2.2.1 Projection tests

I will first test the accompaniment relation and the alternative implication for their projection properties. In their overview of projective contents, Tonhauser et al. (2013) argue that the standard family-of-sentence diagnostic for projective content (Chierchia & McConnell-Ginet 1990) should be applied in different ways depending on whether an expression is subject to so-called Strong Contextual Felicity or not. Let us therefore start with the latter. Strong Contextual Felicity tests whether a content is strongly presupposed, that is, whether it must be contextually given and cannot be accommodated. The example in (33a) shows that auch is at odds with a context that does not introduce an explicit alternative; auch is thus subject to Strong Contextual Felicity. (This is also the standard assumption for the additive too in English; see Tonhauser et al. 2013.) The example in (33b) shows that mit_adv is different. The alternative implication (‘Someone different from the bus driver is working on a broken-down car.’) is compatible with the given context and thus not subject to Strong Contextual Felicity. The same is true for the accompaniment relation (‘The bus driver is accompanying an implicit working on a broken-down car.’), which need not be introduced before either. In other words, while auch introduces strong presuppositions, mit_adv does not.

With this distinction in place, we can turn to the family-of-sentence diagnostic. According to this diagnostic, only projective content survives if it is embedded under family-of-sentence variants such as modals, conditionals, or negation. As mit_adv is not subject to Strong Contextual Felicity, the relevant variants need not be contextualized in a particular way. The examples in (34) then show that the accompaniment is clearly not projective: None of the examples conveys that Ben is accompanying an implicit tinkering with a soapbox.

Furthermore, as the accompaniment requires that there are alternatives, the alternative implication does not project either; see (35).

The situation for auch is again not the same. The family-of-sentence diagnostic shows that the alternative presupposition associated with auch is projective (see Tonhauser et al. 2013 for the same claim regarding the additive too in English). For instance, in (36), it survives the embedding under a modal and is therefore at variance with the given context.⁸

Tonhauser et al. (2013) discuss the so-called Obligatory Local Effect as a third diagnostic for projective content. It tests whether a (projective) content must scope under an embedding operator such as glauben ‘believe’ (see also Gazdar 1979; Potts 2005). auch and mit_adv are both subject to the Obligatory Local Effect and thus do not contrast here. However, this commonality can be used in order to reveal that both expressions introduce different propositional contents; compare (37).

By hypothesis, mit_adv involves an accompaniment by participation; therefore, a context that negates any knowledge of a cooperation by the attitude holder is incompatible with a belief report to the contrary. This is different for auch. By hypothesis, it is not bound to an accompaniment; therefore, the given context is compatible with the given belief report.

In sum, all three projection tests reveal clear differences between mit_adv and auch: in contrast to auch, mit_adv introduces neither strong presuppositions nor projective content. Furthermore, only mit_adv contributes an accompaniment by participation.

2.2.2 Tests for discourse transparency

Although both the accompaniment and the alternative implication as introduced by mit_adv are not projective, they do not share the same semantic-pragmatic status. In particular, according to (26b), the accompaniment is identified as explicit content, whereas the host situation including its participants is identified as merely implicit content. This suggests that only the former is discourse-transparent and thus a potential target for anaphors, cross-sentential operators, and explicit questions; see Farkas & de Swart (2003); Potts (2005); Amaral et al. (2007); Jayez (2010); Tonhauser (2012) for elaborate discussions of these diagnostics.

The example in (38) shows that mit_adv does not license a pronominal anaphor to the alternatives or to the relevant team. Similarly, the anaphor das ‘that’ in (39) can relate to Mia’s accompaniment by participation, but not to the cooperation as such.

Notably, given mit_adv, corresponding anaphoric descriptions are feasible, as shown in (40). In contrast to pronouns, definite descriptions can convey indirect anaphors that lack an explicit antecedent. The examples thus support the assumption that mit_adv introduces the relevant information implicitly.

