Zur Semantik der Spezifizität
bei indefiniten DPs und Satztopiks
Cornelia Endriss
Institut für Kognitionswissenschaft
Universität Osnabrück
[email protected]
Kompaktseminar Universität Tübingen Juli/August 2008
Wednesday
Wednesday, 10-12 (s.t)
I A choice function approach based on data from St’at’imcets
Vera Hohaus: (Matthewson, 1999)
I An empirical argument against the choice function approaches – based on VP-ellipsis
Ok Soon Jung: (Schwarz, 2004)
Wednesday, 13-15.15 (s.t.)
I A domain restriction approach towards specificity
Christian Eisenreich: (Schwarzschild, 2002)
I Wrap up: choice function approaches and domain restriction approaches
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I. Choice Function Approaches
Choice Functions
I An indefinite is interpreted as a free restricted choice function (CF) variable (e.g. Egli and
von Heusinger, 1995; Reinhart, 1997; Winter, 1997; Kratzer, 1998; Matthewson, 1999).
I A choice function is a function that, when applied to a set, yields an element of this set. A
(simplified) choice function definition:
(1) [Choice Function 1]
CF(fhhe,ti,ei) ↔ ∀Xhe,ti[X 6= ∅ → f (X) ∈ X]
I The choice function f introduced by the indefinite is bound via existential closure. Reinhart
(1997) and Winter (1997) propose that existential closure is possible from any position.
(2) a. Every girl likes some horse.
b. ∀x[girl(x) → ∃f [CF (f ) ∧ likes(x, f (horse))]]
c. ∃f [CF (f ) ∧ ∀x[girl(x) → likes(x, f (horse))]]
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I. Choice Function Approaches
Motivation
I This approach is motivated by the mentioned problems of the other approaches, in
particular the assumption of island free QR.
I Even if island-free QR was possible, one would predict exceptional wide scope distributive
readings – contrary to fact.
(3) a. [three relatives of mine]i IF ti die THEN I will inherit a fortune]
b. three rel of mine(x) [die(x) → inherit fortune(I)]
I Aim: account for exceptional wide scope and the locality of distributivity.
I CF approach inspired by the unselective binding approaches of Heim (1982); Kamp and
Reyle (1993), where an indefinite introduces a free individual variable that can be bound at
some point.
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I. Choice Function Approaches
Donald Duck Problem
I However, binding of individual variables from some distance delivers wrong results in
certain configurations (see Heim 1982; Reinhart 1997):
(4) a. If we invite some philosopher, Max will be offended. (Reinhart, 1997)
b. ∃x[[philosopher(x) ∧ invite(we, x)] → offended(max)]
c. ∃x[philosopher(x) ∧ [invite(we, x) → offended(max)]]
I (4a) is represented as (4b), but should really be as (4c). This has been dubbed the Donald
Duck problem.
I In the CF approach, this problem is non-existent.
(5) a. If we invite some philosopher, Max will be offended.
b. ∃f [CF (f ) ∧ [invite(we, f (philosopher))] → offended(max)]
I Furthermore, the locality of distributivity is predicted.
(6) a. If three relatives of mine die I will inherit a fortune.
b. ∃f [CF(f ) ∧ [f (three relatives of mine)(die)] → inherit fortune(I)]
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I. Choice Function Approaches
Intermediate Scope Readings: (Alleged) Advantage
I Intermediate scope readings are always derivable (except when ruled out or dispreferred
by context).
(7) a. Every student has announced that he will leave the party immediately if some
lecturer shows up.
b. ∃f [CF(f ) ∧ ∀x[student(x) → announce(x, show up(f (lecturer))
→ leave party(x))]]
c. ∀x[student(x) → announce(x, ∃f [CF(f ) ∧ show up(f (lecturer))
→ leave party(x)])]
d. ∀x[student(x) → ∃f [CF(f ) ∧ announce(x, show up(f (lecturer))
→ leave party(x))]]
I Reinhart (1997) and Winter (1997) consider this to be an advantage of their approaches,
but Kratzer (1998) thinks it is a disadvantage and makes a different proposal (see below).
