Singular count NPs in measure constructions

Count Ns like fence, wall or twig notoriously pose problems for the semantic analysis of the mass/count distinction, given that they exhibit grammatical count behavior, thus patterning with bona fide count Ns like cat, but unlike the latter, fail to denote quantized predicates (in Krifka\u27s (1989) original sense); at the same time, they do not denote cumulative predicates, unlike mass Ns, such as mud or water. This puzzling class of count Ns has another intriguing property, so far largely neglected in contemporary mass/count debates in formal semantics: most of its members felicitously occur in pseudo-partitive (measure) NP constructions. Take, for instance, wall, as in Thick woolen drapes of red and gold covered every inch of wall (COCA). We argue that count Ns like fence, wall or twig fail to denote quantized predicates, because they admit of multiple overlapping individuation schemas with respect to what counts as \u27one\u27. In a nutshell, (i) fence, like cat, but unlike mud is quantized at specific counting contexts (and so grammatically count), (ii) fence, like mud, but unlike cat is non-quantized at the null counting context (the union of interpretations across all specific counting contexts), which make them felicitous in pseudo-partitive (measure) NPs