On the Semantics of Comparative Conditionals

On the Semantics of Comparative Conditionals
*
Sigrid Beck,
Seminar für Sprachwissenschaft,
Tübingen
1. Introduction
This paper is an investigation of the semantics of comparative conditional constructions as
in (1):
(1) a.
b.
The longer John has to wait, the angrier he gets.
Je
müder Otto
ist,
desto aggressiver
The
tired -er
Otto
is
the
ist
er.
aggressive -er is
he
"The more tired Otto is, the more aggressive he is."
This type of construction has been named "comparative conditional" by McCawley (1988).
(1a) is an English comparative the...the... construction and (1b) a German je -desto
*
I would like to thank Jochen Geilfuß most of all, who I had many inspiring discussions
with. He got me interested in this construction in the first place and shared all his information
with me. I am also very grateful to Franz d’Avis, Kirsten Brock, Gennaro Chierchia, Elisabet
Engdahl, Kai von Fintel, Thilo Götz, Fritz Hamm, Irene Heim, Angelika Kratzer, Manfred
Krifka, Uli Lutz, Jürgen Pafel, Marga Reis, Mats Rooth, Bernhard Schwarz, Arnim von
Stechow and Karina Wilkinson; moreover, to the audiences at the 1994 Blaubeuren
conference "Recent Developments in Natural Language Semantics", at the University of
Düsseldorf and at IATL 11, University of Tel Aviv.
Thanks a lot to my informants for data and discussion: Lansun Chen for Chinese, Ivan
Derzhanski for Russian and Bulgarian, Ray Fabri for Maltese, Caroline Féry for French,
Hanneke van Hoof and Guido Minnen for Dutch, Shin-Sook Kim for Korean and Ana
Santisteban and her colleagues for a great number of data from various languages. Finally, I
would like to thank two anonymous reviewers for L&P.
1
construction. While I will frequently use German examples, I expect most of what I say about
the semantics to carry over to comparative conditionals in other languages. In particular,
English comparative the...the... constructions seem to have very much the same properties as
German je - desto constructions.
This paper gives a semantic analysis of comparative conditionals (henceforth: CCs),
including how the desired semantics is derived from the syntax. In accordance with other
publications on CCs (e.g. Wold (1991)), they are analysed as a special type of conditional.
They differ from ordinary conditionals in that in both the main clause and the restrictive
clause a comparison is made, as indicated by the comparative. I am particularly interested in
one property of CCs that comes unexpectedly: While they are obviously comparative
constructions, it is impossible to add an als (than) clause or phrase, i.e. to have an overt item
of comparison:
(2) *Je
The
müder Otto
ist
als
Hans, desto aggressiver
tired -er
Otto
is
than
Hans, the
ist
er.
aggressive -er is
he
*The more tired Otto is than Hans, the more aggressive he is.
Since an item of comparison is an obligatory part of the semantics of comparative
constructions, we might ask ourselves whether we have a genuine comparative construction
in CCs, and if so, what comparisons are actually made? The answer I will give to this
question is that an item of comparison is already implicitly present in the semantics, so that
an (additional) overt item of comparison would be uninterpretable.
The structure of the paper is as follows:
In section 2. I will present those empirical properties of comparative conditionals that are
going to be looked into (2.1.). Since one focus of this paper will be the derivation of the
appropriate interpretation from S-Structure, some syntactic considerations are in order (2.2.).
2
Section 3. starts with the interpretations that comparative conditionals intuitively have
(3.1.): They are indeed a particular type of conditional. In order to be able to derive these
interpretations, I will introduce the way I want to treat the comparative (in ordinary
comparative constructions) in 3.2. This will enable us to derive the desired truth conditions
via the level of Logical Form (3.3). In 3.4. I will look at some consequences that emerge from
this treatment. 3.5. is a digression: A completely different alternative treatment has
(sketchily) been suggested in the literature and to me personally. I am going to relate this
treatment to my own proposal and argue at length why it is not a viable option.
In section 4 I will give a summary of the analysis and of the motivation for its main
features (4.1.). Section 4.2. explores a more general consequence of my proposal. It
necessitates a treatment of the comparative which does not combine Adj + -er at a lexical
level. Not only does this exclude some current analyses of comparative constructions, but it
also means that the comparative form of the adjective (adverb) is not an atom for our
interpretation procedure. Rather, the comparative morpheme constitutes a separate
meaningful entity at LF.
2. Empirical & Syntactic Basis
2.1. Data
Comparative conditional constructions exist in various languages. Here are some more
examples of comparative conditionals in English and German:1
1The
construction can be equivalently formed with umso instead of desto. I will not
distinguish between the two, although they differ somewhat in distribution, compare e.g. (i):
(i)
a.
b.
müder
-er
Otto wurde umso/??desto müder,
je
Otto became the
tired -er,
the
"Otto got more tired, the later it got."
Wenn Otto schneller gelaufen
wäre, wäre
if
Otto faster run
had,
3
später es
later it
wurde.
became
er umso/?desto
would-have he
the
tired
(3) a.
Uli
ist
umso müder,
je
heißer es
ist.
Uli
is
the
the
hotter it
is
tired -er,
"Uli is the more tired, the hotter ist is."
b.
The faster you drive, the sooner you´ll get there.
McCawley (1988) gives a syntactic analysis of comparative conditionals in English,
German and Mandarin. 2 We also find them, e.g., in Dutch, French and Maltese. Examples are
given in (4):
(4) a.
Hoe
langer
het
ongeduldiger
c o l l e g e w o rddueunr t ,
de {hoe/des
studenten.
How longer the seminar lasts, {how/the}
impatient -er get
the students
"The longer the seminar lasts, the more impatient the students get."
b.
Plus
quelqu´un
est
grand, plus
is
tall,
il
a
de
grand
has
of
big
pieds.
More somebody
more he
feet
"The taller somebody is, the bigger his feet are."
c.
aktar ma
jkun
more PART is
kiesah avukat,aktar ikollu success.
cold
attorney
more has
success
geworden.
become
"If Otto had run faster, he would have got tired more quickly. "
2I
have not included Mandarin since there is no overt marking of the comparative form of the
adjective/adverb (neither in CCs nor in general). McCawley nevertheless argues that it is a
comparative construction.
4
"The colder an attorney is, the more success he has."
In all these languages, there is a main clause and a subordinate clause, each of which
contains a comparative. (5) is an example from Korean:
(5) nalssi-ka
t§ou-my§on
weather-Nom hot-cond
t§ou-lsurok
Uli-n§un
hot-(marker) Uli-Top
t§o
p’ikonha-§oss-ta.
more tired-Imp-Decl
"Uli was more tired, the hotter it was"
Here, interestingly, we have a conditional marker "my§on", and another marker "lsurok",
which seems to occur only in this construction (see Lee (1989)). The comparative marker
"t§o" is normally optional, but is obligatory in the main clause of CCs.
CCs exist in various other languages (e.g. Danish, Hebrew, Russian, Hungarian etc.).
While they seem to work in a very similar way in the other languages, I will from now on
concentrate on English and, in particular, German.
In ordinary comparative constructions, the item of comparison (printed in italics in (6a)) is
semantically obligatory. When it´s missing, as in (6b), we have to understand it as being
provided by the context.
(6) a.
Otto ist größer als Luise.
Otto is taller than Luise.
b.
Otto ist größer.
Otto is taller.
5
In CCs, we don´t normally find an item of comparison, and adding one leads to
ungrammaticality:3
(7) a.
*Je
müder Otto ist
The
tired -er
als
Otto is than
Hans, desto
aggressiver
ist er.
Hans, the
aggressive -er is he
*The more tired Otto is than Hans, the more aggressive he is.
b.
*Je
müder Otto ist,
The
tired -er
desto aggressiver
Otto is,
the
als
Luise ist er.
aggressive -er than
Luise is he
*The more tired Otto is, the more aggressive than Luise he is.
c.
*Je
müder
Otto ist
als
Hans, desto aggressiver
than
Hans, the
als Luise ist
er.
The
tired -er Otto is
aggressive -er than Luise is
he
*The more tired Otto is than Hans, the more aggressive than Luise he
is/ the more aggressive he is than Luise.
So, although we have a comparative in the subordinate clause and in the main clause, we
cannot add an item of comparison to either of them. Any successful analysis has to provide an
explanation of these data.
The je - desto construction not only cannot have an overt item of comparison, it doesn´t
allow difference specifications like (um) eine Stunde ((by)an hour) or (um) drei Grad
((by)three degrees) either, as shown in (8):
3This
seems to be the case in all languages that I could check, for instance (apart from
6
(8) *je
the
(um) eine Stunde später es wurde, desto (um) drei Grad
by
one hour
later it got,
the
by
heißer wurde es.
three degrees hotter got
it
"For each hour later it got, the temperature rose by three degrees."
This again differs from normal comparative constructions, which optionally have a
difference specification, see (9).
(9) a.
Otto kam eine Stunde später als Luise.
Otto arrived one hour later than Luise.
b.
Heute ist es drei Grad heißer als gestern.
Today it is three degrees hotter than yesterday.
The information provided by a difference specification is compatible with the information
provided by the CC, as the wellformedness of (10) as opposed to the potentially synonymous
(8) shows.
(10)Es
wurde jede
Stunde drei
It
every hour
got
Grad
wärmer.
three degrees
hotter
"It got hotter every hour by three degrees."
The explanation I will offer for these data is mixed syntactic (section 2.2.) and semantic
(section 3.3.).
English and German) Korean and Dutch, as well as Mandarin Chinese.