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I. Choice Function Approaches
Intermediate Scope Readings: Problem
I Recall that ISRs are sometimes not available even if contextually preferred (contra
Reinhart, 1997; Winter, 1997):
(8) (Last week, I went to a horse-race every day. It was funny:)
#
All horses won all races that took place on a day/some day/one day.
[∀ horse ∀ race ∃ day]
narrow scope
contextually excluded
[∀ horse ∃ day ∀ race]
intermediate scope
unavailable
[∃ day ∀ horse ∀ race]
widest scope
contextally excluded
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I. Choice Function Approaches
The Empty Set Problem
I Many people have pointed to the problems of the choice function approaches: (Geurts,
2000; von Stechow, 2000; Ruys, 1999).
I Reconsider the definition in (1).
I Here comes the empty set problem.
(9) a. A green horse ate all the bananas.
b. ∃f [CF(f ) ∧ ∀x[bananas(x) → ate(f (green horse), x)]]
I Formula (9b) would be true according to Definition 1 under the assumption that no green
horses exist and some other element satisfies the sentence predicate ate all the bananas,
i.e. (9a) comes out as equivalent to Someone/Something ate all the bananas.
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I. Choice Function Approaches
How to Overcome the Empty Set Problem
I There are different ways out. Geurts (2000):
(10) [Choice Function 2]
CF(fhhe,ti,ei) ↔ ∀Xhe,ti[[X 6= ∅ → f (X) ∈ X] ∧ [X = ∅ → f (X) = ∗]],
where the symbol * denotes a special object which does not satisfy any predicate,
i.e. the following holds for every n-ary predicate P : if ai = ∗ for any 1 ≤ i ≤ n,
then ha1, . . . , ani is not in the extension of P .
I Winter (1997) proposes lifting the type of the choice function:
(11) [Choice Function 3]
CF(fhhe,ti,hhe,ti,tii) ↔ ∀Xhe,ti[X 6= ∅ → ∃xe[X(x) ∧ f (X) = λPhe,ti.P (x)]] ∧
f (∅he,ti) = ∅hhe,ti,ti
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I. Choice Function Approaches
The Bound Pronoun Problem
I Another problem (Kratzer, 1998; Geurts, 2000):
(12) a. Every girl gave a flower to a boy she fancied.
b. ∃f [CF(f ) ∧ ∀x[girl(x) → gave flower(x, f (λy[boy(y) ∧ fancied(x, y)]))]]
I The derivable and thus predicted wide scope reading in (12b) does not exist. The choice
function approach overgenerates.
I When there are several girls x who fancy the same group of boys, the argument of f , i.e.
λy[boy(y) ∧ fancied(x, y)], is the same for each of these girls. Because f is a function,
it cannot yield different results when applied to the same argument. That is, if Miriam and
Anne happen to fancy exactly the same group of boys, say Peter, John, and Chris, this
representation states that both, Anne and Miriam, must have given a flower to the same
boy, e.g. Peter. But this is obviously not a distinct reading for the sentence.
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I. Choice Function Approaches
How to Overcome the Bound Pronoun Problem
I This problem can be overcome in Kratzer’s (1998) approach. Kratzer proposes that CFs
should be left free and interpreted by the context. However, CFs can be parameterized.
Parameterization is induced by functional dependent elements such as bound pronouns.
(See also (Matthewson, 1999) who proposes that CFs can only be closed from the
outermost position.)
(13) ∀x[girl(x) → gave flower(x, fx(λy[boy(y) ∧ fancied(x, y)]))]
I As f is now dependent on the quantifier every girl via the variable x, the choice function can
return different results for different values of x, even if the set λy[boy(y) ∧ fancied(x, y)]
is the same for these x.
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I. Choice Function Approaches
Support for Kratzer’s Approach
I Kratzer’s and Matthewson’s approaches are supported by the empirical fact that
intermediate scope readings are not always available.
(14) a. Each teacher overheard the rumor that some student of mine had been called before
the dean.
b. Each teacheri overheard the rumor that some student of hisi had been called before
the dean.
