1. The architecture of comparatives: ‘classical’ and ‘deg‐headed’ approaches Comparatives and Superlatives at the Syntax/Semantics Interface  Selectional restrictions suggest that the degree clause is the complement of ‐er. Roumyana Pancheva University of Southern California  The morphological evidence is that ‐er forms a constituent with the gradable predicate (e.g., taller) to the exclusion of the degree clause.  The analytic more and the degree clause are nonadjacent in the majority of EALING 10, ENS, Paris 14 – 16 August 2012 cases, more often than not they may not even appear together as a constituent that excludes the gradable predicate (e.g., tall).  As a result of the conflicting evidence, there are two types of degree‐based structural analyses of comparatives. Class 2 1
2  The structure in (1) ignores the individual argument of gradable adjectives; a 1.1 The ‘classical’ analysis of comparatives fuller representation would be as in (2), where, on analogy with the syntax of verb phrases (where a ‘little v’ introduces the external argument), a ‘little a’ introduces the individual argument of the gradable predicate.  The classical analysis – the earliest generative analysis of comparatives – assigns constituency to ‐er and the degree clause. The two form a degree quantifier, which is a syntactic specifier of the gradable predicate (Chomsky 1965, Selkirk 1970, Bresnan 1973, Heim 2000, Hackl 2000, Bhatt and Pancheva 2004, a.o.). DegP
-er
than ...
aP
DP
AP
(1) 
(2) a
AP
A
tall
DegP
(‐er stands for the comparative degree determiner) DegP [‐er than…] saturates the degree argument of gradable predicates. -er
than ...
A
tall
3
4  As a quantifier, DegP undergoes QR to the matrix TP, leaving behind a variable  The structure in (3) works with the quantificational semantics for –er discussed of type d, see (3b). We ignore issues of linearization. in handout 1, with the additional assumption that at the sister node of moved quantifier phrases and DPs we abstract over the variable left behind by the movement (the Predicate Abstraction rule of Heim and Kratzer 1998). (3) a. John is taller than Mary is. TP
b. TP
DegP 2
Deg
-er
DP1
John
T
is
aP
x1
TPt
(4) TPt
PP
than
CP
Mary is
DP
John
AP
d2 A
tall
Deg <<d,t>,<<d,t>,t>>
-er
a
AP
d2 A
tall
5
6 TP
(6) DP
John
 A representative alternative structure for comparatives, assigning constituency to –er and the gradable predicate, is illustrated in (5) (see Abney 1987, Larson 1988, Corver 1990, 1993, Kennedy 1999, 2002, for variants on this structure). T
is
DegP
DegP
(5) PP
Deg
-er
than...
Deg
-er
AP
tall
CP
Mary is
aP t
x1
1.2 The Deg‐headed analysis of comparatives PP<d,t>
than
t
T
is
2
<e,t>
1
a
DegP <<d,t>,t>
<d,t>
AP
tall
than
CP
Mary is  On the Deg‐headed approach –er is not quantificational; it is interpreted in situ. 7
8  A semantic implementation in Kennedy (1999): gradable adjectives denote 2. QR of ‐er: scope ambiguities, ellipsis resolution, late merger of the than‐CP measure functions (type <e,d>); degree morphemes have three arguments: a measure function, denoted by the adjective, a degree and an individual. (7) a. [[ tall ]] = x [x’s height] b. [[ ‐er]] = G<e,d> d x [G(x) > d]  Semantic type of the degree quantifier (9) a. ‐er than XP compare with b. every baby TPt
(8) QP <et,t>
DegP <dt,t>
DP
John
Deg <dt,<dt,t>>
-er
<e,t>
Q <et,<et,t>>
every
<dt>
than XP
NP <et>
baby
 There is a mismatch between the logical types of the DegP and the adjective: T
is
DegP <e,t>
(10) taller than XP AP
PPd
Deg <<e,d>,<d,<e,t>>>
-er
AP<e,d>
tall
CP
Mary is
than
DegP <dt,t>
Deg
-er
A <d,et>
tall
than XP
9
 DegP must undergo Quantifier Raising (QR) and leave behind a trace of type d. The same holds for quantifiers over individuals – they QR and leave behind a variable of type e.  On the quantificational approach to the semantics of –er (the ‘classical’ analysis), it is expected that –er will interact scopally with other quantifiers. AP
VP
b.
