CHAPTER NINE: PREDICATES AND PROPERTIES
9.1. Predicates.
In this section we will discuss an alternative analysis of be along the lines of Partee 1987 and
an alternative analysis of seek along the lines of Zimmermann 1990, and in fact bring the two
together. I will follow the spirit rather than the details of their analyses.
We saw before that Montague's analysis assumes that be is unambiguously the be of identity,
and we saw that the type shifting theory we assumed gets us automatically the predicative
and the subsective readings of be as well. We also saw that Montague's analysis also has
problematic aspects.
In the first place, copula constructions allow expressions of all sorts of types in predicative
position ( i.e. as the complement of the copula), and in predicative position these expressions
can be freely combined, e.g.
(1) John is a linguistics professor and proud of it.
Secondly, the analysis predicts that all kinds of DPs should be fine in predicative position,
and that doesn't seem to be the case. Definite and indefinite DPs are ok:
(2) a. John is the president.
b. John is a linguist.
c. The guests are three boys and two girls.
But quantificational DPs do not seem to be as good.
More precisely, when quantificational DPs allow an interpretation as a plural definite DP
they are ok:
(3) The boys are all the guests.
Many people judge an DP like every boy to be not very good in predicative position. Other
people don't object to it as much:
(4) John is every professor.
However, there is evidence that DPs like every professor can also in other contexts be
interpreted as plural definites rather than as true quantifiers. In a theory of plurality we
assume that plural definites are interpreted as plural objects in type e. This can explain why
(3) is ok, and why (4) is not as problematic for some people. However, an expression like
each professor doesn't seem to allow that kind of reinterpretation, and (5) is regarded as bad
by everybody:
(5) #John is each professor.
The same for both professors in (6) on the interpretation where both is a determiner:
(6) #John and Bill are both professors
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Presumably a similar explanation can deal with the contrast between (7a), which fine, and
(7b), which is not:
(7) a. John is everything I have always wanted.
b. #John is each thing I have always wanted.
The general observation is that definite and indefinite DPs are ok in predicative position, but
quantificational DPs are not.
Partee captures these facts in a theory which assumes, like Montague, that be is not
ambiguous. Unlike Montague, she assumes that the basic meaning of be is not the be of
identity, but the be of predication.
We will change the analysis of indefinite determiners here.
We will assume that the indefinite article, the determiner a, is semantically vacuous: it is
interpreted as the identity function at the type of predicates:
we add:
D  <<e,t>,<e,t>>
Expression:
a
Category:
D
Interpretation: λP.P
Thus we get:
< DP , BOY >
D
│
a
NP
│
boy
Thus we assume that the DP a boy is of type <e,t> and has the same meaning as the noun
boy: BOY
Partee actually assumes that also a boy is interpreted as an expression of type e. For our
purposes it is better to assume that a boy starts out at type <e,t>. Making the indefinite
article semantically vacuous fits the fact that languages that do have an indefinite article
differ in whether they require the indefinite article in predicative position. Even in English,
which usually wants the indefinite article there, you find cases where you don't need it:
(8)
John is professor of linguistics at Cornell University.
So we get three types of DPs:
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< DP , σ(BOY) >
D
│
the
of type e
NP
│
boy
< DP , BOY >
D
│
a
of type <e,t>
NP
│
boy
< DP , λP.x[BOY(x)  P(x)] > of type <<e,t>,t>
D
NP
│
│
every boy
Next we assume that there is a syntactic category PRED for predicates, and we assume that
expressions from the right category can become predicates. This is a rule of predicate
formation. We add the following operation:
α if α  EXP<e,t>
PRED[α] =
LIFT[α], if LIFT[α]  EXP<e,t>
undefined otherwise.
Predication (for DPs):
PRED[DP, DP'] = <PRED , PRED[DP']>
│
DP
We assume that the copula be is semantically vacuous:
Expression: be
Category:
I
Interpretation: λP.P
This fits the fact that there are many languages in which predicative constructions do not
have the copula, and also the fact that other predicative constructions in English do not have
the copula. I.e. we can use those facts as an indication to not tie predication to the be itself.
Now we add two lifting rules to the type shifting theory:
Following Partee:
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LIFT: e  <e,t>
LIFT[α] = λx.x=α
Thus, the be of identity is part of the type shifting theory here: we can lift an individual to the
property of being that individual.
And following Partee 1987 and Bittner 199?:
LIFT: <e,t>  <<e,t>,t>
LIFT[α] = λP.x[α(x)  P(x)]
If we lift j from e to <e,t>, we get: λx.x=j.
If we lift this on to <<e,t>,t>, we get:
λP.x[λx.x=j(x)  P(x)] =
λP.x[x=j  P(x)] =
λP.P(j)
If we lift the interpretation of a boy, BOY, from <e,t> to <<e,t>,t> we get:
λP.x[BOY(x)  P(x)]
We see that in both cases we get the right interpretation.
A warning flag here: generating indefinites at type <e,t> and lifting them to <<e,t>,t> with
LIFT works fine for the examples that I discuss here, but is in general problematic (in
particular, for indefinite noun phrases like no girl, at most three girls. The analysis
developed here, while inspired by Partee 1987, is not Partee's. The problems are discussed
and the analysis is defended in Landman 2001, 2003.
We will assume that in predicative position DPs are interpreted at type <e,t>, while in
argument position they are interpreted at type e or <<e,t>,t>.