(15) a. ∀x[teacher(x) → overheard(x, sent to dean(f (student of mine))]
b. ∀x[teacher(x) → overheard(x, sent to dean(fx(student of x))]
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I. Choice Function Approaches
Further Support for Kratzer’s Approach
I There is another advantage of Kratzer’s approach:
(16) a. No mani hates a woman hei went to school with.
b. ∃f [CF(f ) ∧ ¬∃x[man(x) ∧ hates(x, fx(woman x went to school with))]]
I The truth conditions of (16b) are hopelessly weak and (16a) certainly does not have such
a weak reading, but all CF approaches predict such a reading, because the representation
in (16b) can be derived.
man
hates
•
woman
man
f
woman
•
•
−→
•
•
•
−→
•
&
%
•
sentence: (16a) false
Kompaktseminar Tübingen 2008
representation (16b): true
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I. Choice Function Approaches
Further Support for Kratzer’s Approach
I Again, Kratzer’s approach does better.
(17) a. No mani hates a/some woman hei went to school with.
b. ¬∃x[man(x) ∧ hates(x, fx(woman x went to school with))]
I As the function fx gets its value from the context it cannot denote just any function
whatsoever. The function must be somehow salient.
I And, indeed, (16a) can have a functional wide scope reading:
(18) Namely his first girlfriend from school.
I However, I doubt that salience is the best way to restrict the domain of functions:
(19) a. Every boy brought along some picture of him.
b. Strangely enough, it was a picture showing him eating noodle-soup.
I A more serious problem: Kratzer’s approach (or better: the choice function mechanism part
of her approach) cannot account for all kinds of intermediate scope readings (Chierchia,
2001; Schwarz, 2001).
(20) Exactly three students announced to leave the party if some lecturer shows up.
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I. Choice Function Approaches
A Problem for CF-Kratzer’s Approach
I This sentence has the following two intermediate readings:
– a functional wide scope reading: there is a function into lecturers such that the number of
students such that they announced to leave the party if their functionally corresponding
lecturer shows up is exactly three.
⇒ This reading is representable in a CF-framework:
(21) ∃f [CF(f ) ∧ |λx.student(x) ∧ announce(x, show(fx(lecturer)) → leave(x))| = 3]
– a genuine intermediate scope reading
(22) |λx.student(x) ∧ ∃y[lecturer(y) ∧ announce(x, show(y) → leave(x))]| = 3
The number of students such that there is a lecturer and they have announced to leave
the party if this lecturer shows up is exactly three.
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I. Choice Function Approaches
Problems
I The readings have different truth conditions:
student
has announced to leave if . . . shows up
lecturer
•
supervisor
•
•
supervisor
•
•
supervisor
•
•
−
−?−
→
•
−−−−−→
−−−−−→
−−−−−→
I The functional wide scope reading is true; the genuine intermediate scope reading is false.
⇒ there is a genuine intermediate scope reading that cannot be represented via the choice
function mechanism.
I Hence, most CF approaches overgenerate and predict intermediate scope readings that
do not exist. Others get rid of this problem, but then undergenerate and cannot account for
all kinds of intermediate scope readings.
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I. Choice Function Approaches
Intermediate Scope Readings vs. Functional Wide Scope Readings
I It is important to notice that there is a crucial difference between genuine ISRs and
functional wide scope readings:
(23) a. Every student will leave the party if some lecturer shows up.
b. Every student announced that she will leave the party if some lecturer shows up.
I Continuations differ in acceptability:
Continuation
OK after (23a)?
OK after (23b)?
Namely, Prof. Humpty
(statement of individual)
yes
yes
Her supervisor
(statement of functional dependence)
yes
yes
For Ann its Prof. Hob, for Mary Prof. Nob, . . .
(pair list)
no
yes
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I. Choice Function Approaches
Intermediate Scope Readings vs. Functional Wide Scope Readings
I Different continuations ⇒ different kinds of co-variation ⇒ different readings
Continuation
∃ lecturer takes. . .
statement of individual
wide scope
[∃ lecturer ∀ student]
pair list
ISRs
[∀ student ∃ lecturer]
statement of functional dependence
functional wide scope
[∃f→lecturer ∀ student]
I Function/pair-list distinction occurs with
• questions (Groenendijk and Stokhof, 1984; Chierchia, 1993),
• functional relative clauses (Sharvit, 1997),
• scope phenomena (Endriss, to appear; Ebert and Endriss, 2007).
