In this response to Erlewine & Gould (
Erlewine & Gould (
A secondary goal of this response is to suggest that the salient set reading does not arise from an IHRC but rather a headless relative with a gap, a conclusion independently supported by Grosu & Hoshi (
E&G focus on IHRCs of the form in (1). These have an external quantifier
(1)
Erlewine & Gould (
Junyawa
Junya
[_{IHRC}
[Ayakaga
Ayaka
[_{IH}
ringoo
apple
three
muita]no]o
peel
zenbu
all
tabeta.
eat
‘(lit.) Junya ate all of [that Ayaka peeled
‘Ayaka peeled
The expected interpretation of such an IHRC with an internal head is one in which the numeral takes internal scope, rather than taking the whole RC as its restrictor, as it would in an externally headed relative (
(2)  
(i) Junya ate the three peeled apples.  
(ii) Junya ate the twelve apples. 
(3)  
(i)  Junya ate the three peeled apples.  
(ii)  Junya ate the six apples in the first group. 
One popular analysis of Japanese (and Korean) IHRCs is an Etype anaphora analysis. Essentially, the IHRC is semantically interpreted as a clause coordinated with the matrix clause, resumed by crosssentential anaphora (
(4)  [Ayaka peeled 
It is claimed in E&G that the Japanese translation of (4) using crosssentential anaphora does not have the salient set reading.
As noted, E&G attempt to derive the regular and the salient set readings from a single structure for IHRCs. They propose that all relative clauses derive from a
(5)  
In order to interpret such structures, with multiple copies of the determiner, the general strategy since Fox (
(6)  
a.  Ayaka peeled every apple.  
b.  Narrow syntax  
[every apple]_{1} Ayaka peeled [every apple]_{1} (QR with copy)  
c.  LF after Trace Conversion  
[every apple] 
Trace Conversion has two components: variable insertion and determiner replacement. Variable insertion (7a) adds an (identity) predicate that introduces a variable, and this predicate intersects with the NP. This essentially equates the lower copy with the variable indexed by movement. The second component is determiner replacement: the quantifier in the lower copy is replaced by the definite determiner
(7)  a.  Variable insertion 
every 

b.  Determiner replacement  
every [ 
Erlewine (
(8)  Every apple isn’t rotten.  
a.  Narrow syntax  
[every apple]_{1} 

b.  LF after Inverse Trace Conversion  
[ 
In this case, variable insertion introduces a predicate that mereologically relates the lower copy to the higher copy: the individuals in the restrictor of the quantified lower copy constitute an atomic individual part (⊑) of the plurality of apples that the higher copy refers to.
E&G use ITC to compose IHRCs, which as noted, involve movement on their account just as externally headed relatives do. The difference is in which copy is pronounced. In IHRCs, the lower copy is pronounced and the higher copy undergoes ITC. Applying the process to the syntactic representation in (5), this results in the higher copy as a definite description, while allowing the quantifier to be interpreted in the lower copy (
(9)  
a.  [_{DP} 

b.  [DP] = ⟦ 
The IHRC as a whole, then, denotes the plurality of apples such that Ayaka peeled three apples in that plurality. This of course is the salient set reading: the IHRC denotes the larger set from which the lower quantifier takes its domain. The different contexts in (2)/(3) make different domain sets salient, hence the referent of the whole IHRC differs. The referent of the IHRC DP in (9) is the apple sum 1+2+3+4+5+6+7+8+9+10+11+12 in context (2), and 1+2+3+4+5+6 in context (3).
To generate the regular reading—where the IHRC denotes just the three peeled apples in the examples above—from the LF after ITC, E&G invoke a recent analysis of definite descriptions found in von Fintel et al. (
(10)  the number of children that John has 
(11)  ⟦ 
The restrictor of
(12)  a.  
b.  Context: John has exactly four children.  
c.  1 < 2 < 3 < 

d. 
von Fintel et al. (
(13)  the amount of walnuts sufficient to make a pan of baklava 
If we used the maximalitybased semantics of
(14)  
a.  ⟦ 

b.  For all 
The recipe here is, as before, to look at the individuals that satisfy the restrictor, but unlike the standard account, we collect the propositions each of these individuals/degrees form with the restrictor. The next step is then to identify the proposition that entails all the other propositions.
