## 1. What is 'the perception of time'?



The very expression 'the perception of time' invites
objection. Insofar as time is something different from events, we do
not perceive *time* as such, but changes or events *in*
time. But, arguably, we do not perceive events only, but also their
temporal relations. So, just as it is natural to say that we perceive
spatial distances and other relations between objects (I see the
dragonfly as hovering above the surface of the water), it seems
natural to talk of perceiving one event following another (the
thunderclap as following the flash of lightning), though even here
there is a difficulty. For what we perceive, we perceive as
*present*--as going on right now. Can we perceive a
relation between two events without also perceiving the events
themselves? If not, then it seems we perceive both events as present,
in which case we must perceive them as simultaneous, and so not as
successive after all. There is then a paradox in the notion of
perceiving an event as occurring after another, though one that
perhaps admits of a straightforward solution. When we perceive B as
coming after A, we have, surely, ceased to perceive A. In which case,
A is merely an item in our memory. Now if we wanted to construe
'perceive' narrowly, excluding any element of memory, then
we would have to say that we do not, after all, perceive B as
following A. But in this article, we shall construe
'perceive' more broadly, to include a wide range of
experiences of time that essentially involve the senses. In this wide
sense, we perceive a variety of temporal aspects of the world. We
shall begin by enumerating these, and then consider accounts of how
such perception is possible.


## 2. Kinds of temporal experience



There are a number of what Ernst Poppel (1978) calls
'elementary time experiences', or fundamental aspects of
our experience of time. Among these we may list the experience of (i)
duration; (ii) non-simultaneity; (iii) order; (iv) past and present;
(v) change, including the passage of time. It might be thought that
experience of non-simultaneity is the same as experience of time
order, but it appears that, when two events occur very close together
in time, we can be aware that they occur at different times without
being able to say which one came first (see Hirsh and Sherrick 1961).
We might also think that perception of order was itself explicable in
terms of our experience of the distinction between past and present.
There will certainly be links here, but it is a contentious question
whether the experience of *tense*--that is, experiencing
an event as past or present--is more fundamental than the
experience of order, or vice versa, or whether indeed there is such a
thing as the experience of tense at all. This issue is taken up below.
Finally, we should expect to see links between the perception of time
order and the perception of motion if the latter simply involves
perception of the order of the different spatial positions of an
object. This is another contentious issue that is taken up below.


## 3. Duration



One of the earliest, and most famous, discussions of the nature and
experience of time occurs in the autobiographical *Confessions*
of St Augustine. Augustine was born in Numidia (now Algeria) in 354
AD, held chairs in rhetoric at Carthage and Milan, and become Bishop
of Hippo in 395. He died in 430. As a young adult, he had rejected
Christianity, but was finally converted at the age of 32. Book XI of
the *Confessions* contains a long and fascinating exploration
of time, and its relation to God. During the course of it Augustine
raises the following conundrum: when we say that an event or interval
of time is short or long, what is it that is being described as of
short or long duration? It cannot be what is past, since that has
ceased to be, and what is non-existent cannot presently have any
properties, such as being long. But neither can it be what is present,
for the present has no duration. (For the reason why the present must
be regarded as durationless, see the section on the specious present,
below.) In any case, while an event is still going on, its duration
cannot be assessed.



Augustine's answer to this riddle is that what we are measuring,
when we measure the duration of an event or interval of time, is in
the memory. From this he derives the radical conclusion that past and
future exist only in the mind. While not following Augustine all the
way to the mind-dependence of other times, we can concede that the
perception of temporal duration is crucially bound up with memory. It
is some feature of our memory of the event (and perhaps specifically
our memory of the beginning and end of the event) that allows us to
form a belief about its duration. This process need not be described,
as Augustine describes it, as a matter of measuring something wholly
in the mind. Arguably, at least, we are measuring the event or
interval itself, a mind-independent item, but doing so by means of
some psychological process.



