McTaggart’s Argument for the Unreality of Time:
The Paradox of Past, Present and Future Reality

by Keith Wilson

 

 

“Time past and time future
What might have been and what has been
Point to one end, which is always present.”

— The Wind’s Four Quarters, T S Eliot

 

This essay examines J M E McTaggart’s argument that the distinctions of past, present and future can have no basis in reality, thereby removing any justification for the existence of time itself (McTaggart 1927). I will argue that, despite reaching the correct conclusion, his argument is flawed because it relies upon a notion of simultaneity that is incompatible with modern physics. I will begin by briefly outlining McTaggart’s argument, followed by some of the major objections to it, and their difficulties, before discussing the more fundamental problem of simultaneity. I will conclude by sketching out a novel alternative view that supports McTaggart’s conclusion, in which past and future reality are seen as secondary qualities of a timeless and ever-changing present. 1

The structure of McTaggart’s argument is quite simple and can be summarised as follows:

P1    The existence of past, present and future relationships / qualities is required in order for time to be real.

P2    Past, present and future relationships / qualities contain an inherent contradiction, and therefore cannot exist.

C1    Time is not real.

If we wish to deny C1 then we must dispute either P1 or P2, as the logic of the argument is inescapable. McTaggart’s case for P1 is that time necessarily involves change, and so only the movement of events from future, through the present and into the past (the so-called ‘A-series’) can provide a convincing explanation of this phenomenon (McTaggart: 261). Any view of time that does not contain a reference to the present moment or observer, and orders events solely by whether they are ‘earlier’ or ‘later’ than one another (McTaggart’s ‘B-series’), can only provide a static and unchanging view of temporal relationships. Since these relationships do not vary in any way, McTaggart argues that they cannot explain the nature of change or the flow of time as we experience them. 2

P2 arises from the fact that past, present and future are mutually exclusive attributes, and yet the A-series requires events to satisfy all three as they move from future to present to past. The obvious rebuttal to this is that no event is in all three states simultaneously, so they are successive rather than conflicting attributes. However, it is unclear what we should take ‘simultaneously’ to mean in this context except ‘at the same time’, which makes the argument circular because we are using time to try to explain the notion of time. Worse than that, this approach does not even fix the problem as we must then explain the notion of tense and what it means to say that an event was future, is present and will be past. This again refers to particular ‘times’ at which the event is, was, or will be present, and such times must also inhabit past, present and future as they undergo the same succession of changes as events. Now the same contradiction has arisen with respect to times, and can only be solved by introducing yet another external point of reference, which must itself be simultaneously past, present and future, and so on ad infinitum . This regression leads McTaggart to conclude that the A-series cannot be real and so, according to P1, time itself must not be real.

Several solutions have been proposed to try to resolve this paradox. Lowe (2002: 313–9) posits an adverbial account of time that attempts to restrict the number of tenses to nine combinations: ‘pastly past’, ‘presently past’, ‘futurely past’, and so on. Even though events must still satisfy more than one tense, many of these combinations are compatible, and no event ever has to satisfy conflicting tenses simultaneously. Unfortunately, this account also runs into problems when we try to account for the meaning of simultaneity, or the passage of events through time, at which point the infinite regress recurs. A more radical approach is suggested by Prior (1993) who argues that tensed statements (e.g. ‘Margaret Thatcher had big hair’), should be understood in terms of their truth conditions . Such statements may be broken down into a naming clause (‘Margaret Thatcher’), a predicate (‘has big hair’) and a ‘tenseless’ truth condition (there is some past time such that X is true). Unfortunately, this also refers to times, and has the effect of explaining the A-series in B-series terms relative to the moment at which the statement is made, which actually supports McTaggart’s conclusion as if only the B-series is real then time itself cannot be real, as it depends upon the primacy of the A-series.