7
2.2. Syntax
Since deriving the semantic interpretation of CCs from the syntax is one concern of this
paper, some remarks on the syntax of je - desto constructions are in order.
I will follow von Fintel (1994) in analysing comparative conditionals as in (11) as
correlative constructions. That means that the je-clause (when the sentence starts with it) is in
the same position as a left-dislocated element, presumably adjoined to CP, as illustrated in
(11').4
(11)Je schneller Hans rennt, umso schneller wird er müde.
The faster Hans runs, the faster gets he tired
"Hans will get tired faster, the faster he runs."
(11')
CP
CP
DegP
je
Deg'
schneller
C'
Hans rennt
CP
DegP
umso
Deg'
C'
wird er müde
schneller
4While
this is the most obvious option, it might be problematic in one respect: In an ordinary
left dislocation structure, the element which occupies the Specifier of CP has to be some sort
of pronominal referring to the material in dislocated position, compare e.g. (i):
(i)
Den Karl, den
kann ich
nicht leiden.
The Karl, him can
I
not
stand
" I can´t stand Karl."
As will become clear later, umso and desto are not pronominal, and would thus constitute an
exception to an otherwise uniform regularity.
8
That means, I will assume that the subordinate clause and the main clause are sentential
projections, presumably CPs. Their specifier positions contain the je-phrase and the
umso/desto-phrase, respectively. The same presumably holds for English the-phrases. This is
very similar to the suggestions made by Thiersch (1982).
The je-clause can occur extraposed as in (12).
(12)Hans wird
umso schneller
Hans gets
the
müde, je
faster
tired
schneller
the
er rennt.
faster
he runs
"Hans will get tired faster, the faster he runs."
For (12) I propose a structure roughly like (12'), i.e. the subordinate clause is adjoined to
some projection lower than the surface position of the subject:5
(12')
[CP Hansi [ wirdk ... [VP ti umso schneller müde tk [CP je schneller er rennt]]]
While I will mostly concentrate structures as in (11'), I will show in section 3.3. that
structures like (12') are covered by my analysis. See Fillmore (1987), McCawley (1988),
Thiersch (1982) and Wold (1991) for more information on the syntax of CCs.
I will assume a DegP analysis for je- and umso/desto-phrases and comparative the-phrases.
The comparative morpheme is the functional head. The specifier position in ordinary
comparatives can be filled by difference specifications like drei Meter (three meters). For the
DegP analysis, see e.g. Corver (1994), Heim (1990a), also Rapp (1992) on comparison
5I
will generally ignore problems of verb position and functional projections that do not play
a role for the analysis (in this case IP).
9
constructions in German. I suggest that je/desto/umso/the also occupy the specifier position of
DegP:
(13)[DegP drei Meter/wieviel/je/umso/desto [Deg' größer]]
Thus, a difference specification and je/umso/desto are in complementary distribution
because they occupy the same position. This accounts for the ungrammaticality of (14):
(14)
* je
the
(um)
eine
Stunde
später es
wurde, desto
by
one
hour
later
got,
(um) drei
by
Grad
three degrees
it
the
heißer wurde es.
hotter got
it
"For each hour later it got, the temperature rose by three degrees."
See also section 3.3. for some semantic motivation for this step.
3. Semantics
3.1. Intuitive Interpretation of CCs
In (15) - (17), I have given examples of CCs that illustrate some of the relevant semantic
properties of the construction.
10
(15)Je
besser Otto vorbereitet
The
ist, desto besser wird sein Referat werden.
better Otto prepared is the
better will his talk
become
"The better Otto will be prepared, the better his talk will be."
(16)Je
schleimiger
The
ein
slimy -er
Anwaltaussieht, desto erfolgreicher ist er.
an
attorney
looks
the
uccessful -er is he
"The slimier an attorney looks, the more successful he is."
(17)Uli
war
umso müder,
Uli
was
the
je
tired -er
heißer es
the
war.
hotter it
was.
"The hotter it was, the more tired Uli was."
In (15') - (17') are the first rough formulations of the meanings of (15) - (17).
(15')
"w 1 w2 [Otto is better prepared in w1 than in w2 ]
=>
[Otto´s talk is better in w1 than in w2 ]
(where w1 R w0 , w2 R w0 a, for a modal base R cf. Kratzer
(1991). w0 is the real world).
(16')
[attorney(x) & attorney(y) & x looks slimier than y]
"x,y
=>
(17')
"t1 ,t2
[x is more successful than y]
[ it was hotter at t1 than it was at t2 ]
=>
[Uli was more tired at t1 than he was at t2 ]
11
(16'') and (17'') give paraphrases for (16') and (17'):
(16'')
If an attorney looks slimier than another attorney, he is more successful
than the other one.
(17'')
If it was hotter at one point in time than it was at another time, then Uli was
more tired at the first time than he was at the second.
(16) probably has got another reading, which means something like "Generally, the slimier
an attorney becomes, the more successful he will be". Presumably, an attorney is understood
generically, and we talk about a development in the sliminess of one and the same attorney
(i.e. we are not comparing different attorneys). (16''') gives a formalization of that reading:
(16''')
Gen x [attorney(x)]
["t1 ,t2 [ x is slimier at t1 than at t2 ]
=>
[x is more successful at t1 than at t2 ]]
Here, we have a temporal interpretation of the comparative conditional. The generically
interpreted indefinite is outside the scope of the temproral conditional. I will disregard that
reading from now on.
(15') - (17') do not as yet spell out the semantics of the comparative. I will come to that in
3.2. Some comments first:
We always have universal quantification over pairs. That can be worlds as in (15), times as
in (17), or individuals as in (16). In (16), we have quantification over individuals in the same
sense as in the synonymous sentence (16''), i.e. as in donkey sentences. Quite generally, the
12
global structure of these interpretations is that of a conditional. The subordinate clause always
enters into the restriction, similarly to the if-clause in conditionals. The nuclear scope is
provided by the matrix clause. A number of parallels between CCs and ordinary conditionals
are immediately obvious:
In conditionals, too, quantification apparently can be over different types of things,
including worlds, times and individuals.6 In the case of individuals, an indefinite in the
antecedent clause gets bound by the matrix quantifier.
A further parallel is the additional restrictions on the world variables in (15). In an
ordinary conditional like (18), we don´t want to make a claim about just any world that
satisfies the restrictive clause. For instance, we would want to disregard a state of affairs in
which Otto is very well prepared, but a brick drops onto his head upon entering the seminar
room.
(18)If Otto is well prepared, his presentation will be good.
We would want to do the same when evaluating the truth of (15). I assume that the work is
done by the usual means. This could, for instance, be an accessibility relation, cf. Kratzer
(1991).7 Having made the point that additional restrictions are needed in principle, I will not
specify them in the future.8
6This
is according to the "classical" analysis, cf. Heim (1982). I will disregard the possibility
that conditionals involve quantification over situation variables (see e.g. von Fintel (1994)).
7I will disregard ordering sources for the moment, because they seem unnecessary for the
examples to be discussed and might complicate things. However, it is possible that they are
needed, after all.
8An anonymous reviewer raises the question whether the interpretational range of CCs is
really identical to that of ordinary conditionals, in particular, whether we can get
counterfactual CCs. We certainly get CCs that look like counterfactuals, e.g. (i):
(i)
Je
schneller
Otto gerannt
wäre, umso müder
wäre
jetzt.
the
faster
Otto run
had
the
tired -er
would be he
The faster Otto had run, the more tired he would be now.
13
er
now
In CCs as well as in other conditional sentences, universal quantification seems to be a
default; some crucial data is (19):
(19)a.
Meistens
ist ein Kletterer
Mostly
is a
umso besser, je stärker
climber
the
better
er ist.
the stronger
he is
"The stronger a climber is, the better he is usually."
b.
Oft
ist ein Mathebuch
Often is a maths book
umso langweiliger,
je
dicker es ist.
the
the
fatter it is
boring -er
"A maths book frequently is the more boring, the fatter it is."
c.
Meistens
war
Otto
Mostly
was
Otto the
umsomüder,
je
heißer
es
the
hotter it was
war.
tired -er
"The hotter it was, the more tired Otto was usually."
(19a) (in one reading; we get another one as in the case of (16)) intuitively has the
interpretation given in (20a), and (19b) has that in(20b):
(20)a.
MOST x,y
[climber(x) & climber(y) & x is stronger than y]
[x is a better climber than y]
b.
MANY x,y
[maths book(x) & maths book(y) & x is fatter than y]
[x is more boring than y]
I am not 100% certain about the interpretation of CCs like (i), in particular, whether it is
exactly like counterfactual conditionals. I will leave the matter open.
14
If this is correct, then we don´t have universal quantification here, unlike in the cases
looked at so far. This suggests that universal quantification can be overwritten by an overt
adverb of quantification. Thus we have another parallel to ordinary conditional sentences (see
Kratzer (1991), Heim (1982)). Compare e.g. (21a) and (21b) to (16) and (19) respectively.
(21)a.
Wenn ein
Hund geschlagen
If
a
dog
wird, wird
beaten is
er
bissig.
becomes he vicious
"If a dog is beaten it becomes vicious."
b.
Meistens
wird
ein
Mostly
becomes a
Hund bissig, wenn er geschlagen wird.
dog
vicious if
he beaten
is
"A dog usually becomes vicious if it is beaten."
This first attempt at an interpretation for CCs already gives a preliminary answer to the
most important question raised in section 2.1.: The comparative is real in the sense that it
induces a comparison to be made in the semantics. The comparison in the subordinate clause
of (15), for instance, is between Otto´s preparedness in two different worlds, and the one in
the matrix clause is between the respective qualities of his presentation in these worlds. In
(16), on the reading under discussion, we compare two attorneys with respect to their
sliminess and their success.
