A note on the transitivity of parthood

That parthood is a transitive relation is among the most basic principles of classical mereology. Alas, it is also very controversial. In a recent paper, Ingvar Johansson has put forward a novel diagnosis of the problem, along with a corresponding solution. The diagnosis is on the right track, I argue, but the solution is misleading. And once the pieces are properly put together, we end up with a reinforcement of the standard defense of transitivity on behalf of classical mereology. 1. Is parthood transitive? Classical mereology says it is. If x is part of y and y is part of z, then x is part of z—no matter what x, y, and z are. Indeed, on standard models of extensional mereology, parthood is isomorphic to set inclusion, and there is no question that the latter relation is transitive. Nonetheless, an increasing number of authors have been protesting that many legitimate senses of ‘part’ appear to violate this principle. Typical examples would include: (1) The handle is part of the door, which in turn is part of a house, but the handle itself is not part of the house. (2) The nucleus of a cell is not a part of the organ of which that cell is part. (3) An arm may be part of a musician who is part of an orchestra, yet no arm is part of an orchestra. (See [11, 7, 9], respectively). Authors who find such examples convincing have offered various accounts of the underlying phenomena. For example, it has been suggested that ‘part’ is context-sensitive [3], or that transitivity only holds relative to certain conditions [8], or that there really are several meronymic relations, only some of which are transitive [5], or again that each such relation can be meaningfully (and transitively) predicated only relative to entities of a restricted sort, such as individuals, groups, quantities, etc. [10, 14]. One way or the other, the failure of transitivity as a general part-whole principle would appear to have important philosophical ramifica-