On Some Problems of (In)definiteness
within Flexible Semantics
Yoad Winter
Technion – Israel Institute of Technology
[email protected]
Abstract
This paper studies the ramifications of the flexible semantics in Winter (2001a)
for the analysis of some of the facts in ”the core set” for this special issue. Within
this framework, it argues (i) for a general ”anti-economy” principle in the application of choice functions to (non-)specificity markers; (ii) for DP structure as the
main trigger of different scope potentials; (iii) for lexical structure as characterizing the common/proper noun distinction and the special class of bare “presidentlike” nominals; and (iv) for Danon’s (2001) notion of purely-syntactic ”definiteness spreading” in Hebrew construct states.
Keywords: indefinite, choice function, specificity, noun, DP
1 Introduction
Definiteness phenomena involve a variety of syntactic, semantic and pragmatic factors, which any theory of nominals has to tease apart. This paper aims to study the
ramifications of the flexible semantics in Winter (2001a) for the analysis of some of
the facts in “the core set” for this special issue, especially in relation to the division of
labor between syntax, semantics and pragmatics.
After giving some background on the theoretical framework in section 2, some of
the problems that the phenomena in the core set introduce for flexible semantics will
be addressed. Section 3 claims that (non)specificity markers like a certain or some...or
other impose a semantic condition on the possible scopes for the existential closure
of choice functions. However, a more global “anti-economy” principle is also at work
with such items. This principle allows more than one scopal position for existential
closure in cases where the different positions lead to equivalent readings.
The differences among indefinites in the possibility of taking wide-scope are addressed in section 4. It is claimed that these differences are essentially a reflection of
different DP structures. According to this claim, wide-scope behavior, quite independently of indefiniteness, is a property of the so-called flexible nominals – those nominals that do not have a filled specifier DP position. According to this proposal, many
indefinite items (e.g. complex numerals, the item no) sit in the specifier of DP. Therefore, they give rise to non-flexible nominals that are “purely quantificational” and lack
the choice function interpretation that leads to wide-scope readings with other indefinites. On the other hand, proper names and some other definite nominals are flexible
1
and are interpreted using choice functions, but their unique reference often neutralizes
potential scope ambiguities.
Section 5 claims that bare predicate nominals with a uniqueness requirement are to
be expected in English by the general treatment of proper names in flexible semantics.
According to the proposal in Winter (2001a), proper names are flexible nominals with
a lexical D’ structure that contains a covert definite article at the NP level and a covert
choice function at the D’ level. Similarly, singular bare predicate nominals are treated
as lexical NPs, with only the covert definite article, but without the D’ position for
the choice function. English singular nominals require an overt “determiner” item at
D, spec-NP or spec-DP. However, this requirement is not applicable to lexical NPs or
D’s. Consequently lexical NPs are bare in predicate positions, but only lexical D’s (i.e.
proper names) are bare in argument positions.
Section 6 follows Danon (2001), and argues that “definiteness agreement” with
Hebrew construct state nominals is a purely syntactic phenomenon, which does however show complex interactions with the semantic definiteness of these nominals.
2 Flexible semantics and DP structure
The DP hypothesis of Abney (1987) has led to interesting proposals concerning the
syntax-semantics interface in the interpretation of nominals.1 Notably, the works
of Higginbotham (1987) and Zamparelli (1995) introduced important ideas about semantic layers within the DP that distinguish between predicate-denoting layers and
argument-denoting layers. The theory in Winter (2001a:ch.4) combines these proposals with Partee’s (1987) approach to flexible interpretation of nominals, and distinguishes between three classes of nominals according to their syntactic analysis:
Nominals that contain a full spec-DP position. These nominals can only be
analyzed as DPs.
Nominals that contain an empty spec-DP and a full D position. These nominals
can be analyzed as either DPs or D’s.
Nominals where both spec-DP and D are empty. These nominals can be analyzed as DPs, D’s or NPs.
This three-way syntactic distinction has the following semantic reflections:
Under their NP analysis, nominals unambiguously denote predicates (sets of
entities).
Under their DP analysis, nominals unambiguously denote generalized quantifiers (sets of sets of entities).
Under their D’ analysis, the interpretation of nominals is free to move back and
forth between predicates and quantifiers.
1
I use the theory-neutral term nominal as a collective label for all the linguistic expressions that are
analyzed in this paper as NPs, D’s and DPs.
2
The flexible interpretation of the D’ level is by virtue of phonologically covert operators that apply at this level and map predicates to quantifiers and vice versa. These
operators are called category shifting principles.
In Winter (2001a) I propose two such principles: a choice function (CF) operation that maps predicates to quantifiers, and a minimum operator that maps quantifiers
to predicates. Among these operations, only the CF mechanism is relevant to the issues discussed in this paper. We can furthermore assume for simplicity the following
common definition of CFs, where they are used as category shifting principles from
predicates to entities, rather than generalized quantifiers.
(1) For any set E , a choice function over E is a function that maps every non-empty
subset A of E to a member of A.