(11) a.
Deg
-er
than XP
A <d,et>
tall
 We do not get ambiguity in cases like (12), but this is not strong argument V <e,et>
feed
against the quantificational theory because the two LFs are logically equivalent (Kennedy 1999, Heim 2000) QP <et,t>
Q
every
NP
baby
(12) Every girl is taller than 4 feet.  every girl is such that her height exceeds 4ft 2.1 Scope of ‐er wrt quantifiers over individuals DegP <dt,t>
10
 If the DegP ‐er than 4 ft can scope either below or above the subject, there will be two LFs for each of the above sentences: (13) a. [every girl]1 [ [‐er than 4 ft]2 [ [t1 is d2 tall ]]] b. [‐er than 4 ft]2 [ [every girl]1 [ [t1 is d2 tall ]]] 11
12
 With the semantics assumed by Heim (2000), two logical forms are predicted,  A stronger argument against the quantificational theory comes from (15). The corresponding to the two LFs, but the two LFs yield equivalent interpretations. two scope scopes would yield different interpretations but –er receives only narrow scope (Kennedy 1999, Heim 2000) (14) a. x[girl(x)  max{d: tall(x,d)} > 4']  every girl is such that her height exceeds 4ft b. max{d: x[girl(x)  tall(x,d)]} > 4'  the shortest girl is such that her height exceeds 4ft (15) Exactly two girls are taller than 5 feet. a. [exactly two girls]1 [[‐er than 5']2 [[t1 are d2 tall]]] |{x: girl(x) & max{d: tall(x,d)} > 5'}| = 2  no more and no less of 2 girls exceed 5’ b. [‐er than 5'] 2 [[exactly two girls]1 [[t1 are d2 tall]]] max{d: |{x: girl(x) & tall(x,d)}| = 2} > 5'  the two tallest girls exceed 5’ (other girls may as well)  The reading in (15b) is not equivalent to (15a) and is not a reading that the sentence has. Therefore DegP QR, if it exists, has to result in a narrow scope for the DegP with respect to QPs. 13
 Next to consider are comparatives with exactly differentials. The two LFs are 14
 In sum, to check for scope, check with non‐monotone QPs, or comparatives not equivalent, and (16b) is not a possible reading of the sentence. with exactly differentials, or less‐comparatives. (16) (John is 4' tall.) Every girl is exactly 1" taller than that.  In all of those cases where scope can be detected, DegPs scope below QPs, a. x [girl(x)  max{d: tall(x,d)} = 4' + 1"]  all girls are 4’1” tall prompting the formulation of Heim‐Kennedy’s generalization b. max{d: x[girl(x)  tall(x,d)]} = 4' + 1"  the shortest girl is 4’1” tall (18)  Finally, in less comparatives the wide scope interpretation for DegP does not obtain either (17) (John is 4' tall.) Every girl is less tall than that. a. x [girl(x)  max{d: tall(x,d)} < 4' ]  each girl is less than 4' tall HEIM‐KENNEDY GENERALIZATION (Heim 2000, ex. (27)) If the scope of a quantificational DP contains the trace of a DegP, it also contains that DegP itself a. * DegP1 … QP … d1 b. QP … DegP1 … d1 b. max{d: x[girl(x)  tall(x,d)]} < 4'  the shortest girl is less than 4' tall 15
16
 Not all modal predicates show the ambiguities. Heim (2000) suggests that wide 2.2 Scope of ‐er wrt modals scope is syntactically available for DegP with the predicates in (22b), but is semantically not detectable as the LFs are equivalent.  exactly‐differentials and less comparatives ensure non‐equivalence between the LFs with low and high DegPs. Here, different readings emerge (Heim 2000) (21) a. require, allow, need, be able to (allow wide scope for DegP) b. might, should, be supposed to, want (do not allow wide scope for DegP) (19) (This draft is 10 pp.) The paper is required to be exactly 5 pages longer than that. a. required [[exactly 5 pp. ‐er than that] [the paper be d long]] w  Acc: max{d: longw(p,d)} = 15pp  in each world that meets the requirements the paper is 15pp., not longer b. [exactly 5 pp. ‐er than that] [required [the paper be d long]] max{d: w  Acc: longw(p,d)} = 15pp  the paper is exactly 15pp. long in those worlds where it is the shortest (22) a. No deposit is required (not > must > a deposit) b. You shouldn’t give a deposit (must > not > a deposit)  Scope possibilities are reflected in truth conditional ambiguities for some class of modal predicates and QPs. There must be DegP QR – supporting the classical architecture for comparatives – but it also must be constrained, to obey the Heim‐Kennedy generalization. (20) (This draft is 10 pages.) The paper is required to be less long than that. a. required [[less than that] the paper be d long] w Acc: max{d: longw(p,d)} < 10pp  in each world that meets the requirements the paper is less than 10pp b. [less than that] [required [the paper be d long]] max{d: w Acc: longw(p,d)} < 10pp  the paper is less than 10pp in those worlds where it is the shortest 17
