1. Lecture 8 Time: McTaggart’s argument
Dr. Donnchadh O’Conaill
16/2/2017
Metaphysics University of Helsinki

2. 1. Introduction: the A-series and the B-series
Positions in time: times at which events occur (McTaggart 1908, 458)
Two ways in which positions or events can be ordered:
A-Series: past, present or future
These positions not permanent: an event which is now present, e.g. this lecture, was in the future, and will become past
B-series: earlier than, later than, or simultaneous with
Permanent positions: if x is earlier than y, then it is always earlier than y

3. McTaggart’s argument against the reality of time
P1: If there is no change, then time is not real
P2: Change requires that events form an A-series (because the B-series cannot accommodate change)
P3: The A-series entails contradictions
P4: Therefore the A-series is impossible
C: Therefore time cannot be real
P1: “A universe in which nothing whatever changed (including the thoughts of the conscious beings in it) would be a timeless universe” (McTaggart 1908, 459)

4. 2. Change requires the A-series
McTaggart: what is it which could change in a time formed by the B-series alone?
One suggestion: change consists in M ceasing to be an event, while N begins to be an event
McTaggart: this is not possible
If “time is constituted by a B series alone, N will always have a position in a time series, and has always had one. That is, it will always be, and always has been, an event, and cannot begin or cease to be an event” (1908, 459)

5. Second suggestion: M merges into N, preserving a common element throughout?
This requires that M cease to be M, but “no event can cease to be, or begin to be, itself, since it never ceases to have a place as itself in the B series” (460)
“Take any event – the death of Queen Anne, for example – and consider what change can take place in its characteristics. That it is a death, that it is the death of Anne Stuart, that it has such causes, that it has such effects – every characteristic of this sort never changes” (460)

6. The only characteristics of events which can change are the determinations of each event by the A-series: e.g., an event which was at one time in the future, then is present, before receding into the past
“Thus we seem forced to the conclusion that all change is only a change of the characteristics imparted to events by their presence in the A series” ( )
Therefore, time would not be possible without the A- series – not would the B-series be possible, since its relations are clearly temporal

7. 4. Russell’s objection
McTaggart assumes that change must consist in some difference in events (e.g., their coming into being, or acquiring a new position in a time-series)
This view of what change is can be questioned:
“Change is the difference, in respect of truth or falsehood, between a proposition concerning an entity and the time T, and a proposition concerning the same entity and another time T’, provided that these propositions differ only by the fact that T occurs in the one where T’ occurs in the other” (Principles of Mathematics, § 442; quoted in McTaggart 1968, 14)

8. On this view, change does not occur in events, but in the entities to which they happen:
“If my poker, for example, is hot on a particular Monday, and never before or since, the event of the poker being hot does not change. But the poker changes, because there is a time when this event is happening to it, and a time when it is not happening to it” (McTaggart 1968, 14)

9. McTaggart’s reply
It is always true of the poker that it is hot on that Monday, and it is not hot on the Tuesday:
“Both these qualities are true of it at any time – the time when it is hot and the time when it is cold [...] The fact that it is hot at one point in a series and cold at other points cannot give change, if neither of these facts change” (McTaggart 1968, 15)
But no change can occur unless some facts change, i.e., some propositions change truth-value

10. McTaggart compares Russell’s account of change to differences in spatial location (1968, 15):
‘At latitude 55° North, the Greenwich meridian passes through the UK’ – this proposition is true
‘At latitude 55° South the Greenwich meridian passes through the UK’ – this is false
But the difference in truth-values between these propositions is not sufficient for change – in particular, the Greenwich meridian does not undergo any change because of this difference

11. 4. Against the A-Series
Past, present and future are incompatible characteristics – no event or position in time can be past and present and future:
“But every event has them all. 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” (McTaggart 1908, 468)

12. Possible response M is never simultaneously past, present and future
Rather, it has these characteristics successively – it is present, has been future, will be past
“The characteristics are only incompatible when they are simultaneous, and there is no contradiction to this in the fact that each term has all of them successively” (McTaggart 1908, 468)
McTaggart: what is meant by these tensed terms (i.e., is present, has been future, will be past)?
They refer to positions in the A-series: “the event in question is present in the present, future in the past, past in the future” (1908, 469)

13. “Accordingly the A series has to be pre-supposed in order to account for the A series. And this is clearly a vicious circle” (McTaggart 1908, 468)
To avoid this one could appeal to a second A-series
But the same problem arises here, which will require appeal to a third A-series, etc. - a vicious regress
“You can never get rid of the contradiction, for, by the act of removing it from what is to be explained, you produce it over again in the explanation” (1908, 469)

14. 5. Broad’s criticism
“We must now consider whether this argument of McTaggart’s is valid. I should suppose that every reader must have felt about it as any healthy-minded person feels about the Ontological Argument for the existence of God, viz., that it is obviously wrong somewhere, but that it may not be easy to say precisely what is wrong with it” (Broad 1938, 313)
Broad: why accept McTaggart’s analysis of A-series predication?
i.e., ‘X is now present’ = ‘there is a moment T, such that X has presentness at T, and T is present’

15. Broad: we can distinguish
temporal copula: ‘She is now writing’
Non-temporal copula: ‘37 is a prime number’
“If the word ‘is’ in [a sentence] were a non-temporal copula, every utterance by me of the same sentence would record the same fact, no matter whether it were earlier than, contemporary with, or later than this utterance of mine” (Broad 1938, 272)
Sentence with temporal copula: its truth depends on when it is uttered relative to the event designated

16. Broad thinks McTaggart assumes “that what is meant by a sentence with a temporal copula must be completely (and more accurately) expressible by a sentence or combination of sentences in which there is no temporal copula, but only temporal predicates and non-temporal copulas”
Therefore, “the regress arises because there remains at every stage a copula which, if taken as non-temporal, involves the non-temporal possession by a term of certain temporal predicates which could only belong to it successively” (1938, 314)

17. Broad: refuse to follow McTaggart’s analysis
“there is nothing necessary or self-evident about this assumption” (1938, 315)
“it seems to me that the proper interpretation of the regress is that it disproves the assumption that temporal copulas can be replaced by temporal predicates and non-temporal copulas” (1938, 315)
Since McTaggart has not shown why we need to follow his analysis of sentences with temporal copulas, no need to embark on the regress

18. Further problem with McTaggart’s analysis: it fails to express what we mean by temporal sentences
“When I utter the sentence ‘It has rained’, I do not mean that, in some mysterious non-temporal sense of ‘is’, there is a rainy event, which momentarily possessed the quality of presentness and has now lost it […] What I mean is that raininess has been, and no longer is being, manifested in my neighbourhood” (Broad 1938, 316)

19. Works cited
C. D. Broad (1938) ‘Ostensible Temporality’ in An Examination of McTaggart’s Philosophy (volume II). Cambridge: Cambridge University Press, esp. pp
J. E. McTaggart (1968) ‘Time’ in The Nature of Existence (vol 2). Cambridge: Cambridge University Press.
S. Shoemaker (1969) ‘Time without Change’ Journal of Philosophy 66 (12):