For instance, if E = fa; bg then there are only two choice functions over E : the
function that maps fag to a, fbg to b and fa; bg to a, and the function that maps fag to
a, fbg to b and fa; bg to b. An indefinite like a student is interpreted by applying a CF
to set of students, which gives one of the members in this set, in case it is not empty.2
DP
SPEC
D’
D
NP
some, φcf , φmin
SPEC
N
the, a, φthe
Figure 1: DP structure for (in)definites
Reinhart (1997) proposes that CFs are responsible for wide-scope effects with indefinites. More will be said about these effects and CFs in sections 3 and 4. For the
time being, let us summarize and exemplify the proposed three layer account of the
differences between nominals. Figure 1 summarizes our main assumptions concerning simple definites and indefinites. Simple definites and a indefinites are treated as
NPs, since the articles a and the sit at spec-NP. For reasons that will be discussed
in section 5, we assume that in English there is also a possibility to have an empty
definite article the at spec-NP. The some article in English and the covert category
shifting cf (for choice functions) and min (for the minimum operator) are analyzed
as Ds. Quantificational items such as no, exactly one, every etc. are assumed to sit at
spec-DP.
2
The more general treatment of CFs in Winter (2001a) as mappings from predicates to generalized
quantifiers is also used in order to treat the case where the set (in this case, the set of students) is empty.
3
The distinction that is made between the rigidly quantificational DP level and the
flexible D’s level has direct implications for the different wide-scope potentials of various indefinites. This point will be discussed in section 4. The distinction between the
D’ level and the NP level is motivated in Winter (2001a) by the phenomena of verbless
predication (see Doron (1983)) and appositional conjunction (see Hoeksema (1988)).
These two phenomena are illustrated by the following examples.
(2) I consider John (to be) a/the scientist.
(3)
a. A great man and a good father has passed away.
b. The great man and the good father has passed away.
In (2) we see that in a small clause construction with a predicative definite or a predicative a indefinite, a be copula is only optional. In (3), the conjunction of the (in)definites
does not force plural agreement. This is in contrast to the following examples with
some indefinites.
(4)
a. *I consider John some scientist I know.
b. I consider John to be some scientist I know.
(5) *Some great man and some good father has passed away.
In Winter (2001a) it is proposed that these contrasts follow from the D’/NP distinction
between the article some and the articles a and the. While the D’ level at predicate
positions requires an overt copula, the NP level does not. Further, conjunctions of
singular D’s are plural, whereas conjunctions of singular NPs inherit their number
features (if any) directly from their conjuncts. This is in parallel to conjunctions of
other predicative categories such as VP/IP, PP and AP. For instance, smiles and sings
is a singular conjunction of singular VPs, like the NP conjunctions in (3) and unlike
the D’ conjunction in (5).
The three levels of analysis within the DP correspond in this proposal to different
phrasal distributions of nominals within the sentence.
Under their DP analysis, nominals can only appear in argument positions.
Under their NP analysis, nominals can only appear in predicate positions.
Under their D’ analysis, nominals can only appear in predicate positions with
overt copula.3
3 (Non)specificity markers
As said above, the choice function (CF) analysis of indefinites assumes that indefinites
like a student or some student are interpreted by applying a CF to the set of students.
According to Reinhart (1997), CFs are variables that should be bound by a free process of existential quantification, similar to existential closure in DRT. Thus, Reinhart
proposes that a simple sentence like (6a) below is interpreted as in (6b).
3
In principle, as quantifiers D’s should be able to appear also in certain argument positions, though I
am not aware of any argument position that selects for D’ and not for DP.
4
(6)
a. Some student smiled.
b. 9f[CF(f) ^
smiled (f(student ))]
0
0
In words, formula (6b) means that there is a choice function f , and the student that f
chooses from the set of students smiled.4 By contrast to Reinhart, Kratzer (1998) treats
CFs as covert deictic elements that are specified by the context of utterance, without
the existential quantification in (6b).
According to Reinhart’s line, there is no need to distinguish between “specific”
and “non-specific” interpretations of indefinites. In her account, the difference between the two kinds of interpretation is the scope at which existential closure applies
to the CF variable. According to Kratzer, only the “specific” interpretation is derived
by the CF mechanism. In Kratzer’s proposal, other scopal interpretations of indefinites are obtained by an additional mechanism: the standard analysis of indefinites as
existential quantifiers. For instance, consider the scope ambiguity of the indefinite in
sentence (7) below between the “non-specific”/“narrow-scope” paraphrase in (7a) and
the “specific”/“wide-scope” paraphrase in (7b).
(7) If some woman in this room thinks she knows the answer to this question then
we can go on to the next question.
a. If there is some woman or other in this room who thinks she knows the
answer to this question then we can go on to the next question.
b. There is some (specific) woman in this room such that if she thinks she
knows the answer to this question then we can go on to the next question.
The two analyses of (7) according to Reinhart and Kratzer are given in (8) and (9)
respectively.
(8)
woman in this room
0
a. if 9f[CF(f) ^ [f(
) thinks she knows the answer
to this question]] then we can go on to the next question
woman in this room
0
b. 9f[CF(f) ^ [if [f(
) thinks she knows the answer to this question] then we can go on to the next question]]
(9)
woman in this room
0
a. if 9x[
(x) ^ x thinks she knows the answer to this
question] then we can go on to the next question
woman in this room
0
) thinks she knows the answer to this quesb. if f(
tion then we can go on to the next question
In Reinhart’s analysis, the difference between the two readings is in the relative scope
of the existential quantifier 9f with respect the conditional: narrow in (8a) and wide
in (8b). In Kratzer’s analysis, the difference is in whether it is the CF mechanism or
the standard existential mechanism that applies. When the CF mechanism applies as in
(9b) (with no existential process) we get the “specific” (or “wide-scope”) interpretation
of the indefinite. When the standard mechanism applies, as in (9a), we get the “narrowscope” (or “non-specific”) interpretation.5
4
As said in footnote 2, we ignore here the case where the set of students is empty, which is treated in
Winter (1997,2001a).
