Times can be thought of as past, present and future or as earlier and later.
Is one of these ways of thinking about time more fundamental than the other?

The essay title refers to the two ways of thinking about time identified by J.M.E. McTaggart in his 1908 article "The Unreality of Time"(1).  In that landmark article, he identified what he called the "A Series" and the "B Series" basis of the sequencing of events within time.  Since his article, just about every discussion of the nature of time makes use of, or refers to, McTaggart's two "Time-series". 

The essay's title question can be understood as asking whether the more fundamental manner of thinking about the nature of time is McTaggart's "A-series" or his "B-series".  Or, equivalently, whether it is the A-Series that is derivative of the B-Series, or vice versa.  I will argue here that it is the B-series (the relations of earlier and later) that is the more fundamental.

The A-Series

McTaggart's "A-series" sequences events within time by making use of our notions of "past, present, and future" (and related English phraseology) resulting in a temporal sequence of events ordered from the far past, through the present into the far future.  His "B-series" sequences events within time by making use of our notions of "earlier and later" (and related English phraseology) resulting in a temporal sequence of events ordered from earlier moments to later moments. 

"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."
                                                                      (The Nature of Existence §§305-6)

McTaggart does not pretend that these two different time-series represent different sequences of events within time.  Rather they represent two different ways in which the single sequence of events within time can be seen to gain their sequence.  It was McTaggart's argument that the A series was a necessary (and in this sense a more fundamental) component of any full theory of time.  He reasoned that the B series alone cannot constitute a proper time series because the A series is essential to time.  His entire structure of reasoning is based on his premise that change is essential to time.  But, he argued, the B series alone does not involve genuine change since events in the B series are forever "fixed."   Only events in the A series, he claimed, are constantly changing. 

"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."                                                        (The Nature of Existence §§309-310)

He further argued that if events are not ordered by the A series then there cannot be said to be change.  But his reasoning was based on a rather eccentric notion of "change".  At the centre of his concept of "change" is the example he offers of the death of Queen Anne.

'take any event the death of Queen Anne, for example and consider what changes can take place in its characteristics. That it is a death, that it is the death of Anne Stuart, that it has such causes, that it has such effects every characteristic of this sort never changes.  . . .  And in every respect but one, it is equally devoid of change. But in one respect it does change. It was once an event in the far future. It became every moment an event in the nearer future. At last it was present. Then it became past, and will always remain past, though every moment it becomes further and further past."                                                 (The Nature of Existence §§311)

McTaggart's peculiar concept of change, that he deems necessary to an understanding of time, is tied tightly to the changing characteristics of the events within the time-series, rather than the usually expected focus on the changing characteristics of entities that participate in the events.  By so coupling change with events in this fashion, he has set up his argument as circular.  His definition of change pre-supposes the A-series ordering of events.  So naturally, a B-series ordering of events independent of an A-series understanding of time, is impossible.  This faux pas is reinforced by his discussion of Bertrand Russell's hot poker.

"What, then, is change? We find Mr Russell's views on this subject in his Principles of Mathematics, Section 442. 'Change is the difference, in respect of truth or falsehood, between a proposition concerning an entity and the time T1, and a proposition concerning the same entity and the time T2, provided that these propositions differ only by the fact that T1 occurs in the one where T2 occurs in the other.'  That is to say, there is change, on Mr Russell s view, if the proposition 'at the time T1 my poker is hot' is true, and the proposition 'at the time T2 my poker is hot' is false. I am unable to agree with Mr Russell. I should, indeed, admit that, when two such propositions were respectively true and false, there would be change. But then I maintain that there can be no time without an A series. If, with Mr Russell, we reject the A series, it seems to me that change goes with it, and that therefore time, for which change is essential, goes too." (The Nature of Existence §§313-314)

Certainly, the more usual concept of change is (more in line with, if not exactly) Russell's.  The normal concept of change is a difference in the characteristics of things between two times (or two places).  Hence, on the usual view of change, McTaggart's reference of the event of Queen Anne's death is irrelevant to his argument.  One can see the change in Queen Anne being alive at T1 and dead at T2, just like Russell can see his poker hot at T1 and cold at T2.  In essence, then, McTaggart's argument for the primacy (more fundamentalness) of the A-series understanding of time is fatally flawed. 

