McTaggart on the Unreality of Time
J. E. McTaggart, "The Unreality of Time", Mind, 1908, pp. 457-474.
This is the subject treated by Katsuhiko Sano in his graduation thesis in 2000. But, since it seems to me that his treatment was somehow prejudiced by A. N. Prior's representation of McTaggart's view, I wish to summarize McTaggart's original argument by my own reading.
(1) 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. (458)
(2) The A series and the B series: The series of positions in the 'past, present, and future' is the A series, and that in the 'earlier than' relation is the B series.
(3) Both series are essential; the events of time, as observed by us, form an A series as well as a B series. (458)
(4) Why A series is essential and objective. Time involves change, and change is impossible without an A series. (458-461)
In a B series without an A series, change is impossible. For in a B series, every relation in it is permanent, and each event is always the same; no event can begin to be, or cease to be. Each event itself is immutable, yet change must be possible with such an immutable event. Since this cannot be denied, there remains only one possibility, namely, change in time is due to the determination of the event in question by the terms of the A series.
[Notice that this notion of change is rather peculiar; McTaggart is saying that for time to be real, change must also be real, and real change is possible only with a real A series.]
This argument shows that the A series is more fundamental than the B series, as far as time is concerned. The B series (as temporal series) cannot exist without the A series, because no time without change, and no change without the A series.
(5) If we take away the temporal character (and hence the determination as an A series) from a B series, there still remains a C series; it has permanent relations among its members, it is not temporal, but it has an order. In other words, a mere order does not determine the direction, and the A series gives that direction and hence time. Thus a time-series is given by a C series together with an A series. (461-463)
(6) McTaggart takes it that the argument so far establishes that time cannot exist without the A series. Now, as regards the reality of time: There can be two lines of argument. One presumes the reality of time, and argues that the distinctions of present, past, and future cannot be true of reality, thus trying to save the reality of time at the expense of denying that the A series is essential to time. The other, which McTaggart takes, holds that since time is destroyed by removing the A series (in other words, the A series is essential to time), the unreality of time follows from the unreality of the A series. (464)
(7) The argument that the A series cannot exist is as follows: On the one hand, (a) past, present, and future are incompatible determinations (whether relations or qualities) of an event; if any event is present, it cannot be past, nor be future. On the other hand, (b) every event has them all; if any event is past, it has been present and future. These two, (a) and (b), are simply inconsistent, and therefore the A series, and consequently change and time, cannot exist. (468) Notice that we cannot presuppose the existence of time, in order to evade this argument.
[On McTaggart's view which regards the A series as real, that event E is present is a fact in the world (reality), and so are 'E is past' and 'E is future'; so he is saying any two of these are incompatible, yet the 'moving now' demands all of them.]
(8) An obvious objection against this argument is that (a) or (b), or both, involves equivocation in terms of verb-forms for tense; the determinations as past, present, and future are only incompatible when they are simultaneous, and there should be no contradiction when an event has all of them successively. However, this objection involves a vicious circle, because it presupposes the existence of time, in that those determinations are supposed to be taking place in time. (468)
(9) Thus the previous conclusion cannot be evaded. Since the notions of A series and of time contain a contradiction, they cannot be applied to reality, and hence time is unreal. (470-471) It must be remembered that this whole argument is taking place within the context of attributing time to the reality itself, not to subjective consciousness. (471-472)
(10) Finally, McTaggart reminds us of the way he started the whole argument (recall the italicized parts of (1) and of (3)); and he says as follows:
It [the denial of the reality of time] was called paradoxical because it seemed to contradict our experience so violently---to compel us to treat so much as illusion which appears prima facie to give knowledge of reality. But we now see that our experience of time---centering as it does about the specious present---would be no less illusory if there were a real time in which the realities we experience existed. (473)
And he adds that even though the A series and the B series do not exist (in reality), the C series may really exist.
Let me summarize McTaggart's argument as I understand, by the following figure. The 'moving now' generates an A series, and hence a B series, out of a permanent C series. And since changes generated by this A series are supposed to be a part of reality, temporal facts, such as 'E is present', must also belong to reality; these requirements lead to a contradiction.
Figure. How an A series yields a contradiction
Thus summarized, McTaggart's argument has some relevance to our question of temporal order and the direction of time, despite its seeming 'aprioristic' character and old-fashioned terminology. Compare McTaggart's view, for instance, with Reichenbach's or Gruenbaum's.
Further, his argument can be obviously divided into two parts: (i) the proof of the indispensability of the A series for time (up to (5) above), and (ii) the proof of the unreality of time ((7) and (8)), presuming (i). Thus, the 'unreality of time' depends on both, but (i) and (ii) can be evaluated independently. Many eminent philosophers, such as Prior, questioned (ii), but they disregarded that this argument is made on the presumption of (i). Of course we can make objections against (i), but this does not justify their unfair rendering of (ii), dismissing its necessary assumption. In particular, if you pay too much attention to paraphrasing tensed statements in (8), you may easily lose sight of the essential point of (ii), i.e., that you cannot presuppose independent time in this context.
Last modified Sept. 9, 2003. (c) Soshichi Uchii