Whatever the process in question is, it seems likely that it is
intimately connected with what William Friedman (1990) calls
'time memory': that is, memory of when some particular
event occurred. That there is a close connection here is entailed by
the plausible suggestion that we infer (albeit subconsciously) the
duration of an event, once it has ceased, from information about how
long ago the beginning of that event occurred. That is, information
that is *metrical* in nature (e.g. 'the burst of sound
was very brief') is derived from *tensed* information,
concerning how far in the past something occurred. The question is how
we acquire this tensed information. It may be direct or indirect, a
contrast we can illustrate by two models of time memory described by
Friedman. He calls the first the *strength model* of time
memory. If there is such a thing as a memory trace that persists over
time, then we could judge the age of a memory (and therefore how long
ago the event remembered occurred) from the strength of the trace. The
longer ago the event, the weaker the trace. This provides a simple and
direct means of assessing the duration of an event. Unfortunately, the
trace model comes into conflict with a very familiar feature of our
experience: that some memories of recent events may fade more quickly
than memories of more distant events, especially when those distant
events were very salient ones (visiting a rarely seen and frightening
relative when one was a child, for instance.) A contrasting account of
time memory is the *inference model*. According to this, the
time of an event is not simply read off from some aspect of the memory
of it, but is inferred from information about relations between the
event in question and other events whose date or time is known.



The inference model may be plausible enough when we are dealing with
distant events, but rather less so for much more recent ones. In
addition, the model posits a rather complex cognitive operation that
is unlikely to occur in non-human animals, such as the rat. Rats,
however, are rather good at measuring time over short intervals of up
to a minute, as demonstrated by instrumental conditioning experiments
involving the 'free operant procedure'. In this, a given
response (such as depressing a lever) will delay the occurrence of an
electric shock by a fixed period of time, such as 40 seconds,
described as the R-S (response-shock) interval. Eventually, rate of
responding tracks the R-S interval, so that the probability of
responding increases rapidly as the end of the interval approaches.
(See Mackintosh 1983 for a discussion of this and related
experiments.) It is hard to avoid the inference here that the mere
passage of time itself is acting as a conditioned stimulus: that the
rats, to put it in more anthropocentric terms, are successfully
estimating intervals of time. In this case, the strength model seems
more appropriate than the inference model.


## 4. The specious present



The term 'specious present' was first introduced by the
psychologist E.R. Clay, but the best known characterisation of it was
due to William James, widely regarded as one of the founders of modern
psychology. He lived from 1842 to 1910, and was professor both of
psychology and of philosophy at Harvard. His definition of the
specious present goes as follows: 'the prototype of all
conceived times is the specious present, the short duration of which
we are immediately and incessantly sensible' (James 1890). How
long is this specious present? Elsewhere in the same work, James
asserts 'We are constantly aware of a certain duration--the
specious present--varying from a few seconds to probably not more
than a minute, and this duration (with its content perceived as having
one part earlier and another part later) is the original intuition of
time.' This surprising variation in the length of the specious
present makes one suspect that more than one definition is hidden in
James' rather vague characterisation. 



There are two sources of ambiguity here. One is over whether
'the specious present' refers to the object of the
experience, namely a duration in time, or the way in which that object
is presented to us. The second is over how we should interpret
'immediately sensible'. James' words suggest that
the specious present is the duration itself, picked out as the object
of a certain kind of experience. But ' immediately
sensible'admits of a number of disambiguations. So we could
define the specious present as:


1. the span of short-term memory;
2. the duration which is perceived, not as duration, but as
instantaneous;
3. the duration which is directly perceived -- i.e. not through
the intermediary of a number of other, perhaps instantaneous,
perceptions;
4. the duration which is perceived both as present and as extended in
time.



