2 projecting the adjective - chris...
TRANSCRIPT
2 Projectin
g the Adjective
Th
is chapter m
otivates and develops a sem
antic an
alysis of gradable adjectives as measu
re
fun
ctions: fu
nction
s from objects to degrees. I argu
e that proposition
s in w
hich
the m
ain
predicate is headed by a gradable adjective ϕ
have th
ree primary sem
antic con
stituen
ts: a
reference value, w
hich
denotes th
e degree to wh
ich th
e subject is ϕ
, a standard value, which
corresponds to an
other degree, an
d a degree relation, wh
ich is in
troduced by a degree
morph
eme an
d wh
ich defin
es a relation betw
een th
e reference valu
e and th
e standard
value. B
uildin
g on a syn
tactic analysis in
wh
ich gradable adjectives project exten
ded
fun
ctional stru
cture h
eaded by a degree morph
eme (A
bney 19
87, C
orver 199
0, 19
97,
Grim
shaw
199
1), I show
that th
is analysis su
pports a straightforw
ard composition
al
seman
tics for comparatives an
d absolute degree con
struction
s in E
nglish
, and th
at it explains
the restricted scopal properties of com
paratives that w
ere problematic for th
e traditional
scalar analysis of gradable adjectives, in
wh
ich gradable adjectives are relation
al expressions
and com
paratives quan
tify over degrees.
2.1 Measure Fun
ctions an
d Degree C
onstruction
s
2.1.1 Puzzles
Ch
apter 1 conclu
ded with
a puzzle. A
nu
mber of facts, in
cludin
g cross-polar anom
aly,
incom
men
surability, an
d comparison
of deviation, provided stron
g support for th
e seman
tic
analysis of gradable adjectives as expression
s that defin
e a mappin
g between
objects in th
eir
domain
and degrees on
a scale. An
importan
t compon
ent of th
is analysis w
as the claim
that
the basic m
eanin
g of a gradable adjective is that of a relation
al expression: a gradable
adjective introdu
ces two argu
men
ts, an object an
d a degree, and defin
es a mappin
g between
them
. A gen
eral characteristic of argu
men
t expressions is th
at they can
be quan
tified; it
follows th
at if degrees are actual argu
men
ts of a gradable adjective, they sh
ould provide a
domain
for quan
tification. T
he gen
eral success of th
e analysis of com
paratives as
87
expressions th
at quan
tify over degrees–th
is analysis played an
importan
t role in th
e
explan
ations
of in
comm
ensu
rability,
cross-polar
anom
aly, an
d
comp
arison
of
deviation–appears to verify th
is prediction.
Th
e assum
ption th
at degree constru
ctions are qu
antification
al expressions raises
other expectation
s, how
ever. If these con
struction
s quan
tify over degrees, then
we expect
them
to participate in scope am
biguities in
contexts in
wh
ich oth
er quan
tificational
expressions (e.g., qu
antified N
Ps) sh
ow sim
ilar ambigu
ities. Th
e facts discussed in
section
1.4 of chapter 1 in
dicated that th
is is not th
e case for the com
parative constru
ction, h
owever:
there is n
o evidence th
at the qu
antification
al force introdu
ced by a comparative participates
in scope am
biguities; in
effect, a quan
tified degree argum
ent alw
ays has n
arrow scope w
ith
respect to other qu
antification
al operators. At th
e same tim
e, the facts sh
owed th
at a
subcon
stituen
t of the com
parative constru
ction–
the com
parative clause–
does show
the
scopal characteristics of an
argum
ent-den
oting expression
. Th
ese observations lead to th
e
followin
g conclu
sions. F
irst, if comparatives n
ever show
scope ambigu
ities, then
the
hypoth
esis that th
ey are quan
tificational m
ust be called in
to question
. Alth
ough
one cou
ld
modify th
e traditional an
alysis so that th
e quan
tification in
troduced by a degree con
struction
mu
st take narrow
scope by explicitly encodin
g this con
straint in
the in
terpretation of th
e
comparative m
orphem
e (as in e.g., von
Stech
ow 19
84a, R
ullm
ann
199
5), an altern
ative
explanation
in w
hich
the scope facts are derived sh
ould be preferred. S
econd, if a property
of argum
ents is th
at they provide a dom
ain for qu
antification
, then
the sem
antic beh
avior of
the com
parative clause su
ggests that it is an
argum
ent-den
oting expression
. In th
e
traditional accou
nt, h
owever, th
is is not th
e case: the com
parative clause is part of th
e
restriction of th
e quan
tifier introdu
ced by the com
parative, but it does n
ot denote th
e
degree argum
ent of th
e adjective. 1
1Overlyin
g the scop
e issues w
as a separate p
roblem
wh
ich arose sp
ecifically in th
e case of analyses
wh
ich treat th
e comp
arative in term
s of existential q
uan
tification: th
e interp
retation of com
paratives w
ith
less. As ob
served in
chap
ter 1, if the in
terpretation
of the ab
solute con
struction
is stated in
terms of an
“at
least as” relation, as in
(i), it is imp
ossible to con
struct accu
rate truth
cond
itions for com
paratives w
ith less.
The logical rep
resentation
of (ii), show
n in
(iii), is satisfied even
if Molly’s h
eight exceed
s Max’s h
eight, sin
ce it
wou
ld be tru
e in su
ch a situ
ation th
at for some d
ordered
below th
e degree of M
ax’s tallness, M
olly is at least
88
A m
ore general problem
for a relational an
alysis of gradable adjectives can be
described of as the “problem
of composition
ality”. A stron
g them
e in w
ork on gradation
,
dating at least to Sapir 19
44 (see also Fillm
ore 196
5, Cam
pbell and W
ales 196
9, B
artsch an
d
Ven
nem
ann
1972, C
resswell 19
76, B
ierwisch
198
9), is th
at comparison
(i.e., a partial
ordering relation
) is a psychological prim
itive, and th
at the basic in
terpretation of gradable
adjectives shou
ld be stated in term
s of such
a relation. In
deed, this h
ypothesis is th
e basis
for the scalar an
alysis sketched in
the last ch
apter, in w
hich
the core m
eanin
g of a gradable
adjective is defined in
terms of a partial orderin
g relation. T
his is m
ost clearly illustrated by
considerin
g the tru
th con
ditions of a typical absolu
te constru
ction su
ch as (1), w
hich
are
stated in term
s of a partial ordering betw
een tw
o degrees.
(1)B
enn
y is tall.
Benny is tall is tru
e just in
case the degree to w
hich
Ben
ny is tall is at least as great as som
e
contextu
ally determin
ed standard of talln
ess (possibly relativized to the com
parison class to
wh
ich B
enn
y belongs). T
his is form
alized in (2), w
here δ
tall denotes a fu
nction
from objects
to degrees on th
e scale associated with
the adjective tall, an
d s denotes th
e appropriate
standard value.
(2)||tall(B
enny,s)|| = 1 iff δtall (B
enny) ≥ s
Th
e problem of com
positionality, articu
lated by McC
onn
ell-Gin
et (1973) an
d Klein
as tall as d.
(i)|| ϕ
(a,d)|| = 1 iff th
e degree to wh
ich a
is ϕ is at least as great as d
.
(ii)M
olly is less tall than
Max is.
(iii)∃d
[d < max(λ
d’.tall(Max,d’))][tall(M
olly,d)]
Alth
ough
a stipulation
that th
e nu
clear scope of a less constru
ction h
as an “equ
als” interpretation
wou
ld salvage this
approach (see e.g. R
ullm
ann
199
5), an an
alysis wh
ich derives th
e right resu
lts shou
ld be preferred over one w
hich
mu
st rely on su
ch stipu
lations. In
section 2.4, I w
ill present an
analysis th
at achieves th
is goal.
89
(1980
, 1982), is th
at the assu
mption
that th
e comparison
relation is som
ehow
“basic” is not
supported by th
e morph
osyntactic facts of n
atural lan
guages. If th
e comparison
relation
were a psych
ological or seman
tic primitive, th
en th
e expectation sh
ould be th
at the
comparative form
of the adjective sh
ould be less m
arked than
the absolu
te form. T
his
expectation is n
ot supported by th
e facts, how
ever: it appears to be true th
at in lan
guages
that h
ave both a com
parative and absolu
te form, th
e comparative is m
orphologically (an
d
syntactically) m
ore complex th
an th
e absolute (M
cCon
nell-G
inet 19
73:96
). 2 Given
the fact
that com
parative constru
ctions are alw
ays morph
ologically or syntactically com
plex, plus th
e
observation th
at gradable adjectives appear in a variety of sem
antically distin
ct degree
constru
ctions, n
ot all of wh
ich obviou
sly involve a n
otion of com
parison (see footn
ote 2),
consideration
s of composition
ality dictate that th
e basic interpretation
of gradable adjectives
shou
ld be specified indepen
dently of a n
otion of com
parison, an
d that th
e interpretation
s of
complex degree con
struction
s shou
ld be derived as a fun
ction of th
e mean
ings of gradable
adjectives and th
e mean
ings of degree m
orphology. T
his poin
t is articulated by K
lein
(1980
:4), wh
o says:
We also requ
ire a seman
tic theory for E
nglish
to analyse th
e interpretation
of
complex expression
s in term
s of the in
terpretations of th
eir compon
ents. A
n
2It shou
ld also be observed
that if a com
parison
relation is an
inh
erent com
pon
ent of th
e mean
ing of
a gradab
le adjective, som
e notion
of comp
arison sh
ould
be in
volved in
the in
terpretation
of any sen
tence in
wh
ich a grad
able ad
jective app
ears. This is n
ot obviou
sly true, h
owever. C
onsid
er the case of too/en
ough
constru
ctions. Th
e truth
cond
itions of a sen
tence lik
e (i) can be stated
in term
s of a notion
of comp
arison, as
in (ii) (see von
Stechow
1984a:68-69 for this typ
e of analysis).
(i)Pu
g is too stink
y to go to the R
itz (ii)
In ord
er for Pug to go to th
e Ritz, h
e wou
ld h
ave to be less stinky th
an h
e is.
Alth
ough
(ii) is clearly an en
tailmen
t of (i), it is not ob
vious th
at it is the b
est analysis of th
e mean
ing of (i).
Argu
ably, a more accu
rate characterization
of the m
eanin
g of (i) is (iii), wh
ich d
efines th
e truth
cond
itions of
(i) with
out referen
ce to a comp
arison relation
(cf. Moltm
ann
1992a:301).
(iii)Th
e degree of Pu
g’s stinkin
ess makes it im
possible for h
im to go to th
e Ritz.
Alth
ough
too an
d en
ou
gh con
struction
s will n
ot be a focu
s of this th
esis, I will in
clud
e some d
iscussion
of
them
below.
90
expression of th
e form [A
P A-er than X
] is clearly complex. H
ow do its
compon
ents con
tribute to th
e mean
ing of th
e wh
ole?
I take it that a m
inim
al requirem
ent of an
y seman
tic analysis of com
paratives and gradable
adjectives is to provide a satisfactory answ
er to Klein
’s question
.
With
these con
siderations in
min
d, we can
constru
ct a list of requirem
ents th
at an
analysis of th
e seman
tics of gradable adjectives and degree con
struction
s shou
ld aim to
satisfy. First, it sh
ould provide a prin
cipled explanation
for wh
y the qu
antification
al force
introdu
ced by a degree constru
ction does n
ot participate in scope am
biguities. S
econd, for
comp
arative constru
ctions at least, it sh
ould exp
lain w
hy a su
bpart of th
e degree
constru
ction–th
e comparative clau
se–does participate in
scope ambigu
ities. Th
ird, it shou
ld
sup
port
an
explan
ation
of th
e cru
cial em
pirical
facts d
iscussed
in
ch
apter
1:
incom
men
surability, cross-polar an
omaly, an
d comparison
of deviation. F
inally, in
order to
adequately satisfy requ
iremen
ts of composition
ality, it shou
ld characterize th
e mean
ing of
gradable adjectives indepen
dently of a n
otion of com
parison, an
d the in
terpretations of
complex degree con
struction
s shou
ld be explained in
terms of th
e interaction
of the
mean
ing of th
e adjective and th
e mean
ings of degree m
orphem
es.
Th
e goal of this ch
apter is to develop an altern
ative to the tradition
al scalar analyses
that satisfies th
ese requirem
ents. Specifically, I w
ill reject the tradition
al claim th
at gradable
adjectives have a degree argu
men
t, arguin
g instead th
at gradable adjectives denote m
easure
fun
ctions: fu
nction
s from in
dividuals to degrees (cf. B
artsch an
d Ven
nem
ann
1972,
Wu
nderlich
1970
), and I w
ill claim th
at degree morph
emes do n
ot introdu
ce quan
tification
over degrees, but rath
er combin
e with
a gradable adjective to form a com
plex property
wh
ose mean
ing is rou
ghly th
e same as th
e mean
ing of a gradable adjective on
the tradition
al
view (in
particular, th
ese expressions are of th
e same sem
antic type). C
rucially, n
o notion
of
comparison
is incorporated in
to the core m
eanin
g of a gradable adjective on th
is view;
instead, a gradable adjective den
otes a fun
ction th
at projects the objects in
its domain
onto
the scale w
ith w
hich
it is associated, and th
e relational (i.e., com
parative) characteristics
91
associated with
absolute an
d degree constru
ctions are in
troduced by degree m
orphology.
Moreover, becau
se this an
alysis of degree constru
ctions is n
ot quan
tificational, th
e
expectation th
at they sh
ould participate in
scope ambigu
ities disappears.
Th
e rest of this ch
apter is organized as follow
s. In th
e remain
der of this section
, I
will ou
tline th
e core properties of the an
alysis. In section
2.2, I will in
troduce th
e syntactic
analysis of degree con
struction
s that I w
ill adopt, in w
hich
adjectives project fun
ctional
structu
re headed by degree m
orphem
es (see Abn
ey 198
7, Corver 19
90
, and G
rimsh
aw
199
1). In th
e remain
der of the ch
apter, I will sh
ow th
at this an
alysis supports a robu
st
composition
al seman
tics of degree constru
ctions, focu
sing on
the an
alysis of absolute an
d
comparative con
struction
s in E
nglish
.
2.1.2 Identifyin
g the Standard
To isolate th
e general differen
ces between
the an
alysis of gradable adjectives that I w
ill
propose here an
d the relation
al analysis ou
tlined in
chapter 1, it is u
seful to start w
ith a
closer look at the gen
eral notion
of a “standard”. A
claim com
mon
to all scalar analyses (an
d
implicit in
vague predicate an
alyses) is that th
e truth
of a senten
ce contain
ing a gradable
adjective ϕ is determ
ined by evalu
ating som
e relation betw
een th
e degree to wh
ich th
e
subject is ϕ
and som
e other valu
e, wh
ich I w
ill refer to as the standard valu
e. Th
is is most
clearly illustrated by th
e interpretation
of absolute con
struction
s, both w
ith an
d with
out
measu
re phrases, su
ch as (3) an
d (4).
(3)T
he n
eutron
star in th
e Crab N
ebula is den
se.
(4)
Ben
ny is 4 feet tall.
For exam
ple, (3) is true ju
st in case th
e degree to wh
ich th
e neu
tron star in
the C
rab Nebu
la
is dense is at least as great as a stan
dard degree of densen
ess (for galactic objects), and (4) is
true ju
st in case th
e degree to wh
ich B
enn
y is tall is at least as great as the degree den
oted
by 4 feet (I assum
e that m
easure ph
rases denote degrees; see von
Stech
ow 19
84a,b and
92
Klein
199
1 for general discu
ssion).
Com
parative and equ
ative constru
ctions su
ch as (5)-(7) can
also be analyzed in
terms
of a relation betw
een th
e standard an
d a subject-orien
ted degree, but th
e determin
ation of
the stan
dard value is m
ore complex.
(5)T
he H
ale-Bopp com
et was brigh
ter than
Hyaku
take was.
(6)
Th
e Mars P
athfin
der mission
was less expen
sive than
the V
iking m
issions.
(7)T
he earth
is as large as Ven
us.
In an
analysis in
wh
ich degree con
struction
s quan
tify over the degree argu
men
t of a
gradable adjective, comparatives an
d equatives fu
nction
as indefin
ite descriptions of a
standard valu
e: the valu
e of the stan
dard is a fun
ction of th
e denotation
of the com
parative
clause an
d the m
eanin
g of the degree m
orphem
e that h
eads the com
parative. 3 Th
is is
illustrated by th
e seman
tic analyses of th
ese senten
ces in (8)-(10
), usin
g the form
alism
adopted in ch
apter 1.
(8)
∃d[d > m
ax(λd’.bright(H
yakutake,d’))][bright(H
ale-Bopp,d)]
(9)
∃d[d < m
ax(λd’.expensive(the V
iking missions,d’))][expensive(the M
P m
ission,d)]
(10)
∃d[d ≥ m
ax(λd’.large(V
enu
s,d’))][large(the earth,d)]
For exam
ple, the com
parative in (8) con
strains th
e standard valu
e to be some degree th
at
exceeds the (m
aximal) degree to w
hich
Hyaku
take was brigh
t; the en
tire senten
ce is true
just in
case the degree to w
hich
Hale-B
opp was brigh
t is at least as great as the stan
dard.
Note
that
althou
gh
the
differen
t relation
s in
trodu
ced
by th
e com
parative
degree
morph
emes play a cru
cial role in determ
inin
g the valu
e of the stan
dard, they do n
ot affect
3For now
, I will con
tinu
e to abstract away from
the d
ifference betw
een com
paratives like (5), in
wh
ich
the su
rface comp
lemen
t of than
or as is a (possibly p
artial) clausal con
stituen
t, and
comp
aratives like (6)-(7), in
wh
ich th
is expression
is a DP, referrin
g to the com
plem
ent of th
an or as in
these con
struction
s un
iformly as
the “com
parative clau
se”. In section
2.4, I will focu
s specifically on
this d
istinction
(see e.g., Han
kam
er 1973,
Pink
ham
1982, Hoek
sema 1983, N
apoli 1983, H
eim 1985, an
d H
azout 1995 for relevan
t discu
ssion).
93
the relation
between
the su
bject and th
e standard: in
each of (8)-(10
), as in th
e absolute
constru
ctions in
(3) and (4), th
e relation betw
een th
e degree to wh
ich th
e subject is ϕ
and
the stan
dard degree is a partial ordering relation
.
Alth
ough
(8)-(10) provide accu
rate characterization
s of the tru
th con
ditions of (5)-(7),
the in
terpretations of th
ese senten
ces could h
ave been ch
aracterized more directly in
terms
of a relation betw
een tw
o degrees, rather th
an qu
antification
over degrees. Specifically, (5)-
(7) could h
ave been an
alyzed in term
s of a relation betw
een th
e degree to wh
ich th
e subject
is ϕ an
d a standard valu
e, with
the follow
ing adju
stmen
ts: the com
parative clause, rath
er
than
the en
tire comparative con
struction
, provides the stan
dard, and th
e relation betw
een
the stan
dard and th
e subject-degree is determ
ined by th
e comparative m
orphem
e. 4 On
this
view, th
e truth
condition
s of (5)-(7) shou
ld be stated as in (11)-(13).
(11)T
he Hale-B
opp comet w
as brighter than Hyaku
take was is tru
e just in
case the degree
to wh
ich H
ale-Bopp w
as bright exceeds th
e degree to wh
ich H
yakutake w
as bright.
(12)T
he Mars P
athfinder mission w
as less expensive than the Viking M
issions is true ju
st in
case the degree to w
hich
the M
ars Path
finder m
ission w
as expensive is exceeded by
the degree to w
hich
the V
iking m
issions w
ere expensive.
(13)T
he earth is as large as Venus is tru
e just in
case the degree to w
hich
the earth
is large
is at least as great as the degree to w
hich
Ven
us is large.
Th
e analyses in
(8)-(10) an
d (11)-(13) differ in tw
o importan
t ways. T
he first is th
e relation
between
the stan
dard values in
comparative an
d absolute con
struction
s. In (8)-(10
), the
comparative qu
a degree description is sem
antically parallel to th
e measu
re phrase an
d
contextu
ally determin
ed standard in
(3)-(4), w
hile in
(11)-(13), the sem
antic role of th
e
comparative clau
se is parallel to that of th
e standard-den
oting expression
s in th
e absolute
4The ob
servation th
at comp
aratives can b
e analyzed
along th
ese lines goes b
ack at least to R
ussell
1905, wh
o characterizes th
e de re in
terpretation
of (i) as (ii):
(i)I th
ough
t your yach
t was larger th
an it is.
(ii)Th
e size that I th
ough
t your yach
t was is greater th
an th
e size your yach
t is.
94
constru
ctions. T
he secon
d difference in
volves the relation
between
the degree to w
hich
the
subject is ϕ
and th
e standard valu
e. In (8)-(10
), this relation
remain
s the sam
e regardless of
the p
articular degree m
orph
eme in
volved. In con
trast, in (11)-(13) th
is relation is
determin
ed by the particu
lar degree morph
eme u
sed.
Th
ese differences represen
t the core of th
e alternative an
alysis of gradable adjectives
and degree con
struction
s that I w
ill develop here. S
pecifically, I will argu
e that th
e
interpretation
of senten
ces constru
cted out of a gradable adjective ϕ
shou
ld be characterized
in term
s of three sem
antic con
stituen
ts, wh
ich are specified in
(14).
(14)
i.A
reference value, wh
ich in
dicates the degree to w
hich
the su
bject is ϕ;
ii.a standard value, w
hich
corresponds to som
e other degree; an
d
iii.a degree relation, w
hich
is asserted to hold betw
een th
e reference valu
e and th
e
standard valu
e.
Th
e analysis con
sists of three fu
ndam
ental claim
s. First, gradable adjectives den
ote
measu
re fun
ctions–
fun
ctions from
individu
als to degrees–an
d the referen
ce value in
senten
ces like (3)-(7) is derived by applying th
e adjective to the su
bject. Secon
d, the con
text-
depen
dent stan
dard in an
absolute con
struction
, a measu
re ph
rase in an
absolute
constru
ction, an
d the com
parative clause (th
e complem
ent of than or as) perform
the sam
e
seman
tic fun
ction: th
ey introdu
ce the stan
dard value. T
hird, degree m
orphem
es denote
relations betw
een th
e reference valu
e and th
e standard valu
e, i.e, they in
troduce th
e degree
relation. In
the follow
ing section
s, I will con
sider these claim
s in m
ore detail.
2.1.3 Measure Fun
ctions
Con
sider again th
e traditional an
alysis of absolute con
struction
s like (3) and (4). W
hat is
imp
ortant
to recogn
ize is
that
the
un
derlyin
g relation
al ch
aracteristics of
these
constru
ctions in
an an
alysis in w
hich
gradable adjectives denote relation
s between
individu
als
and degrees com
es from th
e mean
ings of th
e adjectives them
selves. In order to con
struct
95
the correct tru
th con
ditions for th
e absolute form
, the m
eanin
g of a gradable adjective mu
st
inclu
de a fun
ction from
objects to degrees, an assu
mption
that is im
plicit in th
e truth
condition
s provided for the absolu
te in ch
apter 1 (see also (2) above). For exam
ple, the
mean
ing of den
se mu
st be someth
ing like (15), w
here δ
dense is a fun
ction from
objects to the
scale associated with
dense.
(15)dense = λ
dλx[δ
dense (x) ≥ d]
On
this view
, the m
eanin
g of the adjective in
cludes th
ree compon
ents: a degree argu
men
t,
a partial ordering relation
, and a fu
nction
from in
dividuals to degrees, i.e., a m
easure function
(for a detailed analysis alon
g these lin
es, see Bierw
isch 19
89). If th
e relational com
ponen
t
and th
e degree argum
ent are rem
oved, how
ever, wh
at remain
s is a measu
re fun
ction. T
he
proposal that I w
ill develop in th
e followin
g paragraphs represen
ts, in effect, a decom
position
of the tradition
al mean
ing of a gradable adjective alon
g exactly these lin
es.
Th
e hypoth
esis that gradable adjectives den
ote measu
re fun
ctions h
as its roots in th
e
work of B
artsch an
d Ven
nem
ann
(1972) (see also W
un
derlich 19
70). B
artsch an
d
Ven
nem
ann
propose that th
e mean
ings of all gradable adjectives can
be stated in term
s of a
single m
easure fu
nction
f M th
at takes two argu
men
ts: an object x an
d a scale S. 5 T
he
adjectives long an
d wide, on
this view
, have th
e interpretation
s in (16
)-(17): they den
ote
fun
ctions w
hich
project their argu
men
ts onto scales of len
gth an
d width
, respectively.
(16)
long = λx.f M(x, len
gth
)
(17)w
ide = λx.f M(x, w
idth
)
Bartsch
and V
enn
eman
n’s approach
is designed to reflect th
e “psychological fact th
at
5Bartsch
and
Ven
nem
ann
actually claim
that th
e second
argum
ent of th
e measu
re fun
ction f M
is a
“dim
ension
” rather th
an a scale. A
lthou
gh th
ey do n
ot explicitly d
efine scales, th
eir defin
ition of a d
imen
sion
as a “linearly ord
ered set of valu
es” (p. 67) in
dicates th
at their n
otion of “d
imen
sion” is eq
uivalen
t to the
notion
of “scale” that I h
ave adop
ted in
this th
esis (see the d
iscussion
below).
96
‘measu
ring’ is a u
nitary process” (19
73:69
; cf. Bierw
isch 19
89). W
hile it m
ay indeed be tru
e
that th
e psychological aspects of m
easurem
ent sh
ould be ch
aracterized in term
s of a single,
general cogn
itive apparatus, th
is does not n
ecessarily provide a compellin
g seman
tic
argum
ent for represen
ting th
e mean
ings of all gradable adjectives in
terms of a sin
gle
fun
ction. Su
ch an
approach can
only be ju
stified by lingu
istic evidence; w
hat tu
rns ou
t to be
the case, h
owever, is th
at the lin
guistic eviden
ce argues again
st this view
. To see w
hy, it is
necessary to take a closer look at scales an
d degrees.
As in
chapter 1, I w
ill assum
e that a scale is defin
ed as a totally ordered set of points,
and th
at scales are differentiated by th
eir dimen
sional valu
es (cf. Cressw
ell 1976
). Like
Cressw
ell and B
artsch an
d Ven
nem
ann
, I assum
e that dim
ension
s are seman
tic primitives:
intu
itively, a dimen
sion is a qu
ality or attribute th
at permits gradin
g, or, put an
other w
ay, a
property with
respect to wh
ich tw
o objects can be com
pared (see also Sapir 19
44
and
Bierw
isch 19
89). A
s observed in ch
apter 1, the im
portance of th
e dimen
sional param
eter is
that it provides a m
eans of distin
guish
ing betw
een tw
o scales: a scale S1 an
d a scale S2 are
distinct if an
d only if th
ey are associated with
different dim
ension
s. Th
is distinction
provides
the basis for a straigh
tforward explan
ation of in
comm
ensu
rability (see the discu
ssion in
chapter 1, section
1.3.3.1): for any tw
o degrees d1 an
d d2 , d
1 and d
2 are comm
ensu
rable just in
case they are degrees on
the sam
e scale. 6 For exam
ple, assum
ing th
at the adjectives tragic
and long define fu
nction
s from objects to scales w
ith differen
t dimen
sional param
eters, and
that th
e comparative m
orphem
e more den
otes an orderin
g relation betw
een tw
o degrees,
the an
omaly of (18) is expected.
