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Towards a Referential Analysis of Temporal ExpressionsAuthor(s): Mrvet EnSource: Linguistics and Philosophy, Vol. 9, No. 4 (Nov., 1986), pp. 405-426Published by: SpringerStable URL: http://www.jstor.org/stable/25001253

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MURVET EN(

TOWARDS A REFERENTIAL ANALYSISOF TEMPORAL EXPRESSIONS

1. INTRODUCTIONNatural language tenses are generally treated as sentential operators insemantic theories.What motivates such treatments is the widespreadassumption that the tense of a sentence affects the temporal interpretation of all expressions in the sentence. This in turn rests on theassumption that all expressions are interpreted relative to times.1Thispaper has two goals. First, it aims to show that, in a tensed clause, verbsare the only expressions whose interpretation is neccessarily affected bythe tense, and that this point is obscured if one insists on semanticallyanalyzing tenses as sentential operators. Second, it aims to show thatonlypredicates of individuals are interpreted relative to times, suggesting thattimes should be viewed as individuals selected as arguments by thepredicates in addition to non-temporal arguments.

2. THE SCOPE OF TENSE AND NP'SClassical analyses, where tense is treated as a sentential operator,automatically make predictions about the temporal interpretation ofNP's. I will first summarize these predictions, then show them to beempirically inadequate. The evidence provided will indicate that theinterpretation of NP's is temporally independent of the tense that ispresent in the syntax. This will provide the most significant evidenceagainst treating tense as a sentential operator.At first glance, a semantic analysis which treats tense as a sententialoperator seems to account for certain temporal ambiguities in a simpleand elegant way, by appealing to differences in scope relations betweenNP's and the tense. For example, (1) is taken to be ambiguous, dependingon whether we are talking about a past president or the present president.

(1) the president was a foolThe ambiguity of (1) is explained by saying that the denotation of thenoun presidentwill vary according towhether or not it is in the scope ofthe past tense operator. This is accomplished by providing semantic rulesfor tensed sentences along the lines in (2).2Linguistics and Philosophy 9 (1986) 405-426.? 1986 byD. Reidel Publishing Company.


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(2) Where qp s a sentence, P isPast and F isFuture,(i) Pqp is true at time t iff there is a time t' such that


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TEMPORAL EXPRESSIONS 407

3. PROBLEMS FOR THE CLASSICAL ANALYSIS

The analysis of tense outlined above predicts that (3) below, like (1),willhave two readings, depending on the relative scope of the subject NPand tense.(3) all richmen were obnoxious children

These readings are represented by (4) and (5).4(4) Vx [rich-man(x)-> P obnoxious-child(x)](5) PVx [rich-man(x) -> obnoxious-child(x)]

In (4), the subject is outside the scope of the past tense operator. Thesentence will be true on this reading if and only if there is a past timewhen everybody who is a richman now was an obnoxious child. In (5),the subject is inside the scope of the past tense operator, and thesentence will be true on this reading if and only if there is a time in thepast when everybody who was a rich man at that time was an obnoxiouschild at that time. Note that the sentence will never be true on thisreading, because it requires that the individuals be richmen and obnoxious children at the same.According to traditionalanalyses, then, (3) cannever be used to make a true statement about past rich men.

(4) and (5) are the only alternatives for the relative scope of thequantifier and the tense operator in (3).We can quantify either overpresent richmen or over past richmen. But supposewe want to quantifyover both present and past rich men simultaneously. It is easy formanyspeakers to imagine (3) as saying something about every person who is arich man now or was a rich man in the past. Given standard analyses,there is no way we can allow the universal quantifier to range over bothpast and present richmen. The subject is eitherwithin the scope of tenseand gets interpreted at a past time, or it isoutside the scope of tense andgets interpreted at the present.

Below is another example where we may want to quantify inmore thanone tense slot at a time. Suppose that there is a successful investmentclub whose members are assured of getting rich.The members can thenafford to buy a house.

(6) every member of our investment club will buy a houseThere is a readingwhere (6) says of everybody who is a member of ourinvestment club now or will be amember in the future that he will buy a

house, whether or not he is amember at the time of the purchase. Again,this reading is unavailable in standard analyses. If the subject has wide


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scope over future tense,we will be saying something of present membersonly. If it has narrow scope with respect to the future tense, we will besaying something of future members only, and furthermore,we will beclaiming that theywill still be members when they buy a house.What weneed for the readingwe want is to be able to quantify over present andfuture (and possibly past) members simultaneously,without making anyclaims about theirmembership when they buy a house.The two examples I have given involve subjectNP's. But the problemis not restricted to subjects.

(7) the Citizens' Committee will sue every politician violatingconflict of interest lawsIn (7), the universal quantifier in the object NP must be able to rangeover present and future politicians, and even of past politicians. If, forexample, Bob is not a politician now but will be one in the future and willviolate conflict of interest laws, on one reading of the sentence, we canexpect him to be sued along with present crooked politicians.The difficulties we encountered are not restricted to the interpretationof NP's with universal quantifiers.

