This means that at some time i in the past relative to i0, John caused at an immediately preceding index i that at i an entity is created that is an outfit at i, such that the things the outfit consists of are part of the two shirts and two pairs of pants referred to by *this*. We are not interested in a fine-grade analysis of causality here—this would state that there is some action on John's part at or before i such that without that action the result, here that u exists, would not have been achieved (cf. Lewis 1973, based on the analysis of causality by David Hume). Also, we will not go into the CONST relation for now, but note here that it must allow for a newly created outfit to consist of parts that existed already before. Finally, it should be noted that we often understand (10) in a way that the person that wears the outfit at i is the agent, John, himself—but this need not be the case, e.g. if John is a fashion designer.

It is obvious that when s1, s2, p1, p2 are the only articles of clothing, and any combination of a shirt and a pair of pants satisfies the dress code requirements for an outfit, the four combinations s1 p1, s1 p2, s2 p1, s2 p2 are the only acceptable ones that can be used to create outfits. And as the same article of clothing cannot serve as part of two different outfits at the same index, sentence (11) cannot be true at any particular index i0.

(11) ⟦ ⟧(i 0) = ∃ i[i<i0 ∧ [#( λu[⟦ ⟧(i)(u) ∧ ∃i′[ i′∠i ∧ ¬EXIST(i′)(u) ∧ [John causes in i : [EXIST(i)(u)] u [u CONST(i)(u) u s1 s2 p1 p2]]]) 4] *outfits John made four outfits with this*

This is because (11) requires that four outfits exist at time i. We might think that the modality of the original example (2) helps. However, this is not the case. Consider the following simple interpretation of possibility:

(12) *it is possible* = i p i R(i )[p(i)]

First, the modal may have wide scope with respect to the DP, resulting in the following interpretation at an index i0.

(13) ⟦[ ] [[ ]i [ i ]]⟧(i 0) = λi[⟦ ⟧(i)(λi′[⟦ ⟧(i′)(⟦ ⟧(i′))])](i0) = ∃i∈R(i0)[#( λu[⟦ ⟧(i)(u) ∧ ∃i′[i′∠i ∧ ¬EXIST(i′)(u) ∧ u [u causes in i : [EXIST(i)(u) ] u [u CONST(i)(u) u s1 s2 p1 p2]]]]) 4] *outfit four outfits it is possible four outfits it is possible to make* t *with this to make with this*

This states that there is some index i accessible from i0 such that the cardinality of outfits made with the two shirts and two pairs of pants at i is at least four. Clearly, this is not the intended reading: The sentence does not refer to a possible index in which, for example, a seamstress undoes the two shirts and two pants and makes four shirts and four pants out of them, thus creating four outfits in that world.

Second, the DP might have wide scope with respect to the modal. This results in the following interpretation:

$$\begin{aligned} \text{(14) } & \text{ [[four outfits]} \text{(i is possible [to make \text{ i } with this])]} \text{(i)} \\ &= \lambda \text{i)} [\text{[four outfits]} \text{(i)} (\lambda \text{u} [\text{[i is possible}] \text{(i)} (\lambda \text{i'} [\text{[i to make } with this] (i') (\text{u} [\text{i}])])]} \text{(i\_0)} \\ &= \# (\lambda \text{u} [\text{[fourfit} \text{(i)} (\text{u}) \land \exists i \in \text{R} (\text{i}\_0) \land \exists i' [\text{i'} \angle \text{i} \land \neg \text{EXIST} (\text{i'} (\text{u}) \land \\ & \qquad \exists \text{u} \text{''} [\text{u}'' \text{ causes in i'} \text{:} [\text{EXIST} (\text{i}) (\text{u})] \land \\ & \qquad \forall \text{u} \text{'''} [\text{u}''' \text{€} \text{CONST} (\text{i}) (\text{u}) \to \text{u} \text{'''} \equiv \text{s}\_1 \sqcup \text{s}\_2 \sqcup \text{p}\_1 \sqcup \text{p}\_2 \text{]}])) ) \succeq 4 \end{aligned}$$

This result is even worse because it states that there exist four outfits made with the two shirts and two pairs of pants at the index of interpretation i0 itself.

# **3 An Individual Concept Analysis**

What went wrong? The problem is with the analysis of outfits as simple entities, type e. The representations in (11), (13) and (14) force us to assume that there are four outfits made of the two shirts and two pairs of pants at the same time. The solution I would like to propose is that outfits and their ilk are rather individual concepts, that is, functions from indices to entities, type se. Such functions may be partial, that is, they need not be defined for a particular index. In this case we say that the individual concept does not "exist" at that index, in the sense that it does not have a value. But it exists as a concept, as a function from indices to entities, and this concept may have properties, like being an outfit.

Individual concepts were used by Gupta (1980) to model the meaning of sentences like *National Airlines served two million passengers in 1975.* Gupta pointed out that this does not entail that National Airlines served two million persons, as one and the same person can perform the role of a passenger multiple times. Gupta's solution which analyzes passengers as individual concepts defined only for the time of a person's flight—is problematic, as we find the same interpretation for sentences like *National Airlines served two million persons in 1975*, and persons, unlike passengers, are not individuated by flights (cf. Krifka 1990). But individual concepts appear to be well-suited for configurations.

To illustrate the individual concept analysis, take the four outfits one can make with the two shirts s1, s2 and the two pairs of pants p1, p2. I make use of the notation introduced in Heim and Kratzer (1998) according to which an expression of the form λv. Restriction[v]. [Value[v]] denotes the (possibly partial) function from entities of the type of v that is only defined for arguments for which Restriction[v] holds; if defined, the function gives as value whatever is specified in Value[v].

(15) o1 = λi. s1 and p1 dress a person following cultural norms in i. [s1⊔p1] o2 = λi. s1 and p2 dress a person following cultural norms in i. [s1⊔p2] o3 = i. s2 and p1 dress a person following cultural norms in i. [s2 p1] o4 = i. s2 and p2 dress a person following cultural norms in i. [s2 p2]

For example, o1 is an individual concept that is only defined for indices i if the entities s1 and p1 dress a person following the dress code in i; if defined, o1 maps to the sum entity consisting of the entities s1 and p1. As one piece of clothing cannot be part of two outfits at any given index, the outfit concepts o1, o2 and o3 have non-overlapping domains and cannot exist at the same indices; only the outfits o1 and o4 (and the outfits o2 and o3) can co-exist, as they consist of non-overlapping parts.

It is clear what it means that an individual concept x exists at an index: It exists precisely at the indices in its domain. That is, if x is an individual concept, type se, and EXIST is a predicate of individual concepts, type s(se)t, then we have EXIST(i)(x) = 1 iff i∈DOM(x). For example, the concept o1 exists for all indices i for which o1(i) is defined, that is, for which s1 p1 dresses a person following cultural norms in i. This means that o1 does not exist for all indices i at which s1 p1 does not dress a person, or else s1 p1 dresses a person but the cultural norms are so different that this does not follow the dress code. Consequently, the outfit o1 probably is of a rather punctuated or spotty nature: It may exist on May 1, then again on July 22, and on September 7, the times when o1 is actually used to dress a person, but not in the times in between.

Gupta analyzed common nouns as properties of individual concepts, type s(se)t, and we will follow him in this respect. The common noun *outfit* applies to individual concepts like o1 in (15), and not to simple entities. I first give the extension of this common noun meaning at an index i0 in the set notation; it is of type (se)t.

	- = { i. u consists of articles of clothing worn by a person in i, where the articles and their arrangement in i satisfy the accepted dress code in i0 . [u] | u De}

This is the set of all functions from indices i to entities u in the universe De whose parts are worn by a person in i and form an acceptable dress according to the standards of i0. The condition about the parts of u are expressed by way of a restriction of this function. This accounts for the fact that there might be indices at which we do not consider the arrangement of a striped shirt and a checkered pair of pants a suitable outfit.

We can describe the intension of *outfit* as follows, in a first approximation:

(17) ⟦ ⟧ = λi′λx ∀i∈DEF(x)[x(i) consists of articles of clothing worn by a person in i, where the articles and their arrangement in i satisfy the accepted dress code in i ] *outfit*

Notice that it might happen that at a given index i0, all the individual concepts in *outfit*(i0) are such that they are not defined for i0, because none of them is worn in an acceptable way. Nevertheless, *outfit*(i0) is not empty in this case. To give a concrete example, assume a set of seven indices i0,…i6, and assume that the four outfits mentioned in (15) are the following functions:

$$\begin{array}{llllllll} \text{(18)} & \mathbf{o}\_{1} = [\mathbf{i}\_{1} \multimap \mathbf{s}\_{1} \sqcup \mathbf{p}\_{1}, \mathbf{i}\_{2} \multimap \mathbf{s}\_{1} \sqcup \mathbf{p}\_{1}] & \text{indices:} & \mathbf{i}\_{0} & \mathbf{i}\_{1} & \mathbf{i}\_{2} & \mathbf{i}\_{3} & \mathbf{i}\_{4} & \mathbf{i}\_{5} & \mathbf{i}\_{6} \\ & \mathbf{o}\_{2} = [\mathbf{i}\_{4} \multimap \mathbf{s}\_{1} \sqcup \mathbf{p}\_{2}, \mathbf{i}\_{3} \multimap \mathbf{s}\_{1} \sqcup \mathbf{p}\_{2}] & \text{outputs:} & \mathbf{o}\_{1} & \mathbf{o}\_{1} & \mathbf{o}\_{2} & \mathbf{o}\_{2} \\ & \mathbf{o}\_{3} = [\mathbf{i}\_{5} \multimap \mathbf{s}\_{2} \sqcup \mathbf{p}\_{1}, \mathbf{i}\_{6} \multimap \mathbf{s}\_{2} \sqcup \mathbf{p}\_{1}] & & \mathbf{o}\_{4} & \mathbf{o}\_{4} & \mathbf{o}\_{3} & \mathbf{o}\_{3} \\ & \mathbf{o}\_{4} = [\mathbf{i}\_{2} \multimap \mathbf{s}\_{2} \sqcup \mathbf{p}\_{2}, \mathbf{i}\_{3} \multimap \mathbf{s}\_{2} \sqcup \mathbf{p}\_{2}] & & & & \end{array}$$

Notice that o1 and o4 both are realized at i2, and o2 and o3 both are realized at i5, but that o1 and o3 as well as o3 and o4 do not co-exist. At i0 no outfit is realized at all. But the noun *outfit* denotes for all indices, including i0, the set of all these individual concepts, if what qualifies as outfit is the same for all indices. The meaning of *outfit* is a constant property.

(19) *outfit* = i {i0, ... i6} x[x {o1, o2,o3,o4}]

The meaning in (17) is not restrictive enough. In a situation like (18) it does not prevent us from calling, say, the function [i1 → s1 p1] an outfit as well that is distinct from o1, as it is only defined for the index i1. Clearly, outfits are maximal with respect to indices, in the sense that for every index i at wich s1 p1 is worn by a person, satisfying the dress code, this index belongs to the domain of the individual concept. Furthermore, in a situation like (18) we could not count an individual concept like [i1 → s1 p1, i4 → s1 p2] as an outfit, because it maps its indices to different articles of clothing. This violates the identity criteria that we normally assume for individual concepts, that they consist of the same entities, or the same substance.11 A spelled-out version of (17) that includes these general conditions for cognitively relevant individual concepts would read as in (20), where the second line guarantees substance identity, and the third line maximality.

(20) ⟦ ′ ⟧ same substance = λi′λx [(17) (i′)(x) ∧ i,i DEF(x)[(17) (i )(x) x(i)=x(i )] x [(17) (i )(x ) DOM(x ) DOM(x)]] maximality *outfit*

The semantic type of *outfit*, a property that refers to individual concepts, would have to work with the expressions *outfit* combines with. For example, the predicate *wear* would have the following interpretation, where the object concept x is reduced to the value of x at the index of interpretation.

(21) *wear* = i x u[u is wearing x(i) at i]

11This is no quite true, as incremental changes are sometimes possible, cf. e.g. the example of the ship of Theseus, whose planks are replaced one by one over time, or living creatures that undergo metabolism, or entities like waves that consist in an ever-changing configuration. In all such examples there must be additional criteria of identity beyond material constituency.

Non-extensional predicates like *rise* or *change* are not reducible in this way (cf. Montague 1973).12 This also applies to predicates of creation. The verb *make* states that an agent causes an individual concept to be realized at an index. For example, if John makes outfit o1 at index i then John causes that at i, o1 becomes defined. This presupposes that during the making of i, the individual concept o1 was not defined (one cannot be making something that exists already) and involves some action by the agent on the parts that o1 refers to, s1 p1, during the time before i. The essential parts of this is captured in the following interpretation.

This states that at i the individual concept x is not realized, but the agent u causes that it is realized at the immediately following index i, where x(i) consists of parts of u.

The DP *four outfits*is interpreted as follows in the Generalized Quantifier analysis, where P is a variable for properties of individual concepts, type s(se)t.

(23) [DP *four outfits o* ] = i P [#( x[ *utfit* (i)(x) P(i)(x)]) 4]

We now can give an appropriate interpretation to our example. It states that there are four outfit concepts such that there are accessible indices at which these outfits are made. Notice that the predication is understood as distributive: For each of these individual concepts, there is an accessible index at which it can be made.