(15)  ⋮  
a.  “that 170 g of walnuts is sufficient to make a pan of baklava”  
b.  “that 160 g of walnuts is sufficient to make a pan of baklava”  
c.  
d.  
e.  
⋮ 
Which propositions should we consider? Well, if 150 g is sufficient, then amounts higher than 150 are too simply because of what
(16)  a.  Property: 
b.  Context: 150 g of walnuts is sufficient to make a pan of baklava 
(17)  Whenever “dmuch walnuts is sufficient to make a pan of baklava” is true, it is necessarily true that “d’much walnuts is sufficient to make a pan of baklava” where d’ ≥ d. 
On the MIS account, the correct prediction is made that the referent of the definite description in (13) is the smallest amount of walnuts that would yield a true proposition, namely 150 g.
Returning to IHRCs, E&G claim that the MIS account of definites derives the regular reading from the LF after ITC. Consider the IHRC in (1), repeated below, on its regular reading where it denotes the three apples that are peeled by Ayaka. On the analysis of IHRCs as derived from the protoJapanese relative in (5), along with ITC, the IHRC is a definite description of the form in (19a), where the property
(18)
Junyawa
Junya
[_{IHRC}
[Ayakaga
Ayaka
[_{IH}
ringoo
apple
three
muita]no]o
peel
zenbu
all
tabeta.
eat
‘(lit.) Junya ate all of [that Ayaka peeled
‘Ayaka peeled three apples and Junya ate all those three.’ (regular reading)
(19)  a.  
b. 
In the regular reading of example (1)/(18), the referent of the IHRC DP is 1+2+3 in either context (2) or context (3). The LF is repeated from (9) above.
(20)  
a.  [_{DP} 

b.  ⟦DP⟧ = ⟦ 
To determine the referent of (20b) on the MIS account of definite descriptions, we consider the propositions that result from saturating the property complement of
(21)  a.  
b.  
c.  
d.  
⋮  
e.  
f.  
⋮  
g.  
h.  
⋮  
i.  
⋮  
j. 
We’ve collected all the true propositions in the relevant context. At this point the recipe says to step back from the particular context and identify the entailment relations among these propositions. As E&G show, there
(22)  “that Ayaka peeled at least three atomic apple parts of apples X” entails “that Ayaka peeled at least three atomic apple parts of apples Y” where X ⊑ Y 
So this means that the smaller the value of X is, the more informative the proposition ‘that Ayaka peeled at least three atomic apple parts of apples X’ is. The proposition in (21a) entails all other true propositions in (21).
(23)  “that Ayaka peeled at least three atomic apple parts of apples 1+2+3” entails “that Ayaka peeled at least three atomic apple parts of apples Y” for all Y such that 1+2+3 ⊑ Y 
On the other hand, there is no entailment when going from a larger
(24)  “that Ayaka peeled at least three atomic apple parts of X” does 
What all this means is that putting (22) and (24) together, the strongest proposition is (21a), where the number of peeled apples is the same as the plurality from which they are taken, i.e. three. More technically, based on informativenessbased ordering (14b), then, the ordering in (25) follows.
(25)  E&G (2016: 27)  
a.  X ≥_{φ} Y if and only if “that Ayaka peeled at least three atomic apple parts of X” entails “that Ayaka peeled at least three atomic apple parts of Y”  
b.  X ≥_{φ} Y if and only if X ⊑ Y. 
The ITCMIS analysis of the regular reading thus correctly predicts that the referent of the IHRC DP in (9) in context (2) or (3) is the apple sum 1+2+3. Given (14a) and (25), the apple sum 1+2+3 is the uniquely maximal (or most informative) object in the sense that it creates the most informative or strongest true proposition, “that Ayaka peeled three apple parts of 1+2+3”. So despite the variable insertion that would initially only give us a referent plurality that properly includes the individuals denoted by the internal head, E&G’s proposal lets the entire IHRC denote just those individuals picked out by the internal head with MIS.
When the internal head is universally quantified, the ITCMIS account derives the observed reading. Assume a scenario in which Ayaka peels all 12 of 12 apples.
(26)
Junyawa
Junya
[[
Ayakaga
Ayaka
dono
every
ringomo
apple
muita]no]o
peel
zenbu
all
tabeta.
eat
‘(lit.) Junya ate all of [that Ayaka peeled
‘Ayaka peeled every apple and Junya ate all of them.’
