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