The Semantics of Ellipsis
83
to incorporate the exact meanings of the antecedents. My proposal is that our
examples are to be paraphrased as in the (b) sentences below, where the phrases
in italics hark back to the antecedent VP denotations.
(61)
a.
Bob wants to sail round the world and Alice wants to climb Kili-
manjaro, but neither of them can, because money is too tight.
b.
Bob wants to sail round the world and Alice wants to climb Kil-
imanjaro, but neither of them can perform the particular action or
actions out of sailing round the world and climbing Kilimanjaro
that they desire.
(62)
a.
I did everything Mary did. Mary swam the English Channel and
Mary climbed Kilimanjaro, and I did too.
b.
Mary swam the English Channel and Mary climbed Kilimanjaro
and I performed the particular action or actions out of
swimming the
English Channel and
climbing Kilimanjaro that Mary performed.
(63)
a.
Whenever Max uses the fax or Oscar uses the Xerox, I can’t.
b.
Whenever Max uses the fax or Oscar uses the Xerox, I can’t perform
the particular action or actions out of
using the fax and
using the
Xerox that are being performed.
It can be seen that one form of paraphrase covers all the examples. Informally, in
place of the elided VP we understand “perform the particular action or actions
out of f
1
and f
2
that have property F ,” for VP meanings f
1
and f
2
and properties
of VP meanings F .
I propose to spell out parts of the above paraphrase schema with LF oper-
ators. For example, the LF of the final sentence of (62a) will be that shown in
Figure 3. There is a special set of lexical items with the following semantics:
(64)
For all n >
0, [[A
ND
n
]]
g
= λf
1, s,t
. . . f
n, s,t
.λh
s,t
.h ≤
i
f
1
⊕ . . . ⊕ f
n
The notation is that of Link’s (1983) theory of plurality. An operator A
ND
n
takes
n arguments of type s,t and maps them to the characteristic function of the set
84
Paul Elbourne
TP
I
5
T
λ
4
T
T
past
vP
t
4
v
v
T
HE
P
T
HE
T
HE
RP
R
1, st,t
A
ND
0
P
A
ND
1
P
A
ND
2
VP
swim the English Channel
VP
climb Kilimanjaro
Figure 3: I did too. . .
of s,t functions that are part of the plural individual that has all and only the n
arguments as atomic parts. In the present case, we have the following:
(65)
[[A
ND
2
]]
g
= λf
1, s,t
.λf
2, s,t
.λh
s,t
.h ≤
i
f
1
⊕ f
2
This means that the denotation of A
ND
0
P in the syntax is as in (66). I use the
two italicized phrases to stand for the meanings of the two VPs.
(66)
λh
s,t
.h ≤
i
swimming ⊕ climbing
The point of T
HE
and its argument R
1, st,t
is to introduce the modification of
the VP-meanings that we have seen to be necessary in some of the paraphrases
in (61)–(63). In the present case, as it happens, this item is redundant, but I will
show the argument R
1, st,t
in action for the sake of illustration. (It will play a
The Semantics of Ellipsis
85
central role in analysis of (61a) and (63a); it so happens that (62a) is simple
in ways that make it a good introductory example.) Let us assume, then, that
R
1, st,t
is assigned the value shown in (67):
(67)
[[R
1, st,t
]]
g
= λf
s,t
.∃e(f(e) = 1 & Agent(e, Mary))
This function is not the value of any overt linguistic constituent, but we can
assume that this does not matter for LF variables. The mention of Mary doing
things makes this function salient enough.
Meanwhile, the operator T
HE
has the denotation in (68), which uses some
terminology from Link 1983 defined in (69);
∗
P is the plural predicate, the
one that characterizes both singular entities that are P and plural entities whose
atomic parts are all P .
(68)
[[T
HE
]]
g
= λF
st,t
.λG
st,t
.σf(F (f) = 1 & G(f) = 1)
(69)
σxP x := ιx(
∗
P x & ∀y(
∗
P y → y ≤
i
x))
In other words, T
HE
takes as its arguments two properties of VP-meanings and
maps them to the maximal plural individual composed of individuals that satisfy
the two arguments. (I use individual here not to mean an entity of type e but to
mean an atom within the relevant domain, which is here D
s,t
.)
Given these definitions, the denotation of T
HE
P in Figure 3 is (70a), which
in the present context is equivalent to (70b).
(70)
a.
σf(∃e(f(e) = 1 & Agent(e, Mary)) & f ≤
i
swimming⊕climbing)
b.
swimming ⊕ climbing
Moving upwards in Figure 3, we come to v and T
past
, whose denotations we
wrote in (36) as follows:
(71)
[[T
past
]]
g
= λf
s,t
.∃t(t <
NOW
& at t : ∃e f(e) = 1)
[[v]]
g
= λf
s,t
.λy.λe.f(e) = 1 & Agent(e, y)
These lexical entries will still suffice, but we now have to be sure to understand
the notion of Agent in such a way that one can be an Agent of plural events. Let