BOUND VARIABLES AND 
OTHER ANAPHORS 
Barbara H. Partee 
Univ. of Mass., Amherst 
When a noun phrase or a pronoun occurs in a sen- 
tence, it is frequently appropriate to ask what 
entity it refers to, but it is well known that 
not all uses of noun phrases and pronouns are 
referential in this simple sense. In computation- 
al approaches to language processing, I believe 
the main thrust in this area has been toward 
understanding those referential uses of NP's 
and pronouns which require the use of both linguis- 
tic and non-linguistic inferences to determine 
the most plausible referent for the expression. 
My emphasis in this paper will be somewhat dif- 
ferent. I believe that recent work by linguists, 
logicians, and philosophers is leading to con- 
vergence on the view that there are two fundamen- 
tally distinct uses of pronouns which have to be 
treated quite separately: (i) a use that corres- 
ponds to the logician's use of bound variables, 
and (ii) a use which I will call, for want of"a 
better name, a pragmatic use. It can be argued 
that bound variable pronouns are restricted to 
occurrences in syntactic construction with their 
antecedents, and are fully interpreted at the 
level of semantics, while pragmatic pronouns 
need not have linguistic antecedents at all, and 
require pragmatics as well as semantics for their 
interpretation. 
I. The basic distinction. 
The clearest cases of bound variable anaphora 
involve antecedents like every man and no man 
which are singular in form but do not refer to 
individuals, as in (1) and (2). 
(1) Every man put a screen in front of him. 
(2) No child will admit that heis sleepy. 
When the he of (2) is understood as anaphorically 
related to the noun phrase no child, the he 
clearly does not refer to a particular in~vidual. 
Rather, the sentence can be understood as the 
result of binding an open sentence, (3), with 
a quantifier phrase, no child. 
(3) He 0 will admit that he 0 is sleepy. 
(It is i~aterial for the purposes of this paper 
whether we view the process in question as a gen- 
erative one, as in Montague (1973) or Lakoff (1971), 
or as an interpretive one, as in Jackendoff (1972) 
or the I-grammar Montague variant of Cooper and 
Parsons (1976). The use of subscripted pronouns 
79 
rather than ~'s and ~'s follows Montague's practi-ce,, 
but that distinction is also immaterial here.) 
The semantics of variable binding is well studied 
in logic; a particularly clear and brief account 
can be found in Quine (1970). The crucial point 
here is that the semantics involves consideration 
of a whole range of possible values for the vari- 
ables, not the determination of any single value 
or referent. Equally crucial is that the inter- 
pretation of (2) involves an open sentence with 
two occurrences of the free variable h_~e, one 
in the position of the antecedent noun ~hrase, 
the other corresponding to the surface pronoun. 
Using these clear cases, we can discover strong 
syntactic constraints on the occurrence of bound 
variable pronouns. With few exceptions, it appears 
that bound variables must be in construction with 
their antecedents (the observation is made by 
Evans (1977); the notion "in construction with" 
comes from Klima (1964): a constituent A is in 
construction with a constituent B if and only if 
A is dominated by the first branching node which 
dominates B. The term c-command is a more recent 
alternative name for the same notion.) Thus the 
following do not permit a bound variable reading: 
(4) (a) Every man walked out. He slammed the door. 
(b) John loves every woman, and he hopes to 
date her soon. 
(c) If no student cheats on the exam, he will 
pass the course. 
By contrast, the bound variable reading is permit- 
ted in cases like (1) and (2) above, in which 
the pronoun is in construction with its antecedent. 
The clearest cases of what I am calling pragmatic 
uses of pronouns are cases where a pronoun is used 
with no linguistic antecedent at all, as in (5), 
or where the antecedent occurs in an earlier sen- 
tence of a discourse, as in (6). 
(5) (On walking into a room) Why is he \[point- 
ing\] here? 
(6) I couldn't reach Elliot last night. He 
is probably in Boston. 