If James means the first of these, that would certainly explain his
suggestion that it could last up to a minute. But this does not seem
to have much to do specifically with the experience of
*presentness*, since we can certainly hold something in the
short-term memory and yet recognise it as past. James may be thinking
of cases where we are listening to a sentence: if we did not somehow
hold all the words in our conscious mind, we would not understand the
sentence as a whole. But it is clear that the words are not
experienced as simultaneous, for then the result would be an
unintelligible jumble of sounds. (2) is illustrated by the familiar
fact that some movements are so fast that we see them as a blur, such
as when we look at a fan. What is in fact taking place at different
times is presented as happening in an instant. But this is not
standardly what is meant by the specious present. (3) is a construal
that is found in the literature (see, e.g., Kelly 2005), but it is not
obvious that that is what James had in mind, since James is concerned
with the phenomenology of time perception, and whether or not an
experience constitutes a direct or indirect perception of an interval
does not seem to be a phenomenological matter. (Besides which, as
Kelly points out, we might think it odd to suppose that past parts of
the interval could be directly perceived.)



That leaves us with (4): a duration which is perceived both as present
*and* as temporally extended. This present of experience is
'specious' in that, unlike the objective present (if there
is such a thing -- see
 The metaphysics of time perception
 below) it is an interval and not a durationless instant. The real or
objective present must be durationless for, as Augustine argued, in an
interval of any duration, there are earlier and later parts. So if any
part of that interval is present, there will be another part that is
past or future.



But is it possible to perceive something as extended and as present? If
we hear a short phrase of music, we seem to hear the phrase as
present, and yet -- because it is a phrase rather than a single
chord -- we also hear the notes as successive, and therefore as
extending over an interval. If this does not seem entirely convincing,
consider the perception of motion. As Broad (1923) puts it, 'to
see a second-hand moving is quite a different thing from "seeing" that
a hour-hand has moved.' It is not that we see the current
position of the second hand and remember where it was a second ago: we
just see the motion. That leads to the following argument:




|  |
| --- |
| (1) What we perceive, we perceive as present. |
| (2) We perceive motion. |
| (3) Motion occurs over an interval. |
| *Therefore*: What we perceive as present occurs over an interval. |



Still, there is more than an air of paradox about this. If successive
parts of the motion (or musical phrase, or whatever change we
perceive) are perceived as present, then surely they are perceived as
simultaneous. But if they are perceived as simultaneous, then the
motion will simply be a blur, as it is in cases where it is too fast
to perceive as motion. The fact that we do not see it as motion
suggests that we do not see the successive parts of it as
simultaneous, and so do not see them as present. But then how do we
explain the distinction to which Broad directs our attention?



One way out of this impasse is to suggest that two quite distinct
processes are going on in the perception of motion (and other kinds of
change). One is the perception of successive states as successive, for
example the different positions of the second hand. The other is the
perception of pure movement. This second perception, which may involve
a more primitive system than the first, does not contain as part the
recognition of earlier and later elements. (Le Poidevin 2007, Chapter
5.) Alternatively, we might attempt to explain the phenomena of temporal experience without appeal to the notion of the specious present at all (see Arstila, 2018).


## 5. Past, present and the passage of time



The previous section indicated the importance of distinguishing
between perceiving the present and perceiving something *as*
present. We may perceive as present items that are past. Indeed, given
the finite speed of the transmission of both light and sound (and the
finite speed of transmission of information from receptors to brain),
it seems that we only ever perceive what is past. However, this does
not by itself tell us what it is to perceive something as present,
rather than as past. Nor does it explain the most striking feature of
our experience as-of the present: that it is constantly changing. The
passage (or apparent passage) of time is its most striking feature,
and any account of our perception of time must account for this aspect
of our experience.



