Wednesday, March 02, 2005

Composition: An External Relation or an Internal Relation or Neither?

CAUTION: You are about to enter a hard-core metaphysics zone.

Joseph Jedwab writes in the comments to this post:

Composition is a relation and the holding of every relation implies the existence of the relata: so if the xs compose y, then the xs exist and y exists. It follows that if the xs compose something, there is an entity the xs compose. And it also follows that if y is composed by some things, there are entities y is composed by.

Jedwab would have us conclude that if W is composed of P1 and P2, then there are at least three entities, P1, P2, and W. No doubt this is highly plausible, and will strike some as utterly self-evident; but let’s think about it. I propose to consider whether, and in what sense, composition is a relation. What I will argue is that composition is neither an external relation nor an internal relation, and that this casts doubt on its being a relation at all. If composition is not a relation, then one cannot argue that all the terms of this ‘relation’ exist on the strength of the fact that every relation implies the existence of its relata.

1. Composition is not an external relation. My coffee cup rests on a coaster which rests on my desk. Consider first the dyadic on top of relation the relata of which are the cup and the coaster. This is an external relation in the sense that both the cup and the coaster can exist and have the intrinsic (nonrelational) properties they have whether or not they stand in this relation. Removing the cup from the coaster need not induce an intrinsic change (a change in respect of an intrinsic property or change in existential status) in the cup or in the coaster. One could also put the point modally. In the actual world, the cup is on the coaster at time t. But there is a possible world W in which the cup is not on the coaster at t. In W, cup and coaster both exist and possess the same intrinsic properties they have in the actual world.

Now consider the triadic between relation that relates the members of the ordered triple . This relation is also external. The terms of the relation can exist and have the intrinsic properties they have whether or not they stand in the relation.

If composition were an external relation, then P1 and P2, on the one hand, and W on the other would both be such that they could exist and have the intrinsic properties they have whether or not the relation obtains. But this is not the case: W cannot exist unless P1 and P2 exist. If you balk at that, by denying mereological essentialism, then you must at least accept that no whole can exist without some parts or other. A whole cannot exist without some parts or other, but the entities that happen to be the parts of a whole can exist without the whole existing. So the parts of a whole cannot be externally related to the whole of which they are the parts. The parts compose the whole; but this composing is not an external relation.

2. Composition is not an A-internal relation. If a relation is not external, then it is nonexternal. One sort of nonexternal relation is an A-internal relation, where ‘A’ honors David Armstrong:

Two or more particulars are internally related if and only if there exist properties of the particulars which logically necessitate that the relation holds. (Universals and Scientific Realism, II, 85)

Consider two balls A and B. Each has the property of being red all over. Just in virtue of each being red, A and B stand in the same color as relation. This relation is internal in that the nonobtaining of the relation at a later time or in a different possible world would induce an intrinsic change in one or both of the balls. In other words, the two balls could not cease to be the same color as one another unless one or both of the balls changed color. But the two balls could cease to be ten feet from each other without changing in any nonrelational respect.

A-internal relations can be said to be founded relations in that they are founded in intrinsic (nonrelational) properties of the relata. Thus the relational fact of A’s being the same color as B decomposes into a conjunction of two nonrelational facts: A’s being red & B’s being red.
These nonrelational facts are independent of each other in the sense that each can obtain without the other obtaining.

Now if parts and whole are A-internally related, then there is a nonrelational property P such that the parts have P, the whole has P, and the relational fact of the parts composing the whole analyzes without remainder into a conjunction of two independent nonrelational facts: Parts having P & Whole having P. But these facts cannot be independent of each other. For if one obtains without the other, then there is no composition.

3. Composition is not a B-internal relation. To say that two or more particulars are B-internally related, where ‘B’ honors Bradley and Blanshard, is to say that there is no possible world in which the particulars exist but do not stand in the relation in question. Thus two B-internally related particulars cannot exist without each other. Each is essential to the other. Here is an example. Set S has five members essentially (as opposed to accidentally) , while set T has seven members essentially. These essential properties of S and T found the relation larger than that obtains between them. Although there are possible worlds in which neither set exists, there is no possible world in which both sets exists but fail to stand in the relation in question.

In sum, external relations are not founded in the nonrelational properties of their relata. A-internal relations are founded in accidental nonrelational properties of their relata. B-internal relations are founded in essential nonrelational properties of their relata.

Now it is easy to see that composition cannot be a B-internal relation. My pipe is composed of stem and bowl. Since there are times and possible worlds at which stem and bowl exist, but the pipe does not, it follows that the stem and bowl’s composing of the pipe cannot be a B-internal relation.

4. External in one direction, internal in the other? The parts are external to the whole in the sense that the parts can exist and have the nonrelational properties they have whether or not the whole exists. The whole is B-internal to the parts in the sense that the existence of the whole entails the existence of the parts (if not the precise parts that the whole has, then some parts or other). So can we say that composition is an external relation from parts to whole but a B-internal relation from whole to parts?

That strikes me as nonsense. For that would imply that composition is both unfounded and founded – unfounded as external and founded as B-internal. But I won’t argue this any further now but leave some work for tomorrow. I will simply conclude today’s Forschungsmanuskript with the following argument:

a. All and only genuine relations are ones whose obtaining implies the existence of their relata.
b. Every genuine relation is either external, A-internal, or B-internal.
c. Composition is neither external, A-internal, nor B-internal.
Therefore
d. Composition is not a genuine relation.
Therefore
e. Composition is not a relation whose obtaining implies the existence of its relata.
Therefore
f. (a) does not entail that a whole of exactly two proper parts is a third entity.

What say you, Joseph Jedwab? Will you reject (b) or will it be (c)? And why in either case?