Inversion Patterns with Fronted Quantifier Phrases

INVERSION PATTERNS WITH FRONTED QUANTIFIER PHRASES

THE INFLUENCE OF (C)OVERT SYNTACTIC NEGATIVE FEATURES

Timo Verhulst Stamnummer: 01200994

Promotor: Prof. Dr. Karen De Clercq

Masterproef voorgelegd voor het behalen van de graad master in de richting Taal- en Letterkunde: Engels

Academiejaar: 2016 – 2017

Acknowledgements

First of all, I would like to thank my supervisor, prof. Dr. Karen De Clercq, for the considerable amount of time she has invested in my research. Her insight and feedback have proven extremely valuable in the writing process. This work would certainly not have been possible without her guidance. I would also like to thank my family and friends; especially my parents, who have provided me with the opportunity to pursue the education that I wanted and have always supported me in every step of the way, and Elise, who (with my “permission”) forced me to spend numerous hours in the library and, during the probably one hundred coffee breaks, assured me again and again that we would get there eventually.

Table of Contents

List of Tables…………………………………………………………………………………………………v List of Figures…………………………………………………..……………………………………...... vi

Introduction 1

Chapter 1 Theoretical background ...... 4

1.1 Quantifiers and negativity ...... 4

1.1.1 Quantifier classification ...... 4

1.1.2 Negativity tests ...... 7

1.1.3 Syntactic hierarchy of negation ...... 9

1.1.4 Nonmonotonic QPs ...... 10

1.2 Inversion in Generative Grammar ...... 11

1.2.1 SAI patterns ...... 11

1.2.2 WH-/NEG-criterion ...... 12

1.2.3 The split CP ...... 14

1.2.4 Topic – Focus distinction ...... 16

Chapter 2 Methodology ...... 20

Chapter 3 Results and discussion ...... 22

3.1 Overview ...... 22

3.2 Quantifier-auxiliary combinations ...... 26

3.2.1 Anti-additive/antimorphic QPs ...... 26

3.2.2 Downward entailing QPs ...... 27

3.2.3 Nonmonotonic QPs ...... 29

3.3 Conclusion ...... 29

iii

Chapter 4 Analysis ...... 30

4.1 General overview ...... 30

4.1.1 Ambiguous constituents ...... 33

4.2 Corpus data analysis ...... 36

4.2.1 Anti-additive/antimorphic QPs ...... 36

4.2.1.1 [NEG]-feature ...... 39

4.2.2 Downward entailing QPs ...... 40

4.2.2.1 [NEG]-feature ...... 43

4.2.3 Nonmonotonic QPs ...... 44

4.2.3.1 [NEG]-feature ...... 47

4.2.3.2 Exactly ...... 53

4.2.4 “Misbehaving” quantifiers ...... 54

4.2.4.1 Nothing ...... 54

4.2.4.2 Zero ...... 56

4.2.4.3 Only ...... 57

4.2.4.4 DE quantifiers: rarely ...... 59

4.3 Conclusion ...... 61

Conclusion 63

Bibliography 66

Word count: 21.139

List of Tables

Table 1 QPs ...... 20

Table 2 Auxiliary tags ...... 20

Table 3 BNC results ...... 22

Table 4 COCA results ...... 23

Table 5 Overview results ...... 24

Table 6 Inversion and topicalization structures ...... 36

Table 7 N-word morphology ...... 39

List of Figures

Figure 1 SAI patterns in GG ...... 12

Figure 2 Split CP-structure ...... 15

Figure 3 Search entry ...... 21

Figure 4 Graph overview ...... 24

Figure 5 Results (never) ...... 26

Figure 6 Results (rarely) ...... 27

Figure 7 Results (seldom) ...... 27

Figure 8 Results (few) ...... 28

Figure 9 Results (zero) ...... 28

Figure 10 Results (only) ...... 29

Figure 11 Focalized anti-additive QP structure (never) ...... 38

Figure 12 Focalized anti-additive QP structure (nothing)...... 38

Figure 13 Focalized downward entailing QP structure (rarely) ...... 42

Figure 14 Focalized nonmonotonic QP structure (only) ...... 46

Introduction

It is widely accepted that (constituents with) purely negative quantifiers (e.g. no, never and the negative marker not) give rise to subject-auxiliary inversion when preposed (Biber 2000; Büring 2004; Collins & Postal 2014; De Clercq et al 2012; Haegeman 2000a, 2000b; Jackendoff 1972; Progovac 2005; Quirk et al 1985). Huddleston et al define these as “absolute negators” (2002: 812). As such, these contain an overt syntactic negative marker (cf. section 4.2.1.1). As illustrated in (1) – (3), subject-auxiliary inversion (SAI) occurs in these cases.

(1) a. Not until the next morning did she realise how serious it was. (2) a. None of them did he find useful. b. Nowhere does he mention my book. (3) a. Never had the Cardinal’s policy been more triumphantly vindicated. b. Nowhere is this so noticeable as in the South of France. c. In no case can such a course be justified merely by success. (examples based on Büring 2004: 1)

Negative scalar QPs like few, hardly, rarely, seldom, little, barely, scarcely and the numeral zero ‘normally’ (Quirk et al 1985: 781) give rise to negative inversion when they are in sentence initial position, as illustrated in (4) – (7). Huddleston et al define these as “approximate negators” (2002: 815-816). These quantifiers are negative in meaning, but they do not contain a morphological mark of negation. There is evidence that these do, however, contain a covert syntactic negative feature (cf. section 4.2.2.1).

(4) Rarely had they experienced such a great performance. (5) Hardly ever had he talked to somebody so enlightened. (6) Very few people would they admit to their club. (7) But on zero occasions have I found myself held up, delayed, late to my destination or in any other way inconvenienced by cyclists on the road. (Collins and Postal 2014: 138)

In the case of nonmonotonic QPs like only and exactly it is unclear to what extent inversion is accepted. Some speakers clearly accept it (Collins and Postal 2014: 134), others don’t. Quirk et al (1985:

781) argue that, even though only is not straightforwardly negative, it is to some extent negative in its meaning. Only and exactly may occasionally give rise to subject-auxiliary inversion, as illustrated in (8) – (11). Like negative scalar QPs, nonmonotonic QPs also do not contain a morphological mark of negation.

(8) Only his mother will he obey. (Quirk et al 1985: 781) (9) Only on Sundays do they eat with their children. (Quirk et al 1985: 781) (10) Exactly one feature did I notice in the landscape. (Collins & Postal 2014: 138) (11) In exactly two of these cases did we find traces of the virus. (Büring 2004: 2)

Of the aforementioned forms of ‘negative inversion’ with preposed quantifiers, both purely negative QPs and negative scalar QPs entail sentential negation. The quantifier phrase (i.e. the negative operator) thus take sentential scope (Haegeman 2000b: 21; De Clercq et al 2012) and it is argued that the negative feature in the quantifier is the underlying factor that triggers SAI. In the case of only, it is not sure if negation is the underlying factor that triggers inversion. There are, however, also cases where negative QPs may be preposed without triggering subject-auxiliary inversion. In these cases, there is usually no sentential or clausal negation, but local or constituent negation (De Clercq et al 2012: 11; Horn 1989: 185; Quirk et al 1985: 793). An example of this is (12), where the paraphrase below shows that the sentence is semantically positive. Examples (13) – (14), where the same constituent is used, show the contrast between these two types of negation even more clearly, respectively showing sentential negation and constituent negation. The paraphrase provided below each example show the difference in meaning.

(12) Not even ten years ago you could see such a film. [‘You could see such a film as recently as ten years ago.’] (Quirk et al 1985: 793)

(13) With no clothes is Sue attractive (sentential negation) [‘There are no clothes in which Sue is attractive’] (14) With no clothes, Sue is attractive (constituent negation) [‘While wearing no clothes, Sue is attractive’] (Horn 1989: 185)

In cases (12) and (14), the quantifier negates a constituent instead of rendering the entire clause negative. (Biber 2000: 916; Quirk et al 1985: 790). The negation is part of the adverbial only, while the main statement is affirmative. There is thus, compared to the cases where subject-auxiliary inversion does take place, a scopal

difference. Some more examples of fronted constituents with narrow scope negation are provided in (15) – (16).

(15) No doubt he will issue his instructions. (PICT) (16) Not surprisingly, most studies have concerned themselves with ill effect, notably that of emotional stress. (ACAD) (Biber 2000: 916)

The aim of this paper is to investigate inversion patterns with different types of preposed quantifier phrases. As such, a corpus investigation (in both the BNC and COCA corpora) is set up to uncover the frequency of use of these inversion patterns with regard to the different types of QPs that are mentioned above. In addition, from a theoretical point-of-view, we will look at which mechanism(s) trigger(s) this inversion pattern and what the structure of the sentence looks like. We will argue that there is an overt or covert negative feature present in purely negative (de Swart 2009; Horn 1989) and negative scalar (De Clercq 2017; Horn 1989; McCawley 1998) QPs which is responsible for the inversion facts. When the QP is preposed to a focus position, i.e. specifier of FocP, the auxiliary is forced to move leftward to Foc° (i.e. SAI occurs as it moves to the left of the subject) to satisfy the NEG-criterion (Haegeman 1995; Haegeman and Zanuttini 2014; cf. section 1.2.2). As such, it is argued that there are two features (i.e. a [NEG]-feature and a [focus] feature) that the preposed QP has to have to give rise to SAI. In addition to the above negative QPs, we will argue that, in the case of the nonmonotonic QP only, a (covert) syntactic negative feature is present as well, even though only is not straightforwardly negative. When an only-phrase is thus preposed to SpecFocP, it can also give rise to SAI to satisfy the NEG-criterion in the same way as negative scalar QPs. After an overview of the theoretical background (section 1), which includes a classification of the different quantifiers and some general background on negative contexts (section 1.1), the theoretical framework with regard to inversion is provided (section 1.2). As the analysis will be held against the background of Generative Grammar (GG), some information about SAI patterns in this tradition is provided, as well as the specifics of the WH-/NEG-criterion which can be satisfied by the occurrence of these SAI patterns (Haegeman and Zanuttini 2014; Haegeman 2000a; 2000b; Rizzi 1997). Lastly, the Topic - Focus distinction is discussed more in-depth (Büring 2004; Haegeman 2000b; Kang 2014: Rizzi 1997) as this will be a crucial ingredient in the analysis. In section 2 we discuss the methodology and then in section 3 we present the results of the corpus research. The results include both a general overview and a brief discussion of specific quantifier-auxiliary combinations. Section 4 discusses a possible analysis of the data, drawing on the split CP framework, the Topic-Focus distinction, the NEG-criterion and the presence of a covert negative feature in nonmonotonic QPs like only. Finally, I conclude.

Chapter 1 Theoretical background

The theoretical background consists of two main parts. Initially, the different types of quantifiers and the contexts of negativity these are associated with are discussed, as well as some tests for negativity (section 1.1). Section 1.2 focusses on inversion patterns in Generative Grammar, discussing both what these patterns look like, as well as what the criteria for the occurrence of these patterns are.

1.1. Quantifiers and negativity As subject-auxiliary inversion with preposed quantifier phrases is very likely a negation related phenomenon, it is important to distinguish between different types and strengths of negation as well. After a more in-depth overview of the different types of quantifiers and the different contexts of negation these are associated with (section 1.1.1), some tests for negativity are provided to be able to distinguish which constructions are affirmative and which are negative (section 1.1.2), followed by a syntactic hierarchy of negation (section 1.1.3). Lastly, a brief preliminary discussion of nonmonotonic QPs and their possibility of triggering subject-auxiliary inversion and licensing weak NPIs is provided (section 1.1.4).

1.1.1. Quantifier classification Although different types of quantifiers have already been mentioned above in the introduction, it is important to clearly delineate what a quantifier is, which different categories of quantifiers there are, and what determines the category of a certain quantifier. Quantifiers are determiners which specify the number or amount of entities referred to, as in (17), although many can also be used as pronouns (18), and some even as adverbs (19) (Biber 2000: 71).

(17) He kept whistling at all the girls. (18) Is that all I’ve got dad? (19) Don’t get all mucky. (Biber 2000: 71)

The semantic literature on quantifiers divides them into three groups. The first group are positive scalar quantifiers (Horn 1989: 248), also called upward entailing (UE) or monotone increasing (Peters & Westerståhl 2006: 164-165) quantifiers. These quantifiers (e.g. one, many, some, often, either, always) denote a monotone increasing function (Barwise & Cooper 1981), which means that there is an upward or

increasing entailment relation. This is illustrated by the pair in (20) – (21): the expression in (20) entails the expression in (21). As some men walk slowly, it is clear that this entails that some men walk. The entailment thus goes from the subset (the group of slow walkers) to the superset (the group of walkers), i.e. is upward or increasing. Positive scalar quantifiers are not the topic of this master thesis, so we will not elaborate on them further.

