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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
166
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
change.
1a. We do in fact perceive successive and simultaneous states in
time.
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
168
4. The substratum of everything real is substance; everything that
belongs to existence can be thought only as a determination of
substance.
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):
a
“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
170
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
172
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
a
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
o
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
174
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;
A190/B235)
5. Therefore, the only alternative is to think the succession of states as
necessarily determined or irreversible. (A188/B234; A192“3/B237“
8)
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
176
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-

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