Singular Count NPs in Measure Constructions
Hana Filip and Peter R. Sutton
Heinrich Heine University, Düsseldorf
1. Main idea. N s like fence, sequence, wall, hedge are problematic for any theory of the mass/count
distinction: while grammatically count with respect to a number of the hallmark diagnostics, they
differ from prototypical count N s (boy) in so far as what counts as ‘one’ individuated entity in their
denotation may vary with context, and they notoriously fail Krifka’s QUANTIZATION, his semantic
defining property of count N s (Partee, p.c., Zucchi and White 1996, 2001, and references therein).
Moreover, unlike prototypical singular count N s, singular fence-like N s may occur in a pseudopartitive (measure) construction (?three pounds of cat versus three yards of fence). This raises the
question about how to account for the similarities between prototypical count N s and fence-like
N s, and also to motivate the significant differences between the two. Capitalizing on the prominent
role that context-sensitivity plays in recent theories of the mass/count distinction (e.g., Chierchia
2010, Rothstein, Landman 2011, Sutton and Filip 2016), we propose to integrate Sutton and Filip’s
mass/count semantics with Krifka’s (1989, and elsewhere) semantics for measure expressions.
Within the class of count N s, we distinguish two semantic subclasses, prototypical count versus
fence-like. This distinction enables us to account for the seemingly puzzling differences in their
morphosyntactic behavior, and in particular for their differential compatibility in a pseudo-partitive
(measure) construction. We do this without losing the distinction between fence-like count N s and
mass N s. This proposal and the coverage of these data have not yet been made to our knowledge.
2. Background. Krifka (1989) laid many foundations for mereological theories of the mass/count
distinction. All nominal expressions take their denotation from a SINGLE non-atomic domain
(pace Link (1983)) structured by a complete join semilattice. Mass N s (water) refer CUMULA TIVELY (1.1), and denote predicates specifying a qualitative criterion of application: x[WATER(x)].
Quantitative criteria of application are expressed by extensive measure functions (e.g., OUNCE ,
HOUR ). They derive QUANTIZED P s (1.2) from cumulative P s (also Krifka, 1998). Count N s
(apple) denote quantized P s. Their requisite quantitative criterion is represented by the NU function:
e.g., n x[APPLE(x) ^ NU(APPLE)(x) = n]. NU stands for a ‘natural unit’, a kind of extensive
measure function yielding what counts as ‘one’ minimal entity in the denotation of P . However, the
quantitative criterion, what is ‘one’, is not reducible to some context-independent notion. Krifka
(1989, p.87, due to Partee, p.c.) already observes that there are count N s like twig that fail to be
quantized, as they denote entities with proper parts also falling under the same predicate. Many more
examples are easy to find: e.g., fence, sequence, line, wall, band, bouquet, plane, hedge (fence-like
N s). Hence, QUANTIZATION is not necessary for N s to be grammatically count; fence-like N s fail
it, because they do not come with an inherent stable ‘natural unit’ for counting, what counts as ‘one’
in their denotation varies with context.
Such observations lead Rothstein (2010, and elsewhere) to propose that all count N denotations
require CONTEXTUAL DISJOINTNESS. All lexical N s are associated with a type he, ti root meaning.
For mass N denotations, Nmass = Nroot . Count N denotations (type he ⇥ k, ti) are derived from root
ones by a semantic COUNTk (N) operation (1.3). It selects entities that count as ‘one-atom’ depending
on the choice of the counting context K, and counting is a grammatical operation which depends on
atomicity relative to a counting context. This allows fence-like N s to be count, while at the same
time having N -atoms in their denotation that vary from context to context: e.g., fencing enclosing
a square field may count as four fences in one context and one fence in another. By integrating
context into a unified semantics for count N s, Rothstein 2010 succeeds in obviating some problems
that context-sensitive fence-like N s pose for theories like Krifka’s (1989, and elsewhere). However,
it also raises some issues. First, generalizing the analysis of fence-like N s to prototypical count
N s (boy) implies that there are no (significant) differences between the two, predicting a uniform
grammatical behavior, which is not borne out. Second, it is not entirely clear how to compositionally
derive the postulated context-sensitivity of prototypical count N s (boy), which intuitively supply a
CONTEXT- INDEPENDENT
criterion of individuation: [boyroot ] = BOY denotes an atomic (disjoint)
set, but so does [boycount ] = COUNTk (BOY) = {hd, ki : d 2 BOY \ k}. Similarly, [fenceroot ] =
FENCE is to contain “contextually salient minimal elements” (ibid., p.374) in its denotation, while
[fencecount ] = COUNTk (FENCE) = {hd, ki : d 2 FENCE \ k} “atomic entities” (ibid., p.373).
3. Empirical evidence. Prototypical count N s (boy) and fence-like N s pattern alike in so far as
they (i) can be directly modified by numerical expressions, (ii) can be pluralized (three boys - three
fences), (iii) occur as arguments of quantifiers that select for count P s (each boy - each fence), and
(iv) cannot occur bare in argument positions (Kim bought *apple/*fence yesterday, *Apple/*Fence
lay on the counter). Interestingly, with respect to aspectual composition, such non-quantized nouns
behave just like count nouns that denote quantized predicates (as defined in (2)), e.g., cat, letter.