(8) every senior will have met a presidentLet us imagine that (8) isuttered in the following context.We are talkingabout the present seniorswho consist of Tom, Mary andBob. Reagan ispresident now and he will lose the next election to Kennedy. Bob metJohnson while Johnsonwas president. Tom will meet Reagan tomorrowwhile he is still president. Mary met Kennedy yesterday. In February1989, itwill be true that every senior has met a president. Therefore it istrue now that every senior will have met a president in February 1989.Let us now look at what readings are allowed for (8) under the classicalanalyses. Since we want a different president for every senior, we wantevery senior to have wide scope over a president. And since we aretalking about present seniors, we want every senior to have wide scopeover the tenses.We then have three options.5

(9) Vx[senior(x) -- F P 3 y[president(y) & meet(x, y)]](10) Vx[senior(x) - 3 y[president(y) & F P meet(x, y)]](11) Vx[senior(x)- F 3y[president(y) & P meet(x, y)]]

In (9), the object NP is inside the scope of both tenses, and the sentencewill be false on this reading because at the timeMary met Kennedy, hewas not yet president. In (10), the object NP has wide scope over bothtenses, and the sentence will be false on this reading because Johnson


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and Kennedy are not presidents now. In (11), the object has narrowscope with respect to the future tense, but wide scope over past tense.The sentence will be false on this reading, because this reading is aboutfuture presidents and Johnson will not be a president in the future. Allavailable readings will thus turn out to be false, although every seniorwill have met a president.In the examples discussed so far, the sentences seemed to havereadings which required NP's to be evaluated in more than one tense slotsimultaneously, e.g. in the past, present and future, something notallowed by classical analyses. The time needed for the NP's properlyincluded the time allowed by the tense operator. The next set of exam

ples indicate that NP's may need to be interpreted at times which do notoverlap either with the present or with the time provided by the tense.Suppose that the president is giving a party for people who were held

hostage in Iran. John will attend this party. We want (12) to be true ifJohn meets all the hostages.(12) John will meet every hostage at the president's party

If we give every hostage wide scope over tense, we will be sayingsomething about present hostages. Ifwe give tense wide scope over everyhostage, we will be saying something about future hostages. Again, theseare the only available alternatives under traditional analyses. This givesthewrong results, since we are talking about past hostages. But there isno past tense in (12), and therefore we will not get the readingwe want.6Note that (12)may be followed felicitously by "and he will ask them howit feels not to be hostages anymore." In one breath, we may refer to theseindividuals as hostages and claim that they are no longer hostages,without uttering a contradiction.

(13) below is a similar example.(13) every fugitive is now in jail

This sentence has present tense and standard analyses predict only thereadingwhich involves individualswho are fugitives now. Therefore thesentence should be contradictory. But clearly, it also has a non-contradictory readingwhere we are saying of individualswho were fugitivesthat they are now in jail. Once again, there is no past tense in thesentence, yet we want the subject to be interpreted at a past time.A similar example was observed inCooper (1978). The following is hisexample (58).

(14) every congressman who remembers a president will be at theparty


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Cooper points out that this sentence should have a reading that turnsoutto be true in the following context. The presidency will be abolished inthe future, and years after that, a partywill be given for individualswhoare congressmen then, and who are old enough to remember a president.We want every congressman to be in the scope of future tense (we aretalking about future congressmen), and a president to be in the scope ofevery congressman (they may remember different presidents). But thisputs a president inside the scope of future tense and gives us a readingabout future presidents. We wanted, instead, a reading about pastpresidents, even though there is no past tense in the sentence.A furtherproblem raised by the classical analysis is that itgives rise toscope paradoxes. Consider (15).

(15) every congressman who remembers an astronaut will be at theparty

Suppose this sentence is about present astronauts and future congressmen, i.e. there will be a party in the future which will be attended byindividuals who are congressmen at that future time andwho rememberthe individualswho are astronauts now. The classical analysis allows us totalk about present astronauts, because we are assuming somemechanismfor taking NP's outside the scope of future. This example is differentfrom (14) in that it does not require us to access a time that is neitherfuture nor present. It does, however, lead to a scope paradox. Thesentence can be true on this reading if the congressmen rememberdifferent astronauts. Therefore, we need to give every congressmanwidescope over an astronaut. every congressman also needs to be inside thescope of the future tense, sincewe are talking about future congressmen.This would put an astronaut also in the scope of the future tense, notallowing a reading about present astronauts. If we gave an astronautwide scope over the future tense, thiswould also give itwide scope overevery congressman, requiring the congressmen to remember the sameastronauts, again an undesirable result. There is no way of giving anastronaut wide scope over the tense and narrow scope with respect toevery congressman ifwe are talking about future congressmen. Thus thedesired reading isunavailable.

4. TENSE OPERATORS IN NP'SThe evidence presented in the previous section is problematic for theclassical analysis only under certain assumptions about themapping fromsyntactic structures to semantic structures.The three crucial assumptions


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in this case are the following: 1) every tense operator allowed in thesemantic representations of the sentences of a natural language corresponds to a syntactic tense, which in turn corresponds to a tense

morpheme (possibly null) found in the surface forms of that language,7 2)a tense operator is introduced into the semantic representation of asentence only if the corresponding tense is present in the syntacticstructure of the sentence and the surface form contains the appropriatetensemorpheme, and 3) the scope of a tense operator always includes apredicate which comes from the verb of the sentence.8These assumptions about tense operators are implicit inmost analysesof tense in natural languages, and they seem to provide the strongestconstraints on the semantics of tense in natural languages, reflecting aview which can roughly be summarized as 'whatyou see iswhat you get'.However, it is also these assumptions that render classical analysesempirically inadequate.Getting rid of the constraints they imposewouldallow us to provide a semantics thatwould avoid the problems discussedabove.9 For example, the readingwe wanted for (13) can be representedas in (16).