(18)
#T
he Idiot is more tragic th
an it is lon
g.
Th
e reference valu
e (the degree to w
hich
The Idiot is tragic) an
d the stan
dard value (th
e
6As observed
in ch
apter 1, th
is follows from
the d
efinition
of orderin
g relations. For an
y two objects x
and y, th
e relations x > y, x < y, an
d x ≥ y are d
efined
only if x an
d y
are mem
bers of the sam
e set. Since scales
associated w
ith d
ifferent d
imen
sions are d
istinct sets, it follow
s that tw
o degrees d
1 and
d2 are com
parable
only if th
ey are degrees on
the sam
e scale.
97
degree to wh
ich T
he Idiot is long) are degrees on
different scales, th
erefore the relation
asserted to hold betw
een th
e two degrees is u
ndefin
ed.
We can
now
return
to the discu
ssion of B
artsch an
d Ven
nem
ann
’s proposal. If the
interpretation
of all gradable adjectives is stated in term
s of a single, gen
eral measu
re
fun
ction an
d a scale specification, th
en it follow
s that n
o two lexically distin
ct adjectives share
the sam
e scale. For exam
ple, since th
e range of th
e measu
re fun
ction in
the m
eanin
g of
the adjective lon
g is different from
that of th
e measu
re fun
ction in
the m
eanin
g of wide, as
illustrated in
(16) an
d (17) above (the form
er is a scale of length
and th
e latter is a scale of
width
), it mu
st be the case th
at the tw
o adjectives project their argu
men
ts onto distin
ct
scales. Th
e problem for th
is analysis is th
at well-form
ed examples of com
parative
subdeletion
such
as (19) in
dicate that degrees of len
gth an
d degrees of width
are
comm
ensu
rable; according to th
e analysis of in
comm
ensu
rability outlin
ed above, (19) sh
ould
be anom
alous, h
owever.
(19)
Billy-B
ob’s tie is as wide as it is lon
g.
Sin
ce the referen
ce and stan
dard values in
(19) are degrees on
different scales, th
e
comparison
relation sh
ould be u
ndefin
ed, and (19
) shou
ld have th
e same statu
s as (18). Th
is
is clearly the w
rong resu
lt, as (19) is perfectly in
terpretable.
Th
is problem cou
ld be avoided by assum
ing th
at long an
d wide sh
are the sam
e
scale–for example, a scale alon
g a dimen
sion of “lin
ear extent”. If th
is were th
e case, then
the fact th
at comparison
s like (19) are possible w
ould n
ot be surprisin
g: degrees of width
and len
gth w
ould be elem
ents of th
e same lin
early ordered set, so the orderin
g relation
introdu
ced by the com
parative wou
ld be defined. 7 T
he problem
is that B
artsch an
d
Ven
nem
ann
’s claim th
at the m
eanin
gs of all adjectives are defined in
terms of a sin
gle
7An
alternative solu
tion to th
e problem
posed
by examp
les like (19) w
ould
involve assu
min
g that th
e
distin
ct scales of wid
th an
d len
gth are som
ehow
similar en
ough
to perm
it a map
pin
g betw
een th
em w
hich
licenses co
mp
arison
. Th
is app
roach
weak
ens th
e stron
g con
straint o
n co
mm
ensu
rability d
efined
abo
ve,h
owever, an
d raises a n
um
ber of qu
estions, m
ost imp
ortant of w
hich
is: wh
en are su
ch m
app
ings d
efined
and
wh
en are th
ey un
defin
ed?
98
measu
re fun
ction is in
compatible w
ith th
is assum
ption. A
crucial distin
ction betw
een e.g.
long and w
ide is that th
ey may im
pose different orderin
gs on th
eir domain
s, even in
contexts
in w
hich
their dom
ains are equ
ivalent. If both
adjectives were associated w
ith th
e same scale
and th
e same m
easure fu
nction
, as in B
artsch an
d Ven
nem
ann
’s analysis, th
is fact could n
ot
be captured. T
hat is, if th
e interpretation
s of long and w
ide were as sh
own
in (20
) and (21),
then
in a con
text in w
hich
their dom
ains are th
e same, th
e analysis w
ould in
correctly predict
that th
e adjectives wou
ld impose exactly th
e same orderin
gs on th
eir domain
s, since th
eir
mean
ings are ch
aracterized in term
s of the sam
e measu
re fun
ction.
(20)
long = λx.f M(x, lin
ear extent)
(21)w
ide =λx.f M(x, lin
ear extent)
Given
these con
siderations, I con
clude th
at the in
terpretations of gradable adjectives
shou
ld not be ch
aracterized in term
s of a single, gen
eral measu
re fun
ction. In
stead, I will
assum
e that every gradable adjective den
otes a distinct m
easure fu
nction
wh
ose domain
is
the set of objects th
at satisfy the selection
al restrictions of th
e adjective and w
hose ran
ge is a
scale. Th
is view allow
s for the possibility th
at distinct lexical item
s such
as long and w
ide have
identical dim
ension
al parameters, an
d so map th
e objects in th
eir domain
s to the sam
e
scale, predicting th
at comparison
s such
as (19) sh
ould be possible. B
ut sin
ce long and w
ide
denote differen
t fun
ctions from
objects to the sam
e scale, they m
ay impose distin
ct
orderings on
their dom
ains. A
t the sam
e time, th
is analysis m
aintain
s an accou
nt of th
e
fun
ctional u
nity th
e class of gradable adjectives, wh
ich B
artsch an
d Ven
nem
ann
derive from
the assu
mption
that th
e mean
ings of all gradable adjectives are stated in
terms of a sin
gle
measu
re fun
ction. In
the an
alysis proposed here, th
is un
ity follows from
the fact th
at
gradable adjectives are all of the sam
e seman
tic type: they are expression
s of type ⟨τ,d⟩,
fun
ctions from
expressions of type τ to degrees.
Th
e interpretation
s of long and wide on
this view
can be stated as (22) an
d (23), wh
ere
λx.long(x) an
d λx.w
ide(x) are distinct fu
nction
s from objects to degrees on
a scale of “linear
99
extent”.
(22)long = λx.long(x)
(23)w
ide = λx.w
ide(x)
Th
e intu
ition u
nderlyin
g the h
ypothesis th
at long and w
ide denote differen
t fun
ctions from
objects to the sam
e scale is that alth
ough
they m
easure objects accordin
g to the sam
e
dimen
sion, th
ey do so according to differen
t (“perpendicu
lar”) aspects.
An
importan
t difference betw
een long an
d wide is th
at the dim
ension
al parameter of
long, un
like that of w
ide, may take on
different valu
es (i.e., long is associated with
more th
an
one scale). A
s show
n by th
e examples in
(24)-(26), long can
measu
re spatial extent, tem
poral
duration
, or “page nu
mber”.
(24)
Billy-B
ob’s tie is long.
(25)T
he film
was lon
g.
(26)
The B
rothers Karam
azov is long.
In section
1.1.2 of chapter 1, I referred to th
e possibility of a gradable adjective being
associated with
more th
an on
e dimen
sion–
and by exten
sion, m
ore than
one scale–
as
indeterminacy. W
ithin
the fram
ework ou
tlined h
ere, indeterm
inacy is represen
ted as a kind
of ambigu
ity. Th
e lexical entry of an
y gradable adjective mu
st provide inform
ation abou
t its
range–i.e., it m
ust in
clude a list of possible valu
es of the dim
ension
al parameter of th
e
adjective, identifyin
g the scale or scales on
to wh
ich it m
aps the objects in
its domain
. Th
e
special characteristic of in
determin
ate (or “non
-linear”) adjectives like lon
g is that th
ey can
measu
re objects with
respect to more th
an on
e dimen
sion. S
ince gradable adjectives are
fun
ctions, h
owever, on
any occasion
of use lon
g mu
st map its argu
men
t to some particu
lar
value, i.e., a degree on
one of th
e scales with
wh
ich it is associated. T
he problem
of
indeterm
inacy is th
e problem of figu
ring ou
t for utteran
ces of senten
ces like (24)-(26
)
100
wh
ich of th
e possible values of th
e dimen
sional param
eter of the adjective is in
tended, w
hich
in tu
rn determ
ines th
e scale onto w
hich
it projects its argum
ent.
2.1.4 Degree C
onstru
ctions
Th
e fun
damen
tal difference betw
een th
e analysis of gradable adjectives as m
easure
fun
ctions an
d the tradition
al scalar analysis is th
at in th
e latter, the m
eanin
g of a gradable
adjective inclu
des a fun
ction from
objects to degrees, but th
is is only on
e compon
ent of th
e
mean
ing of th
e adjective: it also inclu
des a degree argum
ent (th
e standard valu
e) and a
comparison
relation (a partial orderin
g relation). In
the altern
ative approach I h
ave
advocated, the com
parison relation
and th
e degree argum
ent are elim
inated, leavin
g only
the m
easure fu
nction
as the core m
eanin
g of the adjective. T
he in
tuition
un
derlying th
is
analysis is th
at the sem
antic fu
nction
of a gradable adjective is to project its argum
ent on
to a
scale. A resu
lt of the an
alysis is that it provides a startin
g point for an
implem
entation
of the
tripartite analysis of proposition
s constru
cted out of gradable adjectives th
at I introdu
ced in
section 2.1.1. S
pecifically, I suggested th
at the in
terpretation of absolu
te and degree
constru
ctions sh
ould be ch
aracterized in term
s of three sem
antic con
stituen
ts: a reference
value, a stan
dard value, an
d a degree relation. O
n th
is view, th
e mean
ing of a sen
tence like
(27) can be paraph
rased as (28), wh
ich is stated in
terms of a partial orderin
g between
two
degrees.
(27)T
he n
eutron
star in th
e Crab N
ebula is den
se.
(28)
Th
e degree to wh
ich th
e neu
tron star in
the C
rab Nebu
la is dense is at least as great
as some stan
dard of densen
ess (relativized to a comparison
class for neu
tron stars).
Th
e reference valu
e in (28) is th
e degree to wh
ich th
e neu
tron star in
the C
rab Nebu
la is
dense; given
the an
alysis of gradable adjectives as measu
re fun
ctions, th
is value can
be
straightforw
ardly derived by applying th
e adjective to the su
bject, as in (29
), wh
ich retu
rns a
degree: the projection
of the neutron star in the Crab N
ebula on a scale of den
sity.
101
(29)
dense(the neutron star in the Crab N
ebula)
Th
e formu
la in (29
) supplies on
ly one of th
e three con
stituen
ts in (28), h
owever,
raising th
e followin
g question
: wh
ere do the stan
dard value an
d the partial orderin
g relation
come from
? Th
e answ
er that I w
ill pursu
e here is th
at both th
e relational com
ponen
t and
the stan
dard value are in
troduced by th
e degree morph
ology. In th
is section, I w
ill present a
seman
tic analysis of degree m
orphology th
at implem
ents th
is hypoth
esis, and in
section 2.2,
I will in
troduce a syn
tactic analysis of th
e adjectival projection th
at supports a com
positional
seman
tics of degree constru
ctions in
terms of th
e proposals made h
ere. Specifically, I w
ill
claim, follow
ing A
bney 19
87, C
orver 199
0, 19
97 an
d Grim
shaw
199
1, that gradable
adjectives project extended fu
nction
al structu
re headed by degree m
orphology. In
order to
motivate th
e analysis, I w
ill first reconsider th
e relation betw
een absolu
te constru
ctions su
ch
as (27) and th
e more com
plex comparative con
struction
s.
In th
e discussion
up to n
ow, I h
ave main
tained a distin
ction betw
een absolu
te and
comparative con
struction
s. Th
is distinction
is an artifact of th
e relational an
alysis, how
ever,
since a claim
of such
an an
alysis is that th
e absolute form
represents th
e basic mean
ing of
the adjective, an
d the in
terpretations of com
plex degree constru
ctions are stated in
terms of
the m
eanin
g of the absolu
te. On
ce the assu
mption
that adjectives are relation
al has been
discarded, how
ever, the prim
acy of the absolu
te disappears. Instead, th
e line of reason
ing
that I h
ave pursu
ed here is bu
ilt on th
e hypoth
esis that th
e basic mean
ing of a proposition
constru
cted out of a gradable adjective in
the absolu
te form an
d a proposition con
tainin
g a
more com
plex degree constru
ctions is th
e same. B
oth h
ave three prim
ary seman
tic
constitu
ents: a referen
ce value, a stan
dard value, an
d a degree relation. (30
)-(32) reiterate
this poin
t.
(30)
Plu
to is colder than
Neptu
ne.
(31)Ju
piter is less cold than
Neptu
ne.
102
(32)U
ranu
s is as cold as Neptu
ne.
Th
e mean
ings of th
ese senten
ces can be ch
aracterized in exactly th
e same w
ay as (27), as
illustrated by (33)-(35).
(33)T
he degree to w
hich
Plu
to is cold exceeds the degree to w
hich
Neptu
ne is cold.
(34)
Th
e degree to wh
ich Ju
piter is cold is exceeded by the degree to w
hich
Neptu
ne is
cold.
(35)T
he degree to w
hich
Uran
us is cold is at least as great as th
e degree to wh
ich
Neptu
ne is cold.
As in
the case of (27), th
e determin
ation of th
e reference valu
e in th
ese examples is clear: it
is derived by applying th
e adjective to the su
bject. Wh
at distingu
ishes (30
)-(32) from th
e
absolute con
struction
in (27), is th
at in th
e former, it is also clear w
hich
constitu
ents
introdu
ce the degree relation
s and th
e standard valu
es: the degree m
orphem
es and th
e
comparative clau
ses, respectively. Given
the overall parallelism
between
the in
terpretation
of the absolu
te constru
ction an
d the in
terpretations of th
e complex degree con
struction
s as
presented h
ere, the n
atural assu
mption
is that th
e absolute con
struction
contain
s a
phon
ologically nu
ll degree morph
eme (cf. C
resswell 19
76, von
Stechow
1984a). In
addition,
given th
e observed depen
dency betw
een th
e particu
lar degree morp
hem
e and th
e
morph
ological form of th
e “standard m
arker” (i.e., the fact th
at er/more an
d less require
their associated com
parative clauses to be m
arked by than, and as requ
ires its clause to be
marked by as), w
e can assu
me th
at the degree m
orphem
e introdu
ces the stan
dard value.
On
this view
, the absolu
te is not
fun
damen
tally distin
ct from
m
orph
ologically an
d
syntactically com
plex degree constru
ctions, rath
er it is a type of degree constru
ction as w
ell.
If this an
alysis is correct, we can
adopt the gen
eral interpretation
rule for degree
constru
ctions sh
own
in (36
), wh
ere Deg is a degree relation
, Ref is th
e reference valu
e, and
Stnd is th
e standard valu
e.
103
(36)
||Deg(R
ef)(Stn
d)|| = 1 iff ⟨Ref,S
tnd⟩ ∈
Deg
Accordin
g to (36), a proposition
constru
cted out of a gradable adjective is tru
e just in
case the
reference valu
e and th
e standard valu
e stand in
the relation
introdu
ced by the degree
morph
eme. A
lthou
gh th
is analysis provides an
accurate ch
aracterization of th
e truth
condition
s of propositions in
volving degree con
struction
s, it does not yet explain
an
importan
t fact: the predicative con
stituen
ts in (27) an
d (30)-(31) den
ote properties of
individu
als, not relation
s between
degrees. Wh
at remain
s to be developed is a seman
tic
analysis of degree m
orphology in
wh
ich th
e predicative constitu
ents in
these sen
tences
denote properties of in
dividuals.
In order to ach
ieve this resu
lt, I will propose th
at a degree morph
eme com
bines w
ith
a measu
re fun
ction (a gradable adjective) an
d a degree (the stan
dard value) to gen
erate a
property of individu
als, and it is th
is property that is th
e mean
ing of a degree con
struction
.
Th
e basic interpretation
of a degree morph
eme is given
in (37), w
here G
is a gradable
adjective mean
ing, d is th
e standard valu
e, and R
is the relation
introdu
ced by particular
degree morph
emes (e.g., a partial orderin
g for the absolu
te morph
eme, a total orderin
g for
more, etc.).
(37)D
eg = λG
λdλ
x[R(G
(x))(d)]
Th
e intu
ition u
nderlyin
g this an
alysis is that a degree con
struction
denotes a fu
nction
that
picks out th
e subset of th
e domain
of a gradable adjective that con
tains objects w
hose
projection on
to the scale associated w
ith th
e adjective stand in
some relation
–the relation
denoted by th
e particular degree m
orphem
e involved–to th
e standard valu
e. On
this view
,
the m
eanin
g of a degree constru
ction correspon
ds rough
ly to the m
eanin
g of a gradable
adjective wh
ose degree argum
ent h
as been satu
rated in th
e traditional an
alysis–with
one
crucial differen
ce. Th
is difference con
cerns th
e relation at th
e core of a degree
104
constru
ction. In
the tradition
al analysis, th
e interpretation
of a gradable adjective ϕ is
defined in
terms of a partial orderin
g relation, as in
(38) (wh
ere δϕ is a fu
nction
from objects
to the scale associated w
ith ϕ
).
(38)
ϕ = λ
dλx[δ
ϕ (x) ≥ d]
It follows from
this an
alysis that th
e property derived by saturatin
g the degree argu
men
t of a
gradable adjective is always of th
e form “is at least as ϕ
as the stan
dard value”. Q
uan
tification
over the stan
dard value p
rovides a way of distin
guish
ing betw
een differen
t degree
constru
ctions, bu
t the relation
between
the referen
ce and stan
dard values rem
ains th
e
same: it is a partial orderin
g relation.
In con
trast, the an
alysis I have advocated h
ere removes th
e relational com
ponen
t
from th
e mean
ing of th
e adjective, leaving on
ly the m
easure fu
nction
. As a resu
lt, the
relation associated w
ith a particu
lar degree constru
ction is determ
ined by th
e mean
ing of
the degree m
orphem
e that h
eads the con
struction
, allowin
g a range of differen
t degree
properties to be constru
cted throu
gh th
e combin
ation of a gradable adjective m
eanin
g and
wh
atever degree morph
emes th
e langu
age contain
s. Con
sider, for example, (30
) and (31),
discussed above an
d repeated below.
(30)
Plu
to is colder than
Neptu
ne.
(31)Ju
piter is less cold than
Neptu
ne.
Th
e degree morph
emes in
these exam
ples introdu
ce distinct relation
s; as a result, th
e
degree constru
ctions in
the tw
o senten
ces are differentiated by th
e relations th
ey impose
between
the referen
ce value an
d the stan
dard value. A
ssum
ing th
at er/more in
troduces th
e
relation “>” an
d less introdu
ces the relation
“<“, the “m
ore comparative” in
(30) can
be
assigned th
e interpretation
in (39
), and th
e “less comparative” in
(31) can be in
terpreted as
in (40
).
105
(39)
λx[cold(x) > cold(N
eptun
e)]
(40
)λ
x[cold(x) < cold(Neptu
ne)]
(39) den
otes the property of bein
g cold to a degree that exceeds th
e coldness of N
eptun
e;
(40) den
otes the property of bein
g cold to a degree that is exceeded by th
e coldness of
Neptu
ne. T
he properties expressed by (39
) and (40
) are identical w
ith respect to stan
dard
values; th
ey differ only in
their relation
al characteristics.
To su
mm
arize, the sem
antic an
alysis of degree constru
ctions proposed h
ere consists
of two claim
s. First, th
e truth
condition
s of a proposition con
tainin
g a gradable adjective
shou
ld be characterized in
terms of th
ree primary sem
antic con
stituen
ts: a reference valu
e,
a standard valu
e, and a degree relation
. Secon
d, a degree constru
ction com
posed of a
gradable adjective ϕ an
d a degree morph
eme D
eg denotes a property of an
individu
al: the
property of being ϕ
to a degree wh
ich stan
ds in th
e Deg relation
to the stan
dard value. In
sections 2.2 th
rough
2.4, I will go th
rough
the com
positional sem
antic an
alysis of absolute
and com
parative degree constru
ctions in
En
glish in
detail, show
ing h
ow in
terpretations like
(39) an
d (40) are derived from
their syn
tactic representation
s. Alth
ough
I will focu
s on
absolute an
d comp
arative constru
ctions, a su
perficial exam
ination
of other degree
constru
ctions, su
ch as th
e too, enough
, and so...that con
struction
s in (41)-(43), su
ggests that
the basic approach
can be gen
eralized. 8
(41)
Mercu
ry is too hot to su
pport life as we kn
ow it.
(42)
Hale-B
opp was brigh
t enou
gh for u
s to see with
out bin
oculars.
8An
other relevan
t class of degree con
struction
s is how
qu
estions su
ch as (i) an
d (ii).
(i)H
ow close is th
e nearest galaxy?
(ii)Ed
ric asked h
ow lon
g a light year is.
Assu
min
g that h
ow
is a degree m
orph
eme, syn
tactically and
seman
tically on a p
ar with
more
, too, an
d so on
(Corver 1991), th
en a reason
able hyp
othesis is th
at how
question
s involve
quan
tification over d
egree relations (see K
lein 1980 for an
app
roach alon
g these lin
es).
106
(43)
Th
e black hole at th
e center of th
e galaxy is so massive th
at even ligh
t can’t escape
the pu
ll of its gravity.
If these degree con
struction
s fit into th
e paradigm ou
tlined h
ere, then
it shou
ld be
possible to state the tru
th con
ditions of, for exam
ple, (41)-(4
3) in term
s of a relation
between
a reference valu
e (the degree to w
hich
Mercu
ry is hot, th
e degree to wh
ich H
ale-
Bopp w
as bright, th
e degree to wh
ich th
e black hole at th
e center of th
e galaxy is massive)
and som
e other valu
e. Th
e paraphrases of (41)-(43) in
(44)-(46) su
ggest that th
is is indeed
possible (cf. Moltm
ann
199
2a:301).
(44
)M
ercury is too hot to su
pport life as we know
it is true ju
st in case th
e degree to wh
ich
Mercu
ry is hot m
akes it impossible for th
e planet to su
pport life as we kn
ow it.
(45)
Hale-B
opp was bright en
ough for u
s to see withou
t binocu
lars is true ju
st in case th
e
degree to wh
ich H
ale-Bopp w
as bright m
ade it possible for us to see it w
ithou
t
binoculars.
(46
)T
he black hole at the center of the galaxy is so massive that even light can’t escape the pull
of its gravity is true ju
st in case th
e degree to wh
ich th
e black hole at th
e center of th
e
galaxy is massive cau
ses it to be true th
at light can
’t escape the pu
ll of its gravity.
Th
e d
ifference
between
d
egree con
struction
s like
(41)-(4
3) an
d
the
absolute
and
comparative con
struction
s discussed above is th
at the m
eanin
gs of the form
er are
characterized in
terms of cau
sal relations betw
een degrees an
d states of affairs, rather th
an
in term
s of ordering relation
s between
pairs of degrees. As a resu
lt, the qu
estion th
at mu
st
be answ
ered is the follow
ing: w
hat are th
e properties of a causal relation
between
a degree
and a state of affairs, an
d how
is such
a relation con
structed? T
he an
swer to th
is question
has im
portant em
pirical consequ
ences, as statem
ents like (41)-(43) h
ave clear inferen
ces
that m
ust be explain
ed. For exam
ple, althou
gh th
e argum
ent in
(47) is valid, the on
e in (48)
107
is not. 9
(47)
Kim
is too old to qualify for th
e children
’s fare.
Sandy is older th
an K
im.
/∴ San
dy is too old to qualify for th
e children
’s fare.
(48
)T
he bottle of m
ilk in m
y refrigerator is too old to drink.
Th
e bottle of win
e in m
y closet is older than
the bottle of m
ilk in m
y refrigerator.
#/∴ T
he bottle of w
ine in
my closet is too old to drin
k.
Alth
ough
I will leave an
investigation
of these issu
es for futu
re work, it sh
ould be n
oted that
if a satisfactory answ
er to the qu
estion posed above can
be constru
cted, then
the an
alysis that
I have proposed h
ere will su
cceed in providin
g a characterization
of the m
eanin
gs of
senten
ces like (41)-(4
3) with
out referen
ce to a notion
of comparison
, a result th
at is
impossible in
a traditional relation
al analysis, w
hich
takes a comparison
relation to be a basic
compon
ent of th
e mean
ing of gradable adjectives. S
ince it is n
ot obvious th
at the tru
th
condition
s of these sen
tences sh
ould be stated in
terms of a n
otion of com
parison (see
footnote 2), th
is wou
ld be a positive result.
2.1.5 Evaluation
In section
2.1.1, I listed several desiderata that a sem
antic an
alysis of gradable adjectives and
degree constru
ctions sh
ould aim
to satisfy. First, it sh
ould explain
the scopal ch
aracteristics
of the com
parative and th
ose of the com
parative clause. S
econd, it sh
ould su
pport an
explanation
of incom
men
surability, cross-polar an
omaly, an
d comparison
of deviation. T
hird,
in order to satisfy con
cerns abou
t composition
ality, it shou
ld characterize th
e interpretation
of gradable adjectives indepen
dently of a n
otion of com
parison. T
he explan
ation of
9See also Karttu
nen
1971 for a discu
ssion of som
e add
itional p
uzzles in
volving th
e entailm
ents of too
and en
ough
constru
ctions.
108
incom
men
surability in
the an
alysis proposed here w
as outlin
ed in section
2.1.2 and w
ill be
discussed fu
rther in
section 2.4
.1, and th
e explanation
of cross-polar anom
aly and
comparison
of deviation w
ill be the focu
s of chapter 3. It sh
ould be clear th
at the an
alysis
developed here satisfies th
e third requ
iremen
t. Sin
ce the relation
al compon
ent is rem
oved
from th
e mean
ing of a gradable adjective, leavin
g only th
e measu
re fun
ction, n
o notion
of
comparison
is involved in
the core specification
of a gradable adjective’s mean
ing. A
t the
same tim
e, the in
terpretation of degree con
struction
s is stated strictly in term
s of the
composition
of a gradable adjective with
degree morph
ology, a point th
at will becom
e more
apparent in
the follow
ing section
s, wh
ere I will discu
ss the com
positional an
alysis of absolute
and com
parative constru
ctions. T
his leaves th
e first point: w
hat are th
e predictions of th
e
analysis developed h
ere regarding th
e scopal properties of the com
parative and th
e
comparative clau
se?
A cen
tral claim of th
e analysis of degree con
struction
s outlin
ed in th
e previous
section is th
at the degree m
orphem
e has n
o quan
tificational force; in
this respect, it differs
from all of th
e accoun
ts discussed in
chapter 1: th
e scalar analyses of com
paratives as
existential qu
antification
structu
res and gen
eralized quan
tifiers, as well as th
e vague
predicate analysis, w
hich
involved existen
tial quan
tification over degree fu
nction
s. Th
e
empirical con
sequen
ce of this differen
ce is that it explain
s wh
y comparatives do n
ot
participate in scope am
biguities. If degree m
orphem
es do not h
ead a constru
ction th
at
quan
tifies over the degree argu
men
t of a gradable adjective, then
there is n
o expectation
that com
paratives (as a type of degree constru
ction) sh
ould participate in
quan
tificational
scope ambigu
ities. More im
portantly, if degree m
orphem
es are compon
ents of th
e
predicative expression in
a proposition con
structed ou
t of a gradable adjective, then
their
scopal properties shou
ld be the sam
e as those of th
e predicate. Sin
ce predicates, in effect,
always
have
narrow
scop
e (i.e.,
they
have
no
indep
enden
t scop
al ch
aracteristics),
comparatives an
d other degree con
struction
s shou
ld also always h
ave narrow
scope.