This means that we assume that if a verb of type <e,t> applies to an indefinite subject of type
<e,t>, we cannot apply the modification type shifting rule to the verb, but we can only
resolve the type mismatch by applying the argument lifting rule to the subject. We can
enforce this, for instance, by assuming that:
IP maps to t, but not <e,t>.
VP maps to <e,t>, but not <e,<e,t>>
A little excursus into plurality shows another interesting feature of this approach.
Kadmon 1987 observes that while plural indefinites in argument position have, semantically
an at least interpretation (with the exactly effect being pragmatic), in predicative position
plural indefinite DPs have an exactly interpretation.
(9) a. If you are a widow with two children, you get an
allowance.
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(9) shows that two children (which is in argument position) does not mean exactly two
children, but at least two children.
Often there is an exactly implicature associated with such DPs, but that can be canceled, as
can be seen in the continuation (10) of (9):
(9) b. MARY has two children, in fact she has three. So she gets an allowance.
The crucial point is that the in fact statement does not correct the previous statement, but
cancels the implicature.
Compare this with (10), where two children is in predicative position:
(10) Mary's guests were two children.
Here two children means exactly two children. This can be seen in (11):
(11)
Mary's guests were two children. In fact, they were three children.
Here the second statement clearly seems to correct the first, indicating that indeed two
children has an exactly reading.
Assuming that an indefinite DP like a boy starts out at type <e,t>, it is plausible to make that
assumption also for plural indefinites like two children. Quantifying over plural objects, the
plausible interpretation of two children at type <e,t> is:
λp.CHILDREN(p)  │p│=2
the property that a plurality of children has if its cardinality is 3.
If we apply this to a subject DP like Mary's guests, we get in fact the exactly interpretation:
the statement that Mary's guests were children and that there were two of them.
To make two children an argument DP we have to raise it to type <<e,t>,t> and we get:
λP.p[CHILDREN(p)  │p│=2  P(p)]
the set of properties that some plurality of exactly two children has.
If WALK is one of these properties then the statement is:
p[CHILDREN(p)  │p│=2  WALK(p)]
There is a plurality of two children that walk.
This is perfectly compatible with there being more children that walk. Hence the theory
predicts that semantically cardinality DPs have an exactly reading in predicative position and
an at least reading in argument position.
Let us now look at the predictions of the theory.
We produce be a boy:
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< I'
,
I PRED
│
│
be DP
D
│
a
A
λP.P
NP
│
boy
>
PRED
│
A
λP.P
BOY
APPLY[λP.P,BOY] = BOY
PRED[BOY] = BOY
So we get:
< I'
, BOY >
I PRED
│
│
be DP
D
│
a
NP
│
boy
We produce be john:
< I'
I PRED
│
│
be DP
│
john
,
A
λP.P
>
PRED
│
JOHN
PRED[JOHN] = λx.x=JOHN
APPLY[λP.P,λx.x=JOHN] = λx.x=JOHN
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So we get:
< I'
, λx.x=JOHN >
I PRED
│
│
be DP
│
john
We see then that for definites and indefinites we make exactly the same predictions as
Montague's theory. The difference comes in with predicates with a quantificational
complement like be every professor. Every professor starts out at the level of generalized
quantifiers <<e,t>,t>. Predicative DPs need to be of type <e,t>, hence we could only form be
every professor if there were a type shifting rule lowering the generalized quantifier meaning
to the predicate meaning. But we have no such rule. Hence we predict that we cannot
interpret be every professor (unless we are able to give every professor a plural interpretation
at type e).
However, things are not as simple as this. We are working now in a theory where we have
storage. Let us see what happens if we store every professor:
<
DP
│
john
IP
A>
I'
I
│
is
λ,<{<n,A[,P]>},n>
PRED
│
DPn
xn

A,{<n,A[,P]>}
A,{<n,A[,P]>}
A
PROFESSOR
JOHN
D
NP
λP.P PRED,{<n,A[,P]>}
│
│
│
every professor
xn,{<n,A[,P]>}
PRED[xn] = λx.x=xn
APPLY[λP.P,λx.x=xn] = λx.x=xn
APPLY[λx.x=xn,JOHN] = JOHN=xn
λ[xn,JOHN=xn] = λx.JOHN=x
APPLY[λx.JOHN=x, λP.u[PROFESSOR(u)  P(u)]]
= LIFT[λx.JOHN=x](λP.u[PROFESSOR(u)  P(u)])
= λT.T(λx.x=JOHN)(λP.u[PROFESSOR(u)  P(u)])
= u[PROFESSOR(u)  u=JOHN]
We see that with quantifier storage, the theory doesn't do what it is supposed to do: in fact, it
makes exactly the same predictions as Montague's theory.
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A solution would be to forbid quantifying in from predicative position. This means that we
assume that predicative position is a scope island.
The problem is that there is no evidence that predicates are scope islands. In particular, if a
DP is embedded in the predicate, we can scope out, as in (12):
(12) Somebody is the mother of each of these kids.
(12) is ambiguous: it either means that somebody is the mother of all of the kids, or it means
that for each of these kids, somebody is its mother. The latter is a wide scope reading for
each of these kids, which we can't get if the predicate is a scope island. So we do not want to
make predicates scope islands.
Compare (12) with (5):
(5) #John is each professor.
The crucial difference between (12) and (5) is that in (12) the quantificational DP is in
argument position, while in (5) it is in predicate position. The correct observation then
seems to be that we can scope DPs out of argument positions in predicates, but we cannot
scope out of predicative position itself: a DP which itself forms a predicate cannot be
scoped:
Argument DPs can be scoped.
Predicative DPs cannot be scoped.