(24) ⟦[ ] λt[ [ ]]⟧(i0) = λi[⟦ ⟧(i)(λx[⟦ ⟧(i)(λi′[⟦ ⟧(i′)(x)]))⟧](i 0) = ⟦ ⟧(i0)( λx[⟦ ⟧(i0)( λi′[⟦ ⟧(i′)(x)]) = #(λx[⟦ ⟧(i0)(x) ∧ ⟦ ⟧(i0)( λi′[⟦ ⟧(i′)(x)]) ≥ 4 = #(λx[x∈{o1, o2, o3, o4} ∧ i R(i0) u i [i i i DOM(x) [u causes in i :[i DOM(x)] x(i ) s1 s2 p1 p2,]]]) 4 *four outfits* t *four outfits four outfits it is possible to make with this to make with this to make with this it is possible it is possible it is possible to make with this outfits*

This is true iff for each of the four individual concepts x there is an index i accessible from i0 such that x is realized by someone at i , and x(i ) is part of the two shirts and two pants. It is crucial that this does not entail that there is an index at which all four individual concepts are realized simultaneously. In particular, (23) is compatible with a situation in which only two outfits can be realized at a time.

It should be pointed out that there is also a consistent interpretation for the following example, if the quantifier scopes over the past tense operator:

12The verb *change* can be used for outfits in its functional sense, as in *Mary changed her outfit*. Let us represent the functional reading OUTFIT-OF as λiλuιx[*outfit* (i)(x) ∧ u is wearing x(i) at i] (alternatively, we can start with a functional reading and derive the sortal reading, as in footnote 10). Then *Mary changes her outfit* is true at i iff there is an i shortly before i, and an i shortly after, such that OUTFIT-OF(i )(Mary) = OUTFIT-OF(i)(Mary).

$$\begin{array}{lcl} \text{(25)} & \text{[John made four outfits with this]} \text{(i)}\_{0} \\ & = & \text{[[}\text{four outfits] \land PASC[\\_John market with this]}\text{]} \text{(i)}\_{0} \\ & = & \# (\lambda \text{x} \{\text{x} \in \{\text{o}\_{1}, \text{o}\_{2}, \text{o}\_{3}, \text{o}\_{4}\} \land \\ & & \quad \exists \text{i}' [\text{i}' \land \text{i}\_{0} \land \exists \text{i}'' [\text{i}'' \land \text{i}' \land \neg \text{i}'' \text{EOM}(\text{x}) \land \\ & & \quad \text{[John cases in i}'' [\text{i}' \in \text{DOM}(\text{x})] \land \text{x} (\text{i}') \subseteq \text{s}\_{1} \land \text{s}\_{2} \bot \text{p}\_{1} \bot \text{p}\_{2}, \text{[}]]) \succeq 4 \end{array}$$

The sentence can be true at a given index, as the individual concepts may come into existence at different times; notice that the existential quantifier ∃i … has scope under the quantifier *four outfits.*

In this section I have proposed a semantic interpretation of sentences like (2) that stays close to the standard Generalized Quantifier analysis of sentences with numerically modified nouns like *four outfits*. The only substantial change is that the noun *outfit* does not refer to ordinary individuals, but to individual concepts. In the next section we will argue that the individual concept analysis should be generalized; it should apply to entities such as shirts and pairs of pants as well.

# **4 Generalizing the Individual Concept Analysis**

# *4.1 Is Everything an Individual Concept?*

There are good reasons to apply the individual concept analysis to other individuals than to just configurational individuals, like outfits. Take, for example, Ludwig Wittgenstein; he can be represented by an individual concept that maps all indices i at which Wittgenstein exists to Wittgenstein—in our world, these are all indices from April 26, 1889 to April 29, 1951. In contrast to the domains of configurations that fade in and out of existence, this is a convex set of indices: If i and i are indices of the same possible history that are in this set, and if i is an index of the same possible history that is temporally in-between i and i , then i is in this set as well.13 As another example, take role concepts like *the tallest woman*, or *the Pope*. In contrast to configurations, such concepts may refer to different entities for different indices. As a third example, take individual concepts like the denotation of *the gifted mathematician that John claims to be* (cf. Grosu and Krifka 2008). Such expressions denote individual concepts that refer to the same entity, but are restricted to those indices that are compatible with John's claims. The individual concept analysis also affords for analyses of concepts like a wave (of water), which has a convex set of indices but maps these indices to ever-changing water entities.

If regular individuals are also based on individual concepts, then this also should hold for pants and shirts. After all, they certainly are created, and destroyed. As

13The individual concept view opens a new way to deal with modified names, like *(the) young Mozart* (cf. Paul 1994), as a subconcept; the term refers to the same entity as *Mozart* but is only defined for those indices at which Mozart was young.

individual concepts, they differ from outfits insofar as they have a convex domain: Whenever it holds that i, i ∈DOM(x), then for all i that are temporally in between, i<i < i, it also holds that i∈DOM(x). But what, then, do individual concepts map their indices to? We might think of the substance or matter they consist of (this corresponds to the *h* homomorphism in Link (1983) that maps objects to matter). Hence, the shirt s1 would be also of type se, a function from indices to the matter the shirt consists of, provided that this matter forms a shirt at these indices. Moreover, for concrete objects like shirts we have to assume additional conditions, namely that the matter is more or less the same between indices, allowing for occasional small changes like replacing a button in the case of a shirt, or metabolic exchanges of matter in the case of living creatures.

The outfit o1 consisting of the shirt s1 and the pair of pants p1, which are analyzed as concrete object concepts themselves, can then be defined as follows:

(26) o1 = i. s1 and p1 dress a person following cultural norms in i. [s (i) p (i)] 1 1

That is, o1 maps every index i for which it is defined to the same stuff as the join of the stuff of s1 and p1 at i. In general, we would have the following interpretation of *outfit* as a property of individual concepts; an appropriate maximalization as in (20) would have to be added.

$$\text{(27)}\quad \text{[out:fit]} = \lambda \text{i '\'\'\' x} \\ \text{\textbullet \'i\'e} \text{DEF}(\mathbf{x}) \text{[x consists of articles of obtaining won by a person } i \text{]} \\ \text{\textbullet \'i\', where the articles and their arrangement in i \'i\'} \\ \text{\textbullet \'is\'i\'y the accepted dress code in i\'i\']}$$

The only difference to (17) is that x, not x(i), is required to consist of articles of clothing. That is, for each outfit x there must be articles of clothing x1, x2,…xn such that x = x1 x2 … xn. The material join operation for individual concepts is defined as follows:

(28) x y = i[x(i) y(i)]

This is an individual concept that is defined for all indices for which x and y are defined, and maps these indices to the sum of x and y. This leads to the following definition, where P is the join of all individuals in the set P.

$$\begin{array}{rcl} (29) \ \ [outfit] = \lambda \text{i} \ ' \lambda \text{x} \exists \text{P} \forall \text{i} \in \text{DEF}(\text{x}) [\forall \text{y} \in \text{P}] \text{y} \ \text{is an article of coloring in } \text{i} \text{ } ' ]\\ \qquad \land \text{ x} = \bot \text{P} \\ \qquad \qquad \land \text{ } \exists \text{z} [\text{person}(\text{i})(\text{z}) \land \text{dressed} \cdot \text{with(i)}(\text{z})(\text{x}) \ \text{x} \ \land \text{satisfies -d} \text{result}(\text{i} \text{ } ')(\text{z})(\text{x})] \ . \end{array}$$

This says that whenever x is an outfit, then it applies to the same matter as the sum of some set P of articles of clothing. The sum of the matter of these articles of clothing is the same as the matter of the outfit, but the articles of clothing may be defined for a larger, and typically convex, domain. Even though (28) does not require this literally, we can think of each outfit x being associated with a unique set of articles of clothing P.

# *4.2 Coercion to Constituting Parts*

Commenting on an earlier version of this article, Sebastian Löbner suggested an analysis in which entities like outfits are regular entities, type e, instead of individual concepts. The idea is that any combination of entities that can form an outfit is in the extension of *outfit*; in our example, these are the entities s1 p1, s1 p2, s2 p1, s2 p2. This suggests the following interpretation, where outfits are of type e:

(30) (i0 0 ) = u i R(i )[u is worn by a person in i in a way that satisfies the dress codes in i] *outfit*

Note that under this analysis *outfit* still has an intensional component (an entity s p of type e is an outfit iff in some possible world i, a person wears i, and this satisfies the dress code in i). But the intensionality is not hard-wired in the notion of objects itself, which remain of type e. They are not lifted to individual concepts, se.

A problem of this analysis is that it does not motivate the use of creation verbs like *make, bauen* 'build' and *create* in examples (2)—(5). If the outfit o1 is identical to the sum of entities s1 p1, what does it mean to *make an outfit*? It would perhaps refer to the tailor's sewing of the shirt and the pair of pants, but not to the person that combines this shirt and this pair of pants to wear them together, as suggested in example (2). For this reason, the individual concept analysis, even though it is more complex, appears appropriate.

On the other hand, the interpretation (29) would allow for a straightforward analysis of examples like (30) that are problematic for the interpretations in (17) or (26).

(31) There is an outfit in the wardrobe.

When we understand outfits as entities that are defined only when someone wears them, then (30) could not be true, except in the peculiar case of a person sitting in the wardrobe and wearing an outfit.

I assume that individual concepts with spotted realizations like outfits can be coerced into individual concepts with a more permanent interpretation, and it is these coerced concepts that are involved in sentences like (30). If (30) refers to o1, which consists of the concrete individual concepts s1 and p1, then o1 can be coerced into the individual concept s1 p1 as defined in (27). Let us call this coercion "grounding". Then (30) states that this sum concept is in the wardrobe.

Grounding in general can be interpreted as the following function:

(32) Grounding (coercion to parts) For any individual concept x, if there are cognitively salient individual concepts x1, … xn 1 (i) …xn(i)] , then g(x) = x1 such that i DOM(x)[x(i) = x … xn

Let us assume that s1 and p1, a shirt and a pair of pants, are modeled by individual concepts as suggested in example (25). The outfit o1 would have the following grounded version:

(33) g(o1 11 ) = i[s (i) p (i)]

This is the individual concept that has the same domain as o1 and always refers to the sum of the shirt s1 and the pants p1. As s1 and p1 have convex domains, so has g(o1), the grounded version of x1. In particular g(o1) does also exist at indices i at which no-one is wearing s1 and p1 as an outfit; in our small model (18), g(o1) exists at all indices from i0 to i6. Consequently, g(o1) can have the property of being in the wardrobe at an index like i0 at which o1 does not have any realizations.

It should be noted that, as g is a function, g(x) presupposes that there is a unique cognitively most salient way to analyze x as consisting of concrete objects x1, … xn. These are the elements in the set P in (28). For an outfit, these are the articles of clothing, but not their parts, like the buttons, buckles and the pieces of cloth that they consist of. As they may have existed before the shirt, and may exist after, their sum may lead to an individual concept with a longer duration. If a unique decomposition could not be guaranteed, we would have to model g not as a function, but as a relation that maps x to different decompositions.

When predicates like *be in the wardrobe* are applied to individual concepts, then we can assume coercion by the grounding operation triggered by the meaning of the predicate. This is because such predicates can be reduced to the matter that an individual concept realizes at an index, which requires coercion to a more permanent entity14:

(34) ⟦ ⟧(i )0 0 0 = x[ (i )(x) (i )(g(x))] = x[ (i )(x) g(x)(i ) is in the wardrobe at i ] 0 0 0 *outfit outfit an outfit is in the wardrobe in the wardrobe*

This is true at i0 iff x is an outfit, as before, and the things x consists of—the shirt s1 and the pair of pants p1—are in the wardrobe.

Grounded individual concepts can also explain the use of creation verbs to refer to the entities an individual concept consist of, as in *the tailor made an outfit*. In this case, the object is coerced to its grounded interpretation, due to the knowledge of what tailors typically create.

14This reduction from individual concepts to stages is similar to the reduction from individuals to stages for stage-level predicates in Carlson (1977).

# *4.3 Joining and Counting Individual Concepts*

Grounded individual concepts can be counted, as the examples (34) and (35) show.

Obviously, the regular individual concept analysis of *outfit* in (17) does not work, as outfits are not worn by anyone when they are in the wardrobe or when they are ordered. But the entity analysis (29) and the grounded individual concept analysis (31) also are problematic. They would make our examples true in case 10 shirts and 10 pants that can be randomly combined to outfits are in the wardrobe, or are ordered, because they can be configured to 100 outfits. This is illustrated for the grounded individual concept analysis in (37).

(37) #{x | (i )(x) & (i )(g(x))} = 100 if g(x) = i[s(i) p(i)], s {s 0 0 1 10 1 10 ,…s }, p {p ,…p }, and both conjuncts are true *outfit in the wardrobe*

The problem here is that configurational individual concepts like outfits defy the usual property of additivity under the current interpretation. Additivity would tell us that if x is one outfit, and y is another outfit, then x and y together are two outfits. However, as we have seen, we might end up with four outfits. This is because outfits, other than ordinary individuals like shirts and pants, can overlap. The generalized quantifier strategy of representing numbers inherent in (36) cannot rule out such counting of overlapping objects. A theory that fares better is the one proposed in Krifka (1995), according to which count nouns are measure functions that can be applied to sum entities, and specify the number of the things they are applied to. We need something like count noun variants of nominal predicates (marked here by \*) that map individual concepts to numbers, and that follow the rule of additivity:

(38) a. ⟦ \*⟧(i)(x) = 1 if x consists of one outfit, i.e. ⟦ ⟧(i)(x) b. \* \* (i)(x) = n \* (i)(x ) = n x, x do not overlap at i (i)(x x ) = n+n *outfit outfit outfit outfit outfit*

Here, x ⊕ x stands for the sum of the individual concepts x and x . Notice that (37)(a) and (b) happen to be the same standardization and generalization operations proposed in Krifka (1990) for event-related quantification. Arguably, they belong to the general conceptual tool kit for constructing measure functions in language.