So the comparative signals that a comparison is made, just as it normally does. The
problem will be to derive this semantics from the syntax. In order to do that, I first have to
introduce the way in which I want to treat the comparative (which I have left unanalysed in
the paraphrases so far). This will be done in section 3.2.
15
There is a paper by Dag Wold, "A Few Properties of the...the... Comparative
Constructions" (Wold (1991)), which was only brought to my attention when I had already
developed my analysis almost to its present state. Wold (1991) suggests basically the same
kind of semantics, based on English CCs. I will not discuss his proposal here, the main reason
being that the idea I arrived at independently does not to my judgement differ substantially
from his suggestion, while on the other hand his semantic analysis is not very detailed. But I
think it´s a fairly strong confirmation of our ideas that we arrived at the same conclusion
independently, looking at two different languages.
There is one major type of interpretation of CCs I have come across that I will not provide
a proper analysis for. I will call the additional semantic property these CCs exhibit temporal
continuity.
Bech (1964) observes that in some cases, umso can be substituted by immer (always)
without changing the meaning of the sentence. This seems to be the case, for instance, in (22)
a. and b.:
(22)a.
Uli
wurde umso müder,
Uli b ecame the
je
tired -er,
heißer es
the
wurde.
hotter it
became
"Uli was getting more tired, the hotter it got."
b.
Uli
wurde immer müder, je
heißer es
Uli b ecame always tired -er, the hotter it
wurde.
became
"Uli grew ever more tired, the hotter it became."
I think that immer is more restricted in interpretation than umso. Firstly, we only seem to
get a temporal interpretation, not a modal or individual-type one. I think that immer enforces
an interpretation that in addition presupposes temporal continuity, i.e. that there is a
16
continuous development in how tired Uli is in the period of time in question. That would
mean that immer can be substituted in a meaning-preserving way iff the intended
interpretation is temporal and presupposes continuity anyway. Whether that is the case seems
to depend on the predicate. For instance, werden (become) apparently favours continuity,
while sein (be) does not ((22) vs. (17)).
(23) is a first attempt to formalize (22):
(23)$t[t<t now & "t1 t2
=>
[t1 £t2 & t1 Œt & t 2 Œt & it was hotter at t 2 than at t1
Uli was more tired at t2 than at t1 ]]
The difference between (23) and (17') is that the antecedent of (23) contains the additional
information "t1 £t2 ". Suppose that the universal quantifier presupposes its restriction. Then we
would indeed have the presupposition in (22) that there was a development in hotness over a
certain period of time. At present, I can´t compositionally derive this result.
Once immer is taken into account, a natural extension of the set of pertinent data contains
the sentences in (24):
(24)a.
Uli
wurde immer müder.
Uli b ecame always tired -er
"Uli got more and more tired."
b.
Es
wurde
jede
Stunde drei
It
became
every hour
Grad wärmer.
three degrees hotter
"It got hotter every hour by three degrees."
c.
Es
wird
alle
hundert
kälter.
17
Kilometer
ein
Grad
It
became
haulnl d r e d
kilometers o n e
degree
colder
"It got colder every one hundred kilometers by one degree."
d.
With every step, John grew more tired.
e.
As John advanced up the cliff, he grew more tired.
f.
Each apple war more succulent.
I think that in each case, we have an implicit comparison in the same sense as in CCs. (24)
a. for instance can mean something like (25):
(25)$t[t<t* & "t1 t2
[t1 £t2 & t1 Œt & t 2 Œt
=>
Uli was more tired at t2 than at t1 ]]
The semantic similarity to CCs is obvious. Interestingly, the ordering in the rstriction is
not provided by a subordinate clause, but by some other means. A temporal ordering is
natural, but (24c), (24d) and possibly (24f) show that this type of interpretation does not only
concern temporals, but also what one might call derived temporals.9 However, I´ll leave these
for another time.
3.2. Formalizing the Comparative
As far as I can see, there is not yet such a thing as a standard semantic theory of
comparatives. There seems to be agreement on some points, though. Adjectives have got an
additional argument that denotes a degree. Degrees are entities in our model. They are
9I
owe the English examples and some inspiring considerations on their semantics to an
anonymous reviewer for L&P.
18
ordered, i.e. form a scale. See for example Pinkal (1989a) for details. A comparison is made
between two degrees - the comparative thus denotes some sort of operation on degrees. The
intuition common to many theories of comparison is that (26), e.g., means something like:
there is a degree d to which Luise is tall, and d is greater than any degree d' of which we can
say that Otto is tall to degree d'.
(26)Luise is taller than Otto.
However, there are considerable differences as to how exactly this intuition is expressed,
and how the semantics is linked to the syntax. See Stechow (1984) and Pinkal (1989b) for
discussion, as well as Klein (1991) and Moltmann (1992). Moltmann distinguishes between
two recent types of theories about the semantics of the comparative, which she dubs the
"maximal degree" approach and the "quantificational" approach. I will not enter into the
ongoing discussion at this point. Rather, I will make a concrete proposal on the treatment that
I would like to give the comparative, a maximal degree analysis. The proposal is based on
what I need for CCs. It is not exactly identical to any proposal in the literature, but it is very
similar to Stechow (1984), (1993) and Heim (1985), (1990). What differences there are are
either trivial or will be discussed in due course.
There are, of course, reasons for picking this theory rather than one based on Pinkal
(1989b), for example. The important points will be discussed in sections 3.5.and 4.2.
I propose to express the meaning of (26) as in (27)a.:
(27)a.
-er' (ld[tall(d,Otto)]) (ld[tall(d,Luise)])
b.
The max d1 [tall(d1 , Luise)] > the max d2 [tall(d2 ,Otto)]
19
What exactly this means depends on the interpretation of the comparative morpheme -er'.
A first guess is (28), which gives us interpretation (27b) for (27a).10
(28)[[-er']] (D1 ) (D2 ) = 1 iff The max d2 D2 (d2 ) > The max d1 D1 (d1 )
This is a version I will sometimes use, but which is not quite adequate yet in view of data
like (29a):
(29)a.
Luise is 3 cm taller than Otto (is tall).
b.
-er' (ld[tall(d,Otto)]) (3 cm) (ld[tall(d,Luise)])
c.
The max d1 [tall(d1 , Luise)] = 3 cm + the max d2 [tall(d2 ,Otto)]
3 cm is presumably a name for a degree (of tallness) and specifies the difference between
the degree to which Luise is tall and the degree to which Otto is tall. Thus, we need to have
an additional argument for -er, as in (30).
(30)[[-er]] (D1 ) (d) (D2 ) = 1 iff the max d2 D2 (d2 ) = d + the max d1 D1 (d1 )
10One
obvious difference from Stechow and Heim is that I talk about the degree to which
Luise is tall. In Stechow´s and Heim´s analyses, the degree in the correlate is existentially
bound, rather than bound by the. I don´t see that this has undesirable consequences for any of
the examples I will discuss.
I do this for formal reasons only: I find it more convenient to have the definite description
because it allows me to talk about the degree description as a function from individuals
(worlds,...) to degrees in section 3.5. Although this is a convenient step for me, it might lead
to undesirable consequences in general, when taken seriously. This concerns the interaction
of the maximality operator with negation and negative polarity. Hence, this is not to be
thought of as a new proposal for the semantics of the comparative.
20
Presumably, the difference degree is existentially bound in those cases where there is no
overt difference specification. (28) should really be (31), then, and the interpretation of (27a)
should be (32). (32) is of course equivalent to (27b).
(31)[[-er]] (D1 ) (D2 ) = 1 iff $d[d>0 & the max d2 D2 (d2 ) = d + the max d1 D1 (d1 )]
(32)$d[d>0 & the max d1 [tall(d1 , Luise)] = d + the max d 2 [tall(d2 ,Otto)]]
We need to derive (29b) via an LF like (33) (compare Heim (1985), Stechow (1993)). (33)
is an LF already annotated with translations. Note that the notion of LF here is that of
transparent LF, as in Heim & Kratzer (1991) and Stechow (1993). (33) can be interpreted as
indicated with the usual interpretational mechanisms (in particular, function application), to
give us (29b).
(33)
-er'( ld[tall(Otto,d)]) (3 cm) (ld[tall(Luise,d)])
IP
-er'( ld[tall(Otto,d)]) (3 cm)
DegPi
ld[tall(Luise,d)]
IP
Luise is ti tall
SpecDegP
3 cm
3 cm
-er'( ld[tall(Otto,d)])
Deg'
Deg0
-er
-er'
ld[tall(Otto,d)]
CP
than Otto is tall
21
Now we can get back to CCs. (34) (simplified version) or (35) spell out the meaning of
paraphrase (15') of (15):11
(15)Je
besser Otto vorbereitet
The
ist, desto besser wird sein Referat werden.
better Otto prepared is the
better will his talk
become
"The better Otto will be prepared, the better his talk will be."
(15')
"w 1 w2 [Otto is better prepared in w1 than in w2 ]
=>
[Otto´s talk is better in w1 than in w2 ]
(34)"w 1 w2 [the max d1 [well(d1 , lx[prepared w1(x)]) (Otto)] >
the max d2 [well(d2 , lx[prepared w2(x)]) (Otto)]]
=>
[the max d1 [goodw1(d1 , Otto´s_talk)] >
the max d2 [goodw2(d2 , Otto´s_talk)]]
(35)"w 1 w2 [$d[d>0 & the max d1 [[well(d1 , lx[prepared w1(x)]) (Otto)]=
d + the max d2 [well(d2 , lx[prepared w2(x)]) (Otto)]]
=> [$d[d>0 & the max d1 [goodw1(d1 , Otto´s_talk)] =
d + the max d2 [goodw2(d2 , Otto´s_talk)]]]
11I
will continuously mix object language and metalanguage in order to make the
interpretations more easily understandable.
