McTaggart’s Proof of the Unreality of Time

Jeff Speaks

September 3, 2004

1 The A series and the B series
2 Why time is contradictory
 2.1 The A series is essential to the reality of time
 2.2 The A series is contradictory
3 Responses to the argument
 3.1 Will be past, is present, was future
 3.2 The denial that time essentially involves the A series

John (McTaggart Ellis) McTaggart was, along with F. H. Bradley and a number of other philosophers, one of the most prominent British exponents of neo-Hegelian idealism in the late 19th and early 20th centuries. His most prominent work is The Nature of Existence (in two volumes) from which we will read an excerpt.

McTaggart’s idealism, like that of Bradley, consisted largely in the denial that what we usually take to be central features of reality are, in fact, real. Accordingly, much of his work was devoted to exposing contradictions, or difficulties, inherent in our ordinary picture of the world. Perhaps his most famous, ambitious, and influential such argument is his argument that our ordinary view that things exist in time is false. This was first systematically presented in his 1908 paper, ‘The Unreality of Time.’ We will be looking at his later (1927) exposition of the argument.

1 The A series and the B series

McTaggart’s first central claim is that, as he puts it

“Positions in time ...are distinguished in two ways. Each position is Earlier than some and Later than some of the other positions. To constitute such a series there is required a transitive asymmetrical relation, and a collection of terms such that, of any two of them, either the first is in this relation to the second, or the second is in this relation to the first. ...

In the second place, 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.

For the sake of brevity I shall give the name of the A series to that series of positions which runs from the far past through the near past to the present, and then from the present through the near future to the far future, or conversely. The series of positions which runs from earlier to later, or conversely, I shall call the B series.” (305-6)

We can think of the A and B series as consisting in a group of properties and relations associated with time. We can summarize as follows what McTaggart says about each series, or group of properties:

The A series

The B series

Perhaps the easiest way to get a grip on the two classes of properties is to focus on the fact that some characterizations of temporal properties of events are temporary (A series) and that some are permanent (B series). When we say that, e.g., Tampa Bay won the Stanley Cup in 2004, we are ascribing a property to an event - Tampa’s victory - which that event always has. It will not cease to be true in the future. Thus this kind of dating of events belongs to the B series. If we say that this event had the property of coming later than Montreal’s first Stanley Cup victory, this also attributes a permanent (relational) property to the two events. It will not cease to be true in the future that Montreal’s first Stanley Cup victory came before Tampa’s. Thus the properties of being earlier or later than another event also belong to the B series. But if we say that Tampa’s first Stanley Cup victory is in the past, we do not attribute a permanent property to it. In 2000, this even did not have the property of being past. Hence the properties of being past, present, or future belong to the A series.

2 Why time is contradictory

We can think of McTaggart’s argument that time is unreal as having the following structure:



If time is real, then some things must be past, present, or future. (I.e., Time essentially involves the A series.)


The properties of being past, present, and future involve a contradiction; hence nothing can really be past, present, or future.


Time is not real.

The argument is clearly valid; the question then is whether the premises are true. McTaggart gives arguments for each.

2.1 The A series is essential to the reality of time

Could there be time if there were no properties of being past, present, or future? McTaggart notes (307) that we never experience time without the A series; but he notes that someone might object that this does not show that time essentially involves the A series, on the grounds that “the distinction of positions in time into past, present, and future, is only a constant illusion of our minds.” (308). To counter this view, McTaggart gives two arguments why the reality of time requires the properties included in the A series.

The argument from change

McTaggart argues that time is impossible without change, and that change essentially involves the A series.

Why time is impossible without change; the objection that “in ordinary language ...we say that something can remain unchanged through time.” (309) Why, acccording to McTaggart, change in any object entails change in all objects.

McTaggart’s argument that change requires an A series:

“Let us suppose that the distinctions of past, present, and future do not apply to reality. In that case, can change apply to reality? ...

...this is impossible. If N is ever earlier than O and later than M, it always will be, and has always been, earlier than O and later than M, since the relations of earlier and later are permanent. ...[If] as, by our present hypothesis, a B series by itself constitutes time, N will always have a position in a time-series, and always has had one. That is, it always has been an event, and always will be one, and cannot begin or cease to be an event.