5
In fact, Reinhart also allows indefinites to be interpreted using ordinary existential quantifiers. However, as argued in Winter (1997,2001a), semantically this is not an essential part of her proposal.
5
Let us move on now to our main interest in this section: the specificity marker a
certain and the non-specificity marker some...or other. Consider the following variations of sentence (7).
(10) If a certain woman in this room thinks she knows the answer to this question
then we can go on to the next question.
(11) If some woman or other in this room thinks she knows the answer to this question
then we can go on to the next question.
These sentences, unlike (7), are unambiguous. Sentence (10) has only the “specific”
interpretation (7b),6 whereas (11) can only be interpreted “non-specifically” like (7a).
Let us first consider the specificity marker a certain. Kratzer proposes that this item
unambiguously invokes the choice function interpretation, hence the “specificity” impression.7 Reinhart’s theory cannot use the same straightforward account of a certain,
since, as we have seen, CFs in Reinhart’s treatment can derive all possible existential
scopes for indefinites. Reinhart’s line would have to suggest that a certain invokes a
special kind of CF variables, which must either stay free (as in Kratzer’s account) or
are subject to topmost only existential closure (see Chierchia 2001, p.70). Such an assumption would be theoretically more costly than Kratzer’s account of the difference
between a certain and other indefinites. Thus, we may count this as a reason to prefer
Kratzer’s ambiguity account of indefinites.8
However, I would like to show now that Kratzer’s account of a certain has to face
a problem with there sentences that is not present in Reinhart’s approach, and which
may lead us to reconsider the status of specificity markers. Consider the following
there sentence with a certain.
(12) There is a certain woman in this room who thinks she knows the answer to this
question.
We see that the a certain indefinite here is perfectly acceptable, and this kind of examples is problematic if we want to combine Kratzer’s approach with the semantic
account of the distribution of (in)definite nominals in there sentences. This semantics,
which originates from Barwise and Cooper (1981), distinguishes between existential
(“weak”) and non-existential (“strong”) generalized quantifiers. In Winter (2000) I
show that given Keenan’s (1987) distinction between existential and non-existential
0
quantifiers, denotations like f(
) for the nominal a certain
woman in this room in (12) are classified as non-existential, similarly to proper names.
This classification of indefinites with a free CF variable is also expected under other
woman in this room
6
Susan Rothstein (p.c.) remarks that a certain woman in (10) can also mean “a certain kind of
woman”. I henceforth ignore this other possible meaning of a certain indefinites.
7
In fact, Kratzer uses the more general Skolem function treatment, because of examples such as the
following, where a certain leads to a “dependent” interpretation.
(i) Every man loves a certain woman – his mother. (Groenendijk and Stokhof, 1984;ch.3)
(ii) According to Freud, every man unconsciously wants to marry a certain woman – his mother.
(Hintikka, 1986)
For Skolem function extensions of the choice function treatment see Chierchia (2001), Schlenker (1998),
Schwartz (2001), and Winter (2001b).
8
This is essentially the argument in Matthewson (1998), using other evidence from St’át’imcets.
6
variants of the theory of CFs and indefinites. However, if we adopt Reinhart’s assumption that existential closure can apply at any level, then CF variables within indefinites
do not necessarily remain free. An indefinite such as a (certain) woman in this room
can also denote the following generalized quantifier, where existential closure applies
within the nominal itself.
(13) [ a certain woman in this room] =
fA : 9f[CF(f) ^ f(
woman in this room ) 2 Ag
0
This generalized quantifier, under the formal account of CFs in Winter (1997), is simply the existential quantifier that the indefinite a/some woman in this room is standardly
taken to denote. Consequently, the grammaticality of sentence (12) is expected under
the “narrowest scope” construal (13) for existential closure of CFs.
We are facing the following dilemma: on the one hand, we need a certain to denote
a CF variable that cannot be existentially closed, or can be closed only with matrix
scope. This is needed in order to preserve Kratzer’s account of a certain in (10).
On the other hand, we need this variable to be closed at “narrowest scope” in order
to preserve the semantic account of there sentences with a certain. I would like to
suggest that in fact, we can obtain both objectives if we adopt the following rule about
a certain.
(14) Specificity marking rule: the specificity marker a certain denotes a CF variable
that can be existentially closed at any scope that is equivalent to matrix scope
closure.
According to this rule, sentence (10) shows only widest scope closure because narrowest scope closure would lead to truth conditions that are semantically distinguishable
from the widest scope reading. By contrast, in sentence (12) both matrix scope closure and narrowest scope closure lead to equivalent interpretations, hence both are in
principle available. However, the semantic conditions on there sentences rule out any
scope that is not narrowest.9
From the proposed specificity marking rule, it follows that there sentences with a
certain should become ungrammatical when the widest scope interpretation is distinguishable from the narrowest scope interpretation. This expectation is at least partially
borne out. Consider the following sentence, vis à vis (10).
(15) ?If there is a certain woman in this room who thinks she knows the answer to
this question then we can go on to the next question.
