Material Constitution and the Many-Many Problem

I Introduction

Amongst the virtues extolled within analytic metaphysics are universality and parsimony. We value an account of what there is that includes everything, and we want a metaphysics that not only excludes what there isn't, but that also avoids the vice of double-counting. This vice leads to redundancies in one's ontology, such as asserting or entailing that there are, for example, minds over and above matter (if one is a materialist in the philosophy of mind), or groups of people over and above the individual people in those groups (if one is an individualist in the social sciences). An ontological view must be sufficiently pluralistic to achieve universality or completeness, yet sparse enough to respect parsimony or non-redundancy.

Do constitution views in metaphysics, which hold that a person is constituted by her body, or a statue by a particular piece of marble, achieve these twin goals?² Critics have often charged that such views violate parsimony by positing spatially or materially coincident objects when there is simply one object (e.g., a body) that under certain circumstances has special properties (e.g., those that a person has) or to which we attach distinct descriptions (bodily-like and person-like descriptions). The dialectic between proponents and critics of constitution views here vis-à-vis parsimony is well-worn,³ but it has been conducted with little attention to the question of the universality or completeness of constitution views. Shifting our focus, however, reveals a largely unacknowledged and unexplored problem concerning the parsimony of those views, what I call the Many-Many Problem.⁴

II The Many-Many Problem

To illustrate this problem, and to see how it goes beyond standard objections to constitution views that appeal to parsimony, grant that a person is constituted by her body. In granting this, we are supposing that persons are not simply bodies in a certain state, and more generally that the familiar deflationary strategies for maintaining a 'one-thing' rather than a 'two-thing' ontology do not work.⁵ Then is that person also constituted by a certain aggregate of cells, by a particular causal network of bodily systems, or by a specific arrangement of elementary particles? If such entities exist, then each would seem to be spatially and materially coincident with, yet not strictly identical to, the person, much as the person's body is, and for the same reasons (e.g., Leibniz's Law arguments). The same questions can be posed with respect not simply to an entity and what constitutes it, but with respect to a given constituent and what it putatively constitutes. Consider a person's body, and assume that it constitutes a person. Does that body also constitute a living thing, a member of Homo sapiens, or a social agent, such as a prisoner? If such entities exist, then they appear to be spatially and materially coincident with, yet not strictly identical to, that body, much as the person is, and for the same reasons.

In the abstract, the problem is this: given that we are prepared to countenance pairs of coincident entities, precisely which entities exist to stand in a relation of constitution to one another? The relationship between any given entity (such as a person) and what constitutes it appears to be one-to-many. And the converse relationship between any given constituting entity (such as a body) and what it constitutes also appears to be one-to-many. Putting these together implies that constitution is a many-many relation, implying not just pairs of coincident entities but many, many such coincident entities in a given case, such as that of a person and her body, or a statue and the piece of marble that constitutes it. Since we are granting, with proponents of constitution views, the inadequacy of standard one-thinger responses to the claim that a person and her body are two coincident entities, we cannot simply appeal to such responses in addressing the Many-Many Problem. As we will see, this seriously constrains what a constitution theorist can say in addressing the Many...