Variables in Natural Language

Meredith Landman

University of Massachusetts, Amherst

Abstract

One of the main goals of generative linguistics is to articulate what constitutes a

possible grammar of a natural language. This thesis is a step towards that goal, in

positing a universal semantic constraint on the interpretation of pro-forms and

traces. Semantically, pro-forms and traces are commonly analyzed as variables,

and it is from this perspective that I propose a constraint on their interpretation.

Specifically, I argue that natural language expressions never denote higher-type

variables, i.e., variables of a type higher than that of an individual (type e) so that

the following generalization holds (see Chierchia (1984) and Baker (2003) for

similar proposals):

(1) The No Higher-type Variables Constraint

Variables in natural language are of type e.

Assuming that the domain of individuals, De, includes at least objects, kinds

(Carlson 1977b), locations, times, events (Davidson 1967), and degrees all of

which have been independently motivated as necessary members of De what (1)

predicts not to occur are linguistic expressions that denote variables ranging over,

e.g., generalized quantifiers, relations, or properties. (With respect to properties,

this prediction is complicated by the possibility that certain properties correspond

to individuals (Chierchia 1984a, Chierchia and Turner 1988), as discussed in

detail.) Adopting a semantic framework in which pro-forms and traces are

interpreted directly as variables that receive their values from an assignment

function, I implement (1) as a restriction on the assignment function. Specifically,

I define the assignment function as a (partial) function from indices to individuals

in D (Heim & Kratzer 1998), so that pro-nouns and traces necessarily denote in D.

While (1) predicts a very restricted inventory of possible pro-forms and

traces, I hope to show that it accounts for a surprisingly wide range of data in

characterizing what pro-forms and traces do and do not occur. The bulk of the

thesis is devoted to backing up (1) by closely looking at potential

counterexamples on a case-by-case basis.

In search of potential higher type pro-forms that is, potential

counterexamples to (1) I look closely at the syntax and semantics of pro-forms

in English, German, and Polish that have the syntactic distribution of expressions

commonly taken to be of a higher type, namely, APs, AdvPs, NPs, and VPs.

While all of these expressions are (commonly taken to) denote properties of

individuals, I will argue that pro-forms that have their syntactic distribution

should not be analyzed as property variables, but instead either (i) as individual

variables, or (ii) not as variables at all. Potential pro-forms corresponding to

expressions of any type higher than a property, e.g., generalized quantifiers or

functions from properties to properties, appear to be completely non-existent (see

also Chierchia 1984).

With respect to traces, the situation is similar: if one looks at the kinds of

traces that are possible, the restrictions observed for pro-forms again seem to

hold. I focus empirically on possible traces in wh-constructions in English; as

with pro-forms, there are many kinds of wh-constructions that one could imagine

might exist, that do not. For example, there do not seem to be restrictive relative

clauses whose traces syntactically correspond to conjunctions, determiners,

prepositions, or complementizers, nor, more surprisingly, APs, VPs, NPs, or

certain adverbs (such as again) (see also Baker 2003). The constraint also has

implications for reconstruction phenomena: several authors have argued that

higher-type variables should not be used to account for reconstruction phenomena

(see, e.g., Labeux 1990, Heycock 1995, Romero 1990, Fox 2000), a result that

follows from the constraint in (1) (see also Fox 1999).

Table of contents

Chapter 1: Introduction ....................................................................................... 6 1. What this thesis is about .............................................................................. 6 2. Precedents ................................................................................................. 16

2.1 Property theory and the No Functor Anaphora constraint..................... 17 2.1.1 The problem of adverbs................................................................. 24

2.2 Baker (2003)........................................................................................ 25 2.2.1 Anaphora ...................................................................................... 28 2.2.2 Movement..................................................................................... 31

3. Theoretical framework............................................................................... 33 3.1 Pronouns and traces as variables .......................................................... 37 3.2 The domain of individuals ................................................................... 39

3.2.1 Plural individuals .......................................................................... 39 3.2.2 Kinds as individuals...................................................................... 40 3.2.3 Events and event-kinds ................................................................. 43

Chapter 2: Adjectival Anaphora ........................................................................ 44 1. Whats such? ............................................................................................. 44

1.1 Setting aside the ambiguity .................................................................. 46 1.2 Syntax of such ..................................................................................... 50 1.3 Semantics of such ................................................................................ 56

1.3.1 Such-as-relatives........................................................................... 66 1.3.2 Such-as-phrases ............................................................................ 77

1.4 Summary ............................................................................................. 81 1.5 Restrictions on co-occurring determiners ............................................. 83

2. Like that .................................................................................................... 84 2.1 Syntax of like that................................................................................ 85 2.2 Semantics of like that........................................................................... 87 2.3 Like-relatives ....................................................................................... 91 2.4 Summary ............................................................................................. 98

3. Pro-AdvPs................................................................................................. 98 3.1 Manner adverbials ............................................................................... 99

3.1.1 Uses in the adjectival domain.......................................................107 3.1.2 Adverbial like that........................................................................108 3.1.3 Summary .....................................................................................109

3.2 Temporal and locative adverbials: there and then................................109 4. Chapter Summary.....................................................................................110

Chapter 3: VP and NP Pro-forms......................................................................111 1. VP-Ellipsis ...............................................................................................113

1.2 Binding theory constraints ..................................................................115

1.3 Bound variable readings .....................................................................117 1.4 Backwards anaphora...........................................................................121 1.5 Summary ............................................................................................122

2. VP-pro-forms: do so, do it and do that......................................................122 3. One-anaphora ...........................................................................................128

3.1 One as Num........................................................................................129 3.2 Pragmatic control................................................................................134 3.3 Bound variable readings .....................................................................136 3.4 Binding in...........................................................................................138

4. Chapter Summary.....................................................................................142 Chapter 4: Higher-type traces...........................................................................143

1. Reconstruction..........................................................................................143 1.1 Gap vs. variable..................................................................................148 1.1 How-many questions and movement out of weak islands ....................150

2. Possible wh-constructions.........................................................................152 2.1 Possible relatives ................................................................................152

2.1.1 Possible restrictive relatives .........................................................152 2.1.2 Possible Amount relatives............................................................153

2.1.3 Possible non-restrictive relatives ......................................................159 2.2 Possible wh-questions .........................................................................178

3. Concluding remarks..................................................................................178 References .......................................................................................................178

Chapter 1

Introduction

1. What this thesis is about

One of the main goals of generative linguistics is to articulate what constitutes a

possible grammar of a natural language. This thesis is a step towards that goal, in

positing a universal semantic constraint on the interpretation of pro-forms and

traces. Semantically, pro-forms and traces are commonly analyzed as variables,

and it is from this perspective that I will propose a constraint on their

interpretation. Specifically, I will argue that these expressions never denote

higher-type variables, i.e., variables of a type higher than that of an individual,

type e, so that the following generalization holds (see Chierchia (1984) and Baker

(2003) for similar proposals, as discussed in detail in Section 2 below):1,2

(1) The No Higher-type Variables Constraint

Variables in natural language are of type e.

1 [Alternatively, pro-forms and traces denote variables of type e. See discussion below.] 2 [revise] Its an interesting question how/whether this constraint could be stated in a variable-free framework, e.g., Jacobson (1991, 1994, 1999, 2000b, etc.).

To make clear the predictions of (2), it is first necessary to make clear my

assumptions about what counts as an individual, that is, what constitutes the

domain of individuals of type e, De (henceforth, D). I will assume here that D

includes at least objects, kinds (Carlson 1977b), locations, times, events

(Davidson 1967), and degrees (XXX), all of which have been independently

argued to be necessary members of D. Thus, what (2) predicts not to occur are

linguistic expressions that denote variables ranging over, e.g., generalized

quantifiers, relations, or properties. With respect to properties, this prediction is

complicated by the possibility that certain properties correspond to individuals

(Chierchia 1984, Chierchia & Turner 1988); I address this issue in detail in

Section 2 below.

I will incorporate (1) into the semantic component as a restriction on the

assignment function, assuming a framework in which pro-forms and traces are

interpreted directly as variables and receive their values from an assignment

function. More specifically, I will define the assignment as a (partial) function

from indices to individuals in D (Heim & Kratzer 1998), so that pro-nouns and

traces necessarily denote in D:

(2) A variable assignment is a partial function from |N into D.

