Close Range

Borderline Composition without Metaphysical Vagueness

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?

Philosophers of Language: Help!

Consider the following sentences:

(a) ‘Rabbits are animals’ is a true sentence of my language iff rabbits are animals.
(b) The word ‘rabbit’ refers in my language to an object iff that object is a rabbit.

Scott Soames says “The propositions expressed by these sentences are standardly not regarded as capable of being known apriori.” He has an argument for their a posteriority, which I may blog about later. But what I’m wondering is: does anyone know of any other discussions of the epistemic status of such propositions? Or even of other places where someone takes a stand (perhaps without extensive discussion) on their epistemic status?

Also feel free to state any strong feelings you might have about whether they're a priori.

Hawthorne on Strange Communities

John Hawthorne raises the following objection to commonsense views of material objects, on which there are familiar kinds (islands, statues, snowballs) but no strange kinds (incars, gollyswoggles, snowdiscalls):

“Barring a kind of anti-realism that none of us should tolerate, wouldn’t it be remarkable if the lines of reality match the lines that we have words for? The simplest exercises of sociological imagination ought to convince us that the assumption of such a harmony is altogether untoward, since such exercises convince us that it is something of a biological and/or cultural accident that we draw the lines that we do.” (2006, 109).

We “draw the lines that we do” largely as a result of our intuitive judgments about what kinds of things there are, so the suggestion evidently is that it is a biocultural accident that we have the intuitions that we do. Why exactly are we supposed to be convinced of this by “the simplest exercises of sociological imagination”? There are a number of things that Hawthorne might have in mind. Let me mention a couple. 

(1) Surely Hawthorne doesn’t mean to suggest that the mere fact that we’re able to imagine strange communities should convince of this. After all, we can also easily imagine communities who don’t share our intuitions about the multiple-realizability of mental properties, about the moral impermissibility of torturing babies for fun, about the premises of various arguments against commonsense ontology, and so on. Whatever reasons there may be for global skepticism about intuition, the mere imaginability of communities with different intuitions is not one of them.

(2) Perhaps what Hawthorne has in mind is that we can easily imagine the sorts of circumstances that might have led us to draw the lines differently and that, since these circumstances could easily have obtained, we could easily have drawn the lines differently. There are two ways in which this is right, and one way in which this is far from obvious.

First way in which it’s right: We could easily have found it convenient to categorize things differently. We classify things as infants, toddlers, and adolescents. Had our biocultural circumstances been different, we may well have found it convenient to have different categories, e.g., infoddlers (i.e., humans that are infants or toddlers) and toddlescents (i.e., humans that are toddlers or adolescents). But infoddlers and toddlescents aren’t strange things. They’re familiar things, strangely categorized. So this is no problem for the commonsense ontologist. 

Second way in which it’s right: Had biocultural circumstances been different, we may well have found it convenient to make different kinds of things. In that case, there would have been different kinds of artifacts. Perhaps they’d have strange persistence conditions. In that case, we would have had different (and correct!) judgments about which kinds of things there are. But that’s no reason to worry about our judgments about what sorts of artifacts we have in fact made. So, again, this is no problem for the commonsense ontologist.

The sorts of cases that would be problematic for commonsense ontologists involve strange ways of individuating (vs. merely classifying) nonartifacts. Let a supertoddlescent be a strange thing that comes into existence when a child becomes a toddler, ceases to exist when a child becomes an adolescent, and is colocated with the child at all times in between. Intuitively, there are none. Are there possible circumstances in which a whole community has different intuitions about supertoddlescents (setting aside communities who’ve been subjected to philosophy)? I suppose so -- for instance, they could just all be stupid. But it surely is no less easy for there to have been stupid communities with different intuitions about supertoddlescents than for there to be stupid communities with different intuitions about the indiscernibility of identicals, or multiple-realizability, the supervenience of moral facts on natural facts, etc.. So, setting aside idle skepticism about the quality of our present cognitive conditions, this by itself is hardly reason to worry about the reliability of our intuitions about supertoddlescents, moral supervenience, etc.

[[I’m ignoring one further interpretation of Hawthorne: that these exercises in imagination show us that there’s no ontologically significant difference between the strange and familiar things which could account for the existence of the one but not the other. I’ve got a whole paper on this if anyone’s interested.]]