I recently read John McTaggart’s
The Unreality of Time (
link),
a paper true to its name in that the author argues time is unreal. While very
few philosophers agree with his conclusion, McTaggart’s arguments are not so
easy to refute. He is exceptionally clear – clearer than most of his expositors,
in my experience – and his influence on the metaphysics of time can be compared
to and perhaps even surpasses that of Zeno’s influence on the metaphysics of
motion. Even philosophers who disagree with McTaggart usually accept his basic distinctions
and definitions between different ways in which people often attempt to relate
events:
A-series: Past, present, future (tensed)
B-series: earlier than, simultaneous with, later than (tenseless)
C-series: an ordered set of events without direction (atemporal)
McTaggart summarizes the most obvious difference between the
A-series from the B-series:
Positions in time, as time
appears to us prima facie, are distinguished in two ways. Each position is
Earlier than some, and Later than some, of the other positions. And each
position is either Past, Present, or Future. The distinctions of the former
class are permanent, while those of the latter are not. If M is ever earlier
than N, it is always earlier. But an event, which is now present, was future
and will be past.
Thus, B-series accounts of temporal facts don’t change.
A-series accounts of temporal facts change. “Event X is earlier than (later
than/simultaneous with) event Y” can, if it is a fact, be truly said by anyone
at any time. On the other hand, the truth value of “event X is in the future” allegedly
changes, if ‘future’ be taken as an irreducibly tensed fact. I say “allegedly”
because McTaggart doesn’t believe there is a way one can consistently state
such a change, which I will get to in a moment.
For McTaggart, the essential feature of time is
unidirectional change. The C-series implies change, but not unidirectional
change:
If the C series runs M, N, O, P,
then the B series from earlier to later cannot run M, O, N, P, or M, P, O, N,
or in any way but two. But it can run either M, N, O, P (so that M is earliest
and P latest) or else P, O, N, M (so that P is earliest and M latest). And
there is nothing either in the C series or in the fact of change to determine
which it will be.
A series which is not temporal
has no direction of its own, though it has an order. If we keep to the series
of the natural numbers, we cannot put 17 between 21 and 26. But we keep to the
series, whether we go from 17, through 21, to 26, or whether we go from 26,
through 21, to 17. The first direction seems the more natural to us, because
this series has only one end, and it is generally more convenient to have that
end as a beginning than as a termination. But we equally keep to the series in
counting backward.
In order to account for the possibility of real,
unidirectional change (i.e. time), then, McTaggart argues the C-series must be
combined with the A-series. Why not the B-series? Only A-series facts change,
so only an A-theorist can account for change. This point is disputed by
B-theorists, a point I may address in a future post since I would consider
myself a B-theorist, but for now it is sufficient to note that McTaggart
believed the A-series to be more fundamental than the B-series in that while we
require the ability to temporally relate events by mean of both series (assuming
time is real), the combination of the A-series and C-series can give us the
B-series whereas a combination of a B-series and a C-series wouldn’t be able to
give us the A-series.
With this groundwork, McTaggart has set up all the elements
needed in order to prove that time is unreal: time is unidirectional change,
and the A-series in which events objectively flow from the future to the
present to the past is necessary in order for time to be real rather than a
fictional creation of consciousness. Enter McTaggart’s Paradox:
Past, present, and future are
incompatible determinations. Every event must be one or the other, but no event
can be more than one. This is essential to the meaning of the terms. And, if it
were not so, the A series would be insufficient to give us, in combination with
the C series, the result of time. For time, as we have seen, involves change,
and the only change we can get is from future to present, and from present to
past.
The characteristics, therefore,
are incompatible. But every event has them all. If M is past, it has been
present and future. If it is future, it will be present and past. If it is
present, it has been future and will be past. Thus all the three incompatible
terms are predicable of each event which is obviously inconsistent with their
being incompatible, and inconsistent with their producing change.
It may seem that this can easily
be explained. Indeed it has been impossible to state the difficulty without
almost giving the explanation, since our language has verb-forms for the past,
present, and future, but no form that is common to all three. It is never true,
the answer will run, that M is present, past and future. It is present, will be
past, and has been future. Or it is past, and has been future and present, or again
is future and will be present and past. The characteristics are only
incompatible when they are simultaneous, and there is no contradiction to this
in the fact that each term has all of them successively.