(20) Some men walk slowly (i.e. subset of slow walkers) (21) Some men walk (i.e. superset of walkers) (Ladusaw 1979: 115)

The second group of quantifiers are negative (scalar) quantifiers. These include quantifiers such as never and rarely. Of these two negative quantifiers, however, the former intuitively feels like a stronger negative than the latter. This leads us to believe that not all negatives can be seen as equal because of possible different strengths of negativity. As such, subcategories have to be made on the basis of their (degree of) negativity. As negation is most likely the underlying factor in (negative) inversion, the difference in strength between the different quantifiers might also influence the possibility of inversion in constructions in which these are used. As such, Van der Wouden (1997) poses the question of what it is that constitutes a negative context (i.e. a context where negative polarity items can be licensed). There must be some properties that negative contexts have in common that play a role in polarity licensing. After discussing these different properties, Van der Wouden constructs a ‘natural hierarchical typology of negative contexts’. Van der Wouden (1997) makes a distinction between four types of negative contexts or expressions, with differing degrees of negativity. These are (from the weakest to the strongest forms of negation): monotone decreasing contexts (e.g. few, seldom, hardly), antimultiplicative contexts (e.g. not every, not always) and anti-additive contexts (e.g. nobody, never, nothing), and lastly antimorphic contexts (e.g. not, not the teacher, not Judas). The stronger forms of negation always entail the weaker form(s), while the reverse is not true. Antimorphic, antimultiplicative and anti-additive contexts are thus also monotone decreasing. All negative contexts can license negative polarity items (NPIs), but NPIs do not necessarily show the same behavior in the different negative contexts (Van der Wouden 1997: 112). Examples of the NPI any are provided in (22) – (23).

(22) John didn’t talk to anybody. (23) Nobody said anything. (Van der Wouden 1997: 59)

As such, he also devises a typology of polarity items based on their distribution amongst the different types of negative contexts. A distinction is made between negative polarity items of three different strengths: weak NPIs, medium strength NPIs, and strong NPIs. Weak NPIs can occur in all monotone decreasing contexts; NPIs of medium strength can occur in anti-additive contexts, but not in merely downward monotonic contexts; Strong NPIs can only be licensed in antimorphic contexts (Van der Wouden 1997: 130). Zwarts (1998: 233) makes the same distinction with regard to NPI licensing in the different contexts, although he subdivides NPIs into weak, strong and superstrong (respectively weak, medium strength and strong in Van der Wouden) types. The licensing of certain NPIs can thus also help test and possibly confirm the (degree of) negativity of certain constructions. Negative (scalar) quantifiers are thus all at least downward entailing (DE) (Ladusaw 1979: 112-113) or monotone decreasing (Peters & Westerståhl 2006: 165) quantifiers and will henceforth be referred to as downward entailing (DE) quantifiers. These quantifiers (e.g. no, few, seldom, little, barely and zero) denote a monotone decreasing function, which means that there is a downward or decreasing entailment relation. This can be seen by expression (24) entailing both expression (25) and (26). As no men walk, it is clear that this entails that no men walk slowly and no men walk quickly. The entailment goes from the superset to the subsets and is thus downward or decreasing.

(24) No men walk (i.e. superset of walkers) (25) No men walk slowly (i.e. subset of slow walkers) (26) No men walk quickly (i.e. subset of fast walkers)

Within the group of downward entailing quantifiers, however, there is a subset of purely negative quantifiers. These consist of strong or anti-additive quantifiers (e.g. never, nobody, no) and even superstrong or antimorphic quantifiers (Zwarts 1998; e.g. the negative marker not), which are considered as “stronger” negatives than those that are merely downward entailing. These will henceforth be referred to as anti- additive/antimorphic quantifiers. Quirk et al (1985: 778-780) define these negative adverbials as negative in both form (i.e. they contain a morphological mark of negation) and meaning, while the “weaker” downward entailing quantifiers are defined as negative in meaning but not in form. As McCawley (1998: 608) notes, in the case of rarely, something negative (i.e. not often) is conveyed, but it does not, however, contain an overt “standard morphological mark of negation”. A special case here is the numeral zero. Gajewski (2011) poses the problem of the semantic equivalence of no and (exactly) zero. Although this equivalence is present, only no licenses strong NPIs. Bylinina (2017: 3) states that a possible explanation for this is that the grammar does not have access to the

‘mathematical content’ of numerals (including zero). Because of this, zero might not be able to license strong NPIs like either, while no does have that ability, as in (27).

(27) No/*Zero students like semantics, either. (example based on Bylinina 2017: 1)

In addition, zero cannot occur with a ‘negative appositive tag’ (Klima 1964; cf. section 1.1.2), as seen in (28).

(28) She drank no/*zero martinis, not even weak ones. (example based on Postal 2004: 167)

As zero is clearly not the same as the anti-additive quantifier no in its behavior, it will be categorized as a downward entailing quantifier for the purpose of this research. The last group of quantifiers consists of nonscalar quantifiers, also called nonmonotonic quantifiers. These quantifiers (e.g. only, exactly) denote nonmonotonic or nonscalar functions, as there is no upward or downward entailing relationship. A sentence such as (29) does not entail any subsets or supersets. These will be referred to as nonmonotonic quantifier phrases from here on.

(29) Only men walk. (30) Only men walk slowly. (31) Only men walk quickly.

Subsets such as in (30) – (31) are not automatically entailed, as in that case an assumption would have to be made regarding the pace of their walking. Such an assumption is not readily available.

1.1.2. Negativity tests As inversion is most likely a negation related phenomenon, it is important to be able to distinguish exactly which constructions are affirmative and which are negative. In his work ‘The syntactic phenomena of English’, McCawley (1998: 604-612) discusses some tests for negativity proposed by Klima (1964). These tests were designed to investigate the status of a sentence as affirmative or negative. The first test, applicable to the simplest cases, pertains to the use of too and either, as the acceptability of too or either appears to correlate with the sentence being respectively affirmative, as in (32), or negative, as in (33) (McCawley 1998: 604-608).

(32) John voted for Bergland, and Mary voted for him too/*either (33) John didn’t vote for Reagan, and Mary didn’t vote for him either/*too

The second test consists of the possibility of using so or neither in an inverted reduced sentence, the interpretation of which is based on the given sentence. In the case of an affirmative sentence, this is only possible with so, as in (34), while in the case of a negative sentence, this is only possible with neither, as in (35) (McCawley 1998: 608-611).

(34) John voted for Stassen, and so/*neither did Mary. (35) John didn’t vote for Stassen, and neither/*so did Mary.

The third test consists of the use of tag questions (Brasoveanu et al 2014, Klima 1964). A distinction has to be made between reversal tags (McCawley 1998: 611-612), as illustrated in (36), and reduplicative tags, as illustrated in (37). Reduplicative tags indicate an affirmative sentence; reversal tags indicate either an affirmative sentence (36a) or a negative sentence (36b). Sentences of the former type (36a) anchor a negative question tag; sentences of the latter type (36b) anchor a positive question tag.

(36) a. Anne left, didn’t she? REV tag b. Anne didn’t leave, did she? REV tag (37) Anne left, did she? RED tag (Brasoveanu et al 2014: 175)

The last test discussed by McCawley (1998: 612) is the possibility of the addition of a “negative appositive tag” (Klima 1964: 262-263), which consists of ‘not even X’, with X matching a “special case” of a constituent of the host sentence. Some examples are provided in (38) – (39).

(38) The writer will never accept suggestions, not even reasonable ones. (39) *The publisher often disregards suggestions, not even reasonable ones. (McCawley 1998: 612)

If the addition of a “negative appositive tag” is possible, as in (38), it means that the host sentence is negative in some sense. In the case of (39), this addition is not possible and the host sentence is thus affirmative.

1.1.3. Syntactic hierarchy of negation A type of hierarchy of negative contexts has already been established, but this is not the only thing that influences the negativity of a sentence. Placing negative constituents in different syntactic positions also seems to influence the negativity of the sentences. Brasoveanu et al (2014) quantify the negativity of sentences with different types of negative operators in different syntactic positions. A distinction is made between n-words (e.g. never, nobody) and downward entailing items (e.g. rarely, few) for the negative operators. The different syntactic positions in which these are placed are adverb position, subject position, and direct object position. Comparing the classification of n-words and DE-items to Van der Wouden’s classification of negative expressions, it is clear that n-words (as adverb, subject, or direct object) are anti-additive expressions and thus anti- additive/antimorphic quantifiers, while DE-items (also as adverb, subject, or direct object) are clearly only downward entailing expressions and thus downward entailing quantifiers. Combining these two types of negative constituents with the three different syntactic positions, sentences were constructed. The negativity of these sentences was then tested by using these sentences as anchors for question tags. Participants had to choose between either a positive or a negative reversal tag (cf. section 1.1.2); the former indicating a negative sentence and the latter indicating an affirmative sentence. The negativity was then measured according to the proportion of positive responses. The findings of Brasoveanu et al result in the hierarchy of sentential negativity seen in (40).

(40) {NEG, N-ADV, N-SUBJ} >> N-OBJ >> {DE-ADV, DE-SUBJ} >> DE-OBJ >> POS (Brasoveanu et al 2014: 183)

Both a semantic hierarchy of negativity and a syntactic hierarchy of negativity can be derived from this. The former entails that all n-words are more negative than DE-items; this is in accordance with the degrees of negativity assigned to anti-additive/antimorphic and downward entailing contexts by Van der Wouden. The latter entails that adverbs and subjects are more negative than direct objects. Of these two hierarchies, the semantic hierarchy is the most dominant, as any n-word in direct object position is more negative than any DE-item in adverb or subject position. When applying this hierarchy to quantifiers, one could propose a hierarchy of quantifier negativity, illustrated in (41), based on the contexts they can occur in.

(41) {AA/AM Qs: ADV/SUBJ} >> {AA/AM Qs: OBJ} >> {DE Qs: ADV/SUBJ) >> {DE Qs: OBJ}

A semantic hierarchy applies here as well, the anti-additive (AA) and antimorphic (AM) quantifiers being stronger negatives than downward entailling quantifiers (DE) in all cases. Within that semantic hierarchy then one can subordinate the syntactic hierarchy, with quantifiers functioning as adverbs (ADV) or as subjects (SUBJ) forming stronger negatives than quantifiers functioning as objects (OBJ). A question that remains to be answered, however, is to what extent nonmonotonic quantifiers have the possibility of triggering inversion and/or licensing items typically associated with negative contexts, such as negative polarity items.

1.1.4. Nonmonotonic QPs The question remains how non-monotonic quantifiers like only and exactly can be to some extent negative and have the ability of triggering subject-auxiliary inversion. Nishiguchi (2003: 208) notes that non-monotonic items can trigger weak NPIs such as any and ever, even though they do not even fit the weakest category of negative contexts (i.e. downward entailment). Some examples of this are provided in (42) – (45).

(42) Only Mary showed any respect for the visitors. (43) Only to his girlfriend did John give any flowers. (44) Only last year did John get any grey hairs. (Progovac 2005: 73)

(45) Only Bill had ever read anything about phrenology. (Nishiguchi 2003: 205)

The solution he proposes entails the notion of ‘anti-UEness (Upward Entailingness, i.e. DE plus NM) and an exclusivity condition for non-monotonic NPI licensers (Nishiguchi 2003). The concept of ‘anti-UEness’ would in this case replace ‘DE-ness’ as a description of NPI licensers. The exclusivity condition pertains to non-monotonic operators that share the assertion ‘no other than x is y’ and it refers to the exclusivity of the constituent that is being focalized by the nonmonotonic quantifier, as the expression entails that no other alternatives than that which is focalized are true. Similar to monotone decreasing contexts, a “negative-like meaning”, instead of the negation morpheme not could serve to condition the occurrence of polarity items (Peters & Westerståhl 2006: 199) and possibly negative inversion. Non-monotonic contexts that meet exclusivity condition can thus license weak NPIs (Nishiguchi 2003: 213).

1.2. Inversion in Generative Grammar The analysis will be held against the background of the generative tradition. As such, a brief discussion of subject-auxiliary inversion patterns in Generative Grammar (GG) is provided, followed by the specifics of the WH- and NEG-criterion, of which the latter is assumed to trigger the subject-auxiliary inversion patterns when negative QPs are preposed. Lastly, Rizzi’s (1997) split CP is elaborated on, as well as a more in-depth discussion of the Topic-Focus distinction.

1.2.1. SAI patterns Within generative syntax, SAI patterns are considered a leftward displacement of the auxiliary (or tense). Whilst the subject is in SpecTP, the content of T (e.g. the auxiliary) moves leftward to a head position to the left of the subject in CP. SAI takes place in yes/no-questions, wh-questions (46) and cases of negative inversion (47) (Haegeman 2006: 313-330), such as those discussed in the introduction. As we discussed before, there is also inversion in constructions with preposed only-phrases (48). A representation of the tree structure of examples (46) – (48) is provided in Figure 1 on the next page. Do note, however, that Figure 1 presents a mono-layered CP; the split CP (Rizzi 1997) will be discussed in section 1.2.3 and will from then on serve as the framework for our analysis.

