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The semantics of <emphasis type="italic">together</emphasis>T H E S E M A N T I C S O F T O G E T H E R * The semantic function of the modiﬁer together in adnominal position has generally beenconsidered to be that of preventing a distributive reading of the predicate. On the basisof a new range of data, I will argue that this view is mistaken. The semantic function ofadnominal together rather is that of inducing a cumulative measurement of the groupthat together is associated with. The measurement-based analysis of adnominal togetherthat I propose can also, with some modiﬁcations, be extended to adverbial occurrencesof together.
Together is an expression that can act both as an adnominal modiﬁer, as in(1a), and as an adverbial one, as in (1b) and (1c), and in the two positions itexhibits rather diﬀerent readings: a: John and Mary together weigh 200 pounds.
b: John and Mary together earn more than 100, 000 dollars a year.
a: John and Mary are writing a book together.
b: John and Marysang together.
c: John and Mary sat together.
The function of together in adnominal position as in (1a,b) has usually beentaken to be that of an antidistributivity marker and in adverbial position asspecifying collective or cooperative action (2a,b) or spatiotemporal prox-imity (2c). As always, the preferred analysis would be one that posits a singlelexical meaning of together and derives the various readings from thatmeaning in conjunction with the syntactic and semantic context in whichtogether occurs.
The present account, which is trying to achieve that, takes as its point of departure a reevaluation of the apparent antidistributive reading dis-played by together in adnominal position. I will argue that the function ofadnominal together is in fact not that of preventing a distributive readingof the predicate, but rather that of inducing a cumulative numerical I would like to thank Barry Smith, Kit Fine, and Bob Fiengo, among others, for stimulating discussions on the topic. Research on this project has partially been made possible by aNachkontaktprogramm for a Feodor-Lynen fellowship of the Alexander von Humboldt-Stif-tung in 1999 as well as a research readership from the British Academy in 2002–2004.
Natural Language Semantics 12: 289–318, 2004.
Ó 2004 Kluwer Academic Publishers. Printed in the Netherlands.
measurement of the group together relates to, e.g. in (1a) a measurement interms of weight and in (1b) a measurement in terms of income. With anappropriate generalization of the notion of measurement (from a mappingof entities to numbers to a mapping of entities to events) the account canbe carried over to the readings together displays in adverbial position, aswell as to certain additional readings of adnominal together. What kind ofmeasurement will be induced – that is, what kind of reading together willdisplay – will depend on the measure function that is semantically acces-sible in the syntactic context in which together occurs.
This measurement-based analysis of adnominal together also provides a new motivation for Generalized Quantiﬁer Theory. In order for ad-nominal together to enforce a cumulative-measurement reading of thepredicate, the denotation of the NP with together needs to be construed asa set of properties (namely those properties able to provide a cumulativemeasurement). Further support for the quantiﬁer status of NPs with to-gether comes from the fact that such NPs exhibit just the same scoperestrictions as quantiﬁcational NPs that share the same monotonicityproperties.
I will ﬁrst introduce a number of new observations about together in adnominal position and formally elaborate the measurement account ofadnominal together. I will then more brieﬂy show how the account can becarried over to adverbial together and certain other readings of adnominaltogether, as well as to the related expression alone.
1.1. Some Generalizations and Previous Accounts First some syntactic remarks about adnominal together. Even thoughtogether in (1a) could potentially modify either the VP or the NP, thereis evidence that together in that position always relates to the subject,rather than the VP. First of all, it is easy to see that together can beadjoined to the subject. Together must be in adnominal position in coor-dinate NPs as in (3a), complex NPs as in (3b), and cleft constructions asin (3c): a: John and Mary together and Bill alone weigh 200 pounds.
b: The weight of John and Mary together exceeds 200 pounds.
c: It was John and Mary together who solved the problem.
T H E S E M A N T I C S O F T O G E T H E R Second, it appears that in between subject and VP, together exhibits thesame readings as when it occurs in a syntactic context where it must beadjoined to the subject, namely before auxiliaries, as in (4):1;2 John and Mary together have lifted the piano.
Let me henceforth call an NP modiﬁed by together a together-NP.
Generally, the semantic function of together in adnominal position has been taken to be that of preventing a distributive reading of the predicate.
The antidistributive function of adnominal together seems to be supportedby the observation that the predicate must allow for both a distributive anda collective reading in order to be compatible with adnominal together.
Thus, it appears that adverbial together patterns together with VP-internal adverbs like fast (occurring after the ﬁnite verb), rather than adverbs that could be adjoined to the VP such asquickly or ﬂoated both: John and Mary both/quickly left the room: For some speakers, ﬂoated quantiﬁers and together can occur in postcopular position before theverb: a. # John and Mary have together lifted the piano: In this position, however, together and alone always yield exactly the range of readings ofadnominal, rather than adverbial together and alone.
The phenomenon exhibited by (ii) seems to be related to the one found with ﬂoated quan- John and Mary have each lifted the piano: There are two views one might take. First, the NP originates inside VP and leaves the modiﬁerbehind (Sportiche 1988). Second, the NP and the modiﬁer are base-generated where they are,but the modiﬁer (as an adverbial) may be linked to the NP so as to be interpreted as a modiﬁerof the NP, rather than the VP. In this paper, which is a semantic than a syntactic investigation, Iremain neutral on this matter.
Bayer (1993) notes that together can occur in between a subject-relative pronoun and the VP and takes this as evidence that together in between subject and VP can be adverbial: It was John and Mary who together lifted the piano: However, the evidence shows that together in (i) may very well be adjoined to the pronoun, as in(ii): Concerning John and Mary, they together certainly would make a nice couple: Thus, together seems impossible with obligatorily distributive predicates, asin (5), or with obligatorily collective predicates, as in (6): a: # John and Mary together are asleep.
b: # The two houses together are red.
a: # John and Mary together are married.
b: # John and Mary together are unrelated.
Generally the readings of adnominal and adverbial together do not overlap. This can simply be seen from the fact that when adverbial togetherin (2a,b,c) is put into adnominal position, the results are degraded, as in(20a,b,c). Also, when adnominal together as in (1a,b) is put into adverbialposition, the sentence becomes bad, as in (10a), or it means something dif-ferent, as in (10b) (which implies that John and Mary are paid as a couple): a: # John and Mary together are writing a book.
a: # John and Mary weigh 200 pounds together.