But this explanation involves a
vicious circle. For it assumes the existence of time in order to account for
the way in which moments are past, present and future. Time then must be
pre-supposed to account for the A series. But we have already seen that the A
series has to be assumed in order to account for time. Accordingly the A series
has to be pre-supposed in order to account for the A series. And this is
clearly a vicious circle.
What we have done is this -- to
meet the difficulty that my writing of this article has the characteristics of
past, present and future, we say that it is present, has been future, and will
be past. But "has been" is only distinguished from "is" by
being existence in the past and not in the present, and "will be" is
only distinguished from both by being existence in the future. Thus our
statement comes to this -- that the event in question is present in the
present, future in the past, past in the future. And it is clear that there is
a vicious circle if we endeavour to assign the characteristics of present,
future and past by the criterion of the characteristics of present, past and
future.
The difficulty may be put in
another way, in which the fallacy will exhibit itself rather as a vicious
infinite series than as a vicious circle. If we avoid the incompatibility of
the three characteristics by asserting that M is present, has been future, and
will be past, we are constructing a second A series, within which the first
falls, in the same way in which events fall within the first. It may be doubted
whether any intelligible meaning can be given to the assertion that time is in
time. But, in any case, the second A series will suffer from the same
difficulty as the first, which can only be removed by placing it inside a third
A series. The same principle will place the third inside a fourth, and so on
without end. You can never get rid of the contradiction, for, by the act of
removing it from what is to be explained, you produce it over again in the
explanation. And so the explanation is invalid.
Thus a contradiction arises if
the A series is asserted of reality when the A series is taken as a series of
relations. Could it be taken as a series of qualities, and would this give us a
better result? Are there three qualities -- futurity, presentness, and pastness,
and are events continually changing the first for the second, and the second
for the third?
It seems to me that there is
very little to be said for the view that the changes of the A series are
changes of qualities. No doubt my anticipation of an experience M, the
experience itself, and the memory of the experience are three states which have
different qualities. But it is not the future M, the present M, and the past M,
which have these three different qualities. The qualities are possessed by
three distinct events -- the anticipation of M, the experience M itself, and
the memory of M, each of which is in turn future, present, and past. Thus this
gives no support to the view that the changes of the A series are changes of
qualities.
But we need not go further into
this question. If the characteristics of the A series were qualities, the same
difficulty would arise as if they were relations. For, as before, they are not
compatible, and, as before, every event has all of them. This can only be
explained, as before, by saying that each event has them successively. And thus
the same fallacy would have been committed as in the previous case.
We have come then to the
conclusion that the application of the A series to reality involves a
contradiction, and that consequently the A series cannot be true of reality.
And, since time involves the A series, it follows that time cannot be true of
reality. Whenever we judge anything to exist in time, we are in error. And
whenever we perceive anything as existing in time -- which is the only way in
which we ever do perceive things -- we are perceiving it more or less as it
really is not.
Andrew Turner summarizes McTaggart’s reasons for stating the
A-theorist cannot consistently parry the charge that any event which has one
temporal property like “past,” “present,” or “future” must have the other two (unless
that event is the first or last moment in time, in which case it would still
have two incompatible properties):
The ‘vicious circle’ argument: time
is assumed to explain why ‘past,’ ‘present,’ and ‘future’ do not apply
simultaneously.
The vicious series argument: a
second time series has been introduced to separate these terms; but to separate
these terms within this second series we need to introduce a third time series
and so on. (
link)
I found vicious circle argument is easier to follow than the
vicious series argument (see McTaggart’s paragraphs 3-4 above). Recall that the
A-series is supposed to explain how time is possible. But when the A-theorist
is accused of saying that events are past, present, and future – which is
inconsistent – he resorts to saying that no event is past, present, and future
at the same time. The problem is that one cannot benignly appeal to time in
order to account for the alleged A-series inconsistency if A-series is itself
what is supposed to account for time.
I think the vicious series objection to the A-series is best
presented by Michael Dummett (
link).