22
These are just more precise formalizations of the paraphrase (15'). The other examples
from section 3.1. work in a completely analogous way; more examples will be given later in
the text.
Before proceeding to how I suggest deriving this interpretation, I would like to pause and
consider it in some more detail. In particular, I would like to draw attention to the fact that the
type of interpretation I suggest is rather weak. In the case of (15), for instance, (35) only says
that if there is a positive difference in how well Otto is prepared in w1 vs. w2 then there must
also be a positive difference in the quality of his presentation in w 1 vs. w2 Nothing is said
about the respective sizes of the differences, nor are they related to one another. Many people
I have presented this to have complained that this is too weak. The suggestion is that (15)
means something like: if there is a positive difference in how well Otto is prepared in w1 vs.
w2 , then there must also be a corresponding or resulting positive difference in the quality of
his presentation in w 1 vs. w2 . So, the two difference degrees (the one in the antecedent clause
and the one in the consequent) should somehow be related: Either they ought to be identical,
or proportional, or the second should be functionally dependent on the first. This also seems
to be the intuition underlying the paraphrases of Fillmore (1987) (who would paraphrase (15)
as something like "Changes in the degree of preparedness of Otto yield corresponding
changes in the degree to which his presentation is good") and Thiersch (1982), who proposes
an operator "is proportional to".
I think that CCs can be used to describe functionally dependent relationships, or also
causal relations; perhaps because of their peculiar semantics, they strongly tend to be used in
this way, as for instance in (36). This might be why many people think that it´s part of their
meaning.
(36)Je
größer die
the
Geschwindigkeit,
greater
t hspeed,
e
desto länger der Bremsweg.
the
distance
23
longer
the
stopping
"The greater your speed is, the longer it takes to stop."
But I do not think that anything that expresses a causal relation or a functional dependence
of the difference degrees is actually part of the meaning of CC constructions. Note that
completely different functions can be described:
(37)a.
Je
größer eine
The
natürliche Zahl ist,
greater a
desto größer ist ihr Quadrat.
natural number is,
the
greater is its square
"The greater a natural number is, the greater its square is."
b.
Je größer eine natürliche Zahl ist, desto größer ist ihr
Logarithmus.
The greater a
natural number is,
the
greater is its logarithm
"The greater a natural number is, the greater its logarithm is."
c.
Je größer eine natürliche Zahl ist, desto größer ist ihr Nachfolger.
The greater a
natural number is,
the
greater is its successor
"The greater a natural number is, the greater its successor is."
(37a)-(37c) are true statements. Let´s say, for simplicity, that the degree to which a number
is great is that number, and that the ordering relation is then just the normal ordering relation
of numbers. According to my proposal, (37a)-(37c) then mean (37'a)-(37'c).
(37')
a.
"x,y[ x > y => x2 > y2 ]
b.
"x,y[ x > y => log(x) > log(y)]
24
c.
"x,y[ x > y => s(x) > s(y)]
Or, more elaborately:
(37'')
a.
"x,y[ $d[d>0 & x= d+y] => $d[d>0 & x2 = d+y 2 ]]
b.
"x,y[ $d[d>0 & x= d+y] => $d[d>0 & log(x)= d+log(y)]]
c.
"x,y[ $d[d>0 & x= d+y] => $d[d>0 & s(x)= d+s(y)]]
But only in the case of (37c) are the two difference degrees identical. In the case of (37a),
the difference degrees in the consequent become larger and larger, and in the case of (37b),
smaller and smaller. I think that in the way of (37), one can make a true statement about any
monotonic function. That makes it impossible to give any particular function f, such that for
all CCs, the difference degree in the consequent is f applied to the difference degree in the
antecedent. We could only say that in all CCs, there is such a function, but I don´t think we
would be able to say anything interesting about it.
Moreover, in examples like (38), the differences in question can be very irregular.
(38)Je
größer eine
The
Semantikerin ist,
taller a
semanticist
desto größer ist ihr Mann.
is,
the
The taller a semanticist is, the taller her husband is.
The meaning I suggest for (38) is roughly (38'):
(38')
"x,y[ S(x) & S(y) &
25
taller is her husband
$d[d>0 & the max d[tall(d,x)] = d + the max d[tall(d,y)]]
=>
$d'[d'>0 & the max d[tall(d,x´s husband)] =
d' + the max d[tall(d,y´s husband)]]]
(38') would be true in a situation where semanticist A is 2 cm taller than B, A´s husband is
10 cm taller than B´s, C is 20 cm taller than D and C´s husband is 1 cm taller than D´s
husband. I think that this is intuitively correct. (38) is an accidental generalization, which
does not lead you to expect any deeper underlying relationship, and in fact, there has to be
none.
I conclude that we do not want to end up with stronger interpretations than those I have
suggested.
3.3. Derivation
I will talk about the modal case of comparative conditionals first, repeated for
convenience:
(15)Je besser Otto vorbereitet ist, desto besser wird sein Referat werden.
"The better Otto will be prepared, the better his talk will be."
(39)"w 1 w2 [$d[d>0 & the max d1 [[well(d1 , lx[prepared w1(x)]) (Otto)]=
d + the max d2 [well(d2 , lx[prepared w2(x)]) (Otto)]]
=> [$d[d>0 & the max d1 [goodw1(d1 , Otto´s_talk)] =
d + the max d2 [goodw2(d2 , Otto´s_talk)]]]
26
Let´s concentrate first on the je-clause, the meaning of which is given in (40).
(40)a.
je besser Otto vorbereitet ist
b.
$d[d>0 & the max d1 [[well(d1 , lx[prepared w1(x)]) (Otto)]=
d + the max d2 [well(d2 , lx[prepared w2(x)]) (Otto)]]]
The problem should now be obvious: We do not have an LF as in 3.2. with an overt thanclause giving us the first argument for -er. What we have is the comparative morpheme, je
and the rest of the clause. I will assume that these are the three meaningful components we
have got at LF, and that the transparent LF of the subordinate clause looks like (41):
(41)
je'( w1 ,w2 )(-er')( lwld[well(d, lx[preparedw(x)])(Otto)])
CP
DegPi
lwld[well(d, lx[preparedw(x)])(Otto)]
C'
je
-er
je'( w1 ,w2 ) -er'
Otto ist ti gut vorbereitet
We can get the desired result from this LF provided that je has the following meaning:
(42)[[je']] (w1 ,w2 ) ([[-er']]) (D<s,<d,t>>) iff $d[d>0 & [[-er']] (D(w1 )) (d) (D(w2 ))]
Thus, je denotes a relation between a pair of possible worlds, the comparative morpheme
and a relation between worlds and degrees. The je-relation holds just in case there is a
difference degree d such that the relation denoted by the comparative morpheme holds
27
between the relational argument applied to the first world in the pair, the difference degree d
and the relational argument applied to the second world. For illustration, (43) provides the
interpretation of (41).
(43)[[ je' (w1 ,w2 ) (-er') (lwld[well(d,lx[preparedw(x)])(Otto)]) ]]
iff
$d[d>0 & [[-er']]([[ld[well(d,lx[prepared w1(x)])(Otto)] ]]) (d)
([[ ld[well(d,lx[prepared w2(x)])(Otto)] ]])
iff
$d[d>0 & the max d[well(d,lx[preparedw2(x)])(Otto)] =
d + the max d[well(d,lx[preparedw1(x)])(Otto)]]
So much for the je clause. One point is worth mentioning: I have split the comparative
form of the adjective/adverb into the adjective (or adverb) and the comparative morpheme. I
have reconstructed the adjective/adverb from the SpecCP position. It is not unusual to split
the adjective and the comparative morpheme (Stechow (1984), Heim (1985, 1990)), only
normally reconstruction does not enter the picture, but rather QR of -er together with its first
argument (as in 3.2.). Reconstruction is done in the syntax of LF here, essentially for
convenience. It is probably possible to reconstruct the adjective/adverb via higher order traces
(compare Cresti (1995), Rullmann (1995)). The separation of adjective/adverb and
comparative morpheme, however, is important. See section 4.2 for discussion.
As I have argued in 3.1., the quantificational force comes from an implicit or overt adverb
of quantification, which takes the subordinate clause as its first argument, and the matrix
clause as its second argument. The internal structure of the matrix clause can thus be analysed
in a way completely parallel to the subordinate clause. I have given the complete LF for (15)
in (44), and its interpretation in (45).