Despite this flaw, McTaggart proceeded, in his article, to demonstrate that there is another fatal flaw to the A-Series conception of time.  He demonstrated that the properties of "past," "present," and "future" are both mutually contradictory and possessed by all events.  Hence, he argued, the A-Series concept of time is self-contradictory.  He combines this conclusion with his previous argument that the A-Series is necessary to the concept of time, to conclude that Time is in fact not real.  Since his previous argument that the A-Series conception of time is necessary and fundamental is fatally flawed (as indicated above), McTaggart should have concluded that his self-contradictory demonstration was a reductio proof that his A-Series concept of time was at fault.  Which leaves us with his B-Series understanding of time.

The B-Series

The B-series is fully consistent with the view of time by modern physics as the fourth dimension of a four-dimensional space-time manifold.  In this view, a temporal "event" is just an instantaneous 3-dimensional slice of the four-dimensional manifold.  (I realize that this definition is overly simplistic, but it will serve for the purpose of this essay.)   This is a B-Series based definition of an "event" that is quite consistent with McTaggart's - "The contents of any position in time form an event." (The Nature of Existence §§306)   And events are ordered down the single dimensional "line" of time by the relationships of "earlier" and "later".  In fact these two relationships can be viewed as time-symmetric.  It does not matter from which end of the dimensional "line" one starts, the relationship between any two events will remain the same.

Admittedly, our perception of time is best understood on the basis of the A-series.  At any given instant, any given event on the time-axis is perceived by us to be either past, present or future.  In just the same way, any given event in the spatial axes is perceived by us to be either over here, or over there, and so forth.  But what generates the "A-series" perception of time is the progression through the four-dimensional manifold of space-time of a 3-dimensional wave-front of our conscious awareness - our "Now!"   The A-series ordering of events is therefore inescapably indexical in nature.  If we understand A-Series properties as indexicals relative to a particular point of view, then the A-Series understanding of time can be can be seen to be fully compatible with the B-Series upon which it is based.

As pointed out by both Lowe(2) and Mellor(3), McTaggart failed to recognize this aspect of his A-series.  Not only is the A-series ordering of events indexed to "Now" as Lowe and Mellor argue, it is also indexed to each individual perceiver.  The A-series ordering of events within the four-dimensional space-time manifold offers no firm grounding for the assumption that your "Now" is synchronous with my "Now".  Viewing the A-series ordering of temporal events as the perceived consequence of a 3-dimensional wave-front transiting along the time dimension of a four-dimensional space-time manifold, opens up the intriguing possibility that each consciousness (if there be more than my own) might constitute its own independent wave-front.

Regarding "more fundamental" in the sense of what underlies what, it becomes obvious that the B-series ordering of temporal events (thinking of time in terms of earlier and later) is the more fundamental.  The A-series ordering of temporal events (thinking of time in terms of past, present and future) is derivative.  The changing classification of temporal events as future, present and then past is dependent on our changing perceptions of the underlying static relationship of events.  These are not properties of the events in themselves, but rather properties of our changing relationship to those events.  McTaggart mistakenly regarded the pastness of the death of Queen Anne as a property of the event of her death.  Correctly viewed, the pastness of the death of Queen Anne is a relational property that ties the event of Queen Anne's death with the position of the observer's "Now!" on the B-Series timeline.  McTaggart mistakenly regarded change as a property of events.  Correctly viewed, what McTaggart called the changing A-series properties of events are the changing "distance" between the observer and the event as the point of view of the observer moves along the B-Series time-line. 

From the perspective of ontological realism, therefore, it would clearly be the B-Series (earlier and later) sequencing of events that is definitive of time, while the A-Series (past, present, future) sequencing is necessarily derivative of the movement of our "Now!" across the time dimension.



(1)   McTaggart, J.M.E., The Nature of Existence (2 volumes); Cambridge University Press, Cambridge, England. 1927. ISBN 0-521-35769-1.

(2)   Lowe, E.J., "The Indexical Fallacy in McTaggart's Proof of the Unreality of Time" in Mind, New Series, Vol. 96, No. 381 (Jan., 1987), pp. 62-70, Published by: Oxford University Press on behalf of the Mind Association

(3)   Mellor, D.H., Real Time, Cambridge University Press, Cambridge, England. 1981. ISBN 0-521-24133-2

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, J.M.E., "The Unreality of Time";   Mind, New Series, Vol. 17, No. 68 (Oct., 1908), pgs. 457-474;   Published by: Oxford University Press on behalf of the Mind Association.

McTaggart, J.M.E., "The Nature of Existence" (excerpts from) in Van Inwagen, Peter and Zimmerman, Dean W. (eds), Metaphysics: The Big Questions, Blackwell Publishers. Oxford, England. 1998. ISBN 0-631-20588-8.

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