A priori, given the grammaticality of (12) and (10), we could have expected (15) to
be OK too and equivalent to (10). However, according to my informants’ judgements,
this is not the case: (15) is significantly worse than both (12) and (10). The specificity
marking rule predicts this pattern: in order for the embedded there sentence to be
grammatical, sentence (15) should allow narrowest scope closure of the CF variable;
but this would lead to a reading that is not equivalent to the one that is derived by widest
scope closure, hence the sentence is ruled out according to the specificity marking rule.
9
This reasoning is in a sense the opposite kind of reasoning to Fox’ (1995) economy-scope generalization. In fact, there may be interesting interactions between the two principles, which I do not discuss
here.
7
A similar effect to the contrast between (10) and (15) can be observed in the following pair of sentences, where a certain appears within a downward entailing context.
(16)
a. I doubt/do not believe that a certain woman in this room knows the answer
to this question.
b. ?I doubt/do not believe that there is a certain woman in this room who
knows the answer to this question.
Similarly, negated there sentences do not license a certain, as observed by the contrast
between the following sentence and sentence (12).10 .
(17) ?There isn’t a certain woman in this room who thinks she knows the answer to
this question.
To summarize, the grammaticality of there sentences with a certain leads to the
hypothesis that the semantics of this item is not simply “strong”, as might be expected
by the CF treatment, but its “strength” is determined by the potential scopes of existential closure.11 It should be stressed that the specificity rule is not intended as a
full theory of specificity marking and there sentences. There are some contexts where
a certain appears in there sentences despite potential scope ambiguities. Two such
examples follow.
(18) John talked to every man who believes that there is a certain woman in this room
who knows the answer to this question.
(19) John believes that there is a certain woman in this room who knows the answer
to this question.
According to my informants, these sentences are acceptable. This is not expected
by the specificity marking rule. In sentence (18), widest scope to a certain is surely
different than the narrowest scope interpretation, and in sentence (19) the de dicto/de re
ambiguity may potentially lead to a similar difference. However, the interplay between
CFs and intensionality is not completely clear at the moment, and in sentence (18), also
referential dependency of the indefinite on the universal NP may interfere.12
“Non-specificity” markers like some...or other are easy to account for both in Reinhart’s treatment and in Kratzer’s treatment. Reinhart would take some...or other to include the existential closure operator of CFs within its meaning. Kratzer would equivalently take this item to denote a standard existential quantifier. Now, does a similar rule
to the specificity rule (14) hold with respect to non-specificity too? Note that the argument for (14) came from the there insertion context, which requires “non-specificity”.
Symmetrically, an argument for an analogous “non-specificity” rule could come from
a syntactic context that requires “specificity”. As observed by Ladusaw (1982), one
such context is the partitive construction. In general, partitives as in (20) generally
allow “specific” nominals and disallow “non-specific” nominals.
10
Thanks to Danny Fox for pointing this out to me, as well as for pointing out the kind of examples
that is illustrated in (18) and (19) below.
11
See also Heim (1987) for relevant discussion of there sentences and the scope of indefinites.
12
See footnote 7 for some remarks on the Skolem function account, which is intended to capture
such dependencies. This may lead to interpretations that are not in the relevant “reference set” for the
specificity marking rule.
8
(20)
a. one of the boys/these boys/the two boys
b. *one of no boys/most boys/both boys
Ladusaw follows Barwise and Cooper (1981) and gives a formal semantic characterization of these two groups of nominals using the notion of principal ultrafilters. Intuitively, Ladusaw proposes that those nominals that support partitives as in (20a),
unlike the nominals in (20b), denote generalized quantifiers that define one (possibly
plural) individual. Ladusaw further points out that “specific” interpretations of indefinites in English give rise to the partitive construction just like “specific” nominals. For
instance:
(21) This book could belong to one of three people.
Winter (2000) shows that under the CF treatment of the indefinite three people, this
nominal is characterized as a principal ultrafilter, hence it is “specific” in Ladusaw’s
terms.
The “specificity context” of the partitive construction allows us to check whether
“non-specificity” with some...or other is “global”, similar to “specificity” with a certain, or whether it is a local notion. Consider the following Hebrew example.13
(22) slosa cimxey marpe ka-elu
o axerim yoci’u
three herbs-for cure like-those or others will-take-out
otxa
me-ha-maxala
you-ACC from-the-disease
“what you need in order to cure your disease is any combination of three herbs”
We see here that in Hebrew, the “non-specificity” item ka-elu o axerim (“some or
other”) can appear with numerals. However, this item, unlike bare numeral indefinites in Hebrew, does not allow the partitive construction. Consider for instance the
following contrast.
(23)
a. exad mi-tox slosa cimxey marpe yoci’u
otxa
one of
three herbs-for cure will-take-out you-ACC
me-ha-maxala
from-the-disease
“what you need in order to cure your disease is one of three herbs”
o axerim
b. *exad mi-tox slosa cimxey marpe ka-elu
one of
three herbs-for cure like-those or others
yoci’u
otxa
me-ha-maxala
will-take-out you-ACC from-the-disease
The partitive in (23a), with the simple indefinite “three herbs”, is perfectly OK. By
contrast, the partitive in (23b), with the “non-specific” indefinite “any three herbs”,
is ungrammatical. Note however that the widest and narrowest scopes for existential
closure of CFs in (23a) are both equivalent. These two analyses are sketched below,
0
where
denotes the set of collections X that consist of three herbs.14
three herbs
13
I use the Hebrew parallel to the “some...or other” construction because in Hebrew this construction
can come with a plural numeral. In English, for some reason, constructions such as some three herbs or
other are ungrammatical.
