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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
about time:

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
   never later.

Picturing the two series

A-Series (“tensed” view):

Past                         Present                      Future

                                    Time passes

Waterloo   McTaggart lunch    This lecture dinner   Next President

B-Series (“tenseless” view):

                     Earlier than

Waterloo   McTaggart lunch    This lecture   dinner Next President

                     Later Than

Question is, which one correctly describes time?

McTaggart’s claim:

  The A-series is essential to time—
   without it there could be no time.

His argument:

 1. Change is essential to time, i.e. if
    there were no change, there would be
    no time.
 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
with T2.

  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
real change.

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?

McTaggart: No.
  It was, is and will be a death.
  It was, is and will be the death of a
   monarch, etc.

There is one way it could change:

  From future, to present to past

Conclusion: There is only change if there is
an A-series.

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
higher level:

  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.

Alternative understanding

 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)
  Directionless
  Indistinguishable from space

But time  space, therefore:

  B-series  time

It follows that any temporal concept must be
an A-series concept.

  Since the B-series is not time, only the
   A-series remains.

But M is wrong: there is no contradiction in
the A-series.

  Why not?
The copula (“to be”, “is”)

Tensed copula:
  “It is raining”.
  Equivalent to “It is now raining”.
  Says something currently occurs.

Tenseless copula
  “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
   is future”

Note: “is” must be tenseless, otherwise:

  At some past time, E is (now) future!

Broad notes:

If we follow this analysis, then we get a

  T2 is (tenseless) past, present and
   future, i.e.:
  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

Broad argues:

 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
   tenseless ones.

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
confuses things.

 1. “E was present”

Doesn’t mean:

 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 analysis.


  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?

Leibniz’s Law:

  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
times. I.e.:
   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?

Two views

  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.

  Why not?

If this makes sense, then M’s argument that
we need an A-series is invalid.