The polysemy of measurement

• I observe that DPs are polysemous: they can denote an individual or a degree.
• I observe that the degree must correspond to a monotonic dimension of measurement.
• I adopt a semantics for measurement involving a null measurement operator.
• I show how this accounts for the polysemy and its semantic restrictions.
• I extend the account to amount relatives and quantity adjectives like much.

The first goal of this paper is to argue that a number of independently treated phenomena – the ‘measure’ interpretation of pseudopartitives (Landman, 2004), amount relatives (Heim, 1987 and Grosu and Landman, 1998), the how many ambiguity – are different instantiations of the same phenomenon, the general ability for DPs to denote an individual or a degree corresponding to the measure of that individual. I refer to this as ‘individual/degree polysemy’. I show that a particular semantic restriction on the degree interpretations of DPs indicates that the degree interpretation is derived from the individual interpretation (not vice-versa). And I argue that this pervasive polysemy is a natural consequence of degree semantic theories that postulate a null measure operator to measure, when appropriate, individuals, events or degrees. The second goal of this paper is to tie the behavior of this null measurement operator to the similar behavior of quantity adjectives like many and much, giving further support to the claim that quantity adjectives measure sets of degrees ( Rett, 2007 and Rett, 2008).