This is true if Ayaka peeled all 12 apples and Junya ate those apples. This is a regular reading, and the ITCMIS derives it. The true propositions in this case are:
(27)  a.  
b.  
⋮  
c. 
The entailment relations are such that since
While the ITCMIS analysis correctly derives the regular reading in the two cases discussed above, there are other instances in which it does not. We divide these into three categories. The first involves internal heads with nonmonotonic quantifiers (
The third category of problems involves (nonuniversal) downward entailing quantifiers (
In the last section we noted that it is crucial to interpret numerals with an
(28)  a.  
b.  
c.  
d.  
⋮  
e.  
f.  
⋮  
g.  
h.  
⋮  
i.  
⋮  
j. 
As the reader can verify, no proposition here will entail any other regardless of whether the whole is larger or smaller:
(29)  a.  “that Ayaka peeled exactly 3 apples of W” does 
b.  “that Ayaka peeled exactly 3 apples of Y” does 
The proposition that one peels exactly
(30)
Junyawa
Junya
[ [Ayakaga
Ayaka
[_{IH}
ringoo
apple
exactly
three
muita]no]o
peel
zenbu
all
tabeta.
eat
‘(lit.) Junya ate all of [that Ayaka peeled
‘Ayaka peeled exactly three apples and Junya ate all those three.’
We do not see, then, how a regular reading can arise with predicates that contain nonmonotonic quantifiers.
The nonmonotonic quantifier
(31)
E&G (2016: 5)
Junyawa
Junya
[[Ayakaga
Ayaka
ringoo
apple
half
muita]no]o
peel
zenbu
all
tabeta
eat
‘(lit.) Junya ate all of [that Ayaka peeled
‘Ayaka peeled half of the apples and Junya ate all of them.’
(32)
This is the representation that the syntax generates for the IHRC DP:
(33)  ⟦DP⟧ = ⟦ 
The first step of the MIS recipe is to assemble the true propositions, given a context, in which the property
(34)  a.  
b.  
c.  
d.  
e.  
f.  
g.  
h.  
i.  
j.  
k. 
Note first off, that an
Let’s get back to an
(35)  “that Ayaka peeled at least half of the atomic apple parts of X” does 
So, (34f) does not entail the propositions (34g)–(34k).
Now let’s look at the entailment relations between propositions going from a larger value of the whole X to smaller. In general, if Ayaka peeled at least half of the atomic apple parts of apples X, it does
(36)  “that Ayaka peeled at least half of the atomic apple parts of X” does 
“that Ayaka peeled at least half of the atomic apple parts of W” where W ⊑ X 
There is no entailment relation among these propositions and therefore there is no (unique) strongest, most informative proposition, and so no way for the definite to refer (without resorting to a salient set reading). So the ITCMIS analysis predicts that there is no regular reading available in sentence (31), contrary to fact. More specifically, the ITCMIS analysis fails to derive the fact that the six peeled apples 1+2+3+4+5+6 are the referent of the IHRC DP, because the proposition where the
E&G (2016: 28–29) do discuss the
A reviewer has recommended that alternative propositions be considered when evaluating informativeness, in which case E&G’s ITCMIS analysis delivers the regular reading. The reviewer claims that (modified) numeral expressions such as
(37) 
As a conjunct that is, in the reviewer’s terminology, extensional, the numeral expression simply need not be part of the propositions that are evaluated for informativity and instead we have those in (38), which are weaker existential claims. So, as before, we replace the
(38)  a.  
b.  
⋮  
c. 
In this case the entailment relations are indeed such that the proposition in (38a) entails all others, making it the strongest proposition, which in turn means that the plurality 1+2+3+4+5+6 is the referent for the DP. This is the regular reading. Essentially, this strategy removes entirely the force of the numeral expression from the proposition and the result is simply very weak existential claims. MIS will then always favour the smallest
At present, we think this alternative interpretation of E&G faces a number of challenges. First, we note that factoring numeral predicates out of the evaluation of informativity (if doing so is legitimate at all in (37)) does not solve the undergeneration problems we will discuss in sections 4.3 and 4.4 below, contrary to the reviewer’s claim. The regular reading still would not be derived from E&G’s uniform LF for both the salient set and regular readings (i.e. with a partof relation).