28
(44)
"(lw 1 ,w2 [ je'( w1 ,w2 )(-er')( lwld[well(d, lx[preparedw(x)])(Otto)])])])
(lw 1 ,w2 [ je'( w1 ,w2 )(-er')( lwld[goodw(d,Otto´s_talk)])])
CP
CPlw1w2
CP
CPlw1w2
"
DegPi
DegPi
C'
C'
umso
-er
je'( w1 ,w2 ) -er' O´s Ref. wird ti gut werden
je
-er Otto ist ti gut vorbereitet
je'( w1 ,w2 ) -er'
(45)[[ "
(lw 1 w2 [ je' (w1 , w2 ) (-er') (lwld[well(d,lx[preparedw(x)])(Otto)])])
(lw 1 w2 [ je' (w1 , w2 ) (-er') (lwld[goodw(d, Otto´s_talk)])]) ]]
iff
"w 1 w2 [$d[d>0 & the max d2 [well(d2 , lx[prepared w2(x)]) (Otto)] =
d + the max d1 [well(d1 , lx[prepared w1(x)]) (Otto)]]]
=>[$d'[d'>0 & the max d2 [goodw2(d2 , Otto´s_talk)] =
d' + the max d1 [goodw1(d1 , Otto´s_talk)]]]
je and umso/desto mean the same thing. They denote an operator which semantically
creates two degree descriptions, and they introduce the difference degree argument for the
comparative. In this way they provide the three arguments for the comparative morpheme.
The translations of the CPs corresponding to the je-clause and to the umso-clause,
respectively, contain two world variables each (compare the meaning rule (42) for je, umso,
desto). These variables have to be bound in the same order in the two clauses. I suggest
treating them as a pair for the present purposes. So we end up with universal quantification
over pairs.
29
Let us briefly consider the second, "non-correlative" form of CCs as in (46):
(46)Ottos Referat
wird
Otto´s presentaion
umso besser werden, je besser er vorbereitet ist.
will
the
better become the better he prepared
is
"The better Otto will be prepared, the better his talk will be."
(46) can receive a parallel interpretation to (15) under the assumption that the syntax is as
in (47) (compare section 2.2.) and the LF is, for example, as in (48):
(47) [CPOttos Referati [wirdk [VP ti umso besser werden tk [CPje besser er vorbereitet ist]]]]
(48)
30
ly["(lw 1 ,w2 [ je'( w1 ,w2 )(-er')( lwld[well(d, lx[preparedw(x)])(Otto)])])])
(lw 1 ,w2 [ je'( w1 ,w2 )(-er')( lwld[goodw(d,y)])])] (Otto´s_talk)
CP
Ottos
Referatk
C'
"(lw 1 ,w2 [ je'( w1 ,w2 )
(-er')( lwld[well(d, lx[preparedw(x)])(Otto)])])])
(lw 1 ,w2 [ je'( w1 ,w2 )(-er')( lwld[goodw(d,y)])])
VP
C0
lw 1 ,w2 [ je'( w1 ,w2 )(-er')
(lwld[goodw(d,y)])]
VP
DegPi
lwld[goodw(d,y)]
VP
umso
-er
je(w 1 ,w2 ) -er' tk
V'
"(lw 1 ,w2 [ je'( w1 ,w2 )(-er')
(lwld[well(d, lx[preparedw(x)])
(Otto)])])])
CP
"
CP
je besser Otto vorbereitet ist
wird ti gut werden
I have assumed that [ DegPumso -er] can be raised at LF, as usual for DegPs headed by the
comparative morpheme (compare section 3.2). 12 We might expect different possibilities in
scope interaction in the correltaive vs. the non-corelative CC construction. See section 3.4 for
some data that seem to confirm this.
12It
might have been possible to interpret (46) without raising of the DegP, but consider (i):
(i)
Otto
w isr idc h
ein
g r ö ß e r e us m s o A u t o
j ek a u fmehr
en,
Probleme er sonst
hat.
Otto
w i l lr e f l . t h e bai g g e r
car
t h e m o r e b upyr o b l e m s
otherwise has
"The more problems Otto has, the bigger a car he will buy."
he
The umso-DegP takes scope over the indefinite NP it is contained in. Hence I think we have
to have raising of umso-DegPs.
31
So much for the modal case. The temporal and individual quantifications are, of course, in
principle parallel. Quantification over different types of variables necessitates that we have
additional meaning rules für je/umso/desto for each case.
(49)a. [[je']] (t1 ,t2 ) ([[-er']]) (D<t,<d,t>>) iff
b. [[je']] (x,y) ([[-er']]) (D<e,<d,t>>)
$d[d>0 & [[-er']] (D(t 1 )) (d) (D(t2 ))]
iff
$d[d>0 & [[-er']] (D(x)) (d) (D(y))]
Quantification over individuals seems to be a more problematic case, however. I will
illustrate this by giving an example analysis using rule (49b). For this rule to work, I will
assume with Heim (1982) that indefinites do not get introduced as quantfied expressions.
They are open sentences with a free referential variable, which can get bound either by
default existential quantification or by some unselective binder. Hence, ein Anwalt in (50)
introduces a free variable.
(50)a.
Je schleimiger ein Anwalt ist, desto erfolgreicher ist er.
"The slimier an attorney is, the more successful he is."
32
b.
"(lxy[je'(x,y)(-er')( lxld[attorney(x) & d-slimy(x)])])
(lxy[je'(x,y)(-er')( lxld[d-successful(x)])])
CP
CPlxy
CP
DegPj
CPlxy
"
DegPi
C'
desto -er er tj erfolgreich ist
je'(x,y) -er'
C'
je
-er ein Anwalt ti schleimig ist
je'(x,y) -er'
(51)[[ "
(lxy[ je' (x,y) (-er') (lxld[attorney(x) & d-slimy(x)])])
(lxy[ je' (x,y) (-er') (lxld[d-successful(x)])]) ]]
iff
"xy[ $d[d>0 & the max d[attorney(y) & d-slimy(y)] =
d + the max d [attorney(x) & d-slimy(x)]]
=> $d'[d'>0 & the max d[d-successful(y)] = d' + the max d[d-successful(x)]]]
This is not the most intuitive paraphrase; rather, (52) is what we first would have thought
of:
(52)"xy[ attorney(x) & attorney(y) & $d[d>0 & the max d[d-slimy(y)]
=d + the max d[d-slimy(x)]]
=> $d'[d'>0 & the max d[d-successful(y)] = d' + the max d[d-successful(x)]]
33
As far as I can see, the truth conditions of (51) and (52) differ in exactly one point,
namely, when there are no attorneys. In that case, (51) does not have a truth value, because
the definite descriptions in the antecedent do not denote. (52), on the other hand, comes out as
true. This is not too bad for (51), really, because it might be argued that (50) does in fact
presuppose that there are attorneys.
There are some more problematic aspects of (50), however, which concern the binding of
the variable named x occurring in the two C's in (50'). This variable is introduced by the
indefinite expression in the restrictive clause and by the pronoun in the nuclear scope. It gets
bound by an ordinary lambda operator. It is not quite clear to me just how problematic this is.
See Beck (1996) for discussion of potential problems and possible alternatives.
3.4. Some immediate Consequences
Quite generally, the analysis captures the parallels to ordinary conditional sentences,
simply because CCs are conditionals. This concerns quantificational variability, additional
restrictions in the modal case, quantifiability of indefinites in the antecedent, and
quantification over different types of things (see 3.1.). Moreover, since CCs are conditionals
semantically, we can expect them to be syntactically similar to conditionals, too. Hence, the
analysis is very much in accordance with the findings of Fillmore (1987) and McCawley
(1988). They observe that CCs inherit certain syntatic properties, most importantly, what verb
forms are permitted, from their status as conditionals.
The analysis provides an explanation for the missing item of comparison in the syntax: we
do have a genuine comparison in the interpretations given above. We get the two elements to
be compared with the help of the operator denoted by je/umso/desto. This operator allows us
to use the information provided by the syntax twice. Thus, to add an item of comparison in
the syntax is impossible because we already have one, although one that is not visible as such
at S-Structure. It is implicitly present with the operator.
34
The meaning of je and desto/umso is identical, namely, as specified in (42). This is made
plausible by data like (53a), where we have two umso clauses rather than a je in the
subordinate clause, as well as by idiomatic expressions like (53b). Moreover, in the
corresponding construction in Dutch, we can have hoe twice, as we have the 13 in English.14
(53)a. % Umso länger du
The
wartest,
longer you
umso schlimmer
wait,
the
wird
es.
worse becomes it
"The longer you wait, the worse it will become."
b.
Je
länger,
je
lieber.
The
longer,
the
better
je/umso/desto/the have a second function according to (42), namely to introduce the
difference degree that is to be the second argument of [[-er']]. I could have used the "reduced"
form of [[-er']] with that argument existentially bound from the start. The outcome would
have been the same. I have chosen the other option because of data like (54):
(54)Gestern
war
Yesterday
es
kühl. Heute ist
was
it
cool.
es
Today is
umso heißer.
it
the
hotter
"It was cool yesterday. Today it´s all the more hot."
13(42)
and (49) are, of course, also the meanings I assign to English the in CCs. I hope that it
has become clear that the in this case has nothing to do with the definite article. Indeed,
English is the only language that uses the same form for the CC operator and the determiner.
Thiersch (1982) quotes Jespersen, saying that the in CCs is historically unrelated to the
definite article the. Note also that the introduces a clause, not an NP.
14In Mandarin Chinese, the marker that presumably would do the same job is yue, which also
occurs twice.
35
I will not offer an analysis of these data. My intuition is that (54) means that it was cool
yesterday and that it is hotter today than it was yesterday, and implicates that the difference
between yesterday´s and today´s temperature is considerable. Maybe there is more to say
about this difference, but the idea is that umso does say something about it. I think my
analysis should make it possible to get a handle on that. This step provides additional
justification for putting je/umso/desto/the in the position reserved for the difference argument
of the comparative, SpecDegP.
