Ling216: Pragmatics II
Maribel Romero
May 11/18, 2010
! Kadmon's DRT analysis of the implicature of n NP in ARGUMENT position.
X is a set discourse referent (cf. a plural individual).
Numerals in DRT
Idea: (i) The NP is translated as a free formula and ! comes from discourse, as usual.
(ii) Three is just an adjective predicated of the relevant variable: |variable| = 3
(Kadmon chapter 3)
! Data on numeral NPs:
• BARE NUMERAL NPS of shape n NP:
In ARGUMENT position, they sometimes have an "at least" reading and sometimes an
"exactly" reading: (1)-(2). As we saw, the first one is the pure semantic interpretation
and the second reading results from a conversational implicature.
In PREDICATE position, they only have the "exactly" reading: (3) cannot mean that
there are at least 4 women and 1 man among the guests; and (4) is definitely false.
(1)
(2)
Lisa has three cats.
Lisa has three cats -in fact, she has six.
(3)
(4)
The guests are four women and one man.
# Bill, John and Adam are two boys.
(8)
Three cats are pink.
(9)
n NP:
Literal meaning "there is a set X consisting of pink cats whose cardinatily equals 3".
X
cats(X)
X are pink
|X| = 3
(10)
n NP:
Literal meaning "there is a set X consisting of pink cats whose cardinatily equals 3".
Plus implicature "X contains all the pink cats" or "there is no pink cat other than the
ones in X".
X
cats(X)
X are pink
|X| = 3
" Issue 1: Why doesn't n NP have the "at least" reading in predicate position? In other
words, how can we make the "exactly" reading in predicate position be their pure
semantic interpretation, while maintaining the usual analysis for argument position?
• MODIFIED NUMERAL NPS of shape at least n NP:
They only have the "at least" reading, both in argument and in predicate position.
(5)
Lisa has at least three cats.
(6)
The guests are at least four women and one man.
" Issue 2: Why doesn't at least n NP give rise to the implicature "exactly n" in
argument position?
" Issue 3: What are the formal representations (in DRT) of n NP and at least n NP that
derive the observed differences?
! Classical (Horn's) analysis of the conversational implicature in (1):
(7)
Lisa has three cats.
! ¬(Lisa has four cats)
! ¬(Lisa has five cats)
! ...
That is: ! ¬ (Lisa does has more than three cats)
QUESTION 1: Formulate the implicature in DRT.
! Kadmon's DRT analysis of the lack of implicature of at least n NP in ARGUMENT
position.
Idea: (i) The NP is translated as a free formula and ! comes from discourse, as usual.
(ii) At least three is just an adjective predicated of the relevant variable:
|variable| " 3
(11)
at least n NP:
Literal meaning "there is a set X consisting of pink cats whose cardinality is greater or
equal to 3".
X
cats(X)
X are pink
|X| " 3
QUESTION 2: Add to (11) the same implicature that we added in (10). What is the result?
2
! Anaphora to n NP and to at least n NP:
(12)
Eleven kids walked into the room. They were tired.
(13)
At least eleven kids walked into the room. They were tired.
QUESTION 3: Describe the sets that they refers to in (12) and in (13).
! Kadmon's DRT analysis of the lack of implicature of n NP in PREDICATE position.
Idea: The indefinite NP denotes a property predicated of the subject. No discourse
referent is introduced by the indefinite.
(14)
Bill, John and Adam are three boys.
{b,j,a}
boys({b,j,a})
|{b,j,a}| = 3
3