As will be spelled out in Section 3, I follow Heim and Kratzer (1998) in taking a

variable to be a lexical item whose denotation varies with the assignment:

(3) A terminal symbol is a variable iff there are assignments g and g such

that ||||g ||||g

In effect, lexical items whose denotations vary with the assignment will

necessarily denote in D.3,4 Although I will restrict my attention to pro-forms and

traces here, these are not the only expressions that have been analyzed as

variables: implicit, or covert, variables have also been posited to account for

contextual information, for example, higher type, covert variables have been used

to account for contextual restrictions on quantifier domains (e.g., Westerstahl

1984; von Fintel 1994; Mart 2003), and may present counterexamples to (1). I

will not look at such uses of variables in this work, but note that it is promising

that Kratzer (2004) proposes an alternative account of contextual restrictions on

quantifier domains that does not make use of covert property variables (she in fact

presents arguments against this type of account).5

3 Need to say something lexical items that are context dependent, and treatments thereof using implicit variables (Partee 1989, and othersmore recently Carlson & Storto, to appear.) 4 I assume that variables such as those bound in the denotation of determiners, e.g., [f . [g . for all x, if f(x) then g(x)]], are not affected by the assignment function and correspondingly are not subject to this constraint. 5 An alternative implementation of (1) would be to incorporate it into an interpretation rule for pronouns and traces, thereby targeting only these expressions. This could be done, for example,

It is, I think, a natural first response to (1) to try to think of

counterexamples, and it may at first not seem to hard to think of some. Before

going further, then, let me stress the motivation behind this constraint. The broad

question here is whether there are pro-forms and traces that are systematically

missing from natural language. While (1) predicts a very restricted inventory of

possible pro-forms and traces, I aim to show that it accounts for a surprisingly

wide range of data in characterizing what pro-forms and traces do and do not

occur. The bulk of this thesis is devoted to backing up (1) by closely looking at

potential counterexamples on a case-by-case basis.

In search of potential higher type pro-forms that is, potential

counterexamples to (1) I will look closely at the syntax and semantics of pro-

forms that have the syntactic distribution of expressions commonly taken to be of

a higher type. Interestingly, it appears that the only such pro-forms that is, the

only such potential counterexamples are those that have the distribution of

property-denoting expressions, i.e., expressions of type . Potential pro-

forms corresponding to expressions of any type higher than , e.g.,

with the following interpretation rule, a modified version of the Pronouns and Traces rule of Heim and Kratzer (1998); the rule differs from theirs only in that it targets pro-forms of any syntactic category, not just pronouns: (1) Pro-forms and Traces

If is a pro-form or trace, i is an index, and g is a variable assignment whose domain includes i, then g(i) D and ||i||g = g(i).

generalized quantifiers or functions from properties to properties, appear to be

absent, as observed in Chierchia (1984) (again see Section 2):

In general determiners, prepositions, complementizers, etc. do not undergo wh-movement and have no pro-forms. Similarly there is no analogue of VP-deletion or one-anaphora for these items. [Chierchia 1984: pp. 83-84]

To illustrate what such pro-forms might look like, consider the following

examples, in which hypothetical pro-forms corresponding to determiners,

conjunctions, prepositions, and (certain) adverbs are represented by the

hypothetical word na; these kinds of pro-forms indeed seem to be systematically

absent.6

(4) !Fred fed every dog, and Martha fed na cat. Det

(5) !She likes school and sports; he likes sleeping na TV. Conj

(6) !Mary is under the table, and Bobby is na the bed. Prep

(7) !I went to the store again, and Mary fell asleep na. Adv

In contrast, pro-forms which display the distribution of property-denoting

expressions do occur, as (8)-(11) illustrate: here, we see what appear to be pro-

forms with the distribution of adjectival phrases (APs), adverbial phrases

6 I will use an exclamation point (!) to mark sentences that contain impossible hypothetical expressions, and, in this Chapter, (informally) represent antecedent-pro-form relationships using italics.

(AdvPs), verb phrases (VPs), and noun phrases (NPs, assuming the DP

hypothesis):7

(8) Those little cars look good, but few such cars are safe. AP

(9) You have to dance this dance with a definite sense of pride and

haughtiness, and if danced so/thus, the dance will be beautiful. AdvP

(10) If Jane jumps, Dick will do so/it/that too. VP

(11) Ill wash the big dishes, if youll wash the little ones. NP

Comparing the examples in (4)-(7) to those in (8)-(11), one could imagine a

purely syntactic explanation for these facts: for some reason, only phrases may be

substituted for, and not word categories like P, N, or C.8 However, this would not

explain why certain phrasal constituents may not antecede pro-forms, e.g., I and

C may not:

7 For the immediate discussion, I set aside instances of ellipsis, e.g., alongside (10) and (11) above are (i) and (ii) below (I use to represent ellipsis): (i) She wanted to them to come, so she asked them to . VP (ii) Ill take these keys, and you can take those . NP I will address this issue directly in Chapter 3, where I will argue (as others have) that ellipsis is not an instance of anaphora (for instance, NP and VP ellipses are not interpreted as variables.) 8 Pro-form substitution is in fact a common test for phrasal constituency. The status of word-level categories for constituency tests, however, is unclear to me. Word-level categories are of course constituents themselves, but they generally seem to fail these tests.

(12) a. He had been sleeping, and she na too. I

b. Mary wondered what you saw, and Fred asked who na. C

These examples would need to be ruled out on independent grounds.9 I will

instead claim that they, along with (4)-(7), are ruled out by (1). The acceptable

examples in (8)-(11), on the other hand, I will argue are not property-variables,

but instead are either (i) interpreted as individual variables, or (ii) instances of

ellipsis, and thus arguably are not interpreted as variables at all (see Chapter 3). In

some cases, I will not have a strong case against a property-variable analysis, but

will only be able to show that a property-variable analysis is not necessary. Thus,

at its weakest, my claim will be that there are no pro-forms (or traces) that

necessitate the use of higher-type variables.10

(1) also predicts the absence of higher-type traces. Here, we can similarly

ask: What would constructions containing higher-type traces look like, and do

these constructions occur? My strategy will be again to look for traces (variables)

that have the distribution of (what are commonly taken to be) higher-type

9 For example, I substitution in English might be ruled out because tense must be overt. Null I substitution is certainly possible in other languages, e.g., German Maria auch, but I know of no language which uses an overt pro-form for I. 10 One potential higher-type pro-form in English that I will not be looking at is the use of so as illustrated in (i), where it occurs in a position usually occupied by APs, namely, the object position of appear or seem. (i) I thought she would be happy, but she certainly doesnt seem/appear so/?it/?that. So might thus present a counterexample to (1).

expressions. I will try to show that if we look at what kinds of traces are possible

in these constructions, the restrictions observed for pro-forms again seem to

hold.11 Consider, for example, the kinds of syntactic gaps that may occur in

restrictive relative clauses in English: the gap in a restrictive relative may

correspond to a DP, AdvP, or PP as the examples in (13) illustrate.12

(13) a. Mary liked the movie you made __. DP

b. Matthew runs how you run __. AdvP

c. Matthew runs when you run __. AdvP

d. Matthew runs where you run __. AdvP

e. The room where you put my book __. PP

Assuming that at LF, the internal structure of a restrictive relative contains a wh-

operator in the Specifier of CP, which binds a variable in the position of the gap, I

will argue that all of these relative clauses involve abstraction over an individual

variable: objects in (a), event-kinds in (b) (in the spirit of Landman & Morzycki

2003, see Chapter 2 below), times in (c), and locations in (d) and (e). Further,

11 [revise] Functional (higher-type) traces have been proposed to account for functional wh-questions (XXX; these may provide good counterexamples to (1) (thanks to Chris Potts and Matthew Stone (p.c.) for pointing these cases out.) I am not sure what to make of them; maybe it would be interesting to look at whether some wh-construction dont permit them, and why 12 Note that (13e) does seem syntactically to be a PP gap, as this position cannot be filled by a DP, with the exception of there, e.g., *I put the book the room vs. I put the book in the room vs. I put the book there.

there are many other kinds of restrictive relative clauses that one could imagine

might exist, that do not. For instance, in English, there certainly do not appear to

be restrictive relative clauses whose gaps syntactically correspond to

conjunctions, determiners, prepositions, complementizers, or adverbs that are not

temporal (e.g., when), locative (e.g., there) or manner (e.g., thus), such as again.