Another way to demonstrate the challenges that the alternative interpretation of E&G faces involves English DPs that have the same LF that E&G propose for Japanese IHRCs, as in (39):
(39)  the apples that Ayaka peeled at least 6/half of 
( 
While rather formal, the English DP in (39) is grammatical. And it would have to be given the same basic LF as E&G propose for Japanese LFs (except not derived via Inverse Trace Conversion). However, (39) cannot refer to the 6 apples in the context in (32), unlike an IHRC on the regular reading; (39) can only refer to the larger set of apples, six/half of which Ayaka peeled. So if we allow MIS to give the Japanese IHRC this meaning (from the LF E&G propose) we also make a false prediction about the meaning of (39).
At the beginning of Section 3 we showed how the ITCMIS analysis derived the regular reading for internal heads quantified by bare numerals (crucially under an
Consider the sentence in (40), where the internal head is quantified by a modified numeral
(40)
Junyawa
Junya
[
[Ayakaga
Ayaka
[_{IH}
ringoo
apple
two
than
many
muita]no]o
peel
zenbu
all
tabeta.
eat
‘(lit.) Junya ate all of [that Ayaka peeled more than two apples].’
‘Ayaka peeled more than 2 apples and Junya ate all of them.’
Let’s consider the scenario in (41), where Ayaka peeled four apples. For sentence (40) to be true in this scenario, Junya would have to eat all of the peeled apples. It will be shown below that the ITCMIS analysis fails to produce the correct truth conditions for (40).
(41)
Given the meaning of the quantifier, it turns out that in this context there are several equally informative true propositions. This renders the IHRC DP undefined, as it fails to satisfy the uniqueness presupposition of
(42)  a.  
b.  
c.  
d.  
e.  
f.  
g.  
⋮  
h.  
⋮  
i.  
j.  
k.  
⋮  
l. 
The first problem is that the target proposition (42e) is not the strongest, since (42e) is entailed by all of (42a)–(42d) and (42e) does not itself entail any of (42a)–(42d).
Moreover, there is no unique strongest proposition since no proposition in (42a)–(42d) entails any of the other in that group. So on the MIS, a definite would be undefined (and even if it were, it would deliver a plurality of three as the denotation, which is not the meaning of the IHRC DP in (40) in the context in (41)). And it turns out that the propositions in (42a–d) are not necessarily stronger than all of the other propositions: for instance, (42b) does not entail (42f). (And we would find similar instances for (42a, c, d).) So not only are (42a–d) not stronger than each other—nor the correct proposition to generate the denotation of the IHRC DP in (40)—none are necessarily stronger than all of the other propositions. (They may entail some—(42a) entails (42f), for instance—but not all.) The most salient problem, to repeat, is that (42e) (which would allow the IHRC DP to denote the four apples) is not the strongest proposition and therefore we cannot account for the meaning of (40).
Similar considerations will arise with
(43)
Junyawa
Junya
[
[Ayakaga
Ayaka
[ringoo
apple
at.least
three
muita]no]o
peel
zenbu
all
tabeta.
eat
‘(lit.) Junya ate all of [that Ayaka peeled at least three apples].’
‘Ayaka peeled at least three apples and Junya ate all of them.’
The sentence in (43) is true in the context above in (41), where Ayaka peels four apples of a set of twelve, if Junya ate those four apples (i.e. the maximal apples Akaya peeled) but not if Junya ate just three.
In the next section we will turn to left downward monotonic quantifiers. Aside from the left downward monotonic quantifier
When the internal head bears the quantificational expression
(44)
Junyawa
Junyawa
[Ayakaga
Ayaka
{
apple
six
fewer.than
/
/six
few
number
apple
muitano]o
peeledno
zenbu
all
tabeta.
ate
‘(lit.) Junya ate all of [that Ayaka peeled fewer than six apples]’
‘Ayaka peeled fewer than six apples and Junya ate all of them.’
(45)
This sentence, on the regular reading, is true in context (45), where Ayaka peels four apples of a larger set of twelve, and where Junya eats those four apples. Following the ITCMIS procedure, we collect the true propositions that vary over the
(46)  a.  
b.  
⋮  
c.  
d.  
⋮  
e.  
f.  
⋮  
g.  
⋮  
h.  
⋮  
i. 
