a note on plural pronouns

H. M. CARTWRIGHT

A NOTE ON PLURAL PRONOUNS

ABSTRACT. Gareth Evans proposal, as amended by Steven Neale that a definite pro-noun with a quantified antecedent that does not bind it has the sense of a definite description has been challenged in the singular case by appeal to counter-examples involving failureof the uniqueness condition for the legitimacy of a singular description. This challengeis here extended to the plural. Counter-examples are provided by cases in which a pluraldescription the F s does not denote, despite the propriety of the use of they or themit is to replace, because of failure of cumulativeness. A noncumulative predicate is notdistributive, and conditions for the legitimacy of the F s designed to accommodate nondis-tributive F s are given in the context of a two sorted theory with generalized quantifiers.Failure of cumulativeness is not to be confused with failure of maximality as Neale andothers define it. If not all F s are Gs, The F s are Gs is false; but it does not follow thatthe Fs is illegitimate; and if F s is distributive. it is so only if there are no F s. Thesedifferences granted, I give a partial defense of the EvansNeale proposal from deficienciesin an alternative based on the views of P. T.Geach.

1.

The relation of an anaphoric pronoun with a quantified antecedent to thatantecedent is, as Quine has taught us, regularly that of a variable to a quan-tifier which binds it; but Gareth Evans is surely right about the existence ofpronouns with quantified antecedents for which this is not so.1 One mightsuppose that

Just one man drank champagne and he was ill(1)has the first order symbolization:

(E!x)(Fx & Gx).Exactly one x is such that x is a man who drank champagne and x was ill that is,

Just one man drank champagne and was ill.(2)But (2) is not equivalent to (1). Whereas (1) entails its first conjunct,(2) is compatible with the existence of more than one man who drankchampagne.

Synthese 123: 227246, 2000. 2000 Kluwer Academic Publishers. Printed in the Netherlands.

228 H. M. CARTWRIGHT

If the truth of (1) is to be preserved, the scope of the quantifier cannotextend to the end of the sentence. The pronoun he is, in a quite straight-forward sense, not bound by its antecedent. But then it is not clear how (1)can be assigned a truth value at all, since if he is not bound, (1) seems justto be an open sentence. And it seems that something like Evans solutionto this puzzle as amended by Stephen Neale, at any rate is also right, atleast in this case.2 (1) is true just in case

Just one man drank champagne, and the man who drankchampagne was ill

(3)

is true. The proposal is that whenever an anaphoric pronoun with a quanti-fied antecedent is not bound by it, its sense is that of a definite descriptionrecoverable from the clause in which its antecedent occurs.

In other cases, however, matters are less clear. Given

A man drank champagne and he was ill,(4)

in which the quantifier is existential but not uniquely so, the argumentfor saying that the scope of the quantifier cannot extend to the end of thesentence, as in the case of (1), is not available; for the simple existential Aman drank champagne and was ill entails its first conjunct.

Moreover, because of the uniqueness requirement for the legitimate useof a singular definite description, it may be doubted that the truth of (4), inaccordance with Evans proposal, turns on the truth of

A man drank champagne, and the man who drank champagnewas ill.

(5)

In fact the indefinite article invites the assumption that (4) is compatiblewith

Another man drank champagne, and he was not ill;(6)

and if (4) and (6) are both true, (5) cannot be so.3It has been said that the indefinite article an is sometimes so used that

uniqueness is required.4 So perhaps (4) can be understood in such a waythat it is not compatible with (6). I find this dubious, but I am here lessconcerned to decide the matter than simply to emphasize its origin in whatappear to be straightforward counter-examples to Evans proposal basedon the logic of singular definite descriptions.

It does seem that if I were to meet both Whitehead and Russell,

I met an author of Principia Mathematica(7)

A NOTE ON PLURAL PRONOUNS 229

would be true, because I would have met Russell. And, since Russell wasEnglish, I believe that I could fairly add

He was English.(8)

But this is not enough to guarantee the legitimacy of the author ofPrincipia Mathematica that I met nor, in the circumstances, the truth of

The author of Principia Mathematica that I met was English.(9)

In the circumstances described I did, after all, meet another author ofPrincipia Mathematica. (7) and (8) provide for the existence of an authorof Principia Mathematica that I met, but not for his uniqueness.

