As long as adverbs function as multipliers (diminishers or magnifi
ers) within a particular domain, the convexity principle can be defended.
For example, if certain voice volumes v1 and v2 both count as
speaking loudly, then any volume between v1 and v2, will also count as
loudly. And for adverbs expressing the form of a path, the principles
of path convexity that were mentioned in section 8 will apply. It is an
open question whether the convexity principle can also be applied to
other adverbs.
Next, I turn to the domain specifi city of adverbs. The structure of
the domains underlying adjectives to some extent determines which
adverbs can be combined with the adjective. For example, for scalar do