These are cases where the pronoun is being used 
to refer to a particular individual, and the det- 
ermination of which individual the intended refer- 
ent is requires making use of the linguistic and 
non-linguistic context. Ignoring some complica- 
ted cases that I will discuss later, we may say 
that at the level of purely linguistic description, 
such pronouns function like free variables which 
are not bound at all at the semantic level. A 
sentence containing one expresses a determinate 
proposition only relative to a particular choice 
of value for the variable, much as a sentence con- 
taining the word now expresses a determinate 
proposition only relative to a particular time 
of evaluation. Such choices depend on the context 
of use of the sentence, which is why I call this 
a pragmatic use of pronouns. 
I believe that there are no absolute rules govern- 
ing the choice of referent for pragmatic uses of 
pronouns, but that there are discoverable strategies 
and principles governing the relative likelihood or 
or preference among choices. The other partici- 
pants in this panel know much more than I do about 
what those principles and strategies are; I hope 
they would agree that the output of such princi- 
ples is a probable or expected referent rather 
than an absolute referent for the pronoun. For 
example, in most contexts, the probable referent 
of the he in (6) is Elliot; but one can easily 
enough im---agine a context where speaker and hearer 
are most interested in figuring out where Max is, 
and being unable to reach Elliot is a good clue 
to Max's being in Boston; then he may be intended 
and understood as referring to Max. What matters 
most seems to be the salience and relevance of a 
particular individual, and I see no reason to draw 
any theoretical line between cases where that 
salience comes from the linguistic context as 
opposed to the non-linguistic context. 
Where I do want to draw a sharp line is between 
the bound variable use and the pragmatic use of 
pronouns. The bound variable use is best des- 
cribed at the level of syntactic form and seman- 
tic interpretation of single sentences, and the 
relevant question is not what the pronoun refers 
to, but what quantifier phrase is binding it. 
The pragmatic use is best described at the prag- 
matic level, where the full context of the sen- 
tence in use is considered; on the syntactic level, 
these pronouns are really no different from pro- 
per names, and at the semantic level, they can be 
viewed as free variables or as dummy names. 
2. Structurally ambiguous pronouns. 
I have begun with the clearest examples of the 
distinction; if all uses of pronouns fell unam- 
biguously into these two categories, I could 
stop here. All the rest would be a matter of 
improving the description of the syntactic con- 
straints on bound variable anaphora and unravel- 
ling the processing mechanisms that we use to 
determine the referents of the pragmatic uses of 
pronouns. But the clear cases do not provide a 
set of necessary and sufficient conditions for 
telling the two kinds of pronouns apart. All we 
can conclude so far by way of conditions is the 
following: 
(i) A pronoun can function as a bound variable 
only if it i~ in the same sentence as its 
antecedent. '-j 
(ii) Any pronoun can be used pragmatically. 2-j 
If these are the only conditions, we would expect 
many occurrences of pronouns to be ambiguous as 
to which use they have, and indeed many are. The 
pronouns in (1) and (2) are ambiguous in this way, 
and the sentences have sharply different inter- 
pretations in the two cases. But now consider a 
sentence like (7): 
(7) The prosecutor believed that hewould win 
the case. 
This example can be analyzed either way; if the 
pronoun is analyzed as a bound variable, the 
sentence is interpreted as in (7a), and if the 
pronoun is treated pragmatically, we can repre- 
sent it as in (7b). 
80 
(7a) (The prosecutor: hen) \[He 0 believed that he 0 
would win the cas~.\] 
(7b) The prosecutor believed that he 5 would win the 
case. 
On the pragmatic pronoun reading, the free variable 
~ee will be interpreted as some salient individual 
ermined by the context; and one likely choice 
will be the prosecutor. This looks at first as if 
we are predicting an ambiguity where there is none. 
And this is not just an isolated example, since 
the same situation will arise whenever we have an 
antecedent noun phrase that picks out a particular 
individual. But it turns out that there is strik- 
ing evidence that this is a real structural ambigu- 
ity, and not just an artifact of the analysis. I 
believe that Keenan (1971) was the first to point 
this out; Sag (1976) and Williams (1977) discuss 
such cases extensively. The evidence comes from 
verb phrase deletion, and involves examples like 
the following: 
(8) The prosecutor believed that he would win the 
case, and so did the defense attorney. 