(46) Which letter could John write today? (47) No letter could John write today. (48) Only one letter could John write today. (Veselovská 2011: 5)

SAI is thus triggered by a preposed interrogative (e.g. which) or negative constituent (e.g. no letter). This is due to respectively the WH-criterion and the NEG-criterion (cf. section 1.2.2) (Haegeman 2000a: 121-122). In addition, constituents with only (e.g. only one letter) are also capable of triggering SAI even though they are not straightforwardly negative.

*[+F] = feature that triggers SAI Figure 1. SAI patterns in GG (Veselovksá 2011: 5)

1.2.2. WH-/NEG-criterion The WH- and NEG-criterion are instantiations of the AFFECT-criterion (Haegeman 1995: 93). AFFECT refers to “the feature that all triggers, i.e. all contexts that license NPIs, (are supposed to) have in common” (Van der Wouden 1997: 83). The AFFECT-criterion states that affective elements (Klima 1964), such as a [WH]-element or a [NEG]-element, are subject to a licensing requirement in terms of Spec-head agreement (Haegeman 1995: 93; Rizzi 1996). The AFFECT-criterion is presented in (49).

(49) The AFFECT-criterion (a) An AFFECTIVE operator must be in a Spec-Head configuration with an [AFFECTIVE] X° (b) An [AFFECTIVE] X° must be in a Spec-Head configuration with a AFFECTIVE operator (Haegeman 1995: 93)

The WH- and NEG-criterion, which are specific instantiations of the AFFECT-criterion, are presented in (50) – (51):

(50) The WH-criterion (c) A WH-operator must be in a Spec-Head configuration with an X-[WH] (d) An X-[WH] must be in a Spec-Head configuration with a WH-operator (May 1985; Rizzi 1996; Haegeman 1995: 94)

(51) The NEG-criterion (a) A NEG-operator must be in a Spec-Head configuration with an X-[NEG] (b) An X-[NEG] must be in a Spec-Head configuration with a NEG-operator (Haegeman and Zanuttini 2014; Haegeman 1995: 106)

In examples (46) – (47), the wh-phrase and the negative constituent trigger subject-auxiliary inversion due to the need to get into a spec-head configuration with respectively an X-[WH] and an X-[NEG] (i.e. a head that carries a [WH] / [NEG] feature). In both cases, the auxiliary has moved to the head position C°, which suggests that the inverted auxiliary (or inflectional head) is capable of carrying an interrogative feature [WH] or a negative feature [NEG]. The current literature argues that the [WH]- and [NEG]-features are associated with an inflectional head; more specifically with T in a split-Infl approach (Haegeman 1995: 94; Rizzi 1990: 17-18). Lasnik (1972) also associates the [WH]- and [NEG]-features with auxiliaries (i.e. I, or T and Agr). As such, it will from now on be assumed that auxiliaries in interrogative and negative constructions carry a respectively interrogative or negative feature. In the case of (46), the [WH]-feature is thus on T° (i.e. the auxiliary). As the WH-operator has moved to SpecCP, the tensed auxiliary, which carries the matching [WH]- feature, moves leftward from T° to C° to enable the spec-head configuration with the preposed constituent. Similarly, the NEG-criterion may lead to operator movement in cases where the preposed negative constituent (i.e. a constituent that contains a [NEG]-feature) takes sentential scope, causing the auxiliary to move to C° as well, as it carries the matching [NEG]-feature. An example of this is (47). Do note, however, that the NEG-criterion is not exclusive to inversion contexts. The preposing of negative constituents that give rise to SAI is assumed to be triggered due to a [focus] feature associated with the negative constituent; this [focus] feature could thus be a common feature of preposed constituents that trigger inversion. Do note, however, that focalization itself (e.g. of a constituent without a [NEG]-feature which would triggers the NEG-criterion) is not a sufficient condition for SAI to occur (Haegeman 2000a: 126). In Figure 1 (cf. supra), the application of these criteria is illustrated for both the NEG- and the WH- criterion. An interrogative (i.e. which letter) or negative (i.e. no letter) constituent from within the VP is preposed to the specifier position of CP; due to the respectively [WH] and [NEG]-feature they carry, they require a spec-head configuration with a head carrying the matching feature (i.e. the WH-/NEG-criterion applies) whereby the auxiliary (a head which carries the matching feature) moves from T° to C°. As such, the auxiliary moves to the left of the subject (which is in SpecTP) and subject-auxiliary inversion occurs. The spec-head configuration thus entails that the interrogative or negative constituent is in SpecCP, while the auxiliary (i.e. the head) is in C°. The NEG-criterion will play an important role in the analysis of the data from the corpus research.

1.2.3. The split CP As similar-looking preposed constituents can sometimes occur (in separate sentences; with different meanings) with (52) and without (53) subject-auxiliary inversion (i.e. sentential vs. constituent negation), it must be that these constituents are somehow different. However, if one adopts a mono-layered CP, as has been done above, both can only target SpecCP and hence it cannot be explained why the two constituents in (52) – (53) behave differently with respect to SAI. Rizzi’s (1997) split CP on the other hand allows us to account for the differences between these constituents, as well as the co-occurrence of these constituents in constructions with multiple preposed constituents, as in (54).

(52) With no job would she be happy. (53) With no job, she would be happy. (Haegeman 2000b: 31)

(54) [During the holidays] [on no account] will I do that. (Haegeman 2000b: 46)

Rizzi (1997) decomposes the CP projection into multiple functional projections; it minimally decomposes into ForceP and FinP. ForceP encodes the illocutionary force of the clause; Fin° is endowed with the feature for (non-)finiteness. The split CP may also include a FocP projection, which hosts the focalized constituent in its specifier position and a [focus] feature as its head. In addition, there is a (recursive) TopP, which hosts the fronted topic in its specifier position and hosts a [topic] feature as its head (Haegeman 2000a: 128-129). The structure of the split CP is presented in Figure 2. As it is assumed that a [focus] feature is present in preposed negative constituents that trigger SAI (Haegeman 2000a: 126), it will henceforth be assumed that only constituents that go into SpecFocP can trigger SAI, while those that go into SpecTopP cannot trigger SAI.

ForceP > TopP* > FocP > TopP* > FinP (Rizzi 1997)

Figure 2. Split CP-structure (Rizzi 1997)

In assigning the preposed constituents to the specifier position of either FocP or TopP, a distinction has to be made between topic and focus. The most important distinction is that while focus is quantificational, topic is not. Focus constituents thus work as operators and bind a variable. This means that they work as syntactic operators. Topic constituents, on the other hand, do not work as syntactic operators (Isac 2004: 127; cf. section 1.2.4). The same constituent (e.g. your book) can in some cases serve as either a focus or a topic (but not in the same sentence), as represented respectively in (55) – (56). When “your book” is focalized, as in (55), the focus is “your book”, about which something is then said. As “your book” is not a negative constituent, the NEG-criterion does not apply in this case and SAI does not occur. When “your book” is topicalized, as in (56), the focus lies elsewhere (i.e. “to Paul”).

(55) YOUR BOOK you should give t to Paul (not mine) (56) Your book, you should give t to Paul (not to Bill) (Rizzi 1997: 285)

Rizzi (1997: 285) notes that in focalization, as in (55), the preposed element “bearing focal stress, introduces new information”. In topicalization, as in (56), the topic is “characteristically set off from the rest of the

clause by ‘comma intonation’ and normally expressing old information” (1997: 285) which is salient in previous discourse. The differences between focus and topic are discussed more in-depth in section 1.2.4. Wh-phrases and focalized negative constituents are in complementary distribution, as seen in (57) – (58). As they are both focalized constituents, they thus target the same projection (i.e. FocP) (Haegeman 2000a: 133-134).

(57) *In no way, why would Robin volunteer? (58) *Why, in no way would Robin volunteer? (Haegeman 2000a: 134)

Haegeman (2000b: 27) notes that “in root clauses, negative inversion is compatible with the preposing of adverbial or argumental topics”. The topicalized constituent is, however, required to precede the focalized constituent, as seen in (59) – (60). This is also possible with wh-inversion, as in (61).

(59) During my sabbatical, on no account will I read e-mail. (60) *On no account during my sabbatical will I read e-mail. (61) With no job, where can we go? (Haegeman 2000b: 27)

The Topic-Focus distinction and its effect on subject-auxiliary inversion is elaborated on in section 1.2.4, including some tests to determine if a constituent is a topic or a focus.

1.2.4. Topic – Focus distinction It is not the case that a (preposed) constituent that contains a negative feature necessarily functions as either a topic or a focus exclusively. It is certainly possible for such a constituent to function as either a topic or a focus, although in separate constructions with or without inversion; this also entails semantic differences (Haegeman 2000b: 31). An example of this is the constituent “with no job” which is focalized in (52), but topicalized in (53). Such a constituent is thus ambiguous. A very general view on the Topic – Focus distinction is that topic is what a sentence is about, while focus is what is said about the topic (Kang 2014: 236-237). A first distinction can thus be made on the basis of information structure. Kang notes that “topic is taken to be presupposed in a pragmatically structured proposition, thereby carrying old information”, while “focus is taken to constitute an unpredictable part of the proposition, consequently carrying new information” (2014: 236-237; Rizzi 1997: 285; Veselovská 2011: 7).

A second distinction is noted by Rizzi (1997: 291-295; Isac 2004: 127), namely that focus is quantificational, while topic is not. This means that focus acts as a syntactic operator and binds a (syntactic) variable, as in (62), where “your book” functions as direct object and binds to the verb. Topics, on the other hand, do not act as syntactic operators and do not relate to a syntactic variable in the sentence, as in (63), “in which potential bindees are the clitic and its trace, neither of which qualifies as a syntactic variable” (Rizzi 1997: 292).

(62) IL TUO LIBRO ho comprato t (non il suo) “YOUR BOOK I bought (not his)” (63) Il tuo libro, lo ho comprato “Your book, I bought it” (Rizzi 1997: 289-90)

A third distinction is based on their intonational properties (usually reflected in punctuation). Topicalization shows an intonational phrase break, while focalization does not tolerate that separation (Büring 2004: 2). Some examples of this are provided in (64) – (65), in which “%” indicates the intonational break.

(64) a. Nowhere does he mention my book. b. Somewhere % he mentions my book. c. ?*Nowhere % does he mention my book

(65) a. In no case can such a course be justified merely by success. b. In some cases % such a course can be justified merely by success c. ?* In no case % can such a course be justified merely by success. (Büring 2004: 3)

Haegeman (2000b: 31-32) hypothesized that preposing with inversion (i.e. sentential negation) is an instance of focalization, while preposing without inversion (i.e. constituent negation) is an instance of topicalization. As such, the following tests for sentential negation (the absence of which indicates constituent negation in the following examples) could coincide with tests to distinguish if a constituent is either a focus or a topic. The first tests consists in the use of the neither-tag. Sentences with a preposed negative constituent that takes sentential scope admit this kind of tag, as in (66), while those that take constituent scope do not, as in (67).

(66) Not often does Jack attend parties and neither does Jill. (67) *Not long ago, Jack attended a party and neither did Jill. (Haegeman 2000b; based on Rudanko 1980: 310)

A similar test involves the use of reversal question tags (Haegeman 2000b: 32). In this case, questions with a focalized negative constituent should anchor a positive question tag, as in (68), while those with a topicalized negative constituent should anchor a negative question tag, as in (69).

(68) Not often does Jack attend parties, does he?/*doesn’t he? (69) Not long ago Jack attended a party, didn’t he?*did he? (Haegeman 2000b; based on Rudanko 1980: 310)

A third test is based on the polarity licensing of these constituents. Focalized negative constituents should thus be able to license NPIs both inside the preposed PP (70a) as well as the rest of the sentence (70b), as these have sentential scope. Topicalized negative constituents should only be able to license NPIs within the preposed PP (71a) but not in the rest of the sentence (71b) (Haegeman 2000b: 32).

(70) a. With no job of any kind would she be happy. b. With no job would she ever be happy. (71) a. With no job of any kind, she would be perfectly happy. b. *With no job, she would ever be happy (Haegeman 2000b: 32)

The above tests, however, all rely on the hypothesis that focalization (of a negative constituent) entails sentential negation and that topicalization (of a negative constituent) entails constituent negation. As such, some independent tests are provided below. The first test entails that a topic can involve a resumptive clitic within the comment; which is obligatory if the topicalized constituent is the direct object (72). Focalized constituents cannot occur with a resumptive clitic (73) (Haegeman 2000b: 35; Rizzi 1997: 289).

