In a famous paper published in 1908, J.M.E. McTaggart argued that there is in fact no such thing as time, and that the appearance of a temporal order to the world is a mere appearance. Other philosophers before and since (including, especially, F.H. Bradley) have argued for the same conclusion. We will focus here only on McTaggart’s argument against the reality of time, which has been by far the most influential.
McTaggart begins his argument by distinguishing two ways in which positions in time can be ordered. First, he says, positions in time can be ordered according to their possession of properties like being two days future, being one day future, being present, being one day past, etc. (These properties are often referred to now as “A properties.”) McTaggart calls the series of times ordered by these properties “the A series.” But he says that positions in time can also be ordered by two-place relations like two days earlier than, one day earlier than, simultaneous with, etc. (These relations are now often called “B relations.”) McTaggart calls the series of times ordered by these relations “the B series.”
(An odd but seldom noticed consequence of McTaggart’s characterization of the A series and the B series is that, on that characterization, the A series is identical to the B series. For the items that make up the B series (namely, moments of time) are the same items that make up the A series, and the order of the items in the B series is the same as the order of the items in the A series; but there is nothing more to a series than some specific items in a particular order.)
In any case, McTaggart argues that the B series alone does not constitute a proper time series. I.e., McTaggart says that the A series is essential to time. His reason for this is that change (he says) is essential to time, and the B series without the A series does not involve genuine change (since B series positions are forever “fixed,” whereas A series positions are constantly changing).
McTaggart also argues that the A series is inherently contradictory. For (he says) the different A properties are incompatible with one another. (No time can be both future and past, for example.) Nevertheless, he insists, each time in the A series must possess all of the different A properties. (Since a time that is future will be present and past, and so on.)
One response to this argument that McTaggart anticipates involves claiming that it’s not true of any time, t, that t is both future and past. Rather, the objection goes, we must say that t was future at some moment of past time and will be past at some moment of future time. But this objection fails, according to McTaggart, because the additional times that are invoked in order to explain t’s possession of the 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). Thus, according to McTaggart, we never resolve the original contradiction inherent in the A series, but, instead, merely generate an infinite regress of more and more contradictions.
Since, according to McTaggart, the supposition that there is an A series leads to contradiction, and since (he says) there can be no time without an A series, McTaggart concludes that time itself, including both the A series and the B series, is unreal.
Philosophers like McTaggart who claim that time is unreal are aware of the seemingly paradoxical nature of their claim. They generally take the line that all appearances suggesting that there is a temporal order to things are somehow illusory.
