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away of constituent substances.· After arguing that the increase or
decrease in intensity of consciousness is compatible with the persistence
of substance, he goes on to suggest that consciousness could disappear
altogether through continuous diminution:

It is logically possible for something to exist up to and at a given period of time
and from that moment on not to exist. It ceases to be and begins not to be in the
±·
Time-consciousness in the Analogies
same moment. There is no contradiction in supposing a simple substance to be
annihilated. (Metaphysical Foundations, Ak. ©, p. )

The supposed contrast between the status of the mental and the physical
vis a vis conservation principles raises a worry about whether even
`
material substance can be conserved. Kant uses his distinction between
extensive and intensive magnitudes to argue that material substances
are conserved while there is no conservation principle for mental sub-
stances. But, given his own premises, the preservation of the quantum of
substance needs to be understood as the preservation of both the
extensive and the intensive quantity of substances rather than of exten-
sive quantity alone.
There is a crippling di¬culty for Kant™s attempt to base a conserva-
tion principle on material atomism. As he formulates the conservation
principle for phenomenal substance, it concerns the quantum of sub-
stance. In the Metaphysical Foundations, he clari¬es this notion of a quan-
tum as a collection of units. The number of units of matter in a
collection of matter would have to remain constant, if the quantum of
substance is to be conserved. In order for it to make sense to say that the
quantum of substance is a function of the number of units which make it
up, one must assume that the number of units is ¬nite. If the number of
units in any quantum of substance is in¬nite, the quantum of any
particular substance could not be a function of the number of units of
which it is composed. For one could take away or add units to that
quantum without a¬ecting the quantum. But Kant is committed to the
idea that space is in¬nitely divisible. He maintains that the in¬nite
divisibility of space entails the in¬nite divisibility of matter. The in¬nite
divisibility of matter and the external nature of all relations between
parts of matter leads to the idea of a potential in¬nity of atoms. This
prevents us from claiming that each material object is composed of a
certain de¬nite number of material atoms and that the number of such
material atoms is conserved in any closed system. There just will not be
a fact of the matter concerning the number of units of which an atom is
composed.
Kant is aware of the di¬culty, and opts to measure quantity of matter
by means of quantity of motion (Ak. ©, pp. µ·“µ). Motion and
matter itself are, in turn, traced back to dynamical forces of attraction
and repulsion. The dynamical construction of matter in the Metaphysical
Foundations does indeed provide a way out of this dilemma. Instead of
thinking of conservation in terms of bits of matter, one can move to the
± Kant and the demands of self-consciousness
forces or energy which distinguish matter from space. This allows one to
circumvent problems concerning atomism and the continuum. Some-
thing that is a continuous quantity in one sense can be a discrete
quantity in another sense. This is true of bits of matter. As bits of space
and time, matter is in¬nitely divisible and continuous. As a physical
quantity resulting from the existence of a certain quantity of force,
matter is discrete. It consists of grains with a determinate metric:
In¬nite divisibility refers only to appearance as quantum continuum and is
indivisible from the ¬lling of space; since the basis for the in¬nite divisibility of
space lies in that [¬lling of space]. But as soon as something is assumed to be a
discrete quantity: the number :Menge9 of units is determinate in it; hence
always equal to a number. ( µ·/ µµµ)

Spatio-temporal continuity is consistent with the existence of discrete
atoms endowed with determinate number as physical quantities. But the
argument cannot depend on the fact that matter is an extensive magni-
tude. So, to the extent Kant wants to argue that material substance
rather than mind is the only thing that could be conserved, he must
appeal to the anomalousness of the mental rather than to its lack of
physical extension. In conclusion, we may observe that Kant™s argu-
ment in favor of an Aristotelian conception of substance, as a substrate
of change, is relatively successful, since he has shown that we need
substances to the extent that changes are to be determinate. However,
his own theoretical assumptions raise major reservations about his e¬ort
to privilege matter (in the narrow sense) as substance.