I Note:
Functional wide scope readings are no (genuine) intermediate scope readings.
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I. Choice Function Approaches
Digression: Functional Readings vs. Pair-List Readings
I The function/pair-list distinction occurs with scope phenomena (cf. Schwarz, 2001) in the
same way as it occurs with e.g. questions (cf. Groenendijk and Stokhof, 1984; Chierchia,
1993) or with functional relative clauses (Sharvit, 1997).
I The following example is taken from (Krifka, 2001).
(24) Which dish did every guest make?
Which dish did most/few guests make?
(a) Pasta.
(a) Pasta.
(b) His favourite dish.
(b) Their favourite dish.
(c) Al, the pasta; Bill, the salad; . . .
(c) # Al, the pasta; Bill, the salad; . . .
I Pair-list answers are much more restricted than functional answers. Hence they must be
distinguished.
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I. Choice Function Approaches
Digression: Functional Wide Scope Readings and ISRs are independent
I ISRs + functional wide scope readings are independent (cf. Chierchia, 2001; Schwarz, 2001).
(25) Exactly two students announced that . . . if some lecturer shows up.
I Consider the intermediate scope reading in (a.) vs. the functional wide scope reading (b.):
a. The number of students st. there is a lecturer and the students announced that they
leave if this lecturer shows up is 2.
[exactly two ∃ lecturer IF]
b. There is a func. into lect. st. the number of students st. they announced that they leave
if the functionally corresponding lect. shows up is 2.
[∃f→lecturer exactly two IF]
I The readings have different truth conditions:
student
announced . . . if . . . shows up
lecturer
John
supervisor
−−−−−−→
supervisor
−−−−−−→
Prof. Humpty
−
−−
→
Prof. Hob
Ann
Mary
genuine intermediate scope reading (a.): false
Prof. Dumpty
functional wide scope reading (b.): true
⇒ ISRs cannot be reduced to functional wide scope readings and vice versa.
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I. Choice Function Approaches
Digression: Restrictions on Functions
I Functional wide scope readings should be dealt with by quantification over functions.
I ISRs/narrow scope readings are no functional readings and should be dealt with differently.
I But unrestricted quantification over functions leads to problems:
• narrow scope representations and functional wide scope representations are often truth-
conditionally equivalent (→ Skolemization), e.g.
(26) (PL Reading) ∀x[∃y[P (x, y)]] ≡ ∃f [∀x[P (x, f (x))]]
(Functional Reading)
• We cannot derive two distinct readings to reflect continuation possibilities:
(27) a. Every teenager tried to avoid a certain woman at the school party.
b. For Peter it was Mary, for Bill it was Paula, etc.
∀x[teenager(x) → ∃y[woman(y) ∧ tried to avoid(x, y))]]
c. Namely his mother.
∃f→woman[∀x[teenager(x) → tried to avoid(x, f (x))]]
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I. Choice Function Approaches
Digression: Restrictions on Functions
• Sometimes functional wide scope representations do not correspond to actual readings (cf.
Reniers, 1997; Schwarz, 2001; Chierchia, 2001).
(28) No X V some Y .
Consider all situations where each X does not V all Y s, e.g.
• Then there is always a function f that verifies the sentence:
(29) ∃f [¬∃x[V (x, f (x))]]
Kompaktseminar Tübingen 2008
≡
∀x[∃y[¬V (x, y)]]
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I. Choice Function Approaches
Digression: Restrictions on Functions
I Hence, we have to restrict the stock of functions that can plausibly be quantified over.
I In the literature, it has been proposed that only ‘natural’ (Chierchia, 1993; Jacobson, 1999),
‘salient’ (Sharvit, 1997; Kratzer, 1998, 2003) or ’nameable and informative’ (Endriss, to
appear) functions are involved in the case of functional readings.
I Crucially, an enumeration of ordered pairs is not regarded as ‘natural’, ’salient’, or
’nameable and informative’.