To obtain the regular reading with MIS, we would want the proposition in (46g) to be the maximally informative one; that would set the denotation of the IHRC DP to be the X, where X = 1+2+3+4. There is a unique strongest proposition in (46) but it is not (46g). If Ayaka peeled fewer than six apples of apples 1+2+3+4, it does not follow that she peeled fewer than six apples when we add two more apples—maybe she peeled those two apples. Now, if Ayaka peeled fewer than six apples of apples 1–12, it
As expected, similar considerations apply when the internal head is quantified by
(47)
Junyawa
Junyawa
[Ayakaga
Ayaka
apple
at.most
five
muitano]o
peeledno
zenbu
all
tabeta.
ate
‘(lit.) Junya ate all of [that Ayaka peeled at most five apples]’
‘Ayaka peeled at most five apples and Junya ate all of them.’
We can use the list in (46) above, with ‘fewer than 6’ replaced by ‘at most 5’. To derive the regular reading, we would want ‘that Ayaka peeled at most 5 atomic apple parts of 1+2+3+4’, our target proposition, to be the most informative, so that 1+2+3+4 can be the denotation of IHRC DP (viz., ‘the four apples that Ayaka peeled at most 5 of.’). But as with
In sum, for the downward entailing quantifiers that we have looked at, we derive the regular reading only in the case of the universal. That is because the strongest proposition involves the largest plural individual that meets the description “which Ayaka peeled.” This is equivalent to all the apples. For the other downward entailing quantifiers,
Using various types of quantifiers on internal heads, we have argued that the ITCMIS analysis is not successful in generating the regular reading. In the next section, we address the salient set interpretation. We first point out problems in deriving this reading from an LF that is shared with the regular reading. We then argue that the sentences that have the salient set reading are not IHRCs at all but surface identical headless relatives.
We will now turn to the salient set reading. Notice that with the introduction of MIS, the salient set reading is no longer generated. In order to derive the salient set reading of (1)/(18), the pragmatic condition in (48) is added in E&G. After this condition applies, the referent of the IHRC DP in (9) is the apple sum 1+2+3+4+5+6+7+8+9+10+11+12 in context (2), and 1+2+3+4+5+6 in context (3).
(48)  
The existence of salient sets in the context allows for limiting the set of possible outputs of ⟦ 
The Salient Sets Restriction (SSR) is intended to “formalize the effect of context in definite description evaluation” (E&G 2016: 3), applying generally beyond cases with Inverse Trace Conversion. According to E&G (2016: 29), the sentence in (49) is unambiguously interpreted in context (50) to mean Junya will eat apples 1 and 2 because of the Salient Sets Restriction: it allows us to consider only 1+2 versus 3 as possible referents.
(49)  Junya will eat the two apples. 
(50)
In the ITCMIS analysis, the regular reading and the salient set reading are assumed to be associated with a single syntactic structure for IHRC. A maximal informativeness semantics for definites is supposed to derive the regular reading, while the salient set reading is derived only if there are salient sets in the context, which triggers the pragmatic constraint, the Salient Sets Restriction, to kick in. We will now show (i) that the ITC analysis of the salient set reading makes wrong predictions with certain examples; and in the next subsection (ii) that there is a syntactic parse already available in the narrow syntax from which the salient set reading can be derived without any additional mechanisms, and which does not run into the problem in (i).
The salient set reading of (1), repeated below, is compatible with a scenario where there are some peeled or unpeeled
(51)
Junyawa
Junya
[_{IHRC}
[Ayakaga
Ayaka
[_{IH}
ringoo
apple
mittsu]
three
muita]no]o
peel
zenbu
all
tabeta.
eat
‘(lit.) Junya ate all of [that Ayaka peeled three apples].’
‘Junya ate all of that which Ayaka peeled three apples of.’
(52)  There are two mixed baskets, each containing six apples and six pears. Ayaka peeled three out of six apples in basket 1, while Tsubasa peeled six out of six apples in basket 2. Junya ate all the twelve apples and pears in basket 1. 
The ITC analysis does not predict this reading because in the LF syntax (see (9)) there is a copy of the internal head in the external position, limiting the referent to apple objects. A related problem arises with the example in (53).
(53)
Junyawa
Junya
[_{IHRC}
[Ayakaga
Ayaka
[_{IH}
ringoo
apple
mittsu]
three
muita]no]kara
peel
nashio
pear
hutatsu
two
totte
take
tabeta.
eat
‘(lit.) Junya took and ate two pears from [that Ayaka peeled three apples].’