Technically, we can incorporate this in the theory by the following condition:
Scope condition on predication:
PRED, S if for no α: <n,α>  S
│
x n, S
This means that the DP to which predication applies cannot itself be semantically stored,
though an embedded argument may. This means, then, that we can scope out of predicative
DPs, but we cannot scope predicative DPs themselves.
An alternative line is followed in Landman 2003. There the condition is a condition on type
lifting variables: the variable constraint: variables cannot be lifted from type e to type
<e,t>. This too will block the bottom step of this derivation.
This theory does not deal with examples like the ones in (13):
(13) a. This house has been every color.
b. Olivier has been every Shakespearean king.
I will discuss those after the discussion of seek.
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9.2. Properties.
As we have seen, Zimmermann argues that while indefinite and definite DPs can get a de
dicto interpretation as the complement of seek, quantificational DPs do not:
(14) a. John seeks the president.
b. John seeks a unicorn.
c. John seeks two unicorns.
v.
(15) a. John seeks every unicorn.
b. John seeks each unicorn.
c. John seeks most unicorns.
Let us investigate this matter in a bit more depth here.
First we want to establish that object noun phrases in the infinitive complement of try can
have a de dicto reading, whether or not they are quantificational.
First look at the examples in (16):
(16) a. While there were no mistakes in the paper, the copy editor was trying to remove a
mistake.
b. While there were no mistakes in the paper, the copy editor was trying to make the
paper be without mistakes.
c. While there were no mistakes in the paper, the copy editor was trying to remove each
mistake.
Anybody who knows this notorious copy editor, readily gets the de dicto reading of (16a),
the reading on which (16a) is perfectly coherent: the copy editor is trying to do something
which is not gonna be successful. (16b) similarly has a perfectly coherent very similar
reading.
The important question is: does (16c) have a de dicto reading where it is (roughly)
equivalent to (16b), or does it only have a funny de re reading where the existence
presupposition of each clashes with the previous context?
And the answer seems to be that (16c) does have a reading equivalent to (16b), a de dicto
reading for each mistake.
Next we look at try to find:
(17) a. While there were no mistakes in the paper, the copy editor was trying to find a
mistake.
b. While there were no mistakes in the paper, the copy editor was trying to make the
paper be without undiscovered mistakes.
c. While there were no mistakes in the paper, the copy editor was trying to find each
mistake.
The facts seem to be the same here as for the cases in (16):
both the indefinite in (17a) and the quantificational DP in (17c) have a de dicto reading, i.e.
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(17c) has a reading on which it is equivalent to (17b).
Now substitute seek for try to find in (17):
(18) a. While there were no mistakes in the paper, the copy editor was seeking a mistake.
b. While there were no mistakes in the paper, the copy editor was trying to make the
paper be without undiscovered mistakes.
c. While there were no mistakes in the paper, the copy editor was seeking each mistake.
This substitution makes no difference for (18a), but when we look at (18c) we suddenly do
feel a difference. (18c) does not seem to have a reading which is equivalent to (18b). Thus,
while each mistake can have a de dicto reading under try to find, it doesn't have a de dicto
reading under seek.
Zimmermann assumes that intensional verbs like seek take a property (type <s,<e,t>>) as
their object. Thus we assume the following lexical item for seek:
V  <<s,<e,t>>,<e,t>>
Lexical Item: seek
Category:
V
Interpretation: SEEK  CON<<s,<e,t>>,<e,t>>
We now have to add one more type shifting rule to the theory.
Note that we already have:
LIFT: a  <s,a>
LIFT[α] = α
and hence:
LIFT: <e,t>  <s,<e,t>>
LIFT[P] = P
We add:
LIFT:e  <s,<e,t>>
LIFT[α] = λx.x=α
We add a new *-notation:
SEEK* = λyλx.SEEK(x,λz.z=y)
the relation that two individuals x and y stand in if x stands in the seek relation to the
property of being identical to y.
We get the following derivations:
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Mary seeks John.
SEEK*(MARY,JOHN)
Namely:
APPLY[SEEK,JOHN]
= SEEK(LIFT[JOHN])
= SEEK(λz.z=JOHN).
= λy.SEEK(λz.z=y)(JOHN)
= λyλx.SEEK(x,λz.z=y)(JOHN)
= SEEK*(JOHN)
[JOHN is rigid]
[*-notation]
APPLY[SEEK*(JOHN),MARY]
= SEEK*(MARY,JOHN)
Mary seeks the president.
SEEK(MARY,λz.z=σ(P))
This time, σ(P) is not rigid, hence, we cannot do backward λ-conversion.
Mary seeks a unicorn.
SEEK(MARY,UNICORN)
Namely:
APPLY[λP.P,UNICORN] = UNICORN of type <e,t>
APPLY[SEEK,UNICORN]
= SEEK(LIFT[UNICORN])
= SEEK(UNICORN)
APPLY[SEEK(UNICORN),MARY]
= SEEK(MARY,UNICORN)
Mary seeks two unicorns.
SEEK(MARY,λp.UNICORNS(p)  │p│=2)
Mary seeks every unicorn.
u[UNICORN(u)  SEEK*(MARY,u)]
As before, every unicorn is of type <<e,t>,t>. SEEK wants an argument of type <s,<e,t>>.
We do not have a type shifting rule shifting the meaning of every unicorn to <<e,t>,t>, hence
APPLY is not defined.
This much is the same as the case of predication.
The difference with predication is that in the case of seek the sentence is not uninterpretable,
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rather we get a wide scope reading. This suggests then that we should assume that the
complement position of seek is an argument position, and hence that storage is possible in
that position.
