TY - JOUR AU - Rothstein,, Susan AB - Introduction This paper argues that locative phrases may make reference to individual locations and that our theory of types must thus include locations as individuals, along with other individual entities like 'ordinary' individuals, events, and properties. Locative PPs have been the object of many studies (Jackendoff 1983, Creary, Gawron and Nerbonne 1989, Wunderlich 1991, Zwarts and Winter 2000, Kracht 2002, to name but a few, see Zwarts 2017 for an overview). These studies have for the most part focused on the interpretation of locative prepositions and locative PP phrases as VP modifiers, and have argued that locative PPs should be treated as denoting sets of spatial objects, with different theories giving different accounts of what these spatial objects are (points, vectors, or sets of points in Wunderlich, Zwarts and Winter, and Kracht respectively). In this paper I will focus on different locative data, exploring the interpretation of locative PPs as arguments, and the distribution of bare locative nominal expressions headed by place that can replace locative PPs both as arguments and as adverbials. I will show that in order to explain the distribution and interpretation of these expressions, we need to posit locations as individuals. These individual locations are the individual correlates of the sets of spatial entities that previous studies have argued for. Individual locations and sets of spatial entities are related in the same way that property correlates and properties as sets of individuals are related to each other in the property theory of Chierchia (1984, 1985) and Chierchia and Turner (1988). Positing a domain of locations allows us to make reference to individual locations, and allows for an interpretation for the nominal place in which it denotes a set of individual locations. This will enable us to give a semantics for locations which unifies such apparently diverse phenomena as the distribution of locative PP arguments, complementizer deletion in relative clauses, and the peculiarities of the bare NP adverbials discussed in Larson (1985). In the rest of this introduction, I will give some background on property theory and sortal types, before turning to the topic of locatives. It has long been argued that the domain of individuals in a model for the interpretation of natural language must be sorted. Following Davidson's lead (Davidson 1967), linguists have amassed evidence that, as well as 'ordinary' individuals, entities of type d,1 and truth values of type t, the set of types must include a basic type e of events (Parsons 1990, Landman 1995, 2000, Rothstein 1995, and many others). Chierchia (1984, 1985) and Chierchia and Turner (1988) argue that the type of individuals d includes a subtype π of properties. Properties differ from ordinary individuals, truth values or events, in that they are defined as individual correlates of sets of individuals (of type ). No assumption is made as to whether sets of individuals or properties are ontologically prior. The Chierchia-Turner approach has been extended to include other subtypes of type d in correspondence with sets of object, including kinds (Carlson 1977a, Chierchia 1998a), numbers (Rothstein 2013, 2017), and degrees or amounts (Scontras 2017). I shall argue that the set of available types must be expanded further to include locations of type l, and that locations are a sort of property, analogous to properties of type π. Along with expressions of type l, we will find predicates of locations of type and generalized quantifiers over locations at type <, t>. However, locations differ from properties, kinds, numbers and amounts, since they are individual correlates of sets of points, and not of sets of individuals. Chierchia (1984, 1985) and Chierchia and Turner (1988) give a theory of properties in a Fregean framework, showing that properties have an unsaturated interpretation at the applicative type , as well as a saturated interpretation at type π, the individual correlate of the applicative interpretation. They assume a domain of individuals U which is divided into subdomains, including D the set of individuals of type d, ('ordinary' individuals), the set of propositions of type t, and the set of individual property-correlates of type π. They assume two functions ∩ and ∪ between the domains of and π that relate set expressions and their individual correlates in the following way: (1) ∩ and ∪ are two functions such that:∩: D → π is a one-one function from D into π.∪: π → D is a function such that for P ∈ D: ∪∩P = P. (See Chierchia and Turner 1988 for the property theory making this possible.) The ∩ function can be seen as a nominalizing function, mapping objects of the unsaturated, applicative type onto “that same object” as a saturated individual, its individual correlate in type π. ∪ inversely maps a property in π onto the set of individuals that have that property. As an example, let BLUE be a constant of type . (2) a. The car is blue → BLUE(⁠|$\sigma$|CAR)b. Blue is fashionable → FASHIONABLE(∩BLUE) In (2a), the expression blue is interpreted as a predicate of type , denoting the set of blue individuals. In (2b), blue denotes the property of blueness, the individual correlate ∩BLUE of the predicate, which itself, according to (2b), is in the set of fashionable objects. In this example, the unsaturated predicate denotation and its corresponding nominalized property are not morphologically distinct (both are the denotation of the same predicate blue), but this does not have to be the case: the interpretations of wise and wisdom stand in the same relation as the two interpretations of blue, as in Sally is wise and Wisdom is a quality that I value. Chierchia and Turner's (1988) discussion focusses on properties and the relation between the applicative type expressed by adjectives and the nominalization expressed by nouns. As mentioned above, at least three other types have been identified, which have more or less explicitly been analyzed in analogy to the type of properties. 2 In each case, the saturated individual type has been analyzed as the individual correlate of a predicate at type , and the equations in (1) hold. The nominalization function may have different morphological expressions depending on the category and lexical item. First, Carlson (1977a) and Chierchia (1998a) identify type k, the type of kinds, denoted by common nouns in their kind-denoting usages, illustrated in (3a). These are the individual correlates of common nouns in their unsaturated use, in which the noun denotes a set of individuals instantiating the kind, as in (3b): (3) a. Dodos are extinct.b. Those birds are dodos. Second, Rothstein (2013, 2017) identifies numerals as denoting a special type of property, namely a cardinal property of pluralities with both a saturated realization, as in (4a), and an applicative realization in which the numeral is a modifier of the noun, as in (4b): (4) a. Two is the smallest prime number.b. Two cats are in the barn. Recently, Scontras (2017) argues that a similar analysis should be applied to amounts, with expressions like three kilos denoting either the set of entities which have the property of measuring 3 kilos, or the individual correlate of that set. Associated with each individual type α is |${\Delta}_{\alpha}$|⁠, the family of types with base α. For any individual type α, |${\Delta}_{\alpha}$| will minimally include types α, <α,t> (predicates of α objects) and <<α,t>,t> (generalized quantifiers over the relevant type α). These are the three types related by the Partee triangle (Partee 1987). For types α ∈ {d, e, k, π, n, a}, it can be argued that the full family based on α is linguistically relevant. For example, extinct in (3b) is a predicate of kinds of type ; is a prime number in (4b) is a predicate of numbers of type , while expressions like is a quality I value is an expression of type <π,t>. Since these expressions can be used to restrict quantifiers (possibly with the addition of a noun, as in every extinct kind), each of these types α is also associated with the generalized quantifier type <<α,t>,t>. The first claim of this paper is that there is good evidence that the set of types used in building a semantics for English must include locations at type l and, as a consequence, |${\Delta}_l$|⁠, the family of types associated with l, must include minimally l, the type of locations, , the type of sets of locations, and <,t>, generalized quantifiers over locations. I shall argue that locations are the denotations of locational PPs in argument position in sentences like (5), and that expressions with their denotation in |${\Delta}_l$| occur in other familiar constructions: (5) a. Under the table is a good place for the cat the sleep.b. I put the glass on the table. Like properties (kinds, ‘adjectival’ properties, numbers and amounts) locations are individual correlates of sets, in this case the sets denoted by PPs as modifiers, as for example a verbal modifier in (6): (6) The cat is sleeping under the table. However, unlike properties, these modificational PPs do not denote sets of individuals at type but sets of spatial entities, either points, vectors or regions, depending on the specific theory of locative modification assumed. Thus, despite the similarities between them, locations differ from properties, since locations are individual correlates of sets of spatial entities, while properties are individual correlates of sets of individuals. The second claim of the paper is that locations not only play a role in the interpretation of locative PPs, but also in the interpretation of nominal expressions headed by the noun place. I will argue that place has an interpretation as a domain sortal. Any noun can be seen as a function that maps the domain D onto a subset of D, the set of individuals in D who are in the denotation of the noun.3 The noun place has this kind of interpretation in an expression like: my place in the country. However, place also has an interpretation where it denotes not a subset of the domain of locations L of type l, but domain L itself. This is what a domain sortal is: place is a type marker, which tells us that its denotation is in the family of types |${\Delta}_l$| rather than the family |${\Delta}_{\mathrm{d}}$| (the standard one for nouns). As we will see, there are similarities between locations and events, which are also individuals that are not ‘ordinary’, and place is similar in function to time, which Rothstein (1995) argues has an interpretation in which it denotes the set of events E, and is therefore an eventuality domain sortal. Locative PPs as arguments Jackendoff (1983) documented some of the analogies between locative phrases and nominal arguments, in particular involving quantification and anaphora. In this section, we focus on one property of PP locatives, their ability to appear in what are standardly assumed to be canonical argument positions. One construction in which this occurs is illustrated in (5a) above, and in (7a), where the PP appears in the subject position of a sentence. A second construction is illustrated in (5b) and (7b), where the PP is selected for by the verb and apparently satisfies an argument position in the verb’s thematic grid: (7) a. In the cupboard is a good place to hide.b. I put the letter on the table/in his mailbox/on the mantelpiece. We start by bringing evidence that the PPs in (7a/b) are arguments. We then discuss what these PPs might refer to. In (7a), the locative PP is apparently the subject of the sentence, and the predicate is a good place to hide denotes a property which is asserted to hold of the PP denotation. Since the predicate is a nominal, it might be suggested that (7a) is a case of predicate inversion, and that the PP is a predicate modifying a good place to hide. There are several pieces of evidence to show that this is not the case, and that the PP is indeed the subject of the sentence. First, the verb agrees with the subject in number. In (7a), the verb is singular and in (8), where the subject is a conjunction of PPs each denoting a different place, the verb must be plural.4 (8) Under the sofa in the living room and inside the kitchen cupboard are good places to hide. Second, examples with both strongly indicate that the PP is the subject. While predicate NPs are usually marked plural to agree with a plural subject, as in (8), predicate nominals under the scope of both which distribute over the plural subject can be marked singular, as in (9a) (though the agreement is plural). The same pattern occurs in (9b), where the subject is a conjunction of PPs: (9) a. Exercise and a break from the computer are both a good idea. [www] 5 b. Under the sofa in the living room and inside the kitchen cupboard are both a good place to hide. Third, standard constraints on predicate nominals apply to the post-copula phrase. The nominal headed by place can be indefinite, as in (7a) above, modified by a numerical expression, as in (10a), or definite, as in (10b), but universal quantifiers are strongly degraded in this position, as shown by (10c/d): (10) a. In the closet and under the table are two good places to hide. b. In the closet is the best/the only place to hide. c. #In the closet and under the table are every place to hide. d. #In the closet is every place Martha ever thought of hiding. A second kind of example which suggests that PPs denote locations is example (7b), repeated as (11a), where the locative PP is an obligatory argument of the verb put, which contrasts sharply with the infelicitous (11b) where the locative is missing: (11) a. I put the letter in the drawer. b. #I put the letter. Both internal arguments and subject argument can be replaced by the deictic pronouns here/there (as in 12): (12) a. I put the letter here/there. b. There would be a good place to hide. The obligatoriness of the PP in (11a) suggests that the locative PP is an argument selected by the verb, rather than a predicate predicated of another argument.6Put is a three place lexical relation between an agent, a theme and a location. In a neo-Davidsonian theory of event semantics, verbs are predicates of events, and their lexically selected arguments are mediated by thematic roles, which are operators of type <α,>, which apply to entities of the appropriate kind and yield predicates of events. Plausibly, put should be analyzed analogously to give (to which the literature has paid much more attention), which is analyzed as selecting an agent, a theme and a goal. Put is similarly a triadic predicate with its third argument obligatorily a PP headed by a locative preposition or the pro-forms, there, here.7 At the end of an event of giving, the theme must be in the possession of goal argument, and at the end of an event of putting, the theme must be in the location expressed by the PP. (13) give: I gave the book to John. put: I put the book in the drawer. Crucially, the locative PP argument of put can be distinguished from the locative modifier of the event, as shown in (14): (14) John put flyers in mailboxes on Monday in the north side of town. (14) has both a PP locative argument in mailboxes and a PP event modifier in the north side of town. In mailboxes denotes the (plural) goal of the (plural) putting event, since