‘Junya took and ate two pears from what Ayaka peeled three apples of/in.’
#‘Junya took and ate two pears from the apples that Ayaka peeled three of.’
The relative here, on the ITC account, has a silent external head
We suggest that the interpretation of sentences like (1), repeated below in (54), which was taken to represent a new species of internallyheaded relative with the parse in (54a) in E&G, are really independently attested headless relatives with the parse in (54b). (See also
(54)
Junyawa
Junya
[_{IHRC}
[Ayakaga
Ayaka
[_{IH}
ringoo
apple
three
muita]no]o
peel
zenbu
all
tabeta.
eat
a.
[_{IHRC}
b.
[
The headless relative parse in (54b) does not involve ITC, but rather a standard gap that is the object of a postposition or case marker. It is easy to mistake (54) as something more exotic because postpositions and case markers are deleted as a response to the fact that stranding of postpositions and case markers by relativization is not possible in Japanese. This is shown by the standard externallyheaded relative clause in (56) (built from the independent sentence in (55)). As there is no overt relative pronoun, piedpiping is not an option either, as shown in (57). The result is that the postposition or case marker does not surface, as in (58).
(55)
Yokoga
Yoko
Sotakara
Sotafrom
hono
book
moratta.
receive
‘Yoko received a book from Sota.’
(56)
*[Yokoga
Yoko
kara
from
hono
book
moratta]
receive
hito
person
‘the person who Yoko received a book from’
(57)
*[∅
kara
from
[Yokoga
Yoko
hono
book
moratta]]
receive
hito
person
‘the person from whom Yoko received a book’
(58)
[Yokoga
Yoko
hono
book
moratta]
receive
hito
person
‘the person who Yoko received a book from’
So a gap is sometimes hidden, and this leads to potential ambiguity as in the following example. For interpreting such sentences, context and pragmatic knowledge and expectations play a role.
(59)
Matsumoto (
[hono
book
katta]
bought
gakusei
student
a.
‘the student who bought a book’
b.
‘the student from whom (I) bought a book’
c.
‘the student for/to whom (I) bought a book’
Looking at an example closer to (54), note that in the externallyheaded relativization (61) of sentence (60), the genitive case marker
(60)
Ayakaga
Ayaka
sono
that
yama
mountain
ringoo
apple
mittsu
three
muita.
peel
‘Ayaka peeled three apples in/of the pile.’
(61)
[Ayakaga
Ayaka
ringoo
apple
mittsu
three
muita]
peel
yama
mountain
‘the/a pile that Ayaka peeled three apples in/of’
The headless relative counterpart of (61) is (62), and its LF in (63).
(62)
[Ayakaga
Ayaka
ringoo
apple
mittsu
three
muita]no
peel
‘{that which/the one that/what} Ayaka peeled three apples in/of’
(63)  [_{DP} 
Notice that the headless relative in (62) is stringidentical to the IHRC DP in (54). What is claimed to be a previously unidentified reading of IHRC in E&G is in fact an expected interpretation of independently available headless relatives such as (62). (
We note here that even though we used
(64)
[Ayakaga
Ayaka
ringoo
apple
mittsu
three
muita]
peel
box/basket
‘the/a box/basket that Ayaka peeled three apples in’
(65)
[Ayakaga
Ayaka
ringoo
apple
mittsu
three
muita]
peel
apple/fruit
mountain
‘the/a pile of apples/fruits that Ayaka peeled three apples in’
(66)
[Ayakaga
Ayaka
ringoo
apple
mittsu
three
muita]
peel
those
apples/fruits
‘those apples/fruits that Ayaka peeled three apples of’
(67)
[Ayakaga
Ayaka
ringoo
apple
mittsu
three
muita]noni
peel
atenao
addressee
kaita.
write
‘(I) wrote the addressee’s name and address on the one that Ayaka peeled three apples in.’
Examples such as (51) and (53) from Section 5.2—cases of
A partwhole relation plays a big role in the ITC analysis of IHRC. Relativization that involves a partwhole relation has been discussed in the literature.
(68)
[Yuyaga
Yuya
shippoo
tail
hippatta]
pull
cat/
okotta.
get.angry
‘The cat/one that Yuya pulled the tail of got angry.’
(69)
Yokoga
Yoko
[Yuyaga
Yuya
ashio
leg
nihon
two
kowashita]
break
chair/
naoshita.
fix
‘Yoko fixed the chair/one that Yuya broke two legs of.’