But what does the sum of two individual concepts actually mean? This would need detailed elaboration; I can give here just the basic construction steps. We have to assume that the domain of individual concepts, type se, has a sum structure. Let AIC the set of all atomic individual concepts; this is the set of individual concepts as considered so far. The set of sum individual concepts SIC then is defined as the smallest set such that (a) AIC ⊆ SIC, and whenever x, x ∈ SIC, then also x ⊕ x ∈ SIC. Here, ⊕ is a join operation that is idempotent, commutative, and associative. We understand it in such a way that the resulting set SIC is homomorphic to the power set of all individual concepts, with atomic individual concepts x represented by singletons, {x}, and sum individual concepts like x ⊕ x represented by set union, {x} ∪ {x } = {x, x }.

Sum individual concepts are still functions from indices to entities. In particular, a sum individual concept maps an index to the sum of the parts when they are defined for that index. That is, we require that [x ⊕ x ](i) = x(i) x (i), if x and x are defined for i; [x ⊕ x ](i) = x(i), if only x is defined for i, and [x ⊕ x ](i) = x (i), if only x is defined for i. Notice that different sum individual concepts can have the same functional value. For example, take w to be the Wittgenstein individual concept from 1889 to 1951, wy the individual concept of the younger Wittgenstein defined from 1889 to 1921, and wo the concept of the older Wittgenstein defined from 1922 to 1951, then w and wy ⊕ wo are different sum individuals, but have the same value.

For (37) we still have to define what it means that two individual concepts x, x overlap at an index i; this is the case if there is an entity that is a part of g(x) at i and a part of g(x ) at i, that is, if there is an u such that u g(x)(i) and u g(x )(i).

The truth conditions of an example like (34), here simplified, can be rendered as follows:

(39) (i ) = x[ \* 0 0 *outfit i* (i)(x) = 2 *n the wardrobe* (i )(g(x))] *there are two outfits in the wardrobe*

The sentence is intuitively true under our assumption that the outfit o1 made of s1 and p1 and the outfit o4 made of s2 and p2 are in the wardrobe. According to (37)(a), it holds that *outfit*\*(i0)(o1) = 1 and *outfit\**(i0)(o4) = 1, and as o1 and o2 do not overlap, we have *outfit*\*(i0)(o1 ⊕ o2) = 2. Even if the outfit o2, made of s1 and p2, and outfit o3, made of s2 and p1, are also in the wardrobe, they could not be counted because they overlap with o1 and o4. We of course could also sum up o2 and o3 instead, which would yield the same result.

It appears that sentences like *There are four outfits in the wardrobe* are felt to be ambiguous by some speakers, and can be considered true in one reading in which there are only two shirts and two pants in the wardrobe. This second reading can be generated by another construction of measure functions that differs from (37) by requiring that in the additivity clause, it is sufficient that x = x , that is, x and x may in fact overlap. Such weakened cases of additivity that allow for overlap are also relevant in cases like counting craters on the moon.

# *4.4 Collective and Cumulative Interpretations*

Having sum individual concepts also enables the interpretation of collective interpretations as in the following case:

(40) Two (of the) outfits are rather similar to each other.

This is a predication on a sum individual concept, which is true iff the atomic parts stay in a similarity relation to each other (the strong interpretation of reciprocals; for weaker interpretations see Dalrymple et al. (1998) and subsequent literature on the "strongest meaning hypothesis"). Here, ≤ a is the atomic part relation on sum individual concepts.

$$\begin{array}{ll}(41) & \exists \mathbf{x} [[\![outuff\!]\mathbf{x}\mathbf{\color{red}{l}\mathbf{(x}\mathbf{\color{red}{l})(x)} = 2 \land \forall \mathbf{x'}\forall \mathbf{x''}\mathbf{\color{red}{l}\mathbf{x'}\mathbf{\color{red}{l}x'}\mathbf{\color{red}{l}x'} \leq\_{\mathbf{a}} \land \mathbf{x''} \neq \mathbf{x''}]\\ & \rightarrow [\![simillar\;](\mathbf{\color{red}{l}\mathbf{(i\_{0})(x',\mathbf{x''})}\mathbf{\color{red}{l}})\mathbf{\color{red}{l}\mathbf{(})\end{array}]\end{array}$$

The interpretation of expressions like *two outfits* proposed here is also possible for the non-collective examples we started out with, provided that we assume that verbal predicates, when applied to sets of individual concepts, distribute over their elements. Instead of (23) we can entertain the following analysis:

$$\begin{array}{c} \text{(42)} \quad \text{[[} \text{it is is possible to make four outfits with this]} \text{](i)}\\ \Rightarrow \exists \text{x} \text{[ [} \text{out} \text{ft}^\* \text{](i)} \text{(x)} = 4 \land \text{x} = \text{s}\_1 \oplus \text{s}\_2 \oplus \text{p}\_1 \oplus \text{p}\_2 \land \\ \forall \text{x}' \text{[x}' \leq\_{\text{a}} \text{x} \rightarrow \exists \text{i}' \in \text{R}(\text{i}\_0) \; \exists \text{y} \exists \text{i}'' [\text{i}'' \land \text{i}' \land \neg \text{i}'' \in \text{DOM}(\text{x}') \land \\ \qquad \qquad \qquad \text{[y caues in } \text{i}'' \text{[} \text{i}' \in \text{DOM}(\text{x}) \text{]]]) \end{array}$$

This states that there are four outfits x that consist of the two shirts and two pants, and that it is possible for each atomic part x of x that some agent y brings it about to be realized.

Sum individual concepts are also relevant for cumulative interpretations (Scha 1981). Assume that a kindergarten owns a construction set with which all kinds of vehicles can be constructed, but only one at a time (there are only four wheels in the construction set).

(43) Dozens of children have built hundreds of vehicles with this construction set.

Such interpretations have been explained as a consequence of the cumulativity of verbal predicates (cf. Krifka 1989; Sternefeld 1998). That is, transitive predicates like *build* are interpreted such that if x builds y and x builds y , then x ⊕ x builds y ⊕ y . This interpretation is triggered by Sternefeld's operator \*\*, here adapted as in (43), where R stands for the verbal predicate, type s(se)(se)t, and ≤ is the part relation for sum individual concepts.

$$(44) \quad \forall \mathbf{x} \mathbf{R} = \lambda \mathbf{i} \lambda \mathbf{x} \lambda \mathbf{y} \\ \|\forall \mathbf{x'} \leq \mathbf{x} \exists \mathbf{y'} \leq \mathbf{y} [\mathbf{R}(\mathbf{i})(\mathbf{x'})(\mathbf{y'})] \\ \land \forall \mathbf{y'} \leq \mathbf{y} \exists \mathbf{x'} \leq \mathbf{x} [\mathbf{R}(\mathbf{i})(\mathbf{x})(\mathbf{y})] \\ \|$$

This allows for the following representation of (42) at an index i0, where " 24" and " 200" state that a number is in the range of dozens and hundreds, respectively.

(45) x y[ \* (i )(x) >>24 \* (i0)(y)>>200 \*\* (i )(y)(x)], where \*\* (i )(y)(x) = x x y y i i [i <i i i ¬ i DOM(x ) [y causes in i :[i DOM(x)] ´]]] y y x x[ i i [i <i i i ¬i DOM(x ) [y causes in i :[i DOM(x)] ´]]] *child vehicle built built*

This states that there is a sum individual concept x that are dozens of children and a sum individual concept y that are hundreds of vehicles, and that each part of the children built some part of the vehicles, and each part of the vehicles were built by some of the children. This renders the cumulative reading of (43) in an adequate way.

# **5 The Property Analysis**

In this paper I have argued for individual concepts in our conceptual representation, and in particular, for the ability to count individual concepts. There is a proposal on a related topic, "Counting Concepts" by Condoravdi et al. (2001), which analyzes examples like the following in a way that looks similar to what we have proposed for configurations.

(46) The mayor prevented three strikes.

*Prevent* is analyzed as an intensional predicate, like *seek*, which Condoravdi et al. (2001) interpret, following Zimmermann (1992), as having a property argument:

(47) (i0) = i<i 0 [ (i)( )( )] = i<i 0 [ (i)( i u[u is a strike in i ])(the mayor)] *The mayor prevented a strike prevent prevent strike the mayor*

This captures the reading in which no reference to a specific strike is intended. The object DP, *a strike*, denotes a property of entities.

There is also a specific reading: There was a threat for a strike that was about to form, and the mayor prevented that strike from happening. The normal solution for specific reading, giving the noun phrase wide scope (cf. (3)), does not work. It entails the existence of a strike u—but this is exactly what the next conjunct says was prevented.

```
(48) i<i0 u[ strike (i)(u) prevent (i)( i v[u=v])(the mayor)]
```
Condoravdi et al. propose a solution for the specific interpretation using "subconcepts" (that is, subproperties). No strict definition is given, but we certainly should assume that a superconcept applies to all indices and individuals a subconcept applies to. The specific reading of*the mayor prevented a strike* can be given as follows, where ⊆sc is the subconcept relation.

(49) P [P sc *strike pre* i[i<i 0*vent* (i)(P)(m)]]

For the interpretation of *three strikes*, Condoravdi et al. (2001) discuss various options, settling on a generalized quantifier analysis:

$$\begin{aligned} & \text{(50) } \left[ \text{(the major represented three triples)} \right] (\text{i}\_0) \\ &= \# (\lambda \text{P} [\text{P} \\_ \square\_{\text{sc}} \left[ \text{right} \right] \land \exists \text{i} [\text{i} \land \text{i}\_0 \land \text{[ } \text{prev} \text{ent} \left] \left( \text{i} \right) (\text{P} ) (\text{the major}) \right]) \geq 3 \end{aligned}$$

But for this to work, the notion of subconcept must be properly restricted. One entity may fall under different subconcepts of *strike*, e.g. it might be a strike of the railroad workers and at the same time (as railroad workers are public workers) a strike of the public workers. Obviously, the subconcepts that we count should not be such that one is included in the other. Hence Condoravdi et al. propose to restrict counting to minimal subconcepts, that is, to "maximally specific instantiated concepts".

The use of minimal subconcepts suggests that we actually better work with individual concepts, because then we get minimality for free, as individual concepts can apply to maximally one entity. Hence it seems natural to propose the individual concept analysis to examples of this type as well. The natural reading of (45) is that what the mayor prevented was that three specific strike threats led each to a fullblown strike. In each world at which these strikes would have been realized, there would have been exactly one realization.

(51) (i0) = x[ \* (i 0)(x) = 3 x a x i <i0 [the mayor prevented x at i ]] *the mayor prevented three strikes strike*

This says that the three strikes consists of three individual concepts x that are strikes, and that for each x there exists an index i in the past of the actual time i0 such that the mayor prevented at i the strike x from happening. Where *prevent* denotes a rather involved concept; it means that the subject referent (here: the mayor) caused the object referent (here: x ) not to be realized, which means in turn that, if the mayor would not have acted then x would exist for all normal continuation of i .

But there is still an issue of identity to be considered: For example, assume that an announced strike is declared illegal, and the workers plan another strike with similar goals and methods to circumvent the court ruling, but this strike is declared illegal as well. In which sense can we say that two strikes were declared illegal? This depends on rather specific criteria. Formal semantics can only provide the general format of the objects of lexical semantics.

# **6 Conclusion**

In this paper I have discussed the meaning of sentences that contain reference to what I called "configurational" objects, as denoted by such terms as *outfit* or *tangram figure*, or even *crane* and *word*. Configurational objects consist of parts that can be reconfigured, and exist only at those indices in which they stand in the appropriate configuration. I have argued that configurational objects can fruitfully be analyzed as individual concepts, functions from indices to entities. I have developed ways how such concepts can be counted in count-noun constructions like *four outfits*. I then argued that more regular entities like shirts should also be represented by individual concepts, albeit with more stable temporal properties, and I have shown that there are contexts in which a configurational object like *outfit* can actually be coerced to the object it consists of.

The general direction of this paper points towards a theoretical framework in which the objects referred to in language, and consequently, the objects of our cognition, should be seen as individual concepts. The notion of an object contains the ability to identify the same object over different indices, and this is precisely achieved by individual concepts. Some objects are temporally convex in the sense that they have a continuous existence from an initial time to a final time (such as shirts and pants), others have a more spotted existence (such as outfits). There are various other examples of objects with apparently extraordinary identity criteria, such as waves. Whether this view is suitable, or even sustainable, cannot be answered in this short paper. At least I hope to have shown that it provides us with ways to give truth conditions to sentences that count configurational objects.

# **References**

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# **Structure and Ontology in Nonlocal Readings of Adjectives**

**Marcin Morzycki**

**Abstract** In certain uses, adjectives appear to make the semantic contribution normally associated with adverbs. These readings are often thought to be a peripheral phenomenon, restricted to one corner of the grammar and just a handful of lexical items. I'll argue that it's actually considerably more general than is often recognized, and that it admits two fundamentally different modes of explanation: in terms of the syntactic machinery that undergirds these structures and in terms of the ontology of the objects manipulated by its semantics. Both modes of explanation have been suggested for some of the puzzles in this domain, and I'll argue both are necessary. With respect to adjectives including *average* and *occasional*, the key insight is that their lexical semantics is fundamentally about kinds. But to arrive at a more general theory of adverbial readings, it is also necessary to further articulate the compositional semantics. In this spirit, I'll argue that these adjectives actually have the semantic type of quantificational determiners like *every*. If this way of thinking about adverbial readings is on the right track, it instantiates a means by which these two distinct modes of explanation—and the distinct aspects of cognition they may ultimately be associated with—both play a crucial role in bringing about the apparently aberrant behavior of this class of adjectives.