To say this is to side with Evans prime target of criticism, P. T. Geach;5and Evans counter would be to deny (8) or secure uniqueness by enrich-ing the description recoverable from a sentence like (7) by drawing onits context, for example the reference to time implicit in the tense of theverb. What I shall do here is consider this line of argument in some casesinvolving a plural pronoun to be replaced by a plural definite description inaccordance with the EvansNeale proposal. I want to emphasize a featureof the logic of plural descriptions that is sometimes overlooked and makea suggestion about the merits of the proposal in these cases.

2.

Evidence for the distinction to which Evans means to call attention isstraightforward in many cases in which a pronoun has a plural quantifieras antecedent.6 The sentence

Few congressmen admire Kennedy, and they are very junior(10)is like (1). It entails its first conjunct and is not to be confused with

Few congressmen are such that they admire Kennedy and arevery junior

(11)

which does not entail that clause. In (11) the scope of the quantifier extendsto the end of the sentence. In (10) few congressmen does not bind they;its scope ends at the connective and.

As in the case of (4) above, this argument is not available in the case of

Some congressmen admire Kennedy, and they are very junior,(12)


just because

Some congressmen are such that they admire Kennedy and arevery junior,

(13)

in which the scope of some congressmen runs to the end of the sentence,entails that some congressmen admire Kennedy.

However, another argument is available. If (12) were equivalent to (13),its truth would require only that some of the Kennedy admirers in congressare very junior. But there is a reading of (12) on which its truth like thatof (10) requires that all of them are very junior.

(12) is comparable to

John bought some sheep and Harry vaccinated them,(14)

which is not equivalent to the existential:

Some sheep are such that John bought them and Harry vaccin-ated them.

(15)

For on an obvious reading (14) entails that Harry vaccinated all thosesheep said in the first clause to have been bought by John, and (15) doesnot. Both occurrences of them in (15) are bound by the initial quantifier;but them in (14) is not bound by that quantifier. So, in accordance withthe EvansNeale proposal, the second clause of (14) is true if and only ifHarry vaccinated the sheep that John bought. And, for the same reason, thesecond clause of (12) is true if and only if it is true that the congressmenwho admire Kennedy are very junior.

But now, just as an F invites another F , some F s invites someother F s. The truth of (12) seems to be compatible with that of

Some congressmen admire Kennedy, and they are old hands.(16)

And if it is, then the second clause of neither (12) nor (16) is equivalent tothe result of replacing they by the congressmen who admire Kennedy.So the proposal fails in this case, just as it does in the singular casediscussed above.

There is a difference: The congressmen who admire Kennedy has notbeen shown to be illegitimate or improper in the circumstances envisionedin the sense in which the author of Principia Mathematica is or theauthor of Principia Mathematica I met in the case described above. Theauthor of Principia Mathematica does not exist; the singular descriptionsimply fails to denote. The congressmen who admire Kennedy does not


fail to denote anything in the present case. The existence of some congress-men who admire Kennedy is sufficient for its legitimacy in this sense. Itis true of its denotation that they are, for example, congressmen. It is nottrue of its denotation that they are (all) very junior, if (12) is compatiblewith (16); but it is not true of the denotation of the author of PrincipiaMathematica that it is anything at all.

Now consider a sentence like

Some people on Charles Street have less than two bits betweenthem and they are unhappy

(17)

or

John told some students to share expenses, and Harry gave themmoney.

(18)

(17) is not equivalent to the simple existential

Some people on Charles Street are such that they have less thantwo bits between them and are unhappy.

(19)

The truth of (19) requires only that there be some people who have lessthan two bits between them and are unhappy; that of (17) requires that allthose people are unhappy.7 But the truth of (17) does not, in accordancewith the EvansNeale proposal, require that of

The people on Charles Street who have less than two bitsbetween them are unhappy.

(20)

For the truth of (20) rules out the possibility that there are some otherpeople on Charles Street with less than two bits between them.

And here an objection based on the fact that some invites some otheris just parallel to that raised in the singular case: It seems that we cansuppose (17) is true and also that there are some other people on CharlesStreet with less than two bits between them such that those people, togetherwith those alluded to in (18) have two bits or more between them. In thiscase the definite description that occurs in (20) is improper in the sense inwhich the author of Principia Mathematica is so: it fails to denote. Thereare no such people as the people on Charles Street with less than two bitsbetween them.

And with respect to (18) a similar conclusion is in order. On an obviousreading, (18) is true just in case Harry gave money to all those studentsof whom it is said in the first clause that they were told by John to share


expenses with one another. But this seems to be compatible with the truthof

John told some other students to share expenses, and Harry gavethem money.

