Can a Bundle Theory Accommodate Change?

0.  Peter L. has been peppering me with objections to bundle theories.  This post considers the objection from change.

1. Distinguish existential change (coming into being and passing out of being) from alterational change, or alteration.  Let us think about ordinary meso-particulars such as avocados and coffee cups.  If an avocado is unripe on Monday but ripe on Friday, it has undergone alterational change: it has changed in respect of the property of being ripe.  One and the same thing has become different in respect of one or more properties. (An avocado cannot ripen without becoming softer, tastier, etc.)  Can a bundle theory make sense of an obvious instance of change such as this?  It depends on what the bundle theory (BT) amounts to.

2. At a first approximation, a bundle theorist maintains that a thing is nothing more than a complex of properties contingently related by  a bundling relation, Russellian compresence say.    'Nothing more' signals that on BT there is nothing in the thing that exemplifies the properties: there is no substratum (bare particular, thin particular) that supports and unifies them. This is not to say that on BT a thing is just its properties: it is obviously more, namely, these properties contingently bundled.  A bundle is not a mathematical set, a mereological sum, or a conjunction of its properties.  These entities exist 'automatically' given the existence of the properties.  A bundle does not. 

3.  Properties are either universals or property-instance (tropes).  For present purposes, BT is a bundle-of-universals theory.  Accordingly, my avocado is a bundle of universals.  Although a bundle is not a whole in the strict sense of classical mereology, it is a whole in an analogous sense, a sense sufficiently robust to be governed by a principle of extensionality: two bundles are the same iff they have all the same property-constituents.  It follows that the unripe avocado on Monday cannot be numerically the same as the ripe avocado on Friday.  And therein lies the rub.  For they must be the same if it is the case that an alteration in the avocado has occurred. 

So far, then, it appears that the bundle theory cannot accommodate alterational change.  Such change, however, is a plain fact of experience.  Ergo, the bundle theory in its first approximation is untenable.

4.  This, objection, however, can be easily met by sophisticating the bundle theory and adopting a bundle-bundle theory.  Call this BBT.  Accordingly, a thing that persists over time such as an avocado is a diachronic bundle of synchronic or momentary bundles.  The theory then has two stages.  First, there is the construction of momentary bundles from universals.  Then there is the construction of a diachronic bundle from these bundles. The momentary bundles have properties as constituents while the diachronic bundles do not have properties as constituents, but individuals.  At both stages the bundling is contingent: the properties are contingently bundled to form momentary bundles and these resulting bundles are contingently bundled to form the persisting thing.

Accordingly, the unripe avocado is numerically the same as the ripe avocado in virtue of the fact that the earlier momentary bundles which have unripeness as a constituent  are ontological parts of the same diachronic whole as the later momentary bundles which have ripeness as a constituent.

5. A sophisticated bundle theory does not, therefore, claim that a persisting thing is a bundle of properties; the claim is that a persisting thing is a bundle of individuals which are themselves bundles of properties.  This disposes of the objection from change at least as formulated in #3 above.

6. BBT also allows us to accommodate the intuition  that things have accidental properties.  On the proto-theory BT according to which a persisting thing is a bundle of properties, it would seem that all properties must be essential, where an essential property is one a thing has in every possible world in which it exists.    For if wholes have their parts essentially, and if bundles are wholes in this sense, and things are bundles of properties, then things have their properties essentially.  But surely our avocado is not essentially ripe or unripe but accidentally one or the other.  On BBT, however, it is a contingent fact that a momentary bundle MB1 having ripeness as a constituent is bundled with other momentary bundles.  This implies that the diachronic bundle of bundles could have existed without MB1 and without other momentary bundles having ripeness as a constituent.  It therefore seems to follow that BBT can accommodate accidental properties.

7. That is, BBT can accommodate the modal intuition that our avocado might never have been ripe.  But what about the modal intuition that, given that the avocado is ripe at t, it might not have been ripe at t?  This is a thornier question and the basis of a different objection that is is not defused by what I have said above.  And so we reserve this objection for a separate post.

Comments

[Steven]

BV said: "On BBT, however, it is a contingent fact that a momentary bundle MB1 having ripeness as a constituent is bundled with other momentary bundles. This implies that the diachronic bundle of bundles could have existed without MB1 and without other momentary bundles having ripeness as a constituent. It therefore seems to follow that BBT can accommodate accidental properties."