John and Mary earn more than 100,000 dollar a year There are a number of proposals in the literature to account for the antidistributive eﬀect of adnominal together, namely Bennett (1974),Hoeksema (1983), and Schwarzschild (1992, 1994). The governing idea ofthose proposals is that adnominal together has the function of enforcing anondistributive reading of the predicate; that is, the contribution of togetherto the sentence meaning consists in the following, where < is the relationbetween members and groups to which they belong:3 ½NP together VP ¼ 1 ! 8dðd < ½NP ! : d 2 ½VPÞ Bennett (1974), Hoeksema (1983), and Schwarzschild (1992, 1994) presentdiﬀerent technical elaborations of (7). I will not go into the details of theseproposals and their diﬀerences, but rather focus on the general problemsfaced by an account of together as an antidistributive marker. One suchproblem is that such an analysis does not provide a way of accounting foradverbial together (rather, it imposes or would have to impose an ambiguityon together). Another, more severe problem is that the characterization of See Link (1983), Lasersohn (1989), Roberts (1987), and Moltmann (1997a) among others for T H E S E M A N T I C S O F T O G E T H E R the semantic eﬀect of adnominal together as antidistributive appears to bemistaken. This will be discussed at great length in the next section.
In Moltmann (1997a,b, 1998) I tried to give a uniﬁed account of ad- nominal and adverbial together (and related expressions such as alone)within a semantics based on situations and the notion of an integratedwhole. Even though I now reject that account for adnominal together, somecrucial features of it will be carried over to the extension of the new mea-surement-based analysis of adnominal together to adverbial occurences.
The fundamental idea of my earlier account was that together always expresses a property of entities in situations (or a relation between entitiesand situations), namely the property of being an integrated whole in a sit-uation. Only a rather simple notion of integrity was required for together,according to which an entity is an integrated whole just in case it consistsonly of parts that are all related to each other by some relevant relation andnone of its parts is related to an entity that is not one of its parts. Thediﬀerent readings of together then arise because the situations are diﬀerentto which together applies. For adnominal together, it was assumed that thetogether-NP is evaluated with respect to certain situations (reference situa-tions) that will not be able to include the information content of the pred-icate. When together holds of a group in such a situation (whoseinformation content will be almost empty), it can only specify that the groupis conceived as an integrated whole. There is a purpose, though, to speci-fying a group as a conceived integrated whole, and that is that this willprevent a distributive reading of the predicate. As on most accounts, thedistributive reading of a predicate involved quantiﬁcation over the parts ofthe relevant group argument (either by means of a distributivity operator oras part of the lexical meaning of the predicate). Crucially, a general con-dition, the ‘Accessibility Requirement’, was posited (and independentlyjustiﬁed) according to which a quantiﬁer can range over the parts of a groupin a (reference) situation only if the group is not an integrated whole in thatsituation. In short, adnominal together enforces a collective reading of thepredicate by requiring the group argument to be conceived as an integratedwhole in the reference situation.
The account has much greater plausibility for adverbial together, which, as we will see later, displays various readings depending on the nature of thepredicate, or rather the event described by the predicate. In adverbial po-sition, the situation together applies to is one only containing informationabout the described event. For a group to be an integrated whole in such asituation, its parts must be connected to each other by a relation involvingthat same event, and moreover, for that purpose, the event must be anintegrated whole. If the event is a group activity, it has integrity if the group members interact with each other or the subactivities bear some otherrelation to each other (e.g., being about the same thing). In the case of staticpredicates, the described event can hardly have integrity in another way butby being a state that is (more or less) continuous in space and time (seesection 2).
Even though this account meets the general condition that the readings of together be derived from a single underlying meaning and the semantic andsyntactic context in which together occurs, there are serious problems withit. First, it requires assumptions about situations that lack very strongindependent motivations besides the semantics of adnominal together andrelated expressions: situations are required not only for the evaluation ofindividual NPs, but will also have to form a component of an argument of apredicate. Second, the account makes the truth conditions of sentencesdependent on acts of conceiving entities referred to in a certain way (asintegrated wholes). However, the truth conditions of sentences – includingthose with adnominal together – are independent of whether anyone hasconceived of anything in any way. Thus, (1a) is true even in a world in whichno one conceives of the group of John and Mary as an integrated whole, aslong as their weight is in fact 200 pounds. The main problem for the ac-count, however, as for all the previous proposals concerning the semanticsof adnominal together, is that it is based on wrong empirical generalizationsconcerning adnominal together.
1.2. A New Generalization Concerning Adnominal Together Together in adnominal position behaves diﬀerently from an antidistribu-tivity marker in several ways: 1. Adnominal together is not acceptable with just any predicate allowing for both a distributive and a collective reading.
2. When it is acceptable, it does not always yield the ordinary collective 3. Adnominal together is possible also with certain predicates that only have The predicates in the examples below are among numerous ones that clearly have both a distributive and a collective reading, but are impossiblewith together modifying the subject: a: # John and Mary together are paid monthly.
b: # John and Mary together have applied for a grant.
c: # John and Mary together were carrying the box.
d: # John and Mary together are writing an article.
T H E S E M A N T I C S O F T O G E T H E R These predicates contrast with the following, which do allow for adnominaltogether: a: John and Mary together are paid 100,000 dollars per year.
b: The boxes together weigh 100 pounds.
c: The paintings together are worth 10 million dollars.
What distinguishes the predicates in (9) from those in (8)? As seen bycomparing (8a) and (9a), it is hardly the nature of the event described by theverb that matters, nor does tense or aspect seem to play a role. Rather, whatdistinguishes the predicates in (9) from those in (8) is that they involve somenumerical measurement, expressed by a measure phrase. It appears that thismeasurement is the ‘focus’ and licencer of together. The contribution oftogether then is to specify that adding up the measurements of the membersof the group yields the measurement expressed by the measure phrase. Forexample, what together in (9a) says is that adding the wages of John and ofMary per year amounts to 100,000 dollars. Note that the way (9a) isunderstood shows that the function of adnominal together is truly diﬀerentfrom that of triggering a collective reading: (9a) implies that John and Maryare paid individually rather than collectively.
Just a few words about the notion of measurement (cf. Suppes and Zinnes 1963; Krantz et al. 1971). Measurements serve to represent certain empiricalproperties and relations among objects. They involve an empirical system,consisting of a domain D and relations R1; . . . ; Rn or operations O1; . . . ; Oninvolving elements in D and a numerical (representation) system, consistingof a subset of the real numbers R and relations R10; . . . ; Rn0 involving ele-ments in R. A measure function is a mapping from D to R that preserves therelations R1; . . . ; Rn and operations O1; . . . ; Om: it is a homomorphism be-tween ðD; R1; . . . ; RnÞ and ðR; R10; . . . ; Rn0 Þ; that is, if for x1; x2 2 X,x1 Ri x2, then fðx1ÞR0 fðx 2Þ for i n. Thus, the measure function of weight w preserves the relation ‘is heavier than’ among the numbers assigned toobjects, in virtue of these numbers being ordered by the relation <. That is,if a is heavier than b, then wðbÞ < wðaÞ.
If will assume roughly the account of Link (1983) and related work on the semantics of deﬁnite plurals and NP conjunctions. That is, besidesindividuals the domain of entities includes groups, obtained by sum for-mation from the individuals, which will serve as the semantic values ofdeﬁnite plural NPs. John and Mary will refer to the group consisting of Johnand Mary. Individuals and groups in the domain thus form a set D, which isclosed under sum formation _; that is, if d 2 D and d 0 2 D, then d _ d0 2 D(and moreover, if D0 D, D0 6¼ Ø, then sup<ðD0Þ 2 D – the least upperbound of D0 with respect to <, the relation ‘is a proper part of ’).
