This post will explain Van Cleve’s argument against the “commonsense” restricted composition view regarding the conditions under which a set of objects compose a whole. We will then evaluate Van Cleve’s argument, concluding that we have good reason to revise commonsense.
The commonsense, or restriction composition, view takes a middle road between asserting that “no objects ever form wholes” and asserting that “all objects always form wholes”. That is, objects sometimes compose objects, but not always. So there must be some rule or restriction which determines when objects compose wholes. To say that there is some rule of restriction is to say that a set of objects compose a whole iff those objects all stand in the right kind of relation (R) to each other. Van Cleve considers two candidates for this rule, R. (a) A set of objects compose a whole if they occupy a continuous region of space (i.e. are in contact or connected by a series of contact relations). For example, the pieces of wood compose a chair (a whole) if the pieces are connected to each other in the right way and not broken apart. (b) A set of objects compose a whole if they are “dynamically interconnected”. For example, the front end of my car is dynamically interconnected with the back bumper, insofar as wherever the front end of my car goes, the back bumper follows.
Van Cleve argues that any account which tries to create a rule of restriction to delineate parts and wholes (the “commonsense” view) ineluctably fails. Now we’ll explain Van Cleve’s general argument against restricted composition views. His conclusion is that if we must use some rule of restriction to ascertain R, then that rule must give rise to objectionable arbitrariness or objectionable vagueness.
Suppose that there are some collections of objects which compose wholes (like the collection of particles that compose the Sun) and that there are some collections of objects which do not (e.g. my left shoelace and a bust of Alexander the Great do not form a whole). If so, then there are cases where composition occurs via forming a continuous region of space (again, like the particles which compose the Sun). But consider these regions: they’ll all be adjacent to or connected with objects that purportedly do not constitute wholes. For, something is either a whole or is not – the only objects that the set of all continuous wholes could come into contact with [besides each other] are those objects which do not compose wholes.
But there doesn’t seem to be a distinct “cut-off point” that delineates the continuous compositional objects from those objects that are not wholes. There is no boundary that we can point to and say that the objects to left make a whole, but the objects to the right do not. Consider the black-white spectrum. Black transitions to grey, grey transitions to white, but there is no unique point where you can say, “here, this is the point where it is no longer black but grey”. While, you can tell which end is the black end and which the white, you couldn’t define the point at which black becomes grey.
It is always determinate whether a collection of objects forms a whole. That is, statements of the form “these objects make that whole object” are always strictly true or false. If this were not so, then mereological assertions would be objectionally vague. For what could it mean to say “these objects kinda sorta, or perhaps maybe, constitute that thing”? They either sum up to that thing or do not.
If there is always a fact of the matter as to whether some objects compose a whole, but there does not exist a definite cut-off point between those which compose wholes and those which don’t, then either any collection of objects compose some whole, or no collection of objects composes some whole. That is, there is no “middle road”. How does this follow? If there exists no definite cut-off point between all the many and various objects, then R holds between all those objects or R holds between none of them. If the former, then any collection of those objects are related by R and form a whole. If the latter, then any collection of those objects are not related by R and do not form a whole. If R held between some of the objects, but not all, then there must be a definite cut-off point, but we showed that there is not.
Why does this constitute a revision of commonsense? Because in addition to the atoms, cells, and neurons that compose you as a whole object, there are also whole objects that are composed of the collection of pennies on my desk and the moon. For as we showed, any collection of objects must form some whole. While it may sound counterintuitive to admit an object composed the pennies on my desk and moon, it is not actually so. We are not saying that there exists a material object that, for example, we could hold which is composed of the pennies and the moon. Rather, both the pennies and the moon exist, and taking them together as a system or whole of some kind can be done just as legitimately as taking the cells and neurons together and considering that system or whole they compose (namely, you).
We might wonder whether Van Cleve’s mereological universalism commits us to an explosion of reality, that is, an unnecessary proliferation of the real existences like in Aristotelian mereology. In Aristotelian mereology, Fred the spherical snowball is one object, but when Fred is flattened, he becomes a new object, because the form of his composition has changed – this view adds an indefinite number of entities to the world, without good reason. What, on Van Cleve’s picture, limits the number of entities in the world? Van Cleve subscribes to two “plausible” philosophical principles, (1) two or more things cannot be in the same place at the same time and (2) there cannot be a difference of entities without a difference in content. For Van Cleve, the content of Fred (the matter composing him), and the content of Fred after he’s flattened, are the same, for the material constituents being considered as a whole are all the same – in this way, there is only one Fred, not an indefinite number of Fred’s depending on form. We consider the matter composing the whole without considering the form or the arrangement of the matter – for there is an indefinite number of arbitrary arrangments we could ascribe to any material collection, so consequently if form were taken into consideration we would end up with an explosion of reality.
Van Cleve’s argument concludes that any collection of objects forms a whole or no collections of objects form a whole. If you hold the latter view, then you’ll think that there are fundamental entities whose existence is real, and then ordinary entities like tables whose existence is nominal – that is, when I say “a table exists” I am really saying that “these particles are arranged in a table-like fashion”. But this is not the revision of commonsense that Van Cleve is proposing. For suppose there are no simple entities, we can indefinitely break particles into smaller and smaller pieces. Then tables, and everything else, are in fact nominal entities, for they are always composed of something more fundamental which we just use linguistic shorthand for. For all entities to be nominal is absurd, because then all entities are fictionalized.
Van Cleve relies on the premise that it is always determinate whether a collection of objects forms a whole. You might try to reject this along the following lines. If I have a pile of 500 grains of sand, and continue to add one grain at a time, at what point does the pile become a heap? It is not clear whether this collection of objects forms that heap of sand. Or consider the black-white spectrum: it is not clear where black becomes grey. Doesn’t this mean that it is not determinate whether a collection of objects forms a whole? And, if so, then there doesn’t need to be a distinct cut-off point delineanating wholes and Van Cleve is not entitled to his conclusion.
This reply confuses semantic vagueness with metaphysical vagueness. Whether the grains of sand are a heap or pile is semantic vagueness – there is nothing vague about the physical grains or their collection. All those grains of sand form the total of those grains of sand – whether we choose to call it a pile or a heap has no effect on any of the actual properties of the collection of sand. Disagreement in whether it is a pile or heap is disagreement in language, in what we choose to call a heap – but everyone sees the same collection of sand, the same whole. The same applies to the black-white spectrum. When black becomes grey is going to be a semantic judgment made by a variety of people. But the shade is still whatever shade that it is, and together they still form the spectrum that they do. Nothing about the spectrum itself is indeterminate or vague – only our judgments thereof.