14
See Winter (2001a) for more on the interactions between numerals and CFs.
9
(24)
three herbs ) ^ x will cure your disease]
9f[CF(f) ^ 9x[x 2 f(three herbs ) ^ x will cure your disease]]
a. 9x9f[CF(f) ^ x 2 f(
b.
0
0
The two statements are provably equivalent. Still, if the wide scope construal (24b)
were allowed in (20a-b), then the Hebrew “some or other” construction in (20b) should
have been acceptable according to Ladusaw’s partitive constraint. That this is not the
case indicates that some or other is simply interpreted as a narrowest scope existential.
This can be achieved using narrow scope closure of CFs à la Reinhart or using the standard analysis, as Kratzer proposes. Thus, “non-specific” indefinites do not motivate a
global rule like (14) for “non-specific” indefinites.
4 Differences in scope taking
The differences between various indefinites in their ability to take wide-scope beyond
syntactic islands has been occasionally observed in the literature. See Liu (1990),
Kamp and Reyle (1993:ch.4), Beghelli (1995) and Corblin (1997), among others, for
some of these differences. Winter (2001a) brings the following contrasts as minimal
pairs that distinguish between the scope-taking potential of different indefinites.
(25)
a. If some woman I know gave birth to John then he has a nice mother.
b. ?If exactly one woman I know gave birth to John then he has a nice mother.
(26)
a. If two people I know are John’s parents then he is lucky.
b. ?If exactly two people I know are John’s parents then he is lucky.
The b sentences cannot have the wide-scope interpretations that the a sentences exhibit.
Thus, the a sentences, but not the b sentences, can have the respective interpretations
that are paraphrased below.
(27) There is some/exactly one woman I know such that if she gave birth to John then
he has a nice mother.
(28) There are two/exactly two people I know such that if they are John’s parents
then he is lucky.
Similarly to the indefinites in (25b) and (26b), also other indefinites, notably negative
indefinites such as no student(s) do not give rise to wide-scope readings beyond islands. For instance, sentence (29a) below does not have the reading that is paraphrased
in (29b).
(29)
a. If no student(s) arrive(s) then John will be disappointed.
b. There is/are no student(s) such that if he/she/they arrive(s) then John will
be disappointed.
According to Winter (2001a:ch.4), the difference between complex numerals such
as exactly two and two, and between exactly one and some or a is that the former
items denote determiner functions (functions from sets to generalized quantifiers) and
sit at spec-DP. Consequently, category shifting operators that apply at the D’ level,
especially the CF mechanism, do not apply to such nominals and hence they do not
10
show wide-scope effects beyond islands. By contrast, items like two, a and some are
non-quantificational: two and a denote predicate modifiers, whereas some denotes a
choice function. These items sit lower within the DP structure of figure 1: within the
D’ or NP levels. Consequently, the CF mechanism applies to these expressions and
generates wide-scope interpretations that are not available with standard generalized
quantifiers.
Note that this distinction between “flexible” nominals and “rigid” nominals is independent of the “strength” of the nominals under discussion. Just like the weak nominals, there are strong nominals that show a wide-scope behavior and there are strong
nominals that do not. On the one hand, simple definites, proper names and their coordinations can potentially exhibit wide-scope effects like simple indefinites. For instance, the phenomenon of wide-scope disjunction in sentences like the following, can
be treated using the CF mechanism.
(30)
a. If Bill praises Mary or Sue then John will be happy.
b. If Bill praises this girl or that girl then John will be happy.
Sentence (30a), for instance, can be interpreted as equivalent to the following sentential
disjunction.
(31) If Bill praises Mary then John will be happy, or if Bill praises Sue then John will
be happy.
On the other hand, it is well-known that strong nominals with every, all and most, like
complex numeral indefinites, do not show wide-scope effects beyond islands.
We conclude that the typological distinction between rigid nominals, where the
quantificational element is in spec-DP, and flexible nominals, where it is in D or specNP, is as follows:
1. Rigid nominals:
(a) Complex numerals: exactly one, exactly two, between two and five, more/less than three, at least/most three
(b) Quantificational elements: every, all, most, no
2. Flexible nominals:
(a) Simple (in)definites: a, some, a certain, the, this
(b) Simple numerals: two, three, four etc.
(c) Proper names: Mary, John, etc.
(d) Simple coordinations of the above: Mary and/or John
The overall syntactic justification for this classification is a major task, which is beyond the scope of this paper, and is discussed more extensively in Winter (2001a:ch.4).
For our purposes here, however, it is important to emphasize that the division between
rigid nominals and flexible nominals, along the lines of the above typology, is not only
motivated by the peculiar scopal properties of flexible nominals. At least one additional phenomenon independently motivates this distinction: the collective interpretation of nominals. The different collectivity potential of rigid nominals and flexible
11
nominals is most clearly exemplified by a sub-class of the collective predicates that
contains predicates like be numerous, be a good team or elect the president.15 For
instance, consider the following contrastive pairs.
(32)
a. The/some/those students (I know) are the team that won the cup yesterday.
b. *All the students (I know) are the team that won the cup yesterday.
(33)
a. Eleven students I know are the team that won the cup yesterday.
b. *Exactly/at least/at most eleven students are the team that won the cup
yesterday.