  µ   © ®  ® ¤ °    ° µ  ¬ ©    °  © 
Kant uses the perception of an event as the starting-point for his
discussion of causation. After arguing that we can only determine
whether an event occurs by regarding such events as changes in things
that persist, Kant attempts to establish that we need to appeal to causal
relations in order to be able to determine the objective order of events in
time.We cannot simply read o¬ the objective sequence in which two
phases of an event or set of events occurred from the order of our
perceptions of those events. There are two important reasons for this. (±)
We apprehend things successively ( ±/ ). Succession arises from
the ¬‚ow or elapse of di¬erent states of consciousness, and the changes in
these states may not always re¬‚ect changes in the things observed by
consciousness. The problem is not that we cannot have introspective
±
Time-consciousness in the Analogies
awareness of succession.±° But we may be mistaken about the order in
which we perceived what we perceived. For what we have is at best a
short-term memory of the order in which we perceived the two states.
We need some criterion for distinguishing a (veridical instance of )
memory from a false memory of the sequence. () Even if the order in
which we judge ourselves to have perceived a state x followed by a state
y is, in fact, the correct order of those representations, we cannot be sure
that the order of our perceptions of states x and y corresponds to the
order in which they actually occurred. The distinction between the
order in which we perceive a set of states and the order in which those
states occurred in the object of which they are states is crucial to the
proper understanding of the argument from the irreversibility of a
certain perceptual order to the existence of an underlying causal cover-
ing law.
When we (veridically) perceive an objective change, or an event, the
sequence of percepts in that perceptual sequence corresponds to the
sequence of changes in its object. Following Van Cleve, I shall refer to
the circumstance in which the order in which we perceive a change
corresponds to the order of the states in the change itself as ˜˜perceptual
isomorphism.™™±± Perceptual isomorphism is analytic to what it means to
perceive an event, where an event is to be understood as an objective
change. Now Kant distinguishes the successive apprehension of an
event (of an objective change in state) from the successive apprehension
of an unchanging object. He uses the apprehension of a ship going
downstream, and of the coexisting parts of a house, as examples of
perceptions of changing and unchanging objects, respectively. In both
of these examples, a change of perceptual states is involved, since we
represent the items successively and our spatio-temporal perspective
undergoes a change. But only in the case of the ship going downstream
is the object in a state of change that is isomorphic to that of our
perceptions. The order of our perceptions is said to be ˜˜tied down™™ in
apprehension in the case of the perception (or rather apprehension) of
an event ( ±/ ·).±
The perception of a(n objective) change di¬ers from a mere (subjec-
tive) change in our perceptions. When I perceive the event of a ship
going downstream, the order of my perceptions cannot be reversed. I
cannot see the ship downstream ¬rst and then perceive the ship up-
stream. This would be the perception of a di¬erent event, i.e. it would be
the perception of a ship going upstream. Irreversibility of the sequence
in which an event is perceived is analytic to the perception of an event in
±° Kant and the demands of self-consciousness
the sense that the order of our perceptions must correspond to the order
of objective change. The ship might go downstream again after going
upstream. It is quite improbable that the ship could return to precisely
the same type of state on any understanding of what it is to be an event.
And, if event identity is tied to the relations of that event to other events,
it will be quite impossible for strict recurrence to occur. For if A“B are
di¬erent then A in the change A B will have to be di¬erent in content
from A in the sequence B“A for they will be involved with other events
that will make them di¬erent. And, even if the two A event-tokens in the
sequence A B A were type identical, the change from A to B and B to A
would nevertheless be di¬erent. The sequence A to B and B to A would
be irreversible with respect to event-tokens, if not with respect to
event-types.
The irreversibility of sequence that Kant imputes to perceptions of
changes has sometimes been thought to be the basis for his assertion that
those changes in the state of objects are themselves objective.± By
identifying the order of objective sequence with the order in the subjec-
tive sequence of perceptions, he would come into con¬‚ict not only with
Special Relativity, but also with the way the distinction between subjec-
tive and objective sequence operates in Newtonian (and Leibnizian)
mechanics. For even here the motions in terms of which spatial and
temporal intervals are measured are dependent on the frames of refer-
ence that di¬erent observers have. The identi¬cation of subjective and
objective sequence is incompatible even with our experience of such
phenomena as lightning and thunder. Under normal circumstances our
perception of thunder follows our perception of lightning, although the
lightning and thunder actually occur simultaneously. We also perceive
states of stars as simultaneous with us, many of which may have long ago
ceased to exist. Moreover, if a star lies one light-year from us, we will
perceive the light it emits earlier than the light emitted from a star that is
µ light-years away, even when the light from the star that is ¬ve
light-years away was transmitted almost four years earlier than the light
from the nearer star.