The relevant measure functions for our purposes are functions that preserve the operation of group formation _, by representing it in terms ofthe operation + on the elements in a numerical system; that is, they arefunctions w from the structure ðD; _Þ, closed under the operation _, toðR; þÞ with R being a set of real numbers closed under the operation ofaddition +, such that for entities a, b, c 2 D, if c ¼ a _ b, thenwðcÞ ¼ wðaÞ þ wðbÞ. Functions such as those measuring weight, size, or thenumber of members (parts) can fulﬁll this condition only, however, if theyapply to nonoverlapping entities, that is, if they are ‘additive measurefunctions’ as deﬁned in (10), where is the relation of (mereological) overlap(cf. Krifka 1990): A measure function f is additive iff : x y & fðxÞ ¼ n & fðyÞ ¼ m ! fðx _ yÞ ¼ n þ m: With this notion of additive measurement, the semantic function of to- gether in the examples in (9) can be described as follows. Together ensuresthat the measurement (speciﬁed by the measure phrase) is that of the entiregroup and, moreover, that it is the sum of the measurements of the groupmembers.
In a ﬁrst approximation, the lexical meaning of together can be construed as an (intensional) relation TOGETHER that holds (relative to a world anda time) between a group d, an additive measure function f, and a measuringentity n just in case f applied to yields n: For an additive measure function f from the structure ðD; _Þ;for a set of entities D; to the structure ðR; þÞ; for a set of realnumbers R; for any world w and time t; and entities d 2 Dand n 2 R; < d; n; f > 2 TOGETHERw;t iff fðdÞ ¼ n: The logical form of (9a) can now be simply given as in (12), where(kx [earn(x)]) is the function mapping entities to what they earn (in dollars)and j _ m the sum of John and Mary: earn 100,000 dollars ð j _ mÞ & together ð j _ m;100;000; kx½earn ðxÞÞ The ﬁrst conjunct of (12) gives the meaning of (9a) without together,whereas the second conjunct represents the speciﬁc semantic contribution oftogether. That is, (12) states that the group of John and Mary earns 100,000dollars (individually or together) and that the sum of the earnings of Johnand the earnings of Mary amounts to 100,000 dollars.
I will come to a more explicit analysis of adnominal together below. First some further empirical evidence that measurement is in fact involved in thesemantics of adnominal together. It comes from the behavior of NPs with T H E S E M A N T I C S O F T O G E T H E R together when modifying another NP. It appears that nouns are subject tothe same restrictions as predicates when they take NPs with together as amodiﬁer. Thus, the head nouns in (13) allow for both collective and dis-tributive readings with respect to an of-phrase, but they cannot be modiﬁedby an of-phrase with together: a: # The work of John and Mary together is about history.
b: # The singing of John and Mary together is beautiful.
c: # the invitation of John and Mary togetherd: # the trip by John and Mary together The reason obviously is that the head nouns in (13) do not express mea-surement. By contrast, those in (14) do, and thus accept NP-modiﬁers withtogether:4 a: the weight of the boxes togetherb: the earnings of John and Mary togetherc: the worth of the ten paintings together However, if an NP with a together-NP as modiﬁer does not itself refer tosome measurement, but modiﬁes another NP that does, then also accept-ability results. This can be seen from the contrast between (13a) and (15a),as well as the one between (13c) and (15b) and the one between the examplesin (16) and those in (17): One might think that the examples in (14) should have the analysis in (ib), rather a. the weight of ½the boxes togetherNPb. the ½weight of the boxes But there are good indications that the analysis in (ia), at least for the examples in question, isright. First, together can generally only specify sum formation as in (iia), not addition as in (iib),as would be required for a number-denoting NP like (14a): John and Mary together are a nice couple: Second, an NP with weight as a head noun does not seem to take together in the ﬁrst place, ascan be seen from the unacceptability that results when the boxes is put into speciﬁer position: Finally, note that on the analysis in (ib), it should be possible to extract the complement NPwithout together, but that is in fact impossible: Ã ½Of which boxes ½did John write down the½weight t the amount of work of John and Mary together the number of invitations of John and Mary together a: # the children of John and Mary togetherb: # the books of John and Mary together the number of children of John and Mary together the amount of books of John and Mary together In isolation, (16a) (with together modifying John and Mary) and (16b) areunacceptable even though the head noun would allow for either a distrib-utive or a collective reading with respect to John and Mary – again evidencethat adnominal together is not an antidistributive marker.
The examples in (13) become acceptable not only when modifying another NP that refers to a measurement, but also with particular types of predicates,namely precisely those predicates that would be possible with togethermodifying the subject – that is, predicates that express measurement: a: # The children of John and Mary together are young.
b: # The children of Sue and Mary together are in the room.
The children of John and Mary together outnumber thoseof Bill and Sue together.
The children of John and Mary together are too many to a: # The books of John and Mary together are interesting.
b: # The books of John and Mary together are heavy.
The books of John and Mary together are enough to fill The books of John and Mary together weigh more than Sentences (19a) and (19b) as well as (2la) and (21b) are acceptable, obvi-ously, because the predicates express measurement. In these cases, themeasure function is expressed in part by the VP, but also in part by the headnoun of the subject. That is, in (19a) and (19b) the measure function is thefunction mapping individuals to the number of their children. Composi-tionally, the measurement correlate is not associated with the VP, but withthe VP together with the content of the head noun – that is, the measurefunction is now to be obtained by composing the function expressed by thehead noun with the measure function that is part of the meaning of the VP.
T H E S E M A N T I C S O F T O G E T H E R Thus, for (21b) the measure function would be deﬁned as in (22a) (meant asweight in pounds), so that the logical form of the entire sentence would be asin (22b): a: For any object d; fðdÞ ¼ the weight of(the books ofðd ÞÞb: weigh(the x½booksðxÞ & ofðx; j _ mÞ; 500Þ & togetherðj _ m; n; f Þ l.3. The Relation of the Measure Function to the Content of the Predicate The way the measure function and the measuring entity that together takesas its argument relate to the content of the predicate is often more indirectthan (11) might suggest, and in fact an inspection of a wider range of caseswill require a slight modiﬁcation of (11).
It is easy to see that the predicate need not specify a particular mea- surement. A quantiﬁed measure phrase will do: a: John and Mary together are paid a lot.
b: John and Mary together earn more than 100,000 dollars a year.
In these cases, the measure phrase only expresses a property of measure-ments, rather than naming a particular measurement.
Other cases where no particular measurement is mentioned explicitly are the excessives in (24) and indexicals as in (25): a: John and Mary together are too heavy.
b: Even John and Mary together are not rich enough.
John and Mary together are not that heavy.