(34)
a. Two people I know/Mary and John are the couple that won the prize yesterday.
b. *No/all the/most of the people I know are the couple that won the prize
yesterday.
We see here that the collective interpretation is available with the rigid nominals in the
a sentences, but not with the flexible nominals in the b sentences. For more on this distinction, with a detailed account of its origins and implications, see Winter (2001a:ch.45).
5 Proper names and bare predicate nominals
We have seen above that in the flexible semantics that is assumed in the background of
this paper, proper names should allow the application of category shifting principles
like the CF mechanism in order to enable disjunctions as in (30) to be interpreted
with a wide scope.16 In the framework we assume, this means that proper names
should be analyzed within the D’ level. By considering the behavior of proper names
in predicative positions and “appositional” conjunctions, we can see that they behave
like the some indefinites in (4) and (5). Consider for instance the following contrasts,
and compare them with the contrasts we discussed concerning examples (2)-(5).
(35)
a. *I consider this man John.
b. I consider this man to be John.
(36)
a. *Dr. Jekyll and Mr. Hyde has passed away.
b. *Amy and a long-time lover has passed away.
Like some indefinites, proper names require an overt copula when they appear in predicative positions and require plural agreement when they appear in nominal conjunctions.17 In the framework of Winter (2001a), the conclusion we draw from such examples is that proper names should be analyzed in English as D’ nominals with a filled
D position. In implementing this idea, Winter (2001a) assumes that proper names are
15
See Winter (2001:ch.5, 2002) for a new typology of predicates according to this distinction, and for
a theory of plurality that is based on this classification.
16
In Winter (2001a), also the minimum category shifting operator applies to proper names, in order to
generate collective readings for conjunctions such as Mary and John.
17
The first fact was pointed out by Doron (1983) and the second fact by Hoeksema (1988).
12
bare nouns with an empty spec-NP that imposes a uniqueness requirement. This empty
element is denoted the . In addition, like indefinites in argument position, proper
names require the application of a choice function variable, in order for them to end up
denoting an entity (or a quantifier, in the Montagovian tradition). The resulting lexical
structure of proper names is given in figure 2.
D’
D
φcf
NP
SPEC
N
φthe
Figure 2: D’ structure for proper names
Consider for instance the proper name Mary. The semantics of its lexical structure
is derived as follows:
1. Initially, the nominal material denotes a set of entities M , like any other noun.
2. The empty definite article the , like the singular definite article ,imposes a uniqueness requirement on this set. That is, it maps M to itself in case that M is a
singleton f 0g, and to an undefined value otherwise.18
m
3. The empty element cf denotes a choice function that maps this singleton to the
entity 0.
m
This proposal treats proper nouns in English as bare nouns, with an additional
lexical structure that accounts for their special syntax (the lack of article) and semantics
(their entity denotation). This treatment is quite natural, given the fact that proper
nouns in many languages often behave like common nouns (cf. he’s a real Einstein, the
Vermeer she bought was expensive, etc.). In such cases, the proper noun is analyzed
simply as a common noun, without the additional lexical structure and its “unique
reference” entailments.
Once complex lexical structures are assumed for proper nouns, with the two empty
items the and cf , it is natural to expect that some languages will have lexical entries
for other kinds of bare nouns, with only one of these null elements in their lexical
structure. Specifically, a bare nominal with only the the item is analyzed as an NP
that is interpreted as a singleton set – a predicate with a uniqueness requirement on its
extension. I would like to argue that nominals of this kind appear in English, as bare
predicate nominals.
18
In the Russellian treatment of definites, the definite article is formalized in Winter (2001a) as denoting an operator that maps any singleton set to itself, and any other set to the empty set.
13
Consider the predicative NPs in the following examples.19
(37)
a. John is president (of the US).
b. John is former president.
c. John is ambassador to the US.
d. John is provisional president (of the US).
e. John is sheriff of this town.
f. John is mayor of this city.
According to the theory that is advocated here, a bare noun like president in (37a) has
the following lexical structure.
(38) [NP the [N president ]]
0
The interpretation of this NP is as the singleton set that consist of the (unique) president.
Note first that given this NP analysis, our theory correctly expects the predicative
nominal in these examples to appear in verbless predicative constructions, such as I
consider John president, ambassador to the US etc. Further, there are at least three
questions that the structures in (37) raise:
1. What is the difference between nouns like president or mayor and nouns like
teacher or boy, which are responsible for the contrasts between sentences like
those in (37) and non-sentences like *John is teacher/boy?
2. Why do singular nouns like president appear in bare NPs only in predicative
positions, but not in argument positions? Witness the contrast between (37) and
non-sentences like *president smiled or *I saw president.
3. Which adjectives and PPs adjoin to the lexical structure and lead to an acceptable
interpretation of the bare predicative definite?
Here I will address only the latter two questions.20
Given that English proper nouns can appear in argument positions without an overt
article, the fact that president-like nouns require an overt article in these positions is
quite puzzling: what is the origin for this contrast between proper nouns and presidentlike nouns? I would like to suggest that this difference points to the following rule
about English singular nominals.21
(39) The article rule: Any singular DP, D’ or NP in English must have at least one
of the following positions lexically filled: spec-DP, D or spec-NP.
19
Some of these examples are from Stowell (1991).