(72) Il tuo libro, lo ho comprato “Your book, I bought it.” [topicalization] (73) IL TUO LIBRO ho comprato t (non il suo) “YOUR BOOK, I bought (not his)” [focalization] (Rizzi 1997: 289-290)

Secondly, bare quantifiers such as everything and no one cannot serve as a topic (74a) but only as a focus (74b), as these inherently require an operator-variable relation (Haegeman 2000b: 35; Rizzi 1997: 290). Similarly, negative DPs also inherently have operator status and must bind a variable (75a); they are thus incompatible with topicalization (75b) (Haegeman 2000b: 37).

(74) a. *Nessuno, lo ho visto “No one, I saw him”

b. NESSUNO ho visto t “NO ONE I saw” (Rizzi 1997: 290)

(75) a. No job would she be happy with. b. *No job, she would be happy with. (Haegeman 2000b: 37)

A third test is based on the complementary distribution of wh-phrases and focalized negative constituents. Wh-operators in main questions are thus only compatible with a topic (76) and not with a focus (77).

(76) With no job, where can we go? (77) a. *Where on no account should I go? b. *On no account where should I go (Haegeman 2000b: 27)

Chapter 2 Methodology

The corpora used are the Corpus of Contemporary American English (COCA) and the British National Corpus (BNC). COCA is the largest corpus of American English currently available and is composed of more than 450 million words from more than 160,000 texts from a variety of sources (spoken, fiction, popular magazines, newspapers, academic journals) dating from 1990 to 2015. BNC is a synchronic corpus (i.e. language use from the late 20th century) composed of 100 million words, of which 90% is written language use (i.e. newspapers, journals, (non-)fiction books and other published materials) and the remaining 10% is spoken language use. These corpora are freely available online and are both used as there is no focus on the specifics of American or British English. For our research, we have investigated the number of occurrences of inversion for each type of (preposed) quantifier phrase (i.e. anti-additive and antimorphic QPs; downward entailing QPs; nonmonotonic QPs) in both the BNC & COCA corpora. In order to somewhat enable searches that present a limited amount of useful results, we have used constructions in which the subject that is part of the subject-auxiliary inversion is a personal pronoun (using the _pp* tag incorporated in both corpora). This also limited the amount of manual filtering that needed to be done. As subject-auxiliary inversion (SAI) is expected in the case of anti- additive/antimorphic QPs, only two anti-additive/antimorphic QPs have been researched. In the case of downward entailing QPs, four QPs have been researched. Lastly, for nonmonotonic QPs, only and exactly have been researched. All of the selected QPs are presented in Table 1:

Anti-additive/antimorphic QPs Downward entailing QPs Nonmonotonic QPs Never Rarely Seldom Only Nothing Few Zero Exactly Table 1. QPs

The above QPs were then to be combined with the different auxiliaries, of which all modals are grouped together in both corpora. The specific search tags provided (in both corpora) for each (type of) auxiliary are presented in Table 2:

To have To do To be Modals _vh* _vd* _vb* _vm* Table 2. Auxiliary tags

All quantifier phrases thus needed to be combined with all (types of) auxiliaries, immediately followed by a personal pronoun. This was done using the “collocates” search function, in which each quantifier phrase is entered as a collocate that precedes (up to 4 words) a combination of a given auxiliary (using the tags presented in Table 3), immediately followed by a personal pronoun (using the _pp* tag). This should provide us with most of the cases of subject-auxiliary inversion with a personal pronoun as the subject. A generic example of the search entry is presented in Figure 3 below.

Figure 3. Search entry

The results obtained from these searches were then filtered manually to include only the relevant ones. Cases of “not only” are not counted in the case of “only”, because “not”, which is antimorphic, modifies the QP and most likely already accounts for the inversion that takes place; cases of interrogatives are not counted as well, as wh-phrases also influence subject-auxiliary inversion. This is done for up to 500 results (in each corpus) for each quantifier-auxiliary combination, as in most cases the later results were not relevant for this research (i.e. they were not cases of subject-auxiliary inversion with a preposed quantifier phrase). Note that the results should be considered as close estimates to account for any possible human error. In COCA, all combinations with the auxiliary “to be” result in an error (i.e. “All of the “slots” in your multi-word search string occur more than 40,000,000 times in the corpus”). In these cases, instead of using the _pp* tag, each subject personal pronoun was entered separately (i.e. I, you, he, she, it, we, they). In these cases, more than 500 results in total were analyzed for each quantifier phrase, although these did not skew the results.

Chapter 3 Results and discussion

In chapter 3, the results are provided. After a general overview of these in section 3.1, which includes a general discussion and mention of some limitations of the corpus research, specific quantifier-auxiliary combinations are discussed in section 3.2. A conclusion as to the frequency of inversion patterns is provided in section 3.3.

3.1. Overview Tables 3 and 4 present, respectively in BNC and COCA, the quantifiers that were researched; the number of occurrences of each quantifier (in any form or position) in the entire corpus; the total number of results for each quantifier (with all auxiliaries combined) before filtering (i.e. the limit of 500 cases per quantifier- auxiliary combination does not apply here); the total number of hits (i.e. cases of subject-auxiliary inversion with a preposed quantifier phrase); the percentage of hits in relation to the total number of occurrences in the entire corpus (in any form or position); and the percentage of hits in relation to the total number of results before filtering.

BNC Total (corpus) Total (results) SAI-hits % (corpus) % (results)

Never 52,643 867 200 0.38% 23.07%

Nothing 31,971 257 1 0.00% 0.39%

Rarely 4,064 62 37 0.91% 59.68%

Few 42,792 137 2 0.00% 1.46%

Seldom 1,462 18 16 1.09% 88.89%

Zero 2,257 9 0 0.00% 0.00%

Only 146,936 1,982 414 0.28% 20.89%

Exactly 10,188 297 0 0.00% 0.00%

Table 3. BNC results

COCA Total (corpus) Total (results) SAI-hits % (corpus) % (results)

Never 343,708 3,566 596 0.17% 16.71%

Nothing 164,127 734 4 0.00% 0.54%

Rarely 19,555 407 352 1.80% 86.49%

Few 259,707 649 13 0.01% 2.00%

Seldom 6,009 109 97 1.61% 88.99%

Zero 14,205 64 2 0.01% 3.13%

Only 638,191 9,156 809 0.13% 8.84%

Exactly 72,130 1,725 0 0.00% 0.00%

Table 4. COCA results

Percentagewise, the number of occurrences of subject-auxiliary inversion (in relation to the total number of occurrences in the entire corpus) is rather insignificant. The percentages range from 0.00% to at most 1.80%. Likewise, the number of SAI-hits in relation to the total number of results seems to be of little importance, as the search results also include an arbitrary amount of cases where subject-auxiliary inversion does not take place. This explains the extreme differences, ranging from 0.00% up to 88.99%. The total number of occurrences of each quantifier in the entire corpus will, however, allow us to put into perspective the number of occurrences of subject-auxiliary inversion for each quantifier. A quantifier such as only, which appears to occur approximately double (in COCA) or even triple (in BNC) the amount of never (the second most occurring quantifier in both corpora) could result in a higher number of occurrences of subject-auxiliary inversion. This is indeed the case, as subject-auxiliary inversion with preposed only seems to occur 414 times in BNC and 809 times in COCA; the highest number of all quantifiers (i.e. total of 1223) in the sample of both corpora. Table 5 presents a general overview of the number of cases of subject-auxiliary inversion for each quantifier-auxiliary combination (in both corpora separately and the combined total). Figure 4 is a graph representation of these numbers.

Never Nothing Rarely Few Seldom Zero Only Exactly

To have 105 0 8 1 6 0 40 0 To do 31 0 15 0 7 0 175 0 BNC To be 13 0 6 1 2 0 46 0 Modals 51 1 8 0 1 0 153 0 Total 200 1 37 2 16 0 414 0 To have 269 1 52 0 27 2 170 0 To do 32 0 212 8 47 0 146 0 COCA To be 46 1 58 0 13 0 166 0 Modals 249 2 30 5 10 0 327 0 Total 596 4 352 13 97 2 809 0 To have 374 1 60 1 33 2 210 0 To do 63 0 227 8 54 0 321 0 Total To be 59 1 64 1 15 0 212 0 Modals 300 3 38 5 11 0 480 0 Total 796 5 389 15 113 2 1223 0 Table 5. Overview results

Cases of inversion

Zero

Exactly

Only

Seldom

Few

Rarely

Nothing

Never

0 200 400 600 800 1000 1200 1400

Never Nothing Rarely Few Seldom Only Exactly Zero BNC 200 1 37 2 16 414 0 0 COCA 596 4 352 13 97 809 0 2

Figure 4. Graph overview

In the case of anti-additive quantifiers never and nothing, the expectation was that there would be a lot of cases of subject-auxiliary inversion, as these occur in strong negative contexts. Based on the syntactic hierarchy of sentential negativity, the anti-additive quantifier never, in adverb position, would result in more cases of inversion than the anti-additive quantifier nothing in object position. While never behaves exactly as expected, resulting in 796 cases of inversion, nothing does not behave as expected, resulting in merely 5 cases of inversion. While nothing does have a lower number of results than never, the number of results is far too low as nothing is still an anti-additive quantifier. In fact, all downward entailing quantifiers (i.e. rarely, few, seldom) except for zero, and even the nonmonotonic quantifier only show more cases of subject-auxiliary inversion. In the case of the downward entailing quantifiers rarely, few, seldom and zero, the expectation was that there would be a fair amount of cases of subject-auxiliary inversion, but fewer cases than the anti-additive quantifiers, as these also occur in negative contexts but constitute weaker negatives than anti-additive quantifiers. Rarely, few, and seldom result in respectively 389, 15 and 113 cases of subject-auxiliary inversion. Zero, however, results in only 2 cases of SAI. In the case of nonmonotonic quantifiers, the expectation was that there would possibly be some cases of subject-auxiliary inversion, in cases where the assertion is ‘no other than x is y’ (Nishigushi 2003), but these would be fairly weak negatives as these are ‘negative-like’ and not straightforwardly negative. In the case of exactly, no cases of inversion where it can be certain that exactly triggers SAI were found, as this quantifier was only fronted in interrogative constructions, which already account for the inversion pattern. In the case of only, which, in most cases, asserted ‘no other than x is y’, a surprising 1223 cases of subject- auxiliary inversion were found, the highest number of results for all quantifiers. While this number is definitely significant and leads us to believe that subject-auxiliary inversion is generally accepted with preposed only, it needs to be put into perspective as only occurs the highest number of times in both corpora, which might account for a relatively higher number of results. Do note, however, the limitations of this corpus research. These results only account for cases of subject-auxiliary inversion with personal pronouns in subject position where the quantifier precedes the auxiliary up to 4 words before it. It is very well possible that any other type of subject might result in more cases of inversion for any of the quantifiers in question. The relative number of results of all cases is also influenced by the relative frequency of use of each quantifier (i.e. the total number of occurrences of each quantifier in any form and position in the entire corpora). It is to be expected that if a certain quantifier (e.g. rarely) occurs double the amount of another quantifier (in any construction), it would result in more cases of inversion as well. This might explain the higher number of SAI-hits for only and rarely and the lower number of SAI-hits with few and zero. This corpus research does, however, give an indication of the relative distribution of inversion for each type of quantifier.

In short, most of the quantifiers behave as expected when looking at their negativity, the anti-additive quantifier never showing a high amount of cases of inversion, the downward entailing quantifiers rarely, few, and seldom resulting in a fair amount of cases of inversion, and the non-monotonic quantifier exactly resulting in no cases of inversion. Some outliers are the anti-additive quantifier nothing, resulting in only 5 cases of inversion, the downward entailing quantifier zero, resulting in 2 cases of inversion, and the nonmonotonic only resulting in the highest amount of cases of inversion (i.e. 1223).

3.2. Quantifier-auxiliary combinations Figures 5 – 10 visually represent (for each separate quantifier) the number of occurrences of subject-auxiliary inversion with each (type of) auxiliary.

3.2.1. Anti-additive/antimorphic QPs Never 400

350

300

250 269 200 COCA 249 BNC 150

100

50 105 32 46 31 51 0 13 To have To do To be Modals

Figure 5. Results (never)

The anti-additive quantifier never seems to combine mostly with the auxiliary to have and with modals, with respectively 374 and 300 cases of inversion, compared to 63 cases in combinations with the auxiliary to do and 59 cases in combinations with the auxiliary to be. In the case of nothing (no graph is provided in this case), the amount of cases of inversion is too low to make any conclusions.