Moreover, predicates comparing measurements are acceptable that donot mention any particular measurement at all, as we have seen withoutnumber in (19a), and as we can see with the comparatives below: a: John and Mary together are heavier than Sue.
b: John and Mary together are richer than Bill.
A predicate acceptable with together not only does not have to mention anexplicit measurement of the object;5 the predicate need not even imply anymeasurement having taken place.
It is also a well-known linguistic fact that measure phrases do not act as referential argu- ments of the verb, but rather behave like predicates. For example, they do not allow forpassivization and pattern with adjuncts with respect to extraction (cf. Rizzi 1990). Thus, 100pounds in weigh 100 pounds does not act like a referential expression, referring to a number thatwill act as an argument of the weigh-relation. From a linguistic point of view, it would thereforebe inadequate to take weigh (in weigh 100 pounds) to express a relation between individuals andweights (numbers). The measure phrase is better seen as expressing a property of measurements,rather than referring to a speciﬁc number.
How then should the relation between the content of the predicate and the measure function and measuring entity be conceived? First of all, theapplication of the predicate to an object in any circumstance should beequivalent to a measure function applying to the object and yielding ameasurement that satisﬁes a particular condition. Thus, in (24a), the mea-sure function is the weight function and the condition that of being heavierthan a certain context-dependent limit. In (26a), the measure function isagain the weight function, which will apply to two objects, and the conditionis that the measurement of the ﬁrst be greater than the measurement of thesecond.
But clearly the equivalence between the predicate and the application of a measure function satisfying a particular condition should obtain in allcircumstances, not just the actual one. If it happens that the set of peoplethat are walking is the same as the set of people that are 2 m tall, John andMary together are walking is still unacceptable, since there will be cir-cumstances in which the walkers do not coincide with the people thatare 2 m tall. Thus, we need to make use of intensional measure func-tions, functions that relative to a world and a time map entities to realnumbers.
Together does not presuppose that the predicate as such be equivalent to the application of a measure function from a structure ðD; _Þ to a structureðR; þÞ. It just requires that the predicate in a particular context be corre-lated with such a function. A case where a predicate itself does not expresssuch a function is write n books. The function mapping an individual d tothe books that d wrote is not a measure function of the required sort: d mayhave written a book together with another person d 0; that is, the number ofbooks that d _ d0 wrote will be greater than the number of books that dwrote added to the number of books that d 0 wrote. The reason why aphrase like the number of books of John and Mary together is acceptable isthat in this particular case it is presupposed that John and Mary did notwrite a book together. In this case, the function mapping an entity d to thenumber of books d wrote applied just to the set fJohn,Maryg is a measurefunction.
Thus, what we need is ﬁrst to associate a predicate not with a particular measuring entity, but with a property of measurements (such as being a lot,or more than 100,000), in addition to a measure function. Second, for the setof entities in question, this correlation should obtain in all possible cir-cumstances. I will call the pair consisting of such a measure function and aproperty of measurements the measurement correlate of a predicate. If thepredicate expresses a relation, then together requires a measure function aswell as a relation such that the function applied to the two arguments yields T H E S E M A N T I C S O F T O G E T H E R a pair of numbers that stand in that relation. Thus, the two cases of ameasurement correlate can be deﬁned as below: For an intensional measure function f and a property S ofreal numbers, the pair < f; S > is a measurement correlate ofa property PðMCðf; S; PÞÞ iff for any world w and time t andfor any entity d : d 2 Pw;t iff f w;tðdÞ 2 Sw;t:6 With the notion of a measurement correlate, the lexical meaning of togetherneeds to be modiﬁed accordingly: For an intensional additive measure function f from thestructure ðD; _Þ; for a set of entities D; to the structure ðR; þÞ;for a set of real numbers R; for a property S of real numbers,for any world w and time t; and any entity d 2 D; < d; f; S > There is one potentially problematic case for this account which calls for a brief discussion. Generally, together is not very felicitous with vague usesof the positive of adjectives, whereas it is ﬁne with the comparative, theexcessive, or any use of an adjective involving a speciﬁc measurement or aproperty of measurements: a: # John and Mary together are heavy.
b: ?? John and Mary together are rich.
On the traditional view of adnominal together as an antidistributivitymarker, heavy and rich (as predicates with both a distributive and a col-lective reading) should allow for adnominal together. But noncomparativeheavy and rich are acceptable with adnominal together only when used in acontext in which a particular measurement counts condition for applyingthe predicate (let us say, when it is agreed that something counts as ‘heavy’ One might think that a relational notion of a measurement correlate, as below, is required for predicates like outnumber or is heavier than, which allow for adnominal together for both oftheir arguments: For an intensional measure function f and a two-place intensional relation Mbetween real numbers; the pair hf; Mi is a measurement correlate of a two-placerelation R ðMCðf; M; RÞÞ iff for any world w and time t and for any entities d andd 0 : hd; d 0i 2 Rw;t iff f w;tðhd; d 0iÞ 2 Mw;t: Later, however, we will see that the compositional semantics of sentences with adnominaltogether in fact needs to make use only of the nonrelational notion in (27).
just in case it weighs more than 200 pounds or that only someone with a networth of at least 1 million dollars counts as rich).
It is not obvious how the present account excludes together with vague uses of the positive. Often the positive is analysed as involving a context-dependent degree, as an implicit argument of the adjective (cf. Cresswell1976, Lerner and Pinkal 1992). Any such account, however, would be un-able to explain why a sentence such as (29), which would on that account beequivalent to ð28aÞ; accepts together :7 John and Mary together weigh more than expected.
Thus, it is better not to take the vague positive to involve a particular degreeargument, but rather to just act as a one-place predicate whose content doesnot require a particular measurement.
A better explanation for why the vague positive is incompatible with adnominal together may reside in the nature of its context dependency.
Heavy is context-dependent in quite a diﬀerent way than heavier thanexpected. In particular, generally (that is, when not used in a contextspecifying a particular measurement) heavy has a reading relativized to atype or concept (heavy for a person, heavy for a book, heavy for an insect).
Clearly, then, there is no single measurement condition that would governthe application of together in any circumstance.
There is another approach to the comparative in the literature on which the comparative, but not the positive, involves measurement. Kamp (1975)and, following him, Klein (1980) analyse the comparative in terms of acontext-relative positive. On this account, (18b) would be paraphrased as‘There is a context c such that John and Mary are heavy relative to c and Billand Sue are not heavy relative to c0. Now the number of contexts in whichthe predicate applies or does not apply to an object certainly provides ameasurement of the object. Thus, if the comparative heavier holds betweentwo objects a and b, then there will be a measure function assigning a value athat is higher than the one it assigns to b. By contrast, the positive will apply This is presupposed in one common analysis of comparatives according to which they involve quantiﬁcation over degrees (cf. Cresswell 1976; Lerner and Pinkal 1992; Moltmann1992). For example, on the analysis of Lerner and Pinkal (1992), (ia) is to be paraphrased as:‘There is a degree d 0, such that John and Mary are heavy to degree d 0 and for every degree d towhich Bill and Sue are heavy, d 0 > d ’, as in (ib), where heavy is construed as a relation betweenobjects and degrees: a. John is heavier than Mary:b. 9d 0ðheavyðJohn; d 0Þ & 8dðheavyðBill _ Sue; dÞ ! d > d 0ÞÞÞ T H E S E M A N T I C S O F T O G E T H E R to a single context, and that context does not give a clue as to what measureshould be assigned to a given object.