The example in (41) shows that mit_adv licenses operator attachment to the accompaniment. Ben’s preference for working on his own is a plausible reason against his accompaniment of a tinkering with a soapbox. Therefore, the use of mit_adv in the matrix clause is compatible with a concessive adverbial, but incompatible with a causal one.

By contrast, operators cannot attach to the alternative implication, as shown in (42). Notably, the context provides candidates for relevant alternatives; that is, although beide ‘both’ within the adverbial clause refers to Lilli and Mia, the adverbial cannot relate to their participation in the tinkering. This argues against an ellipsis account of mit_adv: if there were a silent internal argument of the preposition that could be recovered from the context, (42) should be fine.

Finally, the given picture is corroborated by question-answer pairs. The examples in (43) show that mit_adv supports answers to questions that are sensitive to an accompaniment. It is noteworthy that mit_adv can be contrasted with allein ‘alone’; this can only be explained if mit_adv is the bearer of the relevant accompaniment.⁹

The examples in (44) show that questions that are sensitive to the alternative implication are not feasible. Note that the question provides explicit potential alternatives; their inaccessibility is again at odds with an ellipsis account of mit_adv.

In sum, the diagnostics show that mit_adv involves a discourse-transparent accompaniment and a discourse-opaque alternative implication.

Let me conclude this subsection with a brief comparison to mit-PPs. They support anaphors to alternatives, the attachment of alternative-sensitive operators, and answers to alternative-sensitive questions; see the contrast between (45) and (38), (42), (44).

This is as expected, given that the relevant alternatives are explicit here. Recall, however, that the contrasting behavior of mit_adv does not follow from an ellipsis account; the examples in (42) and (44) above show that mit_adv does not introduce analogous silent slots for PP-internal arguments. This is a clear difference between mit-PPs and mit_adv. In the next section, I will argue that the involved accompaniment relations differ as well. The difference in interpretation between the example in (43b) with mit_adv and the analogous example with a mit-PP in (46) is already suggestive of a distinction.

In (43b), mit_adv conveys that Ben is playing only an accompanying role in the tinkering. In (46), however, the mit-PP conveys a condition; it says that Ben is tinkering with the soapbox only if Mia and Lilli accompany him. That is, the forced contrast to allein ‘alone’ shows that the roles are reversed.

2.2.3 Accompaniment by participation: Adverbial mit vs. prepositional mit

With regard to mit-PPs such as (47), Seiler (1974: 235) writes that “it is precisely the function of the Comitative […] to leave unspecified the extent of participation in the action”; see also Strigin (1995: 320) and Rapoport (2014: 161).

Accordingly, this example does not specify whether Mia and Ben are coequal agents or whether Mia is accompanying Ben’s tinkering without tinkering herself (in Strigin’s words, she could just be being cheerful). How does mit_adv fit into this picture?

The continuations (48a) and (48b) in (48) show that mit_adv does not specify the extent of participation either.

However, there are two crucial differences from mit-PPs. First, the co-participant the varying contribution of whom is under consideration in (48) is the subject argument. This comes to light most clearly in cases that make an asymmetric interpretation prominent; see (49) and (50).

This reversal of argument assignments provides clear evidence against an ellipsis account of mit_adv: the co-participant is not introduced as an implicit internal argument of a putative mit-PP.

Second, the co-participant as introduced by mit_adv is related more closely to the explicit event description than the co-participant as introduced by a mit-PP is. Most notably, examples based on mit_adv entail that the event predication is predicated of the subject argument; recall the entailment in (51) (= (8b)). (Qualifications of this observation will be discussed in Section 3.) This is different for mit-PPs such as mit Mia in (47). As said, Mia could just be cheerful and would thus not be an agent of the relevant eventuality.

This difference can be conceived of as a natural byproduct of the fact that mit_adv promotes the co-participant to the subject position. In other words, the subject is not just a ‘comitative’ to an independent event; instead, mit_adv brings about the introduction of a separate event that accompanies an implicit host event. The accompaniment conveyed by mit_adv thus does not relate participants to events, but rather events of the same kind to each other. I suppose that this is also the reason why only mit_adv is sensitive to asymmetric interpretations. For instance, even in a context as given in (50), a mit-PP can be used for the primary participant, as in (52).