(21)

So we can suppose both (18) and (21) are true; and in this case

(22) Harry gave money to the students told by John to shareexpenses

(22)

cannot be true not because it is not true in the circumstances that Harrygive money to (all) the students denoted by the definite description, butbecause the definite description has no denotation. All told, the studentsJohn advised were not told to share expenses with one another. Some ofthem were told to share their expenses with one another to the exclusionof some others, who were told to share their expenses with one another.There are in the circumstances no such students as the students told byJohn to share expenses with one another.

The definite descriptions that occur in (20) and (22), in the envi-sioned circumstances, contain predicates lacking a feature possessed bypredicates like congressmen who admire Kennedy. If some congressmenadmire Kennedy and some other congressmen admire Kennedy, it fol-lows that the former together with the latter are congressmen who admireKennedy. I shall say such a predicate is cumulative.8 It is in virtue of thisfeature that if there exist congressmen who admire Kennedy, a definitedescription based on this predicate must be legitimate.

The predicates people on Charles Street with less than two bitsbetween them and students told by John to share expenses need not becumulative. They are not so in the circumstances given above; and this iswhy the definite description that occurs in (20) is illegitimate despite theexistence of people on Charles Street with less than two bits between them.The definite description that occurs in (22) is also, for the same reason,illegitimate despite the existence of students who were told by John toshare expenses.

3.

Congressmen who admire Kennedy is a distributive predicate one trueof each of those things of which it is true. If F is a distributive predicate, itis the plural of some singular predicate A that is true of all and only those


things of which F is true: i.e., the F . So, if F is a distributive predicate,conditions for the legitimacy of the F are provided by

There are some things that are such that something is one ofthem iff it is an A,

(B)

The relation between a distributive predicate F and a singular predicateA for which it is the plural can be put by saying that if F is true of somethings, then

they are F iff every one of them is an A.9(D)

If, for any distributive F , some things are F and some other things areF , the former together with the latter are such that every one of them isan A, so all are such that they are F i.e. F is cumulative. A distributivepredicate is bound to be cumulative, and it is this that guarantees the truthof every instance of (B), provided only that there are things of which F inthat instance is true.

The predicates contained in the descriptions that occur in (20) and (22)are not distributive. There is no predicate in the singular of which either canplausibly be said to be the plural one guaranteed to be true of each of alland only those things of which one of them is true. Some nondistributivepredicates are like distributive predicates in being necessarily cumulative for example, people with $0.25 or more among them. And a descriptionbased on any such predicate is legitimate if there exist things of which it istrue; but (B) is irrelevant to deciding whether it is so or not.

A schema involving plural predicates for which there is no singularis needed for a principle which determines the legitimacy of a definitedescription based on a nondistributive predicate, one for which those basedon distributive predicates and so instances of (B) constitute a specialcase. But in light of (D) and the fact that if A is a singular predicate,something is A just in case it is one of those things of which the pluralof A is true, such a schema is provided by saying that, where F is anyplural predicate, the F is legitimate iff

There are some things that are such that theyX are F ; and allthings are such that theyY are F only if theyY are some ofthemX .

(S)

It is useful to assume here the resources of a two-sorted theory in whichlower case variables x, y, z, . . . are those of a first order theory with iden-tity, translated by singular pronouns, upper case variables X, Y , Z, . . . aretranslated by plural pronouns, and a formula like Xx is translated itx


is one of themX as in George Boolos interpretation of the language ofsecond order logic.10 In such a theory, (D), (B) and (S) are the translationsof

FX$ 8x.Xx ! Ax/,(D0)9X.8x.Xx $ Ax//(B0)

and

9X(FX & 8Y (FY ! Y < X)),(S0)in which Y < X abbreviates 8x.Yx ! Xx/, every one of themY isone of themX i.e., theyY are some of themX.

Natural models for the sentences schematized by (B) and (S) areprovided by the nonempty subsets of some set, and in such a model, thesome of relation< is a partial order on the extension of any plural predic-ate, distributive or not. Moreover, the extension of any plural predicate Fhas a least upper bound with respect to this relation, the sum of those thingsof which F is true11 which need not, however, belong to that extension.For example, the extension of people on Charles Street who have lessthan two bits between them has a least upper bound with respect to thisrelation in the extension of people on Charles Street whether it containsthat upper bound or not. In these terms, a predicate F is cumulative iff itis true of all sums of things of which it is true. In particular, to say thatcumulativeness may fail for some nondistributive F is to say that in somecircumstances it is true that there are some things such that they are F butfalse that there are some things such that they are F and also such that anythings that are F are some of them.12

It is to be emphasized that a description based on a cumulative predic-ate need not be maximal as Neale defines this term. If F is a cumulativepredicate and there are some things of which it is true, the F is bound tobe legitimate; but the F is maximal only if, in addition, any predicate Gtrue of those things of which F is true is true of every one of them.13 Thusthe congressmen who admire Kennedy, like any other description basedon a cumulative predicate, is legitimate; but if both (12) and (16) are true,it is not maximal.