1.4. The Meaning of Adnominal Together in Diﬀerent Syntactic Contexts Adnominal together obviously has a semantic function that consists in anticipating the content of the predicate. To account for this, GeneralizedQuantiﬁer Theory with its construal of NP denotations as sets of propertiesis an eminently suitable formal tool. In fact, adnominal together providesanother application of Generalized Quantiﬁer Theory, quite diﬀerent fromquantiﬁcation itself. However, unlike for classical applications of General-ized Quantiﬁer Theory, the denotations of together-NPs must be construednot from sets but from properties, in the sense of functions from world-timepairs to sets of individuals. The idea is that John and Mary together willdenote a subset of the set of properties that John and Mary, on the gene-ralized-quantiﬁer construal, would denote (the set of all the properties thatthe group of John and Mary has), a subset restricted in a certain way bytogether (namely the subset of those properties P that the sum of John andMary actually has for which there is a measurement correlate hf; Si such thatfor any world w and time t, j _ m 2 Pw;t iff f w;tðj _ mÞ 2 Sw;t).
The denotation of adnominal together (when modifying the subject) can be taken to be an operation mapping an individual (the denotationof the NP without together) onto a generalized quantiﬁer (the denota-tion of the NP with together), so that John and Mary together will havethe following denotation, where ‘S’ and ‘P’ are variables ranging overproperties: ½John and Mary togetheradnomw;t ¼ fPj9f 9SðMCðf; S; PÞ&hj _ m; f; Si 2 TOGETHERw;tÞg That is, John and Mary together denotes the set of properties (relative to aworld and a time) for which there is a measurement correlate whose measurefunction maps the group of John and Mary onto a measurement that sat-isﬁes the condition given by the measurement correlate.
The meaning of together as an adnominal modiﬁer itself will be the function from individuals to generalized quantiﬁers below: For any world w; time t; and object d; ½togetheradnomw;tðdÞ ¼ fPj9f 9SðMCð f; S; PÞ&hd; f; Si 2 TOGETHERw;tÞg Alternatively, together may be construed as operating on the generalized quantiﬁer expressed by the NP without together. However, conceiving of themeaning of adnominal together as a function from individuals to generalized quantiﬁers is justiﬁed because adnominal together occurs only with deﬁniteand speciﬁc indeﬁnite NPs:8 a: # Most people/At least two people together solved the problem.
b: Two people/These people together solved the problem.
The same denotation can be assigned to together when it modiﬁes an NPthat in turn modiﬁes the subject, as in (19) and (21). All that is needed is theassumption that the together-NP undergoes Quantiﬁer Raising, moving upto sentence-initial position, as in (33), for (21b): [John and Mary together]NP [The books of ti weigh more than Quantiﬁer Raising is plausible in that an NP with together has indeed thedenotation of a quantiﬁed NP. Based on (33), the scope of the together-NPin (21b) is then evaluated as the property below: kx[weigh(book ofðxÞ; more than 500 pounds)] This property involves a complex additive measure function, the functionthat is the composition of the ‘book-of ’-function with the weight-function.
In object position, as in (19a), together-NPs undergo the same shift in denotation as generalized quantiﬁers do: they now denote (partial) functionsfrom relations to one-place properties, as in (35): For any world w; time t; object d and intensional two-place relation R; ½togetherobjw:tjðdÞðRÞ ¼ the function g such that forany world w and time t; gðw; tÞ ¼ fd 0j9f9SðMCðf; the functionh hðw; tÞ ¼ fd 0j hd 0; d i 2 Rw;tg; SÞ & hd; f; Si According to (35), together with an object NP denotes the function thatmaps an object d to a function from relations R to functions (properties)that in turn map a world and a time to the set of objects for which there is ameasure correlate hf; Si for the property of being an entity which stands inthe relation R to d, and f applied to d satisﬁes the property S.
Together can modify indeﬁnites in generic sentences, though, which is brieﬂy discussed later Indeﬁnites in generic sentences like (i), though, are commonly treated as variables, to be boundby some explicit or implicit adverb of quantiﬁcation.
T H E S E M A N T I C S O F T O G E T H E R Exactly the same denotation can be assigned to together for the cases in (14). Thus, the meaning of earnings of John and Mary together in (14b) canbe computed as follows: ½John and Mary togetherobjð½earnings of Þðw;tÞ ¼ fd0j9f9SðMCðf; the function h such that hðw;tÞ¼ fd0jhd0;j_mi 2 ½earnings of w;tg;SÞ &hj_m;f;Si 2 TOGETHERw;tÞg In order to get this meaning compositionally, again Quantiﬁer Raising hasto be invoked, which will adjoin John and Mary together to the entire NP, asin (37): ½thei [[John and Mary together]NP [earnings of t The denotation of the number of children of John and Mary together in (17a)can be obtained analogously, based on Quantiﬁer Raising as in (38): the [[John and Mary together]NP [the number of children of t 1.5. Adnominal Together and the Cumulative Reading It is not just predicates expressing measurement that are acceptable withadnominal together. Also certain other predicates, if they have a quantiﬁedcomplement, yield what looks like a cumulative reading of together:9 a: John and Mary together have published 10 articles.
b: John and Mary together own less than four cars.
The ‘cumulative reading’ is familiar from sentences containing multiple quantiﬁed plural NPs with determiners such as all or 10, exactly 10, fewer than 10, as in (i) (cf. Scha 1981): a. Exactly 10 students solved exactly 12 problems.
b. Fewer than 10 students solved fewer than two problems.
Example (ia) on the cumulative reading means ‘The total number of students that solved aproblem amounts to exactly 10, and the total number of problems solved by a student amountsto exactly 12’, and similarly for (ib).
A cumulative reading with together is harder to get with quantiﬁers such as every and impossible with each, as seen in the contrast between (iia) and (iib): a. John and Mary together climbed all the mountains/10/exactly 10/fewer than 10 ‘John climbed half of the mountains and Mary the other half/John climbed fiveof the mountains and Mary five others/ . . . ’ b. John and Mary together climbed ?? every/# each mountain.
‘John climbed half the mountains and Mary climbed the other half.’ Sentence (39a) means that the sum of the number of articles published byJohn and the number of articles published by Mary is (at least) 10, and (39b)that the sum of the number of cars owned by John and the number of carsowned by Mary is a number less than 4.