By analysing the comparative as meaningful we do not only do justice to the fact that we
obviously have a comparative form of the adjective (or adverb). There is also an interesting
parallel to ordinary comparatives concerning interaction with other operators. For example,
the occurrence of a negative element sometimes leads to ungrammaticality in comparative
constructions:
(55)*Otto ist
größer als
*Otto is
taller
kein
Kind.
than
no
child
The explanation that Stechow (1984) and Rullmann (1995) suggest carries over to my
treatment:
(56)the max d[tall(d,Otto)] > the max d[ÿ$x[child(x) & tall(d,x)]]
In (56), the definite description fails to denote (under the assumption that the algebra of
degrees does not have a maximal element), because then there is no maximal degree such that
no child is tall to that degree. The same can be said of (57a):
36
(57)a. *
Je
größer jemand ist,
desto kleinere Füße hat er nicht.
The
someone is
taller
the
smaller feet has he not
"The taller someone is, the bigger his feet aren´t."
b.
[x is taller than y]
"x,y
=>
[the max d[ÿ[x has d-small feet]]] > the max d[ÿ[y has d-small feet]]]
It is not the occurrence of a negation per se that causes the ungrammaticality of sentences
like (57a), but the way that negation enters into the interpretation. In sentences like (58), the
definite description does have a proper denotation, in spite of the negation contained in it.
Accordingly, the sentence is grammatical.
(58)Je länger Du nicht zum Frisör gehst,
the longer you not
desto doofer wirst Du aussehen.
to the hairdresser go the stupid -er will you look
"The longer you don´t go to the hairdresser´s, the more stupid you will look."
This is not the whole story, however. While we have explained why reading (59b) of (59a)
is impossible, so far nothing prevents the sentence from having (59c) as a grammatical
reading.
(59)a.
*Otto ist
größer als
*Otto is
kein
taller
Kind.
than
no
child
b.
the max d[tall(d,Otto)] > the max d[ÿ$x[child(x) & tall(d,x)]]
c.
ÿ$x[child(x) & the max d[tall(d,Otto)] > the max d[tall(d,x)]]
37
That is, we can´t have a reading with the negative quantifier having wide scope with
respect to the comparative. As those readings would be semantically reasonable, some
additional mechanism is needed to exclude them. See for example Moltmann (1992) for an
explanation. What is important here is that the same phenomenon occurs in je - desto
constructions such as (60).
(60)a. *
Je
größer jemand ist,
desto kleinere Füße hat er nicht.
The
someone is
taller
the
smaller feet has he not
"The taller someone is, the bigger his feet aren´t."
b.
"x,y
[x is taller than y]
=>
[the max d[ÿ[x has d-small feet]]] > the max d[ÿ[y has d-small feet]]]
c.
"x,y
ÿ
d.
[x is taller than y]
=>
[the max d[x has d-small feet] > the max d[y has d-small feet]]
If somebody is taller than somebody else, he does not have
smaller feet than the other person.
While reading (60b) is out for the reasons explained above, reading (60c) (paraphrased in
(60d)) ought to be a possible reading for (60a). It seems impossible to get a wide scope
reading of the negation with respect to the comparative in (60) as well as in (59). Just as in
the case of ordinary comparatives, such a reading is possible in CCs with other quantifiers.
(61a) is an example of that for ordinary comparatives and (61b) for a comparative
conditional.
38
(61)a.
Otto ist
größer als
Otto is taller
jeder
than
andere.
everyone
else.
"x[person(x) & ÿ[x=Otto] -> Otto is taller than x]
b.
Je früher Otto seine Party ankündigt, umso mehr wird jeder mitbringen.
The earlier Otto his party announces, the more will everybody bring
"The earlier Otto announces his party, the more everyone will bring."
d.
"w 1 ,w2
=>
[Otto announces his party in w1 earlier than in w2 ]
["x: x will bring more in w 1 than in w2 ]
Again, the parallel of comparative conditionals to ordinary comparatives is obvious. Any
solution for these facts should treat them in a parallel fashion. We can presumably easily
extend existing accounts for the case of comparatives (e.g. Moltmann´s (1992), provided the
comparative in CCs is interpreted as usual.
Note that in (61b), jeder takes scope between the conditional operator and the
comparative. So far, my remarks concerned only scope interaction with the comparative
operation. In CCs, we can expect interaction with the conditional operator (in our cases,
mostly the default universal operator) in addition to that. This is what the ambiguity in (16)
stems from, for instance. Interestingly, an anonymous referee points out that the "noncorrelative" CC can be expected to behave somewhat differently from the correlative one
with repsect to scope interaction. Here is a minimal pair of CCs due to this reviewer:
(62)a.
Noone becomes the more tired the less he works.
b.
*The less noone works the more tired he becomes.
39
In (62a), the negative subject can take wide scope over the entire conditional. Apparently,
this rescues the sentence, in contrast to (62b). Clearly, there is more to be said about scope
interaction in these constructions than I can do here.
3.5. The functional analysis
In this section, I will consider and reject an alternative to the analysis proposed so far
(henceforth: the comparative analysis), which I will dub the functional analysis. I discuss it
for two reasons. The first is that while the comparative analysis makes intuitively correct
predictions about the interpretation of CCs, it does not seem to be the formulation of those
interpretations that first comes to mind. Many people´s first intuitions seem to revolve around
some higher order operator, like e.g. Thiersch´s (1982) "is-proportional-to". It might be worth
exploring a formalization employing such a higher order operator, since could possibly lead
to an interesting alternative way of formalizing CCs. The second reason for discussing the
functional analysis in some detail is that I think that its shortcomings illustrate rather nicely
the strong points of the comparative analysis, thus motivating why I stick to the latter.
I´m still working on the assumption, of course, that the truth conditions I have suggested
for comparative conditionals are correct. I will therefore only consider alternative solutions
with (approximately) the same truth conditions. The following discussion considers an
analysis of comparative conditionals as in (63). While this kind of formulation has not, to my
knowledge, been made precise, it seems to formalize the intuitions implicit in the phrasing in
Fillmore (1987) and Thiersch (1982), as well as suggestions made to me by Jochen Geilfuss
(p.c.), Arnim von Stechow (p.c.) und Jürgen Pafel (p.c.).
(63) a.
Je schleimiger ein Anwalt ist, desto erfolgreicher ist er.
"The slimier an attorney is, the more successful he is."
b.
$f[MON↑(f) & "x"d[attorney(x) & slimy(x,d) -> successful(x,f(d))]]
40
Here, f is a function from degrees to degrees. "MON ↑(f)" means that f is upward
monotonic.15 (63) b. says that there is a monotonic function f such that, given an attorney x
and a degree d such that x is slimy to degree d, f gives us a degree f(d), such that x is
successful to degree f(d). Since f is monotonic, if an attorney x is slimy to a degree greater
than the degree to which an attorney y is slimy, f(d) will also be greater for x than for y.
This seems quite a reasonable approximation of the truth-conditions I have assumed for
(63a). However, there is a subtle difference, that, I think, disfavours this formalization. I will
come to that difference in a somewhat roundabout way, showing first how the functional
analysis relates to the comparative analysis discussed so far. In order to do so, we first need to
say more about what type of meaning a comparative conditional expresses in general under
the comparative analysis. For this purpose, I will use the simplified meaning of CCs, as
repeated in (64).
(64)a.
Je besser Otto vorbereitet ist, desto besser wird sein Referat werden.
"The better Otto will be prepared, the better his talk will be."
b.
"w 1 w2 [the max d1 [well(d1 , lx[prepared w1(x)]) (Otto)] >
the max d2 [well(d2 , lx[prepared w2(x)]) (Otto)]]
=>
[the max d1 [goodw1(d1 , Otto´s_talk)] >
the max d2 [goodw2(d2 , Otto´s_talk)]]
The interpretations that the comparative analysis ascribes to CCs all fit into the general
schema indicated in (65):
15I
only require the function in question to be monotonic, rather than proportional or any
other stronger requirement. The reasons are the same as those given in section 3.2. for
assuming relatively weak truth conditions. This will become clearer when I discuss how the
two analyses are related.
41
(65)"x,y[ g(x)>g(y) -> f(x) > f(y)]
In the case of (64), e.g., f and g are as follows:
(66)f:
w -> [the max d1 [gutw(d1 , Ottos_Referat)]]
g:
w -> [the max d1 [gutw(d1 , lx[vorbereitet(x)]) (Otto)]]
Note that the way I formalized the meaning of the comparative allows me to talk about the
functions f and g, because I compare two definite descriptions. This will be useful below.
Hence, here is a purely formal reason for choosing this particular semantics for the
comparative. We will see in section 4.2. that the basic intuition behind the comparative
analysis can of course be expressed in other formal accounts of the comparative, too.
Compare (65) to standard upward monotonicity as definied in (67):
(67)"x,y[x>y -> f(x) > f(y)]
The meanings given for the je - desto constructions don´t fit into this definition because
generally, what is compared in the antecedent is not the variables that are quantified over, but
rather some function of these variables. Note that a CC is a statement about standard
monotonicity in case g is the identity function. This is what we assumed for the examples in
(37).16 Generally, a CC is a statement about something similar to monotonicity.
16This
leads us to expect that not only can CCs make a true statement about any monotonic
functions (as observed in section 3.2), but that in fact such a CC will be true iff the function
described is monotonic, because the CC is just the claim that the function is monotonic. This
seems adequate; consider e.g. the obvious falsity of (i):
42
On the basis of f and g, a function j from degrees to degrees can be constructed in the
following way:
(68)j: {d| $x:d=g(x)} -> {d|$x:d=f(x)}
"x: j(d) = d' iff d=g(x) & d'=f(x);
that is: j: g(x) Æf(x)
j will be a well-defined function just in case (69) holds. If that is the case, then j is
monotonic:
(69)"x,y: g(x) = g(y) => f(x) = f(y)
(70)"x,y[ g(x) > g(y) -> f(x) > f(y)]
<=>
"d,d'[ d>d' -> j(d) > j(d')]
(as g(x)=d, g(y)=d' for some d, d' in the domain of j, and
f(x)=j(g(x))=j(d), f(y)=j(g(y))=j(d') by definition)
So, the semantics of CCs can be related to monotonicity in a way that seems to account for
our intuition that CCs can be a statement about monotonicity of some sort.
