Definiteness and Indefiniteness
Semantic structures
Utrecht, Feb 2009
Outline



Classical approach to the definite-indefinite contrast
Challenges
 Plural and mass definites
 Plural and mass indefinites?
 Presuppositionality
 Predicative uses of definites and indefinites
 Domain restriction
 Genericity
 Weak definites
 Scope
Summary
The definite-indefinite contrast
1)
The king cries
2)
A king cries
The definite-indefinite contrast
1)
The king cries
2)
A king cries
Russel (1905): indefinites are definite are quantified phrases such
as the DPs in 3 or 4:
3)
Every king cries
4)
No king cries
The definite-indefinite contrast
Meaning contribution of the definite and indefinite article
according to Russel:
5)
6)
The definite-indefinite contrast
7)
A king of France is coming to
Holland
8)
The king of France is coming to
Holland
The definite-indefinite contrast
7)
8)
A king of France is coming to
Holland
The king of France is coming to
Holland
=1 if
there is at least one king of France and
he is coming to Holland
=0 if
there is no king of France coming to
Holland
=1 if
there is exactly one king of France and
he is coming to Holland.
=0 if
there is a king of France and he is not
coming to Holland.
or
there is no king of France.
or
there are two or more kings of France
coming to Holland
The definite-indefinite contrast
7)
The king of France is coming to
Holland
=1 if
there is exactly one king of France and
he is coming to Holland.
=0 if
there is a king of France and he is not
coming to Holland.
=#
there is no king of France.
or
two or more kings of France are
coming to Holland.
The definite-indefinite contrast
Frege (1892) & Strawson (1950):

Definites phrases are not quantificational but referential

Existence and uniqueness are not part of the meaning
contribution of the definite article but presuppositions that its
use triggers
The definite-indefinite contrast
Meaning contribution of the definite and indefinite article
after Frege and Strawson:
9)
10)
When we use the indefinites, we assert the existence of an entity.
When we use the definites, we presuppose the existence of a
unique entity.
Plural and mass definites
Mass and plural expressions are usually thought to be similar.

Both, unlike singular count nouns, license cumulative inferences:
11)
If A is coffee and B is coffee → A and B together are coffee.
12)
If A are children and B are children→ A and B together are children.
13)
#If A is a child and B is a child→ A and B together are a child.
Plural and mass definites
Russell’ and Strawson´s theory in terms of uniqueness does
not apply straightaway to plural or mass definites:
14)
The children are in the park

The coffee is in the room
Plural and mass definites
Russell’ and Strawson´s theory in terms of uniqueness does
not apply straightaway to plural or mass definites:
14)
The children are in the park ≠
there is exactly one child that is in
the park.

The coffee is in the room ≠
there is exactly one portion of
coffee which is in the room.
Plural and mass definite
Inclusion of the maximality operator in the denotation of the
16)
Plural and mass definites
How maximality works I
CHILD
CHILDREN
Plural and mass definites
How maximality works II
THE CHILDREN
Plural and mass definite
14)
The children are in the park =
there is a maximal group of
children, of which all other
subgroups are part, that is in
the park.
15)
The coffee is in the room =
there is a maximal portion of
coffee, of which all other portions
are part, which is in the room.
Plural and mass indefinites?
16)
*I see a horses
17)
* I drank a water
Plural and mass indefinites?
16)
*I see a horses
17)
* I drank a water
But
18)
I see horses
19)
I drank water
Plural and mass indefinites?
An abstract indefinite determiner?
20)
21)
Presupositionality
Russel, Frege & Strawson :

The existence of entities referred to with a definite DPs is
presupposed rather than asserted.