I wonder if bundles of the sort you are speaking of can have contingent parts. After all, if a bundle of universals has its parts essentially, then how could a bundle of bundles of universals have its parts non-essentially? It is equally a bundle; what difference is there between the first-order bundle (of universals) and the second-order bundle (of bundles)?

Try to think of it this way. Say that in α a bundle of bundles B has as parts B1, B2, B3, etc. And your suggestion is that B could have had different bundles than it did in fact. But, since the bundles of which B is a bundle cause the existence of each other (B1 at t1 causes the existence of B2 at t2, and so on), to change any one of the parts, it seems, would result in radical changes in the later parts.

Suppose the bundle is your avocado, and the part that allegedly could have been unripe is B1. Of course, if B had a different part than B1 at t1 in some possible world W (as opposed to what it did have in α), then it would have had different parts at t2, t3, and so on until the end of the bundle's existence; but why would you have any inclination to call this the same bundle?

If you were to compare the bundles across possible worlds, B-in-α would not resemble B-in-W at all. Nothing would be the same, possibly. Why would you call this the same thing?

[Bill Vallicella]

Very good. That objection occurred just as I was uploading the post.

I agree that if first-order bundles (synchronic bundles) have their parts essentially,then second-order bundles (diachronic bundles) have their parts essentially. I think I gave the wrong argument for the right conclusion.

The question is whether the bundle theorist is forced to say that the avocado has the property of being ripe essentially. He is if he adopts the proto-theory, BT. But on BBT only some of the temporal parts of the avocado have ripeness essentially as a constituent. And if a thing has a property only some times during its existence, then that property is not essential to it.

[Steven]

"The question is whether the bundle theorist is forced to say that the avocado has the property of being ripe essentially. He is if he adopts the proto-theory, BT. But on BBT only some of the temporal parts of the avocado have ripeness essentially as a constituent. And if a thing has a property only some times during its existence, then that property is not essential to it."

Well, it wouldn't be strictly speaking accurate to say that the avocado has the property at a time; what does have the property at a time is some bundle that exists at that time, and that particular first-order bundle is itself a part of the larger bundle that is the avocado.

Even if it is proper to say that the avocado has the property of being ripe, which isn't obvious to me, it is nonetheless essential to the avocado that it have the property of being ripe at t, where t designates the time at which some temporal part of the avocado has the property of being ripe. And perhaps it is the having of this temporally-indexed property as essential to it that is problematic about the bundle theory. After all, you say something along these lines: "My avocado is ripe now at t, but it didn't have to be." What else could you be saying except that the bundle of bundles, the avocado, has a temporally indexed property being ripe at t but it didn't have to? And it is precisely the "it didn't have to" part that seems false.

[Steven]

Let me be as clear as I can.

The objection is that if concrete particulars are bundles, then they have all their properties essentially and hence there is no room for accidental properties. The response is that concrete particulars are really bundles of bundles, and since only some of the bundles composing the second-order bundle have a specific property, then the whole second-order bundle does not have that property essentially.

My first point was (i) it wouldn't be strictly speaking accurate to speak of the second-order bundle as having a property F, if one of the bundles that compose it has as a constituent F-ness. My second point was (ii) even if it did make sense to speak of the whole second-order bundle has having the properties of its constituents, it would still be the case that it has temporally indexed properties like being F at t essentially, because (a) its temporal part at t is F and (b) the temporal part at t is essential to the second-order bundle. So this suggestion doesn't seem to get us anywhere.

You say in your post, "On BBT, however, it is a contingent fact that a momentary bundle MB1 having ripeness as a constituent is bundled with other momentary bundles. This implies that the diachronic bundle of bundles could have existed without MB1 and without other momentary bundles having ripeness as a constituent."

I think I would respond to this as follows. It doesn't follow from the fact that The second-order B has as a temporal part B1 is contingently true that therefore it is non-essential to B that it have B1. That italicized proposition may be contingently true, and perhaps is false in worlds where B doesn't exist, but that has no tendency to show that B1 is not essential to B.

Suppose we adopt a counterpart theory, i.e. deny transworld identity, and further accept 4Dism about concrete particulars. It would be a contingent truth that some particular spacetime worm SW have as a temporal part SW-at-t (this wouldn't be true in possible worlds in which SW doesn't exist), but it doesn't follow that SW-at-t isn't essential to SW.