Then the following equivalence holds (all under the assumption that f is indeed a welldefined function, i.e. that (69) holds).
(71)"x,y[ g(x)>g(y) -> f(x)>f(y)] <=> $f[MON(f) & "x"d[g(x)=d -> f(x)=f(d)]]
(Proof: "=>": f := j, "<=": by contradiction)
(i)
The greater a natural number is the greater is its cosinus.
43
Hence, the truth conditions predicted by the functional analysis are very similar to those
predicted by the comparative analysis. As for the weakness of the proposed truth conditions,
the discussion from 3.2. carries over. f thus has to be monotonic, and we don´t want any
stronger requirement. The relation to (63b) is obvious (rather than "attorney(x) & slimy(x,d)",
we ought to have "the max d'[attorney(x) & slimy(x,d')] = d" ).
Now for condition (69): In our example, for (69) to hold would mean that whenever two
attorneys are equally slimy, they have to be successful to exactly the same degree. This
diverges from my intuition. I think that if (63a) is true, we still don´t know anything about the
situation described, i.e. (63a) simply does not make any claims about how successful two
equally slimy attorneys are. I will provide a more concrete example to bring out clear
intuitions. Consider (72):
(72)Letztes Jahr
hat
last
Tore
Luise bei
den
year
has
Luise at
the
league games the
je
wärmer
es
war.
erzielt,
goals scored the
warmer
Punktspielen umso mehr
it
was
"In last year´s games, Luise scored more often the warmer it was."
I think that (72) is true in the following situation:
game
temperature
number of goals
1
15˚C
1
2
20˚C
2
3
25˚C
3
44
more
4
25˚C
4
5
25˚C
4
6
30˚C
5
7
35˚C
7
So three times the temperature was 25˚C, and Luise scored 3, 4 and 4 goals respectively.
The number of goals scored does not have to be the same for the three games. This is
predicted correctly by the comparative analysis, but not by the functional anaylsis. In the
latter, the function f would be undefined in the situation described. I admit that these
intuitions are rather subtle, but they are shared by the large majority of people I asked. I think
this disfavours the functional analysis.
A functional analysis is possible for the other types of comparative conditionals. I´ve
given the formalizations for the representative examples in (73)-(74).
(73)a.
Je besser Otto vorbereitet ist, desto besser wird sein Referat werden.
"The better Otto will be prepared, the better his talk will be."
b.
$f[MON ↑(f) & "w"d[wellw(d, lx[prepared(x)]) (Otto) ->
goodw(f(d), Otto´s_presentation)]]
(where w is again restricted in the appropriate way)
(74)a.
Uli war umso müder, je heißer es war.
"The hotter it was, the more tired Uli was."
b.
$f[MON ↑(f) & "t"d[hott (d) -> tiredt (Uli,f(d))]]
45
We can get these results by assuming the following meanings for an operator I will call jedesto (whatever it might exactly correspond to lexically):
(75)a.
[[je-desto']]IND (D1<e,<d,t>>) (D2<e,<d,t>>) iff
$f[MON ↑(f) & "x"d[D1 (x)(d) -> D2 (x)(f(d))]]
b.
[[je-desto']]MODAL (D1<s,<d,t>>) (D2<s,<d,t>>) iff
$f[MON ↑(f) & "w"d[D1 (w)(d) -> D2 (w)(f(d))]]
c.
[[je-desto']]TEMPORAL (D1<t,<d,t>> ) (D2<t,<d,t>> ) iff
$f[MON ↑(f) & "t"d[D 1 (t)(d) -> D2 (t)(f(d))]]
(73) would then have an LF like (76):
(76)
CP
lwld[goodw(d,Otto´s_presentation)]
CP
CP
je desto
je desto'
lwld[well(d, lx[preparedw(x)])(Otto)]
CP
Ottos Referat ist t gut
Otto ist t gut vorbereitet
How does this analysis fare in comparison to the comparative analysis?
46
We still need several meanings for je-desto. In this respect, there is no difference betwen
the two. There are several aspects of the functional analysis that I think are problematic,
though (in addition to the difference in truth conditions discussed above).
First, the most interesting semantic generalization about the meaning of je - desto
constructions, viz., that they express some kind of monotonicity, is simply stipulated. It´s part
of the lexical meaning of je-desto. While this is of course possible, it is not very interesting.
In the conditional-type analysis of the construction, the fact that these sentences are
statements about monotonicity fell out as a theorem.
On the functional analysis, CCs are not conditional structures. It is not clear to me how the
examples with an overt adverb of quantifcation like meistens/mostly are to be analyzed. As I
have formulated the semantics at present, we obligatorily have universal quantification, and I
can´t get MOST e.a. to work. In fact, we cannot account for all those properties that CCs
share with ordinary conditionals, at least not without further stipulations. It seems we´re
missing some generalizations here. Moreover, the Korean CC construction has an overt
conditional marker.
Here is what I consider the most serious problem: In the functional analysis, there is
actually no comparison involved at all (neither in the subordinate clause nor in the main
clause). That means that the comparative is semantically empty. Apparently, it´s just an
accident that it occurs at all, and it´s got to be deleted at LF (compare (76)). Unfortunately, it
is not only in German that comparative conditionals are constructed with the comparative
form of the adjective. This is also the case in Dutch, English, French, Korean, Maltese etc.,
and according to McCawley(1988), in Mandarin, too, comparative conditionals are indeed
comparative constructions. It is very implausible that all these languages should have made
the same syntactic "mistake". Rather, this clearly indicates that the comparative ought to be
taken seriously.
47
There is another argument for analysing comparative conditionals as proper comparatives:
The problems with negation can receive a parallel analysis if we have a comparative in the
semantics of je - desto constructions also.
To conclude the discussion, I strongly favour the comparative analysis of comparative
conditionals, and I think there are good reasons for the two main features of the anylysis,
namely, that CCs are a kind of conditional, and that the comparative is real.
4. Summary and Consequences
4.1. Summary of the analysis
I have suggested an analysis of CC constructions for German, which should also work for
English comparative the...the constructions. There are a number of languages that also have
CC constructions. I have used the properties they share with English and German to further
support my suggestions.
I have analysed CCs as conditional sentences. They share a lot of properties with ordinary
conditionals: As I have argued, they are quantified structures semantically,consisting of an
element providing the quantificational force, a restriction and a nuclear scope. The quantifier
can either be an overt adverb of quantification, or the invisible quantifier that Heim (1982)
suggests for conditionals. The restrictor is provided by the subordinate clause, and the nuclear
scope by the matrix clause. The quantifier is unselective, meaning it can bind different types
of variables and a different number of variables. In the modal case, it needs the same
additional restrictions we ordinarily associate with conditionals. We get donkey anaphora
here like we do in ordinary conditionals.
The semantic difference from ordinary conditionals is that we obligatorily quantify over at
least two variables. These variables induce (in each the restrictor and the nuclear scope) the
two items (two descriptions of degrees) to be compared. This leads to the second main feature
48
of the analysis: Despite the lack of an overt item of comparison, I have treated the
comparative as meaningful, i.e. as semantically corresponding to a comparison. I get the two
items to be compared with the help of an operator that I take to be the meaning (or part of the
meaning) of the/je/desto/umso. This operator takes as one argument whatever the clause it ccommands provides in the syntax, and creates two degree descriptions from it, varying over a
variable contained in it. This can be a world, time, or individual variable, whatever gets
quantified over in the conditional structure. We end up with two related comparisons being
made, one in each clause. Thus, an item of comparison is given, although it is not visible as
such at S-Structure. An additional overt item of comparison would be uninterpretable, since
the argument slots of the comparative morpheme are all filled. I have related the type of
meaning that results from this to monotonicity.
the/je etc. syntactically and semantically fill the position of a difference degree, thus
precluding elements like three inches etc.
I have considered an alternative analysis, the functional analysis, which is different from
the comparative analysis in just these two main features: The global structure is not that of a
conditional, and the comparative is not meaningful. I hope to have shown that to depart from
these features would be to miss significant generalizations. Moreover, it would lead to the
conclusion that a number of languages all accidentally express with the comparative form of
the adjective something that has nothing to do with a comparison. This being highly
implausible, the comparative has to be real. Thus, while the details of my proposal are of
course open to debate (the localization of the information I need, the role of the difference
specification etc.), and a number of issues remain open (such as scope interaction in CCs), I
think that the two main properties of my analysis are very much common sense, and are in
fact desiderata of any analysis of CC constructions.
49
4.2. The Comparative
This section takes up the question what consequences my analysis has for possible
semantic treatments of the comparative. The treatment that I have suggested for the
comparative is what Pinkal (1989b) calls a "discontinuous" analysis of the comparative. This
means that the meaning of the comparative morpheme and the meaning of the adjective are
not combined directly, i.e. there is no meaningful expression that is the interpretation of A+er (and nothing else). I will show in this section that this is in fact a consequence of my
analysis of CCs, that is, it is not possible to adopt my analysis and have a continuous analysis
of the comparative in CCs.