Here is one attempt to do so. The first problem is to explain why our
temporal experience is limited in a way in which our spatial
experience is not. We can perceive objects that stand in a variety of
spatial relations to us: near, far, to the left or right, up or down,
etc. Our experience is not limited to the immediate vicinity (although
of course our experience is spatially limited to the extent that
sufficiently distant objects are invisible to us). But, although we
perceive the past, we do not perceive it as past, but as present.
Moreover, our experience does not only appear to be temporally
limited, it is so: we do not perceive the future, and we do not
continue to perceive transient events long after information from them
reached our senses. Now, there is a very simple answer to the question
why we do not perceive the future, and it is a causal one. Briefly,
causes always precede their effects; perception is a causal process,
in that to perceive something is to be causally affected by it;
therefore we can only perceive earlier events, never later ones. So
one temporal boundary of our experience is explained; what of the
other?



There seems no *logical* reason why we should not directly
experience the distant past. We could appeal to the principle that
there can be no action at a temporal distance, so that something
distantly past can only causally affect us via more proximate events.
But this is inadequate justification. We can only perceive a spatially
distant tree by virtue of its effects on items in our vicinity (light
reflected off the tree impinging on our retinas), but this is not seen
by those who espouse a direct realist theory of perception as
incompatible with their position. We still see the *tree*, they
say, not some more immediate object. Perhaps then we should look for a
different strategy, such as the following one, which appeals to
biological considerations. To be effective agents in the world, we
must represent accurately what is currently going on: to be constantly
out of date in our beliefs while going about our activities would be
to face pretty immediate extinction. Now we are fortunate in that,
although we only perceive the past it is, in most cases, the very
recent past, since the transmission of light and sound, though finite,
is extremely rapid. Moreover, although things change, they do so,
again in most cases, at a rate that is vastly slower than the rate at
which information from external objects travels to us. So when we form
beliefs about what is going on in the world, they are largely accurate
ones. (See Butterfield 1984 for a more detailed account along these
lines.) But, incoming information having been registered, it needs to
move into the memory to make way for more up to date information. For,
although things may change slowly relative to the speed of light or of
sound, they do change, and we cannot afford to be simultaneously
processing conflicting information. So our effectiveness as agents
depends on our not continuing to experience a transient state of
affairs (rather in the manner of a slow motion film) once information
from it has been absorbed. Evolution has ensured that we do not
experience anything other than the very recent past (except when we
are looking at the heavens).



To perceive something as present is simply to perceive it: we do not
need to postulate some extra item in our experience that is 'the
experience of presentness.' It follows that there can be no
'perception of pastness'. In addition, if pastness were
something we could perceive, then we would perceive
*everything* in this way, since every event is past by the time
we perceive it. But even if we never perceive anything as past (at the
same time as perceiving the event in question) we could intelligibly
talk more widely of the experience of pastness: the experience we get
when something comes to an end. And it has been suggested that
memories--more specifically, *episodic memories*, those of
our experiences of past events--are accompanied by a feeling of
pastness (see Russell 1921). The problem that this suggestion is
supposed to solve is that an episodic memory is simply a memory of an
event: it *represents* the event simpliciter, rather than the
fact that the event is past. So we need to postulate something else
which alerts us to the fact that the event remembered is past. An
alternative account, and one which does not appeal to any
phenomenological aspects of memory, is that memories dispose us to
form past-tensed beliefs, and is by virtue of this that they represent
an event as past.



We have, then, a candidate explanation for our experience of being
located at a particular moment in time, the (specious) present. And as
the content of that experience is constantly changing, so that
position in time shifts. But there is still a further puzzle. Change
in our experience is not the same thing as experience of change. We
want to know, not just what it is to perceive one event after another,
but also what it is to perceive an event as occurring after another.
Only then will we understand our experience of the passage of time. We
turn, then, to the perception of time order.


