“It doubtless seems highly paradoxical to assert that Time is unreal, and that all statements which involve its reality are erroneous,” and yet, in his 1908 paper ‘The Unreality of Time’, J.M.E. McTaggart attempts to prove just that. This essay will outline his arguments and examine their consequences. At the core of McTaggart’s argument is the distinction between what he calls the ‘A-theory’ and the ‘B-theory’ of time. Positions in time, he says, can be ordered according to their properties, such as being two days future, being one day future, being present, being one day past, and so on.This temporal series of being past, present, and future, he calls the A-series. However, he asserts that positions in time can also be ordered by dyadic relations such as two days earlier than, one day earlier than, simultaneous with, and so on. This temporal ranking of events according to the relation ‘earlier than’, he calls the B-series.
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After making the above distinction, McTaggart’s first step is to show that the A-series theory is essential to our concept time, by highlighting the essential nature of change in any such conception. “It would,” he says, “…be universally admitted that time involves change”. A universe in which nothing ever changed, “…would be a timeless universe.” He argues that the B-series, without the A-series, does not involve genuine change, since where the A-series changes (in that what was future is now past) the B-series positions are true timelessly-they are forever ‘fixed’.
After addressing some possible responses by the likes of Bertrand Russell (which I shall discuss shortly) and establishing to his satisfaction that change can be accounted for only by A-series notions of time, McTaggart second step is to show that any A-series notions are nonetheless ultimately incoherent, and thus so is time itself. To start with, McTaggart argues that being future, being present, and being past, are incompatible determinations-they are mutually exclusive. Yet, in A-series interpretations of time, “…every event has them all.” So, though McTaggart believes the A-series series is essential to time, he also believes it leads to a contradiction, and so cannot be true of anything in reality. Thus, time cannot be true of anything in reality either; therefore time is unreal.
Despite McTaggart’s arguments, most philosophers have remained convinced of the reality of time; partly because the appearance of a temporal order to the world is so strong; partly because the implications of its unreality are so vast and injurious to so many philosophical theories; and partly because, like me, they remain unconvinced of the ‘proof’ itself. These philosophers normally dispute the necessity of the A-series in capturing the nature of time, and defend what P.T. Geach later called the ‘Cambridge’ criterion of change.
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One such philosopher, Bertrand Russell-who Richard Gale hailed as “[t]he father of the modern version of the B-Theory…”- believes that McTaggart looks for change in the wrong place. He says that “[c]hange is the difference, in respect of truth or falsehood, between a proposition concerning an entity and a time T, and a proposition concerning the same entity and another time T’, provided that the two propositions differ only by the fact that T occurs in one where T’ occurs in the other.” In other words, change is simply the difference in the applicability of a predicate to a subject at different points in time. McTaggart addresses this argument using the example of a poker that is hot at T and cool at T’. This, he says, does not constitute real change, because it is always the case that the earlier part of this event is hotter than the later part of this event. However, Russell would most likely have found this not entirely persuasive, as, though it may be true that the poker does not change in regards to it being hot at T, such an argument does give us a criterion for what is for the poker to change.
That is not to say, however, the McTaggart’s ‘proof’ proves nothing. At least one part of McTaggart’s argument, the part about the contradiction inherent in the A-series, seems to be sound. It is easy to dismiss the most obvious objection available to the defender of the A-series. As McTaggart says, one may claim that it’s never true of any event that it is past, is future, and is past. Instead, such an argument would run, the event is present, will be past, and has been future; or it is past, and has been future and present; or it is future, and will be present and past. There seems to be no contradiction here because, though the characteristics are incompatible, “…each term has all of them successively.” But, according to McTaggart, such an objection fails given that the other times called upon to explain the event’s incompatible A-properties must themselves possess all of the same A-properties (as must any further times invoked on account of these additional times, and so on ad infinitum). This objection, therefore, can never resolve the original contradiction inherent in the A-series, because it simply reintroduces further notions of time, and so begs the same question. This does not mean that we must go so far as to deny the reality of time itself, for though McTaggart may establish that the A-series is unreal, he does little to convince B-theorists such as Russell of its necessity.