The missing verb phrase can be understood in just 
two ways, corresponding to the two structures we 
have posited for the first clause. On each read- 
ing, sentence (8) predicates the same property of 
the defense attorney as it predicates of the pro- 
secutor: either the property of being an x such 
that x believed that x would win the case ~the 
bound-variable reading), or the property of being 
an x such that x believes that h_~ 5 (the prosecutor) 
wouTd3~in the case (the pragmatic pronoun read- 
ing). ~J Thus the examples of so-called "sloppy 
identity" (Ross 1967) of pronouns are really exam- 
ples of strict semantic identity of predicates. 
This important generalization can be captured 
only by recognizing that apparently unambiguous 
sentences like (7) are in fact structurally ambi- 
guous. 
Cases with proper names as antecedents to pronouns 
work just like (7) and (8); the unified treatment 
of all noun phrases, including proper names, as 
quantifier phrases proposed by Montague (1973) 
is an important aid in permitting the treatment 
of pronouns advocated here. 
Another major source of pronoun ambiguity is the 
systematic ambiguity of most plural noun phrases 
as between a "group" reading and an "individual" 
reading, as in (9). 
(9) Three men lifted the piano. 
When the plural pronoun they is used as a pragma- 
tic pronoun, it always refers to a group; but when 
it is used as a bound variable, it may be either 
a variable over individuals or a variable over 
groups. Thus we get two bound variable readings 
plus a pragmatic pronoun reading for (lO). 
(lO) The Democrats voted for their wives. 
On the group-level bound variable reading, the 
Democrats as a group voted for their wives as a 
group. On the individual-level bound variable 
reading, each of the Democrats voted for his own 
wife. On the pragmatic pronoun reading, the 
Democrats4-/voted for some group's wives; that group 
might be the Democrats themselves, but might be 
some other group determined by the context. Again 
the three readings lead to corresponding readings 
in sentences with verb-phrase deletion: 
(ll) The Democrats voted for their wives before 
the Republicans did. 
I will not enumerate the readings, but it can be 
seen that the positing of the three structures 
for the first clause plus the requirement that 
verb phrase deletion be interpreted as semantic 
identity of predication makes the correct predic- 
tions about the possible interpretations of the 
full sentence. 
Yet another source of structural ambiguity is the 
fact that noun phrases may have other noun phrases 
embedded within them, and a pronoun may have either 
the whole noun phrase or a subpart as antecedent. 
Sentences (12a) and (12b) do not have this parti- 
cular ambiguity because of the number difference, 
but (13) is ambiguous as between (13a) and (13b). 
(12) 
(13) 
(a) One of the prisoners believed that she 
could escape. 
(b) One of the prisoners believed that they 
could escape.~ 
Two of the prisoners believed that they could 
escape. 
(a) Two of the prisoners believed that they 
could escape. 
(b) Two of the prisoners believed that they 
could escape. 
Each of these sentences is ambiguous between a 
bound variable use and a pragmatic use of the 
pronoun; and sentence (13a) permits either the 
individual-level bound variable reading (each of 
the two believed she could escape) or the group- 
level reading (both believed that both could escape). 
However, (13b) on the bound variable reading must 
be a group-level pronoun, because the antecedent is 
in a partitive construction, which requires a group- 
denoting noun phrase. A fuller discussion of plu- 
ral noun phrases and bound variable pronouns can 
be found in Bennett (1974), although Bennett 
does not specifically discuss the pragmatic uses 
of pronouns. No new principles of pronoun inter- 
pretation are needed for these cases beyond the 
important observation that they can function sem- 
antically as an individual-level pronoun, that is, 
just like a singular pronoun. The complexities 
of these examples result simply fron the joint 
interaction of several individually simple pheno- 
mena: bound variable vs. pragmatic uses of pronouns, 
individual vs. group readings of plurals, and the 
possibility of either a whole noun phrase or a 
subpart of it serving as antecedent for a pronoun. 
