How Many Most’s?
Stephanie Solt
Zentrum für Allgemeine Sprachwissenschaft (ZAS), Berlin
Most is a chameleon: its usage spans multiple contexts and meanings that are at first difficult
to connect. In (1), most is a quantifier meaning (roughly) more than 50% (the majority reading).
Most in (2) acts as the superlative of many: on the most natural interpretation, (2) conveys that
Fred has read more Shakespeare plays than any other member of some contextually relevant
group of individuals (the relative reading). In (3), most seems merely to spell out the superlative
morpheme. Finally, in (4) most is part of a superlative quantifier. (See also Gajewski & Bošković
2009 for evidence that this pattern is not limited to English.)
(1)
(2)
(3)
(4)
Fred has read most Shakespeare plays
Fred has read the most Shakespeare plays
Fred bought the most expensive book
Fred has read at most fifteen Shakespeare plays
majority
relative
adjectival superlative
superlative quantifier
A more subtle variation is exemplified in (5). (5a) (discussed by de Hoop 2006) has the
majority reading, but for some (though not all) speakers it also allows a plurality reading, on
which it is true if more babies are born on Tuesdays than on any other day of the week. The use
of most for proportions less than 50% typically involves partitioning of groups into 3 or more
mutually exclusive subgroups, as in (5b) (based on a corpus example):
(5)
plurality
a. Most babies are born on a Tuesday
b. Most customers (43%) insured two cars; 32% insured one car, and 25% insured 3+
This paper addresses the relationship between the most’s in (1)-(5). Given the similarity in
form, can they all be reduced to the same core semantics, and if not, how can they be grouped?
To begin, note that (1) and (2) are superficially similar, but have distinct truth conditions. If
Fred has read 12 of the 37 Shakespeare plays, and no other contextually relevant individual has
read more than 10, (2) is true but (1) is false; conversely if Fred has read 28 but John has read 30,
(1) is true but (2) is false. Despite this, Hackl (2009) proposes that majority and relative most can
receive a unified analysis as superlative forms of many. Hackl relates these two readings of most
to a well-known ambiguity of superlatives between absolute and relative readings (e.g. John read
the longest Shakespeare play can mean either that he read the longest of all such plays, or a
longer one than any other contextually relevant individual). In both cases, Hackl proposes that
the difference in meaning derives from a difference in the scope of the superlative morpheme,
and a corresponding difference in comparison class. On the majority reading of most (1) (and the
absolute reading of superlatives), -est has DP-internal scope, with the comparison class equated
to its NP sister; the resulting logical form for (1) is (6a), equivalent to the simpler (6b). On the
relative reading of most (and superlatives generally), -est has VP scope, and the comparison class
is a group of which the subject is a member, giving (2) the logical form in (7).
(6) a. ∃x[S-play(x) ∧ read(fred,x) ∧∀y[(S-play(y) ∧ y⊓x=∅)→ max{d:|x|≥d} > max{d:|y|≥d]]
b. |{x: S-play(x) ∧ read(fred,x)}| > |{y: S-play(y) ∧ ¬read(fred,y)}|
(7)
∀x∈C[x≠fred→max{d:∃y[S-play(y) ∧ read(fred,y) ∧|y|≥d]} > max{d:∃z[S-play(z) ∧
read(x,z) ∧|z|≥d]}]
[where by presupposition fred∈C]
Before examining whether (6) and (7) are adequate, let us consider how examples (3)-(5)
relate to these two cases. To start, adjectival superlatives such as (3) are readily addressed if most
here is analyzed as the composition of a null much (per Corver 1997) with the superlative
morpheme -est, such that most expensive has a semantics equivalent to expensive + -est. Thus
superlative most can be aligned to superlatives, rather than to other occurrences of most.
Turning to more interesting cases, de Hoop (2006) analyzes the plurality reading of (5a) as an
instance of relative most. But two factors suggest it should in fact be aligned to majority most: i)
the absence of the definite article (which must occur with relative most in English); and ii) its
typical occurrence in contexts involving a non-overlapping partition of a plurality. The latter is a
characteristic of majority most: the logical forms in (6) involve the comparison of the set of
Shakespeare plays Fred read to non-overlapping subsets of the set of Shakespeare plays; by
comparison, (7) does not require that the sets of plays read by the members of the comparison
class be disjoint. The plurality reading can thus be captured by a generalization of the logical
form in (6b) from the case of two non-overlapping subsets to the case of n non-overlapping
subsets for n>2 (such that most is justified in (5b) is because when individuals are partitioned
according to number of cars insured, the set of people insuring two cars is the largest).
Finally, the superlative quantifier at most n in examples such as (4) has typically been
analyzed separately from other instances of most. But a case can be made that it should be
aligned to relative most. Observe first that (4) can be paraphrased as in (8), suggesting that at
most n expresses a (relative) superlative over numbers:
(8) The largest number of Shakespeare plays that Fred could have read is 15
Also, as pointed out by Nouwen (2010), at most n is necessarily interpreted relative to a range of
values (for example, the utterance of (4) would be infelicitous if the speaker knew precisely how
many Shakespeare plays Fred had read); this parallels a restriction of superlatives to cases where
the comparison class contains multiple members (e.g. the longest book is infelicitous in a context
where there is only one book). Following this line of thinking, (4) can be given a logical form
directly parallel to that in (7) for relative most; the result is (9), which in simpler terms states that
the maximum number of Shakespeare plays that Fred read in any accessible world is 15.
(9) ∀n[n≠15→max{n': ∃wAcc∃x[S-play(x) ∧ readw(fred,x) ∧ |x|=15 ∧ 15≥n']} >
max{n": ∃wAcc∃x[S-play(x) ∧ readw(fred,x) ∧ |x|=n ∧ n≥n"]}]
Having seen how other cases can be related to majority and relative most, let us consider
again whether the difference between these two can be reduced to one of scope. Attractive
though this idea is, there is one central aspect of the semantics of most that it does not capture.
Specifically, majority most is infelicitous for proportions close to 50%; that is, the comparison in
(6b) is tolerant to small differences in set size. For example, (1) is inappropriate (or even false) in
the situation where Fred has read 19 Shakespeare plays, even though that number exceeds the
number he did not read, i.e. 18. In this, majority most is distinguished from relative most, which
allows precise comparisons (if Fred read 19 plays and John read 18, (2) could be true); it is also
distinguished from the absolute reading of superlatives, which Hackl’s account relates it to (for
example, the longest Shakespeare play in the absolute sense might be just one page longer than
the next longest). I show instead that the semantics of majority most must be represented with
reference to a semi-order on set sizes (van Rooij 2009), a less informative ordering than a
traditional degree structure. The conclusion is that not all occurrences of most can be reduced to
a single underlying semantics; to answer the question posed in the title, there are two most’s.
References: Corver, N. (1997). Much support as a last resort. LI, 28, 119-164. Hackl, M.
(2009). On the grammar and processing of proportional quantifiers. Nat’l. Lang. Semantics, 17,
63-98. Gajewski, J. & Bošković, Ž. (2009). Semantic correlates of the NP/DP parameter.
NELS39. de Hoop, H. (2006). Why are most babies born on a Tuesday? Between 40 and 60
Puzzles for Krifka. Nouwen, R. (2010). Two types of modified numerals. Sem. & Pragmatics 3,
1-44. van Rooij, R. (2009). Implicit and explicit comparatives. Vagueness & Language Use.