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June 30th, 2004

More Intolerant Vague Terms

Most of my seminar classes are small, especially if you only count the students who are actually enrolled. By that standard, some of them are very small.

Forget for now about the truth values of those claims (they are truer than I’d normally care to admit) and just focus on their semantic content. I think very small in the last sentence is vague. But it’s a tricky kind of vagueness. In particular, it doesn’t seem susceptible to (normal kinds) of Sorites arguments. Conditionals of the following form don’t seem particularly compelling.

(S) If a seminar class with 3 enrolled students is very small, then a seminar class with 4 enrolled students is very small.

In degree-of-truth-speak, there will be a sizable gap between the truth values of any two sentences on this list (unless they both get truth value 0 or 1).

(0) A seminar class with 0 enrolled students is very small.
(1) A seminar class with 1 enrolled students is very small.
(2) A seminar class with 2 enrolled students is very small.
(3) A seminar class with 3 enrolled students is very small.
(4) A seminar class with 4 enrolled students is very small.
(5) A seminar class with 5 enrolled students is very small.

This seems to me just fatal for definitions of vagueness in terms of either Sorites-susceptibility or smooth variation between applicability and non-applicability. And it strongly suggests (to me at least!) that we’re well off returning to something like the definition in terms of borderline cases.

In case it isn’t completely obvious, I should note that this argument leans very heavily on the ideas presented in Delia Graff’s Gap Principles, Penumbral Consequence, and Infinitely Higher-Order Vagueness, though of course Delia wouldn’t like the conclusions.

Posted by Brian Weatherson in Uncategorized

2 Comments »

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2 Responses to “More Intolerant Vague Terms”

  1. Jonas! says:

    initially, i thought it is because it is a discontinuous series. obviously, there can’t be 1.5 students. but then i think of the hair / bald example, and that’s not the case. so maybe there’s something more. it seems like the number of hairs can be pretty big, approaching infinity, but “seminar” implies like 15 people or whatever, so it is more finite? i am not sure.

  2. Brian Weatherson says:

    Yep, it’s just the size of the jumps that matters here. 15 people by the way would be an enormous seminar, or at least an enormous graduate seminar. I’ve never taught a grad seminar with more than 10, and I’ve only once even sat in on one with as many as 15.