On the transitivity of functional parthood

This paper aims to give an analysis of some aspects of the relation of “functional parthood”. Assuming there is such a concept as “. . . parthood” entails adopting the view that there are several part-whole relations. This view has been defended in linguistics (Lyons, 1977; Cruse, 1986) and psycholinguistics (Winston, Chaffin, & Herrmann, 1987; Iris, Litowitz, & Evens, 1988). It has been acknowledged as well in formal ontology (Simons, 1987; Casati & Varzi, 1999), even though this discipline focuses on mereology, that is, the study of general parthood. Functional parthood departs from general parthood in requiring that there is some sort of functional link between the part and the whole. This relation has been called in a number of ways, e.g., “componentintegral object” in Winston, Chaffin, & Herrmann (1987) or “functional component” in Iris, Litowitz, & Evens (1988). Most descriptions focus on the facts that the part “plays a role” in the whole and that both part and whole are conceived as “integral objects” – i.e., as presenting a clear unity due to a specific function and/or topological properties.1 Examples are usually given in the domains of artifacts (e.g., the engine is part of the car) or biological entities (this cell is part of the heart). In this paper, the discussion will be restricted to relations between material objects, as are biological organisms and many artifacts, although it is by no means clear that functional parthood does not apply to other ontological domains as well.2 My analysis of functional parthood (FP) follows the φ-part pattern introduced in Casati & Varzi (1999): FP(x, y) ≡ P (x, y) ∧ φ(x, y), that is, functional parthood is P , the mereological relation, restricted in some suitable way. A few comments on P are in order before we proceed. I will assume very few properties, so that there is no need here to specify which mereological theory I choose for P . I certainly need transitivity, but I do not use antisymmetry.3 On the other hand, for reasons that will