This is perhaps unsurprising if none of these categories may move. However,

strikingly, there also do not appear to be any restrictive relative clauses that have

gaps corresponding syntactically to VPs or APs (see also Baker 2003, as

discussed in Section 2.2 below):13

(14) a. !Mary cries that you make her __. VP

!Mary runs that you ask her to __.

b. !Mary became angry that you made her __. AP

!Mary felt happy that you felt __.

This is so even though these constituents do seem to be able to move, as the

following fronting constructions illustrate: 13 However, non-restrictive relatives, which also appear to involve wh-movement (Potts 2002a, 2002b) may have gaps that appear to correspond to APs and VPs, (Sells 1985, Potts 2002a, 2002b): (i) She was fond of her boy, which Theobald never was __. AP (ii) I can make words, which you cannot __. VP This is a puzzle I will look at in Chapter 4. Baker 2003 independently observes a similar pattern for other types of wh-constructions.

(15) a. and cried, Mary did __. VP

b. ... and angry, Mary became __. AP

The absence of restrictive relatives with VP or AP gaps is expected given (1):

these constructions would require abstraction over VP and AP meanings, usually

taken to be properties of individuals (but see Section 2.1 below on nominalization

and property theory.) In contrast, the fronted examples in (15) have been argued

to be instances of syntactic reconstruction, that is, these moved constituents have

been argued to syntactically occupy their unmoved positions at LF (see, e.g.,

Labeux 1990, Heycock 1995, Romero 1990, Fox 2000). As will be discussed in

Chapter 4 below, syntactic reconstruction for fronted APs and VPs has been

motivated based on the behavior of these constituents with respect to Principle C

violations. For example, in (16) below, so that these expressions at LF are

syntactically interpreted in their base positions (Lebeaux 1990, Heycock 1995).

(16) a. I dont think you can accuse him of being proud of John.

b. I dont think you can accuse John of being proud of him.

c. *[AP Proud of Johni]j , I dont think you can accuse himi of being tj.

I will discuss these and other possible and impossible wh-constructions in Chapter

4.

To sum up, this thesis posits a constraint on possible types of pro-forms

and traces, in the form of the generalization in (1). The bulk of this thesis is

devoted to backing up this claim on a case-by-case basis. The remainder of this

thesis is organized as follows. In the next two sections, I will first review some

precedents to (1), namely, Chierchia (1984) and Baker (2003), and then spell out

my basic theoretical assumptions for this thesis. Chapters 2 and 3 investigate the

semantics of potential higher type pro-forms: Chapter 2 looks at pro-forms that

have the syntactic distribution of modifiers, namely, English such and adverbial

thus, their analogues in Polish and German, and their more informal paraphrase in

English, namely, like that. Chapter 3 investigates VP and NP pro-forms, focusing

on English do so and one. Chapter 4 looks at potential higher type traces, both

reviewing the reconstruction debate in more detail, and showing that, for English,

the predictions (1) makes for a typology of wh-constructions are borne out.

2. Precedents

Chierchia (1984) and Baker (2003) both propose constraints similar to (1). In the

following, I will present the main points of each, and try to make clear the ways in

which their proposals differ from my own.

2.1 Property theory and the No Functor Anaphora constraint

The constraint in (1) can be taken as a stricter version of the No Functor

Anaphora constraint of Chierchia (1984). Chierchias constraint follows from the

logic of the interpretive system he develops namely, property theory (Chierchia

1985, Chierchia & Turner 1988) which only has variables ranging over

individuals (type e) and predicates (type ), so that, e.g., there are no

grammatical processes that involve quantification over functors (where functors

are those expressions of a type higher than e or ) (Chierchia 1984, p. 77).

This has consequences for possible types of pro-forms, as he points out in the

following:

Saying that there are no variables of a certain logical type amounts to saying that we cannot refer to arbitrary entities of that type. On the assumption that anaphoric processes involve a capacity to refer to arbitrary entities in a given domain (formally represented by a notation with variables ranging over that domain) our system predicts that functors do not enter anaphoric processes in natural languages. Hence, we should expect that processes such as pronominalization, VP-deletion, wh-movement etc. never involve determiners, prepositions, adverbials, etc. It seems to me that there is something basically right about this generalization. For instance, in general determiners, prepositions, complementizers, etc. do not undergo wh-movement and have no pro-forms. Similarly there is no analogue of VP-deletion or one-anaphora for these items. [Chierchia 1984: pp. 83-84]

The main difference, then, between Chierchias constraint and the one I am

proposing here is that his allows for variables of type , while mine does not.

A natural next question to ask, then, is how the two constraints might differ in

their empirical predictions. There are some difficulties in trying answer this,

however. For one, in certain interpretation systems (including Chierchias) (some)

properties correspond systematically to individuals (Chierchia 1984; Chierchia &

Turner 1988). Under such a system, it could be hard to tell whether a given

occurrence of an expression denotes a property or its individual correlate; thus, it

might likewise seem difficult to determine whether a given pro-form or trace

denotes a property or its individual correlate. I can think of at least two strategies

for dealing with this confound, both of which I will pursue in the following

chapters. One strategy is to look for properties that do not correspond to

individuals, and to try to test whether they may antecede pro-forms. To spell this

out more precisely, let me at this point review in more detail the basic mechanics

of Chierchias system.

In Chierchias system, there are just three logical types: individuals (e.g.,

proper names and definite descriptions), predicates (e.g., common noun phrases,

APs, and tensed VPs) and functors (e.g., prepositions, determiners, and

complementizers). Properties but not functors systematically may be mapped

to their individual correlates via a nominalization function, namely, the down

operator, . Individuals may likewise be mapped to their corresponding properties

via the inverse, predicator function: the up operator, . The down operator

nominalizes, while the up operator predicativizes.14 Thus, in this type of system,

properties can be looked at from two different points of view:

Qua predicable entities, they appear to be essentially incomplete or unsaturated structures. Something like runs cannot stand by itself: it is a structure with a gap in it So properties as predicables should be conceived as intrinsically incomplete, gapped, or functional structures Properties, however can be nominalized and nominalized predicative expressions can be subjects in predication acts. This strongly suggests that the unsaturated structures associated with predicative expressions can somehow be projected as individuals, or have individual counterparts, which is what nominalized predicative expressions refer to. So on this view, properties have two modes of being: one as intrinsically functional entities, the other as individuals systematically correlated to those entities. [Chierhica 1984, pp. 54-55]

So, for example, the verb run used as a predicate can be taken to map an

individual to a truth value:

(17) John is running.

Used as a subject, however a gerund, for example it may refer to an (abstract)

individual, say, the activity of running:

(18) Running is nice.

The predicate is nice can even itself be nominalized:

14 I postpone the formal definition of these operators that I will adopt here until Section 3.2.2 below.

(19) Being nice is nice. (Chierchia 1984, p. 12, (8))

The system offers an elegant account of nominalization, and makes possible a

uniform treatment of predication: subjects are (generally) individuals, and

predicates are (generally) properties.15 This view of nominalization also helps

explain why certain expressions may not occur as subjects of predication:

expressions that do not correspond to individuals (i.e., are not nominalizable) may

not occur as subjects. For example, determiners, conjunctions, and certain adverbs

do not correspond to individuals, and correspondingly cannot occur as subjects:

(20) *The/and/again is nice.

This is directly relevant to the main claim of this thesis: the prediction here is that

there should be a direct correlation between those expressions that are not

nominalizable, that is, those that do not correspond to individuals, and thus may

not occur as subjects of predication, and those that do not have corresponding pro-

forms or traces. Interestingly, functors like those in (20), are not the only

expressions that do not correspond to individuals; certain property-denoting

expressions also appear not to correspond to individuals. I will give two examples

15 Some authors have proposed rules of composition which interpret predicative phrases in object position, e.g., Diesing, Chung & Ladusaw (2003); it seems an open question whether such rules should also apply to predicative phrases in subject position.

here. Is (or tensed VPs) provide the first: they may not occur as subjects, as

(21) shows, nor do they have corresponding pro-forms, as (22) shows.

(21) a. *Is running is nice.

b. *Are nice is nice.

(22) *John is screaming and Mary na too.

That Is may not occur are subjects of predication suggests that they do not

correspond to individuals (though it is a very interesting question why they do not,

one which I have no answer for here.)16 It then follows from (1) that also have no

corresponding pro-form. The absence of pro-forms for these expressions would be

unexplained if property variables were possible.