In these examples, the predicate (the VP) is also associated with a measure function. However, the measure function is not expressed bythe verb alone, but by the verb together with the head noun of theobject NP. In (39a), the measure function is the function mapping anindividual to the number of articles he or she published, and in (39b)it is the function mapping individuals to the number of cars they own.
(39b) does not involve a speciﬁc measurement, but only a property ofmeasurements, namely the property of being less than four. Arguablythe same holds for (39a), taking ‘10’ to mean ‘at least 10’. In (39a)and (39b), the measure functions and the measurement propertiesthus are associated with the meanings of the VPs, which are givenbelow: a: kx½9 ! 10yðpublishðx; yÞ & articleðyÞÞb: kx½9 > 4yðownðx; yÞ & carðyÞÞ The measurement correlates of these properties will be as in (41a) and (41b),where f1 is the (partial) function that maps individuals or groups onto thenumber of papers they published and f2 the (partial) function that mapsindividuals or groups onto the number of cars they own: a: hf1; kn½n ! 10ib: hf2; kn½n > 4i The cumulative reading of together cannot be taken as a special case of some more general antidistributive reading. This is quite obvious fromexamples such as (42a), which says that the total number of children ofeither John or Mary is one. (42a) diﬀers thus from (42b), whichonly says something about the children that John and Mary have as acouple: a. John and Mary together have one child.
b. John and Mary have one child together.
An interesting general constraint on the cumulative reading of together isthat it is available only when together is adjoined to the subject, not to anobject. This is seen in (43): T H E S E M A N T I C S O F T O G E T H E R John and Mary together selected 10 students.
(John selected five and Mary another five) b: # Ten students were selected by John and Mary together.
c: # Five doctors saw John and Mary together.
(Two doctors saw John and three others Mary) This constraint does not obtain for comparative measurement predicates,which do allow together modifying an object: a: John’s income exceeds Sue’s and Mary’s income together.
b: The children outnumber the men and the women together.
The diﬀerence between the two cases can be explained if together-NPs mustundergo Quantiﬁer Raising, adjoining to the category that provides themeasure function. In (44b) that category is just the VP, as the measurefunction is associated just with the verb. Hence the together-NP may adjointo the VP, as in (45): The children [[the men and the women together]NP [outnumber t In (43b), by contrast, the measure function is associated with both thesubject and the verb. Hence the together-NP will have to adjoin to the IP, asin (46): But it is well known that not all NPs undergoing Quantiﬁer Raising canmove out of the VP: quantiﬁed NPs with every and each can move out of theVP, taking scope over the subject when occurring in object position, eventhough, quantiﬁed NPs with no, few, or exactly two cannot.
It has been argued that it is monotonicity properties that are crucial for explaining the limitations of Quantiﬁer Raising (cf. Beghelli and Stowell1997 and Szabolcsi 1997): only NPs that denote upward monotone quan-tiﬁers can move out of the VP to sentence-initial position (i.e. NPs withevery or each, but not those with no, few, or exactly two). If this is right, itis clear why together-NPs are also subject to the same constraint: together-NPs, like NPs with no, few, and exactly two, certainly do not denote anupward monotone quantiﬁer. That is, from John and Mary together ownfour cars one cannot infer John and Mary together own cars, just as one can’t infer from Exactly one woman owns four cars Exactly one woman ownsa car and from No woman owns four cars No woman owns any cars.
Thus, on the assumption that together-NPs are subject to Quantiﬁer Raising, together-NPs with measure verbs and with cumulative readings canbe given exactly the same analysis.
The analysis of adnominal together that I have given can be carried over toadverbial together, with certain modiﬁcations.
Let me start with some general facts about the readings of adverbial together. There are at least four prominent readings that together inadverbial position displays: the collective-action reading, as in (47), thecoordinated-action reading, as in (48), the spatiotemporal-proximity read-ing, as in (49), and the temporal-proximity reading, as in (50) (where Johnand Mary took the exam at the same time, but perhaps in diﬀerent places): a: The men lifted the piano together.
b: John and Mary solved the problem together.
a: John and Mary thought together about the problem.
b: John and Mary talked about politics together.
c: John and Mary climbed the mountain together.
d: John and Mary danced together.
a: John and Mary sat on the bench together.
b: The books fell together into the water.
John and Mary took the exam together.
An important fact is that the readings that adverbial together may dis- play are not always all available, but rather are determined, at least in part,by the content of the predicate. The temporal-proximity reading, forexample, is unavailable in the examples in (47) and (48). The collective-action reading is obviously not available in (48) and (49), and neither is thespatiotemporal-proximity reading in the examples in (47) and (48). Roughlythe following correlations hold between types of predicates and the readingsof together: T H E S E M A N T I C S O F T O G E T H E R a: predicates describing actions (lift the piano, solve the problem) ! group action; # spatiotemporal proximity b: predicates describing activities (think about the problem, talk about politics) ! coordinated action; # spatiotemporalproximity c: stative predicates, predicates of movement (sit on the bench, fall into the water) ! spatiotemporal proximity d: predicates describing (nonsocial) activities ðtake the examÞ ! Another general fact about adverbial together is that it can display several readings simultaneously. With human agents, generally a spatiotemporal- ortemporal-proximity reading is accompanied by an implication of socialinteraction or some other connection among the agents. Compare (52a) with(52b), and (52c) with (52d): a. John and Mary were sitting together:b. John and Mary were sitting close to each other:c. John and Mary were laughing together:d. John and Mary were laughing at the same time: Sentence (52a) does not just mean that John and Mary were sitting spatiallyclose and at the same time, but also implies some social interaction betweenJohn and Mary taking place. There is no such implication in (52b). Simi-larly, (52c) does not just mean that John and Mary laughed at the sametime; it also strongly suggests that they laughed about the same thing. Bycontrast, (52d) carries no such suggestion.
The correlation between the content of the predicate and the readings of adverbial together suggests rather strongly that the diﬀerent readings ofadverbial together are not a matter of ambiguity, but rather of the samemeaning manifesting itself diﬀerently in diﬀerent semantic contexts. This isa problem for the account of adverbial together that Lasersohn (1990) gives.
Lasersohn takes together (and related expressions) to be multiply ambigu-ous and traces the various readings of (adverbial) together to distinct,though formally analogous meanings. Simplifying, the group actionmeaning of together on Lasersohn’s account will be due to the meaninggiven in (53), which is a function mapping a verb denotation (construed as afunction from events to sets of participants) and an event to a set of eventparticipants: For a function f from events to participants and e an event;½togetherðf; eÞ ¼ fxjx is a group & x 2 fðeÞ & 8e0ðe0 < e &ð9y y 2 fðe0ÞÞ ! fðeÞ ¼ fðe0ÞÞg Here ‘<’ is the relation ‘is part of ’. According to (53), together maps anevent function f and an event e to a set of groups x such that any subevent e0of e which yields a nonempty set under f has exactly the same participants ase (with respect to f). That is, together prevents e from having subevents (ofthe same type) with just members of the group x that is the event participantof e, thus enforcing a collective reading.
