## Unrestricted Composition: the argument from the semantic theory of vagueness?

May 14, 2009

I’ve seen the following claim made quite a lot in and out of print, so I’m wondering if I’m missing something. The claim is that Lewis’s argument for unrestricted composition relies on a semantic conception of vagueness. In particular, people seem to think epistemicists can avoid the argument.

Maybe I’m reading Lewis’s argument incorrectly, but I can’t see how this is possible. The argument seems to have three premisses

1. If a complex expression is vague, then one of it’s constituents is vague.
2. Neither the logical constants, nor the parthood relation are vague.
3. Any answer to the special composition question that accords with intuitions must admit vague instances of composition.

By 3. one has that there (could be) a vague case of fusion: suppose it’s vague whether the xx fuse to make y. Thus it must be vague whether or not $\forall x(x \circ y \leftrightarrow \exists z(z \prec xx \wedge z \circ x))$. By 1. this means either parthood, or one of the logical constants is vague, which contradicts 2.

I can’t see any part of the argument that requires me to read `vague’ as `semantically indeterminate’. These seem to be all plausible principles about vagueness, and if, say, epistemicism doesn’t account for one of these principles, so much the worse for epistemicism.

That said, I think epistemicists should be committed to these principles. Since it would be a pretty far off world where we used English non-compositionally, the metalinguistic safety analysis of vagueness ensures that 1. holds. Epistemicists, like anyone else, think that the logical constants are precise. Parthood always was the weak link in the argument, but one might think you could vary usage quite a bit without changing the meaning of parthood since it refers to a natural relation, and is a reference magnet. Obviously the conclusion that the conditions for composition to occur are sharp isn’t puzzling for an epistemicist. But epistemicists think that vagueness is a much stronger property than sharpness (the latter being commonplace), and the conclusion that circumstances under which fusion occurs do not admit vague instances should be just as bad for an epistemicist as for anyone else who takes a medium position on the special composition question.

The most I can get from arguments that epistemicism offers a way out is roughly: “Epistemicists are used to biting bullets. Lewis’s argument requires you to bite bullets. Therefore we should be epistemicists.” Is this unfair?

1. I thought the issue here turned on whether you’ve got reason to think that the existential quantifier wasn’t vague. *Very* hard to see what that comes to on a semantic indecision view. On more general precisificational views (including epistemicism) there’s some worries, but I don’t think they’re open and shut.

The metalinguistic safety norm says that if there are close enough possible situations to a where S is false, then “x knows S” is false at a—right? If which objects compose is ‘sharp but unstable’ we’ll get violations of that, even if in each situation the universal quantifier ranges over absolutely everything. I guess if you added to the metalinguistic safety analysis something that said that the violations of safety have to arise “in virtue of semantic plasticity” or something, then maybe this won’t look so good. But anyway, there’s debate to be had, it seems to me.

Again, if you’re a fan of metaphysical indeterminacy in existence, then I reckon you’ll again say that the existential quantifier is indeterminate, since it’s indeterminate what the domain of absolutely everything is. I think you can combine that with a precisificational view of the domains. But there’s some hairy metaphysics to be done there (Rich Woodward has a nice paper on this).

I guess the Siderian tweak is to get rid of parthood from the above, and just work with counting sentences?

By the way, what is it for a subsentential expression to be vague, for an epistemicist? I get the analysis of the sentential operator “it’s vague whether” in terms of metalinguistic safety—but it’s not terribly clear to me how to generalize this.

2. Hi, how can I contact you?

I want to start, a list of philosophy BLOGS. A small presentation of the thing, a library or address book. But one question I don’t know is, how to contact people through blogs, I’m not familiar with this medium.

If time permits, I want you to make a post here,

http://dissidentphilosophy.lifediscussion.net/conversation-f8/

It will get stickied and start a list of philosophy blogs. You could write a small intro too, like “Here is a index and library of PHILOSOPHY blogs ….”

Already an index of BBS is here,
http://dissidentphilosophy.lifediscussion.net/conversation-f8/the-community-of-ephilosophers-philosophy-bbs-sites-t9.htm

Kind regards,

– Niki