The proposed distinction between comitatives on the one hand and accompaniment by participation on the other can explain this as follows. With mit-PPs, the particular justification of the comitative role is left fully unspecified; with mit_adv, by contrast, it is the co-participant’s participation as such that is marked as an accompaniment.

I conclude that mit_adv is clearly different from mit-PPs and thus not elliptical. It introduces a participation in an eventuality that is conceived of as accompanying an eventuality of the same kind.

4.2.1 Accounting for the constraints on the positive, the comparative, and Kimian state verbs

I will first tackle the adjective-related constraints. To this end, a more detailed look at the semantics of adjectives is necessary. Over the last decade, several researchers have argued that typical adjectives provide both an argument position for the bearer of a certain property and an argument position for the property itself; see Moltmann (2009; 2013); Bücking (2012); Maienborn (2015); McNally & de Swart (2015); Maienborn & Herdtfelder (2017) for discussion. Following Moltmann, I will call these particularized properties tropes. A corresponding entry for groß ‘tall’ is given in (79). Nominalizations such as in (80) render the referential trope argument explicit: they denote the properties themselves instead of their bearers (compare the corresponding well-known ‘externalization’ of silent verbal event arguments by event nominalizations).

For the present purpose, the crucial ontological trait of tropes is that they are bound to their bearers in a particularly tight way: they are inherent to their respective bearers without providing a spatio-temporal structure that other tropes could live on. That is, Ben’s height is invariably bound to Ben alone and cannot be extended by the accompaniment of some additional bearer; this then provides a plausible reason why free mit is incompatible with both the positive and the comparative. I will spell out the corresponding compositions in turn.¹⁴

It is a standard assumption that the positive involves a context-sensitive standard of comparison such that a bearer that complies with this standard ‘stands out’ relative to the property under discussion; see Kennedy (2007) for an elaborate defense of such an approach within a degree-based system. I will use the simplified trope-based variant of it in (81).

According to (81), a context-sensitive function f_pos maps the trope-type for height (that is, the set of possible instances of height, roughly corresponding to measure functions in degree-based systems) onto one of its subtypes, namely, the standard of comparison. For instance, a context could be such that one must be 70 inches tall in order to stand out in height. Correspondingly, the standard of comparison f_pos (height′) would be a trope-type R that comprises all possible instances of height (that is, tropes including their bearers) that involve exactly 70 inches. The ordering relation ≥ relates a trope r to either a trope r′ or a trope-type R. If, as is the case here, ≥ relates a trope r to a trope-type R, r must exceed or equal all possible instances of R; in a context as just sketched, this would say that r must be a height that involves at least 70 inches.¹⁵ The simple example in (82) then receives the truth conditions in (83); I assume that the state s comes in via the copula or some other trope-closure operation (see Maienborn 2005; 2015; Maienborn & Herdtfelder 2017; the notation ‘s:’ says that s is characterized by the content that follows): (82) is true iff there is a state s such that Ben’s height exceeds or equals all possible instances of the standard of comparison for height as determined by contextual needs.

Based on the entries in (78) and (81), the combination of the positive with mit_free yields (84), which in turn yields the final result in (86) for the full sentence in (85) (see (66a) above).

In prose: (85) is true iff there is a state such that both Ben’s height and some implicit height of some implicit bearer comply with a standard of comparison for height. Furthermore, the condition accomp′(y, y′_i) requires that both heights form an integrated whole and that Ben’s hight extends the implicit height. However, given that the implicit height is a trope and thus an inherent property of its bearer lacking a spatio-temporal structure that other tropes could live on, it cannot be extended by another trope. Hence, the result is incoherent, and (85) is predicted to be infelicitous for ontological reasons.

It is noteworthy that the following well-formed examples do not contradict this reasoning.