This is interesting in two respects: Firstly, it is necessary to substantially modify some
prima facie attractive treatments of comparative constructions, like Pinkal´s (1989a), if one
wants to use them for CCs. Secondly, it means that words cannot be atoms for the
interpretation procedure: Morphological boundaries have to be visible to the LF component.
In the light of more recent work in syntax, the second consequence does not seem
smashingly surprising: everybody working in the general framework of Baker´s (1985)
incorporation theory assumes that morphological boundaries are visible to syntactic levels
anyway. Still, there are plenty of people who are opposed to this model of grammar. I have
arrived at the same conclusion for completely different reasons, and from a completely
different perspective. One might call this independent evidence for a particular model of
interaction in grammar.
Here again is the interpretation of the comparative morpheme that I suggested in section
3.2.:
(77)[[-er']] (D1 ) (d) (D2 ) = 1 iff the max d2 D2 (d2 ) = d + the max d1 D1 (d1 )
50
For simplicity, I will use the version given in (78), since the difference degree does not
matter for the discussion.
(78)[[-er']] (D1 ) (D2 ) = 1 iff The max d2 D2 (d2 ) > The max d1 D1 (d1 )
Thus, (79a) was expressed as in (79b) and derived via the LF in (79c).:
(79)a.
Luise is taller than Otto (is tall).
b.
-er' (ld[tall(d,Otto)]) (ld[tall(d,Luise)])
c.
IP
DegPi
-er
-er'
ld[tall(d,Otto)]
CP
ld[tall(d,Luise)]
IP
Luise is ti tall
than Otto is tall
It is obvious why this analysis is discontinuous: There is no constituent in (79c) which
would get translated as the meaning of taller.
I need to have the comparative morpheme as a separate entity at LF in order to be able to
state the semantics of the operator associated with the/je etc. in the way I have (as repeated in
(80a)). For the present purposes, I will simplify this, too, and again disregard the difference
degree (80b).
(87)
a.
[[je']] (w1 ,w2 ) ([[-er']]) (D<s,<d,t>>) iff $d[d>0 & [[-er']] (D(w1 )) (d) (D(w2 ))]
b.
[[je']] (w1 ,w2 ) ([[-er']]) (D<s,<d,t>>) iff [[-er']] (D(w1 )) (D(w2 ))
51
To put it bluntly, the comparative morpheme occurs as a separate argument of je because
the rest of the clause is used twice in the semantics, to get the two arguments of -er. The
comparative morpheme itself, of course, is not used twice, and is thus treated differently from
the adjective at the level at which the operation denoted by je applies. One would now like to
know whether this is a necessary consequence of the analysis of CCs I have suggested. I think
that it is, and I will make this point in the following way.
I will look at Pinkal´s (1989a) analysis, which treats taller etc. as a lexical unit, and show
why it cannot be used in my analysis of CCs without modification. This will carry over to
other analyses that, like Pinkal´s, regard the comparative form as a unit. I will then try to boil
things down as far as possible, i.e. state the minimal set of assumptions that I have to make
about the comparative and CCs in order for this point to go through (i.e. in order to conclude
that CCs necessitate a discontinuous treatment of the comparative).
Here is Pinkal´s semantics for ordinary comparatives.17 (81a) gets interpreted as (81b), via
an LF like (81c).
(81)a.
Luise ist größer als Otto (groß ist).
Luise is taller than Otto (tall is)
b.
"d[tall(Otto,d) => taller(Luise,d)]
c.
S
Si
ld[taller(Luise,d)]
S
als Otto groß ist
NP
lD"d[tall(Otto,d) -> D(d)] Luise
17Or
AP
größer ti
rather, a simplified version of it. But I hope to do justice to his main intentions.
52
The comparative form of the adjective is treated as a unit. taller is defined as a relation
between an individual x and a degree d, which holds iff the (maximal) degree to which x is
tall is greater than d. The item of comparison is treated as a free relative, which is interpreted
universally.
The treatment seems very elegant to me: taller is a lexical unit, and there is no need to
raise bound morphemes at LF. Also, the item of comparison and the comparative morpheme
don´t have to form a constituent at LF. It might be quite natural to treat a than-clause as a free
relative, in which case it is also natural that it is raised at LF and receives a universal
interpretation.
Now, what would be Pinkal´s semantics for the comparative in CCs? I have given an
example in (82). If I am right in that (82a) is interpreted as in (82b), then it should in Pinkal´s
analysis be translated as in (82c).
(82)a.
je besser Ottos Referat ist
The better Otto´s presentation is
b.
Otto´s presentation is better in w1 than in w2
c.
"d[good w2(d,Otto´s_presentation) => betterw1(d,Otto´s_presentation)]
But how do we derive (82c)? We cannot have a semantic structure as in (83a), because
there is no operator je that could generate (82c) from (83a). The only similar thing we could
get is (83c).
(83)a.
[[je']] (w1 ,w2 ) ([[ lwld[betterw(d,Otto´s_presentation)] ]])
b.
[[je']] (w1 ,w2 ) (D<s,<d,t>>) iff ???
53
c.
"d[betterw2(d,Otto´s_presentation) => betterw1(d,Otto´s_presentation)]
This is not what we want. The problem is of course that better occurs in the antecedent and
in the consequent. Maybe we could have a structure as in (84).
(84)[[je']] (w1 ,w2 ) ([[better]]) ([[ lAlwld[Aw(d,Otto´s_presentation)] ]])
A is a variable of type <d,<e,t>>, an adjective meaning.18
But again, we want to use the positive form good of better in the antecedent of (82c), and
the comparative form in the consequent. If we only have better, which is inseparable, we
can´t get (82c), i.e. there is no operator je in (85) which would give us (82c).
(85)[[je']] (w1 ,w2 ) (A<d,<e,t>>) (D<<d,<e,t>><s,<d,t>>>) iff ???
Once more, we could only get (83c).
It is possible to derive a Pinkal semantics for CCs. Here is what I could come up with: We
assume a semantic structure for (82a) as in (86a). The operation performed by je is given in
(86b).
(86)a.
[[je']] (w1 ,w2 ) ([[-er']]) ([[good]])
( [[ lAlwld[A w(d,Otto´s_presentation)] ]])
b.
18I
[[je']] (w1 ,w2 ) ([[-er']]) (A) (D<<d,<e,t>><s,<d,t>>>) iff
ignore intensionality here, for simplicity.
54
"d[ D(A)(w 2 )(d)
=>
D ([[-er']](A)) (w1 )(d) ]
This does indeed give us (82c). We now need an appropriate meaning rule for the
comparative morpheme:
(87)[[-er']](A) (d) (x)
iff
type of -er:
the (max) d'[A(d')(x)] > d
<<d,<e,t>>, <d,<e,t>>>
This seems a reasonable variant of Pinkal´s proposal and was in a similar way in fact
suggested in Moltmann (1992). However, we have split up the comparative form of the
adjective into the comparative morpheme and the positive form of the adjective, thus
deviating from an important assumption of Pinkal´s: that the two form a lexical unit.
Moreover, the analysis is now discontinuous in the sense that -er and good are not at first
combined to form a meaningful expression. There is no constituent at LF that means better.
Instead, -er and good are two separate arguments of je.
Why did we fail in our original attempts? To put it simply, because my analysis of CCs
wants to use the comparative morpheme once, but the meaning of the adjective twice. If the
two are inseparable, we can´t do that.
I will now try to make the point as general as possible (i.e. not dependent on the details of
the analysis, but on its general properties, which I hope are well motivated).
Let´s assume that I am correct about the truth conditions I suggest. Then there are strong
arguments in favour of analysing the comparative as meaningful. Thus we have a comparison
in both the main clause and the subordinate clause. The comparative morpheme essentially
expresses the comparison operation between two degrees. In CCs, there is no overt item of
comparison (indeed, we can never have one). This is why I suggest deriving the two degree
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descriptions needed for the comparison from the syntactic material with the help of an
operator, here associated with je etc. We need the information provided by the adjective in
both descriptions, so in some sense or other, the adjective has to be used twice in the
semantics. There is only one comparison operation in each the subordinate clause and the
matrix clause. Thus, the adjective meaning has to enter into composition twice, and the
comparative morpheme once. They have to be distinguished in the operation mentioned
above and treated differently. Therefore, they cannot be one bit of information at the level at
which this operation is performed, i.e. they cannot be the interpretation of a single constituent
at LF.
From this, we can conclude that the comparative form is not a lexical item that is an atom
to LF, because it then would necessarily be a constituent at LF, too. Moreover, the analysis of
the comparative has to be weakly discontinuous, in the following sense: It is not the case that
in all comparative constructions, the comparative morpheme combines with the
adjective/adverb in order to yield a meaningful expression A+-er (if we adopt a Pinkal style
treatment in the way sketched above, they would still combine in most cases; the exception is
CCs.). Note that in the modified form sketched above a quantificational analysis of the
comparative (in Moltmann´s sense) can of course be used to formalize the meaning CCs have
according to the comparative analysis. I have used the maximal degree semantics for formal
reasons (compare section 3.5). I do not think that there is agreement in the literature as to
which is the better analysis; I don´t know of an ultimately decisive argument against one or
the other, and don´t want to argue against the quantificational account. What is important to
me here is the general point concerning morphology and LF: the comparative morpheme
must be a separate entity at LF.
This result is, of course, very much in line with those treatments of the comparative that
are discontinuous (cf. Stechow (1984), Heim (1985)). Moreover, concerning the interface
problem in general this is the same conclusion arrived at e.g. in Stechow (1994) on the basis
of tense phenomena.
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