A second example of properties that do not correspond to individuals

comes from the nominal domain: Carlson (1977b) observes that certain properties

do not seem to have individual correlates, that is, they do not seem to correspond

to kinds. The bare plurals in (23) are a case in point:

16 Potts (2002b) suggests that the nominalization operator occurs syntactically low in a VP, and for this reason does not map tensed VPs into individuals.

(23) a. parts of that machine C. 1977b

b. people in the next room

c. books that John lost yesterday

d. bears that are eating (now)

These properties pick out classes of objects that refer to a finite set of things

that must exist at a certain time in a given world. Like tensed VPs, they seem to

not be in the domain of nominalization function, . As Carlson observes, exactly

these properties may not antecede the pro-form such, a putative property-anaphor

(see Chapter 2 for a more detailed discussion of such):

(24) People in the next room ??such people (are obnoxious) C. 1977b

Thus, it appears that the antecedents for such form the natural class of properties

that have individual correlates. This falls out naturally from (1), and we would not

expect the opposite state of affairs to hold, that is, to find a pro-form that could

only be anteceded by properties that do not correspond to kinds/individuals.

Again, a constraint like Chierchias, which allows for property variables, would

not rule out such pro-forms.

My second strategy for teasing apart the predictions of the two constraints,

as stated in the introduction, is to try to identify syntactic positions that must be

occupied by property-denoting expressions (but not their individual correlates),

and to check whether pro-forms or traces may occupy those positions. It is a

problem for this strategy, however, that even if a particular syntactic node can be

assumed to require a property-denoting interpretation, there might still be a

syntactic layer below that node which is individual-denoting, and sister to some

covert functional structure which maps individuals to their corresponding

predicates. For example, Kratzer (2005), following Krifka (1995) and Yang

(1991) (and, originally, Carlson (1977)), assumes that noun roots, stripped of their

inflectional morphology, are kind-denoting. She further proposes, in the spirit of

Krifka (1995) and Borer (2005), that English has an ambiguous, non-overt

classifier, which may map a kind-denoting noun root into a property of

individuals that realize that kind, as illustrated in (25):

(25) [NP classifier [N zebra]]

Thus, predicative count nouns are syntactically constructed from names of kinds

with the help of classifiers (Kratzer 2005, p. 7). This is relevant here, because

even if NPs can be assumed to be property-denoting, a pro-form or trace with the

syntactic distribution of an NP might itself not necessarily be property-denoting;

the pro-form or trace might be individual-denoting, occupying some lower

position in an NP, which is mapped to a predicate by a covert classifier. With

such possibilities for covert functional structure, it might seem difficult to

determine whether a pro-form is at heart individual-denoting or property-

denoting. I have no good solution for this difficulty at this time.

2.1.1 The problem of adverbs

It is interesting that Chierchia suggests that only certain adverbs provide a

counterexample to the No Functor Anaphora constraint:

Items that might constitute a serious problem for the present hypothesis are obviously adverbs. Adverbs seem to enter various anaphoric processes such as wh-movement or comparative formation, and to have pro-forms (thus, so)

Chierchia goes on to point out that only three types of adverbials are problematic:

manner adverbials, locatives, and temporal modifiers correspond to pro-forms

(thus, there, and then), while adverbs like again and almost do not. Building on

Landman and Morzycki (2003), I will argue below that this is because it is exactly

these three types of adverbials that correspond to individuals thus, there, and then

denote variables over individuals: variables over event-kinds, locations, and

times, respectively.

2.2 Baker (2003)

Baker (2003) also proposes a restriction on possible pro-forms and traces, namely,

that only nouns (and their phrasal projections) can participate in anaphoric

relations (that is, they alone may antecede or occur as pronouns or traces):17

I therefore predict that there should be no such thing as pro-adjectives or pro-verbs in languages of the world that take part in anaphoric relationships with APs and VPs in the same way that pronouns enter into anaphoric relationships with NPs. Prima facie, this seems to be true: virtually every grammar has an index entry for pronouns, but very few mention pro-adjectives or pro-verbs. It is also perfectly possible to work on a language like Mohawk or Edo hard for more than five years and never encounter anything one is tempted to analyze in this way. (Edo is rich in proverbs, but that is another story.) [Baker 2003, p. 129]

Bakers main interests lie in articulating the core differences among lexical

categories; nouns, he argues, have a unique semantic property that permits them

alone to antecede pronouns and traces. Following Geach (1962) and Gupta

(1980), he takes nouns to differ from all other categories in having a criterion of

identity: the idea in a nutshell is that only common nouns have a component of

meaning that makes it legitimate to ask whether some X is the same (whatever) as

Y [Baker, p. 97]. To illustrate this point, he presents the contrast between the

examples in (26) and those in (27), which show that nouns (whether singular,

plural, mass, or abstract) may be used in the frame X is the same __ as Y, while

adjectives and verbs (or their phrasal projections) may not (Geach 1962):

17 In talking with Mark Baker in fall 2004, I found that he independently came to similar conclusions about restrictions on pro-forms and traces in his (2003) book. It has since been very exciting and illuminating to think about the differences between his constraint and my own.

(26) a. That is the same man as you saw yesterday. B. 2003

b. Those are the same women as we saw last night.

c. That is the same water as was in the cup this morning.

d. We want to have the same liberty as they have.

(27) a. #That is the same long as this. B. 2003

b. #She is the same intelligent as he is.

c. #I saw Julia the same sing as Mary did.

d. #I watched Nicholas the same performs a stunt as Kate performed.

He contends that although the examples in (27) would be ruled out on syntactic

grounds, as only nouns may follow a determiner and adjective, these examples are

further semantically incoherent, as only nouns have a criterion of identity.

Analyzing nouns in this way, he argues, explains those properties that seem to set

them apart from other lexical categories, in particular, that they: (i) support

individuation and counting (and thus may occur with number marking); (ii) may

occur with quantifiers and determiners; (iii) may antecede or occur as pronouns,

reflexives and traces; and (iv) they may serve as arguments of predicates. I will

restrict the discussion here to the third property of nouns, i.e., that they alone

participate in anaphora. Before looking at Bakers empirical arguments for this

position, a few comments can be made to begin to compare his proposal to my

own. The differences between the two proposals, I think, are subtle the two in

large part overlap in predictions but they do differ. On the empirical side, his

constraint predicts the absence of pro-forms that are syntactically non-nominal,

while mine does not, and it does seem that such expressions do occur (see

discussion below). On the conceptual side, our proposals are alike in that they

both attribute the potential to participate in anaphora as being tied to

individualhood, his via the criterion of identity. Our proposals differ, however, in

that for my proposal, nouns are not the only category that can be individuated. For

example, verb meanings can be individuated by talking about events, and

accordingly, events not necessarily represented syntactically as nouns can be

counted (?Krifka 1992, ?Landman 1996), quantified (Berman, von Fintel 1994

and others), provide the reference for pro-forms and traces (? Rothstein), and may

serve as arguments of predicates (Chierchia Zucchi). The situation is similar

with adjectives, which can be individuated by talking about degrees, which also

may be counted, quantified, provide the reference of a pro-form or trace, and may

serve as arguments of predicates, without necessarily being nominal (references).

I will try to illustrate these points more clearly in the next sections by reviewing

the empirical evidence presented to support Bakers view, concentrating here on

the predictions his account makes for anaphora and movement.

2.2.1 Anaphora

Baker proposes that nouns having a criteria of identity is represented

syntactically by indexing, so that nouns are the only lexical category to bear an

index. As a result, only nouns may antecede pro-forms. He presents (28) and (29)

to illustrate this: although both genitive nominals and nationality adjectives can

express the agent in a nominalization, as the examples in (28) show, only the

genitive can antecede a pronoun, as the example in (29) shows (Kayne 1984).

(28) a. Abanias resistance

b. the Albanian resistance

(29) a. Albanias destruction of itself grieved the expatriate community.

b. *The Albanian destruction of itself grieved the expatriate community.

These sorts of examples come from Kayne (1984) (as Baker points out) who

concluded from them that adjectives cannot bind pro-forms of a different

syntactic category; this conclusion seems to me plausible here, and would be

consistent with my own proposal. Baker, in contrast, suggests that these examples

follow from his theory of nouns, since nouns alone may bear a referential index.

