal world. Along with the revised Transcendental Deduction, this is a
major change in the B edition, added to clarify Kant™s idealism. In the
Analytic of Principles II 189
A edition Kant tackled the problem of the external world in the fourth
paralogism. There he claimed that transcendental idealism solves
the problem by showing that external objects “are merely appear-
ances, hence also nothing other than a species of my representations”
(A370“1). It is no wonder many readers confused his position with
empirical idealism, according to which physical objects are merely
collections of perceptions. The Refutation also makes an important
correction to Kant™s treatment of space and time. Whereas the Aes-
thetic treats outer and inner sense as parallel, the Refutation estab-
lishes the priority of outer sense to inner sense.
The argument is aimed against empirical idealism, “the theory that
declares the existence of objects in space outside us to be either merely
doubtful and indemonstrable, or else false and impossible” (B274).
Kant attributes the ¬rst variant, which he calls problematic ideal-
ism, to Descartes. The second he labels dogmatic idealism, which he
attributes to Berkeley, who claims that the ideas of mind-independent
space and matter are incoherent.37 Kant agrees with Berkeley if one
takes space to pertain to things in themselves, “for then it, along with
everything for which it serves as a condition, is a non-entity” (B274).
Since space is neither a substance nor a property of substances, it
could have no clear metaphysical status as a thing in itself. But the
conclusions that space is merely a form of intuition and not a thing in
itself refute dogmatic idealism in two ways. First, they show that space
and spatial things are possible as appearances; second, they prove that
space is a necessary condition for experience of particulars distinct
from the subject.
These arguments do not, however, address the possibility that
whereas experience may actually be temporal, it may only seem to be
spatial. Put another way, perhaps only inner sense is real, and outer
sense is imaginary. This is Descartes™s position in the second Medita-
tion, where he argues that his mental states are immediately knowable
and certain, while experience of physical things could be illusory. Not


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