18
2.3.2 The Ellipsis‐Scope Generalization 2.3 Scope of DegP and Ellipsis  Sag (1976) and Williams (1974) note that there is a correlation between ellipsis 2.3.1 Antecedent Contained Deletion (ACD) resolution and scope. This correlation has come to be known as the Sag‐Williams Ellipsis‐
Scope Generalization.  QR of DegP allows for a resolution of ACD (Wold 1995, Heim 2000) (26) Ellipsis‐Scope Generalization The scope of a DegP containing elided material must contain the antecedent of the ellipsis. (23) a. * John was climbing trees that Bill was. b. * John was climbing three trees that Bill was. c. John was climbing more trees than Bill was. (24) LF for (23c) (Δ is the ellipsis site, the underlined constituent is the antecedent): [‐er [(than) wh Bill was Δ ]] [John was climbing d‐many trees]  Extraposition of the than‐clause alone will not resolve ACD (25) John was climbing [‐er‐t1]‐many trees [wh Bill was Δ]1 19
20
 If the problem of antecedent containment is resolved by decreasing the size of (27) Mary’s father tells heri to work harder than heri boss does Δ. the ellipsis, the missing reading (27b) becomes available (see (28a)). a. tell > ‐er, elided material = work d‐hard  Mary’s father tells her: work harder than your boss works. (28) Mary’s father tells her to work harder than her boss tells her to Δ. b. *tell > ‐er, elided material = tell her to work d‐hard  Mary’s father tells her: work harder than your boss tells you to work. a. tell > ‐er, elided material = work d‐hard  Mary’s father tells her: work harder than your boss tells you to work. c. ‐er > tell, elided material = work d‐hard  Mary’s father tells her: work d1‐hard; Mary’s boss works d2‐hard; d1 > d2. b. ‐er > tell, elided material = work d‐hard  Mary’s father tells her: work d1‐hard; Mary’s boss tells Mary: work d2‐hard; d1 > d2. d. ‐er > tell, elided material = tell her to work d‐hard  Mary’s father tells her: work d1‐hard; Mary’s boss tells Mary: work d2‐hard; d1 > d2. 21
 Correlation with Condition C: A pronoun that c‐commands the embedded VP 22
2.4 Scope and late merger of the degree clause can co‐refer with a name in the degree clause only if the comparison takes scope over the matrix predicate.  On the classical analysis, degree clauses are arguments of the degree quantifiers ‐er, yet the dependency is discontinuous. There is obligatory extraposition, and it is undone at LF. (29) Her father tells heri to work harder than Maryi’s boss tells her to. a. * tell > ‐er, coreference impossible  Mary’s father tells her: work harder than your boss tells you to work.  However, the surface position of the degree clause is not arbitrary, it marks b. ‐er > tell, coreference possible the scope of ‐er. (Williams 1974, Guéron and May 1984); exactly so (Bhatt and Pancheva 2004).  Mary’s father tells her: work d1‐hard; Mary’s boss tells her: work d2‐ hard; d1 > d2. (30) Her father tells Maryi to work harder than heri boss tells her to. a. tell > ‐er, coreference possible  Mary’s father tells her: work harder than your boss tells you to work. b. ‐er > tell, coreference possible  Mary’s father tells her: work d1‐hard; Mary’s boss tells her: work d2‐ hard; d1 > d2. 23
(31) Extraposition‐Scope Generalization The scope of a DegP is exactly as high as the extraposition site of the degree clause. 24
(32) a.  The implication for the classical view of degree constructions is that the John is required [to publish fewer papers this year [than that number] in a major journal] [to get tenure].  If John publishes more than a certain number of papers, he will not get tenure. (His university has an unusual tenure policy.) LF: required [er [than n] d [PRO publish d‐few papers]] relation between the degree clause and the degree head has to be re‐
established, somehow, at LF. (33) b. John is required [to publish fewer papers this year in a major journal] XP
[to get tenure] [than that number].  The number of papers that John has to publish to get tenure is upper‐ bounded. He can publish more than that number but he doesn't have to. LF: [er [than n]] d [required [PRO publish d‐few papers]] QR
......