To see th
at this is in
deed so, consider th
e case of negation
. In section
1.4.1 of chapter
1, I observed that a sen
tence like (49
) is not am
biguou
s: it can on
ly be interpreted as a
109
denial th
at Neptu
ne is colder th
an P
luto, n
ot as a claim th
at there is a degree w
hich
exceeds
the degree to w
hich
Plu
to is cold, and N
eptun
e is not th
at cold.
(49
)N
eptun
e is not colder th
an P
luto.
Th
e problem for qu
antification
al analyses of com
paratives was th
at with
out addition
al
stipulation
s, such
a reading can
not be ru
led out: if com
paratives are quan
tificational, th
en
like other qu
antification
al expressions, th
ey shou
ld interact w
ith n
egation to gen
erate scope
ambigu
ities. Th
at is, a quan
tificational an
alysis shou
ld permit th
e two logical represen
tations
for (49) in
(50) an
d (51): one in
wh
ich th
e comparative h
as scope inside n
egation ((50
),
wh
ich represen
ts the actu
al interpretation
of (49)), an
d one in
wh
ich th
e comparative h
as
scope outside n
egation ((51), w
hich
represents th
e impossible in
terpretation).
(50)
¬∃
d[d > m
ax(λd’.cold(P
luto,d’))][cold(N
eptun
e,d)]
(51)∃
d[d > m
ax(λd’.cold(P
luto,d’))]¬
[cold(Neptu
ne,d)]
In con
trast, the an
alysis of comparatives as degree properties gen
erates a single
logical representation
for (49). A
ssum
ing th
at negation
has clau
sal scope, (49) h
as the
interpretation
in (52): it asserts th
at it is not th
e case that N
eptun
e has th
e property of
being colder th
an P
luto.
(52)¬
[(cold(Neptu
ne)) > (cold(P
luto))]
Th
e failure of com
paratives to show
scope ambigu
ities in oth
er contexts (e.g., in
the scope of
un
iversal quan
tifiers, inten
sional con
texts, etc.) can be explain
ed in th
e same w
ay.
Alth
ough
the facts discu
ssed in ch
apter 1 indicated th
at the com
parative constru
ction
did not participate in
scope ambigu
ities, this w
as not tru
e of the com
parative clause.
Exam
ples like (53) and (54), w
hich
have “sen
sible” (de re) and “con
tradictory” (de dicto)
110
interpretation
s were presen
ted as evidence th
at the com
parative clause does sh
ow scope
ambigu
ities in in
tension
al contexts.
(53)K
arl thou
ght N
eptun
e was colder th
an it w
as.
(54)
If Ven
us w
ere less hostile th
an it is, w
e wou
ld be able to land a probe on
its surface.
Un
like the relation
al analysis, in
wh
ich th
e standard valu
e is denoted by th
e entire
comparative con
struction
(wh
ich in
cludes th
e comparative clau
se as a subcon
stituen
t), the
analysis th
at I have ou
tlined in
this section
claims th
at the stan
dard value is den
oted by the
comparative clau
se. In oth
er words, in
the an
alysis proposed here, it is th
e comparative
clause th
at denotes th
e “degree argum
ent” in
a degree constru
ction. If th
e comparative
clause den
otes an actu
al argum
ent, th
en th
e fact that it participates in
scope relations is n
ot
surprisin
g. Th
e exact way in
wh
ich it in
teracts with
other expression
s to trigger scope
ambigu
ities shou
ld be explained in
terms of its in
ternal sem
antics (e.g., w
heth
er it is a type
of definite description
, as I have assu
med h
ere, or a un
iversal quan
tification stru
cture); th
is
is not a qu
estion th
at I will address h
ere, but see K
enn
edy 199
7c for argum
ents th
at the
comparative clau
se is a type of definite description
(see also Ru
ssell 190
5, Hasegaw
a 1972,
Postal 19
74, Horn
1981, von
Stech
ow 19
84a, Larson 19
88a, Lerner an
d Pin
kal 199
2, 199
5,
and oth
ers for relevant discu
ssion).
2.1.6 H
istorical Con
text
Before m
oving on
to a more detailed look at th
e composition
al analysis of specific degree
constru
ctions, th
e approach to th
e seman
tics of gradable adjectives and degree con
struction
s
that I h
ave proposed here sh
ould be situ
ated in th
e context of previou
s work. In
general
terms, th
e analysis of gradable adjectives as m
easure fu
nction
s bears some sim
ilarity to the
analysis of gradable adjectives in
the vagu
e predicate analysis: in
both accou
nts, gradable
adjectives denote fu
nction
s, and th
e interpretation
of complex degree con
struction
s involves
the com
position of degree m
orphology w
ith th
e adjective to generate a com
plex property
111
that is applied to th
e subject. T
he cru
cial difference betw
een th
e measu
re fun
ction an
alysis
and th
e vague predicate an
alysis is that th
e former in
cludes th
e core assum
ptions of a scalar
approach: scales an
d degrees are part of the on
tology, and gradable adjectives defin
e
mappin
gs from objects to degrees. M
ore generally, th
e measu
re fun
ction an
alysis derives
the orderin
g on th
e domain
of a gradable adjective from a sem
antic property of th
e adjective
itself, as does the tradition
al scalar analysis; it does n
ot assum
e an in
heren
t ordering on
the
domain
, as the vagu
e predicate analysis does. Sin
ce a scale is defined as a totally ordered set
of points (degrees), a con
sequen
ce of the an
alysis of gradable adjectives as fun
ctions from
objects to degrees is that th
ey are ordering fu
nction
s, i.e., fun
ctions th
at directly impose an
ordering on
their dom
ains by associatin
g objects with
degrees on a scale. 10
In th
is respect, the m
easure fu
nction
analysis is also sim
ilar to a “fuzzy logic”
approach (see e.g. Lakoff 19
72, 1973, Z
adeh 19
71). Th
e basic claim of a fu
zzy logic approach
is that (at least som
e) expressions th
at are analyzed in
classic model th
eory as fun
ctions
from expression
s of type τ to {0,1} (e.g., adjectives an
d other on
e-place predicates) shou
ld
instead be con
strued as a fu
nction
s from objects of type τ to th
e interval [0
,1]–the set of real
nu
mbers betw
een 0
and 1, in
clusive. In
tuitively, fu
nction
s of this type m
ap objects to
nu
merical valu
es that represen
t the degree to w
hich
the object m
anifests som
e gradable
property, for example, tallness. W
hen
objects that are defin
itely not tall are su
bstituted for x
in th
e formu
la tall(x), the resu
lt is 0, for objects th
at are definitely tall th
e result is 1, an
d for
all other objects, th
e result is som
e real nu
mber betw
een 0
and 1. C
omparison
in th
is type
of approach in
volves evaluatin
g the valu
es of ϕ(x) an
d ϕ(y) again
st a particular orderin
g
relation (i.e., “>“, “ <”, or “≥”).
Klein
(1980
) criticizes this an
alysis for failing to m
ake a distinction
amon
g objects
that defin
itely possess a gradable property like tallness, poin
ting ou
t that in
a context in
wh
ich tw
o objects a and b are both
definitely tall, bu
t a is taller than
b, the valu
e of tall(a) and
tall(b) in a fu
zzy logic analysis w
ould be th
e same: 1. A
s a result, th
e proposition den
oted by
10I will retu
rn to a m
ore detailed
discu
ssion of th
e orderin
g characteristics of m
easure fu
nction
s wh
en
I discu
ss the m
onoton
icity prop
erties of gradable ad
jectives in ch
apter 3.
112
a is taller than b wou
ld incorrectly tu
rn ou
t to be false. Klein
’s objection cou
ld be han
dled by
assum
ing th
at gradable adjectives denote fu
nction
s into th
e set of real nu
mbers betw
een 0
and 1 exclu
sive (the open
interval (0
,1)) such
that for all x an
d y in th
e domain
of ϕ, ϕ
(x) =
ϕ(y) ju
st in case x = y in
ϕ-n
ess.
Given
this assu
mption
, a fuzzy logic an
alysis and a m
easure fu
nction
analysis are
indeed fu
ndam
entally th
e same, except for on
e importan
t and em
pirically significan
t
difference: th
e dimen
sional featu
re of scales. Th
e crucial effect of th
e dimen
sional valu
e is
to distingu
ish on
e scale from an
other, a distin
ction th
at provides the basis for th
e
explanation
of incom
men
surability (see section
1.3.3.1 in ch
apter 1). In a fu
zzy logic analysis,
all gradable adjectives denote fu
nction
s from in
dividuals to (0
,1); as a result, th
is analysis
wou
ld incorrectly predict th
at all adjectives shou
ld be comm
ensu
rable, a prediction th
at is
not su
pported by the facts. 11
Fin
ally, the h
ypothesis th
at the m
eanin
g of a proposition con
structed ou
t of a
gradable adjective shou
ld be characterized in
terms of a referen
ce value, a stan
dard value,
and a degree relation
has its roots in
Ru
ssell’s (190
5) analysis of th
e comparative
constru
ction as a relation
between
two defin
ite descriptions (see fn
. 4), and it is sim
ilar to
the gen
eralized quan
tifier analyses of com
paratives discussed in
chapter 1 (e.g., M
oltman
n
199
2a; see also Postal 19
74, C
resswell 19
76, an
d William
s 1977). F
or example, th
e
interpretation
of a senten
ce like (55) in a gen
eralized quan
tifier analysis is (56
) (see the
discussion
in ch
apter 1, section 1.4.5 for details).
11At th
e same tim
e, the m
echan
ics of the fu
zzy logic analysis m
ay provid
e the b
asis for a formal
analysis of m
etalingu
istic comp
arison, a p
hen
omen
on exem
plified
by (i).
(i)B
ob is more “vertically ch
allenged
” than
“short”.
As n
oted by M
cCaw
ley (1988:673) (see also Klein
1991), a comp
arative like (i) d
oes not com
pare d
egree to wh
ich
Bo
b is vertically ch
allenged
with
the d
egree to w
hich
he is sh
ort, b
ut rath
er the d
egree to w
hich
it is
app
ropriate to d
escribe Bob as vertically ch
allenged
with
the d
egree to wh
ich it is ap
prop
riate to describe h
imas sh
ort. An
imp
ortant ch
aracteristic of metalin
guistic com
parison
s is that th
ey may b
e constru
cted ou
t of
oth
erwise in
com
men
surab
le adjectives (see ch
apter 1, fo
otn
ote 9), w
hich
suggests th
at the fu
zzy logic
app
roach m
ay provid
e a good fou
nd
ation u
pon
wh
ich to bu
ild an
analysis of th
ese constru
ctions, as w
ell as a
basis for explain
ing h
ow an
interp
retation is con
structed
for constru
ctions w
hose stan
dard
interp
retations are
anom
alous. Th
ese are not issu
es that I w
ill attemp
t to add
ress here, h
owever.
113
(55)P
luto is colder th
an N
eptun
e.
(56)
more(λ
d.cold(Neptu
ne,d))(λ
d.cold(Plu
to,d))
Th
e truth
of (56) is depen
dent on
wh
ether th
e argum
ents of th
e comparative operator
(wh
ich are derived by abstractin
g over the degree variable in
troduced by th
e adjective) satisfy
the relation
introdu
ced by more–proper in
clusion
. (56) is tru
e just in
case the set of degrees
to wh
ich P
luto is cold properly in
cludes th
e set of degrees to wh
ich N
eptun
e is cold.
Th
e analysis developed in
the previou
s section is sim
ilar in th
at the com
parative
morph
eme defin
es a relation betw
een tw
o expressions–th
e standard valu
e (the degree to
wh
ich P
luto is cold) an
d the referen
ce value (th
e degree to wh
ich N
eptun
e is cold)–but it
differs crucially in
the sem
antic an
alysis of the com
parative morph
eme. In
stead of
combin
ing w
ith tw
o property-denotin
g expressions, as in
(56), th
e comparative m
orphem
e
combin
es directly with
a gradable adjective and a stan
dard-denotin
g expression to gen
erate
the property in
(57), wh
ich, w
hen
applied to the su
bject, derives the proposition
in (58).
(57)λ
x[cold(x) > cold(Neptu
ne)]
(58)
cold(Plu
to) > cold(Neptu
ne)
Th
e logical representation
in (58) differs from
(56) in
two cru
cial respects. First, sin
ce
gradable adjectives are analyzed as m
easure fu
nction
s, it implem
ents th
e hypoth
esis that th
e
reference an
d standard valu
es are primary con
stituen
ts of the proposition
denoted by (55)
more directly th
an th
e generalized qu
antifier an
alysis, wh
ich ach
ieves this resu
lt only by
abstracting over th
e degree variable introdu
ced by the adjective. S
econd, an
d most
importan
tly, the degree m
orphem
e has n
o quan
tificational force. A
s a result, it does n
ot
make in
correct predictions abou
t the scopal properties of com
paratives and oth
er degree
constru
ctions.
114
2.2 The E
xtended P
rojection of A
Th
e analysis of degree con
struction
s developed in th
e previous section
claimed th
at a degree
morph
eme com
bines directly w
ith a gradable adjective an
d a standard-den
oting expression
to
create a property of individu
als, wh
ich is th
en applied to th
e subject. In
subsequ
ent section
s,
I will go th
rough
the com
positional sem
antic an
alysis of the syn
tactic structu
res in w
hich
degree m
orph
emes
app
ear in
som
e detail,
focusin
g on
absolu
te an
d com
parative
constru
ctions. B
efore I do this, h
owever, I w
ill lay out m
y general assu
mption
s about th
e
syntax of degree con
struction
s.
Follow
ing A
bney 19
87, I assu
me th
at adjectives, like nou
ns an
d verbs, project
extended fu
nction
al structu
re (see also Corver 19
90
, 199
7, Grim
shaw
199
1). Specifically, I
assum
e that th
e extended projection
of A is h
eaded by a degree morph
eme, i.e., a m
ember
of {∂, er/m
ore, less, as, so, too, enough, how
, this, that} (wh
ere ∂ is th
e phon
ologically nu
ll
morph
eme associated w
ith th
e absolute con
struction
). I will fu
rther assu
me th
at the
comparative clau
se–the con
stituen
t headed by than or as in
comparatives an
d equatives, th
e
non
-finite clau
se in a too/en
ough con
struction
, and th
e finite clau
se associated with
so–is
selected by Deg
0 but adjoin
ed to Deg’. 12 (59
) illustrates th
e basic structu
re of the exten
ded
12I.e., the com
parative clau
se is a selected ad
jun
ct, syntactically on
a par w
ith th
e selected ad
jun
cts of
verbs lik
e word
or beh
ave. N
othin
g in th
e analysis h
inges on
this d
ecision, b
ut th
ere is eviden
ce from w
h-
extraction
facts in to
o/en
ou
gh
con
structio
ns th
at the co
mp
arative clause is an
adju
nct rath
er than
acom
plem
ent of D
eg0 (as su
ggested in
Abn
ey 1987). The con
trast between
(i) and
(ii) illustrates th
e well-k
now
n
fact that extraction
of a comp
lemen
t out of an
adju
nct p
hrase is p
ossible, wh
ile extraction of an
adju
nct ou
t ofan
adju
nct is im
possib
le. (iii) and
(iv) show
that, in
contrast, b
oth argu
men
ts and
adju
ncts can
be extracted
out of a com
plem
ent clau
se.
(i)W
ho
i did
Au
drey [V
P [VP leave] [to see ti ]]
(ii)*W
hen
i did
Au
drey [V
P [VP leave] [to see h
er boss ti ]](iii)
Wh
oi d
id A
ud
rey [VP d
ecide [to see ti ]]
(iv)W
hen
i did
Au
drey [V
P decid
e [to see her boss t
i ]]
If the com
parative clau
se were a com
plem
ent of D
eg0, extraction
of argum
ents an
d ad
jun
cts shou
ld be eq
ually
acceptab
le, as in (iii) an
d (iv). If, on
the oth
er han
d, th
e comp
arative clause is an
adju
nct, w
e shou
ld see an
asymm
etry betw
een argu
men
t and
adju
nct extraction
, as in (i) an
d (ii). Th
e followin
g facts show
that th
is is
ind
eed th
e case: (v) and
(vii) show
that argu
men
ts can be extracted
out of th
e non
finite clau
ses introd
uced
by
too an
d en
ough
, wh
ile (vi) and
(viii) show
that extraction
of adju
ncts is im
possible.
115
projection of A
, wh
ere XP
is the con
stituen
t that in
troduces th
e comparative clau
se.
(59)
The extended projection of A
DegP
3 S
pec Deg’
3D
eg’ X
P 3 D
eg A
P 3
Spec A
’ 3 A
Com
ps
Sin
ce degree morp
hem
es are heads, th
ey can im
pose restriction
s on th
e types of
argum
ents th
ey allow. T
hu
s more an
d less can be lexically specified to requ
ire XP
to be a PP
headed by than
; as to require X
P to be a P
P h
eaded by as; and so on
for the oth
er degree
morph
emes.
In
man
y resp
ects, (59
) reflects
a n
atural
app
roach
to th
e syn
tax of
degree
constru
ctions, given
the su
ccess of similar approach
es to nom
inal an
d clausal stru
cture (see
Grim
shaw
199
1 for an overview
). Oth
er than
the w
ork cited above, how
ever, this an
alysis
has n
ot received a great deal of attention
. 13 Th
ere are at least two reason
s for this. T
he first
is the stren
gth of th
e traditional an
alysis of the syn
tax of AP
, articulated in
Bresn
an’s (19
73)
semin
al work on
the syn
tax of comparatives. T
he core of B
resnan
’s analysis, m
odified
slightly h
ere to fit in w
ith m
ore curren
t conception
s of phrase stru
cture, is th
at degree
(v)W
ho
i was A
ud
rey angry en
ough
[to criticize ei ]
(vi)*H
ow obn
oxiously
i was A
ud
rey angry en
ough
[to criticize her boss e
i ]
(vii)W
hich
cari was Tim
too scared [to d
rive ei ]
(viii)*How
qu
ickly
i was Tim
too scared [to d
rive the Fiat e
i ]
13Alth
ough
see Izvorski 1995 an
d Larson
1991 for a related ap
proach
in w
hich
degree con
struction
s
are analyzed
as DP-sh
ell structu
res (cf. Larson’s 1988b an
alysis of dou
ble object constru
ctions).
116
constru
ctions (w
hich
on h
er analysis con
sist of degree morph
emes an
d their associated
clauses) an
d measu
re phrases are base gen
erated as constitu
ents in
the specifier of A
P (see
also Bow
ers 1970
, Selkirk 19
70, Jacken
doff 1977, H
ellan 19
81, McC
awley 19
88, Hazou
t
199
5). Th
e basic structu
re of degree constru
ctions w
ithin
this type of an
alysis is show
n in
(60
) (absolute con
struction
s with
measu
re phrases h
ave essentially th
e same stru
cture,
differing on
ly in th
e substitu
tion of a m
easure ph
rase for DegP
). 14
(60
)A
P 4
DegP
A’
3
gD
eg X
P A
A p
articularly ap
pealin
g aspect of (6
0) is th
at it sup
ports a straigh
tforward
composition
al seman
tics of degree constru
ctions in
the con
text of a relational an
alysis of the
interpretation
of gradable adjectives: the con
stituen
t wh
ich occu
pies the specifier of A
P
denotes th
e degree argum
ent of th
e head of A
P. R
ecall from th
e discussion
in section
2.1
that th
e mean
ing of a gradable adjective ϕ
in th
e relational accou
nt is (6
1), wh
ere δϕ is a
fun
ction from
objects to degrees on th
e scale associated with
ϕ.
(61)
ϕ = λ
dλx[δ
ϕ (x) ≥ d]
Th
e interpretation
of a structu
re like (62) is straigh
tforward: th
e measu
re phrase provides
the degree argu
men
t of the adjective, an
d the sen
tence h
as the in
terpretation in
(63), w
ith
the tru
th con
ditions in
(64).
14In ord
er to derive th
e correct surface w
ord ord
er, Bresn
an (1973) claim
s that th
e comp
lemen
t of
Deg
0–the com
parative clau
se or PP–mu
st extrapose. Th
is assum
ption
is shared
by most syn
tactic analyses in
wh
ich d
egree morp
hem
es are specifies of A
P, in ord
er to captu
re the syn
tactic sub
categorization relation
between
the variou
s degree m
orph
emes an
d th
e clausal or p
reposition
al constitu
ents th
ey are associated w
ith.
An
exception
is the an
alysis in Jack
end
off 1977, in w
hich
the com
parative clau
se is base generated
in a righ
t-
adjoin
ed p
osition.
117
(62)
[IP B
enn
y is [AP
[DP
4 feet] tall]]]
(63)
δtall (B
enn
y) ≥ 4 feet
(64
)||δ
tall (Benny) ≥ 4 feet|| = 1 iff th
e degree to wh
ich B
enn
y is tall is at least as great as the
degree denoted by 4 feet.
More com
plex degree constru
ctions su
ch as th
e comparative in
(65) are in
terpreted
in a sim
ilar way. C
omparatives (an
d other degree con
struction
s) quan
tify over the degree
variable introdu
ced by the adjective; assu
min
g that qu
antification
al expressions are su
bject to
an operation
of Qu
antifier R
aising (M
ay 1977, 19
85), the degree ph
rase in (6
5) adjoins to a
clausal node at LF
, as shown
in (6
6). 15
(65)
Jupiter’s atm
osphere is m
ore violent th
an S
aturn
’s atmosph
ere is.
(66
)[IP
[DegP
more th
an S
aturn
’s atmosph
ere is [AP
ei violen
t]]i [IP Ju
piter’s atmosph
ere is
[AP
ei violen
t]]]
Th
e interpretation
of a structu
re like (66
) can th
en be form
alized either in
terms of
existential qu
antification
over degrees, as in th
e degree description an
alysis discussed in
chapter 1, section
1.4, or in term
s of the gen
eralized quan
tifier analysis discu
ssed in ch
apter
15Follo
win
g Bresn
an 1973 (see also
Hellan
1981, Heim
1985, McC
awley 1988, M
oltm
ann
1992a,
Hazou
t 1995, Ru
llman
n 1995, an
d oth
ers), I assum
e that th
e degree con
struction
is a constitu
ent at LF (i.e.,
that th
e than
-constitu
ent is extrap
osed in
the PF com
pon
ent or is recon
structed
prior to Q
R). I also assu
me
that th
e “missin
g” material in
the com
parative clau
se is recovered th
rough
an ellip
sis-resolution
mech
anism
wh
ereby missin
g material is recon
structed
un
der id
entity w
ith th
e AP in
the m
atrix clause. In
other w
ords, I
assum
e that th
e resolution
of comp
arative “deletion
” in an
examp
le like (65) is p
arallel to the resolu
tion of
anteced
ent-con
tained
deletion
(AC
D) in
an exam
ple lik
e (i), wh
ich h
as the Logical Form
in (ii) after Q
R an
drecovery of th
e elided
material (see M
ay 1985, Larson an
d M
ay 1988, and
Ken
ned
y 1997a for discu
ssion).
(i)K
ollberg recognized
everyone th
at Beck d
id.
(ii)[[everyon
e that [O
pi B
eck did
rr rree eecc ccoo oogg ggnn nnii iizz zzee eedd dd
ee eei ]]i [K
ollberg recognized e
i ]]
Note in
particular th
at, just as in
AC
D, recovery of th
e matrix A
P in
comparative deletion
introdu
ces a A-bar trace. If
the com
parative clause is an
operator-variable constru
ction, as argu
ed in C
hom
sky 1977, th
en th
is trace provides a
variable for the operator in
the com
parative clause to bin
d, just as recovery of th
e elided VP
in A
CD
provides a variablefor th
e relative operator to bind. I w
ill return
to a more detailed discu
ssion of th
e syntax of com
parative deletion in
section 2.4.2 below
.
118
1, section 1.4.6
. In th
e former an
alysis, the in
terpretation of (6
6) is (6
7), in w
hich
the
degree constru
ction provides th
e restriction for an
existential qu
antifier; in
the latter
analysis, th
e interpretation
of (66
) is (68), in
wh
ich th
e comparative m
orphem
e is analyzed
as a relation betw
een th
e comparative clau
se and th
e main
clause.
(67)
∃d[d > m
ax(λd’.violent(S
aturn’s atm
osphere,d’))][violent(Jupiter’s atm
osphere,d)]
(68
)m
ore[λd’.violent(S
aturn’s atm
osphere,d’)][λd.violent(Ju
piter’s atmosphere,d)]
Th
e logical representation
s in (6
7) and (6
8) are exactly the sam
e as those u
sed in ch
apter 1,
and can
be evaluated as discu
ssed there.
Th
is discussion
brings in
to focus th
e second explan
ation for th
e lack of attention
to
the exten
ded projection an
alysis of degree constru
ctions. A
lthou
gh n
um
erous research
ers
have discu
ssed the sem
antic an
alysis of comparatives an
d other degree con
struction
s with
in
the con
text of a syntactic an
alysis along th
e lines of (6
0) (see e.g. H
ellan 19
81, Heim
1985,
McC
awley 19
88, Hazou
t 199
5), there h
as been virtu
ally no discu
ssion of h
ow exten
ded
projection stru
ctures su
ch as (59
) shou
ld be interpreted. 16 A
n im
mediate problem
is that
the syn
tax of extended projection
appears to be incon
sistent w
ith a relation
al analysis of
gradable adjectives, given stan
dard assum
ptions abou
t the syn
tactic representation
of
argum
ent stru
cture. W
ithin
the syn
tactic tradition of th
e Prin
ciples and P
arameters
approach, w
hich
is the fram
ework I am
assum
ing h
ere, the basic assu
mption
about th
e
relation betw
een a h
ead and its argu
men
ts is that argu
men
ts of a lexical head are gen
erated
either as com
plemen
ts or specifiers. In (59
), how
ever, neith
er of these relation
s obtain.
Instead, th
e relation betw
een th
e lexical head (th
e adjective) and its argu
men
t appears to be
reversed: the m
aximal projection
of the adjective is th
e complem
ent of D
eg0
–th
e
expression w
hich
, in a relation
al analysis, sh
ould h
ead one of its argu
men
ts.
In fact, it is exactly th
is relation betw
een th
e degree morph
eme an
d the adjective
16Ab
ney (1987) in
clud
es some gen
eral discu
ssion of h
ow th
e structu
re in (59) m
ight b
e interp
reted,
bu
t this d
iscussion
does n
ot go into th
e level of detail req
uired
for a comp
lete seman
tic analysis (as A
bn
eyh
imself observes).
119
ph
rase th
at m
akes th
e exten
ded
p
rojection
structu
re in
(59
) id
eally su
ited
for a
composition
al seman
tic analysis of degree con
struction
s in term
s of the proposals m
ade in
section 2.1. A
ccording to th
ese proposals, the in
terpretation of a gradable adjective ϕ
is a
fun
ction from
objects to degrees on th
e scale identified by th
e dimen
sional param
eter of ϕ,
and th
e interpretation
of a degree morph
eme is as sh
own
in (6
9), w
here th
e value of th
e
relation R
is determin
ed by the particu
lar degree morph
eme.
