One metaphysical issue that has persisted
for millennia is the nature of time (space):
What is time? What are its properties?
McTaggart argues that the appearance of
time is as misleading as possible:
He argues that time is unreal.
This seems manifestly absurd, but thinkers
in many cultures have defended it.
Two temporal concepts
McTaggart: we have two ways of thinking
The A-series: Times/events are divided into
past, present or future.
Always changing: An event is first
future, then present, and then past.
The B-series: Times are related as earlier
than, later than or simultaneous with.
Permanent: if x is earlier than y, it is
Picturing the two series
A-Series (“tensed” view):
Past Present Future
Waterloo McTaggart lunch This lecture dinner Next President
B-Series (“tenseless” view):
Waterloo McTaggart lunch This lecture dinner Next President
Question is, which one correctly describes time?
The A-series is essential to time—
without it there could be no time.
1. Change is essential to time, i.e. if
there were no change, there would be
2. In the B-series, there can be no
3. Therefore, the A-series is required for
time to exist.
What about #2?
No change on the B-series
Imagine a poker sitting next to the fire today
but in the fire tomorrow
The poker is cold at T1, hot at T2.
The poker being cold is simultaneous with
T1, and the poker being hot is simultaneous
These are B-statements, i.e. statements
entirely in B-series terms.
Hence, they are permanent, i.e. they
are, if true, always true.
Therefore, there is no change here.
There would be change, however, if the
event of the poker being hot was not only
later than the event of it being cold, but was
also first future, then present, then past.
Consider the Greenwich meridian:
At a certain place, P1, it is in England, at
another place, P2, it is not in England.
This is analogous to the poker.
But nobody would say that the Meridian
changes. Hence, nobody should say that
the poker, as described in B-series terms,
Hence, only the A-series can account for
What about “becoming”?
1. Change = an event ceasing to exist and
another coming to exist.
2. But if all that exists is the B-series, then
if E1 is earlier than E2, it is always true
that it is earlier.
3. Thus E1 and E2 must always exist in
the B-series (No truth without being, i.e.
something to make it true).
4. So, in the B-series, all events/times are
equally real; they all have permanent B-
5. So, on the B-series, there can be no
“becoming”, no ceasing to be of events,
no coming into existence of events.
Events don’t change
Consider any event, the death of Queen
Does this event ever change?
It was, is and will be a death.
It was, is and will be the death of a
There is one way it could change:
From future, to present to past
Conclusion: There is only change if there is
So: There is only time if there is an A-series.
Note: Since the B-series is temporal, there
can only be a B-series if there is an A-
Why think time is unreal?
McTaggart’s main argument:
1. There can be no time without change.
2. There can be no change without the
3. But the A-series is contradictory.
4. Therefore, there can be no change
and hence time is unreal.
Why does he think the A-series is
Problems with the A-series
Past, present & future are incompatible:
If E is present, it isn’t past/future
If E is past, not present/future
If E is future, not present/past
But all events have all three:
This is what it means to say time passes
But this is impossible; no event can have all
three properties. So, what the A-series
says cannot be.
Answer: It is never the case that an event
has them at the same time. Rather:
E is present, will be past, was future
E is past, was present/future
E is future, will be present/past.
But now we have higher order A-series
properties: ‘was future’, ‘will be present’, etc.
Are these consistent?
What does it mean to say that E ‘was
McTaggart: At a moment of past time, T,
E is future.
Problem: Each moment of time is past,
present and future.
So if T is past it is also present & future.
Response: T is past, was present and was
Problem: T is past means T is present at a
moment of past time, T1. But T1 must be
past, present and future.
Infinite regress; vicious since the
contradiction never gets removed.
Another way to think about it
In order to eliminate the contradiction, we
introduce higher order predicates; but there
are nine of these:
WAS: past, present, future
IS: past, present, future
WILL BE: past, present future.
Every event must have all nine = change.
But there are incompatible properties here,
WAS past and IS present.
To eliminate this, we need to go to an even
WILL BE WAS past, IS IS present.
But there are incompatible predicates here:
IS IS present and IS WAS present
The A-series is either contradictory or
leads to an infinite regress.
So, the A-series cannot exist.