The example in (87a) with the additive also presupposes that the height of someone different from Ben complies with the contextual standard. In contrast to mit_free, however, the additive does not enforce any specific relationship between both tropes; hence, there is no conflict with the ontological requirement that tropes are bound to their bearers. (This substantiates one more time why I consider the analysis of free mit in terms of an additive wrong.) The example in (87b) receives a straightforward distributive reading; again, the relevant tropes—Ben’s height and Mia’s height—are independent of each other, which renders their copredication unremarkable. The example in (88) is a bit more tricky. It suggests that tropes are closed under sum formation (that is, the sum of two tropes yields a trope; see also Moltmann 2013: 53–54). However, in contrast to examples based on mit_free, the example in (88) involves a simple collective interpretation. Therefore, it is not about a separate trope that extends another separate trope, but about a complex trope (that is, height of 11 feet) that has a collective entity (that is, Ben and Mia) as its unique bearer. In other words, such collective interpretations do not build on the specific accompaniment between distributed tropes that causes mit_free’s conflict with trope predications.

The explanation for the restriction regarding the comparative is now easy. Following standard assumptions, the comparative differs from the positive by involving a context-independent explicit measure for the comparison. For instance, a trope-based implementation such as (89) for größer als Mia ‘taller than Mia’ says that x’s height must exceed Mia’s height.

However, as (89) is still a trope predication, this difference does not affect the combinatorics with mit_free; see the composition in (90). Therefore, (91) (see (66b) above) yields the very same ontological mismatch as the positive does. According to the resulting (simplified) representation in (92), Ben’s height would have to extend the implicit height of some implicit bearer, which is impossible (irrespective of the fact that both heights are also said to exceed Mia’s height).

Next, I will turn to the constraints regarding typical K-state verbs (see Section 4.2.2 for a discussion of the constraints regarding D-state verbs). The general idea is that their semantics also involves tropes and thereby predicts that they are infelicitous with mit_free. In fact, Maienborn (2015) has argued that the predications that characterize the K-state in K-state verbs can be conceived of as trope predications. For instance, Ben weighs 70 kg very obviously relates Ben’s particular weight to a measure of weights in general (see Moltmann 2013: 61–69 for more details on tropes and quantities). The sentences Ben loves Mia and Ben resembles Mia identify Ben as a bearer of relational tropes: he exhibits a particularized feeling for Mia or a particularized similarity to her (irrespective of the fact that the specific content of this similarity is left unspecified). For concreteness, I will go through the composition for the example in (93) (see (71a) above).

Based on the entry in (94) for ähneln, the combination with mit_free yields (95).¹⁶ The inclusion of the object, the subject, and the K-state yields the representation in (96) for the full sentence.

As before, the result is ill-formed due to accomp′: Ben’s similarity to Tim cannot extend the similarity to Tim as borne by someone else. This trope-based explanation is further confirmed by the adjective-based counterpart in (97), which is infelicitous in a fully analogous way.

The given reasoning is based on one noteworthy ingredient. According to the entry in (94), the K-state verb ähneln introduces a trope predication and thus renders the trope argument compositionally accessible to mit_adv. That is, the given proposal takes the decomposition of the K-state verb into a trope predication on the one hand and a superordinate K-state predication on the other seriously. In fact, according to (94), the introduction of the K-state including the closure of the trope argument is not rooted in the verb itself, but it is rooted in some silent operation above it. This strengthens the parallel to copula structures with a trope-denoting lexical core (the adjective) and a closure operation introducing the K-state on a higher level (possibly indicated by the explicit copula). Notably, as mentioned in the introduction in Section 1, Zifonun (1996/1997) argues for a base position of the adverbial free mit in the vicinity of the verbal head below direct and indirect objects. Across frameworks, such a position is associated with the compositional access of modifiers to the lexical core of their target entities (see Maienborn & Schäfer 2011 and Bücking 2018 for overviews). This provides initial independent evidence for the given compositional set-up; a full-fledged analysis of the syntax-semantics interface of K-state verbs will be left for another occasion.

