AGAINST FOUR-DIMENSIONALISM
Quine/Lewis: time is a fourth dimension, not
intrinsically different from space.
Geach: But then there really isn’t change.
 Time slice 1 is P; TS2 is ~P.
 Analogous to: spatial part 1 is P; SP2 is
~P.
 No change on latter, so none on former.
 So, time is really an illusion.
4-D Reply: Considered from the 4-D
perspective, the universe is unchanging.
 However, our perspective on this
unchanging reality changes (Smart).
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Geach: My experience changes:
 I have E (I am hungry) and E* (I am full).
 These are incompatible.
 This is only possible if my experience
changes from E to E*.
So, the 4-D view entails that there is real
change, so real time, in the world.
Compare: If I think I am happy, then I am in
fact happy.
Geach: perhaps we can think of minds as
outside the physical world—“scrolling” along
changeless reality.
 Hence, mental change is not real
change.
Problems:
 Requires dualism.
 Entails fatalism: our minds can only
observe the future, can’t influence it.
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Problems with temporal parts
Geach: temporal parts are distinct “objects”.
 E.g., the ship-at-T1 is not identical to the
ship-at-T2.
It follows that:
 McTaggart-at-1901 is a distinct “object”
from McTaggart-at-1921.
That’s how the following can be true:
A. McTaggart believed in Hegel’s
dialectic in 1901 but not in
1921(according to 4-D-ism).
Geach: “believing in Hegel’s dialectic” is a
property of a philosopher, not a part of a
philosopher.
So, either there are two philosophers here,
or A is in fact a contradiction (it attributes
incompatible properties).
 Both options are absurd.
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Retrenching
4-D-ist: perhaps we could eliminate regular
properties in favour of some that are
appropriate for time slices
Geach: Time slices were introduced
because of regular but incompatible
properties.
 Having introduced time slices, you now
want to eliminate the properties you
started with.
 This undercuts what motivated your
argument in the first place.
But can we avoid commitment to temporal
slices and 4-D-ism?
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Temporary intrinsics and presentism
Temporary intrinsic property: a property that
an object has for a particular duration that is
intrinsic to the object.
Problem: Right now I have a particular
intrinsic property: I have a straight shape.
 Later, I sit down. Now I have another
intrinsic property: a bent shape.
 But these are incompatible properties:
nothing can be intrinsically both bent
and straight.
Conclusion: it is impossible for me to stand
up and sit down.
But we know this is false. The question is
why? What’s the solution to the “problem of
temporary intrinsics”?
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Solutions
Solution 1: Properties are relations
 E.g. shape is not an intrinsic property.
 An object is not simply bent or straight
 Rather, an object is bent-at-T1 and
straight-at-T2
 These are compatible
Solution 2: Presentism
 Other times don’t exist
 The only properties you have are those
you have now
 Nothing is both bent and straight: you
are only (now) one or the other
Solution 3: Temporal parts
 One temporal slice of you is intrinsically
bent
 Another is intrinsically straight
 These are compatible
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Lewis
 Solution 1 entails there are no intrinsic
properties (except those that persist for
all time). This is surely false: red, bent,
etc. are intrinsic properties.
 Presentism is absurd (we’ll look at his
argument shortly).
 Therefore, we must accept 3 (it’s
consistent with B-series anyways).
I.e.: the problem of temporary intrinsics
shows us that:
 Objects are 4-dimensional (with
temporal parts)
 B-series time is true: one can’t limit
reality to just one time.
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Against presentism
Lewis: The following is obviously true:
(PC) There are (at least) two different times;
one at which I am bent, another at
which I am straight.
 But, presentism denies this: it says there
is only one time (the present).
Since (PC) is true, presentism is false.
But: Why believe (PC) is true?
Lewis:
(1) We all say, “I was bent at one time,
straight at another”.
(2) This ontologically commits us to the
existence of non-present time. I.e.,
such claims are true and can only be
true if more than one time exists (one
at which I am S, the other at which I
am B).
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Paraphrase
Suppose you say:
(1) There is a dearth of Champaign in the
fridge
(2) There is a way to beat Gary at chess
(3) Many different outcomes of WWII
were possible
Suppose these are all true. What are the
ontological commitments of (1)-(3)?
 If you think (1) is true, must you believe
dearths exist?
 If you think (2) is true, must you believe
in ways?
 If (3) is true, must you believe possible
events exist?
Zimmerman: No. You needn’t believe any
of this. You just need to find a paraphrase
of the original statements that is true
(enough) to their meanings but avoids
reference to troublesome entities.
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For example, we can paraphrase (1) as:
(1’) There is no Champaign in the fridge
 In this way, we preserve the meaning
without implying that there is something
in the fridge. Note: the claim is still true.