I Restriction to natural functions distinguishes the functional wide scope reading from the
narrow scope reading:
(30) ∃f→woman[f is natural ∧ [∀x[teenager(x) → tried to avoid(x, f (x))]]]
and the derivation of unavailable readings is suppressed.
(31) ∃f [f is natural ∧ [¬∃x[V (x, f (x))]]]
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I. Choice Function Approaches
Digression: Functional Wide Scope Readings are no ISRs
I Let’s go back to the contrast between (23a) and (23b).
a. Every student will leave the party if some lecturer shows up.
b. Every student announced that she will leave the party if some lecturer shows up.
I Recall: (23b) has a genuine ISR, while (23a) has not.
Continuation
Reading
Namely, Prof. Humpty
wide scope
[∃ lecturer ∀ student]
For Ann its Prof. Hob, . . .
intermediate scope
[∀ student ∃ lecturer]
His supervisor
functional wide scope
[∃f→lecturer ∀ student]
I Note:
Often people do not distinguish between ISRs and functional wide scope readings.
Only the availability of ISRs, but not of functional wide scope readings, is restricted.
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II. Domain Restriction Approaches
Extreme Domain Restriction
I The restrictor set of the indefinite is implicitly domain restricted.
I The speaker (or someone else) does not have a referent, but has a certain property in
mind.
I So, here again, there is a speaker-hearer asymmetry.
I This property can be so specific that it holds for only one individual. It denotes a singleton
set (e.g. Schwarzschild, 2002).
(32) a. If a friend of Dena comes to the party, Maria will leave immediately.
b. ∃x[friend of Denawith certain property (x) ∧ comes to party(x)] → leave(Maria)
I The indefinite is interpreted in situ and yet receives an apparent wide scope interpretation.
Furthermore, domain restriction is a mechanism we need anyway.
(33) a. Yesterday, when Maria came to school she saw that every teacher was wearing red
trousers.
b. every teacher 6≡ every teacher in the world
c. every teacher ≡ every teacher in Maria’s school/every teacher Maria met yesterday
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II. Domain Restriction Approaches
Extreme Domain Restriction
I Going back to the problematic examples from before:
(34) a. I bet that, after the next Olympic Games also, everyone will believe
that some athlete had taken illegal substances.
Namely the one that will have won most medals.
b. (Before the 100m race has actually started, someone says:)
All the journalists will try to get an interview with ONE athlete/a certain athlete
after the race.
Namely the winner of the race/the one that will have won.
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II. Domain Restriction Approaches
No Property in Mind
I One can construe examples of exceptional wide scope readings where the speaker neither
knows the intended referent nor a defining property of this referent (nor does anyone else).
(35) a. Imagine a group of people playing a (very strange) game. The rules are as follows:
if a certain word that is agreed upon by the group is uttered by one person,
everyone has to touch the floor with their hands. Furthermore, if another word
that has been agreed on is mentioned, everyone has to clap their hands. Then
Maria enters the scene and asks about the game. Max explains the rules. Then
Maria asks back:
b. (So we are playing several runs of the game, right? And for every run the following
holds:)
If some word that we agree on beforehand is uttered, we all have to touch the floor
as quickly as possible.
c. (Also es gibt verschiedene Runden ja?)
Und in jeder Runde ist es so:
wenn ein Wort, das vorher ausgemacht wurde, fällt, müssen wir alle so schnell wie
möglich den Boden berühren.
I Domain restriction approaches cannot account for the salient reading, indefinite seems to
take genuine wide scope.
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II. Domain Restriction Approaches
Partitives
I It is not always plausible to assume implicit domain restriction to a singleton set, e.g. with
partitives.
(36) If one of my relatives dies, I will inherit a fortune
I An exceptional wide scope reading is available.
I But partitives usually indicate that the restrictor set contains more elements than the ones
just talked about.
(37) a. One of my Mexican relatives rang me up, today.
b. A Mexican relative of mine rang me up, today.
I The partitive construction of (37a), but not the sentence with the ordinary indefinite in (37b)
implies that I have more than one relative.
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