DegP
 The availability of the –er > required reading in (32b) shows that degree -er
abstraction crossing required is allowed. Extraposition AP
A
tall
than CP
 Why is degree clause extraposition obligatory? Why is the relationship between the quantificational degree determiner and the degree clause re‐
established at LF?  Answer: Late merger of the degree clause at the scope position,with some interesting consequences for conservativity (Bhatt and Pancheva 2004)  The lack of the –er > required reading in (32a) shows that the scope of –er is marked exactly by the surface position of the degree clause, i.e. the degree quantifiers [DegP ‐er than n] cannot move further. 25
AP
(34) a. Deg
-er
AP
b. Deg
A
A
-er tall
tall
3. Scope of –est and superlative ambiguities
QR
 The superlative in (35) is 3‐way ambiguous (Heim 1985, Szabolcsi 1986, Gawron 1995, Farkas and Kiss 2000, Sharvit and Stateva2002, a.o.) XP
 In the absolute reading (35a), the comparison class for the superlative is XP
c. determined just on the basis of the DP the largest cake, i.e., cakes in absolute terms (in a given context) without consideration of who has bought or received them. DegP
...
AP
t1
26
A
tall
Deg 1
-er
 In the relative readings (35b‐c), other constituents in the sentence (John or than XP
Mary) determine the comparison class. (35) John bought the largest cake for Mary. a. ‘John bought Mary the cake that is larger than any other cake.’ ABSOLUTE b. ‘JOHN bought a larger cake for Mary than anyone else did.’ RELATIVE c. ‘John bought a larger cake for MARY than he did for anyone else.’ RELATIVE 27
28
3.1 Scope of ‐est determines the comparison class
 There have been two main approaches to the LF syntax of –est: A
B
C
D
E
 Scope Theory: –est moves out of the DP in relative readings. (Heim 1985, 1999, Szabolcsi 1986) Figure 1: The cake display at Sweet Lady Jane (images from their website)  Pragmatic Theory: –est stays inside the DP in relative readings. (Farkas & Kiss 2000, Sharvit and Stateva 2002) (36) Scenarios: a. John bought cake E for Mary. (35a) is true b. c. John bought cake B for Mary and cake E for Martin; Bill bought cake A for Mary, and Ann bought cake C for Mary. (35b) is true; (35a) & (35c) are false John bought cake B for Mary, cake A for Tom, and cake D for Martin, and Bill bought cake E for Mary. (35c) is true; (35a) & (35b) are false  Both theories maintain that –est stays inside the DP in absolute readings. 29
 Both theories can work with a meaning for –est as in (37)1. The degree quantifier –est has a covert restrictor C, the comparison class. (37) a 3‐argument semantics for –est: [[ ‐est ]] = λC λD λx d [D(d)(x)  y [yC  y  x D(d)(y)]] Presuppositions: (i) xC (ii) y [yC  d [D(d)(y)]] i.e., ‐est has 3 arguments: a set of individuals C, a gradable predicate D, and an individual x. ‐est (C) (D) (x) is true iff there is a degree d s.t. x has that degree of D and no other individual in C has that degree of D Presuppositions: (i) x is a member of C; (ii) C consists of individuals which are arguments of D. 30
 The comparison class C is determined from the scope of [‐est C], and partly from context. Given the presupposition of –est that C consists of individuals which are arguments of the D (see (37‐ii)), the LF syntax of [‐est C] determines the elements of C  The absolute reading DP
(38) D
the
NP
-est C
1

D
NP
d1-large cake
(39) ‘John bought Mary the cake that is larger than any other cake.’ 31
32
 The relative readings on the Scope Theory. The comparison class C is determined from the scope of [‐est C] (42) TP1
Mary
 The is claimed to be vacuous TP3  D
-est C
(40) 1
TP1
2
TP
John
John
TP3  D
-est
for x2
C
bought
D
a
1
2
vP
for Mary
D
a
NP
d1-large cake