Maximality is pretty obviously a contextual matter, and in the case of

Harry bought some books. He put them in his office with someother books he bought

(23)

and

Several politicians entered the room. They went straight overand talked to several other politicians.14

(24)


Neale follows Evans in adding content to a definite description recoverablefrom the clause containing the antecedent of a pronoun by drawing on itscontext. The result of replacing the plural pronoun by the books Harrybought in (23) and by the politicians who entered the room in (24)are not false but incomplete. Though a description full enough to securemaximality is not recoverable from the clause containing the antecedentof the pronoun alone, such a description can be gleaned from that clausetogether with information provided by the larger context.

I believe this is the line of defense Neale would give for the problempresented by the congressmen who admire Kennedy if (12) and (16) arecompatible. And assuming that he would say the same in the case of (20)and (22), perhaps it is enough for present purposes to simply underscorethe differences to which I have called attention. There is a differencebetween

The author of Principia Mathematica was English(25)and

The author of Waverley was English.(26)Though neither is true, and this, in each case, is a consequence of the non-existence of a uniquely specified author who is English; only the formerfails to uniquely specify an author at all. Every author of Principia Math-ematica was English. And although there is no distinction among singularpredicates between those which are cumulative and those which are not, itis the failure of cumulativeness for a plural predicate that corresponds tofailure of uniqueness as in the case of (25).

If all this is acknowledged, it may be conceded that the EvansNealeproposal is to be defended by recourse to enriching an incomplete de-scription as Neale suggests. First, however, I wish to press the matter alittle further. It might be thought15 that the difference between (12) and thesimple existential (13) is captured by representing (12) in the two sortedtheory introduced above as something like

9X(X admire Kennedy & 8x(Xx! x is very junior)).(27)In the universe of congressmen, there are some who are such that theyXadmire Kennedy, and everything thatx is such that itx is one of themX isvery junior i.e. all of them are very junior. If this is right, the differencebetween (12) and (13) is not a matter of truth conditions. The plural of isvery junior is distributive and, via an instance of (D), (27) is equivalent to

9X(X admire Kennedy & X are very junior),(28)


which represents (13). So the argument for saying they in (12) is unboundfrom the fact that it requires all of the admirers of Kennedy be very junioris disarmed.

There is perhaps reason to doubt that (27) is an appropriate representa-tion of (12) in the fact that

Few congressmen admire Kennedy and all of them are veryjunior

(29)

plainly does not say that few congressmen both admire Kennedy and aresuch that all of them are very junior. And if (10) is represented in a wayanalogous to (27), this is what it will say; for (29) is equivalent to (10).

But there are other differences between (12) and (10) or (29). The equi-valence of (10) to the result of applying the EvansNeale proposal in thisinstance is not open to the objection that (10) is compatible with (16) orsome variation on it. (10) is not compatible, for example, with

Few other congressmen admire Kennedy and they are old hands(or: . . . and they, too, are very junior).

(30)

Few F does not invite other F in the way that some F does, andthis is a feature which few F shares with the F and all F , no F , notmany F , most F . . . none of which occur inside the scope of a universalquantifier for example, in the place occupied by some donkeys in

Every man who bought some donkeys vaccinated them.(31)

If some is replaced by few (the, all . . . ), it must be given widescope.16 Quantifiers that can occur as I am assuming some donkeys doesin (30) include a few F , several F , three F , three or more F . . . allof which also occur as some congressmen does in (12) and may be calledindefinite descriptions.

4.

Neale, like Evans and others, interprets quantified sentences in terms ofgeneralized quantifiers. Quantifiers in the traditional square of opposi-tion are interpreted via the subject-predicate structure of the sentencesof ordinary English in which they occur. For example, the customaryrepresentation of Every man is mortal, the first order formula,

8x(man x! mortal x),


is recast as something like either

[every x](man x; mortal x),

in which every is taken to denote a binary quantifier, or, in Nealestreatment,

[every x: man x](mortal x),

in which every man is taken to denote a (unary) restricted quantifier.All three representations have the truth conditions expressed by the first

order formula, and so do the representations of the plural All men aremortal as

8X(men X! mortal X)

and

[all X: men X](mortal X).