As for the first question, according to the line that takes proper nouns to be common nouns with a
complex lexical structure, the “inherent” properties of a noun like Einstein that make it “more proper
than common” are rather uninteresting from a linguistic point of view. A similar point may hold for the
difference between president-like nouns and teacher-like nouns. Under this conception, uniqueness in the
first case is a by-product of different lexical structures, and not a characterization of any “deep” semantic
contrast between the two kinds of nouns.
21
Plurals, and especially bare plurals, are beyond the scope of the present discussion.
20
14
This rule means that a simple common noun such as car, whose lexical category is
N, can appear bare neither in argument positions nor in predicate positions. This is
because in its N lexical structure, there is obviously no filled spec-DP, D or spec-NP.
By contrast, I propose that a noun like president has a lexical entry where it is an NP
with an empty SPEC that denotes the definite article. In this case, this is a legitimate
NP in predicate positions since its SPEC is lexically filled. But as we shall see below,
this does not mean that president can appear as a DP in argument positions; its specNP, which is lexically filled, licenses the NP lexically but not any D’ or DP that governs
it. Proper names are licensed as both D’s and DPs, since their spec-NP and D positions
are lexically filled (by the empty definite article and CF, respectively).
Formally, the implementation of these ideas in a concrete grammar can account for
the puzzling facts that surround article-less singular nominals. Assume that the rules
for deriving the NP and D’ levels count the number of the lexically filled spec-NPs
and Ds. At the DP level, it is simply checked whether this counting is one or more.
We assume that the NP and D’ levels within the DP have a “counter” feature A that
implements the article rule. The proposed DP rules with this counter feature are the
following.
NPA=0
NPA=1
NP
DA=x
DA=x+1
D
DP
DP
N
! ART N
where x 1
! NPA=x
! NPA=x
! D NPA=x
! DA=x
where x 1
! D
! SPEC DA=x where x 0
Note that in the NP and D’ levels, the A feature can be optionally “erased” if its value
!
0
0
0
0
0
0
0
0
is one or more. This reflects the fact that a sufficient condition for NPs and D’s to be
licensed (in predicate positions) is when their spec-NP or D position is lexically filled.
In general, these rules guarantee that any DP, D’ or NP (with the A value unspecified) that are derived by the grammar must satisfy the article rule. However, lexical NPs (e.g. president-like nominals with a null definite article) and D’s (e.g. proper
nouns) do not necessarily satisfy this rule, because they are not derived by the above
phrase structure grammar. Thus, in predicate positions, both NPs and D’s can appear
without an article. However, DPs, which can only appear in argument positions, can
only be derived from lexical D’s, but not from lexical NPs.
To see this, consider the English nouns teacher, president and Einstein. Their
proposed lexical values are as follows:
Noun
teacher
president
Einstein
Category (1)
N
N
N
Structure (2)
–
[NP the president]
[D cf [NP the Einstein]]
0
It is easy to see that using these lexical entries and the grammar that was stipulated
above, the bare nominal teacher cannot be analyzed as an NP, D’ or DP; the bare
15
nominal president can be analyzed as NP, but not as D’ or DP; and the bare nominal
Einstein can be analyzed as D’ or DP, but not as NP. Consequently, teacher can never
appear bare in a sentence, president can appear bare only in predicate positions, and
Einstein can appear bare in any position.
The second question that was mentioned about bare predicate nominals in English concerns the correct analysis of compound predicates as in (37). First, following
Stowell (1991) let us observe that only a restricted class of adjectives and PPs can appear as adjuncts to such bare predicates. According to my informants’ judgements, the
following contrasts hold.
(40)
a. John is *(the) current president.
b. John is (the) former president.
(41) John is *(the) best/youngest president we have ever had.
In (40) we see that for some reason, the adjective former can appear with bare predicate nominals, but not the adjective current. However, both adjectives are OK with
predicate nominals with an overt definite article. In (41) we see that similarly to most
adjectives, superlatives like best or youngest do not appear with bare predicate nominals in English. I do not have an account of these different distributions, but only want
to point out that something quite similar is going on with proper names in English.
Consider the following contrastive examples.
(42)
a. Tall Mary has arrived, but short Mary is still missing.
b. ??Attentive Mary has arrived, but indifferent Mary is still missing.
(43)
a. Young Bush is definitely worse than old Bush.
b. *Youngest Bush is definitely worse than oldest Bush.
In (42) we see that also proper nouns exhibit a variation between acceptable and unacceptable adjectives, similarly to bare president-like nouns. In (43) we also see that
superlative adjectives are also unacceptable as modifiers of proper nouns. Although
the principles that govern the acceptability of the above constructions are not clear,
this similarity between proper nouns and bare predicative nouns in English suggests
that the treatment of both constructions using the same DP structure is linguistically
plausible.
6 Some notes on definiteness agreement in Hebrew
It is well-known that construct state nominals in Modern Hebrew show certain agreement phenomena between the definiteness of the head noun and the definiteness of the
whole DP. In a recent article, Danon (2001) convincingly argues that this sort of definiteness agreement (or definiteness “spreading”) in Hebrew is determined by purely
formal rules. Danon shows that the correlation between this sort of definiteness agreement and semantic definiteness is at best partial.