In sum, given a uniform compositional approach, the cross-categorial restrictions for mit_free fall under the purview of a uniform conceptual explanation. mit_free is at odds with trope predications, as tropes denote particularized properties that are inherent to their bearers and thus inaccessible to an extension by the accompaniment of an independent other bearer.

I conclude this section with a note of caution. The following examples seem to challenge the given trope-based restriction; arguably, they are felicitous despite the fact that mit_free is combined with a trope-denoting adjective. ((98b) is an abbreviated version of an example I owe to an anonymous reviewer; see https://www.seniorenportal.de/community/forum/haustiere/hasi-ist-krank?tid=126413&page=1#126413, accessed on 09/24/2018.)

However, it is well known that type-related restrictions of modifiers can often be sidestepped by adaptive strategies at the semantics-pragmatics interface (see de Swart 2011 for an overview). I hypothesize that examples such as (98) build on adaptations as well. (98a) does not say that Carl is joining the anger that is inherent to Mia; it rather says that Carl is joining the situation that is characterized by Mia acting out her anger. Similarly, (98b) does not say that the family members are joining the disease that is specific to the hare; it says that the family members are joining the unfortunate situation the hare is in by themselves being afflicted with a comparable negative sensation. In both cases, the extended entity is not a trope; it is a bigger situation in which the trope is embedded. This situation provides a spatio-temporal structure that supports an extension by further participants and that is therefore compatible with the contribution of mit_free. The more general prediction is that the acceptability of mit_free covaries with the question of whether adequate superordinate situations can be adapted. Arguably, predications that can be related easily to joint activities or to compassion (such as wütend ‘angry’ and krank ‘sick’ in (98)) are particularly appropriate for such adaptations, whereas an objective atemporal property such as height is not. This reasoning is further supported by the following examples. (I owe (99a) to an anonymous reviewer and (99b) to Frauke Buscher.)

(99a) cannot be adapted at all: atemporal mathematical properties do not suggest superordinate spatio-temporal structures that could be relevant for an accompaniment. By contrast, (99b) is acceptable because the frame-setting modifier bei dem Auto ‘regarding the car’ provides an explicit anchor for a relevant superordinate spatio-temporal structure: the dysfunctionality of the clutch can be related to the more general state the car is in, namely, its having dysfunctional parts. Correspondingly, the dysfunctionality of the clutch and the dysfunctionality of, say, the brake are still independent tropes; their integrity only follows from their being part of the superordinate state the car is in. While I will leave a thorough verification of this line of thought to future research, the following discussion will provide independent evidence for the assumption that the distribution of mit_free depends in crucial ways on the distinction between tropes and states.

4.2.2 Accounting for the well-formed locative predications and the behavior of Davidsonian state verbs

The strategy for an account of the feasible options is obvious: mit_free should target a predication that involves an entity that supports an extension by accompaniment. This can be motivated easily for locative predications such as the locative copula structure in (100) (recall (68a) from above).

Intuitively, locative predications do not contribute an inherent property of an individual, but an external relation of that individual to some region. The state of being located at a particular region is thus a spatio-temporal structure that other participants can live on; this is the conceptual foundation of why mit_free is possible here. In order to spell out this intuition, the simplest assumption is that the target predications themselves provide locative state predications; see the meaning representation in (101). The combination with mit_free yields (102); (100) then receives the final representation in (103).¹⁷

The result is well-formed. The state of Ben’s being in the attic is said to accompany the state of someone else’s being in the attic. As motivated above, such an extension of a locative relation is conceptually feasible: being at a particular region is not a trope bound to a unique bearer.

With this explanation in place, it is easy to see why the K-state verb gehören zu ‘belong to’ licenses mit_free; recall (104) (= (71b)).