3.2.2. Downward entailing QPs Rarely 250

200

150 COCA 212 100 BNC

50 52 58 30 0 8 15 6 8 To have To do To be Modals

Figure 6. Results (rarely)

Seldom 60

30 47 COCA BNC 20 27

10 13 10 6 7 0 2 1 To have To do To be Modals

Figure 7. Results (seldom)

Few 9 8 7 6 5 COCA 4 8 BNC 3 5 2 1 1 1 0 To have To do To be Modals

Figure 8. Results (few)

Zero 2.5

1.5 COCA

1 2 BNC

0.5

0 0 0 0 To have To do To be Modals

Figure 9. Results (zero)

The downward entailing quantifier rarely, which resulted in the highest number of results, combines mostly with the auxiliary to do (i.e. 227 cases). This is also the case for seldom (i.e. 54 cases). Although few has a fairly insignificant total number of results, combinations with the auxiliary to do also seem to be most prevalent (i.e. 8 cases). In the case of zero, only combinations with the auxiliary to have were found.

3.2.3. Nonmonotonic QPs Only 600

500

400

300 327 COCA 146 BNC 200

170 166 100 175 153 46 0 40 To have To do To be Modals

Figure 10. Results (only)

The nonmonotonic quantifier only seems to have a fairly equal distribution with all different auxiliaries. The modals do seem to be an outlier, but this can be explained as the modals are a group of auxiliaries instead of a single auxiliary. The nonmonotonic quantifier exactly, disregarding the high number of cases where the interrogative structure triggered subject-auxiliary inversion, resulted in 0 cases of subject-auxiliary inversion.

3.3. Conclusion Although there seem to be some slight tendencies for specific quantifier types to occur with certain (types of) auxiliaries (e.g. negative scalar quantifiers occurring the highest number of times with the auxiliary to do), it appears that for most quantifier phrases that regularly trigger subject-auxiliary inversion, combinations with all auxiliaries tend to occur. It does not seem that the type of auxiliary has much – if any – effect on subject-auxiliary inversion. With regard to the frequency of inversion patterns; it seems that, in addition to anti- additive/antimorphic QPs and downward entailing QPs, the nonmonotonic QP only consistently (and even with a higher frequency) triggers subject-auxiliary inversion when preposed. This indicates that only might carry a [NEG]-feature and thus trigger the NEG-criterion as well.

Chapter 4 Analysis

Initially, a general overview of how the different quantifiers will be analyzed is presented (section 4.1). This is followed by the application of the aforementioned analysis to the corpus data (section 4.2).

4.1. General overview In the corpus data analysis, we will try to account for some cases of SAI that we observed in the corpora by means of Rizzi’s (1997) split CP framework (Figure 2) and Haegeman’s NEG-criterion (Haegeman 2000b; Haegeman and Zanuttini 2014). This section will provide a general overview of the analysis for each type of quantifier; this analysis will then be elaborated on and applied to the corpus data in section 4.2. If a (negative) quantifier phrase gives rise to subject-auxiliary inversion (and there is thus sentential negation), the fronted QP is a focus constituent and should thus go into the specifier position of FocP. If this is not the case, the fronted QP is a topic constituent and should thus go into the specifier position of TopP. As all cases examined are cases of subject-auxiliary inversion, it is expected that they all go into SpecFocP. As such, they should also have the possibility of being preceded by a topic constituent, as in (78).

(78) During my sabbatical, on no account will I read e-mail. (Haegeman 2000b: 27)

As inversion occurs, there must be something in SpecFocP that requires a spec-head configuration with the auxiliary; if the quantifier phrase in question is thus preceded by a topic constituent, this would imply that the quantifier phrase is in SpecFocP. If a negative quantifier phrase is in SpecFocP, the NEG-criterion applies, triggering subject-auxiliary inversion through leftward movement of the auxiliary (i.e. the head which carries the matching [NEG]-feature) to Foc° to obtain the necessary spec-head configuration. As the corpus data indicates, (negative) inversion has the capability of occurring with anti- additive/antimorphic, downward entailing and nonmonotonic quantifier phrases in sentence-initial position. As such, the specifics of how the NEG-criterion is capable of applying when the QPs in question are focalized must be examined. In anti-additive/antimorphic quantifier phrases, it will be argued that the NEG-criterion applies obligatorily when the QP is situated in the specifier position of FocP. This is because anti- additive/antimorphic quantifiers, such as never and not, contain a morphological mark of negation which carries the NEG-feature. Never, for example, is composed of the negative marker not and ever. Besides their

semantic negativity, there is thus also an overt syntactic negative marker within the quantifier which triggers the NEG-criterion (cf. section 4.2.1.1). Haegeman (2000b: 22) notes that inversion is also known to be triggered by preposed ‘weak negators’ such as rarely, scarcely, seldom, only, few, etc. This is in accordance with the results of the corpus investigation. It could thus be argued that these elements are also subject to the NEG-criterion, even though these, on the surface, do not seem to contain a morphological mark of negation. In the case of downward entailing quantifier phrases (e.g. rarely, seldom, few), it will be argued that the NEG-criterion does also apply when the QP is in the specifier position of FocP. Downward entailing QPs, however, do not contain a morphological mark of negation. Haegeman (2000b: 32) does, however, note that preposed negative constituents that trigger subject-auxiliary inversion semantically differ from those that do not trigger inversion in their monotonicity. The former are monotone decreasing (i.e. downward entailing), while the latter are not. If this is the case, this would explain why downward entailing quantifier phrases, which are monotone decreasing, also trigger the NEG-criterion. Because of their downward monotonicity, there might be a covert syntactic negative feature that allows the NEG-criterion to apply in these cases. This analysis is elaborated on in section 4.2.2.1. Likewise, even for nonmonotonic quantifier phrases, we argue that the NEG-criterion seems to be able to apply as well when the QP is focalized to SpecFocP. Like downward entailing quantifiers, these also do not contain a morphological mark of negation. Unlike downward entailing quantifiers, though, they do not express a monotone decreasing function.

(79) Only John eats  No one but/except John eats.

Example (79), which is similar to Nishiguchi’s (2003) ‘no other than x is y’ assertion, does, however, give us reason to believe that nonmonotonic QPs are able to express a negative-like meaning, which might indicate the presence of a covert syntactic negative feature in nonmonotonic quantifier phrases as well. Section 4.2.3.1 provides arguments for the presence of such a covert negative feature. It will thus be argued that besides anti- additive/antimorphic QPs and downward entailling QPs, the NEG-criterion applies to nonmonotonic QPs as well. Besides the application of the NEG-criterion which has been discussed above, an alternative is provided by Collins & Postal (2014). They propose the general condition for negative inversion presented in (80), with the definition of SYNNEG in (81). Their definition of SYNNEG seems to be very similar to the requirements for the application of the NEG-criterion (i.e. a [NEG]-feature within the preposed constituent). However, the Negative Inversion Condition does allow SAI to occur with preposed constituents which are not SYNNEG but have a monotone decreasing function. If nonmonotonic QPs thus do not contain a covert

syntactic negative feature but are somehow monotone decreasing, the Negative Inversion Condition could account for the inversion that occurs.

(80) The Negative Inversion Condition

In a structure K = [FocP Q Aux S], where Q is an NI focus, a. Q is (or dominates) a DP V such that V’s scope position is higher than the position of any other element of K; and b. i. V is SYNNEG or ii. [[V]] is a monotone decreasing function (Collins & Postal 2014: 140)

(81) Definition: SYNNEG An XP Z is SYNNEG if and only if there is a unary-NEG structure V = [NEG X] and i. Z = V, or ii. V is the D of Z (Collins & Postal 2014: 136)

In the above, [[V]] signifies the semantic value of the DP V; S equals TP/IP; and NI stands for Negative Inversion. Briefly summarized, the Negative Inversion Condition requires that, in a structure with a preposed quantifier/determiner phrase, the quantifier is or dominates the determiner phrase such that it scopes over all other elements in the structure K (i.e. sentential scope). This excludes cases of topicalization from fulfilling the condition. In addition to this, the quantifier/determiner phrase must either have the semantic value of a monotone decreasing function; or either have, or have a determiner with, a unary-NEG structure. A unary-

NEG structure is different from a binary-NEG structure in that the former involves a single NEG (i.e. [NEG1

X]), while the latter involves two NEGs (i.e. [ NEG1 [NEG2 X]]) (Collins & Postal 2014: 31). An example of the unary-NEG structure for nobody is provided in (98).

(82) [[NEG1 SOME] body]

The Negative Inversion Condition justifies negative inversion for preposed anti-additive quantifiers (e.g. never, nobody), as these are both downward monotonic and SYNNEG. Downward entailing quantifiers are justified as well, as these have a monotone decreasing function, although section 4.2.2.1 elaborates on current arguments for DE QPs also being SYNNEG. Only-phrases could thus also be justified if they are somehow monotone decreasing or SYNNEG; this will be elaborated on in section 4.2.3.1.

Although it is generally the case that all constituents that are SYNNEG are also monotone decreasing, there are also cases where such constituents are monotone increasing. The Negative Inversion Condition also accounts for such cases that trigger inversion, as in (83).

(83) No fewer than three gorillas were they able to teach French to. (Collins & Postal 2014: 135)

‘No fewer than three gorillas’ is SYNNEG because it contains the negative quantifier no; it is, however, monotone increasing. A question that remains though, is exactly how forms like only, rarely and few can be covertly NEG and might thus be SYNNEG. If they are indeed SYNNEG, condition (80)bii could be excluded, which would render it an entire syntactical account of SAI insofar that it could simply be replaced by the application of the NEG-criterion. This analyis will be elaborated on in section 4.2. Before that, however, section 4.1.1 will analyze preposed quantifier phrases that can occur as either a topic or a focus (in different constructions with different meanings); specifically looking at the difference in structure and meaning.

4.1.1. Ambiguous constituents Based on some cases where the exact same (negative) constituent can serve as either a topic or a focus, some conclusions about the structure and meaning of those constituents can be made. Of the following preposed only-phrases with and without inversion, in (84) – (87), only Quirk et al claim that the non-inverted example is grammatical. All others consider the non-inverted example as ungrammatical.

(84) Only his mother will he obey. Only his mother he will obey. (Quirk et al 1985: 781)

(85) Only George would we invite. *Only George we would invite. (Bayer 1996: 14)

(86) Only in that election did Leslie run for public office. *Only in that election Leslie ran for public office. (Bruening 2015: 16)

(87) Only twice did I go there *Only twice I went there. (Martinková 2010: 66)

In all of the above cases, the only-phrase itself does not have a difference in meaning between the inverted and non-inverted structures. In addition, constructions like those in (88a) and (89a), where the only-phrase can occur with a non-inverted structure, are grammatical because the only-phrase does not have the same meaning as in the inverted structure. This is evidenced by the paraphrases below, which show that on the one hand, in cases of non-inversion, the meaning of the only-phrase is not negative; on the other hand, in cases of inversion, the meaning of the only-phrase is negative.

(88) a. Only yesterday I went there. (Martinková 2010: 66) ‘I went there as recently as yesterday’ b. Only yesterday did I go there ‘I did not go there before yesterday’ or ‘I went there on no other days than yesterday’

(89) a. Only this time, we went to her condo instead of mine. (COCA) ‘But this time, we went to her condo instead of mine.’ b. Only this time did we go to her condo instead of mine ‘No other times than this time did we go to her condo instead of mine’

In addition to the above examples with only-phrases, there are also cases where a negative constituent can occur as either a topic or as a focus and superficially look like exactly the same constituent. The difference, however, lies in their scope. As a topic, the constituent has scope over the constituent (and no subject-auxiliary inversion occurs); as a focus, the constituent has sentential scope (and the auxiliary moves leftward due to the NEG-criterion). As such, the meaning of the sentence is different. However, at the moment, the only cases we have encountered are cases in which the preposed (negative) constituent consists of an anti-additive/antimorphic QP within a prepositional phrase, as in (90) – (93). The differences in meaning/scope are reflected in the paraphrases provided below each example.

(90) a. Not even ten years ago could you see such a film. ‘Even ten years ago, you could not see such a film.’ b. Not even ten years ago you could see such a film. ‘You could see such a film as recently as ten years ago.’ (Quirk et al 1985: 793)

(91) a. With no clothes is Sue attractive (S-negation) ‘There are no clothes in which Sue is attractive’ b. With no clothes, Sue is attractive (constituent negation) ‘While wearing no clothes, Sue is attractive’ (Horn 1989: 185)

(92) a. With no job, she would be happy. ‘Jobless, she would be happy’ b. With no job would she be happy. ‘There is no job such that she would be happy’ (Haegeman 2000b: 31)

(93) a. Not even 10 years ago, you could buy a house for less than 50k. ‘Less than 10 years ago, you could buy a house for less than 50k.’ b. Not even 10 years ago could you buy a house for less than 50k. ‘Even 10 years ago, you could not buy a house for less than 50k.’ (Büring 2004: 4-5)

As these ambiguous constituents which superficially look the same are capable of taking either constituent or sentential negation, it must be that the structure of a topicalized PP is different from that of a focalized PP. A concrete example which shows the different structures is based on (93), of which (93a) is an instance of topicalization and (93b) is an instance of focalization. Büring compares these versions with alternatives that project the same sentence into the future tense, as in (94a) – (94b). Example (94a), where the constituent is topicalized, shows that not even modifies the DP within the PP. Example (94b), however, where focalization occurs, shows that not even modifies the entire PP (‘in ten years’). The structures for examples (93a) – (93b) and (94a) – (94b) are provided in Table 6.