(69
)D
eg = λG
λdλ
x[R(G
(x))(d)]
Given
these assu
mption
s, the com
positional in
terpretation of th
e extended projection
of a
gradable adjective (i.e., DegP
) is straightforw
ard. Con
sider, for example, th
e structu
re in
(70), w
here σ
denotes th
e standard valu
e.
(70)
DegP
g D
eg’ 4 D
eg’X
P 4
g D
eg A
P σ
gg
λ
Gλ
sλx[R
(G(x))(s)] ϕ
In (70
), in w
hich
the adjective h
as a single argu
men
t, the den
otation of A
P is ju
st the
denotation
of its head: a m
easure fu
nction
. 17 Deg
0 com
poses with
AP
to generate a
17Man
y gradable ad
jectives, for examp
le, eager and
qu
ick, can h
ave intern
al argum
ents as w
ell, as in(i-ii).
(i)B
eck w
as eager to finish
the in
vestigation.
(ii)K
ollberg was q
uick to p
oke holes in
Larsson’s th
eory.
Note th
at it is the extern
al argum
ent th
at is graded
in th
ese examp
les, just as in
the sim
pler exam
ples w
ith a
single argu
men
t. Assu
min
g that th
e seman
tic type of ad
jectives like eager and
quick
(on th
e interp
retations in
(i-ii)) is ⟨⟨s,t⟩,⟨e,d⟩⟩, after the in
ternal argu
men
t is saturated, th
e seman
tic type of AP
⟨e,d⟩: AP
denotes a m
easure
fun
ction.
120
fun
ction from
standard valu
es to individu
als–an expression
of the sam
e seman
tic type as a
gradable adjective in th
e relational accou
nt (see th
e discussion
of this poin
t in section
2.1.4).
Th
is complex expression
combin
es with
the stan
dard-denotin
g expression, gen
erating a
fun
ction from
individu
als to truth
values, w
ith th
e result th
at DegP
denotes a property of
individu
als, specifically, the property of h
aving a degree of ϕ
-ness th
at stands in
the relation
introdu
ced by the degree m
orphem
e to the stan
dard value. T
he steps in
the com
position of
(70) are sh
own
in (71).
(71)D
eg(AP
):λ
Gλ
dλx[R
(G(x))(d)](ϕ
) ⇒ λ
dλx[R
(ϕ(x))(d)]
Deg’(X
P):
λdλ
x[R(ϕ
(x))(d)](σ) ⇒
λx[R
(ϕ(x))(σ
)]
DegP
:λ
x[R(ϕ
(x))(σ)]
In th
e followin
g sections, I w
ill take a closer look at the stru
cture an
d interpretation
of absolute an
d comparative degree con
struction
s in predicative position
. I shou
ld point ou
t
that m
y goal here is n
ot to un
dertake a complete syn
tactic analysis of th
e full ran
ge of
degree constru
ctions in
En
glish (see C
orver 199
0, 19
97, an
d Abn
ey 1987 for m
ore detailed
discussion
of these issu
es); instead, I w
ill focus on
show
ing h
ow th
e syntax of exten
ded
projection su
pports a straightforw
ard composition
al seman
tics for comparative an
d absolute
constru
ctions in
terms of th
e proposals in section
2.1.
2.3 Absolute C
onstruction
s
2.3.1 Overview
In section
2.1.4, I claimed th
at gradable adjectives in th
e absolute form
, such
as thin and w
ide
in (72) an
d (73), shou
ld be analyzed as h
eading degree con
struction
s in w
hich
the degree
morph
eme is ph
onologically n
ull.
121
(72)M
ars’ atmosph
ere is thin
.
(73)T
he asteroid belt is 50
million
miles w
ide.
If this is correct, th
en accordin
g to the syn
tactic assum
ptions laid ou
t in section
2.2.1, the
structu
re of (72) shou
ld be (74).
(74)
IP 5
DP
VP
% r
u M
ars’ atmosph
ere V D
egP g g
is D
eg’ 3
Deg
AP
g g
∂
A g th
in
Sim
ilarly, assum
ing th
at the m
easure ph
rase 50,0
00
miles in
an exam
ple like (73) is
generated in
the specifier of D
egP (A
bney 19
87), the syn
tactic representation
of (73) is (75).
(75) IP
4D
P V
P $
ro
the asteroid belt V
DegP
g 4
is DP
Deg’
#
3
50
million
miles D
eg A
P
g g
∂ A
g
wide
122
Let us con
sider first the in
terpretation of absolu
te constru
ctions w
ith overt m
easure
phrases, su
ch as (75). Like oth
er degree morph
emes, th
e absolute m
orphem
e shou
ld
denote an
expression of th
e form in
(69
), repeated below.
(69
)D
eg = λG
λdλ
x[R(G
(x))(d)]
Wh
at needs to be determ
ined is th
e value of R
: the relation
introdu
ced by the absolu
te
morph
eme. F
ollowin
g a tradition of w
ork on gradable adjectives (see B
artsch &
Ven
nem
ann
1972, B
ierwisch
1989
, Gaw
ron 19
95 an
d the discu
ssion in
chapter 1, section
1.3.1), I will
assum
e that th
e ordering associated w
ith th
e absolute is a partial orderin
g relation. 18 T
he
mean
ing of th
e absolute m
orphem
e can th
en be form
alized as in (76
) (wh
ere abs is the
interpretation
of the n
ull m
orphem
e in th
e logical representation
langu
age), and th
e truth
condition
s for absolute con
struction
s can be stated as in
(77).
(76)
[Deg ∂
] = λG
λdλ
x[abs(G(x))(d)]
(77)||abs(d
1 )(d2 )|| = 1 iff d
1 ≥ d2
Given
these assu
mption
s, the com
positional an
alysis of (75) is as show
n in
(78) (I assum
e
that m
easure ph
rases denote degrees; see C
resswell 19
76, K
lein 19
80, 19
91, von
Stech
ow
1984a,b, an
d Gaw
ron 19
95 for discu
ssion).
18Noth
ing h
inges on
the an
alysis of the absolu
te in term
s of a partial ord
ering relation
instead
of one
of equ
ality. If, for examp
le, Carston
’s (1988) claim th
at adjectives are am
biguou
s between
an “at least as” an
dan
“exactly” interp
retation is correct, th
e analysis of th
e absolute p
resented
here can
be rework
ed accord
ingly.
See chap
ter 1, section 1.4.2 an
d H
orn 1992 for d
iscussion
of this issu
e.
123
(78)
IP: λ
x[abs(wide(x))(50,000 m
iles)](the asteroid belt) 4
DP
VP
: λx[abs(wide(x))(50,000 m
iles)] $
ro
the asteroid belt V D
egP: λ
dλx[abs(w
ide(x))(d)](50,000 miles)
g 4
is DP
Deg’: λ
Gλ
dλx[abs(G
(x))(d)](wide)
#
3
50 m
illion miles D
eg A
P
g g
λG
λdλ
x[abs(G(x))(d)] A
g w
ide
Th
e degree morph
eme com
bines w
ith th
e gradable adjective, generatin
g a fun
ction from
degrees to individu
als. Satu
ration of th
e degree argum
ent by th
e measu
re phrase derives a
property of individu
als wh
ich, w
hen
applied to the su
bject, return
s the form
ula in
(79) (I am
ignorin
g the con
tribution
of be and th
e tense m
orphology).
(79)
abs(wide(the asteroid belt))(50 m
illion miles)
Accordin
g to the tru
th con
ditions in
(77), (79) is tru
e just in
case the degree to w
hich
the
asteroid belt is wide is at least as great as th
e degree denoted by th
e measu
re phrase 50
million m
iles.
Th
e analysis of absolu
te adjectives with
out m
easure ph
rases, such
as (72), is
somew
hat m
ore complex, sin
ce, as observed in ch
apter 1, the stan
dard value m
ust be
contextu
ally determin
ed, possibly with
respect to a particular com
parison class. F
or example,
the com
positional an
alysis of a senten
ce like (72) shou
ld reflect the fact th
at (72) is true ju
st
in case th
e degree to wh
ich M
ars’ atmosph
ere is thin
is at least as great as a standard of
thin
ness for plan
etary atmosph
eres. On
e way to ach
ieve this resu
lt is to assum
e that th
e
value of th
e standard argu
men
t can be set in
dexically wh
en th
ere is no overt m
easure
phrase (see e.g. C
resswell 19
76, von
Stech
ow 19
84a, Bierw
isch 19
89, Lern
er and P
inkal
199
2, Gaw
ron 19
95). S
eman
tic composition
is parallel to examples w
ith m
easure ph
rases;
124
the differen
ce is that w
e mu
st introdu
ce a variable to saturate th
e standard argu
men
t, wh
ich
I have in
dicated as ds in
(80).
(80
) IP
: λx[abs(thin(x))(d
s )](Mars’ atm
osphere) 5
DP
VP
: λx[abs(thin(x))(d
s )] %
ru
Mars’ atm
osphere V D
egP: λ
Gλ
dλx[abs(thin(x))(d)](d
s ) g g
is D
eg’: λG
λdλ
x[abs(G(x))(d)](thin)
3
D
eg A
P
g g λ
Gλ
dλx[abs(G
(x))(d)] A g
thin
Sin
ce ds is a free variable, its valu
e mu
st be determin
ed by a fun
ction from
contexts to
degrees. Th
e general form
of this fu
nction
mu
st be such
that it assign
s a value to a degree
based on an
appropriate comparison
class; in th
e interpretation
of (80), sh
own
in (81), th
is
fun
ction sh
ould assign
to ds a valu
e of thin
ness th
at corresponds to a stan
dard for planetary
atmosph
eres. 19
(81)
abs(thin(Mars’ atm
osphere))(ds )
19It shou
ld b
e noted
that it is gen
erally possib
le to override th
e context-d
epen
den
t interp
retation of
an absolu
te constru
ction in
favor of a “global stand
ard”, as observed
by Lud
low (1989). For exam
ple, a sen
tence
like (i) can clearly be con
strued
as a claim abou
t the size of p
lanets in
some very gen
eral sense.
(i)N
o plan
et is small.
This read
ing m
akes th
e claim th
at there are n
o plan
ets that are sm
all in a gen
eral sense of sm
allness, bu
t at
the sam
e time, it allo
ws fo
r the existen
ce of sm
all plan
ets (i.e., plan
ets that are sm
all with
respect to
acom
parison
class mad
e up
of plan
ets and
other celestial b
odies). O
ne w
ay of accoun
ting for read
ings of th
is
sort, suggested
by Lu
dlow
, is to allow th
e comp
arison class to b
e expan
ded
to inclu
de larger p
ortions of th
e
dom
ain of th
e adjective (an
d p
ossibly the en
tire dom
ain).
125
2.3.2 Implicit Standards and C
omparison C
lasses
Klein
(1980
) presents an
importan
t argum
ent again
st an an
alysis that treats th
e standard
variable as an in
dexical expression. K
lein observes th
at a general ch
aracteristic of indexical
expressions is th
at they can
not ch
ange valu
e un
der VP
ellipsis. For exam
ple, the secon
d
conju
nct of (82) can
only m
ean th
at Mars P
athfin
der took pictures of w
hatever V
iking did,
not th
at Mars P
athfin
der took pictures of som
e other th
ing.
(82)
Vikin
g took pictures of it, an
d Mars P
athfin
der did too.
If the stan
dard variable in a form
ula like (81) is in
terpreted indexically, as described above,
then
like the pron
oun
in (82), its valu
e shou
ld remain
constan
t un
der VP
ellipsis. Exam
ple
(83), from Lu
dlow 19
89, sh
ows th
at this n
eed not be th
e case: this sen
tence asserts th
at
that elephant is large for an eleph
ant an
d that flea is large for a flea (i.e., th
at the degrees to
which that elephant an
d that flea are large are at least as great as stan
dards of largeness for
elephan
ts and fleas, respectively); (83) does n
ot mean
that that flea is large for an
elephan
t.
(83)
Th
at elephan
t is large, and th
at flea is too.
(84
)B
eck is tall, and h
is 6 year old dau
ghter is too.
(84) makes a sim
ilar point: th
is senten
ce can on
ly mean
that B
eck is tall for a man
and h
is
daugh
ter is tall for a 6 year old girl (assu
min
g that B
eck is an adu
lt male). W
hat exam
ples
like these sh
ow is th
at the valu
e of the stan
dard variable need n
ot remain
constan
t un
der
ellipsis. If the valu
e of the stan
dard variable were set in
dexically, how
ever, like the pron
oun
in (82), th
en w
e wou
ld expect (83) and (84) to h
ave interpretation
s in w
hich
the respective
comparison
classes do not vary u
nder ellipsis.
In order to con
struct a solu
tion to th
is problem, w
e need to take a closer look at th
e
compu
tation of th
e standard valu
e. In th
e discussion
of (81) above, I claimed th
at the valu
e
of the stan
dard degree is determin
ed relative to an appropriate com
parison class. K
lein
126
(1980
:13) defines a com
parison class as “a su
bset of the dom
ain of discou
rse wh
ich is picked
out relative to a con
text of use”. F
or example, in
a context in
wh
ich it is kn
own
that th
e
individu
al nam
ed Lan
a is a chim
p, (85) is un
derstood to mean
(86); in
other w
ords, the
comparison
class is the set of ch
imps.
(85)
Lana is in
telligent.
(86
)Lan
a is intelligen
t for a chim
p.
(86) illu
strates anoth
er importan
t fact: the com
parison class can
be explicitly identified by an
indefin
ite in an
adjoined for-P
P. (87) an
d (88) make th
e same poin
t.
(87)
Mercu
ry is small for a plan
et.
(88
)M
ookie is short for a basketball player.
Takin
g these exam
ples as a starting poin
t, let us assu
me th
at the in
definites in
(86)-
(88
) introdu
ce properties of individu
als that are u
sed as the basis for con
structin
g a
comp
arison class; for con
creteness, I w
ill refer to such
prop
erties as “comp
arison
properties”. 20 Th
e hypoth
esis that a property-den
oting expression
is used to determ
ine a
comparison
class is a compon
ent of an
alyses in w
hich
the attribu
tive form of a gradable
adjective is taken to be basic (see P
arsons 19
72, Mon
tague 19
74, Cressw
ell 1976
, Lerner an
d
Pin
kal 199
2; cf. Kam
p 1975, K
lein 19
82). In
such
analyses, w
hat I h
ave called the
“comparison
property” is supplied by a com
mon
nou
n m
eanin
g, e.g. planet in (89
).
(89
)M
ercury is a sm
all planet.
20Th
e hyp
othesis th
at the in
defin
ites in exam
ples lik
e (86)-(88) are prop
erty-den
oting exp
ressions
receives some su
pp
ort from an
un
usu
al parallelism
betw
een in
defin
ites in ab
solute for-PPs an
d p
redicative
ind
efinites: th
e former sh
ow th
e same agreem
ent p
atterns as th
e latter, as illustrated
by (i)-(ii).
(i)M
ercury an
d Plu
to are small for p
lanets/*a p
lanet.
(ii)M
ercury an
d Plu
to are plan
ets/*a plan
et.
127
Bu
ilding on
these observation
s, I will propose th
at the absolu
te degree morph
eme is
ambigu
ous betw
een th
e interpretation
given above in
(76) an
d repeated below, in
wh
ich th
e
standard valu
e is introdu
ced by a degree, and th
e interpretation
in (9
0).
(76)
[Deg ∂
]1 = λG
λdλ
x[abs(G(x))(d)]
(90
)[D
eg ∂]2 = λ
Gλ
Pλx[abs(G
(x))(stnd
(G)(P
))]
(90
) differs from (76
) in tw
o crucial w
ays. First, th
e second argu
men
t of the degree
morph
eme is a com
parison property, rath
er than
a degree, and secon
d, the m
eanin
g of the
degree morph
eme in
cludes a “stan
dard-identification
” fun
ction, w
hich
I have represen
ted as
“stnd
” in (9
0). T
his fu
nction
takes a gradable adjective and a com
parison property as
argum
ents an
d return
s the degree on
the scale associated w
ith th
e adjective that represen
ts
the appropriate stan
dard value for th
at property. Alth
ough
I will n
ot attempt to w
ork out th
e
details of this com
putation
, a fairly straightforw
ard hypoth
esis suggests itself: assu
me th
at
stnd
takes the degrees in
the ran
ge of G th
at are related to objects in th
e extension
of P (in
some w
orld), and retu
rns th
e mean
(cf. Bartsch
and V
enn
eman
n 19
73). Note th
at despite
the com
positional differen
ces between
(90
) and (76
), they are th
e same in
an im
portant
respect: since th
e value of stn
d(G
)(P) is a degree, th
e truth
condition
s for absolutes w
ith
implicit stan
dards are exactly the sam
e as those for absolu
tes with
measu
re phrases; i.e.,
they are as stated above in
(77). (90
) thu
s preserves the gen
eral analysis of th
e absolute
constru
ction as a relation
between
a reference valu
e and a stan
dard value, differin
g only in
incorporatin
g the determ
ination
of the stan
dard into th
e mean
ing of th
e degree morph
eme
(see von S
techow
198
4a for a similar proposal in
the con
text of a relational an
alysis of
gradable adjectives). 21
21On
ce the d
egree morp
hem
e in (90) com
poses w
ith a grad
able ad
jective ϕ, th
e resultin
g complex
expression den
otes the relation
between
properties and in
dividuals sh
own
in (i).
(i)λP
λx[abs(ϕ(x
))(stnd
(ϕ)(P
))]
128
Th
e interpretation
of examples like (86
)-(88) is straightforw
ard: the valu
e of P is
supplied by th
e indefin
ite in th
e for-clause. N
ote that sin
ce the in
terpretation of th
e
absolute m
orphem
e in (9
0) “presatu
rates” the degree argu
men
t, the an
alysis predicts that
measu
re phrases an
d comparison
properties shou
ld be in com
plemen
tary distribution
. (91)-
(92), w
hich
show
that sen
tences w
ith both
a measu
re phrase an
d a “for-indefinite” phrase are
ill-formed, verify th
is prediction.
(91)
*Ben
ny is 4 feet tall for a 10
year old boy.
(92)
*Th
e class was 3 h
ours lon
g for a discussion
section.
As it stan
ds, how
ever, this an
alysis does not yet provide a solu
tion to K
lein’s objection
,
because in
examples (72) an
d (85), it is still necessary to su
pply a value for th
e comparison
property. Cru
cially, we can
not assu
me th
at the com
parison property is su
pplied indexically
(as in e.g. Lern
er and P
inkal 19
92), becau
se such
an an
alysis wou
ld also make in
correct
predictions in
the case of V
P ellipsis (see K
lein 19
80:15 for discu
ssion).
Th
e observations m
ade above about th
e mean
ings of exam
ples like (72) and (85)
suggest a solu
tion to th
is problem. T
hese exam
ples indicate th
at wh
en th
e comparison
class
is implicit, its valu
e is in som
e way depen
dent on
the den
otation of th
e subject. M
ore
precisely, the com
parison class is iden
tified based on som
e property possessed by the su
bject
that is determ
ined to be relevan
t in th
e context of u
tterance–in
(85), the property of bein
g a
chim
p; in (72), th
e property of being a plan
etary atmosph
ere. Th
is observation provides th
e
starting poin
t for a seman
tic analysis of absolu
te constru
ctions w
ith im
plicit standards th
at
main
tains a certain
amou
nt of con
text-dependen
cy, but also explain
s the ellipsis facts
discussed by K
lein. S
pecifically, I will assu
me th
at wh
en a com
parison property is n
ot
(i) is very similar to th
e analysis of gradable adjectives in
Lerner an
d Pin
kal 199
2, in w
hich
the attribu
tive form is taken
to be basic. Th
is is a positive result, sin
ce it provides a basis for buildin
g a seman
tics for absolute con
struction
s in
their attribu
tive use. N
ote that th
e question
of wh
ether th
e attributive form
of a gradable adjective is basic disappears in
the an
alysis proposed here, sin
ce the m
eanin
g of the adjective–a m
easure fu
nction
–remain
s constan
t regardless of the
interpretation
of the absolu
te morph
eme.
129
explicitly introdu
ced, as in sim
ple absolute con
struction
s like (72) and (8
5), its value is
determin
ed in on
e of two w
ays. Eith
er P receives som
e default valu
e, in w
hich
case the
degree introdu
ced by the form
ula stn
d(G
)(P) is a “global stan
dard” for G (see footn
ote 19;
for psychological eviden
ce that gradable adjectives are associated w
ith global stan
dards, see
Rips an
d Tu
rnbu
ll 1980
), or the valu
e of P is determ
ined by a con
text-dependen
t fun
ction p
that takes an
individu
al as argum
ent an
d return
s a comparison
property based on th
e value
of its argum
ent. T
o accoun
t for the observation
that th
e comparison
class is determin
ed by
property of the su
bject, I will fu
rther assu
me th
at the argu
men
t of p is con
strained to be
identical to th
e external argu
men
t.
Given
these assu
mption
s, the in
terpretation of th
e degree phrase in
(72), repeated
below, is th
e degree property in (9
3).
(72)M
ars’ atmosph
ere is thin
.
(93)
λx[abs(thin(x))(stn
d(thin)(p(x)))]
(93) den
otes the property of bein
g thin
to a degree that is at least as great as a stan
dard of
thin
ness determ
ined on
the basis of a con
textually salien
t property of the target of
predication. C
omposition
of the property in
(93) w
ith th
e subject derives (9
4).
(94
) abs(thin(M
ars’ atmosphere))(stn
d(thin)(p(M
ars’ atmosphere)))
Assu
min
g that th
e value of p(M
ars’ atmosphere) (th
e comparison
property) is someth
ing like
“is a planetary atm
osphere”, th
e standard valu
e in (9
4) is the degree on
the scale associated
with
thin
that iden
tifies a norm
of thin
ness for plan
etary atmosph
eres. Th
e crucial
difference betw
een (9
4) and th
e logical representation
in (81) is th
at the com
putation
of
(94) in
cludes resolvin
g an explicit sem
antic depen
dency betw
een th
e standard valu
e and th
e
subject, as specified in
(93).
Th
is dependen
cy explains th
e ellipsis facts observed by Klein
. Alth
ough
the an
alysis
130
developed here m
aintain
s the position
that th
e determin
ation of th
e standard valu
e is
context-depen
dent, it locates th
e indexicality in
the fu
nction
p, wh
ich determ
ines w
hich
of
the set of properties associated w
ith its argu
men
t shou
ld be used as th
e basis for
determin
ing th
e standard valu
e. Cru
cially, since th
e argum
ent of p
is constrain
ed to be
identical to th
e subject of th
e predication, th
e domain
from w
hich
it is chosen
mu
st vary in
the tw
o conju
ncts of an
ellipsis constru
ction, even
thou
gh th
e actual ch
oice of comparison
property is context-depen
dent. T
his can
be illustrated by recon
sidering (84), repeated below
.
(84
)B
eck is tall, and h
is 6 year old dau
ghter is too.
Th
e logical representation
of the verb ph
rase in th
e first conju
nct in
(84) is (95); assu
min
g
that V
P ellipsis is licen
sed by identity of logical represen
tations (as in
Sag 1976
and W
illiams
1977), (9
5) also provides the in
terpretation of th
e elided VP
.
(95)
λx[abs(tall(x))(stn
d(thin)(p(x)))]
Sin
ce (95) is predicated of tw
o distinct objects in
the con
jun
cts in (84), th
e actual valu
es of
the stan
dards in th
e two con
jun
cts will vary as a fu
nction
of the den
otations of th
e subjects.
In th
e first conju
nct, th
e standard valu
e is determin
ed with
respect to an appropriate
comparison
property for the in
dividual den
oted by Beck, an
adult m
ale; in th
e second
conju
nct, th
e standard valu
e is determin
ed with
respect to a comparison
property for the
individu
al denoted by his [B
eck’s] 6 year old daughter. 22
In essen
ce, the an
alysis claims th
at absolute con
struction
s in w
hich
the com
parison
property is determin
ed by p are reflexive con
struction
s, analogou
s to verbs with
implicit
reflexive argum
ents, su
ch as bathe. Like (84), th
e implicit argu
men
t of bathe can (an
d in
22I assum
e that id
entity of th
e stand
ard valu
es in exam
ples su
ch as (i) is d
ue to th
e fact that th
e
subjects in
both con
jun
cts are the sam
e sorts of objects.
(i)Ju
piter is large an
d Satu
rn is too.
131
fact mu
st) have a “sloppy” readin
g un
der ellipsis (i.e., its value m
ust vary): (9
6) h
as only an
interpretation
in w
hich
Beck’s 6
year old daugh
ter bathed h
erself, not on
e in w
hich
Beck’s 6
year old daugh
ter bathed B
eck.
(96
)B
eck bathed, an
d his 6
year old daugh
ter did too.
Th
is an
alysis p
redicts
that
“strict” in
terpretation
s of
elliptical
conju
ncts
like
(84)–interpretation
s in w
hich
the com
parison property in
the elided con
stituen
t is the sam
e
as the com
parison property in
the an
tecedent–sh
ould be im
possible. Th
is seems to be tru
e:
as noted above, (84) can
not m
ean th
at Beck’s dau
ghter is tall for a grow
n m
an (assu
min
g
that B
eck is an adu
lt male), alth
ough
it can be in
terpreted as a statemen
t that th
ey are both
tall with
respect to some global stan
dard. In th
e latter case, how
ever, there is n
o
dependen
cy between
the su
bject and th
e comparison
property, so a sloppy reading is n
ot
forced. On
the con
trary, in th
is case a strict interpretation
is required, w
hich
is wh
at we
wou
ld expect if ellipsis involves iden
tity of logical representation
s.
Addition
al evidence th
at this an
alysis is on th
e right track com
es from sen
tences w
ith
quan
tificational su
bjects. Con
sider an exam
ple like (97).
(97)
Everyon
e in m
y family is tall.
(97) can
mean
that every m
ember of m
y family is tall w
ith respect to w
hatever com
parison
property is appropriate for that in
dividual, i.e., th
at each ch
ild is tall for a child, each
man
is
tall for a man
, and each
wom
an is tall for a w
oman
. 23 Th
is interpretation
of (97) correspon
ds
to the logical represen
tation in
(98).
(98
)every
x [mem
ber-of-my-fam
ily(x)][abs(tall(x))(stnd
(tall)(p(x)))]
23(97) can also m
ean th
at every mem
ber of my fam
ily is tall with
respect to som
e global stand
ard.
132
Sin
ce the com
parison property m
ust be calcu
lated for each in
dividual th
at satisfies the
restriction of th
e quan
tifier, the stan
dard value ch
anges accordin
g to the com
parison
property determin
ed by that in
dividual. If, on
the oth
er han
d, the stan
dard value w
ere an
indexically specified degree, its in
terpretation sh
ould rem
ain con
stant. T
his is illu
strated by
an exam
ple like (99
), in w
hich
the pron
oun
her is interpreted in
dexically.
(99
)E
veryone in
my fam
ily is proud of h
er.
(99
) can on
ly mean
that everyon
e in m
y family is prou
d of the sam
e person; it can
not m
ean
that everyon
e in m
y family is prou
d of some fem
ale individu
al.