The verb gehören zu provides an abstract relation of membership; that is, similarly to locatives and in sharp contrast to the K-state verbs discussed in Section 4.2.1, it does not contribute an inherent property of an entity, but an external relation of that entity to some group. As the state of belonging to some group licenses an extension, no conflict with the accompaniment introduced by mit_free arises.¹⁸

The behavior of locative D-state verbs can be traced back to the patterns already established. The corresponding reasoning is based on the intuition that locative D-state verbs contribute a bipartite meaning structure: the subject referent is attributed both a locative state and a posture (see again Kaufmann 1995: 98–120 for a more general discussion). Furthermore, the posture relates to particular parts of the subject referent and their organization (for instance, according to Kaufmann’s work, standing involves a vertical orientation of the subject’s prominent axis). It is thus plausible that the posture amounts to a particularized property, that is, a trope. In well-formed examples such as (105a) (= (72a)), mit_free scopes above the integration of the locative. In fact, Zifonun (1996/1997) shows that the reversed linearization is ungrammatical; see (105b).

I conjecture that mit_free here combines with a predication that makes the locative component compositionally available, while the trope component is already closed; see the sketch in (106) and the result of its composition with mit_free in (107).

Irrespective of how the composition proceeds (see below for a few remarks), (107) predicts (105a) to be well-formed. The state of x’s being at the corner is said to accompany the state of someone else’s being at the corner, which is fully analogous to the simple copula structure in (103) above. It does not matter that x and its implicit alternative x′_i must also be bearers of posture tropes. According to (107), these tropes do not interact and thus do not cause a conceptual mismatch.

The situation is different for mode-oriented readings; recall the ill-formed example in (108) (= (74)).

As this reading demotes the locative component, it is plausible that it makes the posture component compositionally available; manner modification as in (109) corroborates this claim. Correspondingly, mit_free would target a trope predication as sketched in (110), which yields the result in (111).

As desired, (111) predicts that (108) is infelicitous. Due to accomp′(y, y′_i), the particularized posture y inherent to x would have to extend the posture y′_i inherent to some other entity, which is conceptually impossible.

In a nutshell, the idea then is that locative D-state verbs provide two compositional anchors. The first anchor is a trope predication that is incompatible with mit_free; the second anchor is a state predication that is available above a locative PP argument and that is compatible with mit_free. This set-up begs the follow-up question of where the D-state is integrated. Given that locative D-state verbs and locative copula structures differ for instance with regard to perception reports (see Section 4.1 and Maienborn 2003; 2005 for details), the referential argument of the full verbal projection cannot be the locative K-state argument s in (107) as such. One option would be that the locative state predication and the trope predication are integrated within a higher-order D-state predication. This would mirror the situation with K-state verbs as discussed in Section 4.2.1, where I have also suggested that there is an independent higher-order closure operation. The difference would be that the closure introduces a D-state with D-state verbs and a K-state with K-state verbs. I would like to leave a more detailed discussion of these compositional challenges to future work. The solution should not affect the principled idea that I have put forward here in order to explain the distribution of mit_free within the projection of locative D-state verbs.

I will conclude this subsection with a brief comment on D-state verbs that introduce a specific mode of sensory perception and on the D-state verb schlafen ‘sleep’; recall the ill-formed examples in (112) (= (76a)) and (113) (= (75b)).

It is intuitively plausible that the internal structure of these verbs does not introduce an abstract relation of membership, but a trope. More specifically, glänzen introduces a luster, that is, a particularized visual appearance rooted in the surface structure of its bearer. Correspondingly, the cup’s luster cannot extend the luster of the plate, which explains why (112) is odd. Similarly, dormancy as such (that is, the property disposed of its spatio-temporal coordinates; recall the contrast to (75a) above) is inherent to its bearer and thus inaccessible to an extension by someone else’s dormancy.¹⁹

4.2.3 Accounting for the well-formed superlative predications

Finally, I will turn to the intriguing observation that the superlative is generally well-formed with mit_free despite the fact that corresponding positives and comparatives are not. I argue that this contrast has the following principled explanation. The superlative contributes a type of meaning that is very different from the meaning of the positive and the comparative, namely, it partitions a context-set according to some measure. Therefore, mit_free escapes the interaction with underlying trope predications and instead interacts with this partition in a predictable way. I will provide independent reasons for this perspective on the superlative and then spell out a corresponding composition with mit_free.