The existence of entities referred to with an indefinite DPs is
asserted.
Presupositionality
But, would it be possible?
22)
a.
b.
To account for:
23)
.
I don’t know if he sent us any papers with mistakes in them. But if ...
a. there is a serious mistake in this paper, it has to be sent back.
(non-presupposed)
b. ?? a mistake in this paper is serious, it has to be sent back
(presupposed)
Presupositionality
Would it be possible?
24)
a.
b.
To account for:
25)
a. The king of France is wise
b. Our exhibition was visited by the king of France
(presupposed)
(non-presupposed?)
Predicative uses of definites and indefinites
26)
Antonia is a cat
27)
Antonia is the boss
How can a quantified expression (e.g. a cat) or a referential
expression (e.g. the boss) behave as a property (e.g. beautiful)?
How compatible are the main ingredients of the semantics
originally proposed for indefinites and definites (i.e. existential
quantification and presupposition of existence
and uniqueness) with these predicative uses?
Domain restriction
Definites
28)
Very unique definites
a. Neil went to the moon
b. The president of Bolivia made a new constitution
29)
Anaphoric definites
a. Can you pick up the children?
b. If you were married with and Argentinean you would have to learn Spanish… Well, the Argentinean
could also learn Dutch.
30)
Bridging
a. I found a watch under the tent. It was fine, only the battery was empty.
b. The wedding was nice although the bride was completely drank.
Other quantifiers
31)
a. Every child got a present
b. No child complained
Domain restriction
Determiners are represented as having a covert
“resource” argument, which could be the context, the set
of things we have talked about recently, etc.
When DPs are computed, the value of this argument
intersects with the overtly expressed restrictor of a DP
(the NP denotation), thus yielding a subset of it.
Problem: the relevance of this resource argument in the
interpretation of indefinites is not clear:
32)
a. Somebody didn’t turn off the light.
b. An indicator light is broken.
Generic uses of definites and indefinites
Generic sentences
33)
The department chair (always) is appointed by the dean.
34)
John (always) admires a tough administrator
The quantifier GEN
35)
[[GEN]] = λp. λq. every (normal) minimal situation s such that p(s) is part of a
minimal situation s’ such that q(s’)
Generic uses of definites and indefinites
With GEN
33)
The department chair (always) is appointed by the dean
=every situation s that is a minimal chair-appointment situation is such that the
unique chair in s is appointed by the unique dean in s.
34)
John (always) admires a tough administrator
=every minimal situation in which John encounters or thinks about a tough
administrator extends to a minimal situation in which he admires a tough
administrator.
Generic uses of definites and indefinites
Problems with GEN:
35)
Kind readings in definites
a. The domestic cat came to Australia with the first European settlers in the 18th
century.
b. The domestic cat evolved from the African wildcat.
36)
Kind readings in bare nouns
a. Domestic cats came to Australia with the first European settlers in the 18th
century.
b. Domestic cats evolved from the African wildcat.
Weak definites
37)
You should see the doctor.
38)
They serve vegetables from the farm and meat from the supermarket.
39)
They are reading the newspaper.
Weak definites
They do not refer uniquely and they resemble indefinites:
37)
You should see the doctor.
= You should see a doctor.
38)
They serve vegetables from the farm and meat from the supermarket.
=They serve vegetables from a farm and meat from a supermarket.
39)
They are reading the newspaper.
=They are reading a newspaper.
Scope
As quantifiers, indefinites and definites:

Should interact with negation, other quantifiers, intentional
operators, etc.

Should obey the same constrains as the other quantifiers do
(i.e. scope island constraints or locality conditions)
Scope
Definites seem to not to interact with quantifiers or at least they
.
always display wide scope:
40)
Someone loves everyone.
a. someone >everyone: there is someone who loves everyone
b. everyone>someone: for everyone there is someone who loves him
41)
Every man loves the woman.
a. the woman>everyone: there is the woman who every man loves
b. *everyone>the woman: for every man there is the woman he loves
Scope
Indefinites take wide scope in configurations where other
quantifiers cannot:
42)
John overheard the rumor that every student of mine was called before the dean.
43)
John overheard the rumor that a student of mine was called before the dean.
Scope
Bare nouns seem limited to narrow scope:
44)
Every victim is accusing a policeman
(indefinites)
a. a policeman >every victim: ‘there is a policeman that every victim is accusing’
b. every victim>a policeman: ‘for every victim there is a policeman that victim is
accusing’
45)
Every victim is accusing policemen
(bare plurals)
a. *policemen >every victim: ‘there are policemen that every victim is accusing’
b. every victim>a policeman: ‘for every victim there are policeman that victim is
accusing’
46)
Every gangster went to prison
(bare singulars)
a. *prison>every gangster: ‘there is a prison every gangster went to’
b. every gangster> prison: ‘ for every gagster there is a prison that gangster went to’
Scope
Weak definites are always scoped over as well.
47)
Every boxer was sent to the fitness center
a. The fitness center>Every boxer: ‘there is the fitness center every boxer was
sent to’
b. *Every boxer> the fitness center: ‘For every boxer there is the fitness center
that this boxer was sent to’
48)
Every boxer was sent to the hospital
a. ‘there is a hospital that every boxer was sent to’
b. Every boxer> the hospital: ‘for every boxer there is the hospital that this boxer
was sent to’
Summary
Standard analysis of the definite article and the indefinite article:
49)
50)



Definites (e.g. the book) are expressions that denote individuals. When we use them, we
presuppose the existence and uniqueness of a maximal set of entities.
Indefinites (e.g. a book) are existentially quantified expressions. When we use them, we
assert the existence of an entity.
Problems for this account

Presuppositional readings of indefinites and non-presuppositional readings of definites.

When definites and indefinites are used to attribute properties to individuals rather than
to make reference to individuals.

Domain restrictions play a role when we use definites but not clearly when we uses
indefinites

Generic uses of definite and indefinites

Weakly referential uses of definites

Scopal misbehaviors
Coffee!!!!!!