However, FENCE-like count Ns have properties that prototypical count N s lack, and which would
be puzzling on a uniform semantic analysis of these two classes (pace Rothstein 2010). A hallmark
property of SINGULAR (prototypical) count N s (boy) is their inadmissibility in a pseudo-partitive
(measure) N construction (?20 kilograms of boy), while FENCE-like count N s freely occur with
both standard and non-standard extensive measures: 3 km of fence, 100 yards of hedge; On the other
side of town, we saw several more pieces of wall. Furthermore, other non-standard pseudo partitive
measures display the same behavior. Compare: You can find a great many lengths/stretches of dry
stone wall across NE England with ??You can find a heavy piece of boy in NE England.
4. Analysis. We adopt the basic architecture of measure constructions from Krifka (1989). Measure
expressions such as yard(s) (of) introduce an extensive measure function (2.1), presupposed to
be a quantizing modification function (1.4), which derives quantized P s from not-quantized ones
(ibid., see also Schwarzschild 2002 for an alternative proposal). Since non-empty, non-singleton
cumulative P s are not quantized, in the typical case, this means mapping a cumulative P denoting
N (fabric, oranges) to a quantized complex N expression (yards of fabric, pounds of oranges).
Sutton and Filip (2016) generalize the notions of context from Rothstein (2010) and Landman
(2011). Rothstein’s COUNTING CONTEXTS ci>0 2 C map possibly overlapping sets to maximally
disjoint subsets (VARIANTS in Landman (2011)). The NULL COUNTING CONTEXT c0 is the union of
all counting contexts and allows any overlap present between ci 2 C (1.5). N lexical entries consist
of a pair hP, IND(P)(ci )i with P the number neutral predicate and IND(P)(ci ) the set of P -individuals
at counting context ci . While mass N entries are saturated with the null counting context, count
N entries are evaluated at the counting context of utterance (2.1-2.4). Count/mass properties are
derived from the disjointness of the IND-set at ci , as opposed to a purely type-based distinction
such as in Rothstein (2010). This derives count encoding for cat and fence (2.2-2.3) and mass
encoding for fencing (2.4), despite fence and fencing being defined in terms of the same number
neutral property FENCE. The IND-set for CAT is disjoint at all counting contexts, which captures
the context-independent nature of their inherent criterion of individuation. The IND-set for FENCE
is disjoint at ci>0 , but overlapping at c0 .
Integrating Sutton and Filip’s mass/count semantics with Krifka’s semantics for measure expressions allows us to distinguish two types of count N s from mass N s and to account for their
differential behavior in a pseudo-partitive (measure) N construction. As observed above, it sanctions
predicate arguments that have a not-quantized interpretation available. Lexical entries of mass N s
water are saturated with the null counting context. They are cumulative (hence not quantized) at
both null counting and specific contexts. This makes them both mass and felicitous in a pseudopartitive (measure) construction. Count N s like cat and fence are both quantized at every specific
counting context (ci>0 2 C) since their denotations are disjoint at these contexts. This makes them
grammatically countable. However, whereas prototypical count N s (cat) are also quantized at c0
(the set of single cats is the same disjoint set at all counting contexts, hence also disjoint at the null
counting context), fence-like N s are not quantized (fences at some specific counting contexts are
proper parts of fences at other specific counting contexts, hence both parts and sums are fences at
the null counting context). This makes fence grammatically measurable, but cat infelicitous in in a
pseudo-partitive (measure) construction. These patterns are summarized in Table 3.
Table 1: Formal Definitions
Cumulative:
Quantized:
Count function:
Quantizing Measure Function:
Null counting context (c0 ):
8P [CUM(P ) $ 8x8y[P (x) ^ P (y) ! P (x t y)]]
8P [QUA(P ) $ 8x8y[P (x) ^ P (y) ! ¬(x @ y)]]
8X : COUNTk (X) = {hd, ki : d 2 X \ k}
8P 8Q[QMOD(P,
Q) $ ¬QUA(P ) ^ QUA(Q(P ))
S
Xc0 = ci>0 Xci
(1.1)
(1.2)
(1.3)
(1.4)
(1.5)
Table 2: Lexical entries
Jyard(s)K
[[cat]]ci
[[fence]]ci
[[fencing]]ci
=
=
=
=
n P x[P (x) ^ yd(x) = n ^ QMOD(P, P x[P (x) ^ yd(x) = n])]
x.hCAT(x), IND(CAT)(ci )(x)i
x.hFENCE(x), IND(FENCE)(ci )(x)i
x.hFENCE(x), IND(FENCE)(c0 )(x)i
(2.1)
(2.2)
(2.3)
(2.4)
Table 3: Predicting felicity in measure constructions from the property Not-Quantized at c0
cat
fence
water
Cumulative
Quantized at ci>0
Quantized at c0
No
No
Yes
Yes
Yes
No
Yes
No
No
Felicitous in a
pseudo-part. construction
No
Yes
Yes
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