(16) Vx[P[fugitive(x)]-> in-jail(x)]According to our semantic rule in (2), (16) says of past fugitives that theyare now in jail.We are thus able to represent the non-contradictoryreading of the sentence. In this representation, the operator introduced isthe past tense operator and English does indeed have a past tense

morpheme. However, the past tense operator is introduced into thesemantic representation in the absence of past tensemorphology in thesentence. Furthermore, this past tense operator is attached to an atomicformula whose predicate comes from the head noun of the subject NP,thus leaving the predicate contributed by themain verb outside its scope.All three assumptions have to be abandoned in order to account forsome of the readings discussed in the previous section. For example, forthe readings of (6), (7) and (8) thatwe were interested in, it seems thatnoingenuity in the order of introduction of past, present and future operators will get us the desired readings.We could attempt to solve ourproblems, however, by defining new tense operators in addition to past,present and future. Suppose we introduce a new operatorW and define itin the following way:

(17) Wqp is true at time t iff Pep or p or F


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present or in the future.Given this new operator, we can now representthe desired reading of (8) as in (18).(18) Vx[senior(x) --*3 y[W president(y) & F Pmeet(x, y)]]

One could define other tense operators thatmean true-now-or-at-somefuture-time, true-now-or-at-some-past-time, true-at-some-past-timethat-includes-a-sunny-day, true-on-my-birthday, etc. Assuming that theclass of tense operators necessary for analyzing natural languages issomehow constrained, our taskwould be to uncover these constraints.What kinds of tense operators should be allowed, and what particularoperators are required for an adequate treatment of tense in naturallanguages would, then, be an empirical matter. Note that a number ofsuch operators have already been proposed, e.g. Kamp's NOW (Kamp1971), and operators familiar from tense logic, likeG which is 'itwillalways be true that.. .', and H which is 'it has always been true that...'"

5. STRICTLY LOCAL OPERATORSIf we pursued this line, we would hope to end up with an empirically

motivated class of tense operators necessary for the analysis of naturallanguages. Thus one might think that the problems with the analysis oftense reduce to the problem of defining the right operators. However,such an approach raises questions regarding the scope of these operators.Let me note to begin with that the tense operators introduced into thesemantic representations to get NP interpretations right,must have verylimited scopes. For example, having acknowledged the need for something like the past tense operator for (13) (we are saying of past fugitivesthat they are now in jail), we must make sure that the scope of thisoperator is exactly as in (16), and that (19) is blocked as the representation of themeaning of (13).

(19) Vx[P[fugitive(x) -- in-jail(x)]]In (19), the scope of the past tense operator extends over the wholeconditional. (19) would be true if and only if whoever was a fugitive at apast time was also in jail at that past time, clearly a reading neveravailable for (13).

Similarly for (12)(12) Johnwill meet every hostage at the president's party

we would need a past tense operator inside every hostage, since theseindividuals have been hostages in the past on the intended reading. But


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this operator must not have scope over the future tense operator,because all readings of the sentence require the time of meeting to be inthe future, and giving the past operator wide scope over the futureoperator would allow the time of meeting to be in the past.This evidence shows that verbs are always interpreted according to thetense provided by the tense morpheme in the sentence, and whateverapparatus is devised to get theNP meanings right, itmust not affect verbinterpretations. That is to say, the tense operators in the semanticrepresentations of NP's must never have scope over the verb or the verbtense (the 'true' tense).Should anNP tense operator be allowed to have scope over other NP'sin the sentence? In other words, are the various NP's in a sentencetemporally dependent on each other? A brief look at the data shows thatthey are not. Consider (8), repeated here.

(8) every seniorwill have met a presidentWe wanted this sentence to be true in a context where we were talkingabout present seniors and individualswho were presidents in the past,present or future. Therefore the relevant times are different for the twoNP's every senior and a president. Similarly for (14),

(14) every congressman who remembers a president will be at theparty

on the intended reading discussed above, every congressman needs to beevaluated at a future time, whereas a president needs to be evaluated at apast time. It seems that in natural languages, the relevant time for eachNP may be different. Thus the NP's are temporally independent of eachother, andwe must provide an analysis that guarantees this.11

We have seen that the temporal interpretation of an NP does not affectthe interpretation of the verb, the 'true' tense, or anotherNP. Thereforesuch elements must be outside the scope of any tense operator introduced into the semantic representation of an NP. This still leaves openthe question of whether or not the 'true' tense operator, which corresponds to the tensemorphology in the sentence and which affects verbinterpretations, should take scope over the tense operators introducedinto the semantic representations of NP's. In the classical analysis oftense, the verb tense crucially affects the interpretation of NP's. Atwo-way ambiguity is predicted for sentences like (1) because a) thescope of the tense is the minimal sentence which includes the tense, andb) some independentlymotivated mechanism such asQuantifying In (orQuantifier Raising, or Cooper-storage) allows representationswhere the


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NP is not in the scope of the tense operator. I have argued that such anapproach is too restrictive, and blocks readings which the Englishsentences do seem to have. A sentential scope analysis which is augmented along the lines discussed above, with the introduction of newtense operators into the representation of NP's, avoids the problemsdiscussed, and makes it possible to maintain that the verb tense doeshave scope over NP's. This is because there will always be a way ofundoing the effect of the verb tense.