According to Danon, there are two main characteristics of “definiteness agreement” in construct states in Hebrew:
16
1. The accusative marker et is acceptable with construct state DPs if and only if the
head noun is marked as definite:
(44)
a. ra’iti *(et) oved ha-sifriya
I-sawACC worker the-library
”I saw the worker of the library”
b. ra’iti (*et) oved sifriya
I-sawACC worker library
”I saw a worker of a library”
2. Definiteness marking on adjectives is according to the marking of the head noun:
(45)
a. oved ha-sifriya *(ha-)gavoha caxak
worker the-library (the-)tall
laughed
”The tall worker of the library laughed”
b. oved sifriya (*ha-)gavoha caxak
worker library (the-)tall
laughed
”A tall worker of the library laughed”
What we see in these examples is that a DP such as oved sifriya, with no definiteness marking on the second nominal, behaves like any Hebrew nominal that is
unmarked for definiteness: it disallows the accusative et marking or definiteness marking on adjectives. By contrast, oved HA-sifriya, where the second nominal is marked
for definiteness, behaves like any Hebrew nominal that is marked for definiteness: it
requires accusative et marking and definiteness marking on adjectives.
Danon shows that under any known definition of the term “semantically (in)definite
DPs”, there is no clear correlation between this semantic classification of DPs and their
classification according to (in)definiteness spreading in Hebrew. Consider first the semantic/pragmatic view that takes “semantically definite” DPs to involve familiarity or
unique reference. Danon shows that certain DPs in Hebrew can be definite in terms
of definiteness agreement, without giving rise to unique reference. The following contrasts (not given by Danon himself) clearly show this point.
(46) Context:
etmol
neherag tosav sel maxane ha-plitim al-arub
yesterday was-killed resident of camp the-refugees Al-Arub
mi-yeri
koxot cahal
from-shooting forces IDF
”Yesterday, a resident of the refugee camp of Al-Arub was shot to death by IDF
soldiers”
a. gam ha-yom, neherag tosav maxane ha-plitim Al-Arub
also today, was-killed resident camp the-refugees Al-Arub
mi-yeri
koxot cahal
from-shooting forces IDF
”Also today, a resident of the refugee camp of Al-Arub was shot to death
by IDF soldiers”
17
b. gam ha-yom, neherag (*ha-)tosav
sel maxane ha-plitim
also today, was-killed (the-)resident of camp the-refugees
al-arub mi-yeri
koxot cahal
Al-Arub from-shooting forces IDF
”Also today, a/*the resident of the refugee camp of Al-Arub was shot to
death by IDF soldiers”
Sentence (46a) shows that the construct state DP tosav maxane ha-plitim al-arub refers
to an “unfamiliar” entity. By contrast, in (46b), with the free genitive sel, definiteness
marking does involve familiarity, as the unacceptability of the definite marker shows.
This contrast shows that definiteness agreement can appear without unique reference. Conversely, Danon mentions cases where indefiniteness agreement comes with
unique reference. For instance, the demonstrative yeled ze (boy-this, ”this boy”) does
not allow the marker et and can only appear with indefinite adjectives, but semantically
it involves unique reference, just like the demonstrative ha-yeled ha-ze (the-boy-thethis, ”this boy”), which is marked for definiteness. Both kinds of demonstratives also
cannot appear in existential yes (”there”) sentences. This is another reason to think that
definiteness agreement in Hebrew is not in direct correspondence with other notions
of definiteness.
There is another reason, which is not explicitly mentioned by Danon, to doubt
that definiteness agreement in Hebrew is directly related to other definiteness phenomena. The same pattern of definiteness agreement that is observed with construct state
nominals is also observed with construct state adjectives. Consider for instance the
following examples.
(47) pagasti is adom (*ha-)panim
met-I man red (*the-)face
“I met a red-faced man”
(48) pagasti et
ha-is
adom *(ha-)panim
met-I ACC the-man red *(the-)face
“I met the red-faced man”
These sentences exemplify that the construct state adom (ha-)panim (“red faced”) gets
its definiteness agreement feature from the definite marker ha on the second word.
This is similar to the behavior we saw above with construct state nominals. However,
definiteness marking on adjectives does not correspond to any clear semantic notion of
definiteness, and may therefore again indicate that definiteness spreading in Hebrew is
a general syntactic device that is only indirectly related to semantics.
7 Conclusion
In this paper I addressed some of the problems in the “core set” for this volume, and
tried to tease apart certain aspects of their grammar and interpretation within the framework of flexible semantics. It was argued that the interpretation of the specificity
marker a certain is at least partly determined by an economy-scope rule, which also
18
affects the grammaticality of there sentences with this specificity marker. The availability of different scopes for other nominals is also affected by syntactic patterns of
layers within the DP, where the major difference is between flexible nominals (the D’
and NP levels) and rigid nominals (the DP level). A secondary distinction, between
NPs and D’s, was argued to affect the behavior of bare definite predicates in English,
which like proper names, are argued to be lexical items with a complex structure. Definiteness marking in Hebrew, following Danon, was shown to be only partly related to
semantic definiteness.
These various factors, ranging from morphology (in Hebrew), through the syntax
of the DP, formal semantics and considerations of economy and pragmatics, all crucially take part in the grammar and interpretation of indefiniteness. I believe that the
flexible semantic framework, with its powerful but restrictive category shifting mechanism, helps to shed more light on this complex area.
Acknowledgments
I am grateful to Raffaella Bernardi, Gabi Danon, Danny Fox, Susan Rothstein, Bibiana Scelfo and
Roberto Zamparelli for judgements, remarks and discussion.
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Computer Science
Technion - Israel Institute of Technology
Haifa 32000
Israel
E-mail: [email protected]
WWW: http://www.cs.technion.ac.il/˜winter
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