McTaggart’s argument against the temporal A-series


McTaggart’s argument against the temporal A-series serves as one of the foundations upon which the philosopher explicates his argument for the unreality of time.  Before furthering my explication and examination of his negative argument of the temporal A-series, I shall briefly explain the background of, and, the central issue involved in, McTaggart’s discussion of the ontology of time in the first part of this essay, which, I hope, can serves as an overview of the object of discussion, whence I shall then argue, in the second part, that his argument against the temporal A-series is not convincing, for McTaggart seems to have misinterpreted the ontology of the properties of temporal events in two aspects, first, he has erroneously regarded each temporally extended event has, at each time, only one ‘temporal properties’, viz. pastness, presentness and futurity; and, secondly, he has confused ‘absolute becoming’ with ‘qualitative change’.

McTaggart’s argument against the temporal A-series stems from the distinction he made on the idea of time, according to which temporal events can either be expressed in a tensed manner, i.e., in terms of having the properties of ‘pastness’, ‘presentness’ and ‘futurity’; or, tenselessly, by the relations of ‘earlier than’, ‘later than’ and ‘simultaneous with’. He named the former ‘A-series’ and the latter ‘B-series’:—

‘For the sake of brevity I shall speak of the series of positions running from the far through the near past to the present, and then from the present to the near future and the far future, as the A series. The series of positions which runs from earlier to later, I shall call the B series.’[1]

Based on such a distinction, McTaggart argues that, whereas B-series cannot stand on its own feet to be a genuinely temporal series—for time involves change and change cannot be derived from B-series alone, which merely expresses relative temporal positions of events—only A-series can imply and demonstrate the idea of time, because ‘all change is only a change of the characteristics imparted to events by their presence in the A series.’[2] Adding to that point, B-series cannot expect without the context of time, for the ‘distinctions of which it consists are clearly time-determinations.’[3] Whence it follows, as his argument goes, that time is unreal for the reason that A-series is contradictory insofar as it is endowed with incompatible intrinsic temporal properties at different times, and that B-series cannot exist as well, for the mere reason that if there is no A-series there is no time at all:—

‘Past, present, and future are incompatible determinations. Every event must be one or the other, but no event can be more than one. This is essential to the meaning of the terms…If M is past, it has been present and future. If it is future, it will be present and past. If it is present, it has been future and will be past. Thus all the three incompatible terms are predicable of each event, which is obviously inconsistent with their being incompatible, and inconsistent with their producing change.’[4]

McTaggart also maintains that it would have been a bootless task had one attempted to save the A-series by suggesting that no event has all of the A-properties at the same spot of time (on the ground that time is ‘ultimate’ as it cannot be explained without assuming itself[5]), owning to the fact that ‘its application to reality involves a contradiction’[6]—McTaggart’s exposition of the contradiction has already been expounded in the above.

Though contradictory as it might seem to McTaggart, I shall maintain the fact that an event having all three A-properties does not involve any contradiction, with reference to C. D. Broad[7]. Consider the case of two-dimensional spatial extension: if I were to draw a straight line on a piece of white paper with a blue fountain pen, a two-dimensionally unextended line would appear in between the white colour of the paper and the blue ink of the ‘line’ (it is in quotation marks, for a ‘line’ that is drawn with a fountain pen isn’t properly a line but might be considered as a very wide quadrilateral), in neither white nor blue. If I were again to draw with the same pen another ‘line’ which perpendicularly intersects the original ‘line’, at the intersection there would emerge four points which lie at the four intersection points of the two blue ‘lines’ and the white background (Figure 1).

The aforesaid four points which lie at the four corners of intersection would be considered as unextended in two-dimensional Euclidean space. We may apply the analogy to the explication of A-series. Consider a continuous sound in constant pitch being produced by drawing a bow across its strings. Whilst the continuous sound is played I shall strike a drumstick against a wooden table, which will produce a ‘bang’ sound with a background violin sound at ‘C Sharp’. We may conceive in between the ‘bang’ sound and the constant violin tone there emerge a temporally unextended point which is analogous to points in two-dimensional Euclidean space. This temporal point Broad named ‘event particle’[8].

I shall now get back to the discussion of A-series from the seemingly sidetracked discussion. With the idea of ‘event particle’ in mind, we should now be equipped with adequate tools to examine McTaggart’s account of A-properties in a more comprehensive manner. Strictly speaking, ‘presentness’ (so as different degrees of ‘pastness’ and ‘futurity’) should be considered as a temporally unextended notion, for time flows and ‘presentnesses’ continuously slip into the past with the passage of time. That being granted, any event, be it as short (or as quick) as in a millionth of a second or as long as hours, must be temporally extended, for a temporally unextended ‘event particle’ is beyond the reach of perception. Every event is constituted of a number of ‘event particles’ in order for itself to be perceived. Whence it follows that every perceivable event must be constituted of more than one temporal property. That being so, it would be nonsensical to speak of ‘no event has all of the A-properties at the same spot of time’, for ‘a spot of time’ is a temporally unextended notion which is occupied by one ‘event particle’, and no event is constituted of a single particle.