Interestingly however, once such an approach is adopted, it is nolonger necessary to give verb tense scope over NP's. In the classicalanalysis, different readings are the result of different scope relationsbetween the tense and the NP's. Now the same readings can be obtainedby simply defining the necessary operators and introducing them as partof NP meanings. That is to say, the readings can be obtained withoutrelying on the scope of the verb tenses. Thus itbecomes possible to keepthe effects of the 'true' tense entirely local to the verb. For example, theclassical analysis predicts two readings for (20), one about presentsophomores and one about past sophomores, depending on whether ornot the subject is in the scope of the past tense.

(20) every sophomore criedHowever, now the same readings can be obtained by giving the pasttense local scope over cry, and by introducing either a present or a pasttense operator into the semantic representation of the NP.There is a significant difference between the two approaches withrespect to the reading of (20) involving past sophomores. The classicalanalysis predicts that the past sophomores cry while they aresophomores, since there is only one past tense operator which causesboth the NP and the verb to be evaluated at a past time. In contrast, thelocal-scope analysis involves two past tense operators, one for the NPand another for the verb. This allows the timewhere the individuals aresophomores to be disjoint from the time where they cry, as long as bothtimes are in the past. That is to say, the sentence would be true on thisreading if the individuals are sophomores in the past but cry before theybecome sophomores, and also if the individuals cry in the past but aresophomores before then. This reading, not available under the classicalanalysis, does seem to be there. Suppose the discourse is about thereaction of the students enrolled in a college ten years ago to the newsthat they had been accepted at that college. (20) can be used to assertthat the sophomores of ten years ago, i.e. past sophomores, reacted totheir acceptance by crying. The relevant time of crying is also in the past,


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but precedes the time when these individualswere sophomores. For thisinterpretation, then,we need twodifferent past times, one for the time ofbeing a sophomore, and the other for the time of crying. Similarly, wewanted (6) to be true

(6) every member of our investment club will buy a houseif uttered about future members of the club who buy houses after theystop being members. This reading requires two distinct future times, andcannot be obtained under an analysis which obtains the reading aboutfuturemembers only by leaving the subject NP in the scope of the futuretensewhich affects the interpretation of the verb.

If the 'true' tense is strictly local to the verb and does not take scopeover NP's, then we will never get a reading of (20)which requires thatthe individuals be sophomores while they cry. Instead, this analysismerely allows it, by virtue of the fact that itplaces no constraints on therelevant times for the NP and the verb beyond requiring that they bothbe in the past. The analysis, in fact, claims thatwhenever the time ofbeing a sophomore is identical to the time of crying, this is not due to thescope of the tense, but rather to some other restriction on the times.Thisphenomenon seems to be exactly parallel to the interpretation ofpronouns in sentences like (21).

(21) John said that he was tiredIn (21), he can have John as its antecedent, or it can receive its referentfrom outside the sentence. This is usually accounted for by indexing thepronouns, and by stipulating that coindexation yields coreference. Inother words, indexation places a restriction on the interpretation of thepronoun beyond the inherentmeaning of the pronoun. No principle ofpronoun interpretation, however, requirescoindexation. It seems tomethat the simultaneous reading of (20) where the time of being asophomore is the same as the time of crying can be derived in a parallelfashion, and does not have to be due to the scope of the tense.I have not provided here an argument that giving the verb tense scopeover NP's makes incorrect predictions. It seems quite possible to get theright readings even when the verb tense does take scope over NP's, ifweallow ourselves the freedom to introduce other tense operators intoNP's.

However, I hope to have shown that in such an analysis, no readingrequires the verb tense to have scope over NP's. The question facing usnow is how to choose between two analyses, one where the verb tensecan have scope over NP's, and another where it cannot. If we allow theverb tense to have scope over NP's and also have the option of introduc


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ing a number of other operators insideNP's, we have in fact allowedourselves a way of always neutralizing the effect of the verb tense onNP's. This, inmy opinion, greatly trivializes the scope of the verb tense.In the absence of any need to give the verb tense scope over NP's, itseems simpler and more illuminating to treat it as an operator local to theverb, i.e. to treat the 'true' tense operator on a par with the tenseoperators introduced into the semantic representations of NP's, by allowing it to have a very limited scope. The following section furtherexamines the limits that would have to be placed on the scope of tenseoperators.

6. PREDICATES OF INDIVIDUALSAND TEMPORAL ARGUMENTS

I have suggested above that the semantic representations of tensedsentences should include several tense operators, one for each NP andone for the verb, and that the scope of these operators should beappropriately restricted. Given the necessity of constraints on theirscopes, we must first question the assumption that tense operators aresentential, an assumption that natural language semantics has inheritedfrom tense logic.12When we claim that a tense operator in the semantic representation ofa natural language is sentential, we normally mean that its scope is aconstituent analyzed as a sentence by the syntax of the natural language.The data discussed above suggest strongly that the tense operatorsintroduced into the semantic representations of NP's cannot be sententialin this sense, sincewe saw that theymust be prevented from affecting thetemporal interpretation of the verbs, and we have no independentlymotivated mechanism for taking verbs out of the scope of sententialelements. Furthermore, ifwe follow the suggestion made at the end ofthe last section that the scope of the 'true' tense operator should also belocal and that it should not have scope over NP's, then we have, so far,no strong arguments for treating any of the tense operators as sentential.One might wish to claim that the tense operators are sentential at somelevel of representationwhere constituents no longer correspond to thoseprovided by the syntax of the natural language.We could assume, forexample, that there is an appropriate level of representationwhere somepart of the NP is of the same semantic type as sentences. One way toachieve this would be to translate natural languages into a logical languagewhere the noun is represented as a one-place predicate. This is indeed