But those formulated with a binary or restricted quantifier reflect the gram-matical structure of the subject-predicate sentences they represent as thecustomary formulation does not. This is especially striking in Nealestreatment, but both schemes are designed to allow for the generalizationof the notion of a quantified sentence of English to cases for which thereis no combination of quantifier and connective like that of the standardrepresentation of universal and existential statements, for example,

Most men are mortal.17

Any noun phrase is amenable to Neales treatment which consists of adeterminer followed by a nominal construction with a count noun as head,in a subject-predicate sentence. In fact the representation of a sentenceNeales way is to be regarded as a (partial) structural description of thatsentence one that differs from a description of its surface structure onlyin explicitly specifying scope, for example.

If quantifiers are represented as binary, it is natural to suppose they aredeterminers.18 In Neales treatment quantifiers are whole noun phrases. Anoun phrase, for example a pronoun, occurs in the scope of a quantifier andis thus bound by it just in case it is a constituent of the smallest sentenceconstituent of which the quantifier is a proper part. And this is in keepingwith Evans characterization of binding; there it is noun phrases that bindnoun phrases.19


Thus, in particular, definite descriptions, singular and plural, are quan-tifiers. (9) is represented as

[the x: author of Principia x & I met x](x was English),

the truth conditions for which are the same as those for its customary firstorder representation in accordance with Russells theory of descriptions.The condition expressed via a sequence of quantifiers and connectives:

9x.Ax & 8y.Ay ! x D y//(R)is conveyed by [the x: Ax]. Like other quantifiers its instances are variablebinding operators.

So what the EvansNeale proposal comes to, at least in Neales case,is the introduction of a quantifier that binds a pronoun not bound by itsantecedent. (10) and (12) are represented by

[few X: congressmen X](X admire Kennedy) & X are veryjunior

and

[some X: congressmen X](X admire Kennedy) & X are veryjunior

X is, in its last occurrence, unbound. In each case it is to be replaced by adefinite description to obtain

[few X: congressmen X](X admire Kennedy) & [the X: con-gressmen X & X admire Kennedy](X are very junior)

and the result of replacing few by some. The final occurrence of X ineach case is bound by the added quantifier.

But then it seems one can ask, why this quantifier? And here, in thecase of

Every man who bought a donkey vaccinated it,(32)

Neale abandons Evans proposal and chooses another quantifier to bind theanaphoric pronoun. He says,Following Geach (1962), it is pretty generally agreed that (32) is true just in case every manwho bought at least one donkey vaccinated every donkey he bought. We might thereforerender (32) as (320):

8x8y(man x & donkey y & x bought y ! x vaccinated y).20(320)


His objection to (320) is that the indefinite description in the relative clausecalls for existential treatment, and

8x(man x & 9y(donkey y & x bought y! x vaccinated y)(33)leaves the final occurrence of y unbound. But the result of applying theEvansNeale proposal to (32),

Every man who bought a donkey vaccinated the donkey hebought,

(34)

or, in Neales treatment,

[every x: man x & [a y: donkey y](x bought y)]([the y: donkeyy & x bought y](x vaccinated y)),

(35)

does not provide the same truth conditions for (32) as (320). A man x whobought more than one donkey is sufficient to falsify (34) or (35); for in thatcase nothing uniquely satisfies donkey y & x bought y. But this is notsufficient to falsify (320), which requires only that any such man vaccin-ated every donkey that he bought. This is all that (32) requires, and Nealeconcedes that this is a genuine failing in the EvansNeale proposal.21

He does not simply adopt (320) at the expense of (35). He says,There are good grounds for thinking that the universalization of the indefinite description in(320 is a logical illusion. I want to explore the idea that it is, in fact, the anaphoric pronoun,not the indefinite description, that has a universal character.22

And pursuing a suggestion of Davies 1981,23 he take the anaphoric pro-noun in (32) to have the sense of a numberless definite description: [whey: donkey y & x bought y]. (32) is taken to say roughly Every man whobought a donkey vaccinated the donkey or donkeys he bought. The samedevice is to serve for sentences like the plural version of (32), i.e. (31); andthe result has the same truth conditions as (320).24

Now I am not at all sure how this proposal is to be spelled out, espe-cially in cases involving the plural. But instead of attempting to assess itdirectly,25 I want to suggest a partial defense of the NealeEvans proposalin cases like (31), beginning with a rather simple suggestion about thesingular (32).