(94) a. In not even ten years, you will be able to buy a house for 10k. ‘In less than 10 years, you will be able to buy a house for 10k’ b. Not even in ten years will you be able to buy a house for 10k. ‘Even in 10 years, you will not be able to buy a house for 10k’ (examples based on Büring 2004: 5)

Focalization Topicalization

(94b) not even [PP in [DP 10 years]] (94a) [PP in [DP not even 10 years]]

(93b) not even [PP [DP 10 years] ago] (93a) [PP [DP not even 10 years] ago] Table 6. Inversion and topicalization structures (based on Büring 2004: 5)

When the negative quantifier is thus embedded within a PP, the preposition seems to stop the negation from going up and having scope over the entire sentence. As such, the spec-head configuration (due to the NEG- criterion) has to be met within the PP and cannot attract the auxiliary. It can thus be concluded that, if a negative constituent has the possibility of occurring as either a topic or as a focus (in separate sentences), this is because there is a difference in meaning and presumably an underlying difference in structure. . 4.2. Corpus data analysis 4.2.1. Anti-additive/antimorphic QPs Some cases of subject-auxiliary inversion with preposed quantifier phrases with never have been selected from both corpora (out of 796 total hits) and are presented in (95) – (102). In addition, only 5 cases of SAI with a preposed QP containing nothing have been identified; these are presented in (103) – (107).

(95) Never in my life had I done anything like this before. (BNC) (96) Never in his life had he spoken to her in this way. (COCA) (97) Never again did he wish to be God. (BNC) (98) Never in your life did you want to go swimming again. (COCA) (99) Never before were they faced with the threat of losing substantial numbers of accounts. (BNC) (100) Never was he where they said he was. (COCA) (101) Never again would she land herself in such a mess. (BNC) (102) Never again would we all meet in the flowery environs of the nursery school. (COCA)

(103) Nothing had he brought from the Tomb of the Black Dog, save his loot and his body, with every aperture blocked. (COCA) (104) He's a very passionate person, and nothing is he more passionate about than Vietnam. (COCA) (105) Nothing could he view without emotion. (BNC) (106) Nothing can you do now, Paskaal. (COCA) (107) The pain of Suzanne's death, the worse pain of her dying, had taken away his hopes for anything more than simple companionship ever again; and for Clare's companionship alone he was now deeply grateful, although with nothing could he ever again be as happy as he had been. (COCA)

To account for these cases of SAI, it is expected that the (anti-additive) quantifier phrase has been preposed because it is focalized. In the case of QPs containing never, they move from an aspectual position, AspFreq I, in the TP-field (Cinque 1999) to the specifier of FocP. As never contains a morphological mark of negation (cf. section 4.2.1.1), the NEG-criterion applies, requiring the auxiliary (which carries the matching [NEG]-feature) to move leftward to Foc° to allow for the right spec-head configuration; i.e. triggering subject-auxiliary inversion. A representation of this is provided in Figure 11. In the case of the preposed QPs containing nothing, the same analysis applies; the difference being that they do not originate in AspFreq I, but usually in a complement position to the VP as either an NP or within a PP. A representation of this is provided in Figure 12.

Figure 11. Focalized anti-additive QP structure (never)

Figure 12. Focalized anti-additive QP structure (nothing)

In root clauses, negative inversion is also compatible with the preposing of adverbial or argumental topics (Haegeman 2000b: 27) in SpecTopP. As such, this should also be possible for the examples from the corpus research. Some of these examples, including a(n) (altered) version with an added topic, are provided in (108) – (109) for never and in (110) – (111) for nothing.

(108) Never again would she land herself in such a mess. (BNC) ‘After the birth of her child, never again did she land herself in such as mess’ (109) Never was he where they said he was. (COCA) ‘During his kidnapping, never was he where they said he was’ (110) Nothing could he view without emotion. (BNC) ‘During his divorce, nothing could he view without emotion.’ (111) Nothing had he brought from the Tomb of the Black Dog, save his loot and his body, with every aperture blocked. (COCA) ‘From the Tomb of the Black Dog, nothing had he brought back, save his loot and his body, with every aperture blocked.’

To conclude, preposed quantifier phrases with never and nothing behave exactly as expected. As a focalized constituent, they move into SpecFocP. Due to their [NEG]-feature, the NEG-criterion applies, whereby the auxiliary, which carries the matching [NEG]-feature moves leftward to Foc°, triggering subject- auxiliary inversion. What is unexpected, however, is the extreme low frequency of subject-auxiliary inversion with preposed nothing. A possible cause of this is analyzed in section 4.2.4.1.

4.2.1.1. [NEG]-feature The presence of an overt syntactic negative marker in purely negative QPs has already been established in the current literature. There is “morphological incorporation of negation” or “Neg-incorporation” (de Swart 2009: 118; Horn 1989: 253-254). This means that a negative morpheme (i.e. not) is incorporated into an indefinite to form an anti-additive QP. This is demonstrated for some anti-additive QPs in Table 7.

No Not a(ny) No one Not anyone

None Not any Nothing Not anything

Never Not ever Nobody Not anybody

Nowhere Not anywhere Neither Not either

Table 7. N-word morphology

4.2.2. Downward entailing QPs Of the 389 cases of subject-auxiliary inversion with preposed quantifier phrases containing rarely, the cases presented in (112) – (119) have been selected from both corpora. The same has been done for seldom (120) – (127), few (128) – (135) and zero (136) – (139). In the case of zero, only two cases have been identified in the corpora; as such, two more examples have been added from outside the corpora. Although rarely and seldom have essentially the same meaning, the former occurs approximately 3 to 4 times as much as the latter. A possible explanation for this could be that seldom is more formal.

(112) Rarely have I seen the' Whads' play with such composure, flair and skill. (BNC) (113) Rarely have I felt such relief. (COCA) (114) Rarely do I see a parent who has decided to buy a book as a present. (BNC) (115) Rarely do they actually hurt each other. (COCA) (116) Rarely are they negligible. (BNC) (117) Rarely was he ever reprimanded or disciplined. (COCA) (118) Rarely will they define precisely what it is they wish to find out about dinosaurs or railways. (BNC) (119) Rarely will he abandon a piece. (COCA)

(120) Seldom have I seen the House or the Government in quite such a mess. (BNC) (121) Seldom have I been so terribly wrong. (COCA) (122) Seldom do they spend successive winters in the same place, ... (BNC) (123) Seldom do I hark back to the troubles of my youth. (COCA) (124) Now th-- he was saying that, it's being argued here that, that very seldom is it that the punishment exceeded the crime, … (BNC) (125) Very, very seldom are they ever stopped. (COCA) (126) Seldom if ever will he invite you to carry on, and assure you that if things go wrong he will bear the burden of guilt. (BNC) (127) Very seldom will I kill a wild bird over a pup. (COCA)

(128) On few occasions has it shown less moral scruple than when it made a deal with Brezhnev to dispose of the Soviet gold. (BNC) (129) Very few times did we have people step away. (COCA) (130) In very few instances do we find something approaching internal evidence. (COCA) (131) Very few spells do I cast. (COCA)

(132) Few are they who can manage to live with ideas. (BNC) (133) Few days will you find he was even here in Los Angeles. (COCA) (134) In few other places could you still find habitat where, within the space of walking only six or seven miles, you went from forest to swamp to salt marsh to beach. (COCA) (135) But in few places can you fry an egg on a sidewalk as quickly and thoroughly as you can here. (COCA)

(136) Zero times have we done that. (COCA) (137) And I would tell you, when you look at, on balance, over 50 cases that we've help disrupt terrorist plots and contributed information to those, zero times have we come up with a place where we have failed the public's confidence or Congress' confidence in these - in these laws. (COCA) (138) I looked at their last 80 games and zero times have they given up that many points and that many yards. (Collins & Postal 2014: 137) (139) But on zero occasions have I found myself held up, delayed, late to my destination or in any other way inconvenienced by cyclists on the roads. (Collins & Postal 2014: 138)

Once again, subject-auxiliary inversion occurs, suggesting a leftward movement of the auxiliary to Foc°. To justify this, it can be argued that the quantifier phrases with rarely and seldom also focalize by moving from the aspectual position AspFreq I, in the TP-field (Cinque 1999), to SpecFocP. A representation for rarely, which also applies to seldom, is provided in Figure 13 on the next page. Few and zero, like nothing in Figure 12, can originate in the VP as a complement to the verb, although in most of the above cases they originate as an adjunct to the VP. In both cases, they occur in either an NP or a PP. Even though rarely, seldom, few and zero are weak negators, it could be argued that the NEG-criterion applies, which, as suggested by Haegeman (2000b: 22), explains the subject-auxiliary inversion that occurs. The [NEG]-feature in downward entailing quantifiers is elaborated on in section 4.2.2.1.

. Figure 13. Focalized downward entailing QP-structure (rarely)

Adverbial or argumental topics can also precede the “negative” constituent and are assumed to be in SpecTopP. Some examples of this, for all of the above downward entailing QPs, are provided in (140) – (146).

(140) Rarely have I felt such relief. (COCA) ‘Since my accident, rarely have I felt such relief.’

(141) Rarely are they negligible. (BNC) ‘In such cases, rarely are they negligible.’

(142) Seldom have I seen the House or the Government in quite such a mess. (BNC) ‘Since the 90s, seldom have I seen the House or the Government in quite such a mess.’

(143) Seldom have I been so terribly wrong. (COCA) ‘Not surprisingly, seldom have I been so terribly wrong.’

(144) Very few times did we have people step away. (COCA) ‘Back in the day, very few times did we have people step away.’

(145) Few are they who can manage to live with ideas. (BNC) ‘These days, few are they who can manage to live with ideas.’

(146) Zero times have we done that. (COCA) ‘In Belgium, zero times have we done that.’

Negative inversion is thus definitely also possible with preposed quantifier phrases containing a weaker negator such as rarely, seldom, few or zero. In the case of zero, however, only two cases of SAI have been identified; the low frequency of SAI patterns with preposed zero is accounted for in section 4.2.4.2.

4.2.2.1. [NEG]-feature Although the monotone decreasing function that is present in downward entailing quantifier phrases has been argued as a possible reason for triggering subject-auxiliary inversion in these cases, the current literature also argues that forms like rarely, few and seldom have a covert syntactic negative feature which accounts for their negative behavior. If this is the case, these quantifiers would also be SYNNEG as they would then contain an instance of [NEG] and have to satisfy the NEG-criterion (through e.g. SAI when they are focalized). Generally, it can be confirmed that downward entailing quantifiers semantically have a negative-like meaning. Rarely and seldom are semantically equivalent to not frequently (i.e. infrequently) and not often (Horn 1989: 265), in which an overt syntactic negative marker (i.e. not) is clearly visible. Few is semantically equivalent to not many (Horn 1989: 265), where the same overt syntactic negative marker can be seen. This supports the idea of these quantifiers containing a covert syntactic negative feature. Moreover, the claim that these DE QPs consist of a [NEG]-feature can be supported in several ways. Firstly, NPI-licensing tests show that these quantifier phrases are capable of licensing strong NPIs such as either (147). Secondly, the question tag test shows that they are capable of triggering positive question tags (148). Thirdly, as evident from the data in the corpus as well, downward entailing quantifiers can give rise to negative inversion when preposed (149). Lastly, DE QPs can give rise to split scope readings in intensional contexts (150) (de Swart 2000).

(147) Few Americans have ever been to Spain. Few Canadians have either. (Rullmann 2003: 345) (148) Jack rarely/seldom goes out, does he/doesn’t he? (McCawley 1998: 507) (149) Very few times did we have people step away. (COCA) (150) Ze hoeven weinig verpleegkundigen te ontslaan. ‘They need few nurses to fire’ a. For a group Y consisting of few nurses y, it is the case that it is necessary for them to fire each individual member of Y b. It is not necessary for them to fire more than a small number of nurses. (de Swart 2000: 114)

Typological support for a covert syntactic negative feature in “quantity-words” (Q-words) is also provided in De Clercq (2017). De Clercq argues that negative Q-words expressing the meaning of few/little consist of – amongst others – a negation feature. A typological argument for this claim comes from the fact that some languages in her sample express few with an overt negative marker. This occurs in Malagasy, Wolof, Garifuna, Hixkaryana, Western Armenian, Northern Sotho and Japanese (2017: 9).