at the end of the event, the flyers have to be in the mailboxes, and the PP distributes over the individual singular putting events (Landman 1995). On the other hand, the adverbial in the north side of town modifies the whole verbal phrase put flyers in mailboxes on Monday. The adverbial PP expresses where the whole (plural) event of putting flyers in mailboxes was located. This semantic contrast between PP arguments and locative adverbials is supported by a syntactic contrast, since these PPs are generated in different places in the syntactic tree. Arguments are V modifiers generated inside the lowest VP, while adverbials are VP modifiers. This can be seen from their interactions with subject-oriented depictive modifiers. Subject-oriented depictives are attached to the VP at the highest level, outside the VP containing the verb and its arguments. They can be generated either lower or higher than adverbial locative modifiers, as shown in (15), where the depictive drunk is subject-oriented in both positions, but they must be generated higher than PP arguments, as shown in (16). (16b) is infelicitous, since drunk cannot have a subject-oriented interpretation in (16b): (15) A. Johni drove the car in the park drunki. b. Johni drove the car drunki in the park. (16) A. Johni put the car in the garage drunki. b. #Johni put the car drunki in the garage. Put is not the only verb taking a PP argument headed by a locative PP, as shown by the examples in (17), where dropping the locative PP either renders the sentence infelicitous or changes the meaning of the verb: (17) a. Jan lived in Amsterdam. (versus Jan lived.) b. John placed the book on the table. (versus #John placed the book.) c. Mary kept the car in the garage. (versus Mary kept the car.) d. Bill left his keys on the table. (versus #Bill left his keys.) The denotation of locative PPs I take it as a given that the denotation of PPs as arguments in the examples just cited should be related to their interpretation as locative modifiers, and that the interpretation of the PP under the table in Under the table is a good place to hide should be predictably related to its interpretation in The cat is sleeping under the table. Examples like (18a) suggest that locative PPs in predicative position could denote properties of individuals: (18) a. The cat is in the kitchen. b. The cat is eating in the kitchen. Talmy (1985) argues that locative prepositions express a relation between a located object and the reference object (a relation that he calls ‘figure and ground’). In (18a), the cat is located in terms of the reference object, the table, while in (18b), the cat, the located object, is in the kitchen. Under this kind of analysis, locative PPs could be analyzed as properties of individuals, just like adjectival properties in Chierchia and Turner’s analysis, with some adaptation to allow for PP adverbial modifiers like the one in (18b), which would presumably denote a set of events, rather than a set of individuals. However, considerable research on locative PPs has argued that locative PPs cannot be analyzed in this way; but that they must denote sets of spatial entities. There is some variation in what these spatial entities are taken to be. Zwarts (2017) divides analyses of locatives into two groups: the first group models locative PP denotations as sets of points, or regions (e.g. Creary, Gawron and Nerbonne 1989 and Wunderlich 1991) or as sets of regions (i.e. sets of sets of points) (Kracht 2002). The second group consists of theories which analyze locative PP denotations as sets of vectors (i.e. sets of pairs of points) (Zwarts and Winter 2000). In all analyses, the locative preposition denotes a function which applies to an object, the reference object, to yield a PP denotation which is a location or space defined by its relation to the reference object. In under the table, the meaning of the preposition under applies to the table and yields a location, either a region or a set of vectors, which constitutes the space which is under the table. The located object is then said to be located in that location. Different prepositions yield different locations with respect to the same reference object, e.g. under the table, on the table, near the table yield different locations with respect to (potentially) the same table. These differences have been modelled in terms of functional factors, such as support and attachment (Zwarts 2017). Thus, when we compare the denotations of above and on in above the table versus on the table, the latter, but not the former, yields a location which is in contact with the table. So if a balloon is on the table it is usually assumed to be touching the top of the table, while if it is above the table this is not necessary. (Indeed, Gricean principles may lead us to assume that in that case it is not touching the table.) However, if the balloon is on a tray which is on the table, it is still considered to be on the table (due to the functional factor of support). Modelling locative PP denotations as spatial entities allows us to capture a range of semantic entailments as well as explain various grammatical properties. Some of these entailments follow from the meaning of the prepositions: for example, if the book is on the table, then the table is under the book. Others follow from the properties of locations. Here are two examples, based on examples from Creary, Gawron and Nerbonne: (i) If the book is in the bag and the bag is in the kitchen, then the book is in the kitchen. (ii) If the university campus lies partly in town A and partly in town B, then if you are on the campus, you are either in town A or in town B, put differently, you are either in the intersection of the location of the campus with the location of town A or in the intersection of the location of the campus with the location of town B. These examples suggest that locatives should be modelled in terms of sets of spatial entities like points, since then the entailments easily follow: (i) shows that the subregion relation is upwardly monotonic: if a is located in (occupies a subregion of) a region r, and r is a subregion of r’ then, a is located in r’. (ii) shows that regions satisfy a form of distributivity (if you are in a union of two regions, and not in a region overlapping both, you are in the one or in the other). Zwarts and Winter (2000) argue that locations are best modelled as sets of directed vectors, since this will allow an elegant analysis of the semantics of measure modifiers in prepositional phrases, as in the examples in (19): (19) a. The bus stop is ten meters behind the house. b. The package is two meters inside the house. In the theory of Zwarts and Winter, prepositions denote functions from located objects into sets of directed vectors, and measure phrases such as ten meters/two meters in (19) express properties of those vectors. For the purposes of this paper, it is irrelevant whether locational PPs are modelled as sets of points (regions) or as sets of vectors, especially as Zwarts and Winter show that sets of vectors can be mapped onto sets of points in Cartesian space.8Zwarts (2017) suggests that a synthesis of both approaches may be most explanatory: some prepositions profit from being assigned a region semantics, others from a vector semantics, and even different uses of one and the same preposition may profit from having both interpretation strategies available. What is important is that locative PPs denotes sets of spatial entities, which allow us to model the spatial relations and account for the relevant entailments. We will thus assume that PP denotations are modelled as sets of points. We assume a model enriched with a set POINT of three dimensional points. Regions are privileged subsets of POINT. We do not require regions to be convex sets, i.e. it is not the case that for any two points p and p’ in a region P, all the points on the straight line joining them are also in P. This allows regions to have holes in them, as in (20), where the grey area might be the region defined by between the house and the fence (where the fence-region is the black area and the house-region is the white area): (20) However, we do require regions to form single individuable spaces. Discontinuous spaces do not usually count as single locations. This can be seen in locative PPs with plural complements. I put chocolate in the Christmas stockings requires a plurality of putting events such that each location inside a Christmas stocking is the goal of a separate put event. There is no available interpretation which asserts that there is a singular event with a single discontinuous location denoted by in the Christmas stockings, and which is satisfied if chocolate is put in one stocking. Similarly, if Goldilocks slept in the beds of the three bears, there have to be three different sleeping events, each one associated with a different location determined by each of the beds.9 A region then is a set of points P ⊆ POINT, such that any two points p and p′ in P are connected by a path. We define this as follows: We assume a type p for points, with as domain a set POINT of three dimensional points and we assume a domain TOP of sets of sets of points which forms a topological space, i.e. the sets in TOP are related by topological notions. (21) Let X ∈ TOP and x, y ∈ X. A path from x to y inside X is a continuous function f:[0,1] → X such that f(0) = x and f(1) = y. x and y are path-connected inside X if there is a path from x to y inside X. (22) a. A region r is a subset of points r ∈ TOP such that any two points x, y ∈ r are path-connected inside r. b. r, the type of regions, is a subtype of type , and its domain R is a subset of D, the set of regions in TOP. Zwarts and Winter (2000) assume that objects are assigned a location via a function at type > which applies to an entity in the domain D and maps it onto the set of points which the entity occupies, what Wunderlich (1991) calls their eigenplace.Kracht (2002) assumes a similar function and points out that it must be sensitive to temporal parameters, since individuals occupy different spaces at different times. We assume an eigenplace function locwt as in (23a): it is the function which assigns to an individual the region that it occupies at a particular world w and time t. We define a second function, scenewt, which is the eigenplace function for events: it maps an event onto the region where it takes place in w at t, as in (23b): (23) a. locwt: D → R The location of an individual at wt is a region in R. b. scenewt: E → R The scene of an event at wt is a region in R. Still following Zwarts and Winter, we assume that a locative preposition denotes a function from regions to regions. When a locative preposition such as under combines with a DP with an interpretation at type d, such as the table with interpretation |$\sigma$|(TABLE), the preposition meaning does not apply directly to the DP denotation, but to the set of points given by locwt(⁠|$\sigma$|TABLE). The operation locwt, mapping individuals onto their eigenplace is triggered by the mismatch between the interpretation of the DP (of type d) and the semantics of the preposition which must take a region as an argument:10 (24) the table → |$\sigma$|TABLE of type dunder → UNDER: R → R under the table → UNDER(locwt(⁠|$\sigma$|TABLE)) of type r Under the table denotes a region which is related in the UNDER way to the region occupied by the table at wt. We assume a second function indwt which maps a region r ∈ R onto the set of individuals whose location is a subset of r at t, and a parallel function, eventwt, which maps a region onto the set of events whose scene is a subset of r, as in (25): (25) a. indwt: R → pow(D)indwt(r) = λx. locwt(x) ⊆ r The individuals located inside r. b. eventwt: R → pow(E). eventwt(r) = λe.scenewt(e) ⊆ r The events located inside r. In The cat is under the table, the PP is a predicate of individuals of type . This interpretation is derived from (25) via the steps in (26): (26) the cat → |$\sigma$|CAT of type d under the table → UNDER(locwt(⁠|$\sigma$|TABLE)) of type rbe under the table → indwt[UNDER(locwt(⁠|$\sigma$|TABLE))] = λx. locwt(x) ⊆ UNDER(locwt(⁠|$\sigma$|TABLE)) of type The cat is under the table → locwt(⁠|$\sigma$|CAT) ⊆ UNDER(locwt(⁠|$\sigma$|TABLE)) In this case the PP under the table denotes a region, while, in order to apply to the subject, the copular predicate must denote a set of individuals of type . We assume that in this case the copula be triggers operation indwt, which resolves the mismatch, mapping the under-the-table region onto the set of individuals whose eigenplace is a subregion of that. The same PP is an adverbial event modifier in The cat slept under the table, only here the PP at type r shifts to a set of events: (27) under the table → UNDER(locwt(⁠|$\sigma$|TABLE))under the tableADV → eventwt[UNDER(locwt(⁠|$\sigma$|TABLE))]. = λe.scenewt(e) ⊆ UNDER(locwt(⁠|$\sigma$|TABLE)). The cat slept under the table → ∃e[SLEEP(e) ∧ Ag(e) = |$\sigma$|CAT ∧ scenewt(e) ⊆ UNDER(locwt(⁠|$\sigma$|TABLE))]. Note that this analysis easily deals with examples like (28). While the eigenplaces of the cat and the dog are clearly different, (28) asserts that they are both included in the same, bigger region. (28) The cat is under the table and the dog is under the table. So far, we have spelled out a semantics for locative predicates and modifiers which is relatively standard, a semantics in which PPs denote regions, or sets of points. We now extend this to the cases where the locative PP is neither a predicate as in (26), nor an adverbial as in (27), but an argument. Following the approach of Chierchia (1984, 1985) and Chierchia and Turner (1988), we propose that locative PPs are associated with two types of linguistic expressions, a predicative expression of type r (a subtype of ), where it denotes a set of points, and a saturated expression which denoted the individual correlate of the predicate PP. The two are related by the operations ∩ and ∪. We have assumed a domain of points, POINT, and a set of regions, R, the set of path-connected subsets of TOP. We will now enrich the domain POINT with a set L of locations, and we indicate the subtype of type p of locations as l. L is a set of individual correlates of regions. (This means that we allow predicates of type to be either predicates of three dimensional points, or predicate of locations, i.e. of type .) We assume, similar to Chierchia and Turner, the following two functions: (29) ∩: R → L is a one-to-one function from R into L.