To really rule out Kaynes type of explanation, one would want to make sure that

there are also no pro-forms which themselves have the distribution of adjectives

and verbs, which Baker does claim to be the case. He looks in detail at two

candidates in English, so, which appears to have the distribution of a predicate AP

(Corver 1997), as (30) shows, and VP-Ellipsis, which appears to have the

distribution of a VP, as (31) shows, and argues that neither in fact present

counterexamples to his proposal.

(30) a. Chris is brave, and Pat seems so too. B. 2003

b. I consider Chris intelligent, and Mary considers Pat so.

(31) Chris will solve the problem, and Pat will too. B. 2003

So, he argues, is not actually an AP pro-form, as it does not quite have the

distribution of an AP. In particular, unlike APs, so may not occur as a resultative

secondary predicate:18

(32) a. ??John beat the iron flat and Mary beat the copper so. B. 2003

b. ?*The chair is already clean, and Chris will wipe the table so too.

18 He also points out that adjectives can be pre-nominal, whereas so cannot, as (i) shows, but it likely that in these cases so alternates as such (see Chapter 2.) (i) *Mary is an intelligent woman, and John is a so man.

He proposes instead that so functions a pro-PredP, where PredP is a functional

projection that dominates an AP in examples like (XXa) and (b) above.19 It is

unclear, however, how PredP would be in any way nominal (a point Baker does

not seem to address.) This use of so is not one I will be analyzing in detail here

(see fn. 6); however, one promising line of analysis would be to treat it as a pro-

CP, assuming that CP denotations are nominalizable (thanks to Mark Baker, p.c.,

for suggesting this for English so, and Viviane Deprez, p.c., for French le (Kayne

1975), which reportedly has the same distribution as English so.)

Baker also argues that VP-Ellipsis is not a pro-form at all, but instead has

internal syntactic structure. As he points out (and as will be discussed in Chapter

3, although there are parallels between VP-Ellipsis and pronominal anaphora,

there is some evidence that VP-Ellipsis should not be analyzed as a variable over

VP meanings. I will take this up again in Chapter 3.

Baker does not look closely at some of the other potential non-nominal

pro-forms mentioned above. Pro-AdvPs such as so and thus, in particular, it

seems would be problematic for his proposal, unless these pro-forms could be

argued to be nominal (in Polish, for example, they do not inflect as nominals, see

Landman & Morzycki 2003, discussion in Chapter 2, Section X below.)

19 It is unclear to me that this inverted use of so is actually a pro-form, and not something more like the expression too. The following examples suggest that the inverted so may be compatible with the pro-VP do so, suggesting that this so is more like too: (i) a. ??hris is protesting, and so is Pat doing so. b. Chris is protesting, and Pat is doing so, too.

2.2.2 Movement

[Note: It would make more sense to defer Bakers discussion of movement to

Chapter 4 below. I will probably ultimately do this, but for now I will leave the

discussion here.]

It follows from Bakers theory of lexical categories that only NPs should be able

to move, as only they can bind traces. In support of this, he observes that NPs can

undergo certain movement operations that APs and VPs may not. For instance,

restrictive relatives (33), clefts (34), and tough-movement (35), he observes, do

not allow for gaps corresponding to APs or VPs (examples based on Bakers):

(33) Relative clauses

a. *I am not clever that he is __. AP

b. *Mary will sing that Pat will __. VP

(34) Clefts

a. ??Its smart that Chris is __. AP

b. *Its sing that Mary will __. VP

(35) Tough-movement

a. ??Content is hard to be __. AP

b. *Solve this problem is hard to make them __. VP

In contrast, wh-questions, fronting, and so-called though-movement do seem to

permit AP and VP gaps:

(36) Wh-questions

a. How tall is Chris __? AP

b. (none)

(37) Fronting

a. [AP hard-working], he is __. AP

b. and [VP clean his room] he did __. VP

(38) Though-movement

Baker proposes explaining this contrast by construing these two sets of wh-

constructions as forming distinct natural classes: the former involve null operator

movement from the gap within the embedded clause, while the latter are instances

of copy movement. In effect, only the former examples necessitate operator

variable binding structures, and since only NPs bear referential indices, no other

category may correspond to the gap in these structures. Copy movement, he

suggests, does not require operator-variable binding. While it seems appealing to

try to differentiate those wh-constructions which permit APs and VPs from those

that do not, there at least two major problems for this particular proposal. The first

is theoretical: it is not at all clear why certain wh-constructions would be analyzed

as copy-movement, and others not (in fact, both semantically would ultimately be

analyzed as an operator-variable structure (Chomsky 1993, Rullman and Beck

(1998), Sauerland (1998), Fox (2000)). The second is empirical: non-restrictive

relatives (Sells 1985, Potts 2002a, 2002b) as well as as-parentheticals (Potts

2002a, 2002b) also appear to involve movement of a null operator, but both

permit both AP and VP gaps:

(39) a. She was fond of her boy, which Theobald never was __. AP

b. I can make words, which you cannot __. VP

(40) a. Ali was energized, as his trainer suggested he might be __. AP

b. She could see the finish line, as Joan could __ too. VP

I propose a different way of explaining why AP and VP gaps are possible in the

latter set of wh-constructions in Chapter 4.

3. Theoretical framework

I will assume in large part the compositional, type-driven framework articulated

in Heim and Kratzer (1998). In this system, the semantic component directly

interprets phrase structure trees, or, more specifically, Logical Forms (LFs). LFs

are disambiguated representations, which, in addition to representing syntactic

structure, mark anaphoric relations by co-indexing, and represent quantifier scope

as the result of a rule of Quantifier Raising (QR). When movement occurs, an

indexed trace occupies the base position of the moved constituent, and an index

binding that trace is adjoined to the sister of the moved constituent. The LF of

(41a), for example, is that in (41b):

(41) a. Maria described every guest.

b. LF: [tree here]

In the tradition of Montague, expressions are categorized by their semantic

type: assuming as the two basic types individuals (type e) and truth values (type

t), the inventory of possible semantic types and their denotation domains can be

defined recursively as in (42), from Heim and Kratzer (1998), pp. XXX.

(42) Semantic types

(a) e and t are semantic types.

(b) If a and b are semantic types, then is a semantic type.

(c) If a is a type, then is a type.

(d) Nothing else is a type.

Semantic denotation domains

(a) De := D (the set of individuals).

(b) Dt := {0,1} (the set of truth values).

(c) For any semantic types and , D is the set of all functions from D

to D.

The interpretation function, || ||, assigns to each syntactic node of type a an

element of Da, with respect to a variable assignment, g. The variable assignment

is defined as in (43); the interpretation function is defined by the rules of semantic

composition given in (44)-(49), from Heim and Krzter, p. XX.

(43) A variable assignment is a partial function from |N into D.

(44) Lexical Terminals

If is a terminal node occupied by a lexical item, then |||| is specified in

the lexicon.

(45) Non-Branching Nodes

If is a non-branching node, and is its daughter, then, for any assignment g, is in the domain of || ||g if is. In this case, ||||g = ||||g.

(46) Functional Application

If is a branching node and {, } the set of its daughters, then, for any assignment g, is in the domain of || ||g is both and are, and ||||g is a function whose domain contains ||||g. In this case, ||||g = ||||g(||||g).

(47) Predicate Modification

If is a branching node and {, } the set of its daughters, then, for any assignment g, is in the domain of ||@||g if both and are, and ||||g and ||||g are both of type . In this case, ||||g = x : x D . and x is in the

domain of ||||g and ||||g. ||||g = ||||g = 1.

(48) Predicate Abstraction

Let be a branching node whose daughters are and , where dominates only a numerical index i. Then, for any variable assignment g,

||||g = x : x D and is in the domain of || ||g[x/i] . ||||g[x/i].

(49) Traces and Pronouns Rule

If is a pronoun or trace, g is a variable assignment, and i is in the

domain of g, then i is in the domain of || ||g, and ||i||g = g(i).

These rules of composition, together with the assumption that phrase structure

trees are at most binary branching, ensure an extensional, compositional, type-

driven semantic interpretation system.

3.1 Pronouns and traces as variables

As reflected in the Traces and Pronouns Rule, I assume here that pronouns and

traces are interpreted as variables. Variables are defined as in (50); an expression

is a variable iff its denotation may vary with the assignment:20

(50) A terminal symbol is a variable iff there are assignments g and g such

that ||i||g ||i||g.