The examples discussed so far are summarized and 
extended in Table I below. The column headed 
"Pragmatic Pronoun" should be understood as follows: 
the given pronoun can be interpreted as referring 
to an individual or group determinable on the basis 
of the interpretation of the given "antecedent" as 
the relevant linguistic context. Thus, for example, 
while every man does not refer to the group of all 
man, it can promote that group into salience, as 
can no man and no men. 
81 
(14) No students came to the party. They thought 
they weren't invited.6_6/ 
TABLE I 
Antecedent Bound Variable Pronoun Pra/~atic Pronoun 
every ~ he ~he, CK they (group) 
no ~an he ehe, O~ they (~'oup) 
the man he he 
John he he 
one man he he 
~ore than ~e man he ehe, OK they (gZ'Oup) 
at most one man he * 
three men they (ind)t they (group) they (group) 
one of the men he he 
one o£ L~J~o~ th .... they (=o~p) they (grip) 
t'~o Of the men they (ind), they (group) they (group) 
no men they (ind) they (gx'oup) 
John and Bi~ they (ind), they (~A-oup) they (group) ,, 
John o~ B~ he they (grOUp) ?~/ 
3. Are there "pronouns of laziness"? 
Both traditional grammar books and early transfor- 
mational accounts such as Lees and Klima (1963) 
suggest a treatment of pronouns different from 
either of the two I have described. This is the 
view that a pronoun is a substitute for a linguis- 
tically identical nounphrase;(15b) would on this 
view be derived from (15a). 
(15) (a) John spoke to Mary when John walked in.=~ 
(b) John spoke to Mary when he walked in. 
But such a view requires that semantic interpreta- 
tion operate on surface structure, since the appli- 
cation of the rule changes the meaning whenever 
the repeated noun phrase is anything other than a 
proper noun or a definite description. 
(16) (a) John lost a watch and Bill found a 
watch =~ 
(b) John lost a watch and Bill found it. 
Given that pragmatic pronouns must be generated 
directly anyway because of cases where there is no 
linguistic antecedent, there is then no work left 
for such a transformation to do; it simplifies 
neither the syntax nor the semantics. Hence it 
has been abandoned by linguists of just about 
every theoretical persuasion. 
But there are some cases that look as though they 
might be better handled via a syntactic substi- 
tution rule than by either the bound variable 
or the pragmatic treatment. One class was intro- 
duced by Geach (1962), who provides examples 
like (17): 
(17) Every man who owns a donkey beats it. 
On the defensible assumption that ~ should 
be analyzed here as an existential quantifier 
phrase having narrower scope than the every, this 
it cannot be analyzed as a bound variable (see 
Pa---rtee 1975a). But it also does not refer to any 
specific donkey, and so does not appear to be 
functioning as a pragmatic pronoun. Geach suggests 
that a sentence like (17) be analyzed in terms of (18): 
(18) Every man who owns a donkey beats the donkey 
he owns. 
Thus the it is viewed as standing for a descrip- 
tion reco~rable in a complex way from the initial 
part of the sentence. Geach may or may not have 
called this an example of a "pronoun of laziness"; 
the term is his, but it has been used by him and 
others in a variety of ways. What all uses of 
the term have in common is the idea that some 
p~onouns should be analyzed neither as bound vari- 
ables nor as directly referential, but in terms 
of some syntactically definable relation tO an 
antecedent noun phrase. 
Another example for which a "pronoun of laziness" 
treatment has plausibility is (19), from Karttunen 
(Ig6g): 
(19) The man who gives his paycheck to his wife 
is wiser than the man who gives it to his 
mistress. 
This it is also not a bound variable nor directly 
refer~tial; it seems to be a substitute for the 
expression his p~check. In both Partee (1970) 
and Partee (1975b).I argued for the existence of 
a syntacticpronoun-of-laziness rule, intended to 
cover both these examples and those cases of what 
I am now calling pragmatic pronouns in which the 
antecedent is itself a directly referring expres- 
sion such as a proper noun or a definite descrip- 
tion. However, neither I nor anyone else that 
I know of ever succeeded in stating a version of 
the rule which covered all of these cases without 
generating clearly unacceptable results as well. 