**Keywords** Adjectives · Nonlocal readings · Average · Occasional · Kinds · Natural language metaphysics

# **1 Introduction**

It is, of course, not news that the way language organizes the world may tell us something about how the mind does so. Nor is it news that that perhaps the best window into how language organizes the world is how language works: what words mean and how grammars manipulate those meanings. This is the project that Emmon Bach

M. Morzycki (B)

University of British Columbia, Vancouver, Canada e-mail<EMAIL_ADDRESS>
© The Author(s) 2021

S. Löbner et al. (eds.), *Concepts, Frames and Cascades in Semantics, Cognition and Ontology*, Language, Cognition, and Mind 7, https://doi.org/10.1007/978-3-030-50200-3\_4

memorably dubbed 'natural language metaphysics' (Bach 1986, 1989) or 'natural language ontology'. Importantly, it's a project that's worthwhile even if—perhaps especially if—it should fail to coincide with metaphysics proper, because our theory of natural language metaphysics is a repository of linguistic analysis. If we're doing it right, its structure explains the structure of language. The structure of the world is another matter entirely, best left to others.

There is an important trade-off in this domain, however, that I'd like to use to frame this paper. Structures in natural language ontology can serve to explain linguistic phenomena, and when they do, they may lighten the explanatory burden on other components of linguistic theory, including the syntax and semantics. Conversely, introducing complexity in the syntax or semantics can make possible a simpler ontology.

It may help to sketch an example of what I have in mind. It's entirely independent of the one I'll focus on primarily in this paper. It concerns polar antonyms of adjectives, such as*tall* and *short*. No one would defend the view that they are unrelated, of course, so only the question is where to install a theory of their difference. One possibility is ontological. Height is measured in abstract representations of measurement, *degrees*, which include things like '6 feet'. The set of degrees that measure height (as opposed to e.g. weight) tell us the dimension along which a given measurement exists, but they don't actually tell us whether we're measuring how tall someone is or how short. They tell us that the dimension is spatial extent, but not whether the scale is tallness or shortness. To know that, we must know at least one more thing: the ordering imposed on those degrees. '6 feet' is a greater degree of tallness than '5 feet', but a lesser degree of shortness. On such a theory, advocated in Kennedy (1997, 2001) and elsewhere, the key to the relation between *tall* and *short* is that they measure on scales that impose opposite orderings on degrees along the same dimension. Their denotations therefore need not reflect any direct connection between the adjectives beyond specifying which scale they use, because the connection is between the scales, not between adjectives themselves.

The alternative is to suppose that the relation between *tall* and *short* is a matter of grammar, not (primarily) ontology, and that they use precisely the same scale after all. One might suppose, with Heim (2006, 2008) and Büring (2007), that *short* involves a special kind of negation, present in the syntactic tree but not normally pronounced as a separate morpheme. *Short*, on this view, is actually a way of pronouncing 'little tall' or 'untall'. There are a variety of arguments to be made for this more complicated syntax, and with it in place, the ontology needn't provide an independent analysis of the connection between the two antonyms because the richer syntax already does.

It's not the case, of course, that any analysis of any arbitrary phenomenon can be said to be primarily grammatical or ontological. In the context of this volume, it's especially worth noting that an approach that involves decomposition into features might occupy an intermediate position with respect to this distinction: the decomposition is in some respects like decomposing *short* into 'little tall', but of course the decomposition needn't be implemented directly in the syntax in this way, and there are interesting discussions to be had about the relationship between decomposing word meanings and decomposing the underlying concepts themselves. The former seems still a robustly grammatical enterprise; the latter considerably more an ontological one.

All that said, at some point there's a danger of putting more weight on this distinction than it can bear. Its purpose here is chiefly just to situate another empirical puzzle for which a balance has to be struck between grammatical and ontological explanation: adjectives like *average*. The first thing to notice is the curious effect they often have on the referent of the nominal in which they occur:

### (1) The average American has 2.3 children.

This sentence, Carlson and Pelletier (2002) point out, is doubly mysterious. What sort of entity is 'the average American'? Certainly, on its most natural reading, it doesn't refer to some particular American who is especially typical of Americans. Second, what sort of entity is '2.3 children'? If *the average American* referred to a particular American—say, one named Steve—it would suggest, alarmingly, that Steve has only a fraction of one of his children. That's not what the sentence means, at least ordinarily. Nor, indeed, is it possible to straightforwardly disentangle the strangeness of the first nominal from the strangeness of the second. Even if we avoid the reading under which (1) involves direct reference to Steve, it still fails to communicate that it is typical for Americans to have fractional children.

On its face, it would seem that to avoid such morally outlandish outcomes, we must embrace a metaphysically outlandish one. We must accept that there are such things as 'average Americans' in the model underlying the semantics, and indeed perhaps in some extended sense such things as '2.3 children'. I don't think we should dismiss this possibility too readily. For one thing, as Bach would remind us, our judgment in these matters must be guided by language, not a priori notions about what sorts of objects populate the actual world. That's the difference between natural language metaphysics and metaphysics proper. Indeed, this metaphysical direction is precisely the one in which Carlson and Pelletier head. For this reason, Hornstein (1984) was ultimately mistaken in saying that 'no one wishes to claim that there are objects that are average men in any meaningful sense'. Yet, he argued, nominals like *the average American* act no different from more referentially pedestrian ones. He concluded that this was an argument against the enterprise of formal semantics itself.

My aim here will be more modest. Kennedy and Stanley (2009) observed that sentences such as (1) can be analyzed as a special case of a more general phenomenon: readings of adjectives in which the adjective is interpreted as though it were an adverbial. This requires a more complex syntax, but that more complex syntax is a low price to pay for the metaphysical benefit. It frees us from having to posit any spookily abstract and therefore implausible entities in the ontology. I'll argue, building on Morzycki (2016b), these adverbial readings are in fact part of a considerably more general pattern of readings available to a far wider range of adjectives than generally recognized. I'll argue that these readings actually fall into three classes, and that this leads us to an analysis distinct in important respects from Kennedy and Stanley but that, as they argued, places the explanatory burden on the syntax and compositional semantics rather than the ontology.

In Sect. 1, following largely the argument in Morzycki (2016b), I'll present the case that what I'll call nonlocal readings of adjectives (following Schwarz 2006 et seq.) are far more general than is typically recognized, and that they fall into three distinct classes. In Sect. 2, I'll review some ways these problems have been approached in the past, highlighting the interplay between grammatical and ontological explanation. In Sect. 3, I'll propose a strategy for approaching these facts that I hope may eventually scale up to the larger empirical picture and that has components of both kinds of explanation. In particular, I'll combine elements of syntactic assumptions that have widely been made with a new ingredient in the compositional semantics: the idea that adjectives with external readings have determiner-like meanings, and as a consequence have the complex grammar associated with determiners. I'll sketch this idea in general terms for *average* in particular, relating it to Gehrke and McNally (2010, 2015)'s crucial insight that adjectives like *occasional* involve reference to kinds. Finally, in Sect. 4, I'll very briefly return to the larger issues with which we began: the analytical balance between structure in the syntax and semantics and structure in the ontology.

# **2 Nonlocal Readings of Adjectives**

# *2.1 On 'Occasional'*

Let's begin with the classic example of a nonlocal reading of an adjective, which is *occasional* (Bolinger 1967; Stump 1981; Larson 1999; Zimmermann 2003; Schäfer 2007; Gehrke and McNally 2010, 2015; DeVries 2010). It's the best-studied such case, and this will serve as a useful background against which to consider *average*. The standard sentence is (2):

(2) An occasional sailor strolled by. a. internal: 'Someone who sails occasionally strolled by.' b. external: 'Occasionally, a sailor strolled by.'

It has what's called an internal and an external reading. The internal reading is interesting in a number of respects, but from our current perspective, it's the external reading that is most immediately relevant. On this reading, the adjective makes a semantic contribution that is, to all appearances, completely divorced from the nominal in which it finds itself. The sailors that strolled by are sailors simpliciter. There is no question about the frequency of their sailing. But the situation is more puzzling still. On the external reading, the sentence means more or less the same thing as (3), where the definite determiner replaces the indefinite:

(3) The occasional sailor strolled by.

Yet the meaning is essentially the same (but see Gehrke and McNally 2015 for detailed discussion). Indeed, some adjectives of this class (*odd* and *rare*) have the external reading *only* with *the*. 1 Setting apart a subtle change of flavor, the external reading also occurs with *your* and in the bare plural:

(4) a.

So there are three mysteries so far: an ambiguity, unexpectedly wide scope, and unexpected interpretations of the determiner.

There are more still. Another is that, on the external reading, the adjective must occupy the leftmost position in the structure of the nominal:

(5) The angry occasional sailor strolled by.

a. internal: 'Someone angry who sails occasionally strolled by.'

b. #external: 'Occasionally, an angry sailor strolled by.'

Indeed, the range of determiners with which *occasional* is possible on the external reading is relatively limited:

(6) ⎧ ⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎩ Every Some Several Many Most ⎫ ⎪⎪⎪⎪⎬ ⎪⎪⎪⎪⎭ occasional sailor(s) strolled by.

a. internal: '*D* person/people who sail(s) occasionally strolled by.'

b. #external: 'Occasionally, *D* sailor(s) strolled by.'

Yet another idiosyncrasy of the external reading is that it renders the adjective unable to coordinate with ordinary adjectives:

	- a. internal: 'Someone angry who sails occasionally strolled by.'
	- b. #external: 'Occasionally, an angry sailor strolled by.'

Another still: on this reading, the adjective becomes incompatible with degree words such as *very* or the comparative2:

1Berit Gehrke (p.c.) points out that this fact doesn't follow from what will be proposed here—but then, I don't really have an analysis to offer here of the *occasional* class more generally. That said, this fact is precisely what one might expect if, as Larson (1999) has argued, syntactic incorporation into a determiner gives rise to some lexical idiosyncrasy here. See Sect. 5 for more.

2For some speakers, even the internal reading is missing. Others can get an external reading marginally with *very*, but not with *more*.

# *2.2 Returning to 'Average'*

Having noted the crucial features of *occasional*, let's return to *average* with them in mind. First, there was ambiguity. As Carlson and Pelletier (2002), Kennedy and Stanley (2009) among others noted, there is an ambiguity with *average* too:

	- a. internal: 'An American, who is typical, has 2 children.'
	- b. external: 'On average, an American has 2 children.'

For the internal reading to be available without counterpragmatically ghastly background assumptions, we must change our earlier sentence to *2 children*. On this reading, the claim is that there is an American somewhere that is typical and that he has two children. There is another reading of *average* that also occurs in (11) (Sebastian Löbner, p.c.), which is also internal, or in any case fails to be external:

(11) He's so average.

The external reading is the one with which we are now familiar from *occasional*. It's worth noting that it paraphrases naturally with an adverbial, *on average*, which is analogous to how *occasional* morphed into *occasionally*.

Here we encounter a set of properties that elegantly mirror those of *occasional*. There are unexpected interpretations of the determiner. Switching to the definite determiner leaves us, on the external reading, with apparently the same interpretation, and *your* is not much different:

$$\begin{aligned} \text{(12)} \quad & \begin{cases} \text{The} \\ \text{Your} \end{cases} \begin{cases} \text{average American has 2 children.} \end{cases} \\ \text{a. INTERNAL.} \therefore \begin{cases} \text{The} \\ \text{Your} \end{cases} \begin{cases} \text{The} \\ \text{Menerican that's a typical one has 2 children.} \end{cases} \\ \text{b. EXTERNAL. 'On average, an American has 2 children.} \end{aligned}$$

Again, on the external reading, other determiners don't seem to work:

$$(13)\ \#\begin{cases} \text{Every} \\ \text{Most} \\ \text{Some} \\ \text{Several} \\ \text{Two} \end{cases} \text{average American} \\ \text{(s) has/have 2.3 children.}$$

And again, on the external reading *average* has to be leftmost among the adjectives in its nominal:

(15) #An irritable and average American has 2.3 children.

It is incompatible with degree modifiers on this reading:

(16) #A very average American has 2.3 children.

So, once again, the same mysterious patterns manifested themselves as with *occasional*. At a minimum, this supports the connection between the two that Kennedy and Stanley (2009) posited—perhaps indeed more robustly than they intended. But the pattern is more widespread still.

# *2.3 Wrong*

Before considering the bigger picture, it will be necessary to lay out a few more examples of the general phenomenon. A version of the now-familiar pattern emerges once again with *wrong* (Haïk 1985; Schmitt 2000; Schwarz 2006, 2019). It too has an internal/external ambiguity, though perceiving it is slightly trickier. Suppose Floyd is a spy who is required to provide his interlocutor with false information and deprive her of true information. If he succeeds in this, (17) is true on the internal reading, on which the information provided was incorrect:

	- a. internal: 'Floyd gave an answer that was incorrect.'
	- b. external: 'Floyd gave an answer that it was wrong of him to give.'

On the external reading, (17) is false, because Floyd answered as he is supposed to. On the other hand, if Floyd slips up at some point and accidentally answers a question truthfully, the situation is flipped: (17) is still true, but only on the external reading: he provided information that he isn't supposed to provide, namely, true information. Something similar happens in (18):

	- a. internal: 'Floyd killed a person that was wrong (perhaps prone to error or wrong in general).'
	- b. external: 'Floyd killed a person that it was wrong of him to kill.'

Again, the internal reading in (18) is more easily discerned with some context. Consider a dystopian game show in which participants are executed for answering a quiz question incorrectly. Floyd is the executioner. If he killed the contestant that answered incorrectly, (18a) is true only on the internal reading. ('Clyde was wrong, so I killed him,' he might explain.) If Floyd accidentally killed a contestant that provided the correct answer, (18b) would be true only on the external reading.

There is again an odd fact about the interpretation of the determiner: *the* is interpreted as an indefinite. In (17), there need not have been only one wrong answer, and in (18), there need not have been only one person who must not be killed. The picture is slightly different, though. *Your* is impossible here except on its usual possessive reading, irrelevant here:

(19) a. ?Floyd gave your wrong answer. b. ?Floyd killed your wrong person.

Strangely, it's not just that the definite determiner is interpreted as an indefinite, but it's the principal way to say this. The indefinite would be unusual on the external reading:

(20) a. Floyd gave a wrong answer. b. Floyd killed a wrong person.