We derive:
APPLY[SEEK,xn]
= SEEK*(xn)
[xn is rigid, *-notation]
APPLY[SEEK*(xn),MARY]
= SEEK*(MARY,xn)
[λ xn,SEEK*(MARY,xn)]
= λx.SEEK*(MARY,x)
APPLY[λx.SEEK*(MARY,x),λP.u[UNICORN(u)  P(u)]]
= u[UNICORN(u)  SEEK*(MARY,u)]
We correctly predict that quantificational DPs can only have a de re reading.
We find then that types e, <<e,t>,t> and <s,<e,t>> for DPs correspond to argument positions,
while <e,t> does not.
Theoretical motivation for this can be found in Gennaro Chierchia's property theory (see
Chierchia 198?, Chierchia and Turner 198?).
Chierchia assumes that the domain of individuals e is sorted into three subdomains: the
domain of real individuals, in, the domain of properties, pr, and the domain of propositions,
ps, all of which are taken as primitive entities (and hence properties and propositions are
more intensional than they are in intensional logic).
Properties and propositions in domain e are complete entities in their own right, in particular,
they are not functions.
Chierchia assumes a predication operation  which turns a complete property into a
propositional function, a function from individuals into propositions of type <e,ps>.
While a property p is regarded as a complete entity in the domain e, P is an incomplete
entity, a function, which needs an argument to be complete, saturated.
Besides the predication operation : pr  <e,ps>, there is a nominalization operation

:<e,ps>  pr, which turns an unsaturated predicate into a saturated, complete property.
A transitive verb like kiss is interpreted as a function in <e,pr>, it needs an object m to form
a complete property KISS(m).
Inflection involves predication: it turns a property like KISS(m) into a predicate KISS(m)
which needs to be saturated by an argument.
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In this theory, a non-inflected infinitival like to kiss Mary denotes a property KISS(m) in pr,
while an inflected predicate kisses Mary denotes a predicate KISS(m) in <e,ps>.
Similarly, the complement that Mary walks will denote a proposition in ps.
In Chierchia's theory then we can assume that argument DPs are of type e (or <<e,ps>,ps>),
while predicative DPs are of type <e,ps>. The complement of seek in Chierchia's theory, will
be a property of type pr, but not a predicate.
I will not go into the details of Chierchia's theory here, and I will not make the intensional
theory developed here more intensional in the way Chierchia does (though there is good
reason to do so).
However, if we think about which types in our intensional logic correspond to the types that
Chierchia introduces, we see the following:
type e corresponds to Chierchia's in.
type <e,t> corresponds to Chierchia's <e,ps>
type <s,t> corresponds to Chierchia's ps
type <s,<e,t>> corresponds to Chierchia's pr
Given this correspondence it makes perfect sense to regard the intensional types <s,t> and
<s,<e,t>> as argument positions, as opposed to type <e,t>. That is, even though these types
are function types in our intensional logic, the grammar does not think of the entities of these
types as functions, but rather treats them like arguments, complete entities.
The fact that we can scope the complement of seek is itself one argument in favor of this.
Similar arguments for type <s,t> we have seen before. The rules of generalized connectives
do not treat this type as a function type, but as an argument type, like type e. Sentence (19a)
is not equivalent to (19b) but to (19c):
(19) a. John believes that Mary comes or that Mary doesn't come.
b. John believes that Mary comes or doesn't come.
c. John believes that Mary comes or John believes that Mary doesn't come.
This is predicted if conjunction of two propositions cannot take place at type <s,t> itself, but
has to take place at type <<<s,t>,t>,t>, just as in the case of type e.
Similar facts are seen for properties. (20a) is not equivalent to (20b) but to (20c):
(20) a. John tries to walk or not to walk.
b. John tries to smoke or not smoke.
c. John tries to smoke or John tries not to walk.
More relevantly, property conjunction at type <s,<e,t>> would give disastrous results for
(21a): (21a) is not equivalent to (21b) but to (21c):
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(21) a. John seeks a unicorn and a griffin.
b. John seeks something which is both a unicorn and a griffin.
c. John seeks a unicorn and John seeks a griffin.
Again, assuming that type <s,<e,t>> is treated as a primitive type, like type e, as far as
generalized connectives are concerned predicts this.
Yet another semantic argument concerns at least/exactly readings of numerical DPs. Two
unicorns in (22a) clearly has as much an at least reading as it has in other argument
positions:
(22) a. John seeks three unicorns.
Now, here we get a semantic question. We interpret this as follows:
(22) b. SEEK(JOHN,λs.UNICORNS(s)  │s│=3)
Now, before, we saw that with this property in predicative position, we get an exactly
reading. Why don't we then get an exactly reading here? The answer is that we get the
exactly reading because of the meaning of the predicate be three unicorns. We haven't in
fact specified the meaning of seek, so whether we get an exactly reading or an at least
reading depends much on that.
We can clarify this issue by relating the meaning of seek to that of try to find. Obviously, we
are not analyzing seek as try to find; but we can still relate their meanings.
While I have avoided infinitives, and hence try to find, the proposals for the semantics of
(23a) in the literature are (23b), where TRY takes a property complement and (23c), where
TRY takes a propositional complement which encodes the subject control:
(23) a. John tries to find a unicorn.
b. TRY(JOHN,λx.y[UNICORN(y)  FIND(x,y)])
c. TRY(JOHN,y[UNICORN(y)  FIND(JOHN,y)])
d. John seeks a unicorn.
