Tuesday, September 27, 2005

Shifting The Problem?

'Boundary-shifting' approaches to the Sorites paradox propose that Soritical reasoning only looks convincing because the boundary for the correct application of a vague predicate shifts as we consider different items in the Sorites series. On every occasion, the predicate has some precise boundary, but whenever we consider two successive elements in the series our very doing so makes it the case that the boundary does not lie between those two items. As Delia Graff puts it in this paper, ‘the boundary can never be where we are looking’. This boundary-shifting effect is taken to be responsible for the prima facie plausibility of the (false) major premises in Sorites arguments.

But there is a limited range of possibly-acceptable positions for the boundary of a vague predicate (at least, this is true for many vague predicates). Graff accepts this - she describes constraints of the kind I have in mind here as ‘clear-case constraints’ - and it is very hard to see how anyone could deny it.

However, familiarly, what counts as a ‘clear case’ for the application of a vague predicate is itself a vague matter. So clear-case constraints seem to determine a range of acceptable positions for the boundary of a vague predicate which range is itself vaguely defined. (Of course, there will also be other constraints on the extension of the predicate on any given occasion, but these are not relevant here.)

If we adopt any kind of boundary-shifting view, then, we should consider that one important kind of vagueness associated with a vague predicate is vagueness in the range, across contexts, of acceptable positions for the boundary. And this seems to raise issues. For one thing, it looks as though the full account of the vagueness of our original predicate ('is red', say) will in the end have to make mention of the vagueness of another predicate ('is a clear case of redness'). And a similar thing will happen when we come to give an account of the vagueness of the latter predicate, and so on ad infinitum.

Two questions about this:
1. Do we ever really get a proper account of the vagueness of the original predicate if this infinite regress gets going?
2. Isn't the first step problematic enough by itself? Can we really hope to make progress in understanding the vagueness of 'is red' with an account that invokes the vagueness of 'is a clear case of redness'? Surely our understanding of the latter derives from our understanding of the former, not vice versa?

I'd be interested to hear comments and/or indications of where to look for discussions of this sort of point in the literature. (I know Graff has a paper forthcoming in the Proceedings of the Aristotelian Society on boundary-shifting and higher-order vagueness. Anything else?)


craig said...

I surfed for philosophers, and found you writing: "But there is a limited range of possibly-acceptable positions for the boundary of a vague predicate"

I think this statement is the heart of Sorities; there isn't a boundary on a vague predicate. I would say (and am saying here and now) that that lack of boundary is what makes a predicate vague. There's an inside (my pen is red), and an outside (my pants are not red), and you can draw middle zones (my shirt is somewhat red), and as many distinctions as you make, you'll find vagueness, not boundaries, around their edges. I'm ok with that, unlike some. To those who claim that predicates should always have sharp boundaries, I say "Why would you think that, in view of 'red', 'rich', 'pretty', and myriad other vague predicates that you must be familiar with?"

Aidan said...

Craig - this is just to assert what Graff denies. You may be right, but philosophers tend to like to see arguments for claims like this. (There are some - Mark Sainsbury gives a bunch in 'Concepts without Boundaries', but it's fair to say they haven't been widely accepted. And even Mark doesn't think it is a matter of definition that vague concepts lack boundaries, otherwise presumably he wouldn't bother giving arguments to that effect)

Carrie - I think people have tended not to ask these kinds of questions because a lot of the literature has viewed Graff's position as a type of epistemicism, with the boundary-shifting just invoked to explain our ignorance of where the cut-off lies (I'm actually giving a talk here next week objecting to Graff which will be very guilty of this).

So I think these are the kinds of questions we should be asking of Delia's view, and I think they've been somewhat neglected. That said, I'm not sure I see why the particular questions you raise here are any more troubling than analogous thoughts concerning supervaluationism - the range of 'permissible' precifications will itself be a vague matter.

One might think so much the worse for supervaluationism, but actually most people don't seem to think that. Is there a germane contrast between your thought concerning boundary-shifting and the analogous point about supervaluationism which I'm missing which would encourage optimism that the latter but not the former can give an account of vagueness (or do you think both are in trouble here)?

Carrie Jenkins said...

Hi Aidan,

I think it might depend whether you're thinking of supervaluationism as providing an explanatory *account* of vagueness or just a semantics. If the supervaluationists are trying to give an account of vagueness, then things don't seem particularly any worse for Graff than for them. I guess I'm inclined to think that means that both have some explaining to do rather than that both are fine (though I'm far from having a convincing argument to that effect ...).

Aidan said...

Ok, sure, I was thinking of a supervaluationist who thinks of vagueness as some relevant sort of semantic indeterminacy, rather than someone who's just adopting the machinery.

I think I share your inclination then, though unsurprisingly I don't have an argument either (convincing or otherwise). But that does open up the possibility that some of the literature on HOV concerning supervaluationism may contain the seeds of a response for Graff. I can't think of anything off-hand, but it could be interesting to explore.