It's not actually fully clear what reading these receive. For me, an external reading is possible, but only when there is a desire to communicate that there are multiple answers that shouldn't be given and people that shouldn't be killed.

Apart from that quirk, again we encounter restrictions on the choice of determiner on the external reading:

As before, inherently quantificational determiners fail.

The requirement that the nonlocal adjective be structurally higher than other adjectives again emerges:

(22) a. Floyd opened the wrong brown envelope. b. #Floyd opened the brown wrong envelope.

So does the ban on coordination:

(23) #Floyd opened the wrong and brown envelope.

And so does the ban on degree modification:

(24) #Floyd opened the very wrong envelope.

So a rather large class of adjectives that includes *wrong*, *average*, *typical*, *occasional* and a number of its synonyms seems to manifest quite a number of common properties.

# *2.4 'Whole' and 'Entire'*

The parallels continue with *whole* and *entire*, though there will be an important twist. As before, there is an ambiguity (Moltmann 1997, 2005; Morzycki 2002), which I'll assume is a special case of the internal/external ambiguity:

	- a. internal: 'A complete, structurally intact ship was submerged.'
	- b. external: 'A ship was wholly submerged.'
	- a. internal: 'The complete, structurally intact apple, the one with no bites taken out of it, is terrible.'
	- b. external: 'All parts of the apple are terrible.'

The internal reading is actually the unusual one in these cases, and may take a moment to perceive. It's what could be expressed more or less unambiguously with *complete*—indeed, I suspect that it's precisely the existence of this unambiguous alternative that accounts (on broadly Gricean grounds) for the unnaturalness of the internal reading.

As before, there are restrictions on the determiner, but they take a different form. First, *a*, *the*, and *your* retain their usual meanings, and don't become interchangeable. Second, strong quantifiers are still incompatible with the external reading, but weak ones are perfectly compatible with it (I will now indulge in the habit of marking sentences with a # when they are impossible on the external reading)3:

$$(27) \text{ a. } \begin{Bmatrix} \# \text{Every} \\ \# \text{Most} \\ \text{Many} \\ \text{Several} \\ \text{Two} \end{Bmatrix} \text{ whole ship(s)} \begin{Bmatrix} \text{was} & \\ \text{were} \end{Bmatrix} \text{ submerged}$$

3Sebastian Löbner (p.c.) points out that one might explain the ill-formed examples in (27) because one nominal can't express two different quantifications (Löbner 2000), which would accord with the grammaticality of adverbial *entirely* in e.g. *Every ship was entirely white*.

$$\text{b.}\begin{Bmatrix}\#\text{Every}\\ \#\text{Most}\\ \text{Many}\\ \text{Several}\\ \text{Two}\end{Bmatrix}\text{ whole apple(s)}\begin{Bmatrix}\text{is}\\ \text{are}\end{Bmatrix}\text{ terrible.}$$

The other, now increasingly familiar restrictions reemerge in their customary form. The external reading is only possible when the nonlocal adjective occurs high:

# *2.5 Epistemic Adjectives*

Abusch and Rooth (1997) observed a proposition-modifying interpretation of what they called 'epistemic adjectives' that now won't come as a shock. These adjectives include *unknown*, *undisclosed*, *unspecified*, and *unexpected*. They can receive a widescope reading:

	- b. external: 'Solange is staying at a hotel and it is not known which hotel she is staying at.'

The external reading systematically supports concealed-question paraphrases. For many years in the early 2000s, (32) was a kind of running joke in American political discourse, and it's actually very hard to make sense of its internal reading:

(32) Dick Cheney is hiding at an undisclosed location.

The external reading is that Dick Cheney is hiding at a location and it has not been disclosed, for his safety, what location that is. On its internal reading, perhaps it would have to be the very fact that it is a location that is not disclosed.

At this stage, we will encounter the same empirical refrain, and the reader can presumably sing along. On the external reading, there are again restrictions on the determiner. Although *the* and *a* seem to behave normally, strong inherently quantificational determiners remain impossible:

$$\begin{aligned} \text{(33)} \quad \text{Solange steady at} \begin{Bmatrix} \#\text{every} \\ \#\text{most} \\ \text{some} \\ \text{several} \\ \text{two} \end{Bmatrix} \text{unknown hot} \text{(s)}. \end{aligned} $$

As for *whole*, weak determiners are compatible with external readings.

The restrictions on the structural position of the adjective in the DP remain the same. The external reading is, as we have come to expect, possible only when the adjective is high4:

The external reading is unavailable when the adjective occurs in a coordinate structure:

(35) #Solange stayed at a horrible and unknown hotel. *(internal only)*

It's incompatible with degree modification:

(36) #Solange stayed at a very unknown hotel. *(internal only)*

# *2.6 Same and Different*

Other adjectives fall under broadly the same rubric. Among the best-studied of these are *same* and *different* (Nunberg 1984; Heim 1985; Carlson 1987; Keenan 1992; Moltmann 1992; Beck 2000; Lasersohn 2000; Majewski 2002; Alrenga 2006, 2007a, b; Barker 2007; Brasoveanu 2011). The facts in this domain are complicated in ways that muddy the waters considerably, and the terminology is different and confusing, but for our purposes the important point is that there is an ambiguity.

The main terminological confound is that the internal reading involves an anaphoric dependency on preceding discourse. This is in an important sense 'external', but it is not external in the *relevant* sense of seeming to require the adjective to access to the semantic content of the clause outside the nominal itself. This is clearer when considering the readings:

4Sebastian Löbner suggests a mode of explanation of this fact: the concealed question-style semantics reveals these nominals denote individual concepts, which is incompatible with the sort of run-of-the-mill extensional intersective adjectival modification attempted in (34) and (35). Perhaps that strategy could help with the quantificational facts in (33) as well.

	- a. internal (anaphoric): 'Floyd and Clyde read a book that is the same as the one previously mentioned.'
	- b. external: 'Floyd and Clyde read a book in common.'
	- a. internal (anaphoric): 'Floyd and Clyde read a book that is the different from the one previously mentioned.'
	- b. external: 'The book Floyd read was not the same book as the one Clyde read.'

I won't rehearse the full song-and-dance yet again, in part because it presents, in this instance, complications that go considerably beyond the scope of this paper. Suffice it to say that on the external reading, *same* and *different* impose restrictions on the determiner with which they combine:

$$(39)^{\*}\text{Folyd and Clyde read} \left\{ \begin{matrix} \text{every} \\ \text{most} \\ \text{some} \\ \text{several} \\ \text{two} \end{matrix} \right\} \text{same book(s)}.$$

On this reading *same* and *different* are subject to the now familiar structural position requirement:

(40) a. Floyd and Clyde read the same good book. b. \*Floyd and Clyde read the good same book.

# *2.7 Modal Superlatives: 'Possible' and Its Kin*

There is another important class of nonlocal readings of adjectives, which I will mostly set aside. These involve *possible*, *conceivable*, and the like ('modal superlatives'; Bolinger 1967; Larson 2000; Schwarz 2005; Cinque 2010; Romero 2013; Leffel 2014):

	- a. external: 'They interviewed every candidate that it was possible to interview.'
	- b. internal: 'They interviewed every person who was possibly a candidate.'

There are important distinctions between these cases and the ones we've examined so far, but for the moment I will note only the similarity: again, there is an ambiguity between an internal and external reading.

# *2.8 Miscellaneous Obscurities and Novelties*

Without further discussion, I'll note a few examples of nonlocal readings that are either obscure or, to my knowledge, novel:

One shouldn't read too much into these without careful examination, of course, but they collectively suggest that more external readings lurk just over our analytical horizon.

# **3 Three Classes of Nonlocal Readings**

This paper is not a linguistic curio cabinet. We've established, I hope, that there are patterns in this domain. That's not to say that there aren't genuine mysteries here. It's just that the phenomena at issue are mysterious *in parallel ways*. The next stage is to systematize the patterns more robustly so we can move toward an analysis.

There are, I will argue, three distinct classes of nonlocal adjectives. The first class I will set aside here. It includes the aforementioned 'modal superlatives' like *possible*. They differ from the others most strikingly in which determiners are involved in the external readings. In these cases, universal quantifiers license the external reading, not inhibit it:

$$(47)\quad\text{We interviewed}\begin{Bmatrix}\text{every}\\ \text{\#the}\\ \text{\#a}\\ \text{\#no}\\ \text{\#three}\end{Bmatrix}\text{ possible candidate.}$$

Superlatives and *only* also license it:

(48) We interviewed the only the best possible candidate.

Analyses for these cases can be framed around ellipsis, along the lines first proposed in Larson (2000), with structures like (49):

(49) We interviewed the best candidate possible for us to interview.

There is a satisfying account built from standard assumptions about superlatives in Romero (2013).

It will be the other two classes that will be of interest here. These are what I'll call the weak-quantifier class, which includes *whole* and *unknown* and which permits external readings with weak quantifiers, and what I'll call the no-quantifier class, which includes *occasional* and *average* and permits external readings only with nonquantificational determiners. Of course, describing various particular determiners as 'non-quantificational' is already a bit tendentious—though for the moment, I mean this only descriptively, in the sense of Heim (1982), Kamp (1981), and DRT more generally—so more needs to be said for explicitness.

It goes beyond the scope of this paper to advocate a particular theory of how determiner quantification works in general. All we require is some general conceptual machinery to characterize particular classes. I'll refer to *every* and *most* DPs as strong and inherently quantificational; definite descriptions and other DPs that arguably directly refer as strong but not inherently quantificational; and all others as weak.

Setting the ellipsis class aside, all nonlocal readings observe a generalization:

(50) Strong Quantifier Resistance Generalization Strong, inherently quantificational determiners (*every, most*) are incompatible with nonlocal readings.

This has been observed for specific lexical-semantic families of adjectives, but the important point is that it seems to be true of all of them.

As we've seen, a few nonlocal adjectives—*occasional*, *average*, and *wrong* are even more constrained in that they are incompatible with any determiner apart from (some combination of) *the*, *a*, bare plurals, and generic *your*. Stating it more officially:

(51) Broader Quantifier Resistance Generalization Some adjectives with nonlocal readings idiosyncratically resist all inherently quantificational determiners.

These generalizations are the crucial element in the taxonomy, so it may help to summarize things in a table:

(52)

Of course, the challenge now is to explain these generalizations. That's a tall order, inasmuch as it requires a synthesis of a vast array of adjectives and (collectively) a vast literature and set of analytical approaches. This won't happen in any single paper. Nevertheless, having framed the challenge in this way, we are in a better position to assess what an explanation might look like.

# **4 Some Background**

# *4.1 Incorporation*

First, we must dispense with a straw man. One might imagine that external readings of adjectives are brought about simply by moving the adjective from its base position to an adverbial position, where it is interpreted as an adverb. The idea is a natural one, and I'll argue that in a certain sense it's not entirely wrong—but formulated in this crude way, it's unenlightening. Why should this movement happen? Why would an adjective have an adverb meaning? How does this help us understand the interaction of the adjective with the determiner?

More enlightening alternatives are available. There are many analyses on the market of individual instances of the larger problem of nonlocal readings, but they aren't straightforwardly generalizable to the full range of facts. There is one idea, though, that constitutes an excellent starting point. It's Larson (1999)'s proposal (further developed in Zimmermann 2000, 2003) that, in the *occasional* construction, the adjective moves from its base position to incorporate into the determiner in a process of 'complex quantifier formation'5:

5I use 'incorporation' here following Larson and Zimmermann, in the generalized sense derived from Baker (1985) that is standard in the generative syntactic literature.

(53)

This movement creates a single quantificational determiner, *an+occasional*. It is then possible to provide this determiner with a denotation, listed in the lexicon just like that of any other. The advantage of that is that it's straightforward to capture various idiosyncrasies. If we need to stipulate that for *occasional* and *average*, the denotations of *the*, *a*, and *your* should be identical but for *wrong* they shouldn't be, we can reflect it directly. Indeed, we should *expect* such idiosyncrasies, inasmuch as the lexicon is, after all, a repository of the idiosyncratic.

What's less comfortable is that we have to stipulate not just that *an+occasional*, *the+occasional*, and *your+occasional* all have identical denotations, but also to make precisely the same stipulation independently for *a+sporadic*, *the+sporadic*, and *the+sporadic*—and indeed for other combinations of *a*, *the*, and *your* with adjectives of this class (though see Zimmermann 2003) for some inroads on this).6

Some analysis is necessary of why these readings fail to occur with determiners other than *a*, *the*, and *your*. On this approach, it would simply be to fail to stipulate any complex determiners that fail to have these as components. It would be essentially an accidental lexical gap, a mere accident of the development of language.

This approach provides helps in one way right off the bat. Quantificational determiners have access to the VP by perfectly ordinary means: Quantifier Raising (May 1977, 1985; Heim and Kratzer 1998). A generalized quantifier—the type of expression a quantified nominal denotes—takes a VP as its argument. The basic architecture of a quantified sentence is as in (54):

6This isn't uniformly a flaw. Certain combinations of frequency adjectives and determiners do seem to lack external readings for mysterious reasons. *The odd sailor strolled by* gets an external reading, but it's far more difficult to get it for *?An odd sailor strolled by*, as Gehrke and McNally (2015) observe. I'm not entirely sure what to make of these facts, but they don't strike me as sufficient reason to give up on the cause of trying to derive these generalizations from something deeper. In this specific case, the independently pragmatic naturalness of the internal reading may be relevant.

(55) *every dog* = λ*Qe*, *t* . ∀*x*[**dog**(*x*) → *Q*(*x*)]

The determiner *every* here has 'access' to the VP in the sense that its denotation asks for a predicate, *Q* in (55), that it can subsequently manipulate. The manipulation of VP meanings is the signature property of adverbials, of course, so on the incorporation view, what makes it seem like *occasional* has an 'adverbial' external reading is that it incorporates into a quantificational determiner and therefore has access to a VP meaning. Its access to clausal material external to the DP is a side-effect of the access the VP it has by actually being, in a deeper sense, a determiner.