(70) 
For example, the whole IHRC of (68) would denote the tail, such that Yuya pulled the (or a) tail part of it. And the sentence would assert that the larger tail whole got angry. This is not the right interpretation of (68). Clearly, then, we do not want to apply the ITC analysis to such examples. So even within the ITC analysis, it needs to be admitted that such examples should receive a gapped headless relative parse and not an IHRC parse. In sum, even if the ITC analyses exists for some IHRCs, the headless relative parse would have to be assumed in order to generate sentences such as (51), (53), (67), (68) and (69) with appropriate interpretations, as these cannot be handled by the ITC analysis. What remains to be seen is independent evidence for additionally generating IHRCs with ITC, which derives the salient set reading for only a subset of the cases we have discussed.
Finally, recall that on the ITCMIS analysis, the salient set reading is derived when the Salient Sets Restriction (SSR) is invoked by the presence of one or more salient sets in the context. E&G report that three survey participants consistently only had access to the regular reading. Their explanation is that these speakers did not use the SSR, and they speculate that these speakers “did not perceive the schematic grouping as salient enough in the written survey, but would use the SSR for definite description reference in a real world context” (E&G: 31). Related to this, it is further noted that “[t]he directional light noun
In the headless relative analysis, the socalled salient set reading is an expected reading when the
(71)
[Ayakaga
Ayaka
ringoo
apple
mittsu
three
muita]hoono
peel
‘the one that/that which/what Ayaka peeled three apples in/of’
(72)  a.  that which no one peeled any apples in/of  
b.  that which [Yoko]_{F} peeled three apples in/of  (if [Ayaka]_{F} in (71))  
c.  that which Ayaka peeled three [pears]_{F} in/of  (if [apples]_{F} in (71))  
d.  that which Ayaka peeld [five]_{F} apples in/of  (if [three]_{F} in (71)) 
The presence of the marker
(73)
[[Shiroi
White
inuga
dog
hoeteita](??hoo)no]ga
was.barking
nekoo
cat
oikaketa.
ran.after
‘A white dog that was barking ran after a cat.’
This tells us that the structure that the salient set reading is derived from is not an IHRC.
To summarize, we have shown in this section that there are problems in deriving the salient set reading from an IHRC parse using ITC, and that these problems do not arise with an independently available headless relative parse. The ITC analysis would then need to assume a headless relative parse for those cases, and the question boils down to whether we have independent motivation for generating an IHRC parse with ITC.
We have arrived at a picture where the sources of the regular and salient set readings are dissociated. The regular reading is left to be handled by the existing analyses of IHRCs (see
In example (74), the
(74)
Junyaga
Junya
[Ayakaga
Ayaka
that
apple
mountain
ringoo
apple
mittsu
three
muita]noo
peel
zenbu
all
tabeta.
eat
‘(lit.) Junya ate all of [that Ayaka peeled three apples in that pile of apples].’
(75)  a.  Ayaka peeled 
b.  ?Ayaka peeled three apples of 
(76)  a.  Ayaka peeled three apples of that pile of apples and Junya ate all the apples in some salient set the the pile of apples Ayaka peeled three apples from are part of. 
b.  ⟦DP⟧ = ⟦ 
Another example comes from Erlewine & Gould (
(77)
[[Tetsuyashite
all.nighterdid
ronbuno
paper
hanbun
half
kaita]no]o
wrote
senseiga
teacher
yondekureta.
read
(lit.) ‘The teacher read (for me) [(I) pulled an allnighter and wrote half paper].’
‘(I) pulled an allnighter and wrote half a paper and the teacher read it for me.’
Again, the salient set reading may be blocked here as there is no salient set (the whole paper) in the context and the SSR does not kick in. However, such LF with a partof relation is counterintuitive for creation verbs in general (e.g., ‘
In this response, we have demonstrated that the ITCMIS analysis of IHRCs does not derive the observed interpretations for relatives with a number of quantified internal heads. Furthermore, a unified account of IHRCs with the regular reading and those relatives with the socalled salient set reading cannot be maintained. Among other problems, the unification cannot capture readings where the individuals denoted by the internal head are not subparts of denotation of the IHRC as a whole—e.g. the mixed basket scenario of apples and pears. We have suggested that the socalled salient set reading does not arise from a IHRC but rather is just the expected interpretation of a headless relative. Because postposition/case markers stranded by movement are deleted, these headless relatives are surface identical to some IHRCs. When the constructions are disambiguated, it becomes clear that the salient set interpretation needn’t arise from an IHRC.