The temporal- (spatiotemporal-) proximity meaning of together is exactly analogous to (53); it is obtained by replacing ‘f ’ in (53) by ‘t’, representingthe function mapping an event to the time interval (or space-time) at whichthe event takes place, so that any subevent of e of the same type will takeplace at the same time.10 Even though Lasersohn in a way provides a uniﬁed account of the readings of adverbial together, by assigning together formally analogousmeanings, his account has at least two serious shortcomings. First, it doesnot capture the fact that the readings do not seem to constitute an ambi-guity, but depend on the context and, moreover, may be simultaneouslypresent. Second, there does not seem to be a way of carrying the accountover to adnominal together.
The account of adnominal together that I have given can be extended to adverbial together as follows. When occurring in adverbial position, togetherhas the same lexical meaning it has in adnominal position, but it will takediﬀerent arguments; that is, it will take a diﬀerent kind of measure functionand a diﬀerent property of the measuring entity as its argument. Themeasure function will be the function mapping group members to thesubevents of the described event in which those group members are engaged.
The sum of those events will act as the measuring entity. The property thatwill be involved is an essential feature of my previous account of adverbialtogether (Moltmann 1997a, b): the property of the measuring entity will bethe general property of being an integrated whole, and integrity, crucially,can be fulﬁlled in various ways, and even in diﬀerent ways simultaneously.
More precisely, in adverbial position, together speciﬁes that the members ofthe relevant group are engaged in activities or states that together make up Lasersohn (1990) actually posits a spatial-proximity reading, rather than a spatiotemporal- proximity reading. But a pure spatial-proximity reading does not seem to exist. Thus, (i) cannotmean that John and Mary were standing in the same place, but perhaps John stood thereyesterday and Mary only today: # John and Mary were standing together. (in the same place, but at different times) T H E S E M A N T I C S O F T O G E T H E R the described event or state and that that event or state forms an integratedwhole. That is, the sum event composed of the subevents that the groupmembers contribute must be an integrated whole. It is this rather unspeciﬁcproperty of being an integrated whole that together takes as one of itsarguments when occurring in adverbial position and that will then act as theproperty of the measuring entity (the sum event just described).
Take the example in (54) with the cooperation reading of together: In the Davidsonian tradition, I will take work to have an additional argu-ment position for events. If e is the event of working together as described in(54), then the function that TOGETHER takes as one of its argument is thefunction fe that maps John onto the subevent of e of which John is an agentand Mary onto the one of which she is an agent. The property argument oftogether will be the property INT-WH, the property of being an integratedwhole. Thus the analysis of (54) will be as in (55): 9eðwork onðe; j _ mÞ & togetherðj _ m; fe; INT-WHÞÞ This obviously requires a further generalization of the meaning of together,as in (1100): For an intensional additive measure function f from the structureðD;_Þ; for a set of entities D; to the structure ðR;þÞ; for a setof objects R; for any property S of objects in R; any world wand time t; and any object d 2 D;hd;f;Si 2 TOGETHERw;tiff fðdÞ 2 Sw;t: Let us now take the spatiotemporal-proximity reading as in (56): I take stative verbs to also involve an event variable – basically a space-timeregion that instantiates the property expressed by the verb. In (56), therelevant function then maps both John and Mary onto some space-times oftheir sittings so that those space-times coincide in time and their sum iscontinuous in space. Thus, integrity will be fulﬁlled by spatiotemporalproximity.
A bit more diﬃcult is the case of the group-action reading, as in (57): John and Mary solved the problem together: Here together speciﬁes that John and Mary help constitute the event ofsolving the problem, but not in virtue of being the agents of individual eventsof problem solvings, but in virtue of being the agents of some activities that together make up the event of solving the problem. In this case, the mea-suring entity is the sum of the activities of John and of Mary that contributeto the solution of the problem, but that are not themselves solvings of theproblem. Nonetheless, that sum has integrity in that it constitutes a solving ofthe problem. For a sum event to constitute a certain type of single event isanother way of having integrity. The function fe, which maps individuals tothe subevents of (57) in which they are involved, is an additive measurefunction, mapping John to an event e0 and Mary to an event e00 and the groupconsisting of John and Mary j _ m to the event e0 _ e00.
The meaning of adverbial together can now be speciﬁed as a function from relations involving event arguments to relations as in (58a) (for transitive verbs)and (58b) (for intransitive verbs and a subject-oriented reading of together): ð58Þ a. For any world w and time t; and two-place intensional relation R, ½togetheradverbw;tðRÞ ¼ fhd;eijhd;ei 2 Rw;t & hd; fe; INT-WHi b. For any world w and time t; and three-place intensional relation R, ½togetheradverbw;tðRÞ¼ hd;d0;eijhd;d0;ei 2 Rw;t Together thus will have a uniﬁed semantic analysis in adverbial position,with the diﬀerent readings of adverbial together being traced to diﬀerentways for an event to constitute an integrated whole.
It is now clear why adnominal and adverbial together yield diﬀerent readings. Adnominal together has access only to the generalized-quantiﬁermeaning and thus only to the meaning of the predicate as such. By contrast,adverbial together has access to speciﬁc arguments of the predicate, inparticular the event argument. As a result, a diﬀerent measure function isavailable and a diﬀerent property of the measuring entity.11 There are other phenomena where the inaccessibility of information provided by the predicate for the interpretation of referential NPs arguably plays a role. Keenan (1979) observesthat the interpretation of predicates such as cut may be dependent on the interpretation of theNP, but a converse dependency does not seem to occur. An instance of the same generalprinciple, according to Keenan (1979), is the fact that relative adjectives such as ﬂat may dependin their interpretation on the head noun (ﬂat road, ﬂat table, ﬂat tire, ﬂat voice), but a converserelationship does not obtain. From these observations, Keenan draws a correlation between thedirection of agreement and semantic dependency and proposes the following principle: Given A and B distinct constituents of a syntactic structure E, A may agree with B iﬀthe semantic interpretation of expressions of A varies with the semantic interpretationof expressions of E.
T H E S E M A N T I C S O F T O G E T H E R O T H E R R E A D I N G S O F A D N O M I A L T O G E T H E R There are a number of other readings that together in adnominal positiondisplays that I have so far neglected. The reason is that those readings aremore similar to the readings of adverbial than to adnominal together, andthey are thus better analyzed in relation to adverbial together.
First, adnominal together has what one may call a mixture and a con- a. The vinegar and the wine together tasted terrible:b. The pictures together look nice: a. John and Mary together are a nice sight:b. John and Mary together form an interesting couple: In (59a, b), together obviously does not relate to some measurement speci-ﬁed by the predicate. Rather it emphasizes the composition or conﬁgurationof the quantity or group in question: in (59a) the fact that the entity is themixture of the wine and the vinegar and in (59b) that it consists in a par-ticular spatial conﬁguration of the individual pictures. Similarly, together in(60a,b) speciﬁes that John and Mary form a social or spatial unit. Note thatin (60b), the predicate is obligatorily collective and thus provides anothersort of evidence that the function of adnominal together is not that ofenforcing a collective reading.