If an adjective is part of a quantificational determiner meaning, it will gain access to the VP as a matter of course.

Thus this approach accounts for the adverbial scope of *occasional* and its kin, for the idiosyncratic interpretations of determiners in this construction, and (by stipulation) for restrictions on the determiner. It also accounts for the restriction on coordination: any adjective in a coordinate structure would be unable to move out of it without violating the Coordinate Structure Island. In general, movement from outside of one conjunct in a coordinate structure is not possible:

(56) a. Floyd ate rice and beans. b. \*Beans1, Floyd ate rice and *t*1.

That's precisely the sort of movement that, on this view, would be required in (57) to achieve the impossible external reading:

	- b. #[The+occasional1] [*t*1 and angry] sailor strolled by.

The obligatory high position of the adjective is explained as well—any adjectives above it would block its path to the determiner.

The incompatibility of external readings with degree modification would also be expected, because only a bare adjective, and not a phrasal constituent, can do headto-head movement, the kind required here. *Occasional* on its own is the head of an AP, but *very occasional* is not. This approach may even shed light on Zimmermann (2003)'s observation that external readings are often absent where Quantifier Raising is blocked. This analysis can be extended to *average*, *wrong*, perhaps *same*, and maybe others.

Nevertheless, one might have some qualms. The movement required would seem to violate the Head Movement Constraint (Travis 1984), which would normally prevent a head from moving outside of an adjoined phrase (the AP, in this case) as in (53).

More worrying, perhaps: why are *a*, *the*, and *your* alone the determiners that have been targeted for complex quantifier formation? Could it in principle have been any other combination? And why is it that the denotations of these complex determineradjective combinations aren't unpredictable? If they're specified in the lexicon, one might imagine virtually arbitrary variation, but the generalizations we would like to explain aren't arbitrary. Whatever the answers to these questions, more would have to be said to make weak-determiner-compatible adjectives such as *whole*, *unspecified*, and *different* fit in.

# *4.2 Structure Versus Ontology: The First Step*

Framing the current project as a trade-off between structure and ontology, at least with respect to *average*, is as I've said not novel. What I propose here is a variation on a theme from Kennedy and Stanley (2009). They observe the connection between *average* and *occasional*, and that this connection affords an analytical opportunity. For them, *average* incorporates into the determiner, just like *occasional* does for Larson (2000). The actual combinatorics required to achieve the necessary readings are complicated in ways that can be set aside, but they require a non-standard scopetaking mechanism that Barker (2007) dubbed Parasitic Scope, though appeals to it without the brand name can be found in Sauerland (1998) and earlier. The structure they propose is this:

The variable *n* here ranges over real numbers, or what number terms like *2.3* denote. The denotation is built up using the complex determiner *th'average* as in (59):

(59) *th'average* ( λ*n*λ*x . has n children* )(- *American* )(-*2.3* )

The denotation of *th'average* applies to three arguments. The first is a relation between numbers and individuals that have that number of children. The second is a property indicating what population is being averaged over, in this case, Americans. The final one is a real number indicating the computed average.

The details of implementation won't be crucial here, but they involve computing a mean on the basis of the maximal number of children each individual has,7 and |*P*| should be interpreted as the number of individuals that have the property *P*:

$$\text{(60)} \quad \left[\text{th}\,\text{"average}\,\right] = \lambda P\_{\langle e,t\rangle} \lambda f\_{\langle e,nt\rangle} \lambda n . \frac{\sum\_{P(x)} \max\{n \,|f(x)(n)\}}{|P|}$$

The most important point, for current purposes, is that on this view *average* DPs don't refer to anything metaphysically exotic because they don't refer to anything at all. Rather, they have an exotically high semantic type, which, coupled with incorporation from an adjective into a determiner and an unusual scope-taking operation, add up to a semantics that yields the right reading. For them, the right reading is strictly adverbial. It's the reading that can be paraphrased 'on average, Americans have 2.3 children'. It's worth noting, though, that this analysis has many of the same costs as the basic incorporation analysis, including having to stipulate the equivalence of *the, a*, and *your* on this reading.

# *4.3 The Kind Analysis of 'Occasional'*

The balance between the compositional semantics and the ontology is tilted in precisely the other direction in Gehrke and McNally (2010, 2015), building on Schäfer (2007). The distinctive property of *occasional* nominals, for them, is not in their grammar but rather in their referential properties—and it is therefore there that we should locate an analysis. So they seek a simpler syntax-semantics and a richer ontology.

It would require navigating quite a bit off my intended course to do justice to their proposal, but at its heart is an idea on which I will build: kind reference. The observation is that *the occasional sailor* involves reference to realizations of sailorkinds. Very approximately, the truth conditions of the now-familiar sailor sentence can be rendered as in (61):

(61) The occasional sailor strolled by.

Approximately: 'Suitably-distributed realizations of strolling-by event kinds involved realizations of the sailor kind.'

The major advantage to this strategy is that it doesn't require the compositional backflips that the incorporation analysis—and especially the Kennedy and Stanley (2009) variant for *occasional*—requires. Indeed, because there is no movement at all, it doesn't violate the Head Movement Constraint. It also provides insight into why *a*, *the*, and *your* should be the determiners that uniquely have a special status in

7The maximality operator is required because anyone with three children also has two.

this construction. This is precisely the class of determiners that have a special status with respect to kinds and genericity:

	- b. A dog is a better friend than a cat.
	- c. Your purple-breasted snicklewarbler is a magnificent bird. *(dialectal)*

To the extent that this approach is successful, it requires no special stipulations about the denotations of determiners. And because of that, it helps explain why determiner interpretations don't vary freely. No special stipulations are necessary to explain why *your+occasional* or the unattested *\*every+occasional* don't just happen by chance to mean something they don't actually mean.

The main shortcoming of this approach, from the current perspective, is that it's not clear how to make it scale up. On its own, it seems convincing that kind-reference is going to be a crucial ingredient in the analysis of external readings. But it's not clear to me how to make it the principal ingredient in a fully general theory.

# **5 The Modular Strategy**

# *5.1 Determiner-Like Adjectives*

The aim of this paper is not to present a general theory of nonlocal readings, but taking a confident step in that direction requires a theory of how they arise that is modular: that is, one that relies on multiple interacting parts to arrive at an explanation. Such a theory makes it possible to activate or deactivate certain of these components to explain variation among subclasses of adjectives and—most directly at issue here to explain the biggest split among nonlocal readings, the one between adjectives that give rise to Broader Quantifier Resistance and those that don't. (This sets aside, of course, the *possible* ellipsis class.)

One satisfying aspect of the incorporation analysis sketched above is that it reflects that nonlocal adjectives aren't prototypically adjective-like, even on a purely descriptive level. They don't pass standard diagnostics for adjectives, such as the ability to occur in comparatives, with degree modifiers, or in the complement position of*seem*. They don't conjoin with adjectives. Nor do they occur in the same positions as adjectives generally; rather, they are obligatorily high.

This might suggest incorporation or another form of syntactic differentiation, but all these properties also follow from simply assuming that nonlocal adjectives have an unusual semantic type. In the spirit of the incorporation approach, I'll assume these adjectives have precisely the same type of denotation as quantificational determiners, namely type *et*,*et*, *t*. Switching back to *average American*, the picture would be as in (63):

This has as a consequence that the node above the adjective, the NP *average American*, would denote a generalized quantifier. Following standard assumptions (see Heim and Kratzer 1998 for a review), it would therefore have to quantifier-raise and adjoin to the clause to avoid a type clash. I'll leave aside what happens higher in the clause for the moment to focus on the DP. The trace this movement leaves behind would standardly denote an individual. To make these LFs slightly easier to read later in the paper, I'll write it as a variable rather than a trace:

(64) DP D *et*, *e the* NP *e x*1

But this is hardly any help at all. It just gives rise to a different type clash: the NP would now denote an individual, but *the* is of type *et*, *e* and expects a property.

There is a natural solution. It's to adopt the standard be type shift (Partee 1987), which shifts an individual to the property of being that individual:

$$(6\mathbf{\hat{s}})\ \left[ \mathbf{\hat{z}} \mathbf{\hat{z}} \,\right] = \lambda \mathbf{x} \lambda \mathbf{y} \mathbf{\hat{z}} = \mathbf{y} \mathbf{\hat{z}}$$

Applied to Floyd, for example, this shift would yield the property of being Floyd:

(66) be (**Floyd**) = λ*y*[**Floyd** = *y*]

Partee used it for copular constructions, and it has subsequently proven useful elsewhere. In this case, this resolves the type clash by providing *the* with the propertydenoting argument it seeks in (64):

But as it turns out, at the next node up, this shift will achieve for us something more.

# *5.2 Determiners That Work*

One of the things we would like to explain is why *the*, *a*, and *your* seem to work robustly with a number of nonlocal adjectives, and why distinctions in their interpretations seem to be neutralized in the presence of frequency adjectives and *average/typical*. That result follows from the type shift alone. There is one and only one individual that has the property of being Floyd, and it is Floyd. For this reason, *the person who is Floyd* and *Floyd* mean the same thing. So too, here *the* would combine with the property the shifted trace denotes to yield the unique individual that is identical to the one the unshifted trace denotes:

(69) a. *the* = λ*Pe*, *t* . ι*y*[*P*(*y*)] b. *the* (be *x*1 ) = ι*y*[*x*1 = *y*] = *x*1

This is precisely the same individual as the one denoted by the trace alone. The effect is as though *the* were absent entirely, as though the nonlocal adjective and its NP sister had occurred in subject position on their own.

The semantically-bleached variant of *your* that occurs in e.g. *your average American* mostly amounts to a version of *the* with a slight whiff of genericity about it, which would leave us in more or less the same place (see Gehrke and McNally 2010, 2015 for more).

As for *a*, the right result follows from a simple equivalence. To say that there's a person *x* such that *x* is wearing a hat and *x* is Floyd is just to say that Floyd is wear a hat. The same equivalence manifests itself in (70). The standard denotation of the indefinite article in (70a) when combined with the shifted trace denotation, as in (70b), yields an expression that asks for a predicate *Q* and says that some individual identical to *x*1 satisfies *Q*:

$$\begin{aligned} \text{(70) a. } [[a \,]] &= \lambda \, P\_{\langle e, t \rangle} \lambda \, \mathcal{Q}\_{\langle e, t \rangle} \, . \, \exists \mathbf{x} [P(\mathbf{x}) \wedge \mathcal{Q}(\mathbf{x})] \\ &\text{b. } [[a \,]] ([\text{BE} \, x\_{\text{l}} \,]) = \lambda \, \mathcal{Q}\_{\langle e, t \rangle} \, . \, \exists \mathbf{x} [x\_{\text{l}} = \mathbf{x} \wedge \mathcal{Q}(\mathbf{x})] \end{aligned}$$

To say that there is an individual identical to *x*1 of which the predicate *Q* holds is simply to say that *Q* holds of *x*1:

$$\mathcal{Q}(\mathcal{T}\mathbf{l}) \cdot \exists \mathbf{x} [\mathbf{x}\_{\mathbf{l}} = \mathbf{x} \wedge \mathcal{Q}(\mathbf{x})] \Leftrightarrow \mathcal{Q}(\mathbf{x}\_{\mathbf{l}})$$

The result, again, is truth-conditionally identical to what would have happened had the determiner been absent entirely.

To articulate this a little bit further, let's adopt the toy denotation for *average* in (72a). This applies to the denotation of the modified NP, and predicates the VP meaning of the kind that corresponds to the NP meaning, using Chierchia (1998)'s ∩ property-to-kind type shift8:

$$\begin{aligned} \text{(72) a. } \[\text{average}\] &= \lambda \, P\_{\langle \epsilon, t \rangle} \lambda \, \mathcal{Q}\_{\langle \epsilon, t \rangle} \cdot \mathcal{Q}(^{\cap}P) \\ \text{b. } \[\text{average}\,\text{American}\,\text{]} &= \lambda \, \mathcal{Q}\_{\langle \epsilon, t \rangle} \cdot \mathcal{Q}(^{\cap}\text{American}) \end{aligned}$$

This probably isn't adequate on its own as a theory of *average*, and much of Kennedy and Stanley (2009) may have to be layered on top of it. A few more words on this follow in Sect. 6.1 below. But it suffices to sketch the compositional machinery. Thus the updated tree would look like this (I've ornamented the tree with a superscript *k* to reflect that the trace of *average American* denotes a kind):

The result of the computation is just what we need:

$$\begin{aligned} \text{(74) a. } \left\[ \begin{smallmatrix} \text{the BE } \mathbf{x}\_1^k \end{smallmatrix} \right] &= \mathbf{x}\_1^k\\ \text{b. } \left\[ \begin{smallmatrix} \text{the BE } \mathbf{x}\_1^k \end{smallmatrix} \text{has 2.3 children } \right] &= \mathbf{has-2.3-child} \text{rem}(\mathbf{x}\_1^k) \\ \text{c. } \left\[ \begin{smallmatrix} \text{average } American \end{smallmatrix} \right] &= \lambda \, \mathcal{Q}\_{\langle\epsilon,t\rangle} \cdot \mathcal{Q}(^{\uparrow}\mathbf{A}\mathbf{merican}) \\ \text{d. } \left\[ \begin{smallmatrix} \text{average } American \end{smallmatrix} \right] & \left( \begin{smallmatrix} \text{.} \lambda \mathbf{x}\_1^k \text{ the } f\text{BE } \mathbf{x}\_1^k \end{smallmatrix} \right) \text{has 2.3 children } \right] \\ &= \mathbf{has-2.3-child} \text{rem}(^{\uparrow}\mathbf{A}\mathbf{merican}) \end{aligned}$$

So the upshot is a semantics that requires that Americans generally have 2.3 children.

