Compositional and non-compositional trope theories

There are two kinds of trope theories: Those on which the tropes are parts of the particular object—call these “compositional” trope theories—and those on which the relation between the object and its tropes is not a whole-to-part relation. Compositional trope theories have an initial advantage over non-compositional ones: they have no need to introduce a new relation to join objects to their tropes.

But this is only an apparent advantage. Consider this old argument. Assume compositional trope theory. Suppose my toe is blue. Then its blueness trope is a part of the toe, which is in turn a part of me, and so the blueness trope is a part of me. Hence I am blue.

Of course, the compositionalist has an answer to this argument: there are two different kinds of parthood here. The toe is, as the medievals would say, an integral part of me. And the blueness trope is a non-integral part of the toe. Transitivity holds for integral parts. It may or may not hold for non-integral parts, but it certainly doesn’t hold across types of parthood: if y is an integral part of x and z is a non-integral part of y, it does not follow that y is any kind of part of x.

But notice now that the compositionalist has lost the main advantage over the non-compositionalist. The compositionalist’s initial advantage was not having to introduce a new kind of relation over and beyond the familiar composition relation. But the familiar composition relation was the one between wholes and integral parts, and our compositionalist now has to introduce a new relation over and beyond that. Granted, it is a new relation of the same type as the familiar one. But this actually makes the compositionalist’s theory more complicated. For now the compositionalist has two relations, integral composition and non-integral composition, plus a new relation type, composition. But the non-compositionalist need only have two relations, integral composition and the object-to-trope relation. These two relations don’t need to have a new relation type to fall under. In other words, the non-compositionalist has only one mystery in her theory—what is the object-to-trope relation—while the compositionalist has two mysteries—what is the object-to-trope relation and what is the type composition.

The same point applies more generally to compositional ontologies versus relational ontologies.