[Steven]

Sorry for the triple post!

In support of my intuition in (i) that it wouldn't make sense to speak of the second-order bundle has having the properties that its constituent bundles have, consider the following analogy.

Suppose I am a three-dimensional object with spatial parts. Of course, one of my spatial parts will be a particular electron which would be a part of a particular atom composing me; further, this electron would have the property of being a certain charge. It makes no sense, however, to speak of me being such that I am a particular charge. Or consider some spatial property of that electron (being a certain distance from another electron composing me); obviously, I wouldn't also have that property.

So also, just because some particular bundle acting as a constituent of a second-order bundle has some property, it doesn't mean that the second-order bundle itself has that property. In fact, it probably makes no sense to speak that way. So also, continuing with the story in your post, it doesn't make sense to speak of the avocado as being ripe or not, just because some of its constituent bundles have that property, because the avocado itself is a bundle of bundles.

[David Brightly]

Bill,

Is there not an analogous problem with regard to spatial variation? Different spatial parts may be different colours. One might deal with this by postulating a complex universal of the form 'red here, blue there, etc,' though this might be seen as rather ad hoc. Perhaps a more promising approach is to say that a momentary bundle is actually a bundle of spatially located bundles. So we get a bundle-bundle-bundle theory. But now a problem arises: do we bundle spatially first, then temporally, or do we bundle temporally first, then spatially. Is our particular a temporal stack of spatial discs or is it a spatial sheaf of temporal worms? Presumably the order of bundling commutes, but if this is the ontological structure of a particular, rather than an analysis of how we might describe it, then one might expect it to be one rather than the other, and yet there seems no reason for breaking the symmetry either way?

[Bill Vallicella]

David,

I am not clear what your problem is. The post deals primarily with change, one and the same thing's having incompatible properties at different times. The question is: How is this possible on BT? Are you thinking of something that might be called 'spatial change': one and the same thing's having incompatible properties at different places? Why would that be a problem?

[David Brightly]

Hi Bill,

I may be rushing ahead. Can I take a step back and ask how the bundle theory would accommodate spatial variation? For example, a ball that's red in one hemisphere and blue in the other?

[Bill Vallicella]

David,

Why can't I just say that each hemisphere is its own bundle of universals? I am having trouble understanding why there should be a problem with a thing having incompatible properties at different places.

[Bill Vallicella]

Steven,

If an avocado is a diachronic bundle of synchronic bundles, and the avocado is F at t, then the diachronic bundle is F in virtue of one of the synchronic bundles containing F-ness, namely the t-bundle. Now if only some of the synchronic bundles contain F-ness, then F-ness cannot be essential to the avocado.

But I grant that this still leaves the bundle theorist with a problem, the problem of explaining how it is possible for a thing which is F at t to not be F at t given that synchronic bundles have their constituents essentially.

[David Brightly]

Bill,

As I understand it the proposal is to accommodate change over time by saying that an enduring particular is a diachronic bundle of momentary bundles of universals. And to accommodate variation in space we will say that the momentary bundles are bundles of individuals that are themselves bundles of universals. So we have three levels of bundling. The first level bundles universals into individuals 'fixed' in time and space. The second level bundles these individuals into individuals that vary in space but are fixed in time. The third level bundles these momentary particulars into fully-fledged enduring particulars that vary over time. But I claim that we can interchange the order of the temporal and spatial bundlings and get the same result. On this view the first level of bundling of universals into individuals fixed in time and space is as before. The second level of bundling produces diachronic individuals fixed in space, and the third level gives us particulars varying in time and space.

If we drop down to two spatial dimensions we can visualise the difference geometrically in a space-time diagram, with space in the horizontal and time running vertically upwards. Consider as the particular a disc consisting of two semi-discs whose colours may change over time. The first view bundles two spatial semi-discs at each moment in time and then bundles the resulting discs into a cylinder. So the cylinder is a stack of discs of semi-discs. The second view bundles a stack of semi-discs at each of two places into a semi-cylinder (like a log split longitudinally) and then bundles the two semi-cylinders into a cylinder.

To have this ambiguity at the heart of an account of the ontology of particulars strikes me as unsatisfactory, yet I can't find a good reason for choosing one view over the other.