McTaggart's Paradox and Time

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.