Whilst McTaggart is justified in claiming that every event has all three A-series properties with regards to the passage of, and its different positions, in time, his examination of the ontology of time, from which he deduced the contradiction of A-series might seem, nonetheless, not be as convincing as he claimed. Consider a pair of coal tongs that is placed with one end resting in the fireplace and the other end outside of it[9]: if viewed as a whole, it will certainly be contradictory to suggest that the pair of tongs is both hot and cold at the same time; but it will not involve any contradictions in saying that the tip of the tongs, which is placed in the fire, is hot whereas the handle is cold at the same time, for they are distinct spatial parts which each occupies different space[10]. Furthermore, if we, for the sake of brevity, assume a Newtonian absolute space[11], it surely will not involve any contradiction in saying that part of the Big Ben is three hundred feet above ground and part of it is at ground level, nor is it contradictory in suggesting that part of Hyde Park is in Knightsbridge whereas part of it is in Bayswater, for spatial extension involves occupying different spaces. The contradiction would be resolved if one realised, analogously, the fact that being extended in time is in essence occupying different spots of time and hence having different temporal properties. McTaggart is wrong in claiming simply that an event being past, present and future per se are incompatible[12]. As Parsons writes:—

    ‘There is no contradiction in one thing’s being partially past and partially future, and indeed partially present.’[13]

Nevertheless one should not refute McTaggart’s argument against the temporal A-series based on what I so far have expounded, for the argument does not confine itself to viewing temporal extensionality in a stagnant manner. The argument of McTaggart provided to refute temporal A-series hinges on his explication of the impossibility of converting tensed sentences into tenseless sentences without inducing any contradictions and regress:—

‘What we have done is this—to meet the difficulty that my writing of this article has the characteristics of past, present and future, we say that it is present, has been future, and will be past. But ‘has been’ is only distinguished from ‘is’ by being existence in the past and not in the present, and ‘will be’ is only distinguished from both by being existence in the future. Thus our statement comes to this—that the event in question is present in the present, future in the past, past in the future. And it is clear that there is a vicious circle if we endeavour to assign the characteristics of present, future and past by the criterion of the characteristics of present, past and future.’[14]

 The ‘vicious circle’ may be ascribed to the confusion between ‘qualitative change’ and ‘absolute becoming’, for McTaggart seems to have erred in treating A-properties as if they were qualitative attributes[15]. In fact, unlike the notion of ‘becoming hot’ (which is a description of qualitative change), ‘to become present’, or ‘to become past’ is actually, as Broad suggests, an ‘absolute becoming,’ i.e., ‘just to become,’ or, ‘to happen’[16].

Parsons, moreover, has come up with the idea of constructing a ‘counterfactual theory of tense’ with which he solves the contradiction that involved in A-series. He suggests, for instance, that the tensed statement ‘M was wholly future’ and ‘M will be wholly past’ can be converted to ‘there is some past time such that, were it that time, M would be wholly future’ and ‘there is some future time such that, were it that time, M would be whole past’ respectively[17]. I gather that it is an adequate theory to defend A-series to the extent that it has provided a time-neutral position whence one would be able to attribute non-contradictory A-properties to temporal events, given that one ‘remains neutral as to whether time passes or not’[18].

It has to be admitted, nonetheless, that McTaggart does put forward a strong theory against A-series, to the extent that he recognises the incompatibility of the passage of time and the fluid and dynamic nature of A-properties, for it changes constantly as time passes—time cannot be understood without being defined as the dimension of change, whilst change itself implies contradiction with respect to the fact that events have different A-properties[19].

Apart from analysing McTaggart’s critique of A-series from an ontological or metaphysical perspective (as what I have endeavoured to do), it might also worth mentioning that he has overlooked the role that the presence of experience plays in deciding the object reality of ‘temporal becoming’, i.e., the epistemic aspect of A-series. For instance the refutation of A-series would create a great difficulty in explaining experiential notions like ‘thank goodness that’s over’[20]. Chained by the word limit, it seems obvious that I will have to put this explication to an end.   Nonetheless, I think I have fulfilled my goal of showing that McTaggart’s argument is not as sound as some might conceive, insofar as his understanding of temporal extendibility, the ontology of time, and his tensed/tenseless argument are concerned.

[1] J. M. E. McTaggart, ‘The Unreality of Time,’ in Philosophy Studies, idem, ed. S. V. Keeling (London: Edward Arnold & Co., 1934), 111.

[2] Op. cit., 115.

[3] Op. cit., 116.

[4] Op. cit., 123-124.

[5] Op. cit., 126.

[6] Op. cit., 127.

[7] C. D. Broad, Examination of McTaggart’s Philosophy, Vol. II, Part I (Cambridge at the University Press, 1938), 264-317.

[8] Loc. cit.

[9] Josh Parsons, ‘A-Theory for B-Theorists,’ in Philosophical Quarterly, 52/206 (2002): 5-6.

[10] Loc. cit. See also: D. H. Mellor, ‘McTaggart’s Proof,’ in Real Time II (London: Routledge, 1998), 70-83.

[11] I have no intention to dwell on the discussion of relative space and Einstein’s theory of special relativity, for it is not my concern in this essay.

[12] Recall that he wrote: ‘Past, present, and future are incompatible determinations. Every event must be one or the other, but no event can be more than one.’ (See footnote 4)

[13] Parsons, Op. cit., 7.

[14] McTaggart, Op. cit. 124-125.

[15] Broad, Ibid.

[16] Loc. cit.

[17] Parsons, Op. cit., 8-10.

[18] Loc. cit.

[19] Mellor, Ibid.

[20] A. N. Prior, ‘Thank Goodness That’s Over,’ Philosophy 34 (1959): 12-17.



Broad, C. D. Examination of McTaggart’s Philosophy, Vol. II, Part I. Cambridge at the University Press, 1938.

McTaggart, J. M. E. ‘The Unreality of Time.’ In Philosophy Studies, idem, edited by S. V. Keeling. London: Edward Arnold & Co., 1934.

Mellor, D. H. ‘McTaggart’s Proof.’ In Real Time II. London: Routledge, 1998.

Parsons, Josh ‘A-Theory for B-Theorists.’ Philosophical Quarterly, 52/206 (2002): 5-6.

Prior, A. N. ‘Thank Goodness That’s Over,’ Philosophy 34 (1959): 12-17.

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