McTAGGART’S ARGUMENT

One metaphysical issue that has persisted for millennia is the nature of time (space):

  • What is time? What are its properties? Etc.?

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):

PastPresentFuture

Time passes

WaterlooMcTaggartlunch This lecture dinnerNext President

today

B-Series (“tenseless” view):

Earlier than

WaterlooMcTaggartlunch This lecture dinnerNext 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 change.
  1. 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, changes.

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.
  1. But if all that exists is the B-series, then if E1 is earlier than E2, it is always true that it is earlier.
  1. Thus E1 and E2 must always exist in the B-series (No truth without being, i.e. something to make it true).
  1. So, in the B-series, all events/times are equally real; they all have permanent B-relations.
  1. 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 Anne.

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-series.

Why think time is unreal?

McTaggart’s main argument:

  1. There can be no time without change.
  1. There can be no change without the A-series.
  1. But the A-series is contradictory.
  1. Therefore, there can be no change and hence time is unreal.

Why does he think the A-series is contradictory?

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, willbe 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 future’?

  • 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 future.

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, e.g.:

  • 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

Upshot

  • 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

Broad:

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, future)

E.g.:

  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 regress:

  • T2 is (tenseless) past, present and future, i.e.:
  • T2 is present, will be past and was future, that’s true.

So:

  • 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.

But:

  • 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 times.
  3. But succession is a temporal notion.
  4. So M’s analysis presupposes temporal concepts.
  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-series.

It follows that the A-series is conceptually basic!

Therefore:

  • M’s analysis is wrong: it is incorrect to analyze tensed concepts using tenseless ones.

So what’s the correct analysis?

Broad:

  • “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:

  1. At a past time E is present

It just means:

  1. 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.

Upshot

Broad agrees with M that the B-series is not temporal.

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.

Therefore:

  • No contradiction, no regress.

More on Change

M argues that the A-series is required for change.

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-identical.

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. How?

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 here?

To think about:

Why can’t we describe change in a way that doesn’t itself change?

E.g.:

  • Chair is red at T1
  • Chair is green at T2

These facts are always true: they never change.

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.

1