The Unseen Threads: Emergence in Realist Mereological Atomism — Epoche B2
Arrangement is a plural predication, not an extra property The worry Take a familiar objection to any austere account of composition. Here are some atoms. Arranged one way they compose a chair; arranged another they compose a table. The atoms are the same; the intrinsic properties of each are the same; what differs is the arrangement. But "being arranged chair-wise" is not a property that any single atom has. It looks like a property of the collection. And if the theory has to help itself to properties of collections that are not properties of members, then it has admitted something over and above the parts after all [1] , and its claim to have reduced wholes to parts is in trouble. This note argues that the objection fails, and that it fails at an identifiable step: it moves from "not intrinsic to any atom" to "a property of the whole", and the move is unearned. What "these atoms are arranged chair-wise" says is said of the atoms plurally. It requires relations among them, which any such theory already has, and it requires no further item to bear a further property. The real cost of the position lies elsewhere, and the last part of the note says where. A realist about structural universals can deny all of this, and is named below. Lewis is not the atomist he is taken for Before the argument, an attribution needs correcting, because it recurs. David Lewis is not committed to mereological atomism [2] . He treats atomless gunk—matter every part of which has proper parts—as a possibility he cannot exclude, and his mereology is built to work whether or not there are atoms at the bottom. What Lewis is committed to is a different set of theses [3] . The first is Humean supervenience, announced in the introduction to the second volume of his Philosophical Papers : all there is to the world is a vast mosaic of local matters of particular fact, just one little thing and then another. The mosaic consists of intrinsic qualities instantiated at points, together with the spatiotemporal relations among those points. The second thesis is unrestricted composition: any things whatever, however scattered or ill-assorted, have a fusion. He argues for it in the fourth chapter of On the Plurality of Worlds . The third is that composition is ontologically innocent: in committing yourself to some things you are already committed to their fusion, which is, in his phrase, nothing over and above them. That thesis is developed in Parts of Classes . Notice that the second and third theses are what the objection has to attack. Nothing in them turns on there being a smallest level. What innocence claims Innocence is a claim about ontological cost, not about existence. Lewis is not saying that the chair does not exist [4] ; he says it does, since any atoms have a fusion. He is saying that once the atoms are in your ontology, the chair is not a second entry in the ledger, because the chair is those atoms, taken together. Keeping this distinct from a neighbouring view matters for what follows. To say that a whole is nothing over and above its parts is not to say that there is no whole. The two positions are routinely run together, and running them together is what makes the objection about arrangement look stronger than it is. The dissolution Now the sentence at issue. "These atoms are arranged chair-wise" attributes something to the atoms plurally. It is like "these people surround the building", which is true of them jointly and of no one of them, and which does not require a further object, the crowd, to bear a monadic property of surrounding. Three things follow. First, arrangement is not the sum of the atoms' intrinsic properties, and no one claimed it was; the objection's demonstration of this is a demonstration of something conceded. Second, arrangement is a matter of the spatiotemporal relations among the atoms, and those relations are in the supervenience base already, by the second half of Lewis's mosaic. Nothing has been smuggled in. Third, and this is the step the objection needs and does not take, from the fact that arrangement is not a property of any atom it does not follow that it is a property of a further thing. Plural predication is the third option, and it is the one that fits the sentence. So the chair and the table differ, and the difference is fully recorded in the base. Two fusions of the same atoms cannot differ, since a fusion is determined by what it fuses; but the same atoms at different times, or different atoms, stand in different relations, and it is the relations that carry the difference. Lewis on structural properties The objection has a more ambitious form: that "being arranged chair-wise" is a structural property, a genuine universal with internal complexity, and that the austere theory must admit such things. This form is worth stating because it has an answer from Lewis's own hand. In "Against Structural Universals" (1986) he argues that structural universals cannot be made sense of mereologically. Take the universal being a methane molecule . If it is composed of the universals carbon and hydrogen , then it must contain hydrogen four times over, since methane has four hydrogen atoms. Mereology gives no sense to containing something four times over: the fusion of a thing with itself is that thing. Lewis works through the ways of resisting this and finds that each either abandons the composition or makes the structure primitive and unexplained. The upshot for the present question is direct. Far from implicitly relying on structural properties, the theory has an argument that structural properties, taken as universals with parts, are incoherent. The objection began from the thought that austerity needs a resource it disowns; the resource is one its leading proponent argued against at length. Where the cost really is None of this makes the position cheap. It has a price, and the price is unrestricted composition. The argument for unrestricted composition, sharpened by Theodore Sider in