(43) ‘John bought a larger cake for MARY than he did for anyone else.’ x2
bought
DP
DP
NP
d 1-large cake
(41) ‘JOHN bought a larger cake for Mary than anyone else did.’ 33
34
 When the focus is outside the superlative DP, as when the PP modifies the VP, 3.2 Scope of ‐est and DP‐internal focus the relevant relative reading is available (Pancheva and Tomaszewicz 2012) (48) John [met the youngest students] in London. a.  ‘JOHN met younger students in London than anyone else did.’ b.  ‘John met younger students in LONDON than he did in another city.’  In English, the relevant relative readings are absent when the focus is inside the superlative DP.2 (49) John [met the most students] in London. a.  ‘JOHN met more students in London than anyone else did.’ b.  ‘John met more students in LONDON than he did in another city.’ (44) John has [the best [albums of/by U2]]. a.  ‘JOHN has better albums of/by U2 than anyone else does.’ b. * ‘John has better albums of/by U2 than he has of/by any other band.’ (45) John has [the most [albums of/by U2]]. a.  ‘JOHN has more albums of/by U2 than anyone else does. ’ b. * ‘John has more albums of/by U2 than he has of/by any other band.’ (46) John met [the youngest [students from London]]. a.  ‘JOHN met younger students from London than anyone else did.’ b. * ‘John met younger students from LONDON than he did from another city.’ (47) John [met the most [students from London]]. a.  ‘JOHN met more students from London than anyone else did.’ b. * ‘John met more students from LONDON than he did from another city.’ 35
36
 The missing DP‐internal relative reading in English is available in Slavic (in addition to Bulgarian and Polish, the facts also hold for Czech and Serbian/Croatian). (50) a. Ivan ima naj‐hubavi albumi na/ot U2. (Bulgarian) Ivan has naj‐good albums of/by U2 (52) b. Iwan ma naj‐lepsze albumy U2. (Polish) Ivan has naj‐betterAcc albumsAcc U2  ‘IVAN has better albums by U2 than anyone else does.’  ‘Ivan has better albums by U2 than by any other band.’ (53) (51) a. Ivan ima naj‐mnogo albumi na/ot U2. (Bulgarian) Ivan has naj‐many albums of/by U2 b. Iwan ma naj‐więcej albumów U2. (Polish) Ivan has naj‐moreAcc albumsGen U2 Ivan ima naj‐hubavi‐te albumi na/ot U2. (Bulgarian) Ivan has naj‐good‐the albums of/by U2  ‘IVAN has better albums by U2 than anyone else does.’ * ‘Ivan has better albums by U2 than by any other band.’  Bulgarian, unlike the other Slavic languages (except for Macedonian), has a definite article. When the definite article is added, the DP‐internal focus R‐
reading is no longer available, similarly to English (The same also holds for Macedonian.) Ivan ima naj‐mnogo‐to albumi na/ot U2. (Bulgarian) Ivan has naj‐many‐the albums of/by U2  ‘IVAN has more albums by U2 than anyone else does.’ * ‘Ivan has more albums by U2 than by any other band.’  ‘IVAN has more albums by U2 than anyone else does.’  ‘Ivan has more albums by U2 than by any other band.’ 37
Summary of the empirical observations:  In English, when the focus is inside the superlative DP, the corresponding relative reading is blocked. 38
3.3 Interaction of focus and scope of ‐est  The definite article blocks –est/naj‐ movement. This partially follows Szabolcsi 1986, for whom QR of –est is allowed only out of indefinite DPs (i.e., the is interpreted as a on the relative reading).  In Polish, and in other languages without a definite article, this constraint doesn’t hold.  English –est doesn’t move out of DPs, as in the Pragmatic Theory (Farkas & Kiss 2000, Sharvit &Stateva 2002); Bulgarian naj‐ doesn’t either, when the definite article is present.  Bulgarian is like English when the definite article is present in superlative DPs, but like Polish, when it isn’t.  Slavic naj‐ moves out of DPs in the absence of a definite article.  In relative readings, est‐/naj‐ are focus sensitive. 39