∪: L → R is a function such that for every r ∈ R: ∪∩r = r. As we saw above, a PP like under the table has an interpretation at the predicate type r, where it denotes a set of points, as in (30a). Under the table has second interpretation at the argument type l as in (30b), exemplified in the examples in (31): (30) a. under the table → UNDER(locwt(⁠|$\sigma$|TABLE)) ∈ R b. under the tablel → ∩UNDER(locwt(⁠|$\sigma$|TABLE)) ∈ L. (31) a. Under the table is a good place to hide →GOOD PLACE TO HIDE (∩UNDER(locwt(⁠|$\sigma$|TABLE))) b. Mary put the book under the table → ∃e[PUT(e) ∧ Ag(e) = MARY ∧ Th(e) = |$\sigma$|BOOK ∧ Goal(e) = ∩UNDER(locwt(⁠|$\sigma$|TABLE))] The main idea about individual correlates of properties, kinds, or here regions, relates to whatLandman (2006) calls ‘dual perspective intensionality’. On the one perspective, we relate an expression per world-time index to an object in a domain which is endowed with a part-of structure, in which this object is related to its parts and the objects it is part of. On the other perspective the expression is associated with an object which is, so to say, lifted out of that particular part-of structure, and is, so to say, more than the sum of its parts. Thus, a predicate has an interpretation as a function from world-time indices to sets of individuals, with an accessible part-of structure lifted from the sets. And it has an interpretation as a property, which is much more like a singular individual (or a function-in-intension), and which, as such stands in a different part of structure than the one lifted from sets, namely the sum-structures we find in domains of singular and plural objects. The function from world-times to sets then can be seen to represent what the property does in part-of structured domains. Similarly, followingCarlson (1977a,), a noun can have an interpretation where it denotes a kind, an object that is again like a singular individual. And it can be interpreted as a function that maps each world-time index onto the set of (singular or plural) instantiations of the kind, which is, once more, an interpretation inside a part-of structure. AsChierchia (1998a) shows, the operations of ∩ and ∪ can be easily interpreted via the operations on the part-of structures and the instantiation function in such a way that ∪ and ∩ have the required properties (like ∪∩P = P). The same perspective duality is proposed for locations here. Locations as regions are part of topological part-of structures, which is put to good use in the predicative and adjectival uses. In argument position, the denotation of locative PPs is, once again, more like an individual, with the part-of structure that is typical for domains of individuals (i.e. based on notions like singular and plural).11 Kracht (2002) shows that locations are time dependent. Since a table is a moveable object, under the table may denote a different set of points at time t and t’ depending on whether the table has been moved between t and t’. Accordingly, the connection is really between locations as singular individuals, and functions from world-time indices to regions, with the topology lifted from the regions. What if you want to go a step further, and actually, following the relation between kinds and instantiations of kinds, propose to base the theory directly on a relation between a location and the set of individuals whose region is part of the region corresponding to that location? The idea can be worked out quite simply, following what Chierchia (1998a) proposes for kinds and instantiations of kinds. However, there are problems with locations that make this suggestion less attractive here. Most importantly, many regions are ‘uninhabited’, they do not have any entities which are located in them. There may be many of these and since in all these cases for such a region r, λx.locwt(x) ⊆ r will be the empty set, two different empty regions would then by necessity be mapped onto the same location, and hence be indistinguishable by properties of locations. This is not the result that we want, since two empty regions may well give different truth values for a single property in the same world at the same time. Under the wooden table and under the plastic table denote different locations with different properties (Under the wooden table is a safe place to hide, but under the plastic table is not, since it might fall over on you.).12 The conclusion is that we need locations to be identified in terms of spatial entities and not in terms of the objects located there. Note that defining locations as sets of points from which sets of entities and sets of events can be derived via the functions in (25) reflects the fact that locative PPs have an adverbial function as well as an adjectival function, but that neither one is primary. In the next two sections, I will discuss two sets of data which support the suggestion that locatives can be interpreted at an individual type, separate from regions. In section 4 we discuss the relation between locative PPs and the noun place and in section 5 we discuss relative clauses. Predicates of locations: the noun place Chierchia and Turner (1988) point out that predicates allow self-application: predicates of individuals can apply to individual correlates, the borderline case being that a predicate applies to its own individual correlate. So far, the sorting of the theory does not allow anything like this for locations. That is, we have the interpretations in (32), and (32b) cannot apply to (32a) for type mismatch reasons: (32) a. in the boxarg → ∩IN(locwt(⁠|$\sigma$|BOX)) of type l b. be in the study → λx.locwt(x) ⊆ IN(locwt(⁠|$\sigma$|STUDY)) of type This only shows, however, that there is still something missing in the theory. If we have a locational predicate, we will want to be able to apply this to a locational argument PP, for instance in the examples in (33): (33) a. Speaker A: I found the book in the desk. You said it was in the study! Speaker B: Well, in the desk is in the study! b. Behind St Paul’s Cathedral and under London Bridge are both inside the boundaries of the City of London. The obvious way to deal with this is to assume, besides the type shifting operations indwt and eventwt from R into pow(D) and pow(E), a third type shifting rule, locationwt from R into pow(L) with the obvious semantics: (34) locationwt: R → pow(L)locationwt(r) = λl. ∪l ⊆ r. With this, we derive for (32a): (35) a. in the deskarg → ∩IN(locwt(⁠|$\sigma$|DESK)) of type l b. be in the study → locationwt(IN(locwt(⁠|$\sigma$|STUDY)) of type = λl.∪l ⊆ IN(locwt(⁠|$\sigma$|STUDY)) c. In the desk is in the study →. λl. ∪l ⊆ IN(locwt(⁠|$\sigma$|STUDY))(∩IN(locwt(⁠|$\sigma$|DESK))) = ∪∩IN(locwt(⁠|$\sigma$|DESK)) ⊆ IN(locwt(⁠|$\sigma$|STUDY)) = IN(locwt(⁠|$\sigma$|DESK)) ⊆ IN(locwt(⁠|$\sigma$|STUDY)) However, there are strict restrictions on what predicates can apply to locative PP subjects. Aside from locative PP predicates as in (33), predicates which take locative PP subjects are NPs headed by place. (36) a. In the chair is a comfortable place to sit/#a comfortable seat. b. Behind the sofa and under the table are two places/#spaces/?areas that need cleaning.13 This suggests that locative PP arguments can only be the external arguments of nominal predicates which select for them and not for standard predicate nominals at type , which denote sets of individuals.14 On the assumption that locative PP subjects are individuals at type l, predicates headed by place are naturally analyzed at type . As we already noted, place is not unambiguously interpreted at type , but also has a use at type , as can be seen from examples like We went to visit his new place, or. I would never have recognized this place after the renovation. However, this ambiguity of place is irrelevant for (36): what is important is the fact that locative PPs do not satisfy the external argument of NPs at type , but do satisfy the external argument of place nominals. Support for the claim that place has an interpretation at type comes from the distribution of generalized quantifiers in which the nominal complement of the quantifier is headed by place. Individuals at type α and generalized quantifiers at type <<α,t>,t;> are of the types associated with argument position (Partee 1987). This predicts that generalized quantifiers over locations at type <,t>, but not generalized quantifiers at type <,t>, can appear in the positions in which locative PPs at type l can also appear. If place is a predicate at type , generalized quantifiers restricted by place-headed nominals should be of type <,t> and should be able to replace PP arguments where other generalized quantifiers cannot. Example (37) is an attested example with an every place nominal as a sentential subject with a locative PP predicate: (37) Every place I lived was on a tree-lined street or near a small forest. [www] However, because place is ambiguous between an and a expression, the subject in (37) is in principle also ambiguous between a generalized quantifier at type <t> and one at type <,t>. Clear examples of <,t> expressions are found in internal arguments of verbs like put, hang, leave and live, which, as argued in section 2, select for locational PPs. (38) shows that the second internal argument of put/leave is a locative PP, as discussed earlier, and that the preposition is obligatory: (38) a. Mary put/left a pamphlet #(in) every mailbox John indicated. b. Mary put/left a pamphlet #(in) every mailbox John indicated. c. Mary put/left a pamphlet #(in) the three mailboxes John indicated. . In contrast, as (39) shows, bare DPs headed by place can replace the locative PP argument.15 The data in (40) replicate the contrast in the complement of live and hang respectively: (39) a. Mary put/left a pamphlet every place John indicated. b. Mary put/left a pamphlet the three places John indicated. (40) a. I have lived in every city John has lived in. b. #I have lived every city (that) John has lived (in). c. I have lived every place John has lived. d. Mary hung a poster on every billboard. e. #Mary hung a poster every billboard John suggested. f. Mary hung a poster every place John suggested. (41) shows that only bare place DPs replace locative PP adverbials, as first noticed in Larson (1985): (41) a. Mary took a photograph every place the coach stopped. b. #Mary took a photograph every city the coach stopped. These bare NP adverbials are similar in many ways to the bare NP adverbial quantifiers over events, illustrated in (42), and first discussed in Rothstein (1995): (42) Mary took a photograph every time the coach stopped. Crucially, (41a) and (42) are not truth-conditionally equivalent. (42) asserts that there was at least one event of photo taking for each event of the coach stopping, while (41a) asserts that there was at least one event of photo taking in each place that the coach stopped. Suppose the coach we are talking about is on a tour of South Holland, and it stops five times: in The Hague, in Delft, in Leiden, then again in Delft, and finally in Rotterdam. This trip involves five events of the coach stopping, but only four different places. (42) requires Mary to take photograph in at least five places, one corresponding to each of the stops the coach makes. (41a) only requires Mary to take four photographs, one each in The Hague, Delft, Leiden and Rotterdam. We return to the semantics of these examples in some detail in section 7, but in the meantime the contrast between (41a) and (42) adds to the evidence that the every place quantifiers make direct reference to individual locations rather than to properties of individuals or events. While the examples above are all constructed so as to be able to stress the minimal contrasts, examples of bare place nouns in these kinds of constructions are easy to find on the web. The following selection includes place nouns as complements of a universal quantifier, of any and of cardinals. Other examples are easy to find: (43) a. Your customers are looking for this information so do not make them dig for it, put it every place they could possibly look so they'll see it right away. [www] b. I never lived any place where you could work up a sweat in November. [www] c. I've lived three places since moving to DC 5 years ago, all of them scattered about Capitol Hill. [www] These data clearly support the hypothesis that place-based nominal DPs can replace locative PPs in both argument and adverbial expressions. If locative PP arguments denote locations at type l and place denotes sets of locations at type , these data fall out automatically. In the following section we look at data from relative clauses which further support this hypothesis, after which, in section 6, we will look more closely at the semantic analysis of place. Relative clauses and missing complementizers So far, we have seen that PPs can occur both as arguments and as predicates. We have argued that the natural explanation for this is given by the analysis of the relation between argument and predicate PPs in the framework of property theory. Since locative PPs of the predicate type denote sets of spatial entities (in this account, regions at type r), locative PPs at the argument type will denote the individual correlates of these regions, locations at type l. And the theory is that locations are of a different sortal type from ‘ordinary’ individuals, which are of type d. This section presents an analysis of null complementizers in relative clauses which supports this. We begin with the standard relative clause interpretation. Externally headed restrictive relative clauses are standardly assumed to be intersective modifiers (Partee 1975). Relative clauses headed by which and who are of type , and modify nouns that are also of type . If the complementizer is who, then the noun modified must be [+animate], and usually [+human]. In a relative clause, the trace marks a variable, and an abstraction operator at the place of the syntactic wh- expression or that binds the variable translating the trace (Partee 1975) as in (44): (44) a. The book [whichi Mary read ti] b. book which Mary read → λx.BOOK(x) ∩ λx.∃e[READ(e) ∧ Ag(e)=MARY ∧ Th(e)=x] = λx.BOOK(x) ∧ ∃e[READ(e) ∧ Ag(e)=MARY ∧ Th(e)=x] Since the trace in (44b) is the direct object of read, it must be of type d, and the whole relative clause is of type , denoting the set of objects which Mary read. The interpretation of the relative clause and that of the head noun book combine via intersection to give as the interpretation of (44b) the set of books which Mary read. Since both the head noun and the relative clause are of type , modification is no problem. If the trace fills a position where we would expect to find a locative, and the trace is bound by where, then the relative clause should denote a set of locations: (45) a. The shelf [wherei John put the book ti] b. The shop [wherei John met Mary ti] In (45a), the trace is in a locative argument position, and in (45b) it is in locative adjunct position. By analogy to (44), if the trace fills a locative argument and is of type l, we would expect the relative clause to be of type , with a denotation as in (46): (46) λl. ∃e [PUT(e) ∧ Ag(e) = JOHN ∧ Th(e) = |$\sigma$|BOOK ∧ GOAL(e) = l] The set of places where John put the book This leads to an immediate problem of type mismatch. The relative clause is of type , but the noun shelf that it modifies is of type , so modification via set intersection is impossible. Note that the mismatch can be avoided by using (47): (47) a. The shelf [on whichi John put the book ti] b. The shop [in whichi John met Mary ti] In the examples in (47), the trace is an individual level trace bound by a which complementizer and the relative clause is of type , as in (48). Intersective modification of the heads shelf and shop proceeds without problem: (48) a. λx.SHELF(x) ∩ λx.∃e[PUT(e) ∧ Ag(e) = JOHN ∧ Th(e) = |$\sigma$|BOOK ∧ GOAL(e)= ∩ON(locwt(x))] b. λx.SHOP(x) ∩ λx.