## 6. Time order



How do we perceive precedence amongst events? A temptingly simple
answer is that the perception of precedence is just a sensation caused
by instances of precedence, just as a sensation of red is caused by
instances of redness. Hugh Mellor (1998), who considers this line,
rejects it for the following reason. If this were the correct
explanation, then we could not distinguish between *x* being
*earlier* than *y*, and *x* being *later*
than *y*, for whenever there is an instance of one relation,
there is also an instance of the other. But plainly we are able to
distinguish the two cases, so it cannot simply be a matter of
perceiving a relation, but something to do with our perception of the
relata. But mere perception of the relata cannot be all there is to
perceiving precedence. Consider again Broad's point about the
second hand and the hour hand. We first perceive the hour hand in one
position, say pointing to 3 o'clock, and later we perceive it in
a different position, pointing to half-past 3. So I have two
perceptions, one later than the other. I may also be aware of the
temporal relationship of the two positions of the hand. Nevertheless,
I do not perceive that relationship, in that I do not see the hand
moving. In contrast, I do see the second hand move from one position
to another: I see the successive positions *as* successive.



Mellor's proposal is that I perceive *x* precede
*y* by virtue of the fact that my perception of *x*
causally affects my perception of *y*. As I see the second hand
in one position, I have in my short-term memory an image (or
information in some form) of its immediately previous position, and
this image affects my current perception. The result is a perception
of movement. The perceived order of different positions need not
necessarily be the same as the actual temporal order of those
positions, but it will be the same as the causal order of the
*perceptions* of them. Since causes always precede their
effects, the temporal order perceived entails a corresponding temporal
order in the perceptions. Dainton (2001) has objected to this that, if
the account were right, we should not be able to remember perceiving
precedence, since we only remember what we can genuinely perceive. But
there seems no reason to deny that, just because perception of
precedence may involve short-term memory, it does not thereby count as
genuine perception.



There is a further disanalogy between perception of colour and
perception of time order. What is perceived in the case of colour is
something that has a definite spatio-temporal location. The relation
of precedence, in contrast, is not something that has any obvious
location. But causes do have locations, so the perception of
precedence is rather harder to reconcile with the causal theory of
perception than the perception of colour (Le Poidevin 2004, 2007).



In effect, Mellor's idea is that the brain represents time by
means of time: that temporally ordered events are represented by
similarly temporally ordered experiences. This would make the
representation of time unique. (For example, the brain does not
represent spatially separated objects by means of spatially separated
perceptions, or orange things by orange perceptions.) But why should
time be unique in this respect? In other media, time can be
represented spatially (as in cartoons, graphs, and analogue clocks) or
numerically (as in calendars and digital clocks). So perhaps the brain
can represent time by other means. One reason to suppose that it must
have other means at its disposal is that time needs to be represented
in *memory* (I recall, both that *a* was earlier than
*b*, and also the experience of seeing a occur before b) and
*intention* (I intend to *F* after I *G*), but
there is no obvious way in which Mellor's 'representation
of time by time' account can be extended to these.



On Mellor's model, the mechanism by which time-order is
perceived is sensitive to the *time* at which perceptions
occur, but indifferent to their *content* (what the perceptions
are of). Daniel Dennett (1991) proposes a different model, on which
the process is time-independent, but content-sensitive. For example,
the brain may infer the temporal order of events by seeing which
sequence makes sense of the causal order of those events. One of the
advantages of Dennett's model is that it can account for the
rather puzzling cases of 'backwards time referral', where
perceived order does not follow the order of perceptions. (See Dennett
1991 for a discussion of these cases, and also Roache 1999 for an
attempt to reconcile them with Mellor's account.)


## 7. The metaphysics of time perception



In giving an account of the various aspects of time perception, we
inevitably make use of concepts that we take to have an objective
counterpart in the world: the past, temporal order, causation, change,
the passage of time and so on. But one of the most important lessons
of philosophy, for many writers, is that there may be a gap, perhaps
even a gulf, between our representation of the world and the world
itself, even on a quite abstract level. (It would be fair to add that,
for other writers, this is precisely *not* the lesson
philosophy teaches.) Philosophy of time is no exception to this.
Indeed, it is interesting to note how many philosophers have taken the
view that, despite appearances, time, or some aspect of time, is
unreal. In this final section, we will take a look at how three
metaphysical debates concerning the nature of the world interact with
accounts of time perception.