Let us assume that (23a) and (23d) have the same meaning. This means that:
(b)
or
(c)
SEEK(JOHN,UNICORN) = TRY(JOHN,λx.y[UNICORN(y)  FIND(x,y)])
SEEK(JOHN,UNICORN) = TRY(JOHN,y[UNICORN(y)  FIND(JOHN,y)])
And this means that we can define seek in terms of try to find as follows:
(b)
or
(c)
SEEK = λPλx.TRY(x,λx.y[P(y)  FIND(x,y)])
SEEK = λPλx.TRY(x,y[P(y)  FIND(x,y)])
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This definition will indeed make (23a) and (23d) equivalent. In fact, this equivalence will
hold generally for indefinite and definite objects, i.e. also:
(24) a. John seeks two unicorns.
b. John tries to find two unicorns.
This means that we do predict now that definite and indefinite objects of seek behave
semantically as if they are in argument position, because the interpretation of [seek DP] is
the same as that of [try to find DP], and in the latter, the DP is just in argument position.
Hence, the fact that (25a) entails (25b) (= at least-reading) follows from the fact that (26a)
entails (26b), and the latter follows from the semantics of try and the fact that the object of
the verb in the infinitive is an argument.
(25) a. John sought three unicorns.
b. John sought two unicorns.
(26) a. John tried to find three unicorns.
b. John tried to find two unicorns.
Note that all of this does not mean that (27a) and (27b) are equivalent:
(27) a. John seeks each unicorn.
b. John tries to find each unicorn.
The object position of find is a normal argument position. Hence we predict that (27b) can
have a de dicto or a de re reading. The object position of (27a) is a property position.
Quantificational DPs do not have a property interpretation, hence (27a) does not have a de
dicto reading. For the reasons given earlier, we are allowing the storage mechanism to apply
to quantificational DPs in the complement of seek, so (27a) does get a de re reading.
The fact that we can define seek with help of try to find has no influence on that.
3.3. Role interpretations.
Let us now come back to predication and sentences like the examples in (28):
(28) a. This house has been every color.
b. Olivier has been every Shakespearean King.
c. In Kind Hearts and Coronets, Alec Guinness is every noble victim.
d. The prime minister is every minister in the Government.
These sentences are a problem both for Montague's be-of- identity approach and for the beof-predication approach. The problem for Montague's approach is that these sentences just
do not seem to express identity statements at all. (28a) does not mean that this house has
been identical to every color it expresses that it has had every color. (28c) does not express
the identity of Alec ss with any noble victim, rather it expresses that Alec Guinness plays all
of them. (28d) expresses that the prime minister fills all minister's positions. That these are
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259
not identity statements has been argued extensively by Doron 1983.
[(28d) illustrates a problem of politically relevant example sentences. Originally, this
example has Rabin, instead of the prime minister, and it was an ironic comment on how at
some point the problem of vacancies in the then Government was addressed. But irony does
not survive untouched if disaster follows. That's why the example is changed. The present
example should be thought of as separated from its Israeli background, since for the ones that
followed irony is too good.]
The problem for the predicational theory is that we are dealing with a quantificational DP in
predicative position, which cannot be interpreted there, and which cannot be scoped out,
hence these sentences are predicted to be uninterpretable. Yet they are ok.
We see in these cases that the relation between the subject and each of the instances of the
object rather varies: in (28a) the relation is has the color of; in (28c) it is plays the
character of; in (28d) it is fills the position of; and no doubt in other cases, we find other
relations.
To subsume all these cases let us introduce a new relational constant INSTANTIATE and let
us assume that the meaning of INSTANTIATE is context-dependent: the context will
determine the exact nature of the relation INSTANTIATE.
The question we have to address is: what relation is INSTANTIATE? The key to this is
given by the cases where be is interpreted as plays. Look at the following inference, from
(29a) and (29b) to (29c):
(29) a. Derek Jacobi is Lewis Carroll.
b. Lewis Carroll is Charles Dodgson.
c. Derek Jacobi is Charles Dodgson.
Let us assume that (29b) has its normal identity interpretation, but (29a) and (29c) are
statements about a play that is put on about the live of Charles Dodgson. (29a) means that in
the play, Derek Jacobi plays Lewis Carroll. The point is that it is a rather important feature
of the play that Lewis Carroll and Charles Dodgson are played by different actors. hence it
does not follow that in the play, Derek Jacobi is Charles Dodgson. Thus, when (29a) and
(29c) both have the play-interpretation, the inference from (29a) and (29b) to (29c) is not
valid. This shows that in this case we are in fact dealing with an intensional context. That
this is so can be seen also from the following fact:
(30) a. Alec Guinness is five noble victims.
b. Alec Guinness is four noble victims.
On the play-interpretation, the inference from (30a) to (30b) seems to be unproblematic.
Hence in this context five noble victims has an at least-interpretation, rather than an exactly
interpretation.
The two together suggest strongly that the complement of be is not a predicative position
here, but the argument of an intensional operator.
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260
In other words, in the cases we have seen before, predication forms a predicate (of type
<e,t>); in the cases that we look at here, a property is formed.
We assume, following Partee, that what is involved in play-interpretations is reference to
roles, and we assume that roles are analyzed as properties. In the present theory we assume
that the type of properties is <s,<e,t>>. We will assume that names and predicates can be
ambiguous between individual interpretations and role interpretations.
Let us use r for the type <s,<e,t>> and indicate the difference between individual
interpretations and role interpretations by subscripts e and r.