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what we have been doing throughout this paper by representing thereadings of the English sentences by logical formulas, as in (18).However, logical formulaswere used here for the sake of convenienceonly, as part of our descriptive apparatus, rather than as essentialrepresentations of English sentences. Suppose thatwe modified this viewand took the logical representations to be essential for an adequateanalysis of natural language sentences. Then a tense operator would besentential at that level of representation if it had scope over formulas ofthe logical language, although these formulaswould not correspond tothe constituents analyzed as sentences by the syntax of the naturallanguage. That is to say, tense operators would be sentential only withrespect to the logical language.The issue Iwould like to address at this point is whether there are anyadvantages to analyzing tense as a sentential operator at any level ofrepresentation, or whether this is merely an artifact of a particularexecution, with no real semantic significance. The advantage of analyzing tense as a sentential operator is that it allows the tense to potentiallyaffect the interpretation of several elements in its scope. This advantagedisappears if the scope of the tense operator always contains only oneelement whose denotation varies according to times. I suggested abovethat the effect of the tense operators was limited. We were, however,concentrating primarily on the interpretation of nouns and verbs. Inorder to determine whether or not tenses should be analyzed as sententialoperators, we need to examine their effect, ifany, on the interpretationofother expressions. This, in turn, raises a more fundamental question.Exactly which expressions in natural languages need to be interpretedrelative to times?

It iswidely assumed that the intensions of all expressions are functionsfrom world-time pairs, i.e. that the denotations of all expressions aredetermined relative to a time (cf. Cresswell (1973), Dowty (1979),

Kaplan (1977),Montague (1976)). This view allows a uniform treatmentof natural language expressions, but on closer inspection, the uniformityturns out to be only apparent. It has already been pointed out by severalphilosophers that certain classes of expressionsmust be 'neutralized'withrespect to times. For example, if names are rigid designators, then aname always denotes a certain individual, no matter what the evaluationtime is. Thus the intensions of names are constant functions from times.Personal pronouns behave in a similar way. Kaplan (1977) has shownthat the referent of a pronoun is fixed by the context of utterance beforethe proposition expressed by the sentence is determined. Therefore, insome sense, pronouns behave like names; their denotation does not


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depend on the time of evaluation. Kaplan ensures thisby stipulating thatindexicals have constant contents (i.e. their intensions are constantfunctions). There are other expressions which are obviously time-independent. These are the logical constants. None of the logical connectives (and, but, or, negation), or the logical determiners (every, all,the, a, etc.) are sensitive to times, and theirdenotation is stipulated to bethe same at every time of evaluation.So far, then, names, indexicals and logical constants turn out to haveconstant intensions. And this has to be stipulated somewhere in thetheory. I assume that this conclusion isuncontroversial.We now need toask whether there are other classes of expressions which are timeindependent. Let us first examine prepositions.

(22) John died inLondonIn (22), is the preposition in sensitive to time? Suppose that it is, andsuppose that the prepositional phrase in London denotes the set ofindividualswho are inLondon at time t.Suppose further that this time isdistinct from the time of dying. Then if the denotation of the verb phraseis the intersection of the individuals denoted by the verb and theindividualsdenoted by thePP, the sentence would be true if John died ata certain time, and was in London at another time. This is clearly not areading available for (22). Suppose, instead, that the PP denotes afunction which carves out a subset of the set denoted by died. Then inwhat sense can this function be time-sensitive? Quite simply, the value ofdied inLondon depends only on the time of dying, and on no other time.One might argue that the time relevant for thepreposition, and hence forthe PP, is somehow bound by the verb tense. However, this is not onlyunnecessary, but also clouds the issue of temporal dependence. We maysafely conclude that the denotations of prepositions do not vary according to the time of evaluation.A similar argument can be made for adjectives and adverbs.

(23) Johnwalked slowlyIf slowly denotes the set of individualswho do something slowly at a timet and this time is distinct from the time of John's walking, then thesentence would have a reading where John walked at some time andwhere he did something slowly at another time.Again, this reading isnot

available for (23). We would then need to ensure that the time associatedwith the adverb is always bound by the verb tense. If slowly denotesinstead a function from sets to sets, carving out a subset of the set of

walkers in (23), the value of this function is the set of individuals who


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walked slowly at the time determined by the verb tense. The only timethatplays a role indetermining the value of theVP comes from the verbtense, and there is no evidence for a temporal argument for the functiondenoted by the adverb.The generalization that seems to be emerging from the above discussion is that the time dependence of aVP containing amodifier isdueto the time dependence of the head verb, not themodifier. This does notrule out time-dependent expressions inside themodifier. For example, inthecapital contains aNP which is time dependent, given that cities canhave the property of being the capital at some times and not at others.However, once the value of the NP is fixed and the location is determined, there seems to be no further time dependence in the PP.We maythen conclude that the intensions of thesemodifiers are constant functions from times of evaluation.