Th
e analysis of im
plicit comparison
classes outlin
ed here is very sim
ilar in its basic
respects to the on
e developed in Lu
dlow 19
89, bu
t different in
implem
entation
. Ludlow
argues th
at the stan
dard argum
ent in
a senten
ce like (72) is introdu
ced by an operator w
hich
moves from
its base position in
AP
to adjoin to th
e subject, w
hich
is then
used as th
e basis
for determin
ing th
e comparison
class. Specifically, th
e comparison
class is determin
ed
based on th
e lexical material in
cluded in
N-bar. O
n th
is view, th
e non
-identity of th
e
standards in
elliptical contexts follow
from th
e fact that th
e “standard operator” in
the tw
o
conju
ncts adjoin
s to different expression
s–th
e subjects of th
e two clau
ses–as sh
own
in
(100
).
(100
)[[O
pi th
at elephan
t] is large ei ] an
d [[Op
i that flea] is large e
i too]
Th
ere are at least two problem
s with
this type of an
alysis. Th
e first is strictly
syntactic: th
e analysis requ
ires the stan
dard operator to adjoin to an
argum
ent, bu
t this type
of adjun
ction h
as been claim
ed to be impossible (see C
hom
sky 1986
). Th
e second problem
comes from
examples in
wh
ich th
e subject is qu
antification
al, such
as (97) above. If th
e
standard operator adjoin
s to the qu
antification
al subject an
d the lexical m
aterial in N
-bar
determin
es the com
parison class, th
en th
e standard valu
e in an
example like (9
7) shou
ld be
133
some average based on
the com
bined h
eights of th
e mem
bers of my fam
ily. If this is th
e
case, how
ever, then
(97) sh
ould be con
tradictory, because it w
ould alw
ays be true th
at
someon
e in m
y family is n
ot as tall as the average.
2.4 Com
paratives
2.4.1 Initial O
bservations an
d Question
s
2.4.1.1 Dom
ain of In
vestigation
Th
e complexity an
d variety of the class of com
parative constru
ctions in
En
glish provides a
rich dom
ain of syn
tactic and sem
antic pu
zzles, most of w
hich
go beyond th
e scope of this
dissertation. A
s a result, m
y goal in th
is section is n
ot to develop a complete sem
antic (or
syntactic) an
alysis of the com
parative, but rath
er to focus on
a few fu
ndam
ental issu
es in
order to show
that th
e analysis of gradable adjectives an
d degree constru
ctions proposed in
section 2.1 su
pports a robust accou
nt of a core set of facts an
d also provides a starting poin
t
for futu
re work aim
ed at explainin
g some of th
e more com
plex and problem
atic puzzles in
this dom
ain. T
o this en
d, my focu
s in th
is section w
ill be on predicative com
paratives such
as (101)-(10
3).
(101)
Th
e Mars rock called “B
arnacle B
ill” is as wide as it is tall.
(102)
Jupiter is larger th
an Jon
es thou
ght it w
as.
(103)
Mars is less distan
t than
Satu
rn.
I will n
ot discuss attribu
tive comparative con
struction
s, such
as (104
)-(105) (see e.g.
Pin
kham
1982, H
eim 19
85, Lerner an
d Pin
kal 199
2, 199
5, and G
awron
199
5 for relevant
discussion
), nor w
ill I discuss com
parative nom
inals, su
ch as (10
6)-(10
7) (see e.g. Cressw
ell
1976
, Keen
an 19
87).
134
(104
)M
ars has a th
inn
er atmosph
ere than
Ven
us.
(105)
I bough
t a less powerfu
l telescope than
Jaye did.
(106
)M
ore stars are visible from th
e south
ern h
emisph
ere than
the n
orthern
hem
isphere
(107)
Th
ere are fewer black h
oles in th
e galaxy than
there are stars.
Alth
ough
there is reason
to believe that th
e analysis th
at I will develop h
ere is extendable to
an an
alysis of these oth
er constru
ctions (see in
particular K
enn
edy and M
erchan
t 199
7 for
an an
alysis of attributive com
paratives that bu
ilds on th
e proposals in th
is thesis), it sh
ould
be observed that attribu
tive and n
omin
al comparatives in
troduce a n
um
ber of syntactic an
d
seman
tic question
s that do n
ot arise in th
e context of predicative com
paratives, particularly
as regards the role of ellipsis in
the derivation
of the com
parative clause. A
s a result, in
order for the proposals th
at I will m
ake in th
is section to be accepted as a gen
eral theory of
the syn
tactic and sem
antic properties of com
paratives, they m
ust even
tually be evalu
ated
against th
ese other con
struction
s as well, a project th
at I will leave for fu
ture w
ork. My
primary goal in
this section
is to show
that th
e basic approach to th
e seman
tic analysis of
gradable adjectives and degree con
struction
s that I h
ave developed in th
is thesis su
pports a
robust an
alysis of predicative comparatives, an
d by extension
, a foun
dation u
pon w
hich
to
build a gen
eral accoun
t of the fu
ll range of com
parative constru
ctions in
En
glish.
With
in th
e class of predicative comparatives, I w
ill distingu
ish th
ree subtypes based
on th
e superficial ch
aracteristics of the com
plemen
t of than or as–wh
at I have referred to
thu
s far as the “com
parative clause”. (10
1)-(103) exem
plify these th
ree types, wh
ich,
followin
g established tradition
, I will refer to w
ith th
e descriptive labels compa
rative
subdeletion
, comparative deletion
, an
d phrasal com
paratives, respectively. Com
parative
subdeletion
structu
res such
as (101) are com
paratives in w
hich
the com
parative clause is a
constitu
ent th
at could stan
d alone as an
indepen
dent clau
se (see Grim
shaw
1987), bu
t mu
st
not con
tain an
overt degree word or m
easure ph
rase, as illustrated by (10
8)-(110).
135
(108
)T
he S
agan M
emorial S
tation is taller th
an th
e Soju
rner rover is lon
g.
(109
)T
he S
ojurn
er rover is long.
(110)
*Th
e Sagan
Mem
orial Station
is taller than
the S
ojurn
er rover is very/quite/3 feet
long.
Com
parative deletion stru
ctures are com
paratives in w
hich
the su
rface complem
ent of than
or as is a “partial clause”: a clau
sal constitu
ent (as in
dicated by the presen
ce of verbal
inflection
) that appears to be “m
issing” som
e constitu
ent at least as large as D
egP.
Com
parative deletion is illu
strated by (102) above, as w
ell as (111)-(113).
(111)T
he M
ars Path
finder m
ission w
as more su
ccessful th
an an
yone th
ough
t it wou
ld be.
(112)T
he telescope w
as less expensive th
an I expected.
(113)Jon
es thin
ks that Ju
piter is larger than
it is.
Fin
ally, phrasal com
paratives are structu
res in w
hich
the su
rface complem
ent of than or as
is a single, n
on-clau
sal constitu
ent, as in
(103) an
d (114)-(117).
(114)
Th
e Sagan
Mem
orial Station
is taller than
the S
ojurn
er rover.
(115)T
he su
n is less m
assive than
a neu
tron star.
(116)
Su
nspot activity th
is year was m
ore inten
se than
ever before.
(117)T
he atm
osphere is th
inn
er over the poles th
an over th
e equator.
It shou
ld be noted th
at term “com
parative ellipsis” is often u
sed to refer to
structu
res in w
hich
the com
parative clause is “m
issing” m
ore material th
an ju
st DegP
(see
Gaw
ron 19
95 an
d Hazou
t 199
5 for recent discu
ssion); th
is label inclu
des both ph
rasal
comparatives an
d examples of com
parative deletion su
ch as (112). T
he qu
estion of w
heth
er
an ellipsis operation
is involved in
the derivation
of comparatives, an
d if so, wh
ich of th
e
subtypes discu
ssed here are targets of th
is operation, is on
e of the qu
estions th
at this
136
section w
ill address. In order to avoid presu
pposing th
e outcom
e of the discu
ssion, I h
ave
chosen
the labels “su
bdeletion”, “com
parative deletion”, an
d “phrasal com
paratives” based
on a com
bination
of tradition an
d their u
sefuln
ess as descriptive characterization
s of the
surface form
s.
2.4.1.2 Com
parative Relation
s and D
egree Description
s
Accordin
g to the an
alysis of gradable adjectives and degree con
struction
s developed in
section 2.1, it sh
ould be possible to ch
aracterize the in
terpretations of com
parative
constru
ctions in
terms of th
e general sch
ema for degree m
orphology in
(118).
(118)
Deg = λ
Gλ
dλx[R
(G(x))(d)]
Tw
o question
s need to be an
swered: w
hat is th
e value of R
for each of th
e comparative
morph
emes er/m
ore, less, and as, an
d how
are the stan
dard values derived in
each of th
e
three classes of com
paratives that I am
focusin
g on h
ere? Th
e answ
er to the first qu
estion
is straightforw
ard: er/more den
otes a total order between
two degrees, less den
otes its
inverse, an
d as denotes a partial orderin
g between
degrees. 24 Bu
ilding on
the an
alysis of the
absolute degree m
orphem
e in section
2.3, this claim
can be im
plemen
ted by adopting th
e
interpretation
s of the com
parative morph
emes in
(119)-(121) an
d the tru
th con
ditions in
(122)-(124).
(119)
more/er = λ
Gλ
dλx[m
ore(G
(x))(d)]
(120)
less = λG
λdλ
x[less(G(x))(d)]
(121)as = λ
Gλ
dλx[as(G
(x))(d)]
24I assum
e that as d
enotes a p
artial orderin
g relation rath
er than
equ
ality based on
examp
les like (i).
(i)Ju
piter is as large as Satu
rn, in
fact it’s larger than
Saturn
.
The eq
uality in
terpretation
that eq
uatives typ
ically have can
be explain
ed as a scalar im
plicatu
re. For relevant
discu
ssion, see Seu
ren 1973.
137
(122)||m
ore(d
R )(dS )|| = 1 iff d
R > dS
(123)||less(d
R )(dS )|| = 1 iff d
R < dS
(124)
||as(dR )(d
S )|| = 1 iff dR ≥ d
S
Th
is analysis directly im
plemen
ts the proposals from
section 2.1: com
parative morph
emes
denote relation
s between
a reference valu
e, derived by applying th
e gradable adjective that
heads th
e degree constru
ction to th
e target of predication, an
d a standard valu
e.
Th
is return
s us to th
e second an
d more difficu
lt question
: how
is the stan
dard value
derived in each
of the th
ree subclasses of predicative com
paratives? For su
bdeletion
structu
res, the an
swer is straigh
tforward: th
e comparative clau
se denotes a description
of a
degree (see Heim
198
5, Izvorski 199
5). Th
e basic analysis ru
ns as follow
s. If the
complem
ent of than in
an exam
ple like (108) is a clau
sal constitu
ent h
eaded by a gradable
adjective, then
it mu
st contain
a degree variable–the stan
dard variable introdu
ced by the
absolute m
orphem
e. Th
is variable can be abstracted over to derive an
expression th
at
denotes a set of degrees, as sh
own
in (125).
(125)λ
d[abs(long(the Sojurner rover))(d)]
Th
e logical represen
tation in
(125) can be tran
sparen
tly derived from th
e syntactic
representation
of (101) if w
e assum
e, followin
g e.g. Izvorski 199
5 that th
e comparative
clause in
a subdeletion
structu
re is a wh-con
struction
, in w
hich
a nu
ll operator moves from
the position
of the degree variable in
DegP
to SpecC
P (see also C
hom
sky 1977; bu
t see
Grim
shaw
1987, an
d Corver 19
91, 19
93 for argu
men
ts that su
bdeletion does not in
volve wh-
movem
ent). O
n th
is view, th
e Logical Form
of (108) is (126
).
(126)
Th
e Sagan
Mem
orial Station
is [DegP er [A
P tall] [P
P than
[CP O
px th
e Soju
rner rover is
[DegP e
x ∂ lon
g]]]]
138
Alth
ough
I will argu
e in section
2.4.2 that com
parative deletion con
struction
s do involve
actual w
h-movem
ent in
the syn
tax, I will rem
ain agn
ostic as to wh
ether th
e operator-variable
relation in
(126) is th
e result of actu
al movem
ent, or w
heth
er it is derived in som
e other
way. W
hat is im
portant is th
at the sem
antics provides som
e mean
s of abstracting over th
e
degree variable introdu
ced by the absolu
te morph
eme in
(126), in
order to derive the logical
representation
in (125). 25
Th
e expression in
(125) denotes th
e set of degrees d such
that th
e Soju
rner rover is
at least as long as d. A
ssum
ing th
e interpretation
of the absolu
te morph
eme adopted in
the
preceding section
, the expression
in (125) den
otes the set of degrees on
a scale rangin
g from
the degree correspon
ding to th
e length
of the S
ojurn
er rover to the low
er end of th
e scale.
In order to derive a defin
ite description of a degree, I w
ill follow von
Stech
ow 19
84a in
assum
ing th
at the expression
in (125) is th
e argum
ent of a covert m
aximality operator,
wh
ich h
as the in
terpretation in
(127) (wh
ere D is a (totally ordered) set of degrees; see also
Ru
llman
n 19
95, an
d see the discu
ssion of th
is point in
chapter 1, section
1.3.2).
(127)||m
ax(D)|| = ιd∈
D[∀
d’∈D
: d ≥ d’]
Note th
at the assu
mption
that th
e comparative clau
se denotes a m
aximal degree is
necessary even
if we reject th
e seman
tic analysis of th
e absolute m
orphem
e in term
s of a
partial ordering relation
, adopting an
interpretation
in term
s of equality in
stead. Von
Stechow
1984a observes th
at if the com
parative clause den
otes a simple defin
ite description,
then
in an
example like (128), it sh
ould fail to den
ote, since th
ere is no u
niqu
e degree d
such
that Sash
a can ju
mp d-far.
25If furth
er research su
pp
orts the con
clusion
that su
bdeletion
constru
ctions are syn
tactically distin
ct
from com
parative d
eletion, as argu
ed b
y Grim
shaw
and
Corver, th
is wou
ld actu
ally be con
sistent w
ith, an
d
possib
ly provid
e sup
port for, th
e conclu
sion th
at I will d
raw in
sections 2.4.2, th
at the Logical Form
s and
comp
ositional in
terpretation
of subd
eletion an
d com
parative d
eletion con
struction
s are not th
e same. See also
Larson 1988:22, w
hich
arrives at the sam
e result in
the con
text of a differen
t analysis of com
paratives.
139
(128)
Ede can
jum
p farther th
an Sash
a can.
To accou
nt for facts like (128), von
Stech
ow defin
es the m
aximality operator in
(127), wh
ich
provides the correct in
terpretation of th
e comparative clau
se: the m
aximal degree d su
ch
that Sash
a can ju
mp d-far. 26
Given
these assu
mption
s, the in
terpretation of th
e comparative clau
se in (10
8) is
(129): th
e maxim
al degree d such
that B
arnacle B
ill is at least as tall as d.
(129)
max(λ
d[abs(long(the Sojurner rover))(d)])
Th
is expression can
be supplied as th
e standard argu
men
t of the com
parative morph
eme,
giving th
e property in (130
) as the in
terpretation of D
egP in
(126).
(130)
λx[m
ore(tall(x))(m
ax(λd[abs(tall(the S
ojurner rover))(d)]))]
Th
is property can be applied to th
e subject, retu
rnin
g (131) as the in
terpretation of (10
8).
(131)m
ore(tall(the S
agan Mem
orial Station))(m
ax(λd[abs(tall(the S
ojurner rover))(d)]))
Accordin
g to the tru
th con
ditions for m
ore in (122), (131) is tru
e just in
case the degree to
wh
ich th
e Sagan
Mem
orial Station
is tall exceeds the m
aximal degree to w
hich
the S
ojurn
er
rover is long. G
iven th
e assum
ption th
at tall and lon
g have th
e same dim
ension
al
parameter–
i.e., they m
ap their argu
men
ts onto degrees on
the sam
e scale (see the
discussion
of this poin
t in section
2.1.3), this an
alysis accurately ch
aracterizes the m
eanin
g of
(108
).
It shou
ld be noted th
at this an
alysis of subdeletion
also main
tains th
e explanation
of
26It shou
ld also be n
oted th
at von Stech
ow’s an
alysis of the in
terpretation
of the com
parative clau
se
sup
ports an
explan
ation of a n
um
ber of its im
portan
t seman
tic prop
erties, such
as the licen
sing of n
egativep
olarity items an
d an
ti-add
itivity. See von Stech
ow 1984a:70 an
d K
lein 1991:687-8 for d
iscussion
.
140
incom
men
surability ou
tlined in
section 2.1.3. C
onsider, for exam
ple, an an
omalou
s
senten
ce like (132).
(132)#T
he space telescope is m
ore expensive th
an its optics are accu
rate.
Th
e interpretation
of (132) is (133), wh
ich is tru
e just in
case the degree to w
hich
the space
telescope is expensive stan
ds in th
e “>” relation to th
e maxim
al degree to wh
ich its optics
are accurate.
(133)m
ore(expen
sive(the space telescope))(max(λ
d[abs(accurate(the space tele’s optics))(d)]))
Th
e problem is th
at the referen
ce value an
d the stan
dard value are degrees on
different
scales: exp
ensive an
d accu
rate p
roject their argu
men
ts onto scales w
ith differen
t
dimen
sional param
eters, therefore th
eir ranges are disjoin
t. Sin
ce the related degrees in
(133) are not objects on
the sam
e scale (i.e., are not elem
ents of th
e same ordered set), th
e
relation in
troduced by th
e comparative m
orphem
e is un
defined, an
d the sen
tence is
anom
alous.
2.4.1.3 Com
paratives and E
llipsis
Th
e preceding discu
ssion in
dicates that th
e comparative clau
se in su
bdeletion stru
ctures can
be transparen
tly interpreted as a description
of a degree; wh
at remain
s to be determin
ed is
wh
ether
the
same
can
be said
of com
parative
deletion
constru
ctions
and
ph
rasal
comparatives. T
he core qu
estion th
at mu
st be answ
ered is the follow
ing: are com
parative
deletion con
struction
s and ph
rasal comparatives stru
cturally iden
tical to subdeletion
structu
res at a level of Logical Form
, or are the form
er structu
rally distinct from
the latter?
In oth
er words, do th
e derivations of th
e two classes of “redu
ced” comparatives in
volve some
kind of ellipsis resolu
tion, so th
at the com
positional in
terpretations of th
e Logical Form
s of
all three classes of com
paratives are essentially th
e same, or are th
e composition
al
141
interpretation
s of comparative deletion
constru
ctions an
d phrasal com
paratives distinct from
the in
terpretation of su
bdeletion stru
ctures (an
d possibly from each
other)?
27 In section
s
2.4.2 an
d 2.4.3, I w
ill argue th
at the latter is in
fact the case: com
parative deletion
constru
ctions
and
ph
rasal com
paratives
are stru
cturally
distinct
from
comp
arative
subdeletion
at LF, an
d, as a result, th
ey differ in th
eir composition
al interpretation
s. Th
e
primary claim
s can be su
mm
arized as follows. F
irst, “canon
ical” comparative deletion
constru
ctions–exam
ples in w
hich
only a D
egP is apparen
tly elided from th
e surface form
–do
not involve an
y kind of ellipsis; in
stead, the “m
issing” degree ph
rase is actually th
e trace of a
nu
ll operator, wh
ich is categorically a D
egP (cf. K
lein 19
80, Larson
1988). T
his syn
tactic
difference h
as a correspondin
g effect on th
e interpretation
of the com
parative clause: th
e
comparative clau
se in a com
parative deletion con
struction
does not den
ote a description of a
degree, as in com
parative subdeletion
, but rath
er a fun
ction from
gradable adjective
mean
ings to degrees. S
econd, ph
rasal comparatives in
wh
ich th
e surface com
plemen
t of
than or as is a DP
do not h
ave true com
parative “clauses” at all, in
stead, the com
plemen
t of
than or as is a DP
at all stages of the derivation
(see Han
kamer 19
73). Th
ese constru
ctions
receive a “direct” interpretation
, wh
ereby the stan
dard value is derived by applyin
g the
gradable adjective mean
ing to th
e individu
al-denotin
g expression th
at occurs as th
e
complem
ent of than (cf. H
eim 19
85).
A resu
lt of these claim
s is that it w
ill be necessary to p
osit three distin
ct
interpretation
s for the com
parative morph
emes: on
e in w
hich
the stan
dard value is directly
supplied by a degree-den
oting expression
(for comparative su
bdeletion), on
e in w
hich
the
standard valu
e is derived by supplyin
g the in
terpretation of th
e gradable adjective that h
eads
the degree con
struction
as an argu
men
t to the stan
dard expression (for com
parative
deletion), an
d one in
wh
ich th
e standard valu
e is derived by applying th
e interpretation
of the
gradable adjective that h
eads the com
parative to the stan
dard expression (for ph
rasal
27Alth
ough
the su
bseq
uen
t discu
ssion w
ill assum
e a framew
ork in
wh
ich th
e resolution
of ellipsis
involves an
iden
tity relation b
etween
Logical Forms (as in
e.g. Fiengo an
d M
ay 1994), and
so is sensitive to
syntactic rep
resentatio
ns, I in
tend
this q
uestio
n to
inclu
de sem
antic ap
pro
aches to
ellipsis as w
ell. Inp
articular, I w
ill discu
ss Gaw
ron’s (1995) an
alysis of comp
aratives, wh
ich ad
opts D
alrymp
le, Shieb
er and
Pereira’s (1991) High
er Ord
er Un
ification ap
proach
to ellipsis, in
section 2.4.3.2.
142
comparatives). T
hese th
ree interpretation
s are specified for the m
orphem
e er/more in
(134)a-c, wh
ere Q in
(134)b is a fun
ction from
gradable adjectives to degrees, and y in
(134)c
is an in
dividual; exactly th
e same pattern
holds for less an
d as.
(134)
a.er/m
ore1 = λG
λdλ
x[mo
re(G(x))(d)]
(subdeletion)
b.er/m
ore2 = λG
λQ
λx[m
ore(G
(x))(Q(G
))](com
parative deletion)
c.er/m
ore3 = λG
λyλ
x[mo
re(G(x))(G
(y))](phrasal com
paratives)
Alth
ough
the assu
mption
that th
e comparative m
orphem
es are ambigu
ous seem
s
un
desirable, it shou
ld be noted th
at the am
biguity does n
ot reflect a truth
-condition
al
difference betw
een th
e three com
parative constru
ctions, on
ly a composition
al one. T
he
truth
condition
s for each of th
e three su
bclasses of comparative con
struction
s are as
specified above in (122)-(124
): they den
ote relations betw
een a referen
ce value an
d a
standard valu
e; wh
at differs in th
e three con
struction
s is the w
ay in w
hich
the degree th
at
represen
ts the stan
dard value is determ
ined. M
ore imp
ortantly, a com
parison
of
comparative deletion
and ph
rasal comparatives w
ith tru
e ellipsis structu
res provides
empirical su
pport for the an
alysis of comparative m
orphology ou
tlined in
(134). As I w
ill
show
in th
e followin
g sections, com
parative deletion stru
ctures an
d phrasal com
paratives
differ from tru
e ellipsis constru
ctions in
an im
portant w
ay: the in
terpretation of th
e
“missin
g” material in
the com
parative clause is m
uch
more restricted th
an it sh
ould be if
the
derivations
of th
ese con
struction
s actu
ally in
volved ellip
sis.
Sp
ecifically, th
e
interpretation
of the m
issing m
aterial in com
parative deletion con
struction
s and ph
rasal
comparatives m
ust com
e from th
e adjective that h
eads the degree con
struction
. Th
is fact is
completely u
nexpected if com
parative deletion an
d phrasal com
paratives involve ellipsis, bu
t,
it is enforced by th
e seman
tic analysis of com
parative morph
ology in (134).
143
2.4.2 Com
parative Deletion
2.4.2.1 Identity an
d Com
parative Deletion
Tw
o syntactic properties in
particular ch
aracterize comparative deletion
structu
res. First, as
noted above, th
e comparative clau
se appears to have u
ndergon
e some kin
d of ellipsis
operation, w
hich
targets a constitu
ent at least as large as D
egP. S
econd, as observed by
Ch
omsky (19
77), the com
parative clause displays ch
aracteristics typically associated with
wh-
constru
ctions (see also B
resnan
1975, G
rimsh
aw 19
87, and Izvorski 19
95). T
hese properties
are closely intertw
ined, as becom
es evident w
hen
considerin
g the facts discu
ssed by
Ch
omsky as eviden
ce that th
e comparative clau
se is a wh-con
struction
. Descriptively,
wh
enever th
e “missin
g” material in
the com
parative clause is con
tained in
an extraction
island, th
e senten
ce is un
gramm
atical (see Pin
kham
1982 an
d Ken
nedy an
d Merch
ant 19
97
for additional relevan
t discussion
). (135)-(142) provide an overview
some of th
e crucial facts.
Wh-islands
(135)M
ercury is closer to th
e sun
than
I thou
ght it w
as.
(136)
*Mercu
ry is closer to the su
n th
an I w
ondered w
heth
er it was.
(137)*M
ercury is closer to th
e sun
than
I knew
wh
o said it was.
Com
plex NP
s
(138)
Hale-B
opp was brigh
ter than
Carl claim
ed it wou
ld be.
(139)
*Hale-B
opp was brigh
ter than
Carl’s claim
that it w
ould be.
(140
)*H
ale-Bopp w
as brighter th
an a paper th
at said it wou
ld be.
Adjunct islands
(141)
Th
e solar flares were m
ore energetic th
an th
e aurora borealis w
as.
(142)
*Th
e solar flares were m
ore energetic th
an w
e were am
azed wh
en th
e aurora
borealis was.
144
Ch
omsky con
cludes from
facts like these th
at the syn
tactic derivation of th
e comparative
clause in
volves movem
ent of a ph
onologically n
ull operator (h
enceforth
the “com
parative
operator”) from som
e position w
ithin
the com
parative clause. T
his proposal receives
additional su
pport from som
e dialects of En
glish, w
hich
permit an
overt wh-w
ord in th
e
comparative clau
se, as show
n by (143)-(144). 28
(143)
Th
e flooding w
as less than
wh
at we h
ad thou
ght it w
ould be. [N
PR
, 1.29.9
7]
(144
)Ju
piter is larger than
wh
at Saturn
is.
On
the su
rface, the syn
tactic status of th
e comparative clau
se as a wh-con
struction
appears to fit in n
aturally w
ith th
e hypoth
esis that th
e interpretation
of comparative deletion
is completely parallel to th
at of comparative su
bdeletion, an
d that th
e comparative clau
se is a
type of description. T
his approach
assum
es that th
e comparative operator bin
ds a degree
variable in th
e comparative clau
se, generatin
g an expression
wh
ich den
otes a set of degrees
(see e.g. von S
techow
1984a, M
oltman
n 19
92b, Izvorski 19
95). In
an exam
ple like (145), the
comparative operator bin
ds a degree variable in th
e comparative clau
se, and th
e wh
ole
constitu
ent is in
terpreted as the lam
bda expression in
(146
), wh
ich den
otes the set of
degrees d such
that N
eptun
e is at least as great as d.
(145)
Jupiter is m
ore massive th
an N
eptun
e is.