40
3.3.1 DP‐internal focus in the absence of the definite article  The focus operator ~ introduces an anaphor, S, which is presupposed to be a subset of the focus‐value of the constituent to which [~ S] attaches, assumed to be the clause, as usual (e.g., Rooth 1992). (54)3 TP
TP
U2
 naj‐ is focus sensitive. It associates with focus by having its restrictor C dependent on S as in (55) (e.g., Rooth 1992, Heim 2009). TP
(55) (56) (57) naj- C
TP3
~ S
1
TP
2
TP
John
has
DP
by x 2
a. [TP1 U2 [TP2 [naj‐ C] [TP3 [~ S] [TP4 Ivan has [DP d‐good albums by/of xF ]]]]] b. S  [[ TP4]] f = {P: d [P = x [John has d‐good albums by x]]} c. [[ TP3]] = [[ TP4]] o = λd λx [John has d‐good albums by x] a. C = S = {x: d [John has d‐good albums by x]} (focus association) b. U2  C; y [yC  d [John has d‐good albums by y]] (presupp. of naj‐) d 1-good
albums
C = S 41
3.3.2 DP‐internal focus in the presence of the definite article  When the definite article is present, the LF in (54) where ‐est/naj‐ has sentential scope cannot be obtained. est/naj‐ have to stay DP‐internal. 42
(58) TP
TP2
~ S
John
 English (44) and the Bulgarian (52) can in principle have either the LFs in (58)‐
has
(60). None are well‐formed in that –est fails to associate with focus. (Some more options are discussed in Pancheva and Tomaszewicz 2012) DP
the
est- /naj- C

1
d 1-good
albums
by U2
(59) a. S  [[ TP2 ]] f = {p: x [p = John has the best albums by x]} b. C = {x: d [x are d‐good albums by U2]} (presupposition of –est/naj‐ (37ii)) 43
44
 Moving the focus U2 in (58) will not help matters. In (60) ‐est/naj‐ cannot associate with the focus U2 either, as the condition C = S cannot be fulfilled: (60) TP
U2
TP3
~ S
2
TP
John
has
DP
the

est- /naj- C
1
d 1-good
albums
by x2
(61) a. S  [[ TP3 ]] f = {P: P = x [John has the best albums by x]} c. C = S = {x: John has the best albums by x} (focus association) d. C= {x: d y [x are d‐good albums by y]} (presupposition of –est/naj‐) 45
3.3.2 DP‐external focus and relative readings in the presence of the definite article  No problem for focus association (62) 46
Conclusions  We’ve seen evidence for QR of the comparative and superlative operators. This supports the classical architecture, and its associated semantics.  ‐er and ‐est are degree morphemes that introduce degree arguments (similarly TP
to applicative heads) to APs. DP
Endnotes TP2
the
2
TP
~ S
1
This meaning, and the LFs that go with it, are chosen primarily for ease of presentation. An alternative, 2‐argument semantics, as in (i), with corresponding LFs, will also work (see Heim 1999). (i) [[ ‐est ]] = λC <<d,t>,t> λD<d,t> d [D(d)  P [PC  P  D  P(d)]] Presuppositions: (i) DC ; (ii) P [PC  P  D] 2
F&K’00 suggest that a sentence such as (i) does not have a relative reading with John the focus. We have found that not to be the case; (i) is fine in contexts where what t is relevant is who visited a larger city in Europe than anyone else did and no one visited London. (i) John visited the largest city in Europe. 3
For ease of presentation, we diverge from the more standard approach of interpreting focus in‐situ (see Heim 1999), so we can keep the 3‐argument semantics for –est in (37). The role of the focused element in in‐situ theories of focus, is to introduce alternatives. Here, the variable left by QR of U2, has a similar role John
has x2
est- /naj- C
1
d1-good
albums byU2
f
(63) a. S  [[ TP3]] = {P: y [P = x [y has x]} b. C = S = {P: y [P = x [y has x]} (focus association) c. C = {x: d [x is a d‐good album by U2]} (presupposition of –est/naj‐) 47
48