Then we have:
Lexical Item: John
Category:
D
Interpretation: JOHNe  CONe (rigid)
JOHNr  CONr (rigid).
Lexical Item: Boy
Category:
N
Interpretation: BOYe  CON<e,t>
BOYr  CON<r,t>
Lexical Item: the
Category:
D
Interpretation: λP.σ(P) P  VAR<e,t>, σ:<e,t>e
λS.σ(S) S  VAR<r,t>, σ:<r,t>r
Lexical Item: a
Category:
D
Interpretation: λP.P P  VAR<e,t>
λS.S S  VAR<r,t>
Lexical Item: every
Category:
D
Interpretation: λQλP.x[Q(x)  P(x)] P,Q  VAR<e,t>, x  VARe
λSλR.r[S(r)  R(r)] R,S  VAR<r,t>, r  VARe
This gives us the following basic DPs:
DP
│
john
e:
JOHNe
r:
JOHNr
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261
e:
σ(BOYe)
DP
D
│
the
NP
│
boy
DP
D
│
a
r:
σ(BOYi)
<e,t>:
BOYe
<r,t>:
BOYr
NP
│
boy
DP
<<e,t>,t>
λP.x[BOYe(x)  P(x)]
<<r,t>,t>
λS.r[BOYr(r)  S(r)]
D
NP
│
│
every boy
Since we really think of type r as of the same nature as type e (or even as part of type e), we
assume that the same type shifting principles that apply to types e and <e,t> apply to r and
<r,t> as well.
We add a rule of role-predication. Whereas before predication lifted an DP to the predicate
type <e,t>, role-predication lifts an DP to the property type r:
α if α  EXPr
PREDr[α] =
LIFT[α] if LIFT[α]  EXPr
undefined otherwise.
Predication (for DPs):
PREDr[DP, DP'] = <PREDr , PREDr[DP'] >
│
DP
We assume that, unlike in normal predication, in a role-predicate the DP position is an
argument position. This means that it is a position that an DP can take scope out of, and
hence we do not have the prohibition on storage indices on the daughter of PREDr.
Crucially, I will assume that the interpretation of the copula is the same as before:
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262
Expression: be
Category:
I
Interpretation: λP.P where P  VAR<e,t>
This means that if the complement of the copula has a role interpretation, we get a type
mismatch:
APPLY[λP.P,α], where λP.P  EXP<<e,t>,<e,t>> and α  EXPr
This means that we need a type shifting rule to resolve this type mismatch. I will assume
that the type mismatch is resolved by a lifting rule, and not a lowering rule. This means that
we cannot lower the interpretation of the PREDr from r (=<s,<e,t>>) to <e,t>, but we have to
lift the interpretation of the copula from type <<e,t>,<e,t>> to type <r,<e,t>>. I will
assume that this is where INSTANTIATE gets introduced:
Let x  VARe, r  VARr, INSTANTIATE  CON<r,<e,t>>
LIFT: <<e,t>,<e,t>>  <r,<e,t>>
LIFT[α] = λr.α(λx.INSTANTIATE(x,r))
This means that we get the following structure and interpretation for role predication:
<
I'
A >
I
│
be
PREDr
│
DP
λP.P
PREDr
│
DP'
We assume that PREDr is of type r.
APPLY[λP.P, PREDr]
LIFT[λP.P] (PREDr)
= λr.[λP.P(λx.INSTANTIATE(x,r))] (PREDr) =
λrλx.INSTANTIATE(x,r) (PREDr) =
λx.INSTANTIATE(x,PREDr)
Hence we get:
<
I'
λx.INSTANTIATE(x,PREDr) >
I
│
be
PREDr
│
DP
Finally, we impose the following meaning postulate on INSTANTIATE.
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263
For any predicate P such that Pe  CON<e,t> and Pr  CON<r,t>: for every M:
λx.INSTANTIATE(x,Pe) = λx.r[Pr(r)  INSTANTIATE(x,r)]
λx.INSTANTIATE(x,λx.x=σ(Pe)) = λx.INSTANTIATE(x,σ(Pr))
This means the following: if we think of PRINCEe as 'prince-hood' or 'being a prince', then
x instantiates prince-hood iff there is a prince-role that x instantiates.
Similarly, x instantiates 'being the prince' iff x instantiates the prince role.
With these rules, we get the following derivations involving role interpretations for the
examples in (31):
(31) a. Olivier is Hamlet.
b. Olivier is a prince.
c. Olivier is the prince.
d. Olivier is every prince.
(31a) Olivier is Hamlet.
DERIVATION 1
<
IP
DP
│
olivier I
│
is
A>
I'
A
PREDr
│
DP
│
hamlet
λP.P
OLIVIERe
PREDr
│
HAMLETe
PREDr[HAMLETe]
= λx.x=HAMLETe
APPLY[λP.P,λx.x=HAMLETe]
= APPLY[LIFT[λP.P,λx.x=HAMLETe]
= λx.INSTANTIATE(x,λx.x=HAMLETe)
APPLY[λx.INSTANTIATE(x,λx.x=HAMLETe),OLIVIERe]
= INSTANTIATE(OLIVIERe,λx.x=HAMLETe)
= INSTANTIATE*(OLIVIERe,HAMLETe)
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264
So we get:
<
IP , INSTANTIATE*(OLIVIERe,HAMLETe) >
DP
│
olivier I
│
is
I'
PREDr
│
DP
│
hamlet
(31a) Olivier is Hamlet.