Perhaps a more fundamental problem with all of the above accounts arises when we examine the notion of simultaneity. The existence of particular ‘times’, moments in time, and even the present itself 3 is founded upon the idea that events can happen before, after or at precisely the same time as one another. This simply contradicts what we know about the physical nature of our universe. According to Einstein’s special theory of relativity, time proceeds differently for different observers, depending on their velocity and position within the gravitational field. Two observers travelling at speed in opposite directions will not agree upon when different events occur because each occupies a different inertial frame, causing events to appear at different times or in a different sequence relative to the observer. 4 Furthermore, this is not simply a matter of observation being restricted by the speed of light, it is a fundamental feature of the universe itself. There is no single absolute frame of reference that can be used to arrange events into order, like some universal cosmic timekeeper. Each part of the universe observes time (and therefore change) at its own rate, and so the idea of an individual ‘moment’ of time that applies equally to all observers, such as the present moment, is an illusion. 5

The defender of A-series time might respond to this as follows. Given that an objective ordering of events is impossible in a universe where information travels at a finite speed, events must instead be placed in order of their causal relationships. The problem here is which causal relationships. Again, without a global frame of reference, it is impossible to place events into a single linear sequence and would require (at least) four dimensions to represent all of the causal relationships in the universe. 6 There is also the issue of conceptual priority. We can either use causal relationships to explain time, or temporal relationships to explain causality, but not both, otherwise our argument becomes circular. Because we cannot isolate an individual ‘moment’ of time, no matter how small an interval we consider it will inevitably contain some element of change. 7 Change is therefore essential to the nature of matter, and given that causation cannot be explained in terms of anything else, as observed by Hume (1748), we can conclude that it is change, and not time, that is fundamental. 8 As suggested by Aristotle (IV 218 b 21ff), ‘time is the measure of change’, and so time must be explained in terms of change, rather than the other way around.

Armed with this information, we can now sketch out a possible alternative that does not rely upon the theoretical constructs of absolute or ‘frozen’ time. If change is inherent to the nature of things, what we call ‘the present’ must be an ever-changing state of existence. P1 of McTaggart’s argument shows us that time, and therefore past and future, cannot exist without the A-series, which is illusory. We must therefore account for past and future as aspects of the present , where ‘present’ is taken to mean the ever-changing reality that we see all around us . The adverbial relations of ‘pastly present’ and ‘futurely present’ therefore literally mean the causal consequences of past events such as they exist in the present and the causal possibilities of future events such as they exist in the present , respectively. 9 According to this view, past and future do in a sense exist, but their existence is reducible to facts about the present. 10 They are effectively secondary qualities of the present, in the same way that colour is a secondary quality arising from the shape and extension of matter (as described by Locke 1690: §10). In this way, we can account for the existence of past and future events, the meaning of tensed statements and the unreality of time, without resorting to the notion of simultaneity. 11

In summary, then, McTaggart fails to present a convincing case for the unreality of time because his argument fundamentally contradicts one of the principles of modern physics (locality), which rejects the notion of individual fixed moments in time. However, since the alternative views are similarly flawed, we are forced to conclude that time is in fact unreal, although for different reasons from the ones given by McTaggart. By separating the concept of simultaneity from the nature of causation, we arrive at the idea of a constantly changing present in which past and future events exist as causal consequences and potentialities that are inherent to the way that things are now. In this way, past, present and future reality are seen as being bound together in a single, constantly changing and timeless state of flux.

 

Bibliography

Aristotle Physics , Book IV. In J Barnes (ed.), 1984.

Barbour, Julian 1999: The End of Time . London: Orion Books.

Dummett, Michael 2004: The Metaphysics of Time . New York: Columbia University Press.

Hume, David 1748: Enquiry Concerning the Human Understanding , Sect. IV, Pt. 1.

Lewis, David 1979: ‘Counterfactual Dependence and Time’s Arrow’. In Sosa & Tooley (eds.), 1993.

Locke, John 1690: Essay Concerning Human Understanding , Book 2, Ch. 8, Sects. 7ff.

Lowe, E J 2002: A Survey of Metaphysics . Oxford: Oxford University Press.

McTaggart, J M E 1927: The Nature of Existence, Vol. II. Cambridge: Cambridge University Press.

Prior, Arthur N 2002: ‘Changes in Events and Changes in Things’. In Le Poidevin & MacBeath (eds.) 1993, pp. 35–46.

Russell, Bertrand 1903: Principles of Mathematics . Cambridge: At the University Press.

Smolin, Lee 2000: Three Roads to Quantum Gravity . London: Weidenfeld & Nicolson.

 

 

© 2005 Keith Wilson, University of York