∃e[MET(e) ∧ Ag(e) = JOHN ∧ Th(e)=MARY ∧ scenewt(e) ⊆ IN(locwt(x))] In contrast, in (45) there is a type mismatch. This mismatch is resolved by type-shifting the modifier to type . The asymmetric relation between modifier and head means that the modifier shifts to match the head rather than the other way around.16 The relative clause denotes a set of shelves such that the goal of an event of putting the book is a location appropriately related to the shelf. The shift operation, given in (49), makes use of the locwt function. Ploc is a variable over locative preposition meanings which maps the location of x onto an appropriately related location. Given the paraphrase in (47), the default relation is on for (45a) and in for (45b). The choice of default relation is determined by the form of the object. For container-type entities, the natural default Ploc is in. Since shelves are not normally containers, the natural relation is on. Non-default relations are specified using the form in (47) (e.g. the shelf under which I hid the gift). (49) SHIFT: → < d,t> SHIFT[α] = λx.∃l [α(l) ∧ ∪l = Ploc(locwt(x))] (49) allows us to resolve the mismatch in (45a): (50) shelf where Mary put the book →SHELF ∩ SHIFT[λl. ∃e[PUT(e) ∧ Ag(e) = MARY ∧ Th(e) = |$\sigma$|BOOK ∧ Goal(e) = l]] = SHELF ∩ λx.∃l∃e[PUT(e) ∧ Ag(e) = MARY ∧ Th(e) = |$\sigma$|BOOK ∧ Goal(e) = l ∧ ∪l = Ploc(locwt(x))]. = λx.SHELF(x) ∧ ∃l∃e[PUT(e) ∧ Ag(e) = MARY ∧ Th(e) = |$\sigma$|BOOK ∧ Goal(e) = l ∧ ∪l = Ploc(locwt (x))]. = λx.SHELF(x) ∧ ∃l∃e[PUT(e) ∧ Ag(e) = MARY ∧ Th(e) = |$\sigma$|BOOK ∧ Goal(e) = l ∧ ∪l = ON(locwt (x))]. = λx.SHELF(x) ∧ ∃e[PUT(e) ∧ Ag(e) = MARY ∧ Th(e) = |$\sigma$|BOOK ∧ ∪Goal(e) = ON(locwt (x))]. The set of (singular) shelves which have the property that there is an event of Mary moving the book to the location that corresponds to the ON-region of the. eigenplace of that shelf. The shift allows us to specify the properties of the location argument of put in terms of its relation to entities which satisfy the head noun shelf. The interpretation of (45b) involves the same shift: (51) shop where John met Mary → SHOP ∩ SHIFT[λl.∃e[MEET(e) ∧ Ag(e)=JOHN ∧ Th(e)=MARY ∧ scenewt(e) ⊆ ∪l]] = SHOP ∩ λx∃l∃e[MEET(e) ∧ Ag(e) = JOHN ∧ Th(e) = MARY ∧ scenewt(e) ⊆ ∪l ∧ ∪l = Ploc(locwt(x))]. = λx.SHOP(x) ∧ ∃l∃e[MEET(e) ∧ Ag(e) = JOHN ∧ Th(e) = MARY ∧ scenewt(e) ⊆ ∪l ∧ ∪l = Ploc(locwt (x))] = λx.SHOP(x) ∧ ∃e[MEET(e) ∧ Ag(e) = JOHN ∧ Th(e) = MARY ∧ scenewt(e) ⊆ IN(locwt(x))]. This is the set of (singular) shops, which have the property that there is an event of John meeting Mary and the scene of e is included in region inside that shop. Note that the expression derived in (51) no longer contains the location variable l. That just means that the truth conditions of a sentence containing the expression shop where John met Mary can be expressed by making reference to regions rather than locations. Be that as it may, the grammatical derivation goes via locations. Resolution of the type mismatch is apparently connected to the presence of the complementizer. In the examples in (52), the wh-complementizer has been dropped. (52a/b) are grammatical with either that or with no complementizer at all, while (50c/d) are infelicitous with either that or with a null complementizer: (52) a. The book [Øi/that Mary read ti] was very interesting. b. The shop [Øi/that Mary visited ti] is open till 7pm. c. #The shop [thati John met Mary ti] is open till 7pm. d. #The shop [Øi John met Mary ti] is open till 7pm. To make (45b) felicitous, we have to add the wh-complementizer, as in (45b). alternatively, the wh-complementizer can be dropped in non-pied-piped contexts like (53): (53) The shop [Øi John met Mary in ti] is open till 7 pm.. At first sight, this looks like an argument/adjunct asymmetry, since the relative clause modifying the head shop apparently requires a wh-complementizer when the trace is in adjunct position (52c/d, 53), but not when it is in argument position (52a/b). However, this is not the case. In (54), wh-complementizer where binds a trace in locative argument position, but it cannot be deleted: (54) a. the shelf [where1 Mary put the book t1] b. #the shelf [Ø1 Mary put the book t1] c. #the shelf [that1 Mary put the book t1] However, there is no general ban on complementizer deletion with locative variables. (55) shows that the complementizer can been deleted when a locative trace fills either an argument position (as in 55a) or an adjunct position (as in 55b), as long as the nominal head that the relative clause modifies is place: (55) a. the place [Øi Mary put the book ti] b. the place [Øi John met Mary ti] These data suggest that the possibility of dropping where depends neither on the sortal type of the variable nor on the argument versus adjunct status of the trace in the locative relative clause itself, but on the relation between the modifier and the head that it modifies.17 Assuming, following the arguments in the previous sections, that place is a predicate of type , then in (55), the type of the head and the type of the relative clause are both of type . This suggests that the wh- complementizer can be deleted when the relative clause modifier is of the same sortal type as the head that it is modifying. In that case, the interpretation is straightforward. No shifting is necessary, and the result of modifying place by a relative clause at type gives back the original relative clause interpretation: (56) place Mary put the book → λl.PLACE(l) ∩ λl. ∃e[PUT(e) ∧ Ag(e) = MARY ∧ Th(e) = |$\sigma$|BOOK ∧ Goal(e) = l]. = λl.PLACE(l) ∧ ∃e[PUT(e) ∧ Ag(e) = MARY ∧ Th(e) = |$\sigma$|BOOK ∧ Goal(e) = l]]. = λl. ∃e[PUT(e) ∧ Ag(e) = MARY ∧ Th(e) = |$\sigma$|BOOK ∧ Goal(e) = l]. The set of locations which are the goal of an event of Mary putting the book there. (57) place John met Mary → λl.PLACE(l) ∩ λl.∃e[MEET(e) ∧ Ag(e) = JOHN ∧ Th(e) = MARY ∧ scenewt(e) ⊆ ∪l]. = λl.PLACE(l) ∧ ∃e[MEET(e) ∧ Ag(e) = JOHN ∧ Th(e) = MARY ∧ scenewt(e) ⊆ ∪l]. = λl.∃e[MEET(e) ∧ Ag(e) = JOHN ∧ Th(e) = MARY ∧ scenewt(e) ⊆ ∪l]. The set of locations which include the scene of an event of John meeting Mary. This generalization accounts for the absence of the wh-complementizer in (52a/b) and (53), as well as in (55) and for the infelicity of (52c/d). Further minimal contrasts which support this hypothesis are given in (58), where place, but not nouns, allow for a null complementizer: (58) a. The exact place Øi van Gogh painted the picture ti is unknown. b. #The exact field Øi van Gogh painted the picture ti is unknown. c. #The exact location Øi van Gogh painted the picture ti is unknown. These data are summed up in Table 1. Table 1 N head type . relative clause type . relative clause gap . Complementizer . Examples . argument optional (52a/b) adjunct obligatory (52c) argument obligatory (54) argument optional (55a) adjunct optional (55b) N head type . relative clause type . relative clause gap . Complementizer . Examples . argument optional (52a/b) adjunct obligatory (52c) argument obligatory (54) argument optional (55a) adjunct optional (55b) Open in new tab Table 1 N head type . relative clause type . relative clause gap . Complementizer . Examples . argument optional (52a/b) adjunct obligatory (52c) argument obligatory (54) argument optional (55a) adjunct optional (55b) N head type . relative clause type . relative clause gap . Complementizer . Examples . argument optional (52a/b) adjunct obligatory (52c) argument obligatory (54) argument optional (55a) adjunct optional (55b) Open in new tab Note that we do not have entries for relative clauses at type with a trace in adjunct position, since adjuncts are never of this type (whatever the type of the head). We also do not have an entry in the table for an head with a < d,t> relative clause where the trace is in argument position, as in the place (which) Mary bought. Since place also has a reading at type , the relative clause can modify it straightforwardly on that analysis. Notice that where cannot replace which in this example since bought requires a theme argument at type d. The generalization suggested by these data is given in (59): (59) Sortal Congruence Generalization (SCG) A null complementizer is allowed in a restrictive relative clause when the relative clause is of the same sortal type as the head it is modifying. An explicit wh-complementizer is obligatory when the relative clause shifts to a sortal type where it can modify the head noun. A natural explanation of the SCG is that when the head and the relative clause are not of the same sortal type and the relative clause shifts in type to allow modification, the wh- classifier is obligatory in order to keep track of the original type of the relative clause.18 Clearly, we would want the SCG to hold beyond the domains of individuals and locations. An investigation of relative clauses in other domains supports the generalization. The first set of relative clauses that support the SCG are event relatives discussed in Rothstein (1995), illustrated in (60): (60) a. Mary opens the door, every time the bell rings. (Rothstein 1995, example 39) b. Every time I drink whisky, I drink Laphroaig. (60a) asserts that every event of the bell ringing corresponds to a different event of Mary opening the door, while (60b) asserts that every event of my drinking whisky is an event of my drinking Laphroaig (a particular kind of Scotch). Rothstein argues that the quantifiers in (60) are quantifiers over events. Time does not make reference to a temporal domain, but denotes the domain of events E and the relative clause restricts the domain to a particular set of events.19 Rothstein gives the semantic interpretation in (61) for the relative clauses. Since the head time denotes a set of events, the intersection of time with the meaning of the relative cause will return the original meaning of the relative clause, which will then be the restriction on every: (61) a. λe.DRINK(e) ∧ Ag(e) = I ∧ LAPHROAIG(Th(e)) The universal quantifier in (60b) then binds the event variable in the main clause as well, thus the sortal type of time at type and the relative clause at type match: (62) ∀e[DRINK(e) ∧ Ag(e) = I ∧ WHISKY(Th(e)) → DRINK(e) ∧ Ag(e)=I ∧ LAPHROAIG(Th(e))] Every event of my drinking whisky is an event of my drinking Laphroaig. (The interpretation of (60a), which is the focus of Rothstein's 1995 paper, is more complex, and we will have more to say about it in section 7. The added complexities are not relevant at this stage. See also footnote 24.) There is no wh-word heading the relative clauses in (60), nor, according to the SCG, is there any need for one, since the sortal types of time and the relative clause match. Rothstein (1995) claims that time is the only lexical item which denotes the domain of events, and that near synonyms such as occasion as well as apparently event-denoting nouns such as party, performance and so on, in fact are of type and cannot be modified by event predicates because of a type mismatch, as (63) shows: (63) a. #Every occasion the bell rang, Mary opened the door. b. #Every party I drank whisky, I drank Laphroaig. While the SCG predicts that the sortal mismatch should be ‘saved’ by an explicit wh-word, there is no wh-word which binds event variables which is parallel to where in the locative domain. When is a candidate, given the parallelism in (64): (64) a. The cat sleeps wherever she can. b. The cat sleeps whenever she can. However, when as a wh-question and a wh-complementizer binds a temporal variable, and relative clauses headed by when will not be of the same sortal type as time, correctly predicting the infelicity of #every occasion when I drank whisky/#every party when I drank whisky. Sortal mismatches, though, can be resolved in the same way as in (47), repeated here as (65), using PP complementizers where the P governs which: (65) a. The cupboard [in whichi John put the book ti] b. The shop [in whichi John met Mary ti]. (66) a. Every occasion on which the bell rang, Mary opened the door. b. Every party at which I drank whisky, was a party I enjoyed. Here occasion and party of type are modified by relative clauses where the variable is bound by which and must thus also be of type . As the SCG predicts, when the preposition is stranded and governs the trace of type d, a null complementizer is possible, since the relative clause and the head are of the same type: (67) Every party I drank whisky at was a party I enjoyed. The second relevant construction involves manner phrases which, like locatives, occur as arguments (as in 68a/b) and as adverbials (as in 68c/d): (68) a. The way he painted the house surprised me. b. Every way she entertained the children was a success. c. John tried to open the window every way he could: with a screwdriver, with a hammer and with a knife.d. She solved the problem every way the teacher asked her to. Way has a privileged position in relation to manners which parallels the role of time and place in the grammar, restricting the domain of the quantifiers and definite determiner in (68) to expressions of manner. In the examples in (68) there is no explicit wh-word heading the relative clause, suggesting that the sortal type of the relative clause and way match. I assume that manners are properties of events at type , so that with a screwdriver denotes the set of events which are carried out with a screwdriver.20 Extending Chierchia and Turner's (1988) account to properties of events would suggest that manners at type can be associated with an individual correlate: i.e. λe.MANNER(e) = ∩WITH A SCREWDRIVER(e). Way would denote the set of such individual correlates. Predictably, replacing way by a different noun, like manner itself, results in infelicity: (69) #The manner he painted the house surprised me. There is a wh-word, how, which is used to question manners, as in How did you open the window? How did you solve the problem? But, how is not used as complementizer in relative clauses and thus cannot be used to resolve the sortal mismatch, and #the manner how he painted the house is infelicitous. The sortal mismatch can only be resolved by using PP complementizers as in (70a). PP stranding is possible, though it is restricted for independent reasons (Hornstein and Weinberg 1981). When it is possible, and the relative clause has a trace of type d, the null complementizer is again possible (as in 70b): (70) a. The manner in which he painted the house surprised me. b. The manner he spoke in surprised me. This is not the place to speculate on why there is no lexical complementizer for restrictive relatives modifying time (on its event reading) and way, but it is worthwhile pointing out that both these kinds of relatives denote predicates in the domain of events. Restrictives modifying time denote sets of events at type . As expressed above, manner adverbials plausibly denote properties of events (e.g. with a hammer as the set of events which were carried out with a hammer as instrument). Possibly, English lacks lexical items expressing relative clause operators binding variables in the domain of events and related domains. In the absence of such lexical operators, the SCG requires one of two things: -Either a sortal match between the head and the relative, which can be effected by using the appropriate domain sortal as the nominal head, or by using either pied-piped P + which complementizers; -Or a stranded preposition to resolve the sortal mismatch. A