(146
)λ
d[abs(massive(N
eptun
e)(d)]
(146
) can th
en be su
pplied as the argu
men
t of the m
aximality operator, gen
erating a
definite description
of a degree, exactly as in th
e analysis of su
bdeletion discu
ssed in section
2.4.1.2.28Similar facts can
be foun
d in
Afrik
aans an
d H
ind
i, and
in som
e langu
ages, such
as Bu
lgarian, a w
h-
word
is obligatory (see Izvorsk
i 1995 for discu
ssion; see Stassen
1985 for a general cross-lin
guistic su
rvey ofcom
parative con
struction
s).
145
In order for th
is analysis to w
ork, how
ever, it mu
st make th
e crucial assu
mption
that
the derivation
of (145) involves som
e kind of ellipsis operation
wh
ereby the m
issing m
aterial
in th
e comparative clau
se is syntactically represen
ted at LF. 29 In
particular, in
order for the
Logical Form
of (145) to map on
to the in
terpretation in
(146), it m
ust be th
e case that th
e
comparative clau
se in (145) h
as the stru
cture in
(147) (wh
ich is stru
cturally parallel to th
e a
subdeletion
structu
re such
as (126), discu
ssed in section
2.4.1.2), in w
hich
a Degree P
hrase
headed by th
e absolute m
orphem
e has been
reconstru
cted.
(147)
Jupiter is [D
egP m
ore massive th
an [C
P O
px N
eptun
e is [DegP
ex ∂
massive]]]
Th
is analysis raises an
importan
t and extrem
ely problematic qu
estion for th
e
syntactic assu
mption
s that I adopted in
section 2.2. If com
parative deletion is like oth
er
elliptical phen
omen
a in E
nglish
, then
the recovery of elided m
aterial at LF sh
ould be su
bject
to certain con
straints on
identity. In
particular, th
e elided material m
ust h
ave a logical
representation
that is iden
tical to some oth
er constitu
ent in
the discou
rse (Sag 19
76,
William
s 1977, M
ay 198
5, Kitagaw
a 199
1, Fien
go & M
ay 199
4, C
hu
ng, Ladu
saw, an
d
McC
loskey 199
5; for simplicity, I w
ill assum
e that ellipsis is licen
sed by identity of Logical
Form
s, as in F
iengo an
d May 19
94, alth
ough
noth
ing in
the follow
ing discu
ssion h
inges on
this assu
mption
); in th
e case of a comparative deletion
structu
re like (147), the an
tecedent
shou
ld be a DegP
. Th
e problem for th
is approach is th
at the syn
tactic assum
ptions adopted
in section
2.2 wou
ld actually force u
s to assum
e that th
e recovered material in
an exam
ple
like (147), as well as oth
er instan
ces of comparative deletion
, mu
st not be iden
tical to its
anteceden
t.
To see w
hy, let u
s consider in
more detail th
e derivation of (145) on
the assu
mption
that it in
volves ellipsis. Th
e first thin
g to observe is that (145) is an
anteceden
t-contain
ed
deletion (A
CD
) structu
re. As illu
strated by (148), the su
rface representation
of (145), the
29Or, altern
atively, that som
e kind
of seman
tic ellipsis op
eration ach
ieves the sam
e result; see G
awron
1995 for such
an ap
proach
.
146
missin
g DegP
(DegP
2 ) is contain
ed with
in th
e DegP
that su
pplies its interpretation
(DegP
1 ).
(148
)Ju
piter is [DegP
1 more m
assive than
[CP
Op N
eptun
e is [DegP
2 e]]]
Assu
min
g that A
CD
is resolved by adjoinin
g the con
stituen
t that con
tains th
e deleted
expression to a clau
sal node ou
tside the an
tecedent (see M
ay 1985, Larson
and M
ay 1987,
Fien
go and M
ay 199
4, and K
enn
edy 199
7a), the com
parative clause in
(148) mu
st raise to
IP, gen
erating th
e structu
re in (149
). 30
(149
)[IP
[CP
Op N
eptun
e is [DegP
2 e]] [IP Ju
piter is [DegP
1 more m
assive than
e]]]
Even
if we allow
for the possibility th
at the P
P h
eaded by than can be ign
ored and a degree
variable reconstru
cted in its place (cf. C
hu
ng, Ladu
saw, an
d McC
loskey 199
5), the core
problem is th
at the D
egP th
at supplies th
e anteceden
t for the elided ph
rase (DegP
1 ) is
headed by th
e comparative m
orphem
e more. In
order to constru
ct a LF th
at maps on
to the
correct interpretation
of the com
parative clause, h
owever, th
e recovered material m
ust be
headed by th
e nu
ll absolute m
orphem
e. To see w
hy, con
sider wh
at the in
terpretation of th
e
comparative clau
se wou
ld be if the recovered D
egP w
ere headed by th
e comparative
morph
eme, as in
(150).
(150)
[IP [C
P O
px N
eptun
e is [DegP
2 ex m
ore massive]] [IP
Jupiter is [D
egP1 m
ore massive th
an
e]]]
30Th
is assum
ptio
n is co
mp
atible w
ith b
oth
an an
alysis of th
e com
parative clau
se as a defin
ite
descrip
tion as w
ell as an an
alysis of the com
parative clau
se as a un
iversal qu
antification
structu
re, as both
types of exp
ressions su
pp
ort AC
D:
(i)Ju
lio wan
ted to visit th
e plan
et Mau
reen d
id.
(ii)Ju
lio wan
ted to visit every p
lanet M
aureen
did
.
147
If (150) w
ere the actu
al LF of (14
5), then
the com
parative clau
se wou
ld have th
e
interpretation
in (151): it w
ould den
ote the m
aximal degree d su
ch th
at Neptu
ne is m
ore
massive th
an d.
(151)m
ax(λd[m
ore(m
assive(Neptu
ne)(d)])
Th
is analysis can
not be correct, h
owever, as it gives th
e wron
g truth
condition
s for the
comparative. If (151) w
ere the in
terpretation of th
e comparative clau
se, then
in a con
text in
wh
ich Ju
piter and N
eptun
e were equ
al in m
ass, the in
terpretation of (145), stated in
(152),
wou
ld satisfy the tru
th con
ditions for th
e comparative, restated in
(153).
(152)m
ore(m
assive(Jupiter))(m
ax(λd[m
ore(m
assive(Neptu
ne)(d)]))
(153)||m
ore(d
R )(dS )|| = 1 iff d
R > dS
If Jupiter an
d Neptu
ne w
ere equally m
assive, then
the degree to w
hich
Jupiter is m
assive
wou
ld exceed the m
aximal degree d su
ch th
at Neptu
ne is m
ore massive th
an d. T
his is
clearly the w
rong resu
lt. 31
On
e solution
to this problem
wou
ld be to assum
e that th
e identity con
straints
involved in
licensin
g ellipsis do not distin
guish
between
different degree m
orphem
es. On
this view
, more an
d ∂ (th
e nu
ll absolute m
orphem
e) wou
ld coun
t as identical. T
here is clear
evidence again
st this h
ypothesis, h
owever. If it w
ere the case th
at more an
d ∂ cou
nted as
identical, th
en an
example like (154) sh
ould perm
it an in
terpretation alon
g the lin
es of (155).
(154)
Th
e space telescope was m
ore usefu
l this year, an
d the gam
ma ray satellite w
as, too.
(155)T
he space telescope w
as more u
seful th
is year, and th
e gamm
a ray satellite was
usefu
l, too.
31A m
ore general p
roblem, if scales are d
ense lin
early ordered
sets of poin
ts, as I have assu
med
, is that
the com
parative clau
se in (152) w
ould
fail to den
ote, since th
ere wou
ld b
e no m
aximal d
egree d su
ch th
atN
eptu
ne is m
ore massive th
an d.
148
Su
ch an
interp
retation is com
pletely im
possible, h
owever; (154
) can on
ly have th
e
interpretation
in (156
), in w
hich
the com
parative morph
eme is retain
ed un
der ellipsis.
(156)
Th
e space telescope was m
ore usefu
l this year, an
d the gam
ma ray satellite w
as more
usefu
l, too.
Th
e problem of iden
tity in com
parative deletion is m
ade even m
ore complex by
examples like (157), w
hich
has th
e interpretation
paraphrased in
(158), in
wh
ich th
e
anteceden
t for the m
issing m
aterial is the V
P h
eaded by want.
(157)S
mith
wan
ts the n
ovel to be 100
pages longer th
an h
er editors do.
(158)
Sm
ith w
ants th
e novel to be 10
0 pages lon
ger than
her editors w
ant it to be (lon
g).
In order to en
sure th
at the com
parative clause m
aps onto th
e interpretation
paraphrased in
(158), (157) mu
st have th
e Logical Form
show
n in
(159).
(159)
[IP [C
p Op
x her editors do [V
P wan
t it to be [DegP e
x ∂ lon
g]]] [IP S
mith
[VP
wan
ts the
novel to be [D
egP 10
0 pages lon
ger than
e ]]]
Th
e reconstru
cted material in
(159) is clearly n
ot identical to its an
tecedent, h
owever: n
ot
only is th
e degree morph
eme distin
ct from th
e degree morph
eme in
the an
tecedent, bu
t
the m
easure ph
rase 100 pages mu
st be left out of th
e reconstru
ction. A
gain, V
P ellipsis facts
show
that m
easure ph
rases cann
ot be left out in
general: (16
0) h
as only th
e interpretation
in (16
1); the readin
g in (16
2) is impossible.
(160
)Sm
ith’s n
ovel will be 30
0 pages lon
g, and Jon
es’ will be, too.
(161)
Smith’s n
ovel will be 30
0 pages lon
g, and Jon
es’ will be 30
0 pages lon
g, too.
149
(162)
Smith
’s novel w
ill be 300
pages long, an
d Jones’ w
ill be long, too.
Th
is discussion
leads to three possible con
clusion
s: my earlier assu
mption
s about
the syn
tax of degree constru
ctions are in
correct, the con
straints on
identity in
comparative
constru
ctions are looser th
an th
ose for other ellipsis con
struction
s, such
as VP
ellipsis, or
the assu
mption
that th
e missin
g DegP
in com
parative deletion is recovered th
rough
ellipsis
resolution
is incorrect. T
he discu
ssion so far h
as show
n th
at the syn
tax of extended
projection su
pports a straightforw
ard composition
al seman
tics for degree constru
ctions in
terms of th
e seman
tic analysis of gradable adjectives an
d degree morph
ology motivated in
section 2.1; as a resu
lt, we sh
ould be h
esitant to reject th
is syntactic an
alysis too quickly. 32
Sim
ilarly, we sh
ould be h
esitant to stipu
late a relaxation on
the con
straints on
identity
typically associated with
ellipsis if the sole reason
for the stipu
lation is to accou
nt for th
e
problems presen
ted by comparative deletion
. Th
is leaves us w
ith th
e third con
clusion
, that
the an
alysis of comparative deletion
constru
ctions as ellipsis stru
ctures is in
correct. In fact,
there is in
depen
dent eviden
ce that com
parative deletion
differs from tru
e ellipsis
constru
ctions–in
particular, from
VP
ellipsis–in an
importan
t way. T
he relevan
t facts are
discussed in
the n
ext section.
2.4.2.2 Local Depen
dencies in
Com
parative Deletion
A ch
aracteristic of VP
ellipsis is that an
elided verb phrase can
typically locate its anteceden
t
from an
y accessible VP
with
in recen
t discourse. F
or example, th
e elided VP
in th
e second
conju
nct of (16
3) is free to locate its anteceden
t either locally or n
on-locally: th
e second
conju
nct can
have eith
er the in
terpretation in
(164), in
wh
ich th
e elided VP
receives its
interpretation
from th
e VP
headed by read, or th
e interpretation
in (16
5), in w
hich
the
anteceden
t is the V
P h
eaded by bought.
32Moreover, A
bn
ey (1987) and
Corver (1991, 1997) p
rovide a n
um
ber of in
dep
end
ent an
d com
pellin
gsyn
tactic argum
ents in
favor of the exten
ded
projection
analysis.
150
(163)
Marcu
s read every book I bough
t, and I read every book C
harles did.
(164
)... I read every book C
harles read.
(165)
... I read every book Ch
arles bough
t.
Con
sider now
(166
) and (16
7), wh
ich are stru
cturally parallel in
the follow
ing respect:
both con
jun
cts in th
e two exam
ples are “missin
g” some con
stituen
t.
(166
)M
arcus read every book I did, an
d I bough
t every book Ch
arles did.
(167)
Th
e table is wider th
an th
is rug is, bu
t this ru
g is longer th
an th
e desk is.
Th
e difference is th
at the tw
o conju
ncts in
(166
) have u
ndergon
e VP
ellipsis, wh
ile the tw
o
conju
ncts in
(167) are com
parative deletion con
struction
s. If comparative deletion
is
interpreted in
the sam
e way as V
P ellipsis, th
en th
e missin
g DegP
s in (16
7) shou
ld have th
e
same ran
ge of interpretation
s as the m
issing V
Ps in
(166
). Th
is is true of th
e first
conju
ncts: th
e missin
g constitu
ents in
the first con
jun
cts of both (16
6) an
d (167) receive
their in
terpretations locally: th
e first conju
nct of (16
6) h
as the in
terpretation paraph
rased in
(168), an
d the first con
jun
ct of (167) h
as the in
terpretation in
(169
).
(168
)M
arcus read every book I read....
(169
)T
he table is w
ider than
this ru
g is wide....
Th
is fact is not su
rprising: sin
ce there is n
o prior discourse, th
e local VP
and D
egP are th
e
only available an
tecedents.
Wh
at is surprisin
g, if comparative deletion
involves ellipsis, is th
at the parallelism
between
(166
) and (16
7) breaks down
wh
en w
e consider th
e interpretation
of the m
issing
material in
the secon
d conju
ncts. T
he secon
d conju
nct of (16
6) is am
biguou
s: the elided
VP
can eith
er locate its anteceden
t locally, from th
e VP
headed by bu
y, resultin
g in th
e
interpretation
paraphrased in
(170), or it can
find its an
tecedent in
the precedin
g clause
151
from th
e VP
headed by read, givin
g the in
terpretation in
(171).
(170)
... I bough
t every book Ch
arles bough
t.
(171)... I bou
ght every book C
harles read.
In con
trast, the secon
d conju
nct of (16
7) is not am
biguou
s: this sen
tence h
as only th
e
reading paraph
rased in (172), in
wh
ich th
e missin
g DegP
receives its interpretation
locally,
from th
e DegP
headed by long; a readin
g correspondin
g to (173), in w
hich
the m
issing D
egP
receives its
interp
retation
from
the
DegP
h
eaded by
wid
e in th
e first conju
nct is
unavailable. 33
(172)... th
is rug is lon
ger than
the desk is lon
g.
(173)... th
is rug is lon
ger than
the desk is w
ide.
Wh
at these facts in
dicate is that th
e interpretation
of the m
issing D
egP in
a
comparative deletion
structu
re, un
like the in
terpretation of th
e missin
g VP
in V
P ellipsis
constru
ctions, exh
ibits a “local dependen
cy” on th
e comparative D
egP: th
e interpretation
of
the m
issing D
egP in
the com
parative clause is determ
ined by on
the in
terpretation of th
e
comparative D
egP. M
ore precisely, the adjective m
eanin
g that is u
sed to compu
te the
standard valu
e mu
st be the sam
e as the m
eanin
g of the adjective th
at heads th
e
comparative. T
his is qu
ite surprisin
g, given th
e superficial sim
ilarity of clausal com
paratives
to VP
ellipsis structu
res, and com
pletely un
expected if the in
terpretation of com
parative
deletion in
volves some kin
d of ellipsis resolution
.
Th
e facts are complicated by exam
ples like (174), wh
ich is iden
tical to (167) except
33It shou
ld be observed
that n
omin
al comp
arative deletion
constru
ctions sh
ow sim
ilar locality effects:(i) h
as only th
e interp
retation in
(ii); the read
ing in
(iii) is un
available.
(i)K
im bou
ght m
any p
eaches, bu
t Sand
y bough
t more ap
ples th
an K
im d
id.
(ii)...San
dy bou
ght m
ore app
les than
Kim
bough
t app
les.
(iii)*...San
dy bou
ght m
ore app
les than
Kim
bough
t peach
es.
152
that th
e comparative in
the first con
jun
ct is a subdeletion
structu
re.
(174)
Th
e table is longer th
an th
is rug is w
ide, and th
is rug is lon
ger than
the desk is.
Un
like (167), (174) does allow
a non
-local interpretation
of the m
issing D
egP in
the secon
d
conju
nct. T
hat is, th
e second con
jun
ct of (174) is am
biguou
s between
the readin
g
paraphrased in
(175) and th
e one paraph
rased in (176
).
(175)... th
is rug is lon
ger than
the desk is lon
g.
(176)
... this ru
g is longer th
an th
e desk is wide.
Th
is interpretive differen
ce between
(167) an
d (174) is extremely pu
zzling for th
e followin
g
reason. If th
e interpretation
of comparative deletion
involves recon
struction
of elided
material, so th
at comparative deletion
and com
parative subdeletion
are structu
rally identical
at LF, th
en th
e first conju
ncts in
(167) an
d (174) sh
ould be com
pletely parallel in th
e
relevant respects at LF
. Bu
t if this is tru
e, wh
y doesn’t th
e second con
jun
ct in (16
7) display
the sam
e ambigu
ity as the secon
d conju
nct in
(174)?
2.4.2.3 The D
erivation an
d Interpretation
of Com
parative Deletion
Con
structions
Th
e answ
er to this qu
estion, as w
ell as the solu
tion to th
e problem of iden
tity in com
parative
ellipsis and ju
stification for assu
min
g that th
e comparative m
orphem
e can h
ave the
interpretation
given above in
(134)b, is th
e followin
g: comparative “deletion
” does not
involve ellipsis at all, an
d comparative deletion
constru
ctions are n
ot structu
rally parallel to
subdeletion
structu
res at LF. In
stead, the appearan
ce of ellipsis is due to th
e fact that th
e
syntactic category of th
e comparative operator is D
egP (see K
lein 19
80, Larson
1988, an
d
Lerner an
d Pin
kal 199
5 for similar an
alyses, in w
hich
the com
parative operator is
categorically an A
P). T
hat is, I claim
that th
e comparative operator does n
ot bind a degree
variable inside D
egP, as stan
dardly assum
ed, rather th
e syntactic variable bou
nd by th
e
153
comparative operator in
the com
parative clause is itself a D
egP. If th
is is correct, the Logical
Form
of (177) is (178), wh
ich is iden
tical to its surface represen
tation.
(177)Ju
piter is more m
assive than
Neptu
ne is.
(178)
Jupiter is m
ore massive th
an [C
P O
px N
eptun
e is [DegP
e]x ]
An
imm
ediate consequ
ence of th
is analysis is th
at the problem
of identity in
comparative ellipsis disappears. S
ince n
o ellipsis is involved in
the derivation
of (178), there
is no n
eed to assum
e a relaxation of th
e identity con
straints on
ellipsis to accoun
t for the fact
that th
e comparative m
orphem
e mu
st not be part of th
e reconstru
ction (see th
e discussion
of this poin
t in section
2.4.2.1. Th
e problems presen
ted by more com
plex examples su
ch as
(157) (repeated below) are also elim
inated.
(157)I w
ant m
y dissertation to be 10
0 pages lon
ger than
my advisors do.
(157) is problematic for an
ellipsis analysis of com
parative deletion becau
se it appears to
involve tw
o instan
ces of non
-identity: in
order to generate an
appropriate LF for th
is
example, n
either th
e measu
re phrase n
or the com
parative morph
eme can
be inclu
ded in
the recon
structed m
aterial. Given
the assu
mption
that th
e comparative operator is
categorically a DegP
, how
ever, these problem
s disappear. Th
e elided VP
in th
e comparative
clause is recon
structed u
nder iden
tity with
the V
P h
eaded by wan
t, but in
stead of copying
the m
atrix DegP
, a variable is introdu
ced in its place, as sh
own
in (179
). 34
34For simp
licity, I assum
e that th
e option
of replacin
g DegP
1 in (179) w
ith a variable is an
instan
ce ofveh
icle chan
ge, a relation
that estab
lishes id
entity b
etween
a variable an
d an
other con
stituen
t in a Logical
Form
(Fiengo
and
May 1994; see M
oltm
ann
1992a for a sligh
tly differen
t use o
f vehicle ch
ange in
the
derivation
of the com
parative clau
se). Altern
atively, one cou
ld assu
me th
at DegP
1 raises to adjoin
to the
matrix IP (as d
iscussed
in section
2.4.2.1). On
this view
, the LF of (179) is (i), in
wh
ich case recon
struction
of
the V
P head
ed by w
ant d
irectly introd
uce a D
egP variable.
(i)[IP [D
egP 100 pages lon
ger than
[CP O
px m
y advisors d
o [[ [[VV VVPP PP ww wwaa aann nn
tt tt ii iitt tt tt ttoo oo bb bbee ee [[ [[DD DDee eegg gg
PP PP ee ee]] ]]x ]]] [IP I w
ant m
ydissertation
to be [DegP
e]y ]]
154
(179)
I [VP
wan
t my dissertation
to be [DegP
1 100
pages longer th
an [C
P O
px m
y advisors do
[VP w
ant it to be [D
egP2 e]x ]]]]
As th
e discussion
of (157) shou
ld make clear, I am
not claim
ing th
at the derivation
of
comparative deletion
constru
ctions never in
volves ellipsis ((157), for example, clearly in
volves
VP
ellipsis, since th
e missin
g constitu
ent is in
terpreted as a verb phrase h
eaded by wan
t),
only th
at the in
terpretation of th
e “missin
g” DegP
in th
e comparative clau
se is not
constru
cted on th
e basis of ellipsis resolution
. Th
is raises two qu
estions. F
irst, how
is the
interpretation
of the “m
issing” D
egP derived? In
other w
ords, how
do we get from
structu
res like (178) and (179
), in w
hich
the com
parative operator binds a D
egP rath
er than
a degree variable, to expressions th
at introdu
ce a standard valu
e? Secon
d, how
does the
proposal that th
e comparative operator is categorically a D
egP explain
the facts discu
ssed in
the previou
s section? T
he an
swer to th
e second qu
estion follow
s directly from th
e answ
er
to the first, w
hich
requires takin
g a closer look at the m
eanin
g of the com
parative operator.
If the com
parative operator is categorically a DegP
, then
its interpretation
shou
ld be
stated in term
s of the basic m
eanin
g of a Degree P
hrase, i.e., its in
terpretation sh
ould be of
the sam
e sort as other degree con
struction
s, modu
lo its status as a syn
tactic operator.
Moreover, in
order to derive the correct tru
th con
ditions for com
paratives, it shou
ld be the
case that w
e end u
p with
an in
terpretation of th
e comparative clau
se as a maxim
al degree.
To m
ake the discu
ssion con
crete, consider th
e LF of (177) in
(178), wh
ich is repeated below
.
(178)
Jupiter is m
ore massive th
an [C
P O
px N
eptun
e is [DegP
e]x ]
Assu
min
g the com
parative operator occupies S
pecCP
(see Ch
omsky 19
77), it mu
st compose
with
C-bar. C
-bar contain
s a DegP
variable, therefore I w
ill assum
e that its in
terpretation is
Th
is type of analysis, w
hich
essentially describes th
e derivation of exam
ples like (157) in term
s of May’s (19
85) accoun
t
of anteceden
t-contain
ed deletion, is proposed in
Larson 19
88
a in th
e context of K
lein’s (19
80
) seman
tics forcom
paratives.
155
derived by abstracting over D
egP, as in
(180) (ign
oring th
e contribu
tion of ten
se morph
ology
and th
e verb be).
(180
)λ
D[D
(Neptu
ne)]
Assu
min
g the in
terpretation of C
-bar to be a fun
ction of th
e sort in (180
), the in
terpretation
of the com
parative operator can be form
alized as in (181): it den
otes a fun
ction from
a C-
bar/DegP
mean
ing to a fu
nction
from gradable adjectives to degrees (cf. Lern
er and P
inkal
199
5).
(181)
[DegP
Op] = λ
PλG
(max(λ
d[P(λ
x[abs(G(x))(d)])]))
Th
e proposal can be illu
strated by considerin
g the derivation
of the in
terpretation of th
e
comparative clau
se in (178). T
he com
parative operator takes C-bar as argu
men
t, as show
n in
(182), and th
e complex expression
is transform
ed into (183) th
rough
lambda con
version.
(182)
λPλ
G(m
ax(λd[P
(λx[abs(G
(x))(d)])]))(λD
[D(N
eptun
e)])→
λG
(max(λ
d[λD
[D(N
eptun
e)](λx[abs(G
(x))(d)])]))→
λG
(max(λ
d[λx[abs(G
(x))(d)](Neptu
ne)])
→
(183)
λG
(max(λ
d[abs(G(N
eptun
e))(d)]))
Tw
o aspects of the sem
antics for th
e comparative operator in
(181) an
d the
correspondin
g interpretation
of the com
parative clause in
(183) are crucial. F
irst, the core
mean
ing of th
e comparative operator is th
at of a DegP
headed by an
absolute m
orphem
e
(i.e., it introdu
ces a partial ordering on
degrees). In th
is way, th
e analysis satisfies th
e first
requirem
ent m
ention
ed above, and m
oreover reflects the fact th
at the m
eanin
g of the
comparative clau
se in com
parative deletion is th
e same as th
at of the com
parative clause in
a
subdeletion
structu
re: it denotes a m
aximal degree. S
econd, th
e interpretation
of the
156
comparative clau
se in (183) is sem
antically “deficien
t” in an
importan
t sense: it does n
ot
denote a (m
aximal) degree; rath
er, it is a fun
ction from
a gradable adjective mean
ing to a
degree. In order for th
e comparative clau
se to denote a degree, an
d so introdu
ce the
standard valu
e, it mu
st be supplied w
ith a gradable adjective m
eanin
g. Th
is result can
be
achieved if w
e assum
e that th
e comparative m
orphem
e(s) can h
ave the in
terpretation given
above in (134)b, an
d repeated below. 35
(134)
b.er/m
ore2 = λG
λQ
λx[m
ore(G
(x))(Q(G
))]
Th
e crucial ch
aracteristic of (134)b is that th
e comparative m
orphem
e supplies th
e mean
ing
of the gradable adjective th
at heads th
e comparative con
struction
as the argu
men
t to the
comparative clau
se. Th
is has tw
o consequ
ences: it provides th
e type of constitu
ent n
eeded
to ensu
re that th
e standard con
stituen
t denotes a degree, an
d it establishes th
e “local
dependen
cy” observed in th
e previous section
between
the adjective th
at heads th
e
comparative an
d the “m
issing” adjective m
eanin
g in th
e comparative clau
se. I will focu
s on
the latter poin
t in th
e next section
; to see how
this an
alysis derives the correct in
terpretation
of comparative deletion
constru
ctions, let u
s take a closer look at the com
positional an
alysis
of (178).
Accordin
g to the syn
tactic analysis adopted in
section 2.2.1, th
e structu
ral description
of (178) is (184).
35See Klein
1980 and
Larson 1988 for very sim
ilar analyses of com
parative d
eletion w
ithin
the con
text
of a vague p
redicate an
alysis of gradable ad
jectives.
