Imprecision and Scale Structure

1 Context and the positive form Last week we discussed the dynamic analysis of the positive form of vague gradable adjectives developed by Barker (2002). Simplifying a bit, the analysis assigns the meaning in (1) to pos, where d is a function that maps a context and a measure function to a degree. (1) λgλxλc.g(x) d(c)(g) This analysis leads us to expect two kinds of contextual variability in the standard of comparison: variability based on properties of c (e.g., the domain of discourse) and variability based on properties of g (e.g., the domain of the measure function). Both kinds of variability seem attested. Moreover, this analysis ends up predicting the sort of 'dual use' of vague expressions that Barker discusses: a sentence like (2a) can be construed either as 'about Betty' (the desriptive use) or as 'about the context' (the metalinguistic use). (2) a. Betty is tall. b. λc.tall(betty) d(c)(tall) This analysis is also going to be able to support a number of different explanations of the Sorites Paradox and borderline cases/boundarylessness. (3) a. Steve Nash is short (for a basketball player). b. Any basketball player who is 1 mm taller than a short basketball player is also short (for a bb player). c. Shaquille O'Neal is short (for a bb player). (4) a. short(nash) d(c 0)(short) b. ∀x, y, c[[[short(y) ≻ d(c)(short)] ∧ [tall(x) − tall(y) = 1mm]] → [short(x) ≻ d(c)(short)]] c. short(shaq) d(c 0)(short) On pretty much all the analyses we discussed, (4b) turns out to be false; the interesting part is why we think it's true. And if we're wright about the semantics of pos, then I think our options remain open. Well, maybe: now that we have an explicit semantics, let's finally decide on the significance of 'crisp judgments'. Consider a context in which Betty is just a little bit taller than Abe. All of the examples in (5) are bad, while those in (6) are ok. (5) a. #Betty is tall compared to Abe. b. #Betty is the tall one. c. A: What counts as tall around here? Is Abe tall? B: No, but Betty is. (6) a. Betty is taller than Abe. b. Betty is the taller one.