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).

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.

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:

  1. 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.

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?

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”?

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

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.

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).

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.

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.

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.

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.

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.

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?

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 at all times has all the same properties.
  • It is always P at T1 and ~P at T2, etc.

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.

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.

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.

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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