Counterexamples against perceptual isomorphism of this kind are
based on the misunderstanding that irreversibility in perception is
supposed to function as the criterion of temporal and causal sequence.
But knowledge of an irreversible order in perception is supposed to
presuppose knowledge of an objective irreversibility of succession. Thus,
in discussing the example of my perceiving a ship going downstream,
Kant notes: ˜˜In our case, I will therefore have to derive the subjective
±±
Time-consciousness in the Analogies
sequence of apprehension from the objective sequence of appearances,
since otherwise the latter is completely indeterminate and does not
distinguish any appearance from any other™™ ( ±/ ). Kant is not
claiming, to be sure, that we cannot have any beliefs about the temporal
order of our perceptions without knowing the objective sequence of the
objects of which they are perceptions. But we can only know that a given
sequence of states in which we perceive something is irreversible, that is,
must occur in a certain order, if we know the object perceived.
We only become aware of changes in our beliefs and desires by virtue
of the way they represent changes in what we represent outside of
ourselves. Once we have some perception of changes in things outside of
us, then we can assign some order to our representations. For, without
the possible perspective of an outside observer to draw on, I have no
sense that I or my representations are really in time at all ( ). From a
purely ¬rst-person perspective, the temporal order of my representa-
tions is indistinguishable from my present take on the temporal order of
those representations. It is not until I see that my present take might be
false, by thinking that another person might assign a di¬erent temporal
order to my representations, that I am really able to form judgments
about the temporal order of my inner episodes. That order will then
only be knowledge properly so-called to the extent that we are able to
derive the subjective ordering of time-sequences from an objective
ordering of changes in spatial objects by reference to the standpoint of
perception. If A is the ¬rst stage of some event and B is the stage which
follows it, then, given the isomorphism de¬nitive of event perception,
there will be perceptual states A and B corresponding to A and B. The
order of the occurrence of A and B is subject to this irreversibility rule
that is de¬nitive of the concept of event perception.
So far, all we know is that if we perceive an event, then the irreversi-
bility rule applies to perceptions. This does not tell us how we know
what the order of change from state A to state B is. Assuming that one is
perceiving an event, the order of what is perceived is ¬xed. The act of
perceiving A will be followed by the act of perceiving B, just as the
event A will be followed by the event B. We have not yet explained,
however, how it is that, given an act of perceiving A followed by an act
of perceiving B, we are then able to determine that an objective change
from A to B has occurred. For it always seems possible that the order of
our representations A . . . N may not correspond to the order of
changes in things A . . . N that are independent of our particular
standpoint. There must be some connection between A and B such that
± Kant and the demands of self-consciousness
we can know that if A occurs then B occurs. Once we know what this
connection is, we are then in a position to determine whether we are
correct in our belief that A precedes B. We can determine whether the
order of A and B according to which we perceive A and B corresponds
to the actual order of A and B. And only if we are in possession of such
facts are we able to challenge even our belief that A preceded B.
Whenever we perceive what appears to be a change in state, we are
presented with opposite states that are perceived sequentially. Percep-
tion alone does not tell us the objective relation between two successive
states of objects perceived, although we are conscious of the fact that the
one state precedes the other in our consciousness. Now, two temporal
states constitute an event only if they are opposites. It thus appears to be
su¬cient to know that they are opposites in order to know that, if they
are parts of an event, they are non-identical parts of an event or
sequence of events. For, if they are opposites, they cannot be simulta-
neous states of the same thing.± If we perceive a state B and we know we
have immediately previously perceived a state A that is opposite to B
and we know that B is at the same spatial location as A, then we know
that A cannot have occurred at the same time as B. If we know that two
states are opposites and states of the same thing, then we know that the
two states must belong to that thing at di¬erent times. And from the
existence of opposite states at di¬erent times we can conclude that a
change has occurred. However, we can only determine which of the two
states is earlier if there is something about the opposite states such that
the one could only exist after the other.
