"The Argument for the Unreality of Time" is the best-known philosophical work of the Cambridge idealist J. M. E. McTaggart (1866-1925). In the argument, first published as a journal article in Mind in 1908, McTaggart argues that time is unreal because our descriptions of time are either contradictory, circular, or insufficient. A slightly different version of the argument appeared in 1927 as one of the chapters in the second volume of McTaggart's greatest work, The Nature of Existence .
The argument for the unreality of time is popularly treated as a stand-alone argument that does not depend on any significant metaphysical principles (e.g. as argued by C. D. Broad 1933 and L. O. Mink 1960). R. D. Ingthorsson disputes this, and argues that the argument can only be understood as an attempt to draw out certain consequences of the metaphysical system that McTaggart presents in the 1st Volume of The Nature of Existence (Ingthorsson 1998 & 2016).
It is helpful to consider the argument as consisting of three parts. In the first part, McTaggart offers a phenomenological analysis of the appearance of time, in terms of the now famous A- and B-series (see below for detail). In the second part, he argues that a conception of time as only forming a B-series but not an A-series is an inadequate conception of time because the B-series does not contain any notion of change. The A-series, on the other hand, appears to contain change and is thus more likely to be an adequate conception of time. In the third and final part, he argues that the conception of time forming an A-series is contradictory and thus nothing can be like an A-series. Since the A- and the B- series exhaust possible conceptions of how reality can be temporal, and neither is adequate, the conclusion McTaggart reaches is that reality is not temporal at all.
To frame his argument, McTaggart initially offers a phenomenological analysis of how time appears to us in experience. Time appears, he says, in the form of events standing in temporal positions, of which there are two kinds. On the one hand events are earlier than and later than each other, and on the other hand they are future, present, and past, and continually changing their position in terms of futurity, presentness, and pastness. The two kinds of temporal positions each represent events in time as standing in a certain order which McTaggart chooses to call the A-series and the B-series. The A-series represents the series of positions determined as future, present, and past, and who continuously pass from the distant future towards the present, and through the present into the remote past. The B-series represents the series of positions determined as earlier than or later than each other. The determinations of the B-series hold between the events in time, and never change. If an event ever is earlier or later than some other event, then their respective position in time never changes. The determinations of the A-series must hold to something outside of time, something that does not itself change its position in time, but in relation to which the events in time pass from being future, present, and past. Surprisingly, McTaggart does not suggest the present, or NOW, as this something whose position in time is fixed and unchanging. He just says that it will be difficult to identify any such entity (seeing as it is outside time). Broad explains that McTaggart believed that the difficulty of identifying this entity was serious enough in its own right to be persuaded that time is unreal, but thinks that the contradiction of the A-series is still more convincing, wherefore he leaves this particular difficulty aside.