When we refer to monotonicity in this paper, it is the monotonicity on the first argument.
Looking at this particular example, one might ask whether the salient set reading is an independent reading from the regular reading, as the former seems to entail the latter, as pointed out to us by Michael Wagner (p.c.). We can see that the salient set reading is indeed an independent reading when we look at other examples where entailment no longer holds between the two readings. For instance, in the following example in (i), the matrix quantifier
(i)
Junyawa
Junya
[[Ayakaga
Ayaka
[ringoo
apple
mittsu]
three
muita]no]o
peel
hutatsudake
two
tabeta.
eat
‘(lit.) Junya ate only two of [that Ayaka peeled three apples].’
‘Ayaka peeled three apples and Junya ate only two of them.’
We note in passing that the salient set reading sounds less accessible with matrix numerals as in this case, as opposed to
As Andrea Eunbee Jang (p.c.) brought to our attention, we can obtain the salient set reading easily from such an example (E&G’s (17)) if we used connectives such as
See Erlewine & Gould (
For ease of presentation, we use the English word order in the Japanese LF.
This is a simplification. See von Fintel et al. (
We are pretending in (15) that we weigh walnuts only in units of 10 g.
We are thus not expressing the external head, following E&G (2016: 28). However, von Fintel et al. (
Throughout the paper, we follow E&G in using postnominal (modified) numeral quantifiers and other quantifiers of the general form “NPcase Q”. One exception is the case of
It is claimed in E&G (2016: 5) that the sentence (31) does not have the regular reading but only has the salient set reading in context (3). It is not clear to us that the reported judgment is robust. A reviewer also reports that they can easily obtain the regular reading. Perhaps the regular reading is not easily accessed by some speakers because they would have to focus on the first group of apples. However, this line of speculation about the reported lack of the regular reading would not fit with the ITCMIS analysis. Given the proposed derivation of the salient set reading—namely that when there is a salient set in the context, one can ignore MIS—it is not clear to us why the same set is not salient enough to make the regular reading available (“half of the salient set”).
In illustrating their point, the reviewer uses English DPs such as
See footnote 8 for the
In both cases discussed in sections 4.3 and 4.4, we would end up with a presupposition failure.
The reviewer suggests that the existence of English DPs such as
A reviewer has pointed out that he or she finds it difficult to obtain the regular reading in this context. We think it has to do with the ignorance or irrelevance component that
While the SSR is proposed as a general principle for interpreting definite descriptions, it is assumed that “SSR is generally not active for the resolution of crosssentential anaphora” (E&G, footnote 23). E&G is forced to adopt this assumption in order to block the salient set reading from Etype pronouns/definite descriptions in crosssentential anaphora, which they assume to be missing. But see Erlewine & Gould (
Erlewine & Gould (
Grosu & Hoshi (
It is beyond the scope of this paper to review the literature on this and related phenomena. For presentational reasons we indicate the position of a gap in the relevant examples, but we are in principle not committed to the gap analysis of such relatives. Some authors in fact argue for a gapless analysis, relying on, for example, null resumptive proPPs. See, for example, Kuno (
Resumptive pronouns are possible in such relatives with overt P/case marker, as in (i) and (ii), though they would sound better with dependencies across islands, for example.
(i)
[Ayakaga
Ayaka
sokono
there
ringoo
apple
mittsu
three
muita]no
peel
‘that which/the one that/what Ayaka peeled three apples of it’
(ii)
[Sotaga
Sota
sono
that
ashio
leg
nihon
two
kowashita]no
break
‘that which/the one that/what Sota broke two legs of it (a chair, for example)’
See also Minamida (
Note that example (66) with
See, for example, Matsumoto (
For their comments and advice, we would like to thank Luis AlonsoOvalle, Brian Buccola, Alex Grosu, Andreas Haida, Koji Hoshi, Henrison Hsieh, Ivona Kučerová, Bernhard Schwarz, Michael Wagner, John Whitman, audiences at McGill University and the 10th TorontoOttawaMontréal Semantics workshop, as well as four
The authors have no competing interests to declare.