DERIVATION 2
<
IP
DP
│
olivier I
│
is
A>
I'
A
PREDr
│
DP
│
hamlet
λP.P
OLIVIERe
PREDr
│
HAMLETr
which is:
<
IP , INSTANTIATE(OLIVIERe,HAMLETr) >
DP
│
olivier I
│
is
I'
PREDr
│
DP
│
hamlet
I will comment on the readings later, but lets first go through the other relevant derivations:
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265
(31b) Olivier is a prince.
DERIVATION 1
<
IP
DP
│
olivier I
│
is
A>
I'
A
PREDr
│
DP
D
│
a
λP.P
NP λP.P
│
prince
OLIVIERe
PREDr
│
A
PRINCEe
PREDr[PRINCEe]
= PREDr[LIFT[PRINCEe]
= PRINCEe
APPLY[λP.P,PRINCEe]
= λx.INSTANTIATE(x,PRINCEe)
= λx.r[PRINCEr(r)  INSTANTIATE(x,r)] [meaning postulate]
APPLY[λx.r[PRINCEr(r)  INSTANTIATE(x,r)],OLIVIERe]
= r[PRINCEr(r)  INSTANTIATE(OLIVIERe,r)]
So we get:
<
IP , r[PRINCEr(r)  INSTANTIATE(OLIVIERe,r)] >
DP
│
olivier I
│
is
I'
PREDr
│
DP
D
│
a
NP
│
prince
Note that we do not have a direct derivation starting with PRINCEr, because that is of type
<r,t>. We will have an indirect one below.
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266
(31b) Olivier is a prince.
DERIVATION 2
We store the meaning PRINCEe of a prince, using xn  VARe.
<
IP ,
DP
│
olivier I
│
is
A>
I'
λ
PREDr
│
DPn
D
│
a
xn
NP λP.P
│
prince
A
λP.P PRINCEe
A
A
OLIVIERe
PREDr
│
xn
Retrieval forces PRINCEe to lift with LIFT from <e,t> to <<e,t>,t>:
LIFT[PRINCEe] = λP.x[PRINCEe(x)  P(x)]
We derive:
<
IP , x[PRINCEe(x)  INSTANTIATE*(OLIVIERe,x) >
DP
│
olivier I
│
is
I'
PREDr
│
DP
D
│
a
NP
│
prince
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267
(31b) Olivier is a prince.
DERIVATION 3
We store meaning PRINCEr of a prince. We use variable rn of type r for that:
<
IP ,
DP
│
olivier I
│
is
A>
I'
λ
PREDr
│
DPn
D
│
a
rn
NP λP.P
│
prince
A
λP.P PRINCEr
A
A
OLIVIERe
PREDr
│
rn
Which is:
<
IP , r[PRINCEr(r)  INSTANTIATE(OLIVIERe,r) >
DP
│
olivier I
│
is
I'
PREDr
│
DP
D
│
a
NP
│
prince
Thus, derivation 3 yields the same interpretation as derivation 1, given the meaning
postulate.
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268
(31c) Olivier is the prince.
DERIVATION 1
<
IP
DP
│
olivier I
│
is
A>
I'
A
PREDr
│
DP
D
│
the
NP
│
prince
λP.P
OLIVIERe
PREDr
│
A
λP.σ(P)
PRINCEe
PREDr[σ(PRINCEe)]
= PREDr[LIFT[σ(PRINCEe)]
= λx.x=σ(PRINCEe)
APPLY[λP.P,λx.x=σ(PRINCEe)]
= λx.INSTANTIATE(x,λx.x=σ(PRINCEe))
= λx.INSTANTIATE(x,σ(PRINCEr))
[meaning postulate]
APPLY[λx.INSTANTIATE(x,σ(PRINCEr))],OLIVIERe]
= INSTANTIATE(OLIVIERe,σ(PRINCEr))
So we get:
<
IP , INSTANTIATE(OLIVIERe, σ(PRINCEr)) >
DP
│
olivier I
│
is
I'
PREDr
│
DP
D
│
the
NP
│
prince
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269
(31c) Olivier is the prince.
DERIVATION 2
<
IP
DP
│
olivier I
│
is
A>
I'
A
PREDr
│
DP
D
│
the
NP
│
prince
λP.P
OLIVIERe
PREDr
│
A
λS.σ(S)
PRINCEr
This, straightforwardly, derives the same interpretation as derivation 1:
<
IP , INSTANTIATE(OLIVIERe, σ(PRINCEr)) >
DP
│
olivier I
│
is
I'
PREDr
│
DP
D
│
the
NP
│
prince
We can ignore the derivation which applies STOREn to σ(PRINCEr), since, obviously, it
doesn't give us anything new.
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270
(31c) Olivier is the prince.
DERIVATION 3
We store meaning σ(PRINCEe) of the prince under individual variable xn. We get:
<
IP ,
DP
│
olivier I
│
is
A>
λ
I'
PREDr
│
DPn
D
│
the
xn
NP λP.P
│
prince
A
λP.σ(P)
A
A
OLIVIERe
PREDr
│
xn
and we get:
<
IP , INSTANTIATE*(OLIVIERe, σ(PRINCEe)) >
DP
│
olivier I
│
is
I'
PREDr
│
DPn
D
│
the
NP
│
prince
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271
PRINCEe
(31d) Olivier is every prince.
DERIVATION 1
We store the interpretation A[e,PRINCEe] under individual variable xn and derive:
<
IP ,
DP
│
olivier I
│
is
A>
λ
I'
PREDr
│
DPn
xn
D
NP λP.P
│
│
every prince
A
e
A
A
PRINCEe
OLIVIERe
PREDr
│
xn
This gives us:
<
IP , x[PRINCEe(x)  INSTANTIATE*(OLIVIERe,x)] >
DP
│
olivier I
│
is
I'
PREDr
│
DPn
D
NP
│
│
every prince
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272
(31d) Olivier is every prince.