Recent arguments by Terry Parsons (personal commun- 
ication), Robin Cooper (forthcoming), Gareth Evans 
(1977), Emmon Bach (personal communication), and 
others have convinced me that there is no way to 
make the notion of "pronoun of laziness" coherent 
without reducing it to one which covers only a 
small subclass of the pragmatic pronouns and hence 
does no useful work. 
What then can we say about the paycheck sentences 
and the donkey sentences? Many lines of attack 
are being explored currently; one that I find 
particularly promising is proposed by Cooper (forth- 
coming), who suggests a rather natural extension 
of the notion of pragmatic pronoun to handle them. 
Before describing his proposal, I need to fill 
in some background. 
Russell's analysis of singular definite descrip- 
tions (Russell 1905) requires that there be a 
unique object satisfying the description in order 
for the expression to denote anything, and hence 
notoriously fails to account for the successful 
reference of a noun phrase like the clock in (20). 
(20) Did you wind the clock? 
That the missing ingredient is pragmatic has long 
been recognized; Cooper (forthcoming) proposes a 
mechanism that brings in pragmatics in a simple 
way that parallels the account of pragmatic pro- 
nouns given above (which is also basically Cooper's). 
He proposes for definite descriptions a semantic 
interpretation like Russell's but with the addi- 
tion of a free property variable P: the clock 
then denotes (the property set of) the unique 
individual ~ such that clock(x_) and P(~). At the 
82 
semantic level, P is just a free variable; it is 
left to the pragmatic interpretation of the sen- 
tence in context to determine an appropriate 
choice for P. In a context where there is no sal- 
ient distinguishing property, the singular defin- 
ite description would indeed be inappropriate or 
uninterpretable. Cooper's treatment can be seen 
as a formalization of the informal gloss of the 
(by Katz and others) as "contextually defini~. 
As a second background step toward Cooper's pro- 
posal, consider the interpretation of genitive 
phrases like that in (21). 
(21) John's team lost again. 
As is well known, John's team may be the team John 
owns, or plays for, or roots for, or collects 
trading cards of, or writes news stories about; 
there are virtually no limits on the relevant 
relation. I propose that such constructions be 
analyzed at the semantic level as definite descrip- 
tions containing a free relation variable R, 
whose value is to be determined at the pragmatic 
level, by looking for an appropriately salient 
and relevant relation in the linguistic or non- 
linguistic context. Thus John's team would be 
interpreted as (22): 
(22) the x such that team (x) and R (John, x). 
What is common to these analyses of pragmatic pro- 
nouns, definite descriptions, and genitive con- 
structions is the use of semantic free variables 
that are pragmatically assigned particular values. 
Introducing the free variables allows a complete 
specification of the form of the interpretation 
to be given for each sentence at the semantic 
level, while providing an appropriate division 
of labor between semantics and pragmatics in 
the determination of the content. 
Cooper's proposal for the donkey and p~ycheck 
sentences is that pronouns can be analyzed not 
only as free variables, but alternatively as 
expressions composed of more than one free 
variable, utilizing free property or relation 
variables much as in the examples just discus- 
sed. The logical formalism is complex, but I will 
give it for completeness and then try to paraphrase 
it less formally. A singular pronoun (he, she, 
or i_t_t) may have any translation of the follow- 
ing form: 
(23) ~K~x ~y \[\[v~\] (y)__--- y = x\] A K (x)\], 
where ~ is a property-denoting expres- 
sion containing only free variables and 
parentheses. 
What this says is that e.g. i__tt ma~v be interpreted 
as (the property set of ) the unique individual 
x which has property x . For the paycheck exam- 
ple, an appropriate ~ will be R (u), where R is 
a free relation variable and u is a free indivi- 
dual variable that will be bound by the second 
occurrence of the man. The second clause of (19) 
will then say ~n u such that u gives the x 
such that R (x,u) to u's mistress." The pragmati- 
cally appropriate R will be "being the paycheck 
of". The computational complexity of the analysis 
is justified, I believe, by the fact that only 
very salient relations permit the kind of pronoun 
use evidenced by the paycheck example. 