Kant infers that there is a necessary connection between an occur-
rence (an event) and something that precedes it from the rule deter-
minedness of the perceptual sequence in an event perception:

According to such a rule there must therefore lie in that which precedes an
occurrence in general a condition for a rule according to which this occurrence
always and necessarily follows. Thus since it is something that follows, therefore
I must necessarily relate it to something else in general which precedes it and
which it follows according to a rule, i.e. necessarily, so that the occurrence as
that which is conditioned gives certain indication of some condition, and this
determines the occurrence. ( ±/ )

Kant does not directly argue for the claim that objective succession
according to a necessary and strictly general rule is identical with our
notion of causation. One might wonder why succession according to a
necessary and strictly general rule would have to be construed as
±
Time-consciousness in the Analogies
causation. This is ultimately a matter of the appropriateness of terminol-
ogy. Nominal de¬nitions can be as arbitrary as one likes, but a real
de¬nition must be adequate to the explanatory tasks that a concept is to
ful¬ll. The term ˜˜causation™™ is generally taken to mean that which
necessitates a change from some event-type A to some event-type B.
Objective succession that is determined by a necessary and strictly
general rule gives us the regularity of sequence that is generally required
for a conception of causation. It also expresses the idea that a certain
occurrence generates another occurrence. The one occurrence had to
occur given the assumption that a certain other occurrence preceded it.
What then is the basis for the postulated necessary connection be-
tween events? It is tempting to trace the necessity in question back to the
concept of an event perception. But the analytic principle involved in
perceptual isomorphism, based on the concept of what it is to perceive a
perception, cannot itself provide the basis for the categorical necessity
that Kant must justify.±µ Since he regards causal connection as synthetic
and a priori, he does not intend the mere analysis of the meaning of
event perception to be the key premise in his argument.± How can the
claim that there is a necessary connection between individual tokens of
certain event-types be justi¬ed? Part of Kant™s answer is that the exist-
ence of an earlier time is a su¬cient condition for the existence of a later
time. Time is supposed to have a direction that is represented a priori (
±/ ;  ±/ ). This leads to the idea that it is a necessary law
that earlier times determine later times.
Kant takes the direction of causation to be an expression of temporal
direction. However, temporal direction is not simply causal direction or
reducible to causal direction in any interesting sense. Nor is causal
direction just temporal direction. The notion of cause, based as it is in
the non-material conditional and its ability to support counterfactuals, is
irreducible to the direction of time. In this respect, it must be distin-
guished from the essentially temporal notion of causal direction. This
allows for a conception of causal action that is not essentially temporal in
character, since it does not involve causal direction. Now, despite the
manner in which Kant wishes to link causal connection to the direction
of time, his notion of temporal causation is consistent with the possibility
of the backward causation postulated in some recent physical theories.
He nowhere indicates that the direction of time and the direction of
causation are directly linked in a manner that precludes causal vectors
from traveling from the future to the past. In fact, his theory of action,
which provides the model for his more general conception of teleology,
± Kant and the demands of self-consciousness
involves the idea that action is caused by the agent™s anticipation of a
certain outcome from that action. The agent™s beliefs concerning the
outcome of a certain action gives rise to a desire or aversion in anticipa-
tion of the feeling of pleasure or displeasure that the outcome would
bring.
It seems to be a necessary feature of a ¬nite temporal consciousness
that it experience changes in a direction that is irreversible in the order
of succession. But this does not rule out the possibility that the laws or de
facto regularities governing objective change give rise to reversals in the
order of temporal changes. Some objective sequences, such as the
motion of a ship, and perhaps even all objective sequences, may turn out
to be in some sense time-order reversible. The laws of Newtonian
mechanics are, for instance, invariant under time reversal. From the
point of view of the physics of Kant™s time, all processes are, in principle,
reversible. This seems to be true for the fundamental laws of contempor-
ary physics as well. There are phenomenological laws such as the second
law of thermodynamics that are not time-order invariant, but these laws
are based on other statistical laws that are time-order invariant. It seems
quite possible for there to be spatial and temporal regions in which there
is a constant increase in negentropy rather than entropy. This reverse
order of change to our own would not appear to observers in that part of
the universe to be time-order reversed, although our part of the universe
would appear that way to them and theirs to us.