DERIVATION 1
We store the interpretation A[r,PRINCEr] under role variable rn and derive:
<
IP ,
DP
│
olivier I
│
is
A>
I'
λ
PREDr
│
DPn
rn
D
NP λP.P
│
│
every prince
A
r
A
A
PRINCEr
OLIVIERe
PREDr
│
rn
This gives us:
<
IP , r[PRINCEr(x)  INSTANTIATE(OLIVIERe,r)] >
DP
│
olivier I
│
is
I'
PREDr
│
DPn
D
NP
│
│
every prince
Summing up:
Taking into account individual and role predication, and assuming that the subject is of type
e, our theory now derives the following interpretations for the examples in (31):
(31) a. Olivier is Hamlet.
1. OLIVIERe = HAMLETe
2. INSTANTIATE*(OLIVIERe,HAMLETe)
3. INSTANTIATE (OLIVIERe,HAMLETr)
(31) b. Olivier is a prince.
1. PRINCEe(OLIVIERe)
2. x[PRINCEe(x)  INSTANTIATE*(OLIVIERe,x)]
3. r[PRINCEr(r)  INSTANTIATE (OLIVIERe,r)]
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273
(31) c. Olivier is the prince.
1. OLIVIERe = σ(PRINCEe)
2. INSTANTIATE*(OLIVIERe,σ(PRINCEe))
3. INSTANTIATE (OLIVIERe,σ(PRINCEr))
(31) d. Olivier is every prince.
1. x[PRINCEe(x)  INSTANTIATE*(OLIVIERe,x)]
2. r[PRINCEr(r)  INSTANTIATE (OLIVIERe,r)]
Let us now set the context, and assume we find ourselves in the context of the theater.
I will assume that in this context, INSTANTIATE is interpreted as PLAY:
INSTANTIATE(x,r) = PLAY(x,r)
Furthermore, I will assume that in this context, INSTANTIATE* is interpreted as
IMPERSONATES:
INSTANTIATE*(x,y) = IMPERSONATES(x,y)
This means, that in this context, we get the following readings:
(31) a. Olivier is Hamlet.
1. OLIVIERe = HAMLETe
2. IMPERSONATE(OLIVIERe,HAMLETe)
3. PLAY(OLIVIERe,HAMLETr)
(31) b. Olivier is a prince.
1. PRINCEe(OLIVIERe)
2. x[PRINCEe(x)  IMPERSONATE(OLIVIERe,x)]
3. r[PRINCEr(r)  PLAY(OLIVIERe,r)]
(31) c. Olivier is the prince.
1. OLIVIERe = σ(PRINCEe)
2. IMPERSONATE(OLIVIERe,σ(PRINCEe))
3. PLAY(OLIVIERe,σ(PRINCEr))
(31) d. Olivier is every prince.
1. x[PRINCEe(x)  IMPERSONATE(OLIVIERe,x)]
2. r[PRINCEr(r)  PLAY(OLIVIERe,r)]
(31a) is three-way ambiguous.
(31) a. Olivier is Hamlet.
On the first reading, (31a) means that Olivier is identical to Hamlet, which we assume is
false.
On the second reading, (31a) means that there is an actual person Hamlet, say, the crown
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prince of Denmark, and Olivier performs in a play about the life of this prince. For political
reasons, however, the play is set in 18th century Boston, the character is named Rodolfo in
the play, and he is made vice-governor of Boston. Seeing through this, we can still say that
Olivier is Hamlet: he plays a role which impersonates a real character, Hamlet, prince of
Denmark.
On the third reading, (31a) means that Olivier plays the role of Hamlet, say, in the play of the
same name.
We find a similar ambiguity for (31b):
(31) b. Olivier is a prince.
On the first reading, (31b) means that Olivier has the property of being a prince.
On the second reading, it means that Olivier impersonates an actual prince, he plays a role
based on an individual, who happens to be a prince.
On the third reading it means that Olivier plays the role of a prince in the play.
And the same for (31c):
On the first reading, (31c) means that Olivier is identical to the prince.
On the second reading, (31c) means that Olivier impersonates the (actual) prince.
On the third reading, (31c) means that Olivier plays the role of the prince in the play.
(31d), finally, has only two readings:
On the first reading, (31d) means that Olivier impersonates every actual prince.
On the second reading, (31d) means that Olivier plays the role of every prince in the play.
(31d) does not have a reading where it means that Olivier is identical to every actual prince.
Let's finally come back to the inference in (29):
(29) a. Derek Jacobi is Lewis Carroll.
b. Lewis Carroll is Charles Dodgson.
c. Derek Jacobi is Charles Dodgson.
The setting for (29) was a situation where there is a play about the life of Charles Dodgson,
in which both Charles Dodgson and Lewis Carroll are characters in the play, but they are
played by different actors. In particular, Derek Jacobi plays Lewis Carroll, but John Hurt
plays Charles Dodgson.
The relevant interpretations for the sentences in (29) are:
(32) a. PLAY(JACOBIe,LEWIS CARROLLr)
b. LEWIS CARROLLe = CHARLES DODGSONe
c. PLAY(JACOBIe,CHARLES DODGSONr)
In the situation given, the inference from (30a) and (30b) to (30c) is, as it should, invalid.
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275