A parallel situation obtains with modifiers inNP's.(24) Mary spoke to every intelligent linguist

(24) does not seem to have a reading where the individuals thatMaryspoke to are linguists at some time and intelligent at another time.We

may, then, take AP's to also denote functions which are time-independent.13

Apparent exceptions to the above generalization involve relativeclauses and temporal adverbs like yesterday. In the followingNP(25) the president who died ten years after he left the office

the time of dying is not the same as the time of being a president. But thiscase is parallel to PP's like in the capital. die occurs as the main verb ofthe relative clause and its time isdetermined by the tense in the relativeclause. Once that is fixed, however, if the relative clause is interpreted asa function carving out a subset of the relevant presidents, then thisfunction has no further time arguments.Let us assume that temporal expressions like yesterday denote times.Then in (26)

(26) John died yesterdayifwe further assume that the adverb constructed out of yesterdaydenotesa function from sets to sets, itwould carve out a subset of the individualswho died, giving us the set of individualswho died yesterday.14But thefunction that the adverb denotes need not have a further time argument.Similarly for temporalPP's like onMonday.

We have seen that PP's, AP's and relative clauses are time dependent


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only so far as they contain nouns and verbs.15Neither the heads of thesemodifier phrases nor the phrases themselves seem to need a further timeargument. I take it then that we can add these categories to the class ofnatural language expressions whose intensions are constant functionsfrom times. The only time-dependent expressions in natural languagesseem to be nouns and verbs.16

So far, we have assumed the time dependence of nouns and verbswithout questioning it. Given that the 'true' tense fixes a time for verbs,we may safely conclude thatverbs are time dependent.17The most tellingarguments for the time dependence of nouns comes fromLarson (1983)which examines temporal relative clauses inNP's.

(27) the duty officer when Iwas on deck will soon file his reportLarson points out that in sentences like (27), the relative clause when Iwas on deck fixes the time for duty officer.This ispossible only if nounsare interpreted relative to times.Therefore the assumptionwe have beenmaking all along, that nouns are time dependent, seems justified.18Let us now return to the assumption that all natural language expressions have intensionswhich are functions from times (aswell as possibleworlds). We have noted that this allows a uniform treatment of intensions, but have also observed that we need to stipulate that allintensions except those of nouns and verbs are constant functions fromtimes. Such a stipulation captures in perhaps a roundabout and obscure

way what seems to be a true generalization about natural languages, thatonly nouns and verbs are sensitive to times. The generalization that allnatural language expressions have intensions which are functions fromtimes now seems vacuous. This is a point we will return to later. For thetime being, let us assume that there is some such stipulation in ourtheory.We have been exploring an analysiswhere tense operators are introduced at random into NP representations at an appropriate level, withnew tense operators defined as necessary, andwhere all tense operatorsare sentential, although the sentences at this level do not correspond tothe sentences of the natural language syntax.We noted that treatingtense operators as sentential at this level would be advantageous if itcould be shown that tenses affected the interpretationof several elementsin their scope in a significant way. It seems now that this is not the case. Ihave argued that only nouns and verbs are sensitive to times, and alsothat the temporal interpretation of each noun is independent of any othernoun, or the verb, or the 'true' tense. Suppose that these generalizationsare captured by allowing one tense operator for each NP in addition to


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the one corresponding to the syntactic tense, and by stipulating thatintensions of all expressions except nouns and verbs are constant functions. It follows that each tense operator will affect the interpretation ofonly one element, a noun or a verb. Therefore, analyzing tenses assentential operators has no advantages. It does, however, have thedisadvantage of requiring a level of representation where sentences donot correspond to the sentences normally generated by the syntax. I takethis to indicate that the temporal analysis of natural languages should notemploy sentential tense operators.We might want to treat tense operators as elements with strictly localscopes, i.e. as elements which operate only on a noun or a verb. In theclassical analysis outlined at the beginning of the paper, the past tenseintroduces a past time which becomes the new evaluation time of thesentence. Since natural languages do not generally allow iteration oftenses, the tense in effect provides the temporal argument of the intensions of the expressions in the sentence.19Given that only nouns andverbs seem to have non-constant intensions,we might treat tense operators as elements which fix the temporal arguments of the intensions ofthese expressions. How do tense operators work, and at what level ofrepresentation of the object language, if any, are they present? Theanswers to these questions will establish the relation between tenses onthe one hand, and nouns and verbs on the other. But before these issuescan be adequately dealt with, we must ask amore basic question.Why isit that nouns and verbs are time-sensitive? The answer to this questionseems to be straightforward: Nouns and verbs are predicates of individuals. Itmay then be a universal property of natural languages that alland only predicates which take individuals as arguments also take timesas arguments.20This property of natural languages isnot captured under the view thatall intensions are functions from times, since such a view claims thatevery expression has a temporal argument, although in a number of casesthese temporal arguments do not affect the denotation of the expression.The evidence discussed here suggests an alternative approachwhere weabandon the notion that intensions are functions from times and worlds,and maintain perhaps that they are only functions from possible worlds.In addition,we recognize that all predicates of individualshave one moreargument than previously assumed, e.g. analyze kiss as a three-placepredicate, sleep and president as two-place predicates, etc., and requireone of the arguments to come from the temporal domain. Thus temporalarguments are selected by predicates of individuals in a manner nodifferent from the selection of non-temporal arguments.


