Online research in philosophy

A scientific explanatory project, part-whole explanation, and a kind of science, part-whole science are premised on identifying, investigating, and using parts and wholes. In the biological sciences, mechanistic, structuralist, and historical explanations are part-whole explanations. Each expresses different norms, explananda, and aims. Each is associated with a distinct partitioning frame for abstracting kinds of parts. These three explanatory projects can be complemented in order to provide an integrative vision of the whole system, as is shown for a detailed case study: the tetrapod limb. My diagnosis of part-whole explanation in the biological sciences as well as in other domains exploring evolved, complex, and integrated systems (e.g., psychology and cognitive science) cross-cuts standard philosophical categories of explanation: causal explanation and explanation as unification. Part-whole explanation is itself one essential aspect of part-whole science.

In this paper, I present an Aristotelian solution to the problem of material constitution. The problem of material constitution arises whenever it appears that an object a and an object b share all of the same parts and yet are essentially related to their parts in different ways. (A familiar example: A lump of bronze constitutes a statue of Athena. The lump and the statue share all of the same parts, but it appears that the lump can, whereas the statue cannot, survive radical rearrangements of those parts.) I argue that if we are prepared to follow Aristotle in making a distinction between numerical sameness and identity, we can solve the problem of material constitution without recourse to co-location or contingent identity and without repudiating any of the familiar objects of common sense (such as lumps and statues) or denying that these objects have the essential properties we ordinarily think that they have.

Although Aranyosi's claim that McTaggart's "set of parts" is a set rather than a fusion is correct, his attempt to restate McTaggart's conception needs revision. Aranyosi argues that "the fusion of cats is identical with the fusion of all cat-parts, 'regardless of whether all cat-parts are parts of cats or not.'" Fusions have unique decompositions into what David Lewis calls "nice parts." Cats are nice parts of cat fusions, as are maximal spatio-temporally connected parts. Part of Aranyosi's argument fails when it deals with cats; part of it fails when it deals with maximal spatio-temporally connected parts. He does not identify one kind of nice part that allows his whole argument to go through.

An axiomatic treatment of the relation part of is shown to lead naturally to an account of the ways in which parts of things are matched. The determination of matchings by the properties of parts and by the relations between parts is discussed and shown to be relevant to certain classificatory problems in science. The connexions between matchings and symmetries of parts are explored, and a general account is given of the ways in which ambiguities in the matching of parts may be resolved.

Philosophical questions concerning parts and wholes have received a tremendous amount of the attention of contemporary analytic metaphysicians. In what follows, I discuss some of the central questions. The questions to be discussed are: how general is parthood? Are there different kinds of parthood or ways to be a part? Can two things be composed of the same parts? When does composition occur? Can material objects gain or lose parts? What is the logical form of the parthood relation enjoyed by material objects?

1. Universalism (also known as Conjunctivism, or Collectivism) is the thesis that mereological composition is unrestricted. More precisely: (U) Any non-empty collection of things has a fusion, i.e., something that has all those things as parts and has no part that is disjoint from each of them.1 Extensionalism is the thesis that sameness of composition is sufficient for identity. More precisely: (E) No two things have exactly the same proper parts (unless they are atomic, i.e., have no proper parts at all). Clearly these two theses are not equivalent. They are, however, more closely related than one might think. For while (E) does not entail (U), the converse entailment holds —or so I will argue. More precisely, the entailment holds as long as it is agreed that the following postulates are constitutive of the meaning of ‘part’: (1) Transitivity: Any part of any part of a thing is itself part of that thing. (2) Supplementation: Whenever a thing has a proper part, it has at least another part that is disjoint from the first. 2. One way to establish the entailment can be extracted from two results of Simons (1987: 29ff), which concern a set of postulates logically equivalent to (1) and (2). The first is that such postulates license the derivation of (E) from the following strengthening of (2): (3) Strong Supplementation: Whenever a thing is not part of another, the first has at least a part that is disjoint from the the second. 1 I write ‘is disjoint from’ as shorthand for ‘has no parts in common with’. I will also write ‘overlaps’ for ‘has parts in common with’ and ‘is a proper part of’ for ‘is part of, but not identical to’.

Our ordinary view of material things1 has two aspects. One the one hand such things typically have parts. This desk has its legs, its top, and so forth. On the other hand such things typically have locations. This desk is located at some particular region of spacetime in the office. The composition and the location of the desk are, on this view, two quite separable aspects of it. One may therefore change its composition without changing its location, for instance by swapping in a new leg, or change its location without changing its composition, for instance by moving it to the other side of the office. This view of material things remains largely intact in metaphysical inquiries into their natures. On the one hand we have the theory of composition, mereology, which considers what it is for some bits of wood to compose a desk. On the other hand we have the theory of location,2 which considers what it is for the desk to occupy a region of spacetime.

The connection between whole and part is intimate: not only can we share the same space, but I’m incapable of leaving my parts behind; settle the nonmereological facts and you thereby settle what is a part of what; wholes don’t seem to be an additional ontological commitment over their parts. Composition as identity promises to explain this intimacy. But it threatens to make the connection too intimate, for surely the parts could have made a different whole and the whole have had different parts. In this paper I attempt to offer an account of parthood that is intimate enough but not too intimate: the parts generate the whole, but they are not themselves the whole.

Do all actions have parts, and, if so, are their parts also actions? If they have parts, are there basic parts of actions which themselves have no further parts?