(151) Xaj y-u bëri-wul mën a jáng

dog CL.PL-Crel be.many-NEG can INF read ‘Few/Not many dogs can read.’ (De Clercq 2017: 7)

In (151), the syntactic negative marker “-u(l)” in Wolof, which negates “bëri” (many) to form few/not many, is clearly visible. Combining the typological support with the evidence from the tests for sentential negation, it can be argued that, in English, a covert syntactic negative feature is present in DE QPs, which, when the quantifier is preposed and focalized, triggers the NEG-criterion and thus gives rise to subject-auxiliary inversion.

4.2.3. Nonmonotonic QPs In the case of only, 1223 cases of subject-auxiliary inversion with preposed quantifier phrases have been identified. Of those, the cases presented in (152) – (159) have been selected. No cases of subject-auxiliary inversion with preposed quantifier phrases with exactly have been identified in both corpora. In all cases, exactly was part of a preposed wh-phrase in an interrogative construction, which explains the subject-

auxiliary inversion that occurs due to the WH-criterion. Nevertheless, two examples from outside the corpora are provided in (160) – (161).

(152) Only en route had he understood the true implications. (BNC) (153) Only after their lovemaking had he thought to ask her name. (COCA) (154) Only by sharing anxiety do we participate in a meaningful existence. (BNC) (155) Only when he arrived did he realize he realize he had been exiled. (COCA) (156) Only if productivity increases is it possible in the long-run for both groups to be successful. (BNC) (157) Only then was he willing to leave. (BNC) (158) Only after that may they lock antlers and push each other. (BNC) (159) Only in warmer temperatures would it be deleterious. (COCA)

(160) Exactly one feature did I notice in the landscape. (Collins & Postal 2014: 138) (161) In exactly two of these cases did we find traces of the virus. (Büring 2004: 2)

As subject-auxiliary inversion does also occur in these cases, there must be a constituent in SpecFocP that somehow requires the auxiliary to move to Foc°. It thus seems to be that quantifier phrases with only and exactly somehow trigger subject-auxiliary inversion when they are sentence-initial. The above preposed only-phrases originate as an adjunct to the VP; the preposed exactly-phrases originate as either a complement to the verb (160) or as an adjunct to the VP (161). A representation of the structure for only is provided in Figure 14.

Figure 14. Focalized nonmonotonic QP-structure (only)

If the preposed constituent containing only or exactly is indeed in SpecFocP, it should also be the case that these constructions can be preceded by a preposed topic. Some examples of this are provided in (162) – (164).

(162) Only en route had he understood the true implications. (BNC) ‘Being a bit slow in understanding, only en route had he understood the true implications.’

(163) Only when he arrived did he realize he had been exiled. (COCA) ‘Having been freed from prison, only after he arrived did he realize he had been exiled.’

(164) Exactly one feature did I notice in the landscape. (Collins & Postal 2014: 138) ‘During my trip, exactly one feature did I notice in the landscape.’

Although only is not straightforwardly negative, it seems to pattern in a similar manner as never and rarely. It could thus be that only is in some way negative, enabling the possibility of the NEG-criterion to

apply in all these cases. The overwhelming number of inversion patterns with preposed quantifier phrases with only (i.e. 1223 cases) shows that these cases are definitely not exceptions. A possible reason as to why only occurs in sentence-initial position (and thus SpecFocP) with such great frequency is because only is a focusing adverb and thus “focus-sensitive”, which means that it associates with focus elsewhere in the sentence (Erlewine & Kotek 2014: 1). Ladusaw (1979: 129) defines it as a “focus particle”. If only is preposed, it is followed by the constituent that is focalized. This is shown in (165a), where only focalizes John and is not able to focalize any other constituents. In (165b), however, only is not preposed and is capable of focalizing multiple constituents (all of which are capitalized).

(165) a. Only JOHN had given his daughter a new bicycle. b. John had only GIVEN HIS DAUGHTER a NEW BICYCLE (Erlewine & Kotek 2014: 3)

As has been stated in the discussion of the WH-/NEG-criteria; a common feature of constituents that trigger subject-auxiliary inversion might be a [focus] feature, which is also found in preposed wh-phrases and preposed negative constituents as these also go into SpecFocP. This follows from Haegeman’s split CP analysis which shows that preposed constituents triggering SAI are all in complementary distribution (Haegeman 2000b: 46). As such, I argue in section 4.2.3.1 that, similar to anti-additive/antimorphic QPs and downward entailing QPs, only-phrases contain a covert instance of [NEG]. This negative feature enables to application of the NEG-criterion.

4.2.3.1. [NEG]-feature Based on the many cases of subject-auxiliary inversion with preposed only-phrases in the data above (i.e. 1223 cases), it is clear that nonmonotonic quantifiers, such as in this case only, are capable of showing some type of negative behavior or having a negative-like meaning as well. Haegeman (2000b: 22) mentions only when discussing ‘weak negators’ that trigger inversion. Clearly, only thus has the possibility of being semantically negative. This is in accordance with Nishiguchi’s (2003) ‘negative’ assertion ‘no other than x is y’ that he attributes to only. Similarly, Collins & Postal (2014: 138-139) semantically compare only to ‘nobody but/except’, which also contains a negative feature (i.e. in the anti-additive quantifier nobody). Let us start by looking at the meaning of preposed only in some specific cases in (166) – (168).

(166) a. *Only twice I went there. b. Only twice did I go there. (Martinková 2010: 66)

(167) a. Only his mother will he obey. b. % Only his mother he will obey. (Quirk et al 1985: 781)

(168) a. Only yesterday I went there. b. Only yesterday did I go there (Martinková 2010: 66)

In the case of (166) and (167), Martinková argues that only has a restrictive or negative meaning (i.e. the number of occasions on which I went there does not exceed two; no one but his mother). In (168), only can mean “as recently as”, which is not negative and might explain why inversion does not occur (168a). However, the same sentence can be interpreted as being negative. In that case, it means either “not before yesterday” or “no other days than yesterday”. In negative instances, subject-auxiliary inversion (168b) should thus be possible. Only-phrases can thus have both negative and non-negative meanings. When looking at the monotonicity of only, it is clear that it is not monotone decreasing, but nonmonotonic, as has been discussed in section 1.1.1. Von Fintel (1999) proposes, however, that only-phrases satisfy the property of Strawson decreasingness. An example in support of this is provided in (169).

(169) a. Only Nancy eats vegetables. b. Only Nancy eats spinach. (Collins & Postal 2014: 134)

Collins & Postal (2014: 134) state that, in the above example, (169a) entails (169b) under the assumption that the presupposition of (169b) is satisfied. The superset of ‘eating vegetables’ thus entails the subset ‘eating spinach’ if it is presupposed that spinach is one of the vegetables that is being eaten by Nancy. In this case, the fact that only Nancy eats vegetables (including spinach) thus entails that no one else is eating spinach, as spinach is a subset of vegetables. Similar to downward entailing quantifiers, subject-auxiliary inversion might be triggered because of this “decreasingness” similar to downward monotonicity (if one assumes that DE- ness is a sufficient condition for inversion; as in Collins & Postal 2014). In the case of downward entailing quantifiers, however, it has already been argued that the NEG-criterion is triggered due to a covert syntactic negative feature. This possibility for nonmonotonic QPs thus still has to be examined as well. Gast (2013: 103-104) semantically defines focus quantifiers such as only as “expressions quantifying over sets of alternatives” associated with the denotation of the focused constituent. He assumes that sentences constructed with focus quantifiers denote pairs of propositional meanings. He makes a distinction between

the prejacent and the annex. Neeleman & Vermeulen (2011: 1) make a similar distinction between respectively the ‘A-component’ and the (polar) ‘B-component’. An example of this distinction is provided in (170).

(170) Only JohnF attended the meeting. PREJACENT: ‘John attended the meeting’ [A-component] ANNEX: ‘No one other than John attended the meeting’ [(polar) B-component] (Gast 2013: 104)

The prejacent is the “denotation of the material contained in the scope of the relevant operator” (i.e. the meaning of the host sentence minus the focus quantifier), while the annex is constituted by a “quantificational statement” that is contributed by the focus quantifier (i.e. the interpretation contributed by only; the set of alternatives to the focused constituent). In the case of only, it expresses “negated existential quantification over the domain of alternative values” (Gast 2013: 106) and thus states that any alternatives are not truth- conditional. In addition, for only, the prejacent is a presupposition, while the annex is an assertion. In the prejacent, no negation is visible. In the annex, on the other hand, negation is clearly visible (i.e. negative marker no(t)). As such, Gast states that “sentence negation affects the annex but not the prejacent” (2005: 5). Only-phrases are thus negative by means of the assertion that is associated with them. Neeleman & Vermeulen (2005) confirm that the A-component is positive, while the (polar) B-component is negative. This is because it contains a negative operator. If the negative meaning of the ‘annex’ influences the syntactic behavior of only, this might indicate that only inherently carries a covert negative feature. As has been argued before, this would simplify the Negative Inversion Condition (Collins & Postal 2014), leaving out the possibility of monotone decreasingness (or Strawson Decreasingness in the case of only) accounting for inversion, rendering it a purely syntactic account of negative inversion (i.e. through SYNNEG structures). In effect, it could then simply be replaced by the application of the NEG-criterion. Bayer argues that an only-phrase like only George is “an entity that somehow encodes a feature of negation turning it into an affective operator” (1996: 15). In this case, when only is focalized, the covert syntactic negative feature is then responsible for the triggering of subject-auxiliary inversion to satisfy the NEG-criterion. Firstly, support for a syntactic negative feature in only is provided by the high number of times that only gives rise to subject-auxiliary inversion, as confirmed in the corpus research (i.e. 1223 cases of inversion with preposed only-phrases). Although Quirk et al (1985) argue that, in some cases, subject-auxiliary inversion seems to be optional, as seen in the pair (171) – (172) which are semantically equivalent. There is, however, no agreement on the (un)grammaticality of (172). Bayer includes a very similar construction

presented in (173) – (174) where he states that (174), without inversion, is ungrammatical. Another example that is considered ungrammatical without inversion is provided by Bruening in (175) – (176). The optionality of inversion with fronted only-phrases is thus still open for discussion, although I will henceforth assume that cases without inversion are ungrammatical. Some exceptions to this will be discussed in section 4.2.4.3.

(171) a. Only his mother will he obey. (172) b. % Only his mother he will obey. (Quirk et al 1985: 781)

(173) Only George would we invite. (174) *Only George we would invite (Bayer 1996: 14)

(175) Only in that election did Leslie run for public office. (176) *Only in that election Leslie ran for public office. (Bruening 2015: 16)

In addition to the inversion patterns that it gives rise to, only also shows some other negative syntactic behavior. It is, for example, capable of licensing NPIs (Büring 2004: 2) when preposed or in subject position (Progovac 2005: 73). Some examples are provided in (177) – (183).

(177) Only Mary showed any respect for the visitors subject position (178) Only to his girlfriend did John give any flowers preposed (179) Only last year did John get any grey hairs. preposed (Progovac 2005: 73)

(180) Only Anna had any glow. (COCA) (181) Only Sammy put any pressure on Sammy. (COCA) (182) Only once had he ever lost his temper with the Normans. (BNC) (183) Only Billie had ever done this for him. (BNC)

Some only-phrases are also capable of having split scope readings. Penka (2011: 151) notes that “only modifying any category yields a split scope reading in combination with an intensional verb”.

(184) This year, we can only dream of a white Christmas. ‘This year, we can’t do anything other about a white Christmas than dream of it’ ‘This year, we can’t do anything else than dream of a white Christmas’ (examples based on Penka 2011: 151)

(185) a. They were only advised to learn Spanish. ‘They were not advised to learn any other language than Spanish.” b. They were advised to learn only Spanish. ‘They were advised not to learn any other language than Spanish’

(186) a. We are required to only study syntax. ‘We are required not to study any subject other than syntax’ b. We are required to study only syntax. ‘We are not required to study any subject other than syntax’ (Bayer 1996: 30; examples based on Taglicht 1984)

In the case of (185a) and (186a), only the reading provided immediately below it is available. For (185b) and (186b), however, both the reading immediately below and the reading of respectively (185a) and (186a) are available. Lastly, although many languages are similar to English insofar that their translation of only also does not contain an overt syntactic negative maker, there do exist some languages in which such an overt syntactic negative marker is present. This is the case for French, Arabic, Hebrew and Modern Breton (Gast 2005: 2- 3). This typologically supports the idea of a covert syntactic negative feature in English. Examples are provided in (187) – (190).

(187) French ne…que ‘not…but, only’ Je n’ai qu’- un livre. I NEG-have but- a book. ‘I only have a book.’

(188) Arabic mā ... illā ‘not...but, only’ mā yuħibbu illā nafsahu NEG he.loves but SELF.ACC.3SG ‘He loves only himself.’

(189) Hebrew lo...éla ‘not...but, only’ Hem lo hisigu éla heskem Helki they not reached but agreement partial ‘They only reached a partial agreement.’