different challenge to the SCG is posed by amount relatives (Carlson 1977b, Heim 1987, Grosu and Landman 1998 and others), as in (71): (71) a. It will take us the rest of the year to drink the wine that there was at the party last night. b. It will take us the rest of the year to drink the wine that they drank at the party last night. c. It will take us the rest of the year to pay for the wine that there was at the party last night. Amount relatives come in two kinds: their interpretations can involve identity of substance or identity of amount. (71a) is ambiguous between both readings: the most obvious reading of (71b) is the identity of amount reading (it will take us the rest of the year to drink as much wine as there was at the party), but an identity of substance reading is also possible (we ordered lots of wine for the party, but everyone drank sparkling water, so all the wine was left over and it will take us a long time to drink all of it). (71b) has an obvious identity of amount reading: what it will take us the rest of the year to drink is not the actual wine-substance that they drank at the party last night (it has already been drunk), but wine equal in quantity to the wine that they drank at the party. The identity of substance reading is most plausible in (71c)—what we need to pay for is the actual wine that there was at the party last night. (71c) must be an amount relative and not a simple relative of type , because the trace appears in the subject position of a there-sentence, where individual traces cannot occur (as argued by Carlson 1977b, Heim 1987, and Grosu and Landman 1998). Thus it contrasts with It will take us the rest of the year to pay for the wine that they drank at the party. The latter also has an identity of substance reading, but there is no reason to treat the relative as anything other than a simple restrictive relative at type . The interpretation of the relative clause that there was at the party is usually assumed to be something like (72). The trace in the relative clause is analysed as a degree variable, with different analyses giving different accounts of what a degree is. We use a (for ‘amount’), as a variable over amounts/degrees: (72) [λx.WINE(x)] [λa. there was a-much at the party] (72) looks as if there is a sortal mismatch, which needs to be resolved. Resolving it into two predicates of amounts gives the identity of amount reading, while resolving it into two predicates at type gives the identity of substance reading. For us the problem is that on this analysis the SCG would predict, wrongly, that a complementizer should be present in (72). Recent work by Scontras (Scontras 2017) suggests that the sortal mismatch can be resolved without requiring a shift in the sortal type of the relative clause. Scontras treats amounts/degrees as nominalized properties, analogous to the way in which Rothstein (2013, 2017) treats numbers. He argues that degrees share properties with kind terms, and thus should be treated as nominalizations of sets of entities (or portions of substances) which instantiate a kind and which have a certain measurement. (73) is a simplified version of Scontras’ semantics for degrees (Scontras 2017, example 39): For Scontras, a degree is the nominalization of a complex measure property, as expressed in (73a): the property corresponding to the set of objects that have a defined measure value and instantiate some kind. The denotations of three litres and three litres of wine are properties corresponding to sets where number and kind are specified (for details see Scontras 2017): (73) a. degree: ∩λx.∃n∃k[MEASUNIT(x) = n ∧ ∪k(x)] The property of having a defined measure value and instantiating some kind b. three litres:∩λx. ∃k[MEASLITRE(x) = 3 ∧ ∪k(x)] The property of measuring three litres and instantiating some kind c. three litres of wine∩λx. MEASLITRE(x) = 3 ∧ ∪WINE(x) The property of measuring three litres and instantiating the kind wine Deriving the identity of amounts reading in (71b) is straightforward in Scontras’ theory. The trace in the relative clause in (72) is a degree variable, and if it is bound by a null operator, the relative denotes a set of degrees or amounts: (74) a. that they drank at the party → λa. a = ∩λx.∃n∃k[MEASUNIT(x) = n ∧ ∪k(x)] ∧ they drank a-much at the party. b. wine → λa.a = ∩λx.∃n[MEASUNIT(x) = n ∧ ∪WINE(x)] c. wine that they drank at the party → λa.a = ∩λx.∃n[MEASUNIT(x) = n ∧ ∪WINE(x)] ∩ λa.a = ∩λx.∃n∃k[MEASUNIT(x) = n ∧ ∪k(x)] ∧ they drank a-much at the party. = λa.a = ∩λx.∃n[MEASUNIT(x) = n ∧ ∪WINE(x)] ∧ they drank a-much at the party On this analysis, there is no sortal mismatch, and hence modification is straightforward. Note that even if the interpretation of wine as amounts of wine involves type-shifting, the relative clause does not shift in type, and thus no complementizer marking its original type is required. The identity of substance reading in (71a/c) requires shifting the set of degrees to a set of entities at type . Scontras does this via an operation of existential modification which shifts a predicate of degrees into a predicate of individuals, as in (75), using a version of derived kind predication. The result of shifting a degree is the set of individuals which instantiate that degree: (75) λa.∃y[[∪aon-table](y)] ⇒ λx.∃a′[(λa.∃y[[∪aon-table](y)])(a′) ∧ [∪a′](x)] Scontras assumes that the operation in (75) is part of the modification operation relating the relative clause to the head. However, crucially, this kind of shift to identity of substance reading is derived only in existential contexts.21 It is thus reasonable to assume that the shift is triggered by the existential context itself, since existential there is generally assumed to induce existential quantification over predicates at type . If so, the type shift from to will occur within the IP (the sentence), and there will be no sortal mismatch between the relative clause and the nominal head. The SCG captures an important property of wh-complementizers: they are obligatory when there is a sortal mismatch between the relative clause modifier and the sortal head, and the relative needs to shift its sortal type in order to modify the head. Relative clauses with null complementizers are allowed when there is no sortal mismatch. As we have seen, potential sortal mismatches can be avoided in a number of ways. These include utilizing P + which complementizers or choosing a nominal head such as place, time, or way which matches the type of the relative clause, denoting sets of locations, events or manners respectively. In the next section, we look more closely at the semantics of place. Place as a domain sortal In the previous sections we have collected evidence that place is an expression of type denoting a set of locations. However, it differs from other sortal nouns. Sortal nouns (usually at type ) denote subsets of the domain of individuals, e.g. cat denotes the subset of the domain of individuals whose members are all the cats. It thus contains information about what kind of entities in the domain of individuals are members of that set. Place, in contrast, indicates that the denotation of the NP it heads is a set of locations, but beyond that, it does not give any information specifying a subset of the set of locations. Place is thus a domain sortal, indicating the sortal type of the predicate it heads, i.e. it just indicates that its denotation is the set of locations L. This is why, when it restricts every, it usually occurs with either an explicit modifier or a contextual restriction, as in (76): (76) a. I performed every place#(that had a comedy night). [www] b. He wanted to know where we had hidden the treasure, and I showed him the place (= the place where we had hidden the treasure). Place here is similar to the noun time in (60), which Rothstein (1995) argues is a domain sortal at type , denoting the domain of events E, the grammatical function of time being just to indicate that the NP it heads denotes a subset of the set of events. Time similarly requires either explicit or contextual modification, as is shown by the unnaturalness (out of the blue) of sentences like:? John won every time versus John won every time we played Monopoly, which is fine. Another candidate for a domain sortal is way, in the domain of manners, which requires the same kind of contextual restriction. Yet another possible candidate is thing, as a domain sortal for the domain , but discussion of this would take us too far beyond the scope of this paper. A characteristic of domain sortals is that they apply to all and only entities of the relevant type (for events and locations, this is type e or type l respectively) and they thus yield either the value “true” or “undefined”. We now consider the semantics of domain sortal place. Place and noun phrases headed by place must be of type since they denote sets of individual correlates of locations. Individual correlates at type l are individual correlates of regions, sets of points, which are the denotations of locative expressions at the predicate type. These predicate denotations overlap spatially, as we can see from examples like The cat is sitting in the garden under the tree. The set of individual correlates of locations will thus also be a set of overlapping entities. Place, however, has all the grammatical properties of a count noun. It can be the complement of cardinals and count determiners such as every as in (43a/b) and (77a/b/c). It can also be the antecedent of a reciprocal. (77a-d) are attested examples; in (77e), which is constructed, places is the only possible antecedent for the reciprocal since fertiliser is a mass noun: (77) a. The washer dispenser has three places to put detergents and softener. [www] b. The three places rents are actually falling! [www] c. Leave some every place you go! [www] d. We went every place they suggested… [www] e. I put the fertiliser every place you suggested, none of them near each other. Following the accepted position that singular count nouns denote sets of atomic, disjoint elements (Krifka 1989, Chierchia 1998b, 2010, Rothstein 2010, Landman 2011), place, as a count noun, cannot denote the set L of locations, since individual correlates of overlapping regions will be overlapping. Instead, place must denote a contextually determined set of non-overlapping locations which count as single locations relative to that context. As we can see from the data, when we count places, we indeed count non-overlapping locations. In (78a), three places has a locative interpretation, since it is modified by a relative clause in which the null operator Ø binds a trace in locative adjunct position (78b): (78) a. We visited three places Queen Elizabeth I slept. b. places [Øl [Queen Elizabeth I slept ti]] (78a) is true only if we visited three places not contained within each other. I cannot use (78a) to assert that we visited the bedroom that Queen Elizabeth I slept in, the inn that the bedroom was in and the village that the inn was located in. Similarly, if I visited an inn where Queen Elizabeth I slept at point X, it is false that I visited three places where she slept, even if X belongs to three different, well defined, but overlapping regions: (79) What counts as a single place is context dependent. Suppose we are on a tourist bus which stops at various villages. When it stops the first time, John gets off the bus and takes three photos of different views of the village. We can describe this both by (80a) and by (80b): (80) a. John took three photos the first place the bus stopped. b. John took photos three different places in the village. If we are thinking of the village where the bus stopped as one place, then (80a) is accurate, while if we are defining locations in a much more fine-grained way, (80b) is more appropriate.22 What counts as a single place, then, differs in different contexts and must be defined in a context-dependent way. Rothstein (2010) argues that all count nouns are interpreted relative to a counting context, and we can adapt that framework to give a semantics for place. Rothstein (2010) points out that for many count nouns, what counts as one instance of N is context determined. This is illustrated with so called ‘homogeneous count nouns’ like fence and wall, where two fences can be put together to make a single fence, but the observation holds for a much wider variety of nouns including sequence (Krifka 1989), bouquet and stone. In Rothstein’s account, the context-dependence of the choice of atomic countable parts of the objects in the denotation of N is encoded in the count noun meaning. While mass nouns are simple predicates at type , count nouns are indexed for the counting context k relative to which their atomic elements have the property of being ‘one’: in Rothstein’s analysis a count noun N is interpreted as a set Nk, of type , a sets of pairs where x is an object and counting context k determines the cardinality of x relative to Nk. We propose a similar context-dependent analysis of place. Let k be a counting context, as defined in Rothstein (2010), and let R be the set of regions. We assume that counting context k determines a (contextual) partition Rk of the contextual space, a contextually chosen set of regions in R that make up the contextual space, but do not overlap. (81) Placek → PLACEk = λl. ∃r ∈ Rk[l = ∩r] of type Placek denotes the set of locations of type l which are the individual correlates of the sets in Rk. The choice of context k of Rk determines the disjoint set of places, since the disjointness of members of place is inherited from the disjointness of the sets in Rk. Placek, thus determines a set of contextually determined individual locations each of which counts as one separate location in the relevant context. Bare nominal locative adverbials As we have seen, place nominals occur not only in argument position, but also as adverbials. In this final section, we will discuss the interpretation of these adverbials, and outline a way to integrate them into a general account of so-called “Bare NP adverbials”,23 discussed first in Larson (1985), later in Emonds (1987) and, more recently, in Barrie and Yoo (2017). Larson (1985, example 1) draws attention to adverbials such as the ones in (82): (82) a. I met John that day. b. I saw John some place you would never guess. c. John was heading that way. d. Mary pronounced my name every way imaginable. What characterizes these bare NP adverbials is that they occur where PP adverbials normally occur, as in (83), but while the examples in (82) are felicitous, the prepositional head of the adverbials in (83) is obligatory. (83) a. I met John #(on) December 12, b. I met John #(in/at) the British Museum. c. Mary pronounced my name #(with) a heavy French accent. The bare locative adverbials such as (84), which we discussed briefly in Section 4, fit naturally into the class illustrated in (82): (84) a. Mary took a photo every place the coach stopped. b. Mary took a photo the three places the coach stopped. c. #Mary took a photo the three villages/locations the coach stopped. Larson (1985), Emonds (1987) and Barrie and Yoo (2017) propose explanations for why the preposition in (81) is not necessary. Larson argues that prepositions are Case-assigning operators, and suggests that a limited