In reporting the truth conditions required by Geach, the English versionNeale attributes to him involves quantifying over donkeys twice. That sen-tence . . . every man who bought at least one donkey vaccinated everydonkey he bought is, strictly speaking, to be rendered not by (320) butby

8x(man x & 9y(donkey y & x bought y)! 8y(donkey y & xbought y! x vaccinated y))

(3200)


or, in Neales treatment,

[every x: man x & [a y: donkey y](x bought y)]([every y:donkey y & x bought y](x vaccinated y)).

(3200) is demonstrably first order equivalent to (320); and it represents therelative clause with an existential quantifier. The only way in which it dif-fers from (34) is with respect to the quantifier taken to bind the anaphoricpronoun; and that pronoun is, as Neale suggests, taken to itself introduce auniversal quantifier.

It is in keeping with the general strategy with respect to surface struc-ture behind the interpretation of quantifiers Neale adopts to require that theindefinite pronoun be interpreted here in the same way as those that occurin (4) and (7). Also, as Neale notices,26 in a sentence like

Every man who bought two or more donkeys vaccinated them(36)

the interpretation of two or more donkeys as a universal quantifier is notvery plausible at all; and I believe this point extends to a few donkeys,several donkeys, three donkeys, . . . perhaps all plural quantifiersclassified as indefinite descriptions above but some donkeys.

Notice, however, that the view ascribed to Geach as represented by(3200) also extends to all these cases as well as (31). Truth conditions for(31) are provided by

8x(man x & 9X(donkeys X & x bought X)!8y(donkey y &x bought y! x vaccinated y).

(310)

Every man who bought some donkeys vaccinated every donkey he bought.In Neales treatment,

[every x: man x & [some X: donkeys X](x bought X)]([everyy: donkey y & x bought y](x vaccinated y)).

(310) follows from (3200) via an instance of (D). Truth conditions for (36)are provided by

Every man who bought two or more donkeys vaccinated everydonkey that he bought,

(360)

in Neales treatment

[every x: man x & [two or more X: donkeys X](x boughtX)]([every y: donkey y & x bought y](x vaccinated y)).


If it is assumed that some donkeys were bought by x is entailed by twoor more donkeys were bought by x, (360) follows from (310); and similarremarks are in order for all other indefinite descriptions in this context.

It seems then that there is no need for a quantifier other than the firstorder universal quantifier to secure Geachs truth conditions without tam-pering with the interpretation of the indefinite description in any of thesecases. However, this strategy does not accommodate plural predicates forwhich there is no singular i.e. nondistributive predicates as they occurfor example in

Everyone who met some people with less than two bits betweenthem pitied them

(37)

and

Every dean who advised some students to share expenses gavethem money.

(38)

It might be thought that in order to account for these cases the universalquantifier need only be cast in the plural.

8y(donkey y & x bought y! x vaccinated y)(39)is equivalent to

8X(donkeys X & x bought X! x vaccinated X)(40) all donkeys x bought were vaccinated by x. So (40) instead of (39) canbe used to specify truth conditions for (31) and (36) and a plural versioninvoked for sentences like (37) and (38).

But all demands a distributive predicate:

All people with less than two bits between them are unhappy(41)and

He give money to all students advised by him to share expenseswith one another

(42)

are incoherent if not ungrammatical27 if, as I believe, it is fair to drawa firm distinction between (41) and (42) and the result of replacing thequantifier in each of them by a quantified partitive construction; for thesentences

All of the people with less than two bits between them areunhappy

(43)


and

He gave money to all of the students advised by him to shareexpenses with one another

(44)

are quite in order.In fact there is a striking difference here between the F and all other

quantifiers which, like few F , do not invite other F and do not regularlyoccur inside the scope of a universal quantifier. Occurrence of any of thesewith a nondistributive F is at best questionable as, for example, in

Most critics who admire only one another live in Boston;Few people who have less than a nickel among them are happy;John met no students who shared expenses with one another.

(45)

In each case the result of replacing the quantifier determiner by the is notopen to question and neither is the result of adding of the to convert thequantifier into a quantified partitive.

Thus truth conditions for (37) and (38) are specifiable respectively by

Everyone who met some people with less than two bits betweenthem pitied all of the people with less than two bits betweenthem that he met,

(46)

and

Every dean who advised some students to share expenses gavemoney to all of the students advised by her to share expenses.