The first debate concerns the reality of tense, that is, our division
of time into past, present and future. Is time really divided in this
way? Does what is present slip further and further into the past? Or
does this picture merely reflect our perspective on a reality in which
there is no uniquely privileged moment, the present, but simply an
ordered series of moments? *A-theorists* say that our ordinary
picture of the world as tensed reflects the world as it really is: the
passage of time is an objective fact. *B-theorists* deny this.
(The terms A-theory and B-theory derive from McTaggart's (1908)
distinction between two ways in which events can be ordered in time,
either as an A-series--that is in terms of whether they are past,
present or future -- or as a B-series--that is according to
whether they are earlier than, later than, or simultaneous with other
events.)



For B-theorists, the only objective temporal facts concern relations
of precedence and simultaneity between events. (I ignore here the
complications introduced by the Special Theory of Relativity, since
B-theory--and perhaps A-theory also--can be reformulated in
terms which are compatible with the Special Theory.) B-theorists do
not deny that our tensed beliefs, such as the belief that a cold front
is *now* passing, or that Sally's wedding *was two
years ago*, may be true, but they assert that what makes such
beliefs true are not facts about the pastness, presentness or futurity
of events, but tenseless facts concerning precedence and simultaneity
(see Mellor 1998, Oaklander and Smith 1994). On one version of the
B-theory, for example, my belief that there is a cold front now
passing is true because the passing of the front is *simultaneous
with* my forming the belief. Now one very serious challenge to the
tenseless theorist is to explain why, if time does not pass in
reality, it appears to do so. What, in B-theoretic terms, is the basis
for our experience as-of the passage of time?



The accounts we considered above, first of the temporal restrictions
on our experience, and secondly of our experience of time order, did
not explicitly appeal to tensed, or A-theoretic notions. The facts we
did appeal to look like purely B-theoretic ones: that causes are
always earlier than their effects, that things typically change slowly
in relation to the speed of transmission of light and sound, that our
information-processing capacities are limited, and that there can be
causal connections between memories and experiences. So it may be that
the tenseless theorist can discharge the obligation to explain why
time seems to pass. But two doubts remain. First, perhaps the A-
theorist can produce a simpler explanation of our experience. Second,
it may turn out that supposedly B-series facts are dependent upon
A-series ones, so that, for example, *a* and *b* are
simultaneous by virtue of the fact that both are *present*.



What is clear, though, is that there is no direct argument from
experience to the A-theory, since the present of experience, being
temporally extended and concerning the past, is very different from
the objective present postulated by the A-theory. Further, it cannot
be taken for granted that the objective passage of time would explain
whatever it is that the experience as-of time's passage is
supposed to amount to. (See Prosser 2005, 2007, 2012, 2016, 2018.)



The second metaphysical issue that has a crucial bearing on time
perception is connected with the A/B-theory dispute, and that is the
debate between presentists and eternalists. Presentists hold that only
the present exists (for an articulation of various kinds of
presentism, and the challenges they face, see Bourne 2006), whereas
eternalists grant equal reality to all times. the two debates, A-
versus B-theory and presentism versus eternalism, do not map precisely
onto each other. Arguably, B-theory is committed to eternalism, but
A-theorists may not necessarily endorse presentism (though Bourne
argues that they should).



How might his be connected to perception? According to the indirect
(or, as it is sometimes called, representative) theory of perception,
we perceive external objects only by perceiving some intermediate
object, a sense datum. According to the direct theory, in contrast,
perception of external objects involves no such intermediary. Now,
external objects are at varying distances from us, and, as noted
above, since light and sound travel at finite speeds, that means that
the state of objects that we perceive will necessarily lie in the
past. In the case of stars, where the distances are very considerable,
the time gap between light leaving the star and our perceiving it may
be one of many years. The presentist holds that past states, events
and objects are no longer real. But if all that we perceive in the
external world is past, then it seems that the objects of our
perception (or at least the states of those objects that we perceive)
are unreal. It is hard to reconcile this with the direct theory of
perception. It looks on the face of it, therefore, that presentists
are committed to the indirect theory of perception. (See Power 2010a,
2010b, 2018, Le Poidevin 2015b.)