The synthetic a priori necessity that later events follow earlier events
is part of Kant™s reason for thinking that there are necessary (causal)
connections between events. But perhaps a more fundamental reason is
to be found in the idea that changes must be determinable. The
necessity that changes be empirically determinable provides the key
premise in Kant™s argument that every event must have a cause and that
tokens of a certain event-type must be connectable to tokens of some
other event-type according to laws that ¬x the order of their occurrence
in objective time.±· Now, the transcendental or metaphysical realist
simply accepts the possibility that there may be changes that we cannot
explain and that there may therefore be events that have no cause. But,
for Kant, a judgment that a change has or has not occurred must, in
principle, be justi¬able by us. Transcendental idealism not only de-
mands that the subjective conditions under which evidence is available
to individual observers be subject to constraints that apply to all ob-
servers regardless of their standpoint, it also limits empirical judgments
to claims that can, in principle, be supported by evidence. Transcenden-
±µ
Time-consciousness in the Analogies
tal idealism limits change to what, in principle, is determinable by us or
at least by a being with ¬nite powers of understanding. This is why Kant
thinks that ˜˜if appearances were things in themselves, then no human
being would be able to ¬gure out how the manifold is connected in the
object from the succession of representations of that manifold™™ ( ±°/
µ).
The distinction between the subjective order of representeds and
their objective order amounts, for Kant, to a distinction between contin-
gent and necessary connections between those representeds. Represen-
tations are true of an object, if and only if they cohere ˜˜necessarily™™
amongst themselves. Here the object is just whatever all of our beliefs
correspond to when they are internally coherent. The necessity that the
object transmits to those representeds is itself nothing but the necessary
connectedness of those representations ( ±·/ ). This aspect of the
argument is a direct application of the recognition argument in the
A-Deduction, where Kant ultimately based the possibility of conceptual
recognition on the possibility of an impersonal self-consciousness of
diverse representations. Only such an impersonal self-consciousness is
capable of supporting the normative claim implicit in conceptual recog-
nition that one is representing or rather judging the item in question as
anyone ought to do so.
The idea that what makes for objective relations between items that
we experience is that such items must be connectable in self-conscious-
ness in a way that allows conceptual recognition, has an immediate
relevance to the problem of how temporal episodes may be ordered in
time. The only way of assigning a determinate temporal position to
what is experienced is relative to all other items of experience: ˜˜the
appearances must determine for one another their position in time, and
make their time-order a necessary order™™ ( °°/ µ). A necessary
order is invariant with respect to changes in observers and their spatio-
temporal positions. In this invariant spatial and temporal order, a
position is provided for all possible empirical consciousness. By ˜˜carry-
ing the time-order over into appearances and their existence™™ ( °°/
µ), we get the notion of an object that is independent of any particular
standpoint, and at the same time a sequence of percepts that corre-
sponds to the a priori structure of intuition. We must identify di¬erent
times relative to di¬erent events that occupy them because this is the
only way we have of identifying di¬erent times. ˜˜For only in appearance
can we empirically know this continuity in the connection of times™™ (
±/ ). Our perceptions are true of their objects just in case they are
± Kant and the demands of self-consciousness
connected in a lawlike way to those objects. To order perceived events
in time in a way that corresponds to the objective order of those events,
we must identify the causal laws that connect those events to other
events.
When we perceive an event, we take it to be something that necessar-
ily follows something else. We assume that if we perceive the set of
circumstances that ought to bring about a certain event and the event
does not occur, we are merely imagining or dreaming that the appropri-
ate circumstances are on hand ( °/ ·). The information link
between those perceptions and their object is then deviant. To be sure,
in order to determine that an information link is deviant, we would have
to have knowledge of all of the relevant conditions governing a suc-
cession from one state to another. This is unattainable by us, since the
number of ceteris paribus clauses that may be relevant to the occurrence of
events is potentially in¬nite. We rely on knowledge of the most relevant
conditions. Determining which conditions are most relevant is itself a
matter of skill in judgment, and is inherently interest-relative.
Now, in contrast to the holistic account of time-determination that I
have been defending, Allison insists that the argument in the Second
Analogy is concerned only with the succession of one state to another
that makes up an event, rather than with a sequence of di¬erent
events.± His distinction between the sequence of states in an individual
event and in a series of events tends to be undermined by the nature of
the identity conditions for events. Allison admits that an event is to be
construed as a succession of states. Individual momentary states do not
involve either replacement change or changes in state. They cannot
therefore constitute an event, as Kant understands the notion of event.

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