(47)

But apart from the fact that, thus modified, the present strategy amountsto readopting the EvansNeale proposal, universally quantified partitiveconstructions serve in these cases only because they occur with a dis-tributive predicate. All demands a distributive predicate as verb phrase,whether it occurs in a partitive construction or not; and so do most othernon-indefinite quantifier determiners. Sentences like

All (of the) critics in Boston admire only one another;No (none of the) people on Charles Street have less than a nickelamong them;Few (of the) students shared expenses with one another

(48)

are as bad as (41), (42) and those at (45).28 Here, it seems, a quantifiedpartitive construction is no better than a non-partitive quantifier, though theuse of the alone, like that of an indefinite determiner is unexceptionable.


So it seems that if nondistributive predicates are to be accommod-ated, the EvansNeale proposal for specifying truth conditions must bereinstated for sentences containing a plural pronoun with an indefiniteantecedent inside the scope of a universal quantifier. I note only that thiscalls for hedging against failure of cumulativeness as attested to bysentences like

Every man who met some critics who admire only one anotherintroduced them to some other critics who admire only oneanother that he met.29

(49)

NOTES

1 Evans (1977a, b, 1980).2 Neale (1990, 1993).3 This is a variation on an objection due to Geach (Neale, 1990: 247) to which Evans(1980) responds.4 Neale (1980: 228), attributes such a view to Robin Cooper in connection with sentencesof a sort to be considered below.5 Evans (1980: 222223). See also note 3.6 Evans (1980: 217).7 I am supposing that and in (17), by contrast with (19), conjoins two complete clauses.(17) conveys what is conveyed by

Some people on Charles Street have less than two bits between them. They are unhappy

or

Some people on Charles Street have less than two bits between them, and its not surprisingthat they are unhappy.

8 As the term is introduced in Quine 1960 in application to mass terms and extended toplural predicates, e.g., in Cartwright (1993: 223224). Much of what I say here about theplural extends to mass predicates in ways indicated in that paper.9 F is to be at least extensionally equivalent to the morphological plural of A. I do notknow how to guarantee more than this.10 Boolos (1984, 1985a, b). Cartwright (1993, 1996).11 I have long called such a least upper bound the fusion or (mereological) sum of thosethings of which a plural or mass predicate is true, though explicitly, only since 1975 (p. 184and note 10). A structure (M ,


12 That is, such that an instance of (S0) is false. (S0) is Richard Sharvys (1980) conditionfor the legitimacy of a plural definite description. Sharvy notices that if it denotes anythingthe F denotes a mereological sum defined in my way. (On p. 608 he says, in effect, thatmy definition is not his, but that is a slip.) He also notices that the legitimacy of the F requires that F be true of the sum it denotes; and the existence of some X which is boththe least upper bound of the extension of F with respect to < and such that F is true of itis equivalent to (S0) in this instance.13 Neale (1990: 180).14 Neale (1990: 242).15 I thought so in Cartwright (1993: 147).16 For example, as in Few donkeys are such that every man who bought them vaccinatedthem.17 Wiggins (1980).18 This is the view defended by Keenan and Stavi (1986) and taken up by Westerstahl(1989). In Cartwright (1996) I side (very sketchily) with Jackendoff (1977) against thisview in light of features of partitive constructions.19 Evans seeks to generalize on what he says in the plural case:

[C]onsideration of a wide range of examples containing plural quantifiers supports thegeneralization that a pronoun will be interpreted as bound by a quantifier phrase only if itprecedes and c-commands the pronoun. (1980: 219, my emphasis)A quantifier phrase can, I think, only be a noun phrase: A constituent A c-commands aconstituent B if and only if B is dominated by the first branching node which dominates A(ibid.) If a quantifier phrase were some proper part of a noun phrase, it would c-commandnothing outside that noun phrase.20 (1990: 223).21 (1990: 228).22 (1990: 225).23 (1990: 235).24 That is, On Russells assumption that [a y: Fy](Gy) and [some y: Fy](Gy) areequivalent . . . (p. 236).25 It is further elaborated in Ludlow and Neale (1991).26 (1990: 225).27 It may be said that such sentences as these have a group reading on which the quantifierranges over collections of students or people on Charles Street of whom the predicateis true. Compare Most lovers will eventually hate each other attributed by Westerstahl(1989) to Hans Kamp as an example of this phenomenon or All students who weremarried are split up. If this is right, then in the circumstances in which the description thatappears in (18) was said to be illegitimate, it need not be so. Timothy Smiley (1997, withAlex Oliver, The Logic of Plurals, seminar, Lent term, Cambridge University.) holds that

The joint authors of multi-volume treatises on logic

denotes Russell and Whitehead and Hilbert and Bernays two pairs; and this seems right,though all cannot here replace the, I think; and while all and other quantifiers oftendemand a distributive predicate as nominal complement, I do not think that any of them de-mands a group reading in the absence of reformulation with a collective noun like groupor collection.