The crucial component to notice here is not the semantics of *average*, though, so much as the way the combination of the type shift, compositional assumptions, and

8Given this denotation, I could have equivalently dispensed with the λ*Q* in the denotation of *average* and had *average American* denote a kind directly. This is possible here only because I am using a considerably simplified denotation, though.

kind-reference have achieved the effect of ensuring that precisely the determiners that systematically license external readings yield the right result.

# *5.3 Determiners That Don't Work*

What of determiners that *don't* work? Again, the nature of the movement and resulting type shift helps the situation—or rather, undermines it in the right way.

Strong determines like *every* and *most* presuppose that their domain has more than one member. If there is only one person in the corner, for example, (75) gives rise to failure of presupposition:

(75) Every person in the corner left.

I've spelled it out explicitly in the denotation of *every* in (76) (the colon indicates the presupposition; |*P*|, as before, indicates the cardinality of individuals that satisfy *P*)

(76) *every* = λ*Pe*, *t*:|*P*| > 1 . λ*Qe*, *t* . ∀*x*[*P*(*x*) → *Q*(*x*)]

In (77), *every* combines with the property be *xk* 1 :

(77) a. #Every average American has 2.3 children. b. [average American] λ*xk* 1 [ every [be *xk* 1 ]] ] has 2.3 children

$$(\text{78)} \quad \left[\text{BE } x\_1^k\right] = \lambda \text{y} \|x\_1^k = \text{y}\|$$

But (78) is a singleton property—there is only one individual that is identical to *xk* 1 . It therefore violates the presupposition *every* imposes on its first argument.

This presupposition is not a peculiarity of *every*, but rather a property of strong quantificational determiners in general. Thus *most* would work similarly. Because movement below the DP level, in the framework proposed here, systematically gives rise to such singleton properties, it systematically precludes combining with strong quantifiers.

We have thus derived one of the two generalizations articulated earlier: the Strong Quantifier Resistance Generalization. All external readings observed it, so if this mechanism is crucial to deriving external readings, this explains it. Weak quantificational determiners do not have this presupposition, so they don't in general block external readings.

But what of the Broader Quantifier Resistance Generalization, the one only some adjectives observed? Some adjectives—like our test cases, *average* and *occasional* do block the external reading with weak quantifiers too. But despite the absence of the fatal presupposition, these fail in another respect. The denotation of *three* is as in (79), a property of individuals that have a cardinality of 3:

(79) *three* = λ*x*[|*x*| = 3]

When this combines with the shifted trace, it will combine intersectively with its denotation to yield (80):

$$\chi(80) \quad \left[ \text{ three BE } \mathbf{x}\_1^k \right] = \lambda \mathbf{y} \| \mathbf{x}\_1^k = \mathbf{y} \land |\mathbf{y}| = \mathbf{3} \right[$$

This is a property satisfied by a plurality with three elements that is identical to the kind *xk* 1 . That means, naturally, that the kind *xk* 1 has to be a plurality of three elements. But kinds aren't pluralities, and they don't have cardinalities. This is pretty straightforward metaphysically, but again, linguistic evidence makes it clear. As Chierchia (1998) demonstrates especially convincingly, across languages kinds are essentially a kind of mass term. *Cheese*, for example, denotes a kind in English, and *\*three cheese* is ungrammatical.

So in this case, the problem that rules out weak quantifiers has to do with kinds, and it will be only nonlocal adjectives that leave behind kind-denoting traces that will be subject to this additional restriction. *Occasional* is also incompatible with weak quantifiers, and, as Gehrke and McNally (2010, 2015) demonstrate, its semantics also relies crucially on kinds. Nonlocal adjective with no kind overtones such as *whole* or *wrong* or *unspecified* should therefore avoid running afoul of this difficulty and be compatible with weak quantifiers even on their external readings. And indeed they are. More on both of these points follows in the subsequent two sections.

# *5.4 A Word About 'Occasional'*

*Occasional* and its kin aren't the focus here, but a brief word about how they might work in this framework is appropriate. The approach to which I'm most sympathetic would be to simply combine the insights of two competing classes of approaches. Kinds must occupy a central place, for the reasons discussed above. But quantification can play a central role too. In particular, there is no reason not to adopt the Zimmermann (2000)'s quantifier OCCASIONAL, which quantifies jointly over the individuals and events, though here it will be crucial that it be kinds and events (with *s* as the type of events):

$$(81)\ \ [\alpha casional]\ = \lambda \, P\_{\langle e,t\rangle} \lambda \, Q\_{\langle e,\mathbf{v}\rangle}.\ \ \mathbf{O}\mathbf{C}\mathbf{A}\mathbf{S}\mathbf{I}\mathbf{O}\mathbf{N}\mathbf{A}\mathbf{L}\,\mathbf{x}^k, e\ :\ ^\frown P(\mathbf{x})[Q(\mathbf{x}^k)(e)]$$

This denotation would trigger movement to a position just below where the event argument is closed, and yield sentence denotations like (82):

(82) a. The occasional sailor strolled by. b. *occasional sailor* λ*xk* 1 *the* be *xk* 1 *strolled by* = OCCASIONAL *xk* , *e* : ∩**sailor**(*x*)[**strolled-by**(*xk* )(*e*)]

This seems a reasonable happy medium between the two approaches.

# *5.5 The Weak Quantifier Class*

There remains to discuss the class of external readings that *are* compatible with weak quantifiers. For those, though, in one sense there is little to be said. What ensured incompatibility with weak quantifiers above was the role of kinds. Adjectives whose semantics makes no special reference to kinds don't give rise to the problem of computing the cardinality of a kind.

To illustrate, the denotation of *unknown* could be characterized as in (83), where I've used ?*x*φ to abbreviate the embedded question 'which *x* is such that φ?'9:

$$\begin{aligned} \text{(83) a. } & \text{[ } \texttt{unknown} \text{]} = \lambda . P\_{\langle \texttt{e},t \rangle} \lambda . Q\_{\langle \texttt{e},t \rangle} \cdot \exists \texttt{x} [P(\text{x}) \land Q(\text{x}) \land \neg \texttt{known}(\text{?} \text{y}[Q(\text{y})])] \\ & \text{b. } & \text{[ } \texttt{unknown} \text{ hold} \text{]} \\ &= \lambda . Q\_{\langle \texttt{e},t \rangle} \cdot \exists \texttt{x} [\texttt{hot} \texttt{el}(\text{x}) \land Q(\text{x}) \land \neg \texttt{known}(\text{?} \text{y}[Q(\text{y})])] \end{aligned}$$

What *unknown hotel* does is a little complicated. First, it requires that there exist a hotel that satisfies the property formed by raising the whole quantified NP. Second, it requires that it not be known which individuals satisfy this property.

It will help to see how this works in action. The tree for (84a) arrived at by raising would be as in (84b):

(84) a. Solange stayed at three unknown hotels.

b.

This assumes a null existential determiner in the head of the nominal, and that, standardly, it undergoes quantifier raising. The denotation of (84) would be as in (85):

$$\begin{aligned} \text{(85)} \quad &\text{a. } \llbracket \mathtt{BE} \,\mathtt{x}\_{1} \rrbracket = \lambda \mathtt{y} \llbracket \mathtt{x}\_{1} = \mathtt{y} \rrbracket \\ &\text{b. } \llbracket \mathtt{there } \mathtt{BE} \,\mathtt{x}\_{1} \rrbracket = \lambda \mathtt{y} \llbracket \mathtt{x}\_{1} = \mathtt{y} \land \vert \mathtt{x}\_{1} \vert = \mathtt{3} \rrbracket \\ &\text{c. } \llbracket \mathtt{\exists} \rrbracket \,\mathtt{there } \mathtt{BE} \,\mathtt{x}\_{1} \rrbracket = \lambda \mathtt{g} \scriptstyle \mathtt{(e}\_{\textit{e}} \rrbracket \cdot \mathtt{By} \llbracket \mathtt{x}\_{1} = \mathtt{y} \land \vert \mathtt{x}\_{1} \vert = \mathtt{3} \land \mathsf{g}(\mathtt{y}) \rrbracket \\ &\text{d. } \llbracket \mathtt{\exists} \mathtt{x}\_{1} \rrbracket \rrbracket \,\mathtt{there } \mathtt{x}\_{1} \rrbracket \,\mathtt{\lambda} \mathtt{x}\_{2} \emph{ } \mathtt{S} \scriptstyle \mathtt{angle} \,\mathtt{get} \,\mathtt{get} \,\mathtt{at} \,\mathtt{x}\_{2} \rrbracket \\ &= \lambda \mathtt{x}\_{1} \square \mathtt{y} \llbracket \mathtt{x}\_{1} = \mathsf{y} \wedge \vert \mathtt{x}\_{1} \vert = \mathsf{A} \wedge \mathsf{stay} \,\mathtt{-} \mathtt{at} (\mathsf{y}) (\mathtt{Solange}) \rrbracket \\ &= \lambda \mathtt{x}\_{1} \square \mathtt{\|} \mathtt{|} \mathtt{y} \vert = \mathsf{A} \wedge \mathsf{stay} \,\mathtt{-} \mathtt{at} (\mathsf{y}) (\mathtt{Solange}) \llbracket \mathtt{} \mathtt{Q} \mathtt{any} \rrbracket \end{aligned}$$

9One may freely substitute one's favorite theory of indirect questions here, so far as I can see, though what I have in mind is that -?*y*[*Q*(*y*)] should be taken to be the set of propositions formed by varying the value of *y*, i.e., an abbreviation for -{*p* : ∃*x*[*p* = *Q*(*y*)]}.

This is a property that holds of any three-membered plural individual such that Solange stayed at its members.10

What *unknown hotels* adds to this is that this plurality is required to consist of hotels, and that it not be known which hotels precisely these are. The computation for the full sentence is in (86):

$$\begin{aligned} (86) \quad & \{\text{unknown} \land \text{labels} \land \text{x}\_1 \mid \exists \text{ three } \text{x}\_1 \text{} \land \text{x}\_2 \text{ } \text{Solange} \text{ stayed at } \text{x}\_2 \text{ }\} \\ &= \exists \text{x} \begin{bmatrix} \textbf{hostet}(\textbf{x}) \land |\textbf{x}| = \textbf{3} \land \textbf{stay-}\textbf{at}(\textbf{x}) (\textbf{Solange}) \land \\ \neg \textbf{known} \,(\text{?y}[\textbf{stay} \cdot \textbf{at}(\textbf{y})(\textbf{Solange})]) \end{bmatrix} \end{aligned}$$

The result, correctly, is that there must be three hotels at which Solange stayed, and it must not be known which hotels these are.

The crucial element in all this, though, is that there is nothing about *unknown* that prevents cardinalities from being computed, and so nothing that resists, in this instance, *three*, and more broadly any of its kin.

# *5.6 Summary*

The result, then, is that there is no need for incorporation. The external scope facts follow from quantifier raising. The interpretation of determiners is standard. Restrictions on determiners follow from independent considerations. The general resistance of nonlocal adjectives to strong quantifiers follows from the compositional circumstances of their movement, which invoke a type shift with which they are incompatible. The resistance of certain nonlocal adjectives to weak quantifiers follows from independent facts about the lexical semantics of the adjective—specifically, having a kind-based semantics. Other restrictions, like the lack of coordination with ordinary adjectives and absence of degree modifiers, follow from the quantifier type of these expressions.

This means it was not necessary to stipulate which determiners support incorporation and which don't, or what interpretations result for every combination. Nor was it necessary to stipulate why *the*, *a*, and *your* wind up making the same semantic contribution, or to do so repeatedly for each frequency adjective. It also wasn't necessary to stipulate anything about the interaction of quantificational force with external readings. This is possible in part precisely because what I have offered here is only a sketch. The devil, as always, is in the details. But I hope this illustrates an analytical approach to these facts that might hope to scale up to the broader analytical picture I sought to draw.

10I set aside questions of distributivity and collectivity here.

# **6 Taking Stock**

# *6.1 Could Things Be so Simple?*

One issue remains strikingly unresolved. I've characterized the denotation for *average* I've provided above as a toy denotation. I've said, perhaps a bit defensively, that things couldn't possibly be so simple. Surely, it couldn't suffice to say that *the average American* means, essentially, the same thing as the kind-denoting nominal *Americans*, and (87a) and (87b) mean more or less the same thing:

(87) a. The average American has 2.3 children. b. Americans have 2.3 children.

But the truth is, I think the simple toy version of the facts may be onto a deeper grammatical intuition than the more complicated one.

To be sure, we have the option of layering on components of the Kennedy and Stanley approach here, introducing elements of their machinery on top of the bits I propose to achieve their desired adverbial reading. There is a danger of redundancy, though. And the more one does that, the farther one gets to the connection to kindreference, for which Gehrke and McNally provide ample evidence.

The defense of the naïve theory proceeds in several steps. The first is empirical. Suppose we adopt a theory that involves computing a mean. On such a view, (88a) and (88b) would both be predicted to be true, and, therefore, quite probably (88c) too:

	- b. The average human has one testicle.
	- c. The average human has one ovary and one testicle.

Yet they are all false, or in any case false outside of exceptionally odd statistical contexts. Any theory that revolves primarily around calculation of means would fail to predict this. But in a theory that relies on kind reference, it's expected. On such a view, it's the *2.3 children* case that's puzzling.

That, I think, is precisely where we should *want* to be puzzled—that is the case that we should treat as exotic rather than as the core example. Most languages through most of human history had no reason to refer to fractions. Moreover, the semantics of fractions is independently puzzling. They are problematic completely independent of their role in *average* sentences. It makes sense, then, that the theory of *average* shouldn't be itself founded on this independent mystery.