Cooper's analysis of the donkey sentences uses the 
identical device; for details see Cooper (forth- 
coming). 
The conclusion of this section is that there are 
no pronouns of laziness; the cases which seemed 
to require them can be handled by an extension 
of the notion of pragmatic pronouns. The exten- 
sion is somewhat complex, but (a) it makes use 
of the same kind of property and relation vari- 
ables that are needed for an account of definite 
noun phrases and genitive constructions, and (b) 
the examples it is needed for are intuitively 
complex and infrequent in occurrence. 
4. Conclusion. 
There are many problems of pronouns and reference 
that I have not touched on. I have not discussed 
reflexive pronouns, first and second person pro- 
nouns, pronouns in modal contexts, the pro- 
common noun one, anaphoric determiners like same, 
different, or other, or any of a host of other 
topics crucial to a fuller account of the role 
of pronouns in reference. In some cases the 
problem is just lack of space and time, but in 
other cases there are still difficult open prob- 
lems. I hope that some of what I have included 
is relatively unfamiliar and potentially useful 
for computational language processing endeavors, 
and I count on my fellow panelists to fill in 
some of the holes I have left. 
83 
Footnotes 
I. There are apparent exceptions to even this weak 
a statement, but I believe they are best under- 
stood as involving elliptical sentences. Consider 
the following example (from David Kaplan, personal 
communication): 
A: Could a woman become chairman of the Phil- 
osophy Department? 
B: Yes, if she's qualified. 
The she in the second sentence is not a pragmatic 
pronoun; but I think it is best treated as bound 
by an unexpressed antecedent within the second 
sentence, which is not as it stands a complete 
sentence, rather than as bound by an antecedent 
in the previous sentence. 
2. There are exceptions to this statement, too, 
but they all involve idiomatic pronoun-containing 
expressions like "shrugged his shoulders" or "lost 
his cool". Reflexive pronouns are not included 
in this generalization; they are almost invariably 
bound variable pronouns, except for certain cases 
that seem to result from instability in the choice 
of nominative or accusative form. I will not 
go into any details about reflexive pronouns here. 
3. On the pragmatic pronoun reading, the pronoun 
he can of course refer to someone other than the 
prosecutor; in that case the missing verb phrase 
will always be understood as involving reference 
to the same third person. 
4. There is still an individual/group ambiguity 
for the subject in this case, but it does not 
affect the interpretation of the pronoun, so I 
will ignore it. 
5. For simplicity I am ignoring the dialect that 
allows tht.hejcwith a singular antecedent; in that 
dialect (12b) is as ambiguous as (13). 
6. Not every occurrence of a quantifier phrase 
with no has this effect, as the following example 
from Ev---ans (1977) shows: 
(i) *John owns no sheep and Harry vaccinates 
them. 
The role of non-linguistic inference in interpret- 
ing pragmatic pronouns can be seen from the follow- 
ing linguistically similar examples. 
(ii) John owns no sheep because Amherst taxes 
them. 
(iii) John now owns no sheep because Harry 
poisoned them. 
In (ii), them seems to be generic sheep rather 
than any group of sheep; in (iii) the most plaus- 
ible interpretation seems to be the sheep that 
John once owned. Perhaps it would be more accur- 
ate to say that no man and no men never serve dir- 
ectly as antecede'nt to a prag~c they, but 
sentences in which they occur do sometimes permit 
the inference of a suitable referent for a prag- 
matic they. 
7. The group in this case is the group of John 
and Bill. That group can be put into contextual 
salience by any mention of John and Bill separately, 
as in the examples below. 
(i) John saw Bill yesterday. They decided to 
go fishing. 
(ii) I invited John, but not Bill. They both 
came anyway. 
(iii) Ask John or Bill. 
keys are kept. 
They know where the 
8. Montague (1973) treats all noun phrases as 
devoting property sets, and Cooper follows this 
practice. While that treatment seems essential 
for a unified account of noun phrases, I have 
omitted discussion of it here for simplicity. 
84 

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