28 Of course there is

All the kings horses . . . couldnt put Humpty Dumpty together again,

but for various reasons this seems exceptional.29 This work was completed in Cambridge, England during the spring of 1997. Thanks forcomments are due especially to Timothy. Smiley and Alex Oliver and, as ever, to R. L.Cartwright. Thanks are due also to two anonymous referees for this journal, especially toone who alerted me to a real lack of clarity about the difference between cumulativenessand maximality. I hope matters are here improved.

REFERENCES

Boolos, G.: 1984a, To Be Is to Be the Value of a Variable (or Some Values of SomeVariables), Journal of Philosophy 81, 430449.

Boolos, G.: 1985a, Nominalistic Platonism, Philosophical Review 94, 327344.Boolos, G.: 1985b, Reading the Begriffeschrift, Mind 94, 331344.Cartwright, H. M.: 1975a, Some Remarks about Mass Nouns and Plurality, Synthese

31, 395410. Reprinted in Pelletier, F. J. (ed.): 1979, Mass Terms: Some philosophicalProblems, Reidel, Dordrecht, pp. 3146.

Cartwright, H. M.: 1993, On Plural Reference and Elementary Set Theory, Synthese 96,201254.

Cartwright, H. M.: 1996, Some of a Plurality, in Philosophical Perspectives 10, Meta-physics, Blackwell, Oxford, pp. 137157.

Davies, M.: 1981, Meaning, Quantification, Necessity, Routledge, London.Evans, G.: 1977a, Pronouns, Quantifiers and Relative Clauses (I), Canadian Journal of

Philosophy 7, 467536. Reprinted in Evans 1985, pp. 76152.Evans, G.: 1977b, Pronouns, Quantifiers and Relative Clauses (II), Canadian Journal of

Philosophy 7, 777797. Reprinted in Evans 1985, pp. 15375.Evans, G.: 1980, Pronouns, Linguistic Inquiry 11, 337362. Reprinted in Evans 1985, pp.

214248.Evans, G.: 1985, Collected Papers, Clarendon Press, Oxford.Gardenfrs, Peter (ed.): 1987, Generalized Quantifiers, Reidel, Dordrecht.Jackendoff, R.: 1977, X Syntax: A Study of Phrase Structure, MIT, Cambridge, MA.Keenan, E. L. and Stavi, J: 1986, A Semantic Characterization of Natural Language

Determiners, Linguistics and Philosophy 9, 253326.Ludlow, P. and Neale, S: 1991, Indefinite Descriptions: In Defense of Russell, Linguistics

and Philosophy 14, 171202.Neale, S.: 1990, Descriptions, MIT, Cambridge, MA.Neale, S.: 1993, Grammatical Form, Logical Form, and Incomplete Symbols, in A.

D. Irvine and G. A. Wedeking (eds), Russell and Analytic Philosophy, University ofToronto, Toronto, pp. 97139.

Oliver, A. and Smiley, T. J: 1997, The Logic of Plurals, seminar notes, Lent term,Cambridge University, Cambridge.

Quine, W. V.: 1960, Word and Object, MIT Press, Cambridge, MA.Sharvy, R.: 1969, Things, The Monist 53, 488504.Sharvy, R.: 1980, A More General Theory of Definite Descriptions, Philosophical Review

89, 607624.


Westerstahl, D.: 1989, Quantifiers in Formal and Natural Languages, in D. Gabbay and F.Guenthner (eds), Handbook of Philosophical Logic, Volume IV, Reidel, Dordrecht, pp.1131.

Wiggins, D: 1980, Most and All: Some Comments on a Familiar Programme, andon the Logical Form of Quantified Sentences, in M. Platts (ed.), Reference, Truth, andReality, Routledge, London, pp. 318346.

Tufts University6 Whittier Place 3NBoston, MA 02114U.S.A.E-mail: [email protected]

a note on plural pronouns

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