class of nouns, including place and day, are lexically specified as having a feature which allows them to assign abstract oblique case. As a result “certain NPs have the capacity to receive Case and thematic roles through the lexical properties of their own heads” (Larson 1985, p. 595). Emonds (1987) and Barrie and Yoo (2017) argue that place nominals are inherently marked with a locative thematic role (rather than Case), but they essentially follow the same line of thought as Larson. A different approach to bare NP adverbials is presented in Rothstein (1995), who analyzes examples like (85), where the adverbial is a bare NP quantifier over events, as discussed in sections 4 and 5: (85) a. Mary took a photograph every time the coach stopped. (= example 42) b. John opened the door every time the bell rang. Given the similarity between the bare event adverbials in (85) and the bare locative adverbials in (84), it is natural to explore whether the semantic explanation for the first will extend to the second. It turns out that it does so straightforwardly. Rothstein (1995) focused on the scopal properties of adverbial event quantifiers, which take wide scope over the existential quantifier binding the event argument. (85a) asserts that different events of taking a photo can be associated with the various places in which the coach stopped. Not only does the quantifier take wide scope, but the truth conditions involve what Rothstein calls a ‘matching’ effect: “X occurred every time Y occurred” is true if there were at least as many X events as Y events; in other words, it is true if there was a different X event for every Y event. Thus (83a) asserts that a different photo-taking event is associated with each event of the coach stopping. This is not a pragmatic effect derived from the aspectual properties of photo taking events, as we can see from (86a), which requires a different event of making a video to be associated with each event of the coach stopping, even though one continuous video could be made that records the whole trip, including all the stops. The matching effect is associated with the adverbial, as we see from the contrast with (86b), where the quantifier is in argument position as the complement of made a video or filmed, and where both wide and narrow scope readings are possible. Indeed, the wide scope reading of the indefinite, with Mary making a single video which covered all the stopping places, may even be the preferred reading: (86) a. Mary made a video every time the coach stopped. b. Mary made a video of/filmed every time the coach stopped. The analysis in Rothstein (1995) captures the matching effect by positing a matching function M, which maps photo-taking events onto events of the coach stopping:24 (87) a. Mary took a photo every time the coach stopped. b. ∀e[THE COACH STOP(e) → ∃e′[MARY-TAKE-A-PHOTO(e′) ∧ M(e') = e]] The matching effect follows from the conjunction of two facts: (i) M is a function, mapping each event of Mary taking a photo onto an event of the coach stopping (which means that the range of M is a subset of the set of coach stopping events). (ii) The universal quantifier binds the variable which is the value of the matching function M, i.e. each event of the coach stopping must be in the range of the M-function. This means that the range of M is actually the set of coach stopping events itself. Since M is a function with domain the set of all photo taking events, it follows, correctly, that there are at least as many photo taking events as coach stopping events (at least as many, because it is possible that different photo taking events are mapped onto the same coach stopping event). Rothstein’s analysis assumes a null preposition expressing the M function, but nothing requires the semantic function to be expressed by a syntactic node in the tree. In fact, Rothstein’s suggestion is that the M-function is directly analogous to thematic roles, which are also functions from events into unique values, and they do not need to be expressed via prepositions either, so this suggests that a null preposition is not necessary. Bare NP locative adverbials show the same matching effect as bare NP event quantifiers, and again this is not a pragmatic effect. In (88a,b), the quantifier has wide scope and there is a matching effect: there must be at least as many photo/video taking events as there are locations where the coach stopped. In (88c), where the locative quantifier is in argument position, there is no matching effect, since there is no obligatory wide-scope for the universal quantifier: (88) a. Mary took a photo every place the coach stopped. b. Mary made a video every place the coach stopped. c. Mary made a video of/videotaped every place the coach stopped. Given the semantics for locative modifiers assumed in section 3, the interpretation of (88b) is straightforward: (89) a. Every place the coach stopped, Mary made a video. b. ∀l[PLACEk(l) ∧ ∃e[STOP(e) ∧ Ag(e)=|$\sigma$|COACH ∧ scenewt(e) ⊆ ∪l] → ∃e′[MAKE-A-VIDEO(e′) ∧ Ag(e′)=MARY ∧ scenewt(e′) ⊆ ∪l]] (89b) expresses that every contextually determined individual place which hosted an event of the coach stopping, also hosted an event of Mary making a video. As it turns out, the matching effect falls out of the analysis for a combination of reasons: (i) PLACEk is a set of non-overlapping locations. (ii) The sentence expresses that for each location l ∈ PLACEk, there is a video making event e’ such that scenewt(e’) ⊆ l. (iii) For each such video making event e’ in question there is, by the non-overlapping nature of PLACEk, exactly one location l ∈ PLACEk such that scenewt(e’) ⊆ l (otherwise PLACEk would allow overlap). But that means that on the relevant domain of events, scenewt is a function from video making regions to coach stop locations, and exactly the same argument as before shows that there must be at least as many video making regions as coach stop events, hence each place in which the coach stops hosts at least one (though possibly more) events of making a video. Thus, the matching effect falls out exactly the same way as in (87) with the difference that, instead of a null matching function M, we use the independently motivated scenewt function. Crucially, the NP adverbial is bare and no preposition is required because the scenewt function—which maps the events that the event argument of the matrix verb ranges over onto the regions where these are located—is never expressed by a preposition. As we saw in the analysis of example (27) (The cat slept under the table), the role of under is not to relate the table to the event of sleeping. Instead, (as Zwarts and Winter 2000 and Kracht 2002 argue), the meaning of locative preposition under maps the table at type d onto the relevant region r = ∪l. The latter shifts to the adverbial modifier type at type and we derive λe.scenewt(e) ⊆ UNDER(⁠|$\sigma$|TABLE). Since an expression like every place the cat slept at type < t> has its denotation in the family of types associated with l, there is no need for a locative preposition. This correctly predicts that bare NP adverbials will only be acceptable when the nominal head is an appropriate domain sortal. Since the role of the locative preposition is to map an entity at type d onto a region at type r, which can shift to its individual correlate at type l, there is no need for a preposition when the adverbial phrase is headed by a place nominal which is of type , and thus already has its denotation in the sortal domain of locations. This is reflected clearly in (90): the adverbial quantifier headed by place is bare, but the individual locations which are members of the set denoted by place she likes to hide are all expressed via PPs: (90) I looked for the cat every place she likes to hide: in the cupboard, under the table, in the cardboard box. Our account correctly predicts that prepositions are possible with place nominals, although not obligatory, as in (91): (91) a. John left clues (in) the three places that Mary had marked. b. Mary and John met near some place they both like. While locative prepositions like in and outside take DPs as complements, they map regions onto regions. In near the house, the preposition near maps the region occupied by the house onto the region which is near it. The preposition triggers a shift in the denotation of the house from the object |$\sigma$|HOUSE which it denotes to locwt(⁠|$\sigma$|HOUSE), the region which the house occupies, to which the meaning of near applies: NEAR(locwt(⁠|$\sigma$|HOUSE)). Since prepositions map regions onto regions, which can shift down to locations, it is expected that they take place nouns as complements. However, unlike with nominals like the house, the preposition is not required in order to trigger a shift to a locational reading. Note that the intended meaning of (91a) is expressed felicitously by (91a), whether or not the preposition is realized, so the preposition is optional. On the other hand, if we leave out the preposition in (91b), the meaning expressed is not that of (91b), so the preposition in (91b) is obligatory, if you want to express that meaning. This is because the default relation between an event and its location is the at/in relation which is supplied via the subset relation in the statement: scenewt(e′) ⊆ ∪l. In (91a) the preposition repeats the relation inherent in the locative relation and is effectively the identity function and it can be easily dropped. But in (91b) it is not the identity function: it maps the region corresponding to the location which satisfies some place they both like onto the region which is near that place, which is where John and Mary’s meeting took place. Note that for spatial nouns which are not domain sortals, such as location and area, we assume an injection from R → pow(D) which allows locations to be associated with sets of ‘ordinary’ individuals, as ‘ordinary’ as other abstract entities of type d. This is illustrated in example (92), where the preposition in the adverbial mapping from the domain of individuals into regions is obligatory (as in 92a). Predictably, since location is of type , the complementizer can be deleted in a relative clause modifying a < d,t> head (as in 92b): (92) a. We stopped at every location he recommended. b. The location he recommended was superb! The semantic account that I have given of bare locative adverbials exploits the fact that place is of type . Since the role of the locative preposition (following Zwarts and Winter 2000 and Kracht 2002) is to express a function which maps from D into the domain of locations, the preposition is not obligatory when the adverbial already has its denotation in that domain. The account makes a clear semantic prediction. When PP adverbials are headed by a P denoting a function into |${\Delta}_{\alpha}$| where α ≠ d, then this preposition can be dropped when the nominal head of the adverbial is a domain sortal of type <α,t>. The example in (93a), directly analogous to (90), indicates that way is a domain sortal for manners, as we already suggested in section 5. (93b) illustrates a bare NP adverbial in the temporal domain: (93) a. John tried to open the window every way he could: with a screwdriver,with a hammer and with a knife. b. The bell rings every day/hour/week. Temporal adverbials such as those in (93b) raise the question of why a variety of nouns can head bare temporal adverbials, while bare location, event and manner adverbials seem to occur with one noun apiece (place, time, and way respectively). I suspect that this is because day, hour, week and similar nouns denote measures on the temporal domain, while place, time and way denote sets of individuals, and thus are truly domain sortals. However, any further exploration of this would go far beyond the scope of this paper.25 This account of the semantics of bare nominal adverbials can be seen as complementing the Larson-Emonds-Barrie and Yoo perspective on bare NP adverbials. What these authors ask is: what licenses a syntactic DP in adverbial position? The question the present analysis asks is: what enables its semantic interpretation? Temporal, locative and manner adverbials relate event arguments to durations, locations and manners. When a preposition heads an adverbial phrase, it has, in addition to the syntactic function of case-marking its DP complement, the semantic function of mapping the DP denotation onto the relevant duration, location or manner. It will then follow that when the nominal head of the adverbial already has its denotation in the temporal, locative, or manner domains, the preposition may be redundant. One of the goals of this paper was arguing for a type of locations at type l, identified as the set of individual correlates of regions, sets of points. The second goal was to argue that place is a domain sortal which expresses the type of the denotation of the nominal it heads at , the type of sets of locations. Most of this paper (sections 1 through 6) provided support for these two claims. I have argued that representing the meaning of locative PPs requires us to posit both sets of points (regions) and individual correlates of such sets (locations). Locations can be counted and quantified over, while sets of locations sharing a common property can be collected as the denotations of relative clauses. Locations, then, must be added to the set of abstract objects which we use to make sense of the world around us (over and above regions). Recognizing the existence of different sortal domains and the necessity of shifts in meaning from one sortal domain to another has enabled us to explain various grammatical processes, in particular the licensing of null complementizers in relative clauses and the semantic constraints governing the distribution of bare nominal adverbials. It has also opened the way for further exploration into the question of how and when mapping between sortal domains is allowed grammatically. The brief discussion of bare NP adverbials in this final section supports not only the claim that place is a domain sortal, but also the claim that the set of common nouns in English includes a number of other nominals which do not have their domain in type . Not all are simple domain sortals: while way, time, and place seem to denote the set of manners, events and locations respectively, temporal nouns such as day, hour, and year have more complex denotations in the temporal domain. What these denotations might look like is still to be explored. www list of attested examples (9a) https://news.ycombinator.com/item?id=146916 Accessed 03.10.2017 (37) www.ascensionmagic.com/blog/the-wisdom-of-the-trees Accessed 3.12.2018 (43a) http://smallerbox.net/blog/category/ecommerce/ (Accessed 09.10.2017) (43b) James Crumley, The Final Country p. 50 Knopf, Doubleday. (43c) https://theartinlife.blog/2016/05/24/the-little-big-city/ (Accessed 09.10.2017) (76a) http://lubbockonline.com/entertainment/2011-10-13/fan-friendly-comedian-iglesias-loves-being-recognized-public (Accessed 09.10.2017) (77a) https://thecondo.rent/property-details/guest-info/ Accessed 16.10.2017. (77b) http://www.mirror.co.uk/money/three-places-rents-actually-falling-8587410Accessed 16.10.2017. (77c) http://createacardinc.com/newblog/?p=71 Accessed 16.10.2017. (77d) https://www.tripadvisor.co.uk/ShowUserReviews-g40827-d259275-r461722222-Portland_Harbor_Hotel-Portland_Maine.html Accessed 16.10.2017. (footnote 15iii) http://modernmidwest.com/4q1yrlzaqv7a3tm1akd3m5n9fauay5/ (Accessed 03.12.2018) Footnotes 1 Traditionally the type of individuals is given as e, and the type of predicates is . However, in a situation in which a type of events is added to the theory, it is mnemonically simpler to follow Landman (2000) and use e for the type of events (the type of the members of the domain of events E) and d for the type of individuals (the type of the members of the domain of individuals D). 