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We now return to the status of tense operators. I noted the need forone operator for each noun and verb, and also argued that theseoperators should not be sentential. I also pointed out that they could beanalyzed as operators on predicates. But the discussion above indicatesthat labelling such elements 'operators' is not particularly appropriatehere. The facts seem to be simple: a)Nouns and verbs must be providedwith temporal arguments, b) there is a necessary link between the 'true'tense and the temporal argument of the verb, c) there is no necessary linkbetween the 'true' tense and the temporal arguments of nouns. Let usassume a referential theory of tense, i.e. a theory where tense simplydenotes a time.21We may then claim that the temporal argument of theverb is the time provided by the tense in the sentence.22We explored the idea of abstract tense operators forNP's. However,the facts can be accounted forwithout introducing novel tense operatorsinto our semantic system, because a temporal argument for nouns can besupplied without recourse to tense operators. There are two plausible

ways of achieving this.One is to assume that each noun is assigned atime by the context of use. This is the analysis proposed inEng (1980),and highlights the fact that generally, the temporal interpretation of anoun depends on the pragmatic situation.23 It assumes that the timesassigned to nouns have been introduced into the domain of discoursepreviously, plausibly by tenses and temporal adverbs. In such an analysis,the temporal arguments of nouns are not represented by any constituentsin the syntax of the language. Rather, they are supplied in the course ofthe interpretation. An alternative is to assume that the temporalarguments of nouns are represented in the syntax as empty categories,and that they are pronominal. This is the view adopted inEnc (1985).The interpretation of the empty temporal arguments is then exactlyparallel to the interpretation of indexicals like he, and once again thevalue of these arguments is supplied by the context. These two approaches are equivalent from a semantic point of view, and the choicewill depend ultimately on syntacticmatters not addressed here. For ourpurposes, what is important is that each noun is assigned a time by thecontext. To see how an analysis along these lines can account for thedata discussed above, let us turn to (12), repeated here.(12) Johnwill meet every hostage at the president's party

We were interested in the reading about individuals who were hostagesbefore the time of utterance of the sentence. This reading is no longer aproblem, since the time assigned by the context to hostage can be thepast time when these individuals were in fact hostages. Note that this is


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possible only if such a timewas previously introduced into the domain ofdiscourse, i.e. if it is pragmatically recoverable. There does not seem tobe any need for any constraints on the temporal arguments of nounsbeyond the pragmatic ones. Therefore we assume that the context canassign to a noun a specific past time, or a time that includes all of the pastmoments and the present moment, or a time that includes past, presentand futuremoments, etc.24As in the case of personal pronouns, this approach allows the temporalarguments of nouns to have sentence-internal antecedents. Since a nouncan be assigned any time from the context, it can also be assigned thetime introduced by the tense or a temporal adverb in the sentence.25 Forexample, we discussed the two readings of (20) which were about pastsophomores, where the readings differed according towhether or not thepast time of being a sophomore was the same as the past time of crying.

(20) every sophomore criedWe will assume that the past tense yields a past timewhich is the time ofcrying. If this time is assigned as the value of the temporal argument ofsophomore, thenwe have the readingwhich is true if individualswho aresophomores at a past time cry at that same past time.This reading,whichwould have been obtained in the classical analysis by giving the pasttense wide scope over the subject, is now available simply because thetense is a possible antecedent for the temporal argument of the noun.However, it ispossible for the context to assign some other past intervalto the noun in the subject, provided it is pragmatically available. Thiswould give us a reading not available under the classical analysis, areadingwhere we are saying of past sophomores that they cried

in thepast, but allowing the two past times to be distinct.

7. CONCLUSIONI have argued against analyzing natural language tenses as sententialoperators on the grounds that only verbs are necessarily interpretedrelative to the time provided by the tense. I have further argued that thetime-sensitive expressions of natural languages consist of nouns andverbs, which strongly suggests that times should be viewed as individualswhich serve as arguments of predicates of individuals. The naturallanguage data seems to favor a referential analysis of temporal expressions, where temporal expressions are fundamentally similar to nontemporalNP's, rather than the classical analyseswhich employ sententialoperators.


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ACKNOWLEDGEMENTThis paper develops ideas firstput forward inEng (1980) and Enc (1981). I am grateful toRobin Cooper and Larry Horn for very helpful discussions and numerous suggestions, andfor their encouragement and support. I have also benefited from comments and criticismsby Hagit Borer, Michael Byrd, David Dowty, Berent Eng, Elisabet Engdahl, IreneHeim,Frank Heny, Hans Kamp, Lauri Karttunen, Richard Larson, David Pesetsky, StanleyPeters, Geoffrey Pullum, Ivan Sag, Susan Stucky, Johan van Benthem, FrankVlach, TomWasow and an anonymous referee of this journal.