That said, nothing in the general conception of external readings proposed here rests above all on any particular assumptions about kinds. Perhaps other notions could do the necessary work without putting us on thin ice with respect to sentences containing fractions. Indeed, I consider one such possibility in Sect. 6.2 below. The only crucial role kinds play here is to rule out computing cardinalities, which in turn is crucial to distinguishing the weak-quantifier class from the no-quantifier class. That's not nothing, but there may be other means of accomplishing this. Nevertheless, it's worth recognizing that there are several converging lines of evidence that point to kinds or some form of genericity in these sentences: initial intuitions about what *average* sentences mean, the judgments in (88), the role kinds play in distinguishing classes of external readings, and its place in correctly predicting which determiners have which readings. One might be still able to explain *2.3 children* by simply adopting,with Kennedy and Stanley, an extraordinarily high type, but it seems right that special stipulations should be required there and not elsewhere.

It's worth pointing out, though, that one could also follow in the spirit of Carlson and Pelletier (2002) and appeal to fictive entities in place of some form of kind. This analytical avenue may actually be more available on this approach. Kennedy and Stanley argue against the fictive entity approach in part on the grounds that it doesn't explain the limited inventory of determiners possible with *average*. Those facts, however, can be explained independently here. But again, if the relevant notion of fictive entities can emerge with an appropriate kind flavor, that seems preferable on independent grounds to the alternative.

None of that directly addresses what the semantics of *2.3 children* should be. My suspicion is that an ultimately satisfying answer requires not just a theory of nonlocal readings of adjectives, but a better theory of mathematical language, and in particular of what I elsewhere call 'semantic viruses' (Morzycki 2017), in the spirit of Sobin (1997) syntactic viruses (see also Lasnik and Sobin 2000; Schütze 1999). I argue there that some expressions associated with educated, often highly selfconscious language may use special semantic mechanisms not otherwise available in the semantics. Making this distinction may help us distinguish which operations and what grammatical phenomena truly are exotic and may call for some brute-force high-type complexity, and where we should seek simplicity, even occasionally in the face of apparent counterevidence.

# *6.2 Kinds and Concepts*

Sebastian Löbner (p.c.) suggests that a number of the restrictions on external readings of *average* and *occasional* may involve characterizing more precisely the concept types they give rise to. *Average American* on the relevant reading isn't a sortal concept—one that supports counting and is neither uniquely referential nor relational. That accounts for its incompatibility with strong quantifiers (*#every average American*), and perhaps for its incompatibility with stacked or conjoined adjectives (*#an average (and) irritable American*).

This mode of explanation in some respects has the same shape as a kind-based one, or indeed as one organized around fictive entities. They all seek to derive the properties of the expression from the ontological status of the extension of the nominal. Both kinds and the relevant non-sortal concepts are uncountable. It doesn't seem too far-fetched to claim that fictive entities might not be countable either, though that's less obvious. Insomniacs are sometimes advised to count sheep in order to fall asleep, yet under normal circumstances the livestock in one's bedroom are entirely fictive. Likewise, the resistance to quantification that I earlier attributed to a failure of presupposition could be attributed to countability as well. As I expressed it in (76), the presupposition involved determining the cardinality of individuals that satisfy the property expressed by the nominal argument. In this implementation, that is not undefined. Even though this property has in its domain kinds, it denotes a property that holds of precisely one kind. Therefore it is countable. This follows from how the movement and type shift interact. One might imagine, though, an alternative analysis where the inherent countability of the noun is crucial. In order for the analysis of adjective stacking and conjunction to go through, however, one really would have to have the NP *average American* denote this concept kind quite low in the tree, before any type shifts have taken place. On this view, then, the crucial difference could be viewed as being in how high in the structure of the nominal kinds are invoked. But there are good reasons to think properties of kinds are to be found deep in the nominal extended projection, very near the noun (Zamparelli 1995 among others). So this fact too may be insufficient to distinguish these two approaches on a deep level, setting aside particular analytical choices I've made here.

The adjective order facts, however, might be of use. Most evidence for a layer in the nominal projection that is concerned with kinds rather than objects suggests that it is the lower of the two. So-called Bolinger contrasts (Bolinger 1967; see Morzycki 2016a and Leffel 2014 for extensive discussion) such as the one in (89) show that adjectives lower in the nominal ascribe inherent or individual-level properties, and higher ones ascribe contingent or stage-level properties:

	- b. #the visible invisible stars

On its only possible reading, (89a) refers to stars that are visible in principle but invisible at the moment, perhaps by clouds. But (89b) is contradictory, because it refers to stars that are invisible in principle but visible at the moment.  But be it about kinds or not, the domain of genericity in the nominal is low. Yet as we've seen, adjectives associated with external readings are exclusively high. A reminder:

If kinds or non-sortal properties were at issue lower in the nominal, this effect would be expected to be either reversed or absent entirely.

One appeal of such an approach, in either of these incarnations, would be that the quantificational facts and the facts about conjunction and stacking could be brought under the same rubric. As it stands, the latter derive from the quantificational type of the NP. A major disadvantage is that they wouldn't readily extend to the rather large class of adjectives compatible with weak quantifiers. Nor, in the absence of a scopetaking mechanism, would they permit the adjective access to the VP denotation. Yet this access is precisely what seems to be required for e.g. epistemic adjectives such as *unknown*, as shown in Sect. 5.5.

# **7 Final Remarks**

To close, a few words about the commonly expressed intuition that nonlocal readings are a grammatical oddity. These adjectives are indeed odd, but in a precise and interesting sense. They are odd in the way that platypuses and lungfish are odd: they are perhaps metaphorically, or perhaps more than metaphorically—transitional forms in an evolutionary progression, unusual because they combine features of two distinct categories that we normally regard as mutually exclusive. Over succeeding generations of speakers, certain adjectives may emerge from the swampy depths of the inner NP to which they are usually confined, and tentatively make their way onto the dry land of the determiner domain. They can't be expected to make this leap in a single stride, so we can observe them in the midst of their evolutionary journey and thereby discover more about both their evolutionary origin and their destination. Like platypuses and lungfish, they are important and analytically revealing not despite their strangeness, but because of it.

Substantively, the proposal was that nonlocal adjectives have quantificational determiner denotations, trigger raising of the NP in which they occur, stranding the determiner, and sometimes require properties of kinds as their arguments. This isn't a general theory of all nonlocal readings, naturally. That would be far too ambitious for any single paper. But it has the shape of a general theory, and my hope is that further research will be able to fill in the gaps in a similar spirit.

From the broader cognitive perspective, though, one of the larger lessons is the balance between the explanatory burden on the ontology and on the structural machinery. For *average*, for example, one might have gone in the direction of recognizing 'average Americans' as actual, if very abstract, objects in the model, 'fictive persons'. For *occasional*, I followed Gehrke and McNally (2010, 2015) in placing a great deal of explanatory weight on the notion of kinds, if perhaps not quite so much weight as they have.

On the other hand, structural components played a crucial role. For *average*, one could go so far as Kennedy and Stanley (2009) do, and invoke quite highpowered syntactic and semantic machinery to twist the tree into the shape we require. For *occasional*, Larson (1999), Zimmermann (2000) and others provide a path that also requires quite a bit of syntactic machinery.

It is misguided, I think, to ask where we wind up in each respect: how much compositional structure do we need, how much metaphysics, and what the right balance is. Rather, we should recognize that there may be some explanatory tradeoffs, but that inevitably, we will need a bit of both modes of explanation—and it is up to language to tell us how much we need of either.

**Acknowledgements** I've presented various portions and versions of this work to various people and audiences. Thanks to Adam Gobeski, Ai Kubota, Ai Taniguchi, Anna Szabolsci, Anne-Michelle Tessier, Barbara Partee, Berit Gehrke, Bernhard Schwarz, Cara Feldscher, Chris Barker, Curt Anderson, Daniel Gutzmann, Friederike Moltmann, Gabriel Roisenberg Rodrigues, Galit Sassoon, Haley Farkas, Hannah Forsythe, Henry Davis, Hotze Rullmann, Irene Heim, Josh Herrin, Kay Ann Schlang, Kyle Rawlins, Lisa Matthewson, Lucas Champolion, Manfred Krifka, Norbert Hornstein, Omer Preminger, Paul Pietroski, Rose-Marie Déchaine, Sebastian Löbner, Stephanie Solt, Taehoon Hendrik Kim, Yan Cong, and audiences at the University of Maryland, Sinn und Bedeutung in Tübingen, Boston University, New York University, the University of British Columbia, and of course the Cognitive Structures conference. Berit and Sebastian kindly provided written comments on an earlier draft of this paper, and I'm especially grateful to Sebastian for involving me in the intellectual community around Düsseldorf.

# **References**

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**Concept Theory**

# **How Can Semantics Avoid the Troubles with the Analytic/Synthetic Distinction?**

**Roberto G. de Almeida and Caitlyn Antal**

One failure a week is just bracing and good for you. —*Allen Newell* (1991).

**Abstract** At least since Quine (From a logical point of view. Harvard University Press, Cambridge, MA, 1953) it has been suspected that a semantic theory that rests on defining features, or on what are taken to be "analytic" properties bearing on the content of lexical items, rests on a fault line. Simply put, there is no criterion for determining which features or properties are to be analytic and which ones are to be synthetic or contingent on experience. Deep down, our concern is what cognitive science and its several competing semantic theories have to offer in terms of solution. We analyze a few cases, which run into trouble by appealing to analyticity, and propose our own solution to this problem: a version of atomism cum inferences, which we think it is the only way out of the dead-end of analyticity. We start off by discussing several guiding assumptions regarding cognitive architecture and on what we take to be methodological imperatives for doing semantics within cognitive science—that is a semantics that is concerned with accounting for mental states. We then discuss theoretical perspectives on lexical causatives and the so-called "coercion" phenomenon or, in our preferred terminology, indeterminacy. And we advance, even if briefly, a proposal for the representation and processing of conceptual content that does away with the analytic/synthetic distinction. We argue that the only account of mental content that does away with the analytic/synthetic distinction is atomism. The version of atomism that we sketch accounts for the purported effects of analyticity with a system of inferences that are in essence synthetic and, thus, not content constitutive.

R. G. de Almeida (B) · C. Antal

#### C. Antal e-mail<EMAIL_ADDRESS>
© The Author(s) 2021

Department of Psychology, Concordia University, Montreal, QC, Canada e-mail<EMAIL_ADDRESS>
S. Löbner et al. (eds.), *Concepts, Frames and Cascades in Semantics, Cognition and Ontology*, Language, Cognition, and Mind 7, https://doi.org/10.1007/978-3-030-50200-3\_5

**Keywords** Analytic/synthetic distinction · Compositionality · Causatives · Indeterminacy · Coercion · Intentional fallacy · Concepts · Atomism · Cognitive architecture

Our concern in this paper is, on the surface, not new. For long—at least since Quine (1953) in modern times, to say little of Kant's "cleavage" problems way back then it has been suspected that a semantic theory that rests on defining features, or on what are taken to be "analytic" properties bearing on the content of lexical items, rests on a fault line. Simply put, there is no criterion for determining which features or properties are to be analytic and which ones are to be synthetic or contingent on experience. But that is just the glossy if old shell of our concern. Deep down, our concern is what cognitive science and its several competing semantic theories have to offer in terms of solution, if any at all. With this in mind, we analyze a few cases, which run into trouble by appealing to analyticity, and propose our own solution to this problem: a version of atomism cum inferences. We are aware that the proposal we have to offer is at odds with widely held views, but we think it is the only way out of the deadend of analyticity, if one is not to be burdened with producing an analytic/synthetic criterion. We start off by discussing several guiding assumptions regarding cognitive architecture and on what we take to be methodological imperatives for doing semantics within cognitive science—that is a semantics that is concerned with accounting for mental states. We then discuss theoretical perspectives on a range of seemingly disconnected phenomena—in particular lexical causatives and the so-called "coercion" phenomenon or, in our preferred terminology, indeterminacy. And we advance, even if briefly, a proposal for the representation and processing of conceptual content that does away with the analytic/synthetic distinction. We will argue that the only account of mental content that does away with the analytic/synthetic distinction is atomism. The version of atomism we will sketch accounts for the purported effects of analyticity with a system of inferences that are in essence synthetic and, thus, not content constitutive.

# **1 Semantics and the Architecture of Cognition**

It is not uncommon for cognitive scientists working in semantics to mix their metaphors regarding how they envision the nature of mental representations and processes. Perhaps they do so inadvertently, but the price is a lack of clarity on what one takes to be the very nature of the representation of *content* and the computational processes that are content-bearing. And if there is one issue that research in semantics needs to be clear about, it is how it conceives content representation and processing. As an example, consider sentence (1).

(1) Mary began a book.

Imagine now that the issue at hand is how a sentence such as (1) might be interpreted. The proposal quoted in (2) is apropos the sorts of psychological events carried out during the comprehension process of (1). The semantic issues underlying this proposal will be dealt with a little later, but we start off with the commitments of this proposal vis-à-vis cognitive architecture.

	- (b) The mismatch between the verb's selectional restrictions and the stored senses of the noun triggers a coercion process.
	- (c) Comprehenders use salient properties associated with the complement noun and other relevant discourse elements (including but not necessarily limited to the agent phrase) to infer a plausible action that could be performed on the noun.
	- (d) Comprehenders incorporate the event sense into their semantic interpretation of the VP by reconfiguring the semantic representation of the complement, converting [β began[α the book]] into [β began[α reading the book]]. (Conceivably, this could also require reconfiguration of an associated syntactic representation.)" (Traxler et al., 2005, p. 4)

We use this as a convenient example of the kinds of constraints—or lack thereof that may drive semantic proposals within the language processing literature. As we will see, similar proposals abound in semantic theory.