The third and final metaphysical issue that we will discuss in the
context of time perception concerns causal asymmetry. The account of
our sense of being located at a time which we considered under
 Past, present and the passage of time
 rested on the assumption that causation is asymmetric. Later events,
it was suggested, cannot affect earlier ones, as a matter of
mind-independent fact, and this is why we do not perceive the future,
only the past. But attempts to explain the basis of causal asymmetry,
in terms for example of counterfactual dependence, or in probabilistic
terms, are notoriously problematic. One moral we might draw from the
difficulties of reducing causal asymmetry to other asymmetries is that
causal asymmetry is primitive, and so irreducible. Another is that
that the search for a mind-independent account is mistaken. Perhaps
causation in intrinsically symmetric, but some feature of our
psychological constitution and relation to the world makes causation
appear asymmetric. This *causal perspectivalism* is the line
taken by Huw Price (1996). That causal asymmetry should be explained
in part by our psychological constitution, in a way analogous to our
understanding of secondary qualities such as colour, is a radical
reversal of our ordinary assumptions, but then our ordinary
understanding of a number of apparently objective features of the
world--tense, absolute simultaneity--have met with similarly
radical challenges. Now, if causal asymmetry is mind-dependent in this
way, then we cannot appeal to it in accounting for our experience of
temporal asymmetry--the difference between past and future.



Further, it is not at all clear that perspectivalism can account for
the perception of time order. The mechanism suggested by Mellor (see
 Time Order)
 exploited the asymmetry of causation: it is the fact that the
perception of A causally influences the perception of B, but not vice
versa, that gives rise to the perception of A's being followed
by B. We can represent this schematically as follows (where the arrow
stands for an asymmetric causal relation):



> 
> P(A)-P(B)-P(A<B)
> 



But if there is no objective asymmetry, then what is the explanation?
Of course, we can still define causal order in terms of a causal
betweenness relation, and we can say that the perceived order follows
the objective causal order of the perceptions, in this sense: on the one hand, where A
is perceived as being followed by B, then the perception of B is
always causally between the perception of A and the perception of
A's being followed by B (the dash represents a symmetric causal
relation):



> 
> P(A) - P(B) - P(A<B)
> 



On the other hand, where B is perceived as being followed by A, the perception
of A is always causally between the perception of B and the perception
of B's being followed by A:



> 
> P(B) - P(A)) - P(B<A)
> 



But what, on the causal perspectivalist view, would rule out the
following case?



> 
> P(B<A) - P(A) - P(B) - P(A<B)
> 



For such a case would satisfy the above constraints. But it is a case
in which A is perceived by an observer both as following, and as being
followed by, B, and we know that such a case never occurs in
experience. 'Is perceived by *x* as followed by' is
an asymmetric relation (assuming we are dealing with a single sense
modality), and so one that can be grounded in the causal relation only
if the causal relation is itself asymmetric. Now if perspectivalism
cannot meet the challenge to explain why, when B is perceived as
following A, A is never perceived by the same observer as following B,
it seems that our experience of time order, insofar as it has a causal
explanation, requires causation to be objectively asymmetric.



One strategy the causal perspectivalist could adopt (indeed, the only
one available) is to explain the asymmetric principle above in terms
of some objective non-causal asymmetry. Price, for example, allows an
objective thermodynamic asymmetry, in that an ordered series of states
of the universe will exhibit what he calls a thermodynamic gradient:
entropy will be lower at one end of the series than at the end. We
should resist the temptation to say that entropy increases, for that
would be like asserting that a road goes uphill rather than downhill
without conceding the perspectival nature of descriptions like
'uphill'. Could such a thermodynamic asymmetry explain the
perception of time order? That is a question for the reader to
ponder.