20 The discussion here closely follows the discussion in Heim & Krazter, pp. 239-245.

Variables thus contrast with constants, which do not vary with the assignment:

(51) A terminal symbol is a constant iff for any two assignments g and g,

||i||g = ||i||g.

Pro-forms can further be distinguished by their uses as bound or free. Following

Partee (1978), Heim & Kratzer (1998) and others, I will construe both anaphoric

and deictic uses of pro-forms as free variables:

Anaphoric and deictic uses seem to be special cases of the same phenomenon: the pronoun refers to an individual which, for whatever reason, is highly salient at the moment when the pronoun is processed. [H&K, p. 240].

For example, in (52a). he may be construed as a free variable, assuming that an

appropriate context must provide its value by means of a variable assignment. The

referent of the pronoun could be made salient by non-linguistic or linguistic

factors, i.e., the pronoun could be deictic or anaphoric, but in both cases, the

pronoun receives its value from a contextually supplied variable assignment.

(52) Hei left early.

In contrast, pro-forms and traces that are c-commanded by a co-indexed variable

binder are bound. Bound variable uses of pronouns, for example, include those

that are c-commanded by the index binder that results from QR-ing a generalized

quantifier:

(53) [Every woman]1 1 t1 saw herself1.

It follows that the trace in (53) is also a bound variable.

Finding bound-variable uses of pro-forms that have the distribution of

higher-type expressions would provide good evidence that higher-type variables

do indeed exist; I will keep an eye out throughout for potential cases.

3.2 The domain of individuals

Because my analysis rests on the assumption that D is multi-sorted, this section

spells out in more detail my assumptions about what constitutes D.

3.2.1 Plural individuals

Following Link (1983) and many others, I will assume that D contains both

singular and plural individuals. That is, D forms a complete atomic join semi-

lattice, ordered by the part of relation, , as illustrated in (54).

(54) a+b+c

a+b a+c b+c

a b c

In the structure above, a, b, and c are atomic (or singular) individuals, + is an

individual sum operator, and the lines represent the part of relation. Expressions

denoting atomic individuals include names of individuals such as John and Mary,

as well as singular pronouns like he or she. Expressions denoting plural

individuals include plural definite descriptions such as the boys and the girls, as

well as plural pronouns like they or them.

3.2.2 Kinds as individuals

I will also assume that the domain of individuals, D, includes kinds (Carlson

1977b, Krifka et al. 1995, and references therein). Variables ranging over kinds

will be represented as k1, k2, k3. Following Chierchia (1998), I will model kinds as

pluralities, the sum of all instances of the kind. For example, the dog-kind, DOG, is

the sum of all dogs.21 Kinds may be mapped to properties of individuals that

realize them, via the predicativizing operator, , which can now be defined as

follows:

21 Cf. the way Carlson (1977) and Krifka et. al. model kinds. Explain XXX

(55) Predicativization

Let k be a kind. Then, k = [x . x k], where k is the plural individual that

comprises all of the atomic members of k.

Similarly, properties may be mapped to kinds by the nominalizing operator, ,

defined as follows:22

(56) Nominalization

For any property P, P = the largest member of P, if the largest member of

P is a kind; undefined, otherwise.

In line with Carlson and Chierchia, I will assume that the notion of natural kind is

broad and often context-dependent:

By natural kinds, we do not necessarily mean just biological ones or even well-established ones. Artifacts (like chairs or cars) or complex things (like intelligent students or spots of ink) can qualify as kinds, to the extent that we can impute to them a sufficiently regular behavior (cf. on this Carlson1977, pp. 26ff. and Krifka et al. 1995). What counts as kind is not set by grammar, but by the shared knowledge of a community of speakers. It thus varies, to a certain degree, with the context, and remains somewhat vague. Lexical nouns identify kinds. Complex nouns may or may not. [Chierchia 1998]

22 As discussed in Section X above, properties that may not be mapped to kinds that is, are not in the domain of the nominalizaing operator include, e.g., nominals like people in the next room and Is like is running.

Some complex nouns like, then, may correspond to kinds, while others may not,

depending on the context in which they are used. When a complex noun does not

correspond to a kind, e.g., parts of that machine, it can be assumed to be out of

the domain of the down operator.

Because my hypothesis rests on the claim that kinds are individuals, let me

here briefly review some evidence for treating kinds in this way. Some positive

evidence for treating kinds as individuals comes from the observation that across

languages, kind-referring NPs are typically definite (Krifka et al); in this respect,

kind-referring NPs are like proper names (Carlson 1977b, Heyer 1985, see also

Kripke 1972, Putnam 1975). Kind-level predicates may only take definite

descriptions, proper names (of kinds), and bare plurals as arguments:

(57) The dodo became extinct in the 17th century

(58) Raphus cucullatus became extinct in the 17th century.

(59) This kind of bird became extinct in the 17th century.

(60) Bronze was invented as early as 3000 B.C.

As Carlson (1977) points out, the so-called construction also selects for definite

descriptions, proper names, and bare plurals:

(61) a. Slim is so-called because of his slender build. C. p. 100

b. Cardinals are so-called because of their color.

c. The cardinal is so-called because of its color.

d. *All/most/few/some/these cardinals are so-called because of their color.

Also like proper names, bare plurals are also natural as vocatives (Carlson 1977):

(62) a. Fred! Lend me your ears. C. p. 101

b. Friends! Soldiers! Veterans! Lend me your ears.

c. ??Many friends! ?All veterans! *Some man! Lend me your ears.

These sorts of examples provide additional motivation for treating kinds as

individuals (see Carlson (1977b) and Krifka et al..(1995) for further discussion on

this point and a detailed comparison to alternatives.)

3.2.3 Events and event-kinds

I will also assume that D includes events (e1, e2, e3, etc..) (Davidson 1967),

degrees (d1, d2, d3, etc. ), times (i1, i2, i3, etc.), and locations (l1, l2, l3, etc.). See

these references, respectively, for arguments for treating these as individuals in D.

Chapter 2

Adjectival Anaphora

This chapter looks closely at the syntax and semantics of pro-forms that have the

syntactic distribution of adjectives or adverbs (or their phrasal projections). The

empirical focus is the English word such (Bolinger 1972, Bresnan 1973, Carlson

1977b, Siegel 1994, Wood 2002). Following Carlson (1977), I argue that such is

best analyzed as involving not a property variable, but a variable over kinds. I

then extend this analysis both to the more informal counterpart of such,

adnominal like that, as well as, following Landman & Morzycki (2002), the

adverbial analogues of such in Polish and German, tak and so, and adverbial like

that. I then sketch an account of pro-adverbials like then and there. In each case, I

re-examine the evidence for considering these expressions to involve higher type

variables and conclude that they in fact involve variables of type e.

1. Whats such?

Such is, at least at first sight, a very good candidate for an A (or AP) pro-form.

Syntactically, it appears to be adjectival, as it may occur between a determiner

and a noun, a position commonly taken to be reserved for adjectives (or adjectival

projections):

(63) Several/many/three/few/most/many such mistakes were found.

Semantically, it appears to be able to pick up the reference of a preceding

adjective, as reflected by the italicization in the following:

(64) a. Nice people... such people...

b. Big dogs... such dogs

c. Strange ideas... such ideas...

Adjectives like nice, tall, and strange at least at the level of their maximal

projections are commonly taken to denote properties, and these examples thus

suggest a treatment of such as a property variable. An analysis along these lines is

in fact proposed in Siegel (1994). However, following Carlson (1977b), I will

look at evidence that such is not a property variable, but rather its denotation

contains a variable over kinds.

1.1 Setting aside the ambiguity

The word such in English often gives rise to ambiguous sentences (Bolinger 1972,

Bresnan 1973). For example, the following sentences are ambiguous:

(65) a. Hilda is such a scholar. (Bresnan 1973)

b. We have all made such mistakes.

On one reading, (65a) might be paraphrased as Hilda is that kind of scholar or

Hilda is a scholar like that, and on a second reading, as Hilda is so much of a

scholar or Hilda is very much a scholar. (65b) is likewise ambiguous: on one

reading, it can be paraphrased as We have all made those kinds of mistakes or

We have all made mistakes like that, and on a second reading, as We have all

made big mistakes.23 Following the terminology of Bresnan (1973), I will refer to

the first use of such as kind such, and the second as degree such.24 I will for the

most part only be concerned with kind such here, since that is the use on which

such acts like an adjectival pro-form. However, before setting aside degree such,

it will be useful to point out some systematic differences between the two uses, in

order to isolate kind such; the remainder of this section is devoted to this end.