NOTESCf. Montague (1976), where all expressions have intensions which are functions fromtimes and possible worlds.2 Cf. Montague (1976). For the purposes of thispaper, we will go along with the idea thatnatural languages have a future tense, a view rejected in Enc (1985).3We assume here that somemechanism exists for giving NP's wide scope, the exact natureof thismechanism being irrelevant.4 For convenience, logical formulas will be used to represent the readings of Englishsentences.5 I am treating the Present Perfect here as a simple past tense operator. The differences areirrelevant to the point under discussion and are therefore ignored.6 I am assuming that the introduction of tense operators is triggered by tensemorphology.I return to this question later.7 Thus the tense operators of English would be limited to the past, the present and thefuture, ifwill is indeed a future tensemorpheme.8 This is because tense is treated as a sentential operator, and while there are generalmechanisms for giving NP's wide scope over operators, there are none for verbs.9 The problems surface in analyses which are based on these assumptions and which treattenses as sentential operators, whether the semantics is interval-based ormoment-based.10These operators, however, were not proposed to account for the relationship betweenNP's and tense.

1 Ens (1981) provides arguments for the independence of NP's also with respect tolocations.12 It is irrelevant here whether the tense operators occur at some level of representation ofthe object language, or whether they are introduced as part of the interpretive rules.13 It seems the dead president can pick out an individual who is dead now and was apresident in the past. The analysis proposed later for nouns would be extended to adjectivesif they turnout to pattern with nouns.14These comments are relevant only to analyses which treat such modifiers as denotingfunctions from sets to sets, an approach rejected inEnc (1985).15Participles seem to have independent time reference. In a dying president, the time ofdying and the time of being a president need not be the same. I take this to be due to theverbal nature of the participles.16But see Note 13.Also, an anonymous referee of this journalhas brought tomy attentionthe temporal properties of non-restricting modifiers like alleged or fake. In these cases, thetemporal restriction does not seem to come from the head noun alone. A fake gun is not an

object which is a gun at a certain time and which is also fake at that time. Rather, we needan object which, at a certain time, has the property of being a fake gun, i.e. semantically,there is only one relevant property here and this property is obtained from the non


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restrictive adjective plus the noun. Correspondingly, there is only one temporal dependence, the only time needed being the time thisobject has theproperty of being a fake gun.On thispoint, correct resultsmay be obtained by treating fake gun as a compound noun. Inany event, it isnot necessary for the non-restrictive adjective and thenoun to have separatetemporal arguments.17This view differs from Enc (1981) where verbs and nouns were interpreted directly,without reference to times, and tenses contributed pragmatic well-formedness conditions.See Larson (1983) for arguments against thatposition.18This view again differs from Ens (1981), and is the one adopted inEns (1980) whichassigns to every NP independent contextual indices.19This paper ignores the complications arising from aspect and embedded clauses. SeeDowty (1979), Enc (1985).20One might want to treat restrictive adjectives as individual predicates, inwhich casetheywould be expected to patternwith nouns and verbs in this respect. See Note 13.21A referential view of tense isproposed in Partee (1973).22This is an oversimplification. Enc (1985) argues for amore complex relation betweenthe temporal argument of the verb and the tense.23The analysis inLarson (1983), where nouns are assigned independent locations, is also inthe same spirit.24Nor are the times required to be intervals. It seems possible, for example, for thediscourse to be about a time which consists of all the election years, excluding the years inbetween.25This would require the antecedent in the sentence to be processed before the noun. Iassume this depends on the syntactic configuration. See Heim (1982) for the possibleantecedents of definites in general.

REFERENCESCooper, R.: 1978, 'Variable Binding and Relative Clauses', in F. Guenthner and S.Schmidt (eds.), Formal Semantics and Pragmatics forNatural Languages, Reidel, Dordrecht, 131-169.Cresswell, M.: 1973, Logics and Languages, Methuen and Co. Ltd., London.Cresswell, M.: 1977, 'Interval Semantics and Logical Words', in C. Rohrer (ed.), On the

Logical Analysis of Tense and Aspect, TBL Verlag Gunter Narr, Tubingen.Dowty, D.: 1979, WordMeaning andMontague Grammar, Reidel, Dordrecht.Enc, M.: 1980, 'QuantifyingOut', unpublished manuscript of talk delivered at theAnnualLSA Meeting.Enc, M.: 1981, Tense Without Scope: An Analysis of Nouns as Indexicals, University ofWisconsin, Madison dissertation. Distributed by IULC.Enc, M.: 1985, 'Temporal Interpretation', unpublished USC manuscript.Heim, I.: 1982, The Semantics of Definite and IndefiniteNoun Phrases, University ofMassachusetts, Amherst dissertation.Kamp, J.: 1971, 'FormalProperties of "Now"', Theoria 37, 227-273.Kaplan, D.: 1977, 'Demonstratives', unpublished manuscript.Ladusaw,W.: 1977, 'Some Problems with Tense inPTQ', in S. Schmerling and C. Smith(eds.), Texas Linguistic Forum 6, The University of Texas, Austin, 89-102.Larson, R.: 1983, RestrictiveModification: Relative Clauses and Adverbs, University ofWisconsin, Madison dissertation.Larson, R.: 1985, 'Bare-NPAdverbs', Linguistic Inquiry16, 595-621.

Montague, R.: 1976, Formal Philosophy, edited by R. Thomason, Yale University Press,New Haven.


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Partee, B.: 1973, 'Some Structural Analogies Between Tenses and Pronouns inEnglish',The Journalof Philosophy 70, 601-610.Partee, B.: 1984, 'Nominal and Temporal Anaphora', Linguistics and Philosophy 7,243-286.

Department of Linguistics,University of SouthernCalifornia,Los Angeles, CA 90089-1693,U.S.A.

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