The mixture and the conﬁguration readings of adnominal together seem rather diﬀerent from the measurement reading, but they are close to thereading together has in adverbial position. On the mixture and conﬁgurationreading, together just emphasizes that the group in question forms anintegrated whole in some way or another. Formally, I take this to mean thattogether in those cases involves the identity function as the measure functionand takes the property INT-WH as an argument, using the generalizedlexical meaning of together in (110). Thus, in such cases, even though thelexical meaning of together would be the same, a diﬀerent function of ad-nominal together needs to be distinguished, which is then associated with adiﬀerent denotation.
Together sometimes allows for event-related readings even in adnominal position. Thus, for many speakers, an event-related reading is possible in thefollowing cases: a. John and Mary together have lifted the piano:b. John and Mary together have solved the problem: But there are many eventive predicates with which an event-related readingof adnominal together seems universally unacceptable: a. # John and Mary together stood up:b. # John and Mary together were working: Moreover, stative predicates seem to never allow for a space-time relatedreading of adnominal together: a. # John and Mary together were sitting:b. # John and Mary together were standing in the corner: The reason why an event-related reading is possible in (61a) and (61b) maybe this. If the verb describes a telic event – that is, an event that has integrity,then together can specify that the group it applies to helps in constitutingthis event. For telic predicates, there is thus a measurement correlate con-sisting of the event and a function mapping individuals to a sum eventconstituting that event. If no telic event is described by the predicate, thenthere will be no such measurement correlate.
Adnominal together displays an event-related reading also in another context, namely when occurring in generic or modal sentences:12 a. John and Mary together can easily lift the piano: c. John and Mary together would interact well with each other: d. John alone would be unable to perform the task: In such sentences, for all speakers, it appears, an event-related reading wheretogether speciﬁes cooperation is unproblematic. The present account oftogether does not yet tell us, though, how such a reading could come about,except by possibly assimilating such cases to the case of telic events as in (61).
A L O N E A N D O T H E R R E L A T E D M O D I F I E R S Alone is an expression that like together occurs both in adnominal and inadverbial position and in fact displays readings quite analogous to those oftogether. Adverbial alone in (65) displays event-related readings and in (66)space-time related readings; adnominal alone in (67) displays measurementreadings and in (68) a constitution reading: See Krifka et al. (1995) for discussion of generic sentences.
T H E S E M A N T I C S O F T O G E T H E R The readings of alone can in fact be derived in the same way as those oftogether. All that is needed is that alone be assigned a particular lexicalmeaning, namely, as I want to suggest, the relation that holds between anentity d, an additive measure function f, and a property of real numbers (ormore generally objects) S just in case f maps d onto a number (or otherobject) satisfying S and maps no entity that has d as a proper part (<) ontothat number (or object). Thus, the more general lexical meaning (whichcorresponds to (1100)) will be:13 For an intensional additive measure function f from a structureðD; _Þ; for a set of entities D; to a structure ðR; þÞ; for a set ofobjects R; for any property S of objects; any world w and timet; and object d 2 D; hd; f; Si 2 ALONEw;t iff f w;tðdÞ 2 Sw;t andfor no d 0; d < d 0; f w;tðd 0Þ 2 Sw;t: Alone, unlike together, also has another, property-related reading on whichit is equivalent to only: Like the cumulative reading of together (and alone), the property-relatedreading is available only if alone is adjoined to the subject: Example (71a) does not allow for the reading ‘John likes only Mary’ (butonly for the reading ‘John likes Mary when she is isolated’), and (71b) doesnot allow for any reading at all (even though the property-related readingwould make sense). The restriction to subjects, again, indicates that alone on Alone with potentially collective predicates is diﬀerent from together in that it seems to prevent a reading that is hardly available in the ﬁrst place. Only in certain cases, such as (i)below, may the predicate be understood as applying to a larger entity, that is, the box includingits content: This is the reading that is prevented by the presence of adnominal alone, as in (ii): the property-related reading is subject to Quantiﬁer Raising and in (71b)involves a property denoted by the entire IP, including the subject.
It is not easy to assimilate the property-related reading to the measure- ment reading. For that reading, it seems, a slightly diﬀerent meaning ofadnominal alone needs to be posited, one not available for adverbial alone.
That meaning is also based on the relation ALONE, but the measurefunction will be the identity function id, and the property of a measuringentity the property that the predicate itself expresses, as in (72): ½aloneadnom2w;tðdÞ ¼ fPjhd; id; Pi 2 ALONEw;tg There are other modiﬁers related to together such as as a whole, whole (wholly), and individual(ly). They are best called ‘part structure modiﬁers’(cf. Moltmann 1997a, b). Part structure modiﬁers often have similarsemantic eﬀects as together and alone, but it appears that they do not have asemantics involving measurement or constitution. For example, as a wholenot only modiﬁes plural NPs, but also singular ones, as seen in (73a); it doesnot allow for a cumulative reading, as seen in (73b); and it does not displaythe internal reading, as seen in the contrast between (74a) and (74b): b. # The pictures as a whole were seen by 50 people: As a whole in (73 a) triggers a global evaluation of the pictures; together in(74a) requires an evaluation of a particular conﬁguration of the pictures. Allthis suggests that for part structure modiﬁers such as as a whole, the analysisas relations between entities and situations is in fact suitable.
In this paper, I have given a uniﬁed account of together, taking as a startingpoint the semantics of adnominal together when it has a measurementreading. The analysis made crucial use of additive measurement functionsand their values: the lexical meaning of together, on the ﬁrst reading, wasconceived as a relation between groups of entities, measure functions, andproperties of real numbers. The other functions of together were accountedfor by positing somewhat diﬀerent measure functions and properties of themeasuring entity. What is unusual in this analysis is that two of the argu-ments of adnominal together are never expressed or referred to by any T H E S E M A N T I C S O F T O G E T H E R expression in the sentence, but must be obtained by reﬂecting on theapplication conditions of predicates.
Adnominal together also provided an additional application of Gen- eralized Quantiﬁer Theory within an intensional semantics: together in ad-nominal position was in fact analysed as expressing a restriction of the set ofproperties that the NP without together, as a generalized quantiﬁer, woulddenote.
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AZOTEMIA AZOTEMIA CLEARANCE AZOTURIA BARBITURICI (Test qualitativo) BENZODIAZEPINE (Test qualitativo) BETA 2 MICROGLOBULINA BETA 2 MICROGLOBULINA URINARIA BETA HCG BETA HCG URINARIO CALCOLO RENALE CANNABINOIDI (Test qualitativo) CARBAMAZEPINA (Tegretol) CARDIOLIPINA (Anticorpi IgG) CARDIOLIPINA (Anticorpi IgM) CATECOLAMINE TOTALI URINARIE CEA CELLULE PARIETALI (Anticorpi APCA) CI