23 Some English speakers report that they cannot get the degree reading of such for (b). 24 Bolinger (1972) uses the terms identifier such and intensifier such.

There are a number of properties that distinguish the two uses of such, and

they are to some extent in complementary distribution. For example, when such

occurs with a that-clause, only its degree reading is available:

(66) Hilda is such a scholar that all her work is impeccable. B. 1973

In contrast, when such occurs with an as-clause, only its kind reading is available:

(67) Hilda is such a scholar as you were speaking of just now. B. 1973

The two uses also differ in the types of nominals they may modify: degree such is

only available when such modifies a gradable predicate, while kind such is not

subject to this restriction.25 For example, compare the ambiguous sentences in

(68) with the unambiguous examples in (69).

(68) a. Such strange theories have become quite popular.

b. We have made such mistakes.

25 A gradable nominal is one that either contains a gradable adjective, i.e., an adjective that may occur with degree morphemes like so, too, or as e.g., strange) or a gradable noun (e.g., mistake, loudmouth.

(69) a. Such theories have become quite popular.

b. We have found such evidence.

In (68a-b), such occurs with a gradable predicate, e.g., strange theories and

mistakes, respectively, and as a result both readings are available. In contrast, in

(69a-b), such occurs with a non-gradable nominal (e.g., theories, evidence), and

only the kind reading is available.

The two uses also differ with respect to which determiners they may co-

occur with. Only identifier such may occur between a determiner and a noun, as

the following unambiguous examples illustrate:

(70) We have made {three/few/most/many} such mistakes.

Both uses may, however, occur in bare, i.e., determinerless, DPs, e.g., such

mistakes, and both uses may occur with the singular indefinite, e.g., such a

scholar. In the latter case, both uses must (infamously) occur before the indefinite

determiner a, a peculiar, and often observed, fact:

(71) *Hilda is a such scholar.

I will not attempt to account for this curious property of such in this work, except

to note, as have many others, that DegPs also display this distribution:26

(72) a. Bill is that tall/too big/so boring/as smart a linguist.

b. *Bill is a that tall/too big/so boring/as smart linguist.

The two uses are also pronounced differently: degree such always bears a

pitch accent, while kind such may, but need not.

Finally, kind such is of a formal register, while degree such is common in

both informal and formal speech. In informal speech, the expressions like that or

of that kind are preferred in place of kind such, so that, for example, such theories

could be more informally paraphrased as theories like that or theories of that kind.

To sum up, the two uses of such can be distinguished by the following

properties: (i) kind such takes a subordinate as-clause, while degree such takes a

subordinate that-clause; (ii) degree such only occurs with gradable nominals; (iii)

only kind such may occur between a determiner and a noun; (iv) degree such

26 Further, neither use of such can occur with a definite determiner (including possessives): *the/those/johns such mistake See further discussion in Section X below.

bears a pitch accent, while kind such may not; and (v) kind such is of a formal

register, while degree such is not.

Although I will only be analyzing the kind use of such, it is an interesting

question how these two uses of such are semantically related (an intriguing

proposal on this point, due to Marcin Morzycki (p.c.), will be discussed below, in

the context of a concrete proposal for the semantics of such). The two uses are at

least historically related, with kind such predating intensifier such (Schiller and

need 1992; Roger Higgins, p.c.).27 I will set this issue aside, however, and

henceforth simply use such to refer to kind such.

1.2 Syntax of such

Syntactically, such appears to be adjectival, as it may occur between a determiner

and a noun, a position reserved for attributive modifiers:

(73) We found some/no/many/several/three such problems.

27 Bolinger offers the following description of the connection between the two uses: For convenience we will speak as if the identifier and the intensifier were two different words, but this need not be taken literally. The intensifier such also identifies not with a particular individual but with a particular degree and the difference can be assigned to the semantic component of the noun that happens to be determined by such, individuality with nondegree nouns, degree of some quality with degree nouns. (Bolinger 1972: 60). Bolinger sees the semantics of degree such as derived from kind such: ...the identifier has fallen out of many contexts except in formal register, giving way to the intensifier, probably because the suchness of something is so likely to be an intensifiable characteristic. We begin by viewing it as pointed to, and end by viewing it as worthy of note, hence as enhanced.

Carlson (1977b), building on Bresnan (1973), argues that such in fact has the

distribution of a Deg~A sequence, e.g., so tall, where other Degs would include

too, as, how, -er, etc. The syntax of such sequences has received a good amount

of attention in the literature, and a number of different analyses have been

proposed. I will adopt here what Bhatt & Pancheva (2004) refer to as the classical

view, according to which Degree words head a DegP which occupies the specifier

of AP (see Chomsky 1965, Selkirk 1970, Bresnan 1973, Heim 2000, and others,

and cf. Abney 1987, Corver 1990, 1997, Grimshaw 1991, Kennedy 1999, who

take DegP to be the functional projection of AP):

(74) [AP [DegP so] tall ]

I will adopt this syntax for such here:

(75) [AP [DegP such ] ]

This syntax for such is in accord with its historical development, as such derives

from the Germanic compound *swa+lk, so-like (Higgins, p.c.), which, on the

classical analysis, might be assumed to have had the following structure:

(76) [AP [DegP so ] like ]

I will refer to this type of structure (i.e., an AP with a DegP in its

specifier) as a complex AP. In line with Svenonius (1993), I will assume that it

may be adjoined to NP:

(77) [DP most [NP [DegP such ] [NP attempts ] ]

Siegel (1994) argues against analyzing such in this way, and instead

proposes that such has the distribution of a simple adjective:

(78) [DP most [NP [A such ] [NP attempts ] ]

On either proposal, such would be interpreted in a position adjoined to NP. I will,

however, adopt the complex AP analysis here, because my intuitions are more in

line with the data Carlson presents in favor of that analysis, than with Siegels

counterarguments. Further, treating such as a complex AP will make it possible to

provide a semantic account of such parallel to that of other complex APs, a move

I will motivate based on the semantic behavior such has in common with other

Degree words, like er and so. The remainder of this section reviews the syntactic

evidence for the complex AP analysis of such.

There are several ways in which such behaves like a complex AP, and

unlike a simple adjective. Just as complex APs must precede all other modifiers of

the head noun, as (79) shows (i.e., the AP sicker must precede the modifier fat),

so must such, as (80) shows.

(79) a. He is a sicker fat boxer than I had remembered. (Carlson 1977)

b. *He is a fat sicker boxer than I had remembered

(80) a. They are such glorious victories. (Carlson 1977)

b. *They are glorious such victories.

Simple adjectives, in contrast, may often precede or follow other modifiers:

(81) a. He is a sick fat boxer.

b. He is a fat sick boxer.

Similarly, just as complex APs may not co-occur with one another, or stack, as

(82) shows, such cannot modify an NP that already contains another complex AP,

as (83) shows.

(82) a. *They are fat enough sicker boxers. (Carlson 1977)

b. *They are sicker fat enough boxers.

(83) a. *They are quicker such rabbits. (Carlson 1977)

b. *They are such quicker rabbits.

Simple adjectives, in contrast, may co-occur with complex APs:

(84) They are quicker brown rabbits.

Also like (at least some) other complex APs, such is positioned to the left of the

indefinite determiner a:28

(85) a. Bill is that tall/too big/so boring/as smart a linguist.

b. *Bill is a that tall/too big/so boring/as smart linguist.

(86) a. *Such a man was here earlier.

b. A such man was here earlier.

Simple adjectives of course do not occur in this position:

(87) a. A well-dressed man was here earlier.

b. *Well-dressed a man was here earlier.

28 I will not attempt an explanation of this puzzling property of such here. Roger Higgins (p.c.) suggests that the inversion (both for such as well as complex APs like so big) may due to the otherwise phonological ill-formedness of having two adjacent phonologically weak functional heads. For example, so big a boy would be a so big boy without inversion, which results in a and so being adjacent. See Section 1.6 for a brief discussion of the semantics of this construction.