Nor can such change be looked for in the different moments of absolute time, even if such moments should exist. For the same argument will apply here. Each such moment will have its own place in the B series, since each would be earlier or later than each of the others. And, as the B series depends on permanent relations, no moment could ever cease to be, nor could it become another moment.” (309-310)

The argument from the direction of time

It is essential to time that it have a direction; but it could not have a direction without the properties of being past, present, and future.

2.2 The A series is contradictory

At this stage of the argument (325), McTaggart takes it as established that time cannot be real if there is no A series, and hence no properties of being past, present, or future. The next stage of his argument is to show that these properties involve a contradiction.

This part of the argument involves two central claims:

(1) “Past, present, and future are incompatible determinations. Every event must be one or the other, but no event can be more than one. If I say that any event is past, that implies that it is neither present nor future, and so with the others.” (329)

(2) “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 three characteristics [of being past, present, and future] belong to each event.” (329)

The problem, McTaggart argues, is that (1) and (2) and simply inconsistent. This is why the A series involves a contradiction. If any events are past, present, or future, then both (1) and (2) must be true. But (1) and (2) contradict each other; hence the supposition that events are past, present, or future involves a contradiction.

McTaggart has already argued that time essentially involves the A series properties of being past, present, and future; his conclusion that these properties involve a contradiction then licenses the further conclusion that the supposition that time is unreal involves a contradiction.

3 Responses to the argument

3.1 Will be past, is present, was future

One immediate response to the argument, which McTaggart takes up in 330 ff., is to deny claim (2). McTaggart puts the objection well:

“It may seem that this can easily be explained. Indeed, it has been impossible to state the difficulty without almost giving the explanation ...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. ...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.” (330)

McTaggart states his objection in 331-332. We can summarize it as follows. (For further discussion, see Dummett, ‘A Defence of McTaggart’s Proof of the Unreality of Time.’)

McTaggart’s argument was that every event is both past, present, and future, which is a contradiction. The objector responds that some events may be (e.g.) such that they will be past, are present, and were future; but never such that they are present, are past, and are future.

But what does it mean to say that something, e.g., was present? Presumably it just means that there is some point in the past at which it was present. We can combine any two of our predicates ‘past’, ‘present’, and ‘future’ in this way, so that just as any event can have any of the three 1st-level properties


so any event can have any of the nine 2nd-level properties

past in the past
present in the past
future in the past
past in the present
present in the present
future in the present
past in the future
present in the future
future in the future

The objector is suggesting that instead of describing events in terms of the first-level properties, we describe them in terms of the second-level properties.

But, McTaggart argues, the contradiction remains at the second level. For just as it is true of any event (again, for simplicity ignoring first and final events) that it is past, present, and future, it is true of any event that it is past in the present, present in the present, and future in the present. But these are no more compatible than our original three.

To escape this reply on McTaggart’s part, the objector might reject the claim that every event is past, is present, and is future. Instead, she might say, it is true that some event might be, e.g., such that it will be past in the present, is present in the present and was future in the present.

How should McTaggart reply?

3.2 The denial that time essentially involves the A series

Change without the A series.

Causation, entropy, and explanations of the direction of time.


   Dummett, Michael, ‘A Defence of McTaggart’s Proof of the Unreality of Time’, Philosophical Review, 69 (1960), pp. 497-504, Reprinted in Dummett, Truth and Other Enigmas, pp. 351-357.

   Dummett, Michael, Truth and Other Enigmas, (Cambridge, MA: Harvard University Press Press, 1978).

   McTaggart, John, ‘The Unreality of Time’, Mind, 17 (1908), pp. 457-474.

   McTaggart, John, The Nature of Existence, Volume 2, (Cambridge: Cambridge University Press, 1927).

See also Baldwin, Thomas (1998). McTaggart, John McTaggart Ellis. In E. Craig (Ed.), Routledge Encyclopedia of Philosophy. London: Routledge.