2 It is not yet clear whether kinds, numbers and amounts really are subtypes of properties at type π, or whether they are different sorts of individuals that instantiate the same relation between sets of individuals at type and their individual correlates at type π. Rothstein (2013, 2017) and Scontras (2017) suggest that numbers and amounts/degrees are subtypes of the type of properties, while Chierchia (1998a) remarks that the theory of kinds that he develops in that paper is “…still to be cashed out eventually in terms of a theory of properties” (Chierchia 1998a, page 351, note 11). 3 This is an oversimplified extensional account. More properly noun N maps the domain Drelative to a world w and time t onto the subset of objects in D which have the property denoted by N in wt. 4 If the PP conjunction can be taken as denoting a single place, then it seems that the verb can be in the singular. In (i) and is interpreted as (spatial) intersection and the subject PP denotes a single location which is both in the corner and behind the curtain. But in (8), and denotes the sum operation and the subject PP denotes a plurality of locations, and the agreement must be plural. (i) In the corner and behind the curtain is a good place to hide. 5 Editorial comment: [www] indicates that the example is attested on the web, with reference details at the end of the paper. 6 One might try to argue that the PP in (11a) is predicated of the direct object and that the letter in the drawer is a small clause complement of put. But there is not any good evidence to support this view. Unlike in other small clause complements, for example [consider DP XP], the predicate is constrained syntactically to be a PP and is constrained semantically to be a locative. In small clause complements, there is no direct relation between the V and the accusative DP following. So John saw Mary leave does not require a direct relation of seeing between John and Mary, and John considers Mary a genius does not requires direct relation of John considering Mary. However (11a) does require a direct relation of ‘putting’ between the subject and the direct object, suggesting that the direct object is indeed the theme of the V and not the subject of a small clause. 7 There is also one kind of DP that can be used here, as we will see in section 4. 8 In this paper we will not be concerned with directional or path PPs, as in He walked out of the house/into the house towards the door/around the house. But, as Kracht (2002) and Zwarts (2008) show, modelling locational PPs in terms of spatial entities allows for a principled extension to path arguments, while Zwarts (2005) shows that directional PPs denote paths which are constructed out of sets of points. Thus the domain of points used in constructing locative PP denotations is crucial for the interpretation of other PPs too. 9 There may well be some exceptional cases where discontinuous single locations should be allowed. One of the referees has suggested the example of a palace which can consist of a set of buildings. Inside the palace has an obvious interpretation where it means inside a single path-connected region constituted by the buildings and the grounds which connect them. However, there also seems to be a use of inside the palace which denotes the location which is the sum of the spaces inside all of the buildings. This will make it true that the princess is inside the palace if she is inside any one of the buildings and false if she is not in a building but within the perimeter of the grounds. This problem can be solved by modelling regions in terms of regular open sets of points. However, this use of inside would seem to be triggered by the lexical meaning of the singular count noun palace. I will in this paper continue to use the definition in (22a). See also footnote 22 for related issues. For an in depth discussion of the complex issues involved in spatial representation and the definition of locations see Casati and Varzi (1999). 10 It is also possible to assume that the preposition denotes a function from individuals into regions and thus to incorporate the locwt function into the meaning of the preposition. But as we will see later in section 7, example (91), prepositions can apply to nominal locative phrases as well as to expressions at type d. So we will continue to follow Zwarts and Winter (2000) and Kracht (2002) in distinguishing the shifting operation triggered by the preposition from the meaning of the preposition itself. (See also Partee’s 1987 discussion about expressions like be John, where John shifts from an argument at type d to λx.x = JOHN at type . Partee discusses the merits of incorporating argument-to-predicate shift within the meaning of be of predication versus allowing be to trigger such a shift, and chooses the latter option.) Note that names of cities and countries do not denote locations, but (presumably) institutions. Thus the locative preposition is as obligatory in I live #(in) Berlin as in I put the book#(on) the table. 11 Editorial comment: the above italicised paragraphs replace a page in the manuscript about an analogy with Chierchia’s analysis of kinds in Chierchia (1998a) that was, in my view, in the present stage of the manuscript not worked out well enough. I replace it by a brief reconstruction of discussions we have had at various points about this issue. 12 Maybe the spaces in the example given aren’t really empty. I suppose both locations have different molecules of oxygen in them. But we can recreate the problem with two spaces which are vacuums created in two different laboratories at the same time. Defining locations as individual correlates of properties of events (as a reviewer suggested) leads to the same undesirable results, since two distinct regions where no events occur would denote the same set. And we would not have the advantage of assimilating locations to a well-defined set of properties at type π either. 13 Editorial note: One of the Journal of Semantis editors disagrees with the felicity judgements of Susan’s informants and accepts all cases in (36b). 14 Adjectival predicates are freer. For example, is important can take kinds, properties and locations as an external argument: (i) Wisdom is important. (ii) Worms are important (though no individual worm is particularly important) (iii) Even under the table is important… [www] 15 An anonymous reviewer suggests that spot works the same way that place does. e.g. I took a photo every spot the coach stopped. Not all speakers share this intuition. 16 A reviewer asked why the shift was not available for predicate nominals. i.e. #John is a good place to hide, is infelicitous because the predicate nominal does not shift to a < d,t> interpretation. I assume that the shifting operation is triggered by the need to resolve N′-internal mismatches and is not available when the predicate is a sentential predicate. 17 Larson (1985) was the first to point out the peculiarities of the noun place, showing that bare place headed nominals can fill PP adverbial positions, and relating this to the lack of a where complementizer in place that Max has lived (Larson 1985, example 3). We return to a discussion of Larson (1985) in section 7. 18 As a reviewer pointed out, where does not bind traces in subject position in relative clauses, as in #place/room where is a good place to hide, although where can bind a trace in questions as in Where is a good place to hide? I do not have any explanation for this. Note that when has the same restrictions, as in the day when I met you versus #the day when is a good day for us to meet. Note that That day is a good day for us to meet is fine. How, of course, does not occur in relative clauses at all (see examples (69/70). I leave these puzzles for further research. 19 I will not rehearse all the arguments that time denotes a set of events in this paper but refer the reader to the original paper. Landman (2006) adds an illuminating additional example to Rothstein’s original data. Imagine a businessman sitting in front of a wall of lights and saying “Every time a light flashes, I have made $20,000”. Three lights flash simultaneously and he says “Ah, another $60,000!”. Clearly, he is quantifying over events of lights flashing, irrespective of the temporal points at which they flash. 20 Any in depth analysis of what manner adverbials are is far beyond the scope of this paper. They clearly include instrumental phrases like with a screwdriver and adverbials such as carefully. 21 More precisely, it can only be identified reliably as an amount relative in existential contexts, since (as argued extensively in the papers on amount readings mentioned) individual level traces cannot occur in existential contexts. We will never be able to drink the wine that they brought to the party has an identity of substance reading (….because our guests drank it all) as well as an identity of amount reading (….because they brought so much) but the identity of substance is identical to the standard interpretation where they brought to the party denotes a set of individuals at type . So it is not necessary to derive that reading via an amount relative. 22 A reviewer suggested that place can include discontinuous locations, citing 1947 Pakistan which consisted of two non-adjacent territories with no shared border. If John lived in both East Pakistan and West Pakistan, and Mary only lived in East Pakistan, is it true to say that Mary has lived every place that John has? My intuition, as well as that of my informants is ‘no’, suggesting that the two parts of Pakistan were not a single place, although the (single) administrative institution constituting Pakistan may have been deployed over two locations. Similar arguments to those made in section 3, note 10 can also be made. If John looked in the cupboards and Mary looked every place John looked, she has to look in each of the cupboards, showing that the spaces inside each of the cupboards cannot be summed into a single discontinuous location. More problematic examples were already discussed in note 10. 23 Strictly speaking these are bare DP adverbials, but they have become known in the literature as bare NP adverbials, and it seems inappropriate to rename the phenomenon now. 24 In section 5, we gave (62) as the representation of (60b) Every time I drink whisky, I drink Laphroaig. In that representation there was no matching operator. This simplification was possible because the universal quantifier in (60b) can bind the event argument of drink in both the adverbial and the main clause, giving the reading every event of my drinking whisky is (itself) an event of me drinking Laphroaig. A full derivation of (60b) would be parallel to (87b) and would be simplified to (62) since here the matching relation would be the identity relation (since Laphroaig is a kind of whisky). 25 Clearly relevant is Pratt and Francez (2001), who explore a variety of temporal adverbials as well as temporal interpretations of expressions like every meeting, which they argue are generalized quantifiers over intervals of time. References Barrie Michael, & Yoo , Isaiah Wonton ( 2017 ), ‘ Bare nominal adjuncts ’. Linguistic Inquiry 48 : 499 – 512 . Google Scholar Crossref Search ADS WorldCat Carlson , Gregory ( 1977a ), ‘ A unified analysis of the English bare plural ’. Linguistics and Philosophy 1 : 413 – 57 . Google Scholar Crossref Search ADS WorldCat Carlson , Gregory ( 1977b ), ‘ Amount relatives ’. Language 53 : 520 – 42 . Google Scholar Crossref Search ADS WorldCat Casati , Roberto & Varzi , Achille ( 1999 ), Parts and Places: The Structure of Spatial Representation . MIT Press . Cambridge, Mass . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Chierchia , Gennaro ( 1984 ), Topics in the Syntax and Semantics of Infinitives and Gerunds . Ph.D. dissertation . University of Massachusetts, Amherst . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Chierchia , Gennaro ( 1985 ), ‘ Formal semantics and the grammar of predication ’. Linguistic Inquiry 16 : 417 – 43 . OpenURL Placeholder Text WorldCat Chierchia , Gennaro & Turner , Raymond ( 1988 ), ‘ Semantics and property theory ’. Linguistics and Philosophy 11 : 261 – 302 . Google Scholar Crossref Search ADS WorldCat Chierchia , Gennaro ( 1998a ), ‘ Reference to kinds across languages ’. Natural Language Semantics 6 : 339 – 405 . Google Scholar Crossref Search ADS WorldCat Chierchia , Gennaro ( 1998b ), ‘Plurality of mass nouns and the notion of 'semantic parameter'’. In Susan Rothstein (ed.), Events and Grammar . Springer . Berlin . 52 – 103 . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Chierchia , Gennaro ( 2010 ), ‘ Mass nouns, vagueness, and semantic variation ’. Synthese 174 : 99 – 149 . Google Scholar Crossref Search ADS WorldCat Creary , Lewis , Gawron , Jean Mark & Nerbonne , John ( 1989 ), ‘ Reference to locations ’. In Proceedings of the 27th Annual Meeting of the Association for Computational Linguistics. 42 – 50 . Association for Computational Linguistics . Shroudsburg, PA . Davidson , Donald ( 1967 ), ‘The logical form of action sentences’. In Nicholas Rescher (ed.), The Logic of Decision and Action . University of Pittsburgh Press . Pittsburgh . 81 – 95 . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Emonds , Joseph ( 1987 ), ‘ The invisible category principle ’. Linguistic Inquiry 18 : 613 – 32 . OpenURL Placeholder Text WorldCat Grosu , Alexander & Landman , Fred ( 1998 ), ‘ Strange relatives of the third kind ’. Natural Language Semantics 6 : 125 – 70 . Google Scholar Crossref Search ADS WorldCat Hornstein , Norbert & Weinberg , Amy ( 1981 ), ‘ Case theory and preposition stranding ’. Linguistic Inquiry 12 : 55 – 91 . OpenURL Placeholder Text WorldCat Heim , Irene ( 1987 ), ‘Where does the definiteness restriction apply? Evidence from the definiteness of variables’. In Alice ter Meulen and Erik Reuland (eds.), The Representation of (In)definiteness . MIT Press . Cambridge, Mass . 21 – 42 . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Jackendoff , Raymond ( 1983 ), Semantics and Cognition . MIT Press . Cambridge, Mass . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Kracht , Marcus ( 2002 ), ‘ On the semantics of locatives ’. Linguistics and Philosophy 25 : 157 – 232 . Google Scholar Crossref Search ADS WorldCat Krifka , Manfred ( 1989 ), ‘Nominal reference, temporal constitution and quantification in event semantics’. In Renate Bartsch, Johan van Benthem and Peter van Emde Boas (eds.), Semantics and Contextual Expression . Foris . Dordrecht . 75 – 115 . Google Scholar Crossref Search ADS Google Scholar Google Preview WorldCat COPAC Landman , Fred ( 1995 ), ‘Plurality’. In Shalom Lappin (ed.), Handbook of Contemporary Semantics , 1st Edition. Wiley-Blackwell . Oxford . 