If we suppose that every event has more complex A-times than ‘past,’ ‘present,’
and ‘future’ which supposedly resolve the paradox, because each phase of
complex A-times has two or more mutually exclusive properties which are
applicable to the event, there is no stage at which the A-theorist can escape
the paradox. For example, if we say that an event ‘will be past,’ ‘is present,’
and ‘was future,’ there is no contradiction. Here we have constructed a sort of
second-level A-series. But this complex A-series implies other complex A-times
such as ‘has been past,’ ‘has been present,’ ‘is past,’ ‘is future,’ ‘will be
present,’ and ‘will be future.’ And McTaggart will argue that as in the first
level, any event that has one of these properties has all of them. That is, any
event is {past, present, future} in the {past, present, future}. Instead of
three A-times, there are now nine; but some of these A-times are contradictory,
so that these are predicated of events does not resolve the paradox but just pushes
it to another stage. Obviously, an event cannot consistently be referred to as,
for example, ‘is [now] present,’ ‘is [now] past,’ and ‘is [now] future.’ The
A-theorist will say these are not properties possessed at the same time. But in
so doing, he will merely be generating 27 complex A-times instead of 9 or 3. And
since at no stage will the paradox be resolved – since several of these A-times
would be contradictory if predicated of any single event – a vicious infinite
regress is the result.
Prominent A-theorists have recognized that this paradox
presents a real challenge and responded accordingly; viz. by denying that the
past and future are real. William Lane Craig and Quentin Smith, among others,
have accepted presentism in part to attempt to block the thrust of McTaggart’s
Paradox. Presentism denies the reality or existence of the ‘past’ and ‘future.’
A-theorists like Craig find experiences of an objective ‘present’ to be
plausible and intuitive, warranting the defense of the A-series to such a
purist extremity. But sometimes our intuitions, upon more rigorous examination,
contradict one another. Paul
Helm, in
Time and time again: two volumes by William Lane Craig, finds
this to be the case with the implications of accepting the “purist” A-theorist’s
account of time:
By contrast Craig believes that
A-theory presentism can handle change, since it takes the notion of having a
property to be a present-tense notion. Any object only exists in the present,
so the question of its possessing different properties at different times does
not arise. Lewis claims that this proposed solution rejects the very idea of
persistence (B, 192), but Craig, in responding that on the A-theory an object
can be said to exist at times other than the present, appears to concede what
is distinctive about presentism. If the A-theorist affirms chronal realism, it
concedes its position. If it does not, where is persistence through time? On
responsibility, one might ask about the reasonableness of holding someone
responsible for what a person who no longer exists did. Is this not
counterintuitive too? Why should I be responsible for the debts arising from
spendthrift actions which no longer exist, whether these are the actions of my
great-grandfather or of an earlier present me?
Furthermore, B-theorists have argued that presentist
ontology either fails to provide truthmakers for past and future tense events
or wind up caught in McTaggart’s paradox (
link, pg. 101ff. and 160ff.);
link, pg. 66ff.). Essentially, if the past and future aren’t real, how can we truly
speak about them? Or if we can truly speak about them and in light of the idea
that temporal becoming requires something other than the present from which a
thing has become, how is it that they aren’t real and thus can avoid McTaggart’s
Paradox? Especially in Craig’s case, these questions seem similar to those
presented in the grounding objection to Molinism.
As for the theistic implications of a B-theory of time,
which I would not push has been demonstrated in this modest post – though I
believe it does at least put the onus on the A-theorist to explain how his
position could be consistent – what it would do is establish that God’s
knowledge is unchanging. It would not mean that God is Himself necessarily
outside time. A B-theoretic would be a necessary but insufficient condition for
divine timelessness. For instance, several B-theorists like Helm and Mellor
believe causation is what can account for uni-directional change along the
B-series. Causes are earlier than effects. But God is a cause of all things, in
which case God could be in time – He or His creative activity would be the
earliest of all events – unless further qualified in some respect such as by distinguishing
between ultimate and secondary causation (cf.
here).
While I haven’t satisfactorily related the philosophy of
time to issues of divine timelessness, eternal generation and procession, the
incarnation, and our own experience, then, I believe I’ve made some headway in
understanding what time itself is and how it can accurately be modeled.