No A-series = no change = no time.
1. E is future at T1
2. E is present at T2
3. E is past at T3
These are all consistent, so why not use this
understanding of passage?
Answer: Because now A-series
predications are understood as relations,
i.e. as relations events have to time.
That is, what could 1 mean other than E
is later than T1?
Similarly, 2 reduces to E is simultaneous
with T2 and 3 to E is earlier than T3.
Hence, the A-series has been re-
conceptualized as a B-series.
Broad on McTaggart
I agree with M on one thing: whatever it is,
the B-series is not time.
It is static (permanent)
Indistinguishable from space
But time space, therefore:
It follows that any temporal concept must be
an A-series concept.
Since the B-series is not time, only the
But M is wrong: there is no contradiction in
The copula (“to be”, “is”)
“It is raining”.
Equivalent to “It is now raining”.
Says something currently occurs.
“3 is a prime number”
Not = “3 is now prime”
Claims being prime is timelessly a
property of 3
Tenseless claims are permanent: E.g.:
B-series: “Poker is hot at T”.
Math: 4 is twice 2
If true, these are true at all times.
Broad: McTaggart makes an assumption
that he never justifies.
He assumes that temporal claims must be
analyzed into claims that have only:
1. A tenseless copula
2. Temporal properties (past, present,
1. “E will be past” = “At T3 (a future time),
E is past”
2. “E is present” = “At T2 (the present
time), E is present”
3. “E was future” = “At T1 (a past time), E
Note: “is” must be tenseless, otherwise:
At some past time, E is (now) future!
If we follow this analysis, then we get a
T2 is (tenseless) past, present and
T2 is present, will be past and was
future, that’s true.
At a future time, T3, T2 is past
At the present time, T2, T2 is present
At a past time, T1, T2 is future
And we are facing a regress.
The regress is not vicious!
At no point is there a contradiction.
However, regresses are still to be avoided.
Can we eliminate it?
Tenseless copulas require the A-series
1. The “is” in M’s analysis is tenseless.
2. So all events are (tenselessly) past,
present and future, but at successive
3. But succession is a temporal notion.
4. So M’s analysis presupposes temporal
5. But the B-series is insufficient for time
– it is indistinguishable from space.
6. So, succession requires A-concepts.
7. Therefore, M’s analysis requires an A-
It follows that the A-series is conceptually
M’s analysis is wrong: it is incorrect to
analyze tensed concepts using
So what’s the correct analysis?
“Has been”, “will be”, “is”, etc. are
primitive and easily understood.
There is no reason to analyze them: M only
1. “E was present”
2. At a past time E is present
It just means:
3. E is past (no longer occurring).
There is no reason to analyze (1) as (2)
instead of (3).
If we refrain from analyzing them further,
there will be no regress.
Broad agrees with M that the B-series is not
But, he argues that:
There is no contradiction in the A-series.
The B-series requires the A-series.
There is only a regress if we analyze
tensed claims into tenseless ones.
Tensed claims are primitive and require
No contradiction, no regress.
More on Change
M argues that the A-series is required for
Consider regular change:
The chair changes from red to green.
Problem 1: how can something retain its
identity if it has different properties?
If you and I look at the same chair, that
is because the chair you see has all the
properties mine has?
If A is identical to B, then any property of
A must be shared by B and vice versa.
So a chair that changes colour must
become something different.
So, nothing can remain the same over time.
A solution: properties are really relations to
Red = Red at T1
Green = Green at T2
Since the chair is always red at T1 and
always Green at T2, then it has all the same
properties at both times and remains self-
But then, is this really change?
Broad defends the A-series: he thinks
past, present, future are part of reality.
Others agree that the A-series is
impossible, but still think time is real.
They adopt the B-series view of time:
The only temporal properties are earlier
than, later than, simultaneous with.
All events/times are equally real.
Change involves different properties
occurring at different times.
So the question is, is there really change
To think about:
Why can’t we describe change in a way that
doesn’t itself change?
Chair is red at T1
Chair is green at T2
These facts are always true: they never
But they describe change, i.e. different
things being true at different times.
If this makes sense, then M’s argument that
we need an A-series is invalid.