The first observation relates to the lacking entailment in (114) (= (8a)).

For Zifonun (1996/1997) and Bücker (2012), this behavior is idiosyncratic and thus a key argument for the treatment of free mit plus superlative as a separate construction: mit would eliminate the uniqueness condition of the superlative; moreover, the adverbial counterpart supports the corresponding entailment, which would speak against a uniform treatment in a principled way. However, this reasoning does not take into account that this entailment pattern is fully regular for the superlative in distributive contexts; see the simple plural superlative in (115). Notably, (115) still involves uniqueness. The difference from a standard singular predication is merely that the predication does not relate to a unique individual, but to a unique set of individuals, which in this case consists of Ben and Paul.

It is thus highly plausible that the entailment patterns in (114) and (115) have a common source. Both predications involve unique sets of individuals that comply with a certain height; as sets of individuals are involved, it is impossible for both cases to deduce which particular individual is the tallest. The difference between them is the following. The standard plural in (115) exhaustifies the individuals in the relevant set by explicit reference to them; mit_free in (114), by contrast, merely indicates that there must be others in the relevant set without, however, specifying their number and identity. Furthermore, the distribution obtained by mit_free does not yield an ordinary plural predication; it is still a modifier to the given singular predication, which is why (114) and (115) are morphologically distinct. In other words, mit_free does exactly the same in the combination with the superlative as it does in its other uses. It is a modifier that marks the existence of implicit co-participants and thereby triggers plurality effects.

Given the analogy between mit_free and the plural, a closer look at plural superlatives in general is necessary. The research on plural superlatives has identified two crucial challenges to their proper analysis: the distributivity problem and the cutoff problem; see Stateva (2005); Herdan (2008); Fitzgibbons et al. (2008). The distributivity problem is a direct consequence of the lacking entailment in (115). It says that the combination of a standard degree-based semantics for the superlative, as in (116) (see Heim 1999; Coppock & Beaver 2014), with a standard distributional operator for plural predication, as in (117) (see Lasersohn 1998; 2011), yields a contradictory and, thus, wrong result, as in (118). (I assume that G is some appropriate functor from sets of singular individuals to plural individuals.)

In prose: A sentence such as Ben and Paul are the tallest would be true iff Ben is taller than everyone else in the context-set, and Paul is taller than everyone else in the context-set. This is clearly impossible, as Ben would have to be taller than Paul, while Paul would have to be taller than Ben. Intuitively, there is an obvious way out. The superlative should induce a partition of the context-set such that Ben and Paul are taller than all others in the context-set, irrespective of how their heights are ranked to each other. This already suggests an analysis of the superlative that is not about the assignment of particularized properties, but about the bipartite partition of a context-set into the set of those individuals that comply with a certain height and those that do not.

This reasoning becomes even more evident with regard to the second challenge, the so-called cutoff problem. This problem can be illustrated by the dialogue in (119), adapted from Fitzgibbons et al. (2008: (6)).

Despite the fact that Ben and Paul could be the tallest students in the given scenario, A can accept a correction of his corresponding statement and include Eric in the set of the tallest students. This makes sense only on the assumption that the superlative semantics involves a context-sensitive cutoff that divides the context-set into the unique group that complies with this cutoff and the remaining individuals that do not comply with it. The given scenario could be such that a difference of just one inch should not matter for the partition, for instance, because all others in the context-set are significantly shorter than Eric. Fitzgibbons et al. (2008: 303) conclude that “the context supplies a natural cutoff point on the relevant scale which determines, for a given gradable predicate R, a unique group of R-est individuals”. In other words, the superlative contributes a cutoff that must be such that it is satisfied by exactly those individuals the superlative predicates of. Crucially, superlative constructions differ in the degree to which this unique group of individuals is made explicit. Standard direct predications exhaustify the members of the unique group of R-est individuals within their minimal predication domain. Therefore, A identifies different sets in his two statements in (119). This is also the reason why (120) with two separate minimal predications is infelicitous (irrespective of Ben’s and Paul’s actual heights). The first conjunct identifies Ben as the only member of the set, while the second conjunct identifies Paul as its single member.²⁰

