A slightly different version of the argument appeared in 1927 as one of the chapters in the second volume of McTaggart's most well known book, The Nature of Existence.
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).
To frame his argument, McTaggart initially offers a phenomenological analysis of how time appears to us in experience.
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.
There can be change in the B-series in the form of objects bearing different properties at different times (Braithwaite 1928; Gotshalk 1930; Marhenke 1935; Smart 1949; Mellor 1981 & 98; Oaklander 1984; LePoidevin 1991; Dyke 2002).
McTaggart admits that the contradictory nature of the A-series may not be obvious, because it would appear that events never are simultaneously future, present, and past, but only successively so.
However, there is a contradiction, he insists, because any attempt to explain why they are future, present, and past, at different times is (i) circular because we would need to describe the successive order of those "different times" again by invoking the determinations of being future, present or past, and (ii) this in turn will inevitably lead to a vicious infinite regress.
It is the validity of the argument in favour of a vicious infinite regress that has received the most attention in 20th Century philosophy of time.
This is, arguably, because by then he has come to treat tense as a simple and indefinable notion, and thus cannot contend that the terms need to be explained at all in order to be applied.
Philosophers who favour the B-view of time tend to find McTaggart's argument against the A-series to demonstrate conclusively that tense involves a contradiction.
Hence it is wrong to think of the expression as an attribution to M of futurity, presentness, and pastness, all at once (Marhenke 1935; Broad 1938; Mink 1960; Prior 1967; Christensen 1974; Lloyd 1977; Lowe 1987).
However, since it starts from the premise that the future and past can only be real by existing, then it remains to show that this is what the A-view of time assumes.
McTaggart does not say much about the C-series in the original journal article, but in The Nature of Existence he devotes six whole chapters to discuss it (1927: Chs.
34 of The Nature of Existence that reality cannot really be material), which are related to each other on the basis of their conceptual content in terms of being included in and inclusive of (1927: sect.
Prior (1967) took McTaggart's phenomenological analysis as their point of departure in the development of modern tense logic.
The controversy about McTaggart's argument for the unreality of time continues unabated (see, for instance, Smith 2011; Cameron 2015; Mozersky 2015; Ingthorsson 2016).