(190) Modern Breton ne...nemet ‘not ... except, only’ ne welis nemet daou labous-ig en neizh not saw except two bird-DIM in nest ‘I only saw two birds in the nest.’ (examples based on Gast 2005: 2-3)

The overt syntactic negative markers are “ne” (French), “mā” (Arabic), “lo” (Hebrew) and “ne” (Modern Breton). As such, the concept of a covert instance of syntactic negation in the English quantifier only is certainly feasible. Collins & Postal propose an analysis in terms of “[only DPx] as a reduction of [no

Y but/except DPx]” (2014: 138-139).

(191) Only Michael goes (192) Nobody but/except Michael goes (Collins & Postal 2014: 138)

Examples (191) and (192) are semantically equivalent. Example (192), however, where an overt syntactic negative marker (i.e. in nobody) is used, includes both the prejacent and the annex. Both the presupposition (i.e. Michael goes) and the assertion (i.e. Nobody but/except Michael goes; no one else goes) are clearly distinguishable. The latter example also more clearly resembles the typological examples in French, Arabic, Hebrew and Modern Breton. There are, however, some cases where the syntactic behavior of only is not negative. This is evidenced by the question tag test (193) – (196), as well as the too/either (197) – (199) and so/neither (200) – (201) tags and the ‘negative appositive tag’ (202) – (203).

(193) He could only buy books, *could/couldn’t he? (194) Only his mother does he obey, *does/doesn’t he? (195) There is only one bottle, *is/isn’t there? (196) Only his mother had any glow, *did/didn’t she?

(197) He could only buy books, and his brother could only buy books *either/too (198) Only his mother does he obey, and his brother only obeys her *either/too. (199) There is only one bottle, and over there is only one bottle *either/too.

(200) He could only buy books, and *neither/so could his brother. (201) Only his mother does he obey, and *neither/so does his brother

(202) *Only blue ones will he accept, not even light blue ones. (203) *Only men does he obey, not even tall ones.

Only-phrases take negative question tags, as well as the (affirmative) too and so tags, and do not take ‘negative appositive tags’. These tests show that only-phrases constitute syntactically affirmative sentences, even though they are clearly capable of being semantically negative, triggering subject-auxiliary inversion and licensing NPIs. This goes against the idea of only containing a covert syntactic negative feature. A possible explanation for this, however, can be found in the distinction between the prejacent and the annex. As sentence negation is part of the annex instead of the prejacent, it might be that the above tests only apply to the prejacent, which requires a negative (reversal) question tag (as well as the too and so tags) even when the annex has a negative meaning. In both (204) and (205), the latter being the prejacent of the former, a negative question tag is triggered.

(204) Only John attended the meeting, *did/didn’t he? (205) John attended the meeting, *did/didn’t he?

In both (204) and (205), the subject (i.e. John) is repeated (although as a personal pronoun) in the question tag (i.e. he). As such, it is clear that the question tag relates only to the presupposition (i.e. the prejacent). This seems to be the case for the other ‘tag tests’ as well.

4.2.3.2. Exactly For exactly, no cases of SAI were identified in the corpora, although the following two examples were available in the current literature.

(206) Exactly one feature did I notice in the landscape. (Collins & Postal 2014: 138) (207) In exactly two of these cases did we find traces of the virus. (Büring 2004: 2)

Similar to only, it could be argued that exactly expresses negated existential quantification over the domain of alternatives. As such, a sentence with exactly also denotes a pair of propositional meanings, of which a prejacent (A-component) and an annex (polar B-component) can be distinguished. Applying the prejacent-annex distinction to the above examples is possible, as exemplified in respectively (208) and (209).

(208) PREJACENT : ‘I noticed one feature in the landscape’ ANNEX : ‘No other features did I notice in the landscape’ (209) PREJACENT : ‘We found traces of the virus in two of these cases’ ANNEX : ‘In no other cases did we find traces of the virus’

The similarities between exactly and only can also be reflected in a sentence such as in (210), in which both quantifiers contribute the same prejacent (i.e. ‘he returned home one time’) and annex (i.e. ‘he did not return home any more/other times’)

(210) Exactly once and only once did he return home.

There is thus reason to assume that exactly, like only, could contain a covert syntactic negative feature. However, as no cases of SAI with preposed exactly-phrases were found in the corpus, we will not elaborate on these further.

4.2.4. “Misbehaving” quantifiers 4.2.4.1. Nothing Negative inversion with preposed quantifier phrases containing nothing is certainly possible, as evidenced by the corpus data. Nothing is an anti-additive quantifier and as such has an overt syntactic negative marker, as can be seen by it consisting of [not] and [anything]. When it goes into SpecFocP, as in the corpus data, subject-auxiliary inversion is triggered in order to satisfy the NEG-criterion. Even though negative inversion is certainly possible with focalised negative constituents containing nothing, the corpora show that, unlike other anti-additive quantifier phrases, these cases are significantly less prevalent (i.e. only 5 cases have been identified). This indicates that, although nothing [not anything] closely resembles other anti-additive quantifiers such as never [not ever] and nowhere [not anywhere] as to how it is formed, it has a unique type of behavior that somehow prevents it from being preposed as frequently as, for example, never. A possible explanation for this is that, in some cases, nothing behaves more like a numeral than like a negative or focused constituent.

Postal (2004: 159-169) argues that nothing has some non-negative instances. To account for this, he proposes that, in such instances, nothing behaves like a type Z vulgar minimizer. Two examples of type Z vulgar minimizers are squat and fuck-all; these denote a minimal element on a scale, and can do so in many dimensions (Postal 2004: 159-160), as illustrated in (211) – (212).

(211) Olmstead knows fuck-all about Botswana. (212) Olmstead doesn’t understand squat about topology. (Postal 2004: 159)

Although all these forms seem to uniformly mean “nothing”, Postal notes that they do not contain a negative feature; they do, however, contain an invisible cardinal numeral zero as their determiner, as represented in (213), which enables the reading that is equivalent to “nothing” (2004: 166).

(213) Type Z-squat = [DP [D zero] + [N squat]] (Postal 2004: 166)

An example of a sentence with nothing where it can behave as either a negative or a non-negative is provided in (214).

(214) a. John said nothing, and Mary said nothing, too. b. John said nothing and Mary said nothing, either. (Postal 2004; based on McCawley 1998: 607)

Even though there is no difference in meaning between these two sentences, (214a) occurs with too, and is thus affirmative; (214b) occurs with neither, and is thus negative (cf. section 1.1.2). As such, Postal proposes that the non-negative instance of nothing is possible in cases where it has the structure of a type Z vulgar minimizer, as presented in (215).

(215) Nothing = [DP [D zero] + [N, vulgar minimizer nothing]] (Postal 2004: 168)

Postal provides some tests to confirm that the behavior of nothing can be like that of a type Z vulgar minimizer. Three of these tests, which confirm the possible non-negative behavior (and which are found in section 1.1.2) will be presented here, although Postal provides much more evidence of this behavior. As type

Z vulgar minimizers do not contain a negative feature, they cannot license NPIs; they cannot permit positive reversal tags; and they cannot be strengthened by “not even”-phrases (i.e. ‘negative appositive tags’ in Klima 1964) (Postal 2004: 169). This type of behavior can be seen with the ‘non-negative’ nothing in examples (216) – (218).

(216) NPI licensing a. Claudia said nothing at any time and I said nothing at any time, either. NEG b. *Claudia said nothing at any time and I said nothing at any time, too. POS (217) Reversal tags a. Jerome ate nothing and Stan ate nothing, either, *didn’t/did he? NEG b. Jerome ate nothing and Stan ate nothing, too, didn’t/*did he? POS (218) Negative appositive tag The president said nothing and the vice president said nothing, either/*too, not even goodbye. (Postal 2004: 169)

Collins & Postal (2014: 169) do note, however, that “when nothing is a negative fronting target, only behavior consistent with the negative analysis is possible”, as in (219).

(219) Negative fronting Nothing/*Squat did Claudia say to Henry and nothing did Louise say, either/*too (Postal 2004: 169)

Just like type Z vulgar minimizers, nothing can thus also behave like a non-negative according to syntactic tests. If most cases of nothing are indeed such “positive” instances, it might thus be that negative fronting with a “negative” nothing, such as in (219) with the either-tag, occurs less frequently. The structure for this “positive” nothing, in (215), also shows the invisible cardinal numeral zero as its determiner. As will be discussed in section 4.2.4.2, zero might prevent quantifier raising. If somehow the “negative” nothing also behaves like the numeral zero, this might be a possible explanation for the low number of cases of preposed QPs containing nothing that give rise to SAI.

4.2.4.2. Zero In the case of the (preposed) downward entailing quantifier zero, only two cases of subject-auxiliary inversion have been identified in the corpora. There must thus be a reason why QPs containing zero might not easily prepose to the specifier position of FocP.

As zero is categorized as a numeral, a possible explanation for its unusual behavior could be found in the behavior of other numerals. If QPs including other numerals, such as two and eighty-four, also infrequently undergo quantifier raising, the same might occur in the case of the numeral zero. Do note, however, that zero is different from other numerals (e.g. two and eighty-four) as the latter are plural numeral indefinites. The current literature has indeed argued that plural numeral indefinites cannot scope out of VP (Beghelli and Stowell 1997). This means that they “cannot have wide distributive scope, when they occur VP internally” (Reinhart 2006: 292). This can be shown using example (220).

(220) a. Three men lifted two tables.

b. [two tablesi] D [three men lifted ei] (Reinhart 2006: 292)

In (220a), the sentence means that exactly three men lifted two tables. Reinhart argues that when two tables undergoes quantifier raising above the distributive operator D and thus has wide scope, as in (220b), the meaning of the sentence can be altered. In this case the meaning might change to Two tables were each lifted by three men, which involves six men in total. As such, quantifier raising is blocked in these cases. Although zero is not plural, it might be possible that, as the grammar does not have access to the ‘mathematical content’ of numerals (Bylinina 2017: 3), the same applies in some cases. Some people, however, do seem to allow sentences with preposed QPs containing zero, as evident from the corpus data (and the additional examples). A possible explanation for this is provided by Collins & Postal, who speculate that for speakers who do allow these inversion constructions with zero, their representation of zero differs, namely [ zero], in which only is covert (2014: 139). In this case, this null only then permits the subject -auxiliary inversion that occurs (cf. section 4.2.3).

4.2.4.3. Only As there is currently only a limited amount of data to support the claim that preposed only-phrases that do not trigger inversion are ungrammatical/marginal, such as in (221) (cf. section 4.2.3.1), a (very limited) additional corpus research has been performed, similar to the corpus research previously performed, to uncover the frequency of preposed only-phrases that do not trigger inversion.

(221) *Only George we would invite (Bayer 1996: 14)

Using the ‘collocates’ search function, the quantifier only was entered as the ‘collocate’ that precedes (up to 4 words) a combination of any personal pronoun (using the _pp* tag), immediately followed by any verb (using the _v* tag). This should provide us with at least some cases of preposed only without subject- auxiliary inversion. The entry resulted in 15,510 results in BNC; the first 500 results of these were analyzed and 5 cases of preposed only-phrases without subject-auxiliary inversion were identified. These are presented in (222) – (226).

(222) Only a month ago we were told by the Engineering Council that technology lessons under the national curriculum were a' farce' -- and teachers didn't have a clue what they should be doing in the classroom (BNC) (223) Only the other day he was saying to me' Tim it's abart time I answered sum a them letters I' ave pilin' up from poor folk as' ave' ad personal problems. (BNC) (224) After only half an hour we can tack left and right - … (BNC) (225) His funeral took place at SS Peter and Paul, Yeadon where only five months before he had celebrated the silver jubilee of his ordination. (BNC) (226) Only 52 tall, he turned his diminutive height into an asset, wriggling through towering defenders in the old' tanner ba' tradition. (BNC)

Of the above cases, we argue that all but example (226) are cases where the meaning is not negative, but (similar to) ‘as recently as’ and are thus a topic. In these cases, both the non-negative meaning and it being a topic block subject-auxiliary inversion. Regarding the last case, I argue that ‘only 52 tall’ functions as a topic, whereby the [NEG]-feature cannot scope over the clause. In COCA, the same search entry resulted in the error “All of the "slots" in your multi-word search string occur more than 40,000,000 times in the corpus”. As such, specific personal pronouns had to be used. As all cases that were identified for BNC occurred with the personal pronouns he or we, these two were used, resulting in 12,412 results for he and 7,783 for we. The first 500 results were analyzed here as well (first 250 for each personal pronoun). This resulted in 5 hits for we (227) – (230) and 6 hits for he (231) – (236).

(227) Only in his case we had enough money to just buy right into the top shelf. (COCA) (228) I had dreamed this before, with Mitchell on the chair, my hands wrapped around the rough wood of the chair, only in my dream we had been in the woods, with no light on us. (