Other uses of the superlative do not make the relevant set explicit. This is typical for the superlative in referential position (see Herdan 2008 for a general discussion). For instance, (121) does not identify the relevant family members directly; however, contextual needs guide the partition. If there are three rows, the cutoff should be such that roughly one-third of the people in the context-set belong to the unique group of the tallest family members. A speaker can also be precise about the cardinality of the relevant group and thereby guide the determination of the cutoff that is relevant for the partition; see (122), which could be used in a scenario with six apples that are all small, but distinguishable in size.

It now nearly goes without saying that mit_free plus superlative involves facets of both direct predications and referential uses. While it is made explicit that the subject argument belongs to the unique set of R-est individuals, the alternatives are not made explicit, which is why the relevant unique set is not clearly identified. Crucially, however, this is exactly as expected, given the usual semantics of mit_free in terms of implicit co-participants.

Based on this overview, I propose the meaning representation in (123) for the superlative; (124) defines the crucial context-sensitive function f_sup. The proposal resorts to tropes instead of degrees because this makes it consistent with the above analyses of the positive and the comparative.²¹

This proposal direcly implements the idea that the superlative effectuates the partition of a context-set according to some appropriate cutoff, namely, an appropriate subtype of the trope type under discussion. It comes along with two crucial traits. For one, it is compatible with run-of-the-mill distribution; for instance, a standard direct plural predication receives the truth conditions in (125): Ben’s height must exceed or equal the cutoff f_sup(height′), and Paul’s height must exceed or equal this cutoff.

This simple distribution is feasible because the value of the relevant cutoff is independent of the distribution, but dependent on the minimal predication domain as a whole. Therefore, the cutoff must be such that Ben’s height and Paul’s height comply with it (Ben and Paul are in C_pred), whereas the heights of all others do not comply with it (all others are in C_contrast).

The second crucial trait is that the superlative does not contribute a trope predication, but a state predication with the relevant trope arguments being closed and thus having narrow scope. This is conceptually sound: the superlative does not assign a certain particularized property; instead, it affects the question of whether an existing particularized property licenses the membership of its bearer to the unique group of individuals that comply with a certain cutoff.

Both traits facilitate a straightforward combination of the semantics of the superlative with the semantics of mit_free; see (126). (127) provides the corresponding final representation for the initial example.

In prose: (127) is true iff the state of Ben bearing a height that exceeds or equals a context-sensitive cutoff for heights accompanies the state of someone else’s bearing a height that exceeds or equals this cutoff. This is as desired. The accompaniment does not relate tropes, but states of being bearers of certain tropes, which is ontologically well-formed. Furthermore, given that the minimal predication domain involves both the explicit individual in subject position and the implicit individuals as introduced by the modifying mit_free, the cutoff must be such that Ben’s height and at least someone else’s height comply with it (Ben and the implicit bearers are in C_pred), whereas all others do not comply with it (all others are in C_contrast). As expected, there is thus only partial explicit knowledge of who belongs to the unique set of the tallest individuals in the context. Therefore, and similarly to the situation with referential plural superlatives, contextual needs control the specification of the cutoff: it must be such that a reasonable partition of the context-set emerges.

Finally, I would like to mention one further welcome prediction. For the given analysis of mit_free plus superlative, it is crucial that mit_free interacts with a level of representation that is about the context-sensitive partition of individuals. However, there are also uses of the superlative that are not about this partition, but about the assignment of high-ranking particularized properties. This ‘elative’ interpretation comes along with the absence of the definite determiner, as in (128a). As expected, mit_free is incompatible with this interpretation of the superlative, as shown by (128b).