Similarly:
(2’) Gary is not a perfect chess player
 In other words, one can beat him, which
is what (2) claims.
(3’) Some alternate descriptions of how the
war ended are consistent with how it
was fought
 That is, the claim is about actual
descriptions, not possible events.
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Misleading language
Our normal ways of talking sometimes
mislead us.
 We sometimes appear to commit
ourselves to the existence of something
when in fact we are not so committed.
 We don’t have to refer to things like
dearths, ways and possible events.
Zimmerman: The same applies to talk about
the non-present.
 The presentist thinks that talk about the
future/past is literally talk about what
doesn’t exist.
 It is like talking about dearths or ways.
 The presentist aims to paraphrase such
language so that it doesn’t actually refer
to the non-present.
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Upshot
Zimmerman: Lewis assumes that
presentism is false because we all refer to
non-present times in true statements.
 But he hasn’t shown that the presentist
is unable to paraphrase such reference
away.
 Until he has shown that, his argument
against presentism is not decisive.
Presentism remains one way out of the
problem of temporary intrinsics.
Problem: Nobody has succeeded in such
paraphrase.
Zimmerman: There are some promising
approaches out there: let’s give them a
chance.
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Summary
An apparent dilemma:
1. Objects are 3-D
2. Objects retain their (strict) identity as
they change (gain/lose parts) in time.
3. Leibniz’s Law
If 3, then not both (1 and 2)
Solutions:
Chisholm/Arnauld/Nicole:
 2 is false – change destroys identity
 Identity is a convention (overlap, etc.)
adopted to relate (strictly) different 3-D
objects.
Quine/Lewis/Smart:
 1 is false: Objects are 4-D
 They never gain/lose parts
 Therefore, identity is preserved
 Change = different temporal parts have
different intrinsic properties.
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Zimmerman/Prior:
 Objects are 3-D (can’t be spread out in
time)
 Objects are wholly present each time
they exist
 They only ever have present properties.
 So, incompatible properties are
impossible.
 As soon as P exists, ~P doesn’t exist.
 This is change.
 What remains identical from T1 to T2?
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Relationalism: An overlooked solution?
All properties are relations (to times):
 Objects are 3-D, not spread out in time.
 Change = object has different relational
properties (at all times).
 Hence, strict identity is preserved:
 O has: [(P at T1) & (~P at T2) & (Q at
T3) & (~Q at T4) & …]
Strengths of this view:
 Objects are 3-D
 Objects survive.
 Consistent with B-series (relations to
different times).
 Respects Leibniz’s Law:
o O at all times has all the same
properties.
o It is always P at T1 and ~P at T2,
etc.
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Objections to relationalism
Geach: properties such as “P-at-T” are
derivative.
 Our primitive temporal concepts are “X
(and Y) is (are) happening now”.
 I.e., we learn about time by learning that
different things can happen together,
now.
 Before we know this, we can’t learn to
tell the time.
 Other languages mark this difference
more clearly—English misleads us (“at
the same time” = “happening now”).
So temporal concepts like “P-at-T” are
based on our understanding of “now”, and
the latter can’t be replaced by the former.
 Physics can’t deny this, for even
physicists have to base their
observations on their most basic
concepts.
 Compare to Broad’s view.
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Paraphrase
Geach: It is easy to replace talk of events—
Queen Anne’s death—with talk of objects—
Queen Anne died.
 Indeed, we should avoid talking about
events as if they were objects.
“Queen Anne’s death” cannot name an
object
 It is possible to doubt whether Queen
Anne died.
 It is not possible to doubt whether an
object.
So it is foolish to try to replace talk of people
and objects with talk of collections of
events.
 I.e., we are not 4-D spacetime worms.
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Space and time differ
Spatial terms: join names of objects.
 E.g. Tom is to the left of Joe.
It seems we can do the same with temporal
terms:
 X and then Y.
 This way it seems that “X” and “Y” name
entities, events, just as “Tom” and “Joe”
name objects.
Geach: this is misleading; there is a logical
difference between the two cases.
 We can iterate temporal clauses, but not
spatial ones:
 While Z (X and then Y) is logical.
 Bill is between (Tom is to the left of Joe)
is illogical.
Moral analogy: I can prevent someone from
attending a meeting by changing its date or
by locking him in a room.
 Temporal barriers ≠ spatial barriers.
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Conclusion
Geach’s position can be summed up as
follows:
 Our basic understanding of time is
based on concepts such as “when”,
“now”, “and then”.
 These differ logically from spatial
concepts.
 So our basic understanding of time
differs from that of space.
 All investigations into the world
presuppose these basic understandings.
 So, it is illegitimate to conclude that time
is just like space, a fourth dimension.
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