10  The Problem of Change

Material objects persist through change. One and the same leaf may be green in summer and red later in the fall. But nothing is both green and red, since these are incompatible qualities. How can one and the same object exemplify incompatible qualities?

Sally Haslanger spells out the problem more precisely in (Haslanger 2003):

Suppose I put a new 7-inch taper on the table before dinner and light it. At the end of dinner when I blow it out, it is only 5 inches long. We know that a single object cannot have incompatible properties, and being 7 inches long and being 5 inches long are incompatible. So instead of there being one candle that was on the table before dinner and also after, there must be two distinct candles: the 7-inch taper and the 5-inch taper. But of course the candle didn’t shrink instantaneously from 7 inches long to 5 inches long: during the soup course it was 6.5 inches long; during the main course it was 6 inches long; during dessert it was 5.5 inches long. Following the thought that no object can have incompatible lengths, we must conclude, it seems, that during dinner there were several (actually many more than just several) candles on the table in succession.

We seem to have an argument for the conclusion that there have been several candles on the table in succession:

  1. There is a 7-inch candle before dinner.
  2. There is a 5-inch candle after dinner.
  3. Nothing is both 7-inches and 5-inches long.
  4. There have been at least two candles during dinner.

But this is now how we would describe the situation, whereby one and the same candle has been on the table throughout dinner.

10.1 Four Presuppositions

Part of the problem is how to respond to the inconsistency of four common presuppositions involved in the assumption that objects persist through change:

Persistence One and the same object persists through change.
Proper Subject The proper subject of the attribution of incompatible qualities is the object to which the change applies.
Incompatibility Change involves incompatible qualities.
Non-Contradiction Nothing exemplifies incompatible qualities.

By Persistence:

  1. The candle before dinner and the candle after dinner are one and the same object.

By the Proper Subject Condition:

  1. The candle itself (as opposed to a temporal part or a further complex object) is the proper subject of the qualities being 7-inches long and being 5-inches long.

By Incompatibility:

  1. Being 7-inches long and being 5-inches long are incompatible qualities.

Finally, by Non-Contradiction:

  1. The candle does not exemplify incompatible qualities.

Since we have arrived at a contradiction, something must give. Perdurance and endurance suggest different avenues of response to the problem of change.

10.2 Perdurantist Change

Perdurantists deny the Proper Subject condition. The candle is a four-dimensional object, and it is not 5-inches or 7-inches long. It is only instantaneous temporal parts of the candle that exemplify the incompatible qualities.

From the perspective of a perdurantist, change is akin to spatial variation:

  • The candle varies in color from place to place because different spatial parts of the candle exemplify different colors.

  • The candle varies in length from time to time because different temporal parts of the candle exemplify different lengths.

Here is (Sider 2003), p. 2:

A person’s journey through time is like a road’s journey through space. The dimension along which a road travels is like time; a perpendicular axis across the road is like space. Parts cut the long way – lanes – are like spatial parts, whereas parts cut crosswise are like temporal parts. US Route 1 extends from Maine to Florida by having subsections in the various regions along its path. The bit located in Philadelphia is a mere part of the road, just as it is only a mere part of me that is contained in 1998.

A road changes from one place to another by having dissimilar sub-sections. Route 1 changes from bumpy to smooth by having distinct bumpy and smooth subsections. On the four-dimensional picture, change over time is analogous: I change from sitting to standing by having a temporal part that sits and a later temporal part that stands.

10.3 Endurantist Change

This is not open to those endurantists for whom the candle is a temporally extended simple. They deny, for example, that the candle has momentary temporal parts with different lengths. Endurantists tend to deny the Incompatibility condition.

There is, however, more than one way in which the relevant qualities may be made to be compatible.

10.3.1 Taking Tense Seriously

The A-theoretic approach takes tense seriously. The relevant attributions are tensed. Compare with McTaggart’s original puzzle. The A-theorist takes sense seriously in order to accommodate change from future to present to past. That is, we should distinguish between the fact that a moment of time will be present and the fact that it is now present, and the fact that it has been present. Likewise, for the A-theorist, we should distinguish between the fact that the candle will be 5-inches long, the fact that the candle is now 6-inches long, and finally, the fact that the candle has been 7-inches long. There is no incompatibility between those lengths provided their attribution is properly understood.

10.3.2 Relativizing to Times

The B-theoretic approach construes the qualities as relations to times. That is, you may be an endurantist even if you subscribe to the B-theoretic picture of time as a static fourth dimension of variation. You may now draw a distinction between the fact that the candle is 5-inches long at one time, and it is 7-inches long at another time.

David Lewis claims that the B-theoretic approach rests on a mistake in (Lewis 1986):

[Maybe] shapes are not genuine intrinsic properties. They are disguised relations, which an enduring thing may bear to times. One and the same enduring thing may bear the bent-shape relation to some times, and the straight-shape relation to others. In itself, considered apart from its relations to other things, it has no shape at all. And likewise for all other seeming temporary intrinsics… The solution to the problem of temporary intrinsics is that there aren’t any temporary intrinsics. This is simply incredible, if we are speaking of the persistence of ordinary things.… If we know what shape is, we know that it is a property, not a relation.

  • A quality is temporary if and only if it is had at some times but not others, e.g., being a student, being married, being bent, etc.

  • A quality is intrinsic if and only if it is had by a material object merely in virtue of the way the object is and not in virtue of the fact that it stands in certain relations to other objects, e.g., being round, being bent, etc. Intrinsic qualities are shared by duplicates.

Here is a route from temporary intrinsics to perdurance:

  1. Material objects change from being bent to being straight.

Change in shape is simply inconsistent with the thesis that (i) being bent and being straight are incompatible qualities, and the thesis that (ii) they are temporary intrinsics. So, one of (i) and (ii) have to be false:

  1. Either being bent and being straight are not temporary intrinsics or else they are not incompatible.
  2. Being bent and being straight are incompatible.

So, it follows by 2:

  1. Being bent and being straight are not temporary intrinsics.

There are two ways in which being bent could fail to be a temporary intrinsic. Therefore:

  1. Either being bent is not intrinsic or being bent is not temporary.

The perdurantist will insist that shape is instrinsic:

  1. If being bent is not intrinsic, then it is a relation to times.
  2. Being bent is not a relation to times.
  3. Being bent is intrinsic.

The last stage of the argument begins with an inference from 5 and 8 above:

  1. Being bent is not temporary.
  2. If being bent is not temporary, then it can only be instantiated by a temporal part of the object.
  3. So, there are temporal parts.

10.3.3 Adverbialism

There is one more option to consider. We have looked at two different relativization strategies:

  • relativize exemplification to temporal parts

  • relativize exemplification to times

But (Haslanger 2003) adds one more option to the menu:

  • relativize exemplification to ways

One and the same leaf could be green summerly and red fallenly. These are two different ways in which one and the same object can exemplify intrinsic qualities such as being green or being red.