425 – 457 . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Landman , Fred ( 2000 ), Events and Plurality . Springer . Berlin . Google Scholar Crossref Search ADS Google Scholar Google Preview WorldCat COPAC Landman , Fred ( 2006 ), ‘Indefinite time-phrases, in situ-scope and dual perspective intensionality’. In Svetlana Vogeleer and Liliana Tasmowski (eds.), Non-definiteness and Plurality . John Benjamins . Amsterdam . 237 – 66 . Google Scholar Crossref Search ADS Google Scholar Google Preview WorldCat COPAC Landman , Fred ( 2011 ), ‘Count nouns—mass nouns, neat nouns—mess nouns’. In Baltic International Yearbook of Cognition, Logic and Communication , vol. 6 . New Prairy Press . Manhatten, KS . https://doi.org/10.4148/biyclc.v6i0.1579 . Larson , Richard ( 1985 ), ‘ Bare NP adverbs ’. Linguistic Inquiry 16 : 595 – 621 . OpenURL Placeholder Text WorldCat Parsons , Terence ( 1990 ), Events in the Semantics of English . MIT Press . Cambridge, Mass . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Partee , Barbara ( 1975 ), ‘ Montague grammar and transformational grammar ’. Linguistic Inquiry 6 : 203 – 300 . OpenURL Placeholder Text WorldCat Partee , Barbara ( 1987 ), ‘Noun phrase interpretation and type-shifting principles’. In Jeroen Groenendijk, Dick de Jongh and Martin Stokhof (eds.), Studies in Discourse Representation Theory and the Theory of Generalized Quantifiers . GRASS 8 . Foris . Dordrecht . 115 – 43 Reprinted in: Portner, Paul & Partee, Barbara (eds.) (2002), Formal Semantics: The Essential Readings. Wiley-Blackwell. Oxford. 357–81 . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Pratt , Ian & Francez , Nissim ( 2001 ), ‘ Temporal prepositions and temporal generalized quantifiers ’. Linguistics and Philosophy 24 : 187 – 222 . doi: doi.org/10.1023/A:1005632801858 . Google Scholar Crossref Search ADS WorldCat Crossref Rothstein , Susan ( 1995 ), ‘ Adverbial quantification over events ’. Natural Language Semantics 3 : 1 – 31 . Google Scholar Crossref Search ADS WorldCat Rothstein , Susan ( 2010 ), ‘ Counting, measuring and the mass count distinction ’. Journal of Semantics 27 : 343 – 97 . Google Scholar Crossref Search ADS WorldCat Rothstein , Susan ( 2013 ), ‘A Fregean semantics for number words’. In Maria Aloni, Michael Franke and Floris Roelofsen (eds.), Proceedings of the 19th Amsterdam Colloquium . 179 – 86 . http://www.illc.uva.nl/AC/AC2013/uploaded_files/inlineitem/23_Rothstein.pdf. Rothstein , Susan ( 2017 ), Semantics for Counting and Measuring . Cambridge University Press . Cambridge . Google Scholar Crossref Search ADS Google Scholar Google Preview WorldCat COPAC Scontras , Gregory ( 2017 ), ‘ A new kind of degree ’. Linguistics and Philosophy 40 : 165 – 205 . Google Scholar Crossref Search ADS WorldCat Talmy , Leonard ( 1985 ), ‘Lexicalization patterns: semantic structure in lexical forms’. In Timothy Shopen (ed.), Language Typology and Syntactic Description, vol. 3 Grammatical Categories and the Lexicon . Cambridge University Press . Cambridge . 57 – 149 . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Wunderlich , Dieter ( 1991 ), ‘ How do prepositional phrases fit into compositional syntax and semantics? ’ Linguistics 29 : 4 . Google Scholar Crossref Search ADS WorldCat Zwarts , Joost ( 2005 ), ‘ Prepositional aspect and the algebra of paths ’. Linguistics and Philosophy 28 : 739 – 79 . Google Scholar Crossref Search ADS WorldCat Zwarts , Joost ( 2008 ), ‘Aspects of a typology of direction’. In Susan Rothstein (ed.), Theoretical and Crosslinguistic Approaches to the Semantics of Aspects . John Benjamins . Amsterdam . 79 – 106 . Google Scholar Crossref Search ADS Google Scholar Google Preview WorldCat COPAC Zwarts , Joost ( 2017 ), ‘ Spatial semantics: modelling the meaning of prepositions ’. Language and Linguistics Compass 11 : 1 – 20 . Google Scholar Crossref Search ADS WorldCat Zwarts , Joost & Winter , Yoad ( 2000 ), ‘ Vector space semantics: a model-theoretic analysis of locative prepositions ’. Journal of Logic, Language and Information 9 : 171 – 213 . Google Scholar Crossref Search ADS WorldCat A. Afterwords by Fred Landman. 1. About the Editing This paper has a very long history. Not long after Susan finished her 1995 paper on every time the bell rang, I opened the door, she started thinking about examples like Every place the plane stopped, the pope kissed the ground. Some time in the second part of the nineties, she wrote a Palaeolithic version of this paper that we discussed extensively, but that she wasn’t happy with at the time. Over the next 20 years, she came back to the topic off and on, discussing her results with me and many other people, occasionally giving a colloquium talk on the topic. She wrote another version of the manuscript in 2010, when we were on sabbatical in Holland, but still not to her satisfaction. Finally, when we were Humboldt fellows in Tübingen, she decided that she had had enough, and there was so much nice stuff in this work that it had to come out, and she finally needed to get her act together and write the damn thing. She still had a book to finish before that, but by the end of 2017 a version of the paper existed which she thought was good enough to allow me to lay a critical eye on. True Love is shown by the fact that I gave her 17 pages of comments, and Even Truer Love by the fact that she accepted those gracefully. This is actually the last I saw of the paper until now, and I do take quite some pleasure in the fact that I found out that she actually did take my comments very seriously (I can hear her voice now: “You may not notice, but I do actually listen to you, you know.”) In the meantime, a version of this paper was submitted to the Journal of Semantics, went through review stages, got rewritten, and went through review again, and then it stopped, because Susan got taken ill suddenly, and died two months later, leaving the paper, I would say, one stage away from what I would regard as a final version. Normally, when she had written a final version, she would ask me for one more round of comments, add those, and then give it to me for editing. Susan hated proof reading, and was happy with me dealing with formatting issues and correcting typos, with suggesting clarifying reformulations of paragraphs, and doing, when necessary, further little bits of cleaning up in the formal part. In this way, I have edited the final stages of practically all of her papers and books since 1992. The editorial work this paper needed was somewhat more than usual, but I have made sure not to try and improve the paper beyond repair, and of course to maintain Susan’s own voice. As I indicate in the text, there was a one page discussion in the manuscript in section 3 that I could not see how to make right, so I deleted that and added a bridge passage in italics, bringing out the fact that this kind of editorial work is at times really like restoring a fresco. Of course, we would all have preferred if I had been able to edit the next version written by Susan, but, in the circumstances, this has, in my opinion, turned out to be an important and mature Rothstein paper. I am glad it is there. 2. A footnote on the use of Chierchia and Turner’s type theory In Chierchia and Turner’s theory the denotation of blue of type is a propositional function BLUE, a function that maps every object d onto the proposition BLUE(d), and not a function from individuals into truth values. This re-interpretation of type is essential for their property theory avoiding inconsistency and paradox. Of course, this function BLUE determines the set of blue individuals. While Susan skipped this step in this paper, her discussions of regions and locations too should be thought of as underlyingly formulated in terms of propositional functions (or be reconstructed in a less type-free theory, see the remark on Chierchia in footnote 2). 3. A footnote on simple regions In the paper Susan restricted the set of regions to ‘single regions’ and she assumed that preposition meanings map single regions onto single regions. This is by no means a trivial assumption and to make it she had to exclude from consideration complex preposition meanings like left and right of in a sentence like the trees stand left and right of the house, the output of which is not a simple region. I decided that generalizing the theory to non-singular regions would at this stage be too strong an editorial step (but it will have to be considered, of course). As a consequence I have taken the liberty of using in the paper regions and the type r of regions, even if in some cases Susan used sets of points and type . 4. Some thoughts on separating the analysis from the specifics of the implementation A lot of the discussions that Susan and I have had on this topic over the years concerned the need for using property theory. My position was that practically everything in Susan’s paper could be reformulated, and in fact simplified, in a theory that does not rely on property theory, and that in fact it might be useful to do so. The theories that I came up with over time in these discussions were, for various reasons, not to Susan’s taste. Now that there is only version left, I still think it may be useful to continue this discussion one more step, and present a version which is almost the same as Susan’s analysis, but does not use the property theory in its derivations. The alternative assumes basic types d of objects, e of events, r of regions, and their corresponding domains, D, E, R. It does not assume that types e, r are subtypes of d. With Susan, I assume here that domain sortals are count nouns that denote contextual partitions of their domains, where partition is defined in terms of the relevant notion of overlap on the relevant domain: thing → Dk with Dk ⊆ D. time → Ek, with Ek ⊆ E. place → Rk, with Rk ⊆ R. Unlike Susan, I assume that the argument denotation and predicate denotation of PPs are the same. That means that no shifts between PP adjuncts and PP arguments are necessary. The shift operations indwt and scenewt stay as they are. The shift operation locationwt gets simplified to an operation mapping a region onto the set of its subregions: locationwt(r) = λr’: r’ ⊆ r. In this analysis, the only thing that changes for the examples in Sections 1–4 is that the examples in (30)–(35) are done without ∩: in this version of the theory, regions in Drcan be the denotations of the arguments of predicates and can be the values of roles. The relative clause derivations in section 5 are simpler: There is no difference in the derivation of shelf + on which John put the book, but the denotation of the relative clause where John put the book is not of type , so the shift operation in (49) is simplified to: SHIFT: → < d,t>. SHIFT[α] = λx.∃r[α(r) ∧ r = Ploc(locwt(x))]. With this we derive for shelf + where John put the book: SHELF ∩ SHIFT[λr. ∃e[PUT(e) ∧ Ag(e) = John ∧Th(e) = |$\sigma$|BOOK ∧ Go(e) = r]]. = λx[SHELF(x) ∧ ∃e[PUT(e) ∧ Ag(e) = John ∧Th(e) = |$\sigma$|BOOK ∧ Go(e) = ON(locwt(x))]]. As in Susan’s analysis no shift is needed for place + where John put the book: Rk ∩ λr. ∃e[PUT(e) ∧ Ag(e) = John ∧Th(e) = |$\sigma$|BOOK ∧ Go(e) = r]. = λr ∈ Rk:∃e[PUT(e) ∧ Ag(e) = John ∧Th(e) = |$\sigma$|BOOK ∧ Go(e) = r]. This means that differences that Susan’s analysis postulates for cases where the head noun and relative match in type and where they do not (the SCG) are exactly preserved in this variant analysis (pace what is said below on nouns like location). Also in Scontras’ degree analysis, it is not the switching between degree and degree as individual that is crucial for Susan’s analysis, but the switching between type d and type a of degrees. So here too the simplified theory can do what Susan’s theory does. The discussion of the matching effect in relative clauses with time and place is similarly unaffected: the argument for place depends on place being a count noun, they do not depend on the type: every place the coach stopped →. ∀r ∈ Rk[∃e[STOP(e) ∧ Ag(e) = |$\sigma$|COACH ∧ scenewt(e) ⊆ r →. ∃e’[Made-Video(e’) ∧ Ag(e’) = Mary ∧ scenewt(e’) ⊆ r]]. In sum, the difference between this analysis and Susan’s is that we do not need to use the operators ∪ and ∩ of the property theory in the derivations, making the theory a little simpler. Nevertheless, Susan’s theory gives what I think is a good argument for assuming that there are locations inside domain D. It’s not to do with place, but with intuitively locative nouns that do not behave like place, nouns like location and region. The examples in (1) and (2) are Susan’s examples, or based on them: (1) a. ✓Behind the sofa and under the table are two places that need cleaning b. #Behind the sofa and under the table are two spaces/locations that need cleaning. (2) a. ✓Mary left a pamphlet every place John indicated. b. ✓Mary left a pamphlet in every location John indicated. c. #Mary left a pamphlet every location John indicated. d. ✓Mary left a pamphlet in every shop John indicated. e. #Mary left a pamphlet every shop John indicated. Susan explains these data by making one more assumption, namely that place is a noun of type , but shop, space and location and region are nouns of type and not . This is a very attractive assumption, because it corresponds directly to the observation shown in (2) that location patterns with count nouns of type , and the simplest reason for that would be that location is a count noun of type . In the simplified analysis given here, we would want to make the same assumption, and in fact, nothing in the simplified analysis tells us that we cannot, so we do, and that way we make exactly the same predictions as Susan about the data discussed in her paper. But then we assume that the nouns location and region are predicates of objects in type d, individuals that are locations and regions in a subsort Dr of type d. And presumably we would like these regions as individuals in domain Dr and regions proper in domain R to be related. I would propose at this point to re-instate the property theory, but keep the above simplified analysis, and restrict the use the property theory to the lexical semantics of the locational nouns of type : location → λx.∃r ∈ Rk: x = ∩r. This means that the property theory is only used to express that, lexically, location is a nominalized noun in the sense of property theory, which is not an unattractive idea. I think that this reformulation of Susan’s analysis can deal with all her examples. This is not a surprise, because, of course, the above analysis is just a version of Susan’s theory. It has the advantage that it is ‘lite’ on the property theory: if you feel like adopting Susan’s analysis, but do not feel comfortable about the ins and outs of the property theory, you can keep the property theory on the periphery. In this sense we can separate the ideas expressed in Susan’s paper from the specifics of her implementation of them in property theory. © The Author(s) 2020. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model) TI - Locations JF - Journal of Semantics DO - 10.1093/jos/ffaa007 DA - 0031-02-10 UR - https://www.deepdyve.com/lp/oxford-university-press/locations-2fXWV0uUWn SP - 1 EP - 1 VL - Advance Article IS - DP - DeepDyve ER -