Ted Sider argues that composition is unrestricted on the grounds that, were it restricted, there’d have to either be sharp cut-offs with respect to composition or borderline cases of composition, and there can’t be either. The conventional wisdom is that embracing borderline composition is going to lead either to metaphysical vagueness or else some sort of relativism. That not quite right: I know of at least four ways (one due to my blogmate Chad Carmichael) to be a non-relativist borderliner without abandoning a linguistic theory of vagueness. I want to sketch one way here. It’s kind of crazy, but not obviously crazier than unrestricted composition.
Some background: numerical sentences are sentences of the following form that say that there are exactly n concrete things (for some number n, in this case 2): ‘∃x∃y(Cx & Cy & x≠y & ∀z(Cz → (x=z v y=z)))’. One premise of Sider’s argument is that whenever there’s borderline composition, some numerical sentence will lack a determinate truth value. After all, it’ll be indeterminate whether there are just some things, or those things *plus* an additional thing that’s composed of them. The strategy I have in mind is to concede that some such sentence lacks a determinate truth value, but insist that the only indeterminacy at issue is semantic indeterminacy. I’ll develop this in three phases. Phase 1: identifying the representational indeterminacy. Phase 2: eliminating everything from the ontology that might lead to nonrepresentational vagueness. Phase 3: ignoring possible objections.
Phase 1: There are countless perfectly precise ways for simples to be arranged: they may be in arrangement1, arrangement2, arrangement3, and so forth. These are monadic properties, collectively instantiated by pluralities of simples, and each of which has a perfectly determinate extension. The envisaged borderliner will countenance states of affairs involving mereological simples and their precise arrangements. Such states of affairs are all that will be needed for securing the semantic indeterminacy of the numerical sentence. To see why, let us say that some things compose something iff they are arranged objectwise, where the vague expression ‘arranged objectwise’ may be replaced by any vague restriction on composition (e.g., arranged lifewise.) Assuming that some simples cannot compose more than one thing at a time, the numerical sentence for some number n will be true iff the arithmetic sum of the number of simples and the number of sets of simples whose members are arranged objectwise is n. Because it is a vague restriction there will be borderline cases of being arranged objectwise. Suppose that simples in arrangement1 through arrangement10 are the clear cases of being arranged objectwise, and that simples in arrangement11 are a borderline case of being arranged objectwise. The sparse borderline can then say that the numerical sentence for n is semantically indeterminate insofar as it is indeterminate which of the following two (perfectly determinate) states of affairs it represents as obtaining:
(i) There being m simples and n minus m sets of simples who members are either in arrangement1 or arrangement2 or … or arrangement10.
(ii) There being m simples and n minus m sets of simples who members are either in arrangement1 or arrangement2 or … or arrangement10 or arrangement11.
One might naturally think of these states of affairs as precisifications of the numerical sentence for n.
Phase 2: Linguistic theorists agree that it’s indeterminate whether Paul is bald, but avoid de re vagueness by denying that there is such a property as the property of being bald; there are only the perfectly precise properties: bald1, bald2, bald3, etc. There also is no such proposition as the proposition that Paul is bald (which would be a borderline instance of the property of being true) or such a state of affairs as the state of affairs of Paul’s being bald (which would be a borderline case of the property of obtaining).
Our sparse borderliner piggybacks this strategy: there is no such property as being arranged objectwise; there are just the precise properties of being in arrangement1, etc. There also is no such proposition as the proposition that ∃x∃y(Cx & Cy & x≠y & ∀z(Cz → (x=z v y=z))), and no such state of affairs as the state of affairs of there being an x and a y such that (Cx & Cy & x≠y & ∀z(Cz → (x=z v y=z))). So there is nothing in the ontology that exhibits de re vagueness. Mission accomplished!
Phase 3: What, me worry?