In
the eleventh book of the Confessions, Augustine offers what appear to
be a series of arguments designed to show that time (or present time)
must be regarded as an indivisible instant or "slice," or so that is the
conclusion I will assume for this post. Augustine also regards present
time as the only time that exists. In contemporary philosophical
parlance, in other words, Augustine is a presentist.
However, Christopher
Kirwan has challenged the cogency of the assumption that Augustine's present
can be divided to a single point or instant. Kirwan's representation of
Augustine's argument is as follows:[1]
(10) When a time is not present, it does not exist;
(11) when a time does not exist, it is not long;
(12) when a time is present, every part of it is
present;
(13) when a time is divisible, not every part of it
is present;
(14) No indivisible time is long;
(15) Therefore, no time is long.
The argument, according
to Kirwan, is logically valid. But he further contends that its premises (10)
and (12) are false. The basis behind (10) is Augustine's reasoning that if the
past does not in some sense exist, it would not be possible for someone to
refer to the past on the grounds that the times in question no longer exist.
Kirwan challenges Augustine's reasoning by arguing that the object of reference
Augustine has in mind are not times but events, which, he claims, are much more
plausible to exclude from present existence.[2] One
can challenge this claim, however, on the simple grounds that even though
events do not wholly exist at a time
(or so one might possibly hold), it seems indisputable that they exist from one
time to another time. And if one is unable to refer to times because they do
not exist (and Kirwan does not dispute this claim), it is unclear why
non-present events should be excluded from this same requirement. One might
also point out that even if events do not wholly exist at any one time, they
still exist at a time, as long as one
part of the event exists at that time. For example, the Battle of Waterloo
existed at the seventy-third minute at which it was being fought.
Kirwan's second objection is that Augustine's premise
(12) relies on a supplementary argument that rests on an equivocation. The
supplementary argument Kirwan refers to is Augustine's attempt to demonstrate
the non-existence of a year on the grounds that not all of the twelve months in
the year are present all at once. Kirwan argues that 'twelve months' must be
taken collectively in one sense and distributively in a second sense.[3]
One might, however, try to defend premise (12) by another
route, using premises that Augustine seems to affirm, if but implicitly, in
other parts of his Confessions
treatment of time to construct another argument. One such argument might go as
follows:
(A1) Either a duration of time d is present or it is not.
(A2) If it is not, then d is not present.
(A3) If it is, then d can be divided.
(A4) Either d can be infinitely divided or it cannot.
(A5) If it cannot, then one must arrive
eventually at a unit of time that is indivisible.
(A6) If It can, then d must contain an infinite number of
countable points.
(A7) But it is impossible that there is
an infinite number of countable points in a finite duration.
(A8) Every duration of time can be
finitely divided to a single indivisible point.
The
argument, at least so it seems to me, is
logically valid. So, the question comes down to the truth of its
premises. The two
disputable premises, I think, are (A6) and (A7). (A7) raises the
question of
whether Aristotle's distinction between an infinitely divisible line or
duration and an infinitely divided one is a correct one to make, and
this would involve a pretty serious digression from
Augustine. So, for the sake of continuing my investigation, I will
merely
stipulate that (A7) is correct; in any case, it does not seem obviously
incorrect. As for (A6), I believe one can support it on the following
grounds. By
definition (at least as Augustine sees it), no point of time has any duration. Moreover, any duration
necessarily has or is bounded by at least two points. Now, borrowing
from the
assumed premise (A7), it seems obvious that a finite duration cannot
contain
infinitely many points. But if one divides a duration into two smaller
durations, each duration must itself contain at least two points. But,
then, if
a duration is infinitely divided it will contain infinitely many points.
Hence,
because it cannot, an infinitely divided finite duration is impossible.
In
my next post, I will consider whether Augustine's concept of time as an
indivisible instant is a cogent one. In this connection, I will judge
whether his attempt to preserve the reality of time in light of some of
its more perplexing elements, i.e., its fleetingness, through what I
will call his "psychological" understanding of time makes sense.
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