Vagueness and grammar: the semantics of relative and absolute gradable adjectives

A conservative theory of gradable modality

“…Following Kennedy (1997Kennedy ( , 2007 in treating the denotation of an adjective as a measure function, for a given proposition p, important will simply return the highest degree such that p holds in all worlds associated with that degree. That is, if ASSOC c (w, d) is the set of worlds associated with d in context c, given a world of evaluation w, then important will have a denotation along the lines of (10):…”

“…Before discussing how these definitions adequately capture the entailments between must p, it is important that p, and should p, it is necessary to address how the positive use of gradable adjectives (e.g., John is tall, in contrast to John is taller than Bill) is handled within a theory in which the denotations of gradable adjectives are measure functions. Kennedy (1997Kennedy ( , 2007, who adopts such a theory, follows von Stechow (1984) in positing the presence of an unpronounced morpheme POS, which combines with the adjective to make an implicit comparative that returns true iff the extent returned by the measure function is no less than some contextually determined standard extent. If ε s is this standard extent, the denotation of POS important will be as seen in (25): (25) POS important c = λ pλ w. cl({d | ∀w ∈ BEST( + g c 2 ,w,d , DOM c (w))[p(w )]}) ≥ e ε s Assuming that the pronoun it in it is POS important that p is semantically idle, the denotation of it is POS important that p will be the denotation in (25) applied to p.…”

A new metalinguistic degree morpheme

“…What -ish asserts is that the degree to which an individual holds a property is below the standard for that adjective. For open scale adjectives, this is a vague relative standard, and for an upper bounded adjective it is the maximal degree on the scale, i.e., the upper bound (Kennedy 2007). So -ish is looking for a degree that is slightly less than a relative or maximal degree.…”

“…Morzycki makes the assumption about the upper-boundedness of the scale of precision without much argument, and indeed, given Grice's (1975) maxim of Quality, by which speakers only say what they believe to be true and have good evidence for, it seems right to think of the scale of precision as including an upper bound, and further that the standard d s for this scale is that upper bound. 15 Given Kennedy's (2007) theory that adjectives whose scales include scalar endpoints will have standards that default to those endpoints, the connection between metalinguistic expressions and the nature of the scale of precision becomes clearer.…”

Japanese comparatives are semantically conjuncts: a dynamic view

“…As argued in von Stechow 1984, Klein 1991, and Kennedy 2007 among others, the contextually specified value of a standard of comparison is provided by the null morpheme pos. In the dynamic setting, I define pos as follows.…”