Likewise, such, like other DegPs, may not occur with the definite determiner, the

(Bresnan 1973):29

(88) *Bill is the that tall/too big/so boring/as smart linguist.

(89) *The such man was here earlier.

Simple adjectives are fine with the definite determiner:

(90) The young man was here earlier.

Finally, such, like other Degree words, may take what appears to be an optional

clausal complement that has the structure of a relative clause:

(91) a. Bill is too tall a player for us to have on the team. (Carlson 1977)

b. Smarter men than we have seen today do exist.

c. Bill is as nice as Julie is.

d. Such people as we have seen today should be locked away.

29 The incompatibility of DegPs with the definite determiner is probably a semantic issue, and not a syntactic one, but the parallel still holds.

To summarize, such is like a complex AP, and unlike a simple adjective,

in that it (i) must precede other nominal modifiers, (ii) cannot stack, (iii) precedes

the indefinite determiner, a, (iv) may not occur with the definite determiner the,

and (v) occurs with an optional complement clause that has the structure of a

relative clause.

Siegel finds the sentences in (80b) and (83) acceptable, and concludes that

such is a simple adjective. Although Carlson and Siegel are disagreeing over

sentences that are sometimes rather hard to judge, I find my own intuitions more

in line with Carlsons, and so will adopt his syntax.

1.3 Semantics of such

As observed above, examples like the following (repeated from (64) above)

suggest an account of such as a property variable, as such appears to pick up the

reference of a preceding adjective (or adjectival projection):

(92) a. Nice people... such people...

b. Big dogs... such dogs

c. Strange ideas... such ideas...

Such in fact, as Carlson observes, appears to be able to pick up the reference of

virtually any sort of NP modifier, be it adjective, PP, relative clause, or

participle. He provides the following examples, in which such appears to refer

back to different sorts of NP modifiers:

(93) a. Old ladies such ladies [C., 84]

b. People owning dogs... such dogs...

c. Cats without tails such cats

d. People who eat fish such people

Treating such as a property variable, as these examples suggest, would require

some modifications to the system I have been assuming here, which is set up so

that pro-forms are assigned to individuals in De. Although I will ultimately argue

against this type of analysis for such, it will be useful to first spell out a precise

version of it. Following Heim and Kratzer (1998), the system could be modified

to account for higher-type variables by assuming that an index (associated with a

pro-form or trace) is not just a number, but a pair of a number and a semantic

type. Accordingly, the variable assignment could then be redefined as in (94).

(94) A variable assignment is a partial function g from the set of indices to the

set of all denotations, such that, for every dom(g), g(i, ) D.

The formulation of the Pronouns and Traces rule could then also be modified as

in (95).

(95) Pronouns and Traces.

If is a trace or pronoun, and i and are a number and a type

respectively, then, for any assignment g, ||||g = g().

Given these modifications, such could then be assigned the semantics in (96).30

(96) ||such||g = g()

The occurrence of such in (64a), then, would be interpreted as in (97):

(97) ||such||g = g() = ||[AP nice]|| = [x . x is nice]

By this account, then, such would be a pro-modifier of nominals: it would be

assigned a property that corresponds to an expression that may modify a nominal,

e.g., an AP, PP, CP, or gerund.31

30 I will adopt the convention of italicizing object language. 31 Note that since there is no formal way to distinguish properties denoted by modifiers (e.g., tall) from properties denoted by nominals (.e.g, women), there is nothing here that would ensure that such would be assigned an adjectival property rather than a nominal property. This point will be relevant for the discussion of Siegels account of such below.

There are, however, several empirical problems for this sort of approach.

For one, such seems to be able to pick up the reference of constituents that are not

modifiers. For example, in the following, such seems to refer back to whole DPs:

(98) a.Honest money lenders? There are no such people.

b. ... with politicians, journalists, and other such important personages.

C. [87], attributed to Jespersen (1927)

Examples like these as both Carlson and Siegel observe suggest that it is

whole DPs that antecede such, and not simply nominal modifiers. Thus, in an

example like (64a), repeated below, the antecedent of such seems to be the whole

DP nice people, and not just the modifier nice:

(64) a. Nice people... such people...

Similarly, examples like (99), in which such, as a pro-modifier, would appear to

have a discontinuous antecedent (i.e., old who mend shoes), can be

straightforwardly accounted for if such takes as its antecedent the whole DP:

(99) old ladies who mend shoes such ladies should be paid more C, [85]

Carlson and Siegel, however, draw different conclusions from these sorts of

examples. Siegel argues that such is indeed a property variable, but subject to the

restriction that, if bound, its antecedent must be a common noun phrase (here, an

NP), and not an AP. NPs, like APs, are commonly taken to denote properties;

thus, by this account, such would still receive the semantics in (96), but require a

nominal antecedent when bound. This, Siegel points out, explains the contrast in

(100) below: (100b) is bad because the NP tall men binds such, so that such

women yields the intersection of the contradictory predicates woman, and tall

man.

(100) a. All tall men believe that employers prefer such people. S., [28]

b.*All tall men believe that employers prefer such women.

The main problem with this analysis, however, is that not just any nominal may

antecede such. In particular, nominals that do not correspond to kinds do not make

good antecedents for such:

(101) a. People in the next room ??such people (are obnoxious) C. [90]

b. Elephants that are standing there ??such elephants

c. Men that Jan fired this morning ??such men

d. Quarters that I put in the meter yesterday ??such quarters

It is important to note here that these examples are judged unacceptable only in

the case that such takes as antecedent one of the underlined bare plurals; the

examples may in fact be acceptable if such instead picks up its reference from

some salient DP-meaning in the discourse. For example, if everyone in the next

room happened to be loud, (101) could be judged acceptable, as long as such

meant something like loud people, and not people in the next room; the important

point here is that such cannot take as antecedent any of the bare plurals underlined

above.32

Kinds, here, are modeled as a special type of individual in D. Linguistic

expressions that denote kinds bare plurals, for example have unique

properties, which the bare plurals in (101) do not share. For instance, only kind-

denoting bare plurals may occur as arguments to the so-called kind-level

predicates, e.g., extinct, widespread, common, and rare. While bare plurals are

generally fine as arguments to these predicates, as (102) shows, the bare plurals in

(101) are odd, as (103) shows.33

32 Siegel in fact judges these examples grammatical, and so sees such as denoting a semantically unrestricted property variable. 33 Angelika Kratzer (p.c.) points out that kind-level predicates may not be justification enough for positing kind entities. In particular, this may just be something about the argument structure of these adjectives (the kind-level predicates).

(102) a. People are common.

b. Elephants are extinct.

c. Men are widespread.

d. Quarters are rare.

(103) a.??Polar bears in the next room are extinct.

b. ??Elephants that are standing there are widespread.

c. ??Men that Jan fired this morning are common.

d. ??Quarters that I put in the meter yesterday are rare.

In light of these facts, Carlson proposes to analyze such as denoting a property of

individuals that instantiate a free kind-variable (a proposal I will modify shortly

below):

(104) ||suchi||g = x . x g(i)

This explains the unacceptable examples in (101): because such contains a

variable over kinds, it may not be anteceded by non-kind-denoting nominals. Note

that this denotation for such does not violate (1); although such itself is of a

higher-type, the variable it contains is itself of type e.34

Given this denotation, such may combine with the nominal it modifies by

Predicate Modification, yielding, e.g., in (105), a property of individuals that both

realize a contextually salient kind and are dogs:35

(105) ||such dogs||g = x . x g(i) & dogs(x)

34 Angelika Kratzer, p.e., points out that examples like the following suggest that such is associated with an object variable rather than a kind variable; quantification here appears to be over object individuals (i.e., particular mistakes), and such seems to co-vary with each mistake: (i) Every time a mistake occurred, we wondered whether some such mistake might occur again. (ii) For every mistake that occurred, we wondered whether some such mistake might occur again. These examples are puzzling, however, given that co-variation with such is in general not possible with a quantificational subject, e.g., the following example is true iff everyone must likes reading some contextually salient type of books: (iii) Everyone likes reading such books. I am not sure how to reconcile these facts. 35 Carlsons semantics for such in fact includes a presupposition that I have left out here, specifically, under Carlsons account, the value of the variable associated with such must be subkind of whatever kind corresponds to the nominal such modifies. This is to account for the contrast in (i): (i) a. German Shepards such dogs Carlson 1977b

b.#Dogs such German Shepards (ib) is