157
(184
) IP
5D
P V
P @
4 Ju
piter V
DegP
g
g is
Deg’
wp
D
eg’ P
P 3
rp
Deg
AP
P C
P 1
@ g
% m
ore m
assive than
Op
x Neptu
ne is e
x
Assu
min
g the in
terpretation of er/m
ore in (134)b, com
position proceeds as follow
s. Deg
0
combin
es with
AP
, generatin
g the expression
in (185) as th
e denotation
of the low
er Deg’.
(185)
λQ
λx[m
ore(m
assive(x))(Q(m
assive))]
Deg’ th
en com
bines w
ith th
e comparative clau
se, generatin
g (186) (ign
oring than, w
hich
I
take to denote th
e identity fu
nction
; see Larson 19
88).
(186
)λ
x[mo
re(massive(x))(λ
G(m
ax(λd[abs(G
(Neptu
ne))(d)]))(m
assive))]
Th
e comparative clau
se needs a gradable adjective as argu
men
t; this argu
men
t is supplied by
the com
parative morph
eme. Lam
bda conversion
in th
e standard con
stituen
t derives the
property show
n in
(187) as the in
terpretation of th
e comparative degree con
struction
in
(178): the property of bein
g more m
assive than
the m
aximal degree d su
ch th
at Neptu
ne is
at least as massive as d.
(187)
λx[m
ore(m
assive(x))(max(λ
d[abs(massive(N
eptun
e))(d)]))]
Th
e final step in
the com
positional an
alysis of (184) involves applyin
g the property in
(187) to
158
the su
bject, generatin
g (188).
(188
)m
ore(m
assive(Jupiter))(m
ax(λd[abs(m
assive(Neptu
ne))(d)]))
(188) is true ju
st in case th
e degree to wh
ich Ju
piter is massive exceeds th
e maxim
al degree
d such
that N
eptun
e is at least as massive as d, w
hich
is exactly wh
at we w
ant.
2.4.2.4 Local Depen
dencies in
Com
parative Deletion
Revisited
Th
e final piece of th
e puzzle is to sh
ow h
ow th
e analysis ou
tlined in
the previou
s section
provides an explan
ation for th
e facts discussed in
section 2.4.2.2. T
he cru
cial facts are
exemplified by th
e contrast betw
een (189
) and (19
0).
(189
)T
he table is w
ider than
this ru
g is, but th
is rug is lon
ger than
the desk is.
(190
)T
he table is lon
ger than
this ru
g is wide, an
d this ru
g is longer th
an th
e desk is.
Recall from
the earlier discu
ssion th
at the secon
d conju
nct in
(189) is u
nam
biguou
s, havin
g
only th
e interpretation
paraphrased in
(191), bu
t the secon
d conju
nct in
(190
) is ambigu
ous
between
the readin
g in (19
1) and th
e one in
(192).
(191)
... this ru
g is longer th
an th
e desk is long.
(192)
... this ru
g is longer th
an th
e desk is wide.
Th
e puzzle presen
ted by these facts for an
ellipsis analysis of com
parative deletion stem
s
from th
e assum
ption th
at the Logical F
orm of th
e first conju
nct in
(189) is stru
cturally
parallel to the su
bdeletion stru
cture in
the first con
jun
ct of (190
). If this w
ere true, an
d if
comparative deletion
involved recon
struction
of a DegP
un
der identity w
ith som
e other
DegP
in recen
t discourse, th
en it sh
ould be th
e case that th
e second con
jun
ct in (189
) has
159
the sam
e range of possible in
terpretations as th
e second con
jun
ct in (19
0). 36 T
he fact th
at
the secon
d conju
nct in
(189) perm
its only a “local” in
terpretation of th
e missin
g material in
the com
parative clause rem
ains a pu
zzle.
Th
e analysis of com
parative deletion ou
tlined in
the previou
s section provides a
solution
to this pu
zzle by denyin
g the assu
mption
that th
e first conju
ncts in
(189) an
d (190
)
are structu
rally parallel. Accordin
g to this an
alysis, the LF
of the first con
jun
ct in (189
) is
(193), in
wh
ich th
e comparative operator directly bin
ds a DegP
trace.
(193)
Th
e table is wider th
an [C
P Op
x this rug is [D
egP e]x ]
In con
trast, the LF
of the first con
jun
ct in (19
0)–a su
bdeletion stru
cture–is (19
4), in w
hich
the com
parative operator binds a degree variable in
DegP
.
(194
)T
he table is lon
ger than
[CP O
px this ru
g is [DegP e
x wide]]
Th
e crucial stru
ctural differen
ce between
(193) an
d (194
) is that th
e former does n
ot
contain
an occu
rrence of th
e adjective wide. It follow
s that even
if the su
rface string in
(167)
is compatible w
ith a derivation
that establish
es an elliptical relation
between
the first an
d
second con
jun
cts–note th
at noth
ing ru
les out th
is possibility, a fact that is cru
cial to the
explanation
of the am
biguity of (19
0)–th
is wou
ld not trigger an
observable ambigu
ity. Th
e
reason is th
at the derivation
that in
volves ellipsis and th
e one th
at doesn’t cu
lmin
ate in
structu
rally identical LF
s: in both
cases, the LF
of the secon
d conju
nct in
(167) h
as the
structu
re show
n in
(195).
(195)
... this ru
g is longer th
an [C
P Op
x the desk is [D
egP e]x ]
36Recall th
at examp
les of VP ellip
sis structu
rally parallel to (167) are
amb
iguou
s (see e.g. (163) in
section 2.4.2.1).
160
Accordin
g to the sem
antic an
alysis outlin
ed in th
e previous section
, the com
parative clause
in (19
5) has on
ly one possible in
terpretation: on
e in w
hich
the adjective th
at heads th
e
comparative con
struction
(long, in (19
5)) is supplied as argu
men
t to the com
parative clause,
deriving th
e expression in
(196
).
(196
)m
ax(λd[abs(lon
g(the desk))(d)]))
(196
) denotes th
e maxim
al degree d such
that th
e desk is at least as long as d; th
us even
if
the LF
in (19
5) is derived by establishin
g an ellipsis relation
with
the D
egP in
the first
conju
nct, th
e only possible in
terpretation of th
is structu
re is the on
e paraphrased (19
1).
Th
e crucial differen
ce between
(189) an
d (190
)–and th
e reason for th
e ambigu
ity of
the latter–con
cerns th
e structu
re of the first con
jun
ct. Un
like the first con
jun
ct in (189
),
the first con
jun
ct in (19
0) is an
actual su
bdeletion stru
cture; as a resu
lt, the su
rface string in
the secon
d conju
nct is com
patible with
two derivation
s: one in
wh
ich th
e comparative clau
se
is itself a subdeletion
structu
re that h
as un
dergone ellipsis u
nder iden
tity with
the first
conju
nct, an
d one in
wh
ich th
e comparative clau
se is a comparative deletion
constru
ction, in
wh
ich a D
egP operator h
as moved from
its base position to S
pecCP
. In th
e former case, th
e
LF of th
e second con
jun
ct of (190
) is (197), in
wh
ich a D
egP h
as been recon
structed u
nder
identity w
ith th
e DegP
in th
e first conju
nct; in
the latter case, th
e LF of th
e second con
jun
ct
is (198), in
wh
ich th
e comparative operator bin
ds a DegP
variable.
(197)
...this ru
g is longer th
an [C
P Op
x the desk is [D
egP ex ∂
wide]]
(198
)...th
is rug is lon
ger than
[CP O
px this desk is [D
egP e]x ]
Th
e structu
re in (19
7) maps on
to the in
terpretation in
(192), w
hile th
e structu
re in (19
8)
has th
e interpretation
in (19
1); as a result, th
e second con
jun
ct in (19
0) is predicted to be
ambigu
ous.
161
2.4.2.5 Summ
ary
Th
e basic claim of th
e analysis of com
parative deletion th
at I have presen
ted here is th
at the
“missin
g” DegP
in com
parative deletion is n
ot the target of an
ellipsis operation, bu
t rather a
trace boun
d by the com
parative operator, wh
ich is itself categorically a D
egP. T
he
interpretation
of the com
parative operator is such
that after it com
poses with
C-bar, th
e
comparative clau
se denotes a fu
nction
from gradable adjectives to a (m
aximal) degree.
Assu
min
g that th
e comparative m
orphem
e er/more can
have th
e interpretation
in (134)b,
the “m
issing” gradable adjective m
eanin
g in th
e comparative clau
se is supplied w
hen
the
clause com
poses with
Deg’ (sim
ilarly for less and as). Despite th
is composition
al difference
between
comparative deletion
and com
parative subdeletion
, the proposition
s derived in both
types of constru
ctions are expression
s that fit w
ithin
the gen
eral paradigm for degree
constru
ctions proposed in
section 2.1.2. S
pecifically, they h
ave the form
in (19
9): th
ey
denote relation
s between
two degrees, a referen
ce value an
d a standard valu
e.
(199
)d
eg(d
R )(dS )
2.4.3 Phrasal C
omparatives
2.4.3.1 Are P
hrasal Com
paratives Derived from
Clausal Sources?
Ph
rasal comparatives are exem
plified by (200
)-(202).
(200
)M
ars is less distant th
an Satu
rn.
(201)
Th
e asteroid belt is more distan
t than
Mars.
(202)
Neptu
ne is as brigh
t as Uran
us.
Th
e first question
that m
ust be an
swered in
developing an
analysis of ph
rasal comparatives is
wh
ether th
ey are derived from a clau
sal source, i.e., w
heth
er examples like (20
0)-(20
2) are
structu
rally parallel to either su
bdeletion or com
parative deletion stru
ctures at th
e level of
162
interpretation
.
Th
e assum
ption th
at phrasal com
paratives are derived from a clau
sal source (see
Sm
ith 19
61, Lees 19
61, B
resnan
1973, Lern
er and P
inkal 19
95, H
azout 19
95) h
as strong
seman
tic motivation
: if comparative m
orphem
es define relation
s between
degrees, as
suggested in
section 2.1.4, th
en it is n
ecessary to constru
ct interpretation
s of senten
ces like
(200
)-(202) in
wh
ich th
e complem
ent of than den
otes a degree; in (20
2), for example, th
e
degree to wh
ich U
ranu
s is bright. If th
e complem
ent of than
in ph
rasal comparatives is
derived from a clau
sal source, th
en th
e seman
tic analysis of ph
rasal comparatives can
be
subsu
med u
nder th
e seman
tic analysis of eith
er subdeletion
or comparative deletion
. Th
e
problem is th
at there is syn
tactic evidence to in
dicate that at least som
e phrasal com
paratives
are not derived from
clausal sou
rces. Han
kamer 19
73 presents an
importan
t argum
ent to
this effect from
extraction facts. H
ankam
er observes that in
constru
ctions like (20
0)-(20
2),
in w
hich
the su
rface complem
ent of th
an in
a phrasal com
parative is interpreted as th
e
subject of a “m
issing” predicate, th
is constitu
ent can
un
dergo A-bar m
ovemen
t. Th
is is
illustrated by (20
3)-(204).
(203)
You
finally m
et somebody you
’re taller than
.
(204)
Wh
ich plan
et is Neptu
ne as brigh
t as?
Wh
en th
e complem
ent of than con
tains clau
sal material, extraction
is impossible, h
owever:
(205)
*You
finally m
et somebody you
’re taller than
is.
(206
)Y
ou’re taller th
an Jorge is.
(207)
*Wh
ich plan
et is Neptu
ne as brigh
t as is?
(208)
Neptu
ne is as brigh
t as Uran
us is.
Han
kamer n
otes that th
e un
acceptability of (205) an
d (207) follow
s from th
e well-kn
own
fact
that th
e comparative clau
se is an extraction
island. T
he fact th
at extraction is possible in
the
163
phrasal com
paratives (203) an
d (204
) indicates th
at these con
struction
s do not in
volve
ellipsis: assum
ing th
at gramm
atical constrain
ts–inclu
ding th
e calculation
of chain
well-
formedn
ess–are calculated at Logical F
orm (see C
hom
sky 199
5), then
(203) an
d (204) m
ust
not h
ave LFs in
wh
ich th
e complem
ent of than
or as is a clausal con
stituen
t. If they did,
their LF
s wou
ld be structu
rally parallel to those of (20
5) and (20
7), and so th
e senten
ces
shou
ld be ill-formed.
Th
e claim th
at the “stan
dard expression” (th
e overt constitu
ent u
sed to determin
e
the stan
dard value; w
hat I h
ave referred to as the “com
parative clause” u
p to now
) can be a
nom
inal expression
rather th
an a clau
se is also supported by a n
um
ber of cross-lingu
istic
facts. Man
y langu
ages, inclu
ding Latin
, Greek, R
ussian
, Serbo-C
roatian, an
d Hu
ngarian
,
have com
parative constru
ctions in
wh
ich th
e standard expression
is a nom
inal m
arked with
some design
ated case morph
ology (typically an ablative case; see S
tassen 19
85). Hu
ngarian
,
for example, h
as both a preposition
al comparative an
d a case-based comparative, as sh
own
by
the exam
ples in (20
9) an
d (210).
(209
)Ján
os magasabb m
int P
éter.
Janos taller th
an P
eter
‘Janos is taller th
an P
eter’
(210)
János m
agasabb Pétern
él.
Jan
os taller Peter-abl
‘Janos is taller th
an P
eter’
In all of th
ese langu
ages, how
ever, wh
enever th
e complem
ent of than is clearly clau
sal–i.e.,
wh
en it con
tains eith
er a remn
ant of clau
sal material or a fu
ll clause–th
e comparative m
ust
use th
e prepositional form
. It is not su
rprising, th
en, th
at only th
e case-markin
g
comparatives perm
it extraction (see H
ankam
er 1973:184). T
his is illu
strated for Hu
ngarian
by the con
trast between
(211) and (212).
164
(211)*M
int ki m
agasabb János?/*K
i magasabb Ján
os min
t?
Th
an w
ho taller Jan
os/Wh
o taller Janos th
an
‘Th
an w
hom
is Janos taller/W
ho is Jan
os taller than
’
(212)K
inél m
agasabb János?
who-abl taller Jan
os
‘Wh
o is Janos taller th
an’
Th
e distribution
of reflexives provides a second argu
men
t against an
ellipsis analysis
of phrasal com
paratives. As n
oted by Han
kamer (19
73), a reflexive boun
d by the su
bject can
introdu
ce the stan
dard expression on
ly in ph
rasal comparatives, n
ot in clau
sal comparatives:
(213)N
o star is brighter th
an itself.
(214)
*No star is brigh
ter than
itself is.
Th
e un
acceptability of (214) is not su
rprising: th
e reflexive is the su
bject of an em
bedded
finite clau
se, and so is n
ot boun
d in its m
inim
al governin
g category, wh
ich in
curs a violation
of Con
dition A
of the B
indin
g Th
eory (see Ch
omsky 19
81, 1986
). If (213) is actually a
reduced clau
se, then
assum
ing th
at Con
dition A
mu
st be satisfied at LF (C
hom
sky 199
3,
Heycock 19
95, etc.), (213) sh
ould also be ill-form
ed. If the con
stituen
t headed by than h
as
the syn
tax of a prepositional ph
rase, how
ever, as in (215), th
en th
e reflexive is boun
d in its
min
imal govern
ing category, satisfyin
g Con
dition A
.
(215)[IP n
o stari is [DegP
brighter [P
P than
[DP itselfi ]]]]
Th
e conclu
sion to be draw
n from
these facts is th
at at least some p
hrasal
comparatives h
ave syntactic represen
tations in
wh
ich th
e complem
ent of than is a n
omin
al,
rather th
an clau
sal constitu
ent. T
his resu
lt raises the follow
ing qu
estion: if th
e
complem
ent of than is an
individu
al-denotin
g expression (i.e., a D
P), an
d if the sem
antics of
165
comparative con
struction
s is stated in term
s of a relation betw
een degrees, as I h
ave
claimed, h
ow is th
e interpretation
of a phrasal com
parative derived? In oth
er words, h
ow do
we get from
an in
dividual to a degree?
Before attem
pting to develop an
answ
er to this qu
estion, I sh
ould poin
t out th
at
there is eviden
ce that som
e phrasal com
paratives do in fact h
ave clausal sou
rces. Th
is
evidence com
es from a con
trast between
examples like (216
) and (217) (cf. H
ankam
er
1973:180
; for additional eviden
ce from H
ebrew th
at some su
perficially phrasal com
paratives
are derived from clau
sal sources, see H
azout 19
95).
(216)
Max is m
ore eager to meet S
usan
than
Alice.
(217)W
ho is M
ax more eager to m
eet Su
san th
an?
Wh
ereas (216) is am
biguou
s between
the in
terpretations in
(218) and (219
), (217) is not: it
has on
ly an in
terpretation correspon
ding to (219
), in w
hich
the w
h-trace binds th
e argum
ent
of eager.
(218)
Max is m
ore eager to meet S
usan
than
he is eager to m
eet Alice.
(219)
Max is m
ore eager to meet S
usan
than
Alice is eager to m
eet Su
san.
Th
is contrast follow
s if the n
on-elliptical stru
cture requ
ires the com
plemen
t of than to have
a seman
tic role parallel to that of th
e subject. (216
) is ambigu
ous becau
se it can be
interpreted eith
er as a simple ph
rasal constru
ction or as an
ellipsis constru
ction. In
contrast,
wh-extraction
requires th
e syntactic stru
cture of (217) to be a sim
ple phrasal con
struction
,
since a clau
sal structu
re wou
ld not perm
it extraction (see (20
5) and (20
7) above). Wh
at
remain
s to be explained is w
hy th
e simple ph
rasal constru
ction requ
ires the argu
men
t of
than to have a sem
antic role parallel to th
at of the su
bject. I will retu
rn to th
is point below
.
166
2.4.3.2 Local Depen
dencies P
hrasal Com
paratives
Tw
o solution
s to the problem
of interpretin
g phrasal com
paratives have been
proposed in
the literatu
re. Th
e first approach, developed in
Gaw
ron 19
95, m
aintain
s the position
that
phrasal an
d clausal com
paratives (subdeletion
and com
parative deletion) h
ave basically the
same in
terpretation–th
e complem
ent of than den
otes a description of a degree–bu
t claims
that th
e interpretation
of phrasal com
paratives is derived throu
gh ellipsis resolu
tion in
the
seman
tic compon
ent, rath
er than
throu
gh a recon
struction
operation in
the syn
tax. 37
Gaw
ron’s an
alysis adopts the position
that ph
rasal comparatives h
ave the sim
ple syntactic
structu
re in (215), th
us m
aintain
ing an
accoun
t of the facts discu
ssed in H
ankam
er 1973, bu
t
derives an in
terpretation of th
e complem
ent of than as a description
of a degree by utilizin
g
the H
igher O
rder Un
ification an
alysis of ellipsis developed in D
alrymple, S
hieber, an
d
Pereira 19
91. W
ithin
the con
text of the an
alysis of gradable adjectives as measu
re fun
ctions,
Gaw
ron’s proposals can
be sum
marized as follow
s. Th
e basic interpretation
of the stan
dard
expression in
a simple ph
rasal comparative is an
un
derspecified relation betw
een an
individu
al and a degree; specifically, th
e relation is u
nderspecified for a gradable adjective
mean
ing. F
or example, th
e logical representation
of the com
plemen
t of than in (220
), prior
to ellipsis resolution
, is (221), wh
ere G is th
e missin
g adjective mean
ing.
(220)
Th
e asteroid belt is more distan
t than
Mars.
(221)λ
x[max(λ
d[abs(G(x))(d)])](M
ars)
Th
e problem of fin
ding th
e standard valu
e boils down
to the problem
of findin
g an
appropriate fun
ction from
individu
als to degrees, and in
serting th
at fun
ction in
to the logical
representation
in (221) as th
e value of G
. With
out goin
g into details, th
e basic claim of th
e
High
er Order U
nification
approach is th
at this fu
nction
is recovered by abstracting over a
37In G
awron
’s analysis, th
e comp
arative clause is actu
ally interp
reted as a u
niversal q
uan
tification
structu
re, rather th
an a d
efinite d
escription
(of a maxim
al degree), bu
t this d
ifference is n
ot imp
ortant to th
ecu
rrent d
iscussion
.
167
parallel elemen
t in th
e main
clause. In
the case of (220
), the parallel elem
ent is th
e subject,
and th
e fun
ction th
at is recovered is the m
eanin
g of the adjective distant. T
his fu
nction
can
then
be supplied as th
e value of G
in (221), derivin
g (222).
(222)m
ax(λd[abs(distant(M
ars))(d)])
(222) denotes th
e maxim
al degree d such
that th
e degree to wh
ich M
ars is distant is at least
as great as d, wh
ich is correctly iden
tifies the stan
dard value for (220
).
A stron
g point of G
awron
’s analysis is th
at it provides a mean
s of constru
cting an
appropriate interpretation
for the com
parative clause u
sing a gen
eral ellipsis-resolution
mech
anism
, wh
ich is in
dependen
tly required to h
andle oth
er cases of ellipsis (see
Dalrym
ple, Sh
ieber, and P
ereira 199
1 for discussion
). Th
is also turn
s out to be a problem
for the an
alysis, how
ever, as phrasal com
paratives show
exactly the sam
e kind of local
dependen
cy between
the “m
issing” adjective m
eanin
g in th
e standard expression
and th
e
adjective that h
eads the com
parative DegP
that w
e saw in
the case of com
parative deletion in
section 2.4
.2.2. Recall from
that discu
ssion th
at a general ch
aracteristic of elliptical
constru
ctions is th
at any con
stituen
t of the appropriate sem
antic type can
be recovered as
the m
eanin
g of an elided con
stituen
t. For exam
ple, (223) is ambigu
ous betw
een a readin
g in
wh
ich th
e second con
jun
ct mean
s I read every book Charles read
, and on
e in w
hich
it mean
s I
read every book Charles bought.
(223)M
arcus read every book I bou
ght, an
d I read every book Ch
arles did.
Th
e ambigu
ity of this exam
ple show
s that th
e anteceden
t for the elided verb ph
rase can
either provided by a local an
tecedent–th
e VP
headed by read, or by a m
ore distant on
e–the
VP
headed by bou
ght in th
e relative clause of th
e first conju
nct. A
lthou
gh th
e more local
interpretation
may be preferred, it is n
ot obligatory.
If the sam
e general m
echan
isms for recoverin
g elided material are in
volved in th
e
168
interpretation
s of phrasal com
paratives, then
the secon
d conju
nct in
an exam
ple like (224)
should also be am
biguou
s.
(224)T
he table is w
ider than
the ru
g, and th
e rug is lon
ger than
the desk.
(224) is not am
biguou
s, how
ever. Th
is senten
ce has on
ly an in
terpretation in
wh
ich th
e
length
of the ru
g is asserted to exceed the len
gth of th
e desk; it does not h
ave a reading in
wh
ich th
e length
of the ru
g is asserted to exceed the w
idth of the desk. 38 T
he con
clusion
to
be drawn
from th
is example is th
at just as w
e saw w
ith com
parative deletion, th
ere is a local
dependen
cy between
the in
terpretation of th
e standard valu
e and th
e adjective that h
eads a
phrasal com
parative. In effect, th
e standard valu
e mu
st be derived by applying th
e mean
ing
of the adjective th
at heads th
e comparative to th
e complem
ent of than. W
ithout additional
stipulation
s, how
ever, an ellipsis accou
nt of th
e sort proposed by Gaw
ron can
not derive th
is
result.B
efore movin
g on to an
alternative an
alysis, I shou
ld point ou
t an in
teresting
difference betw
een ph
rasal and clau
sal comparatives: (225), u
nlike (226
) (cf. (174) in section
2.4.2.2), is not ambigu
ous.
(225)T
he table is lon
ger than
the ru
g is wide, an
d the ru
g is longer th
an th
e desk.
(226)
Th
e table is longer th
an th
e rug is w
ide, and th
e rug is lon
ger than
the desk is.
Th
e ambigu
ity of (226) w
as explained in
the follow
ing w
ay: the secon
d conju
nct is
structu
rally ambigu
ous betw
een an
analysis as a su
bdeletion stru
cture th
at has u
ndergon
e
VP
ellipsis and an
analysis as a com
parative deletion stru
cture, w
hich
does not in
volve
38As w
as the case w
ith n
omin
al comp
arative deletion
, similar facts are ob
served in
ph
rasal nom
inal
comp
aratives. (i) has on
ly the in
terpretation
parap
hrased
in (ii); it can
not be in
terpreted
as in (iii) (cf. fn
. 33).
(i)K
im bou
ght m
any p
eaches, bu
t Sand
y bough
t more ap
ples th
an K
im.
(ii)K
im bou
ght m
any p
eaches, bu
t Sand
y bough
t more ap
ples th
an K
im bou
ght ap
ples.
(iii)K
im bou
ght m
any p
eaches, bu
t Sand
y bough
t more ap
ples th
an K
im bou
ght p
eaches.
169
ellipsis. Th
e fact that (225) is u
nam
biguou
s suggests th
at it does not have an
analysis as an
ellipsis structu
re, wh
ich creates a pu
zzle. At th
e end of section
2.4.3.1, I noted th
at there is
evidence th
at phrasal com
paratives are potentially am
biguou
s between
simple ph
rasal
structu
res and clau
sal analyses, w
hich
presum
ably involve ellipsis (see H
ankam
er 1973,
Hazou
t 199
5). If this is tru
e, then
it shou
ld be possible to analyze (225) as an
ellipsis
structu
re. Bu
t this w
ould lead u
s to expect that (225), like (226
), shou
ld be ambigu
ous. I
will leave th
is puzzle for fu
ture w
ork.
2.4.3.3 A D
irect Interpretation
of Phrasal C
omparatives
Th
e second approach
to the problem
of phrasal com
paratives, developed in H
eim 19
85,
differs from G
awron
’s in m
aking an
explicit distinction
between
the in
terpretation of ph
rasal
and clau
sal comparatives. In
Heim
’s analysis, clau
sal comparatives–both
subdeletion
and
comparative deletion
–have th
e same an
alysis: the com
parative clause den
otes a description
of a degree, wh
ich is u
sed to compu
te the stan
dard value. 39 P
hrasal com
paratives, on th
e
other h
and, h
ave a more “direct” in
terpretation, in
wh
ich th
e comparative m
orphem
e takes
three argum
ents: th
e subject, th
e complem
ent of than, an
d a degree property. In H
eim’s
analysis, w
hich
is developed in th
e context of a relation
al seman
tics of gradable adjectives, the
interpretation
of an exam
ple like (220) is (227), w
hich
is evaluated w
ith respect to th
e truth
condition
s in (228), w
here a an
d b are individu
als and f is a fu
nction
from in
dividuals to
degrees.
(227)m
ore(the asteroid belt)(M
ars)(λx[m
ax(λd.distant(x,d))])
(228)||m
ore(a)(b)(f)|| = 1 iff f(a) > f(b)
A positive resu
lt of this an
alysis is that it derives th
e local dependen
cy between
the stan
dard
value an
d the adjective w
hich
heads th
e comparative con
struction
. Th
e same fu
nction
from
39That is, for H
eim, com
parative d
eletion stru
ctures are ellip
sis constru
ctions th
at are structu
rallyid
entical to su
bdeletion
at LF, an an
alysis that I argu
ed again
st in th
e previou
s section.
170
individu
als to degrees is applied to both of th
e individu
al argum
ents of th
e comparative
morph
eme–
the adjective th
at heads th
e comparative con
struction
–an
d as a result, n
o
variation is possible.
Th
is approach to th
e seman
tics of phrasal com
paratives can be straigh
tforwardly
implem
ented in
a system in
wh
ich gradable adjectives den
ote measu
re fun
ctions by
assum
ing th
at the com
parative morph
emes can
have th
e interpretation
given above in
(134)c, repeated below (again
, I focus on
the an
alysis of er/more for perspicu
ity, but m
y
remarks h
old of less and as as w
ell).
(134)
c.er/m
ore3 = λG
λyλ
x[mo
re(G(x))(G
(y))]
Th
e importan
t aspect of (134)c is th
at the syn
tactic constitu
ent u
sed to compu
te the
standard valu
e has th
e seman
tic type of an in
dividual, an
d a degree is derived by applying th
e
mean
ing of th
e gradable adjective that h
eads the com
parative constru
ction to th
is individu
al.
Th
is analysis is n
ot only con
sistent w
ith th
e syntactic facts of ph
rasal comparatives observed
in th
is section, it also explain
s the depen
dence betw
een th
e standard valu
e and th
e adjective
wh
ich h
eads the com
parative constru
ction. P
hrasal com
paratives are interpreted by directly
applying th
e adjective mean
ing both
to the su
bject and to th
e complem
ent of th
an
,
explainin
g the failu
re of phrasal com
paratives to show
the kin
d of variability in in
terpretation
associated with
true ellipsis stru
ctures. 40
40This an
alysis also provid
es an exp
lanation
of the in
terpretation
of structu
res in w
hich
there is n
o
app
ropriate sou
rce for ellipsis. For exam
ple, N
apoli (1983), citin
g William
s (see also Heim
1985), poin
ts out
that m
etaph
orical senten
ces like (i) h
ave no ap
prop
riate source: (i) is in
terpreted
as (ii), but an
ellipsis an
alysisw
ould
requ
ire it to have th
e source in
(iii).
(i)M
ary eats faster than
a tornad
o.
(ii)M
ary eats faster than
a tornad
o ii iiss ss ff ffaa aass sstt tt
(iii)M
ary eats faster than
a tornad
o ee eeaa aatt ttss ss ff ffaa aass sstt tt
With
in th
e analysis p
roposed
here, th
is prob
lem d
isapp
ears. Th
e nom
inal a torn
ado
directly p
rovides th
estan
dard
argum
ent, gen
erating an
interp
retation for th
e entire d
egree constru
ction as in
(iv) (wh
ich I assu
me
to receive an ad
verbial interp
retation by virtu
e of its syntactic statu
s as an ad
jun
ct).
171
Th
e seman
tic analysis of ph
rasal comparatives ou
tlined h
ere fits together very n
eatly
with
the syn
tactic analysis of th
e extended projection
of the adjective th
at I adopted in section
2.2. Th
e structu
ral description of a ph
rasal comparative like (229
) is (230), w
hich
has th
e
interpretation
in (231).
(229)
Plu
to is more distan
t than
Mars.
(230)
IP 3
DP
VP
! 3
Plu
to V D
egP g g is
Deg’
4
Deg’
PP
3 #
Deg
AP
than
Mars
gg g
more A
g
distan
t
(iv)λx
[more
(fast(x))(fast(a tornado))]
172
(231)
IP: λ
x[mo
re(distant(x))(distant(Mars))](P
luto)
3D
P V
P !
3 P
luto V
DegP
: λx[m
ore(distant(x))(distant(M
ars))] g
g is
Deg’:λ
yλx[m
ore(distant(x))(distant(y))](M
ars) t
p λG
λyλ
x[mo
re(G(x))(G
(y))](distant):Deg’
PP
3 #
Deg
AP
than Mars
g g
λG
λyλ
x[mo
re(G(x))(G
(y))] A
g
distant
Th
e comparative m
orphem
e combin
es with
the gradable adjective an
d applies the adjective
to each of its rem
ainin
g two argu
men
ts, wh
ich are provided by th
e nom
inal argu
men
t of
than and th
e subject, respectively. T
he resu
lt of the com
position in
(231) is (232), wh
ich h
as
the tru
th con
ditions in
(233): Plu
to is more distant than M
ars is true ju
st in case th
e degree
to wh
ich P
luto is distan
t exceeds the degree to w
hich
Mars is distan
t.
(232)m
ore(distant(P
luto))(distant(M
ars))
(233)||m
ore(distant(P
luto))(distant(M
ars))|| = 1 iff
distant(Plu
to) > distant(Mars)
An
interestin
g consequ
ence of th
e syntactic an
d seman
tic analyses of ph
rasal
comparatives ou
tlined h
ere is that it explain
s wh
y the sem
antic role of th
e extracted elemen
t
in exam
ples like (217) mu
st be the sam
e as that of th
e subject.
(217)W
ho is M
ax more eager to m
eet Su
san th
an?
Sin
ce extraction is licen
sed only if th
e complem
ent of than is a D
P, rath
er than
a reduced
173
clause, th
e comparative is in
terpreted by applying th
e AP
mean
ing to th
e trace of the w
h-
expression. In
(217), the m
eanin
g of AP
is (234) (wh
ere eager to meet S
usan
is a fun
ction
from in
dividuals to degrees), w
hich
is the sam
e fun
ction th
at is applied to the su
bject.
(234)λ
z.eager(z, ^meet(z,S
usan))
As a resu
lt, the extracted elem
ent an
d the su
bject mu
st have th
e same sem
antic role.
2.4.3.4 Summ
ary
Th
e syntactic eviden
ce outlin
ed in section
2.3.3.1 clearly show
s that in
at least some ph
rasal
comparatives, th
e complem
ent of than is a sim
ple phrasal con
stituen
t, not a redu
ced clause.
I have dem
onstrated th
at the sem
antic an
alysis of gradable adjectives as measu
re fun
ctions,
combin
ed with
the syn
tax of extended projection
, supports a “direct” in
terpretation of
phrasal com
paratives similar to th
e one proposed in
Heim
1985. T
his an
alysis not on
ly
accurately ch
aracterizes the tru
th con
ditions of ph
rasal comparatives, it also explain
s the
local dependen
cy between
the “m
issing” adjective m
eanin
g in th
e standard expression
and
the adjective th
at heads th
e comparative clau
se. Alth
ough
it was n
ecessary to postulate a
composition
al difference betw
een ph
rasal comparatives an
d their clau
sal coun
terparts, the
truth
condition
s of phrasal com
paratives are exactly the sam
e as those of su
bdeletion
structu
res and com
parative deletion con
struction
s. Sin
ce the com
plemen
t of than/as in a
phrasal com
parative denotes an
individu
al and th
e gradable adjective denotes a m
easure
fun
ction, sem
antic com
position resu
lts in a proposition
that expresses a relation
between
degrees. As a resu
lt, the tru
th con
ditions of ph
rasal comparatives follow
the gen
eral pattern
of other degree con
struction
s: they defin
e relations betw
een a referen
ce value an
d a
standard value.
174
2.4.4 The P
hrasal/Clausal D
istinction
and the Scope of the Stan
dard
A n
um
ber of researchers h
ave observed seman
tic differences betw
een ph
rasal and clau
sal
comparatives (see, for exam
ple, McC
awley 19
67, N
apoli 1983, H
oeksema 19
83, von S
techow
1984a, as w
ell as Heim
1985). T
hese distin
ctions are exem
plified by the in
terpretation of
phrasal an
d clausal com
paratives in in
tension
al contexts. F
or example, N
apoli (198
3)
observes that in
a context in
wh
ich th
e speaker and h
earer know
that earth
is 4.5 billion
years old, the galaxy is 6
billion years old, an
d that Jon
es believes the E
arth to be 4.5 billion
years old but h
as no idea of th
e age of the galaxy, (235) is felicitou
s but (236
) is not.
(235)Jon
es thin
ks the earth
is youn
ger than
the galaxy is.
(236)
Jones th
inks th
e earth is you
nger th
an th
e galaxy.
Th
is type of example is clearly related to th
ose originally discu
ssed by Ru
ssell 190
5
(see the discu
ssion of scope am
biguities in
chapter 1), w
hich
show
that th
e comparative
clause sh
ows scope am
biguities parallel to defin
ite descriptions in
inten
sional con
texts. For
example, (237) is am
biguou
s between
the readin
g paraphrased in
(238), in w
hich
Jones is
mistaken
about Ju
piter’s size, and th
e one paraph
rased in (239
), in w
hich
he h
as a
contradictory belief abou
t the size of Ju
piter.
(237)Jon
es thin
ks that Ju
piter is larger than
it is.
(238)T
he size th
at Jupiter actu
ally is is greater than
the size Jon
es thin
ks it is.
(239)
Jones h
olds the belief th
at Jupiter exceeds itself in
size.
Wh
at is importan
t to note is th
at if the com
parative clause in
comparative deletion
constru
ctions is an
alyzed as a type of definite description
, as claimed in
section 2.4.2, th
en
the am
biguity of (237) is expected: like oth
er definite description
s in in
tension
al contexts,
the com
parative clause in
(237) can h
ave both a de re an
d a de dicto interpretation
(wh
ich
correspond to th
e readings in
(238) and (239
) respectively). How
exactly the readin
gs are
175
derived will depen
d on th
e theory of th
e scope of descriptions; all th
at is importan
t to note
here is th
at if the com
parative clause is a description
, then
these facts follow
(see Ru
ssell
190
5, Hasegaw
a 1972, P
ostal 1974, H
orn 19
81, Hellan
1981, von
Stech
ow 19
84a, Hoeksem
a
1984, H
eim 19
85, and K
enn
edy 199
5, 199
6b for differen
t approaches to th
is ambigu
ity).
An
importan
t fact, observed by McC
awley (19
67), H
ellan (19
81), Napoli (19
83), and
Heim
(1985), is th
at phrasal com
paratives do not sh
ow a sim
ilar ambigu
ity: (240) h
as only
the in
terpretation in
(239); th
e de re reading in
(238) is un
available. 41
(240)
Jones th
inks th
at Jupiter is larger th
an itself.
Th
e analyses of ph
rasal comparatives an
d comparative deletion
constru
ctions developed in
the previou
s sections provides a straigh
tforward explan
ation of th
ese facts. Alth
ough
phrasal
and clau
sal comparatives are fu
ndam
entally th
e same–
they den
ote relations betw
een a
reference valu
e and a stan
dard value–th
ey also differ in an
importan
t way: th
e standard
value in
a clausal com
parative is a description of a degree, as n
oted above; the stan
dard value
in a ph
rasal comparative is n
ot (this distin
ction is also m
ade by Heim
(1985)). If stan
dard-
denotin
g expression in
a phrasal com
parative is not a description
of a degree, therefore
wh
atever operations are respon
sible for the am
biguity of (237) sim
ply don’t apply. T
he facts
observed by Napoli (19
83), can presu
mably be explain
ed in th
e same w
ay. 42
41The con
trast between
(ia-b) and
(iia-b) show
s that th
e same facts h
old in
other in
tension
al contexts.
(i)a.
If Jup
iter were sm
aller than
it is, it migh
t have a solid
core.b.
If Jup
iter were sm
aller than
itself, it migh
t have a solid
core.
(ii)a.
Jones cou
ld h
ave been less obn
oxious th
an h
e was.
b.Jon
es could
have been
less obnoxiou
s than
him
self.
42Alth
ough
the facts d
iscussed
here m
ight b
e constru
ed as an
other argu
men
t against an
ellipsis
analysis o
f ph
rasal com
paratives (see e.g. N
apo
li 1983), Heim
(1985) po
ints o
ut th
at these facts d
o n
ot
necessarily p
rovide su
ch an
argum
ent, p
rovided
that th
e cond
itions w
hich
license ellip
sis are formu
lated in
such
a way as to req
uire id
entity of variab
les in th
e elided
constitu
ent an
d an
teceden
t (see Sag 1976). In an
examp
le like (240), th
is will req
uire th
e world
variables in th
e two con
stituen
ts to be the sam
e, generatin
g the
contrad
ictory interp
retation.
176
2.4.5 Com
paratives with Less
An
importan
t aspect of the an
alysis of degree constru
ctions th
at I have developed in
this
chapter is th
at the in
terpretation of th
e comparative in
dependen
t of the in
terpretation of
the absolu
te. In th
is sense, th
e analysis differs from
the relation
al approaches discu
ssed in
chapter 1, in
wh
ich th
e interpretation
of the com
parative (qua degree description
or
generalized qu
antifier) w
as stated in term
s of the sem
antics of th
e absolute form
of the
adjective (see also the discu
ssion of th
is point in
section 2.1.2). A
result of th
is difference is
that th
e analysis proposed h
ere derives the correct tru
th con
ditions for com
paratives with
less with
out givin
g up an
analysis of th
e absolute in
terms of a partial orderin
g relation.
Recall from
the discu
ssion in
chapter 1, section
1.4.2 th
at an an
alysis of less
comparatives in
terms of restricted existen
tial quan
tification fails to accu
rately characterize
the tru
th con
ditions of th
ese constru
ctions if th
e interpretation
of the absolu
te form is
stated in term
s of a partial ordering relation
. Assu
min
g that expression
s of the form
ϕ(a,d)
are true ju
st in case th
e degree to wh
ich a
is ϕ is at least as great as d, th
e logical
representation
of a senten
ce like (241), show
n in
(242), is satisfied even if M
ars Path
finder
was m
ore expensive th
an th
e space telescope, since it w
ould be tru
e in su
ch a situ
ation th
at
for some d ordered below
the degree to w
hich
the space telescope w
as expensive, M
ars
Path
finder is at least as expen
sive as d.
(241)
Mars P
athfin
der was less expen
sive than
the space telescope.
(242)∃
d[d < ιd’.expensive(the space telescope,d’)][expensive(Mars P
athfinder,d)]
In con
trast, since th
e analysis of com
paratives developed in th
e preceding section
s is
not stated in
terms of th
e absolute con
struction
, this problem
disappears. Th
e truth
condition
s for less comparatives (as w
ell as those of m
ore comparatives, equ
atives, and th
e
absolute con
struction
) are formu
lated directly in term
s of a relation betw
een tw
o
degrees–the referen
ce value an
d the stan
dard value. G
iven th
e truth
condition
s for less and
more th
at I have assu
med, w
hich
are stated below in
(243) and (244), th
e relations den
oted
177
by less and m
ore cann
ot hold of th
e same pair of degrees in
the sam
e context.
(243)||less(d
R )(dS )|| = 1 iff d
R < dS
(244
)||m
ore(d
R )(dS )|| = 1 iff d
R > dS
It follows th
at (241), wh
ich h
as the logical represen
tation in
(245) is true if an
d only if th
e
degree to wh
ich M
ars Path
finder w
as expensive is ordered below
the degree to w
hich
the
space telescope was expen
sive on th
e scale associated with
the adjective expensive.
(245)less(expen
sive(Mars P
athfinder))(expensive(the space telescope))
2.4.6 C
omparative an
d Absolute
Before con
cludin
g this section
, a few fin
al words on
the differen
ce between
comparative an
d
absolute con
struction
s are in order. A
lthou
gh th
e truth
condition
s of propositions
constru
cted out of com
parative and absolu
te adjectives are fun
damen
tally the sam
e–they are
stated in term
s of the sam
e three con
stituen
ts, a degree relation, a referen
ce value, an
d a
standard valu
e–th
e seman
tic differences betw
een th
e comparative an
d absolute degree
morph
emes m
ake an im
portant distin
ction betw
een th
ese constru
ctions.
Wh
at is comm
on to both
comparative an
d absolute degree con
struction
s is that th
ey
establish a relation
between
projection of an
object on a scale–specifically, th
e target of
predication–an
d some oth
er scalar value (th
e standard). A
bsolute con
struction
s are more
limited in
their m
eans of accom
plishin
g this th
an com
paratives, how
ever, because th
ey are
constrain
ed to use on
ly degree-denotin
g expressions (m
easure ph
rases) or properties to
identify th
e standard. In
contrast, th
e fun
damen
tal characteristic of com
parative
constru
ctions is th
at they m
ake it possible to identify th
e standard valu
e as a fun
ction of
virtually an
y object in th
e discourse, provided th
at it is the sort of object th
at can be projected
onto th
e scale associated with
a gradable adjective. Th
is difference explain
s the w
ell-know
n
fact that in
typical examples, n
o entailm
ent relation
holds betw
een com
parative senten
ces
178
and th
e correspondin
g absolutes. F
or example, n
one of th
e argum
ents in
(246)-(248) are
valid.
(246)
A w
hite dw
arf is brighter th
an a brow
n dw
arf.
#∴ A
wh
ite dwarf is brigh
t.
(247)
Saturn
’s gravitational field is less in
tense th
an Ju
piter’s.
#∴ Satu
rn’s gravitation
al field is (not) in
tense.
(248
)A
t certain poin
ts durin
g its orbit, Plu
to is as close to the su
n as N
eptun
e.
#∴ P
luto is close to th
e sun
.
In order for argu
men
ts such
as (246)-(248) to be valid, it w
ould h
ave to be the case th
at the
“constru
cted” standards in
troduced by th
e comparatives necessarily stood in
some relation
to
the con
text-dependen
t standards associated w
ith th
e correspondin
g absolutes. C
onsider, for
example, th
e interpretation
s of the prem
ise and con
clusion
in (248) in
(249) an
d (250).
(For sim
plicity, I will ign
ore the adverbial con
stituen
t in (249
) and I w
ill analyze th
e phrase
close to the sun as a single adjectival con
stituen
t.)
(249)
as(close-to-the-sun(P
luto))(close-to-the-su
n(Neptu
ne))
(250)
abs(close-to-the-sun(P
luto))(stn
d(λ
x.close-to-the-sun(x))(p(P
luto)))
(249) an
d (250) h
ave essentially th
e same tru
th con
ditions: th
ese expressions are tru
e if the
first argum
ent of as/abs (th
e reference valu
e) is at least as great as the secon
d argum
ent
(the stan
dard value) (see (124
) and th
e truth
condition
s for the absolu
te given in
(77),
section 2.3). In
order for (250) to follow
from (249
), then
, it mu
st be the case th
at the
standard valu
e in (249
)–the degree to w
hich
Neptu
ne is close to th
e sun
–is at least as great
as the stan
dard value in
(250)–a valu
e on th
e scale associated with
close-to-the-sun th
at is
contextu
ally determin
ed based on som
e property of Plu
to. Alth
ough
it is possible that th
ese
two valu
es are related in th
is way, it is certain
ly not n
ecessary. As a resu
lt, the en
tailmen
t
179
doesn’t go th
rough
. Similar argu
men
ts apply to (246) an
d (247).
2.4.7 Summ
ary: Curren
t Results an
d Future D
irections
Bu
ilding on
the syn
tax of extended projection
, this section
demon
strated that th
e analysis of
gradable adjectives and degree m
orphology ou
tlined in
section 2.1 su
pports a straightforw
ard
composition
al seman
tics for predicative comparatives th
at implem
ents on
e of the m
ain
claims of section
2.1: comparative con
struction
s are not qu
antification
al expressions, rath
er
they den
ote properties of individu
als. An
importan
t aspect of the an
alysis is that th
e
interp
retations
of th
e th
ree classes
of com
paratives
that
I con
sidered–su
bdeletion
structu
res, comparative deletion
constru
ctions, an
d phrasal com
paratives–differ according to
the stru
cture an
d interpretation
s of the stan
dard expression. In
both su
bdeletion an
d
comparative deletion
structu
res, the stan
dard expression is a clau
sal constitu
ent (th
e
“comparative clau
se”), but in
the form
er, the com
parative clause is directly in
terpreted as a
description of a degree, w
hile in
the latter, th
e comparative clau
se denotes a fu
nction
from
gradable adjectives to degree descriptions, an
d the gradable adjective m
eanin
g is supplied by
the adjective th
at heads th
e comparative con
struction
. In con
trast, the stan
dard expression
in a ph
rasal comparative is a D
P, an
d the stan
dard value is derived by applyin
g the m
easure
fun
ction in
troduced by th
e adjective that h
eads the com
parative DegP
to this expression
.
Alth
ough
the an
alysis requires th
e assum
ption th
at the com
parative degree morph
emes
have th
ree distinct in
terpretations, it w
as show
n to be ju
stified both syn
tactically, as it
provides a direct interpretation
for phrasal com
paratives, and sem
antically, as it accou
nts for
the local depen
dency observed in
phrasal com
paratives and com
parative deletion betw
een
the in
terpretation of th
e “missin
g” adjective mean
ing in
the stan
dard expression an
d the
adjective that h
eads the com
parative. More gen
erally, the th
ree interpretation
s of the
comparative m
orphem
es are truth
-condition
ally equivalen
t, differing on
ly the derivation
of
the stan
dard value. A
s a result, all th
ree classes of comparatives give rise to proposition
s that
have th
e seman
tic constitu
ency h
ypothesized to h
old of all degree constru
ctions: th
ey
express ordering relation
s between
two degrees, th
e reference valu
e and th
e standard valu
e.
180
A fin
al point sh
ould be em
phasized. A
s observed at the ou
tset of this section
, in
order for the an
alysis developed here to be accepted as a gen
eral accoun
t of the sem
antic an
d
syntactic properties of com
paratives, it mu
st be show
n th
at it can be exten
ded to the fu
ll
range of com
parative constru
ctions in
En
glish, in
cludin
g attributive A
P com
paratives and
nom
inal com
paratives. Of particu
lar importan
ce is an evalu
ation of th
e analysis of
comparative deletion
with
respect to these oth
er types of comparative con
struction
s, in
particu
lar, the h
ypoth
esis that th
e missin
g degree ph
rase in com
parative deletion
constru
ctions in
dicates that th
e comparative operator is categorically a D
egP, rath
er than
the
application of an
ellipsis operation. A
lthou
gh th
is hypoth
esis provided a principled
explanation
of the sem
antic an
d syntactic properties of predicative com
parative deletion
constru
ctions, w
heth
er it generalizes to n
omin
al and attribu
tive comparatives is a qu
estion
that rem
ains to be an
swered (th
ough
see Ken
nedy an
d Merch
ant 19
97 for argu
men
ts that
this an
alysis actually provides th
e basis for an explan
ation of som
e otherw
ise puzzlin
g
characteristics of attribu
tive comparatives). W
hat I h
ope to have dem
onstrated in
this
section is th
at the overall stren
gth of th
e analysis of gradable adjectives an
d degree
constru
ctions th
at I have advocated in
this th
esis makes th
is a question
that is in
deed worth
pursu
ing.
2.5 Con
clusion
Th
is chapter m
ade two prim
ary claims. F
irst, gradable adjectives shou
ld be analyzed n
ot as
relational expression
s, but rath
er as fun
ctions from
objects to degrees. Secon
d, degree
morp
hem
es introdu
ce relations betw
een degrees, an
d degree constru
ctions den
ote
properties of individu
als, rather th
an expression
s that qu
antify over degrees. B
uildin
g on a
syntactic an
alysis in w
hich
gradable adjectives project fun
ctional stru
cture h
eaded by a degree
morph
eme, I dem
onstrated th
at these assu
mption
s support a straigh
tforward com
positional
seman
tic analysis of a ran
ge of degree constru
ctions in
En
glish. C
rucially, sin
ce degrees are
not argu
men
ts of a gradable adjectives, and degree con
struction
s are not an
alyzed as
181
quan
tificational expression
s, the fact th
at they do n
ot participate in scope am
biguities follow
s.
In a gen
eral sense, th
e seman
tic analysis ou
tlined in
section 2.1 provides su
pport for
the exten
ded projection syn
tactic analysis of degree con
struction
s developed in A
bney 19
87,
Corver 19
90
, 199
7, and G
rimsh
aw 19
91. A
s demon
strated in section
s 2.3 and 2.4, th
e
syntactic represen
tations of degree con
struction
s derived with
in th
is approach, in
wh
ich a
gradable adjective projects extended fu
nction
al structu
re headed by a degree m
orphem
e, can
be given a tran
sparent com
positional in
terpretation in
wh
ich th
e adjectival head is
interpreted as a m
easure ph
rase and th
e degree morph
eme as a relation
between
degrees.
Th
e adjective combin
es with
the degree m
orphem
e to generate an
expression th
at denotes
a relation betw
een degrees an
d individu
als–an expression
of the sam
e seman
tic type as a
gradable adjective on th
e traditional view
. Th
is expression in
turn
combin
es with
a standard-
denotin
g expression
, with
the resu
lt that D
egP den
otes a prop
erty of individu
als.
Com
position of th
is property with
the su
bject generates a proposition
that m
anifests th
e
three-part con
stituen
cy claimed in
section 2.1 to be th
e basic interpretation
of degree
constru
ctions: a relation
between
a reference valu
e and a stan
dard value.
A fin
al and very im
portant poin
t to make is th
at the an
alysis of gradable adjectives and
degree constru
ctions proposed h
ere explains th
e observation th
at formed th
e starting poin
t
for this dissertation
: the fact th
at only gradable adjectives appear in
degree constru
ctions.
On
e of the basic claim
s of the an
alysis of degree constru
ctions developed in
this ch
apter is
that degree m
orphem
es denote orderin
g relations betw
een tw
o degrees. Sin
ce one of
these degrees (th
e reference valu
e) is derived by applying th
e mean
ing of th
e adjective that
heads th
e degree constru
ction to th
e subject, it m
ust be th
e case that th
is adjective denotes
a fun
ction from
individu
als to degrees (a measu
re fun
ction). If th
is were n
ot the case, th
en
the relation
introdu
ced by the degree m
orphem
e wou
ld be un
defined, becau
se one of its
argum
ents w
ould be of th
e wron
g seman
tic type. Th
e conclu
sion th
en, is th
at only
expressions th
at denote m
easure fu
nction
s–i.e., only gradable adjectives–can
head a degree
constru
ction. In
order for a non
-gradable adjective–wh
ich I assu
me to den
ote a fun
ction
from in
dividuals to tru
th valu
es–to appear in a degree con
struction
, it mu
st be someh
ow
182
given a gradable in
terpretation (see th
e discussion
of this poin
t in th
e introdu
ction).
In essen
ce, this explan
ation of th
e distribution
of gradable adjectives is of the sam
e
type as the on
e provided by the vagu
e predicate analysis, w
hich
claimed th
at only gradable
adjectives (qua vagu
e predicates) are of the appropriate sem
antic type to serve as argu
men
ts
to degree fun
ctions. In
a general sen
se, then
, the an
alysis of gradable adjectives and degree
constru
ctions th
at I have proposed h
ere represents a syn
thesis of th
e vague predicate
analysis an
d the tradition
al scalar analysis of gradable adjectives as relation
al expressions.
Like
the
vague
pred
icate an
alysis, grad
able ad
jectives d
enote
fun
ctions,
and
th
e
interpretation
of degree constru
ctions in
volves the sem
antic com
position of th
e degree
morph
eme an
d the gradable adjective. A
t the sam
e time, by ch
aracterizing th
e core
mean
ing of gradable adjectives in
terms of abstract represen
tations of m
easurem
ent–i.e. a
scales and degrees–I h
ave main
tained th
e core assum
ption of th
e scalar analysis. T
his
assum
ption w
ill be examin
ed in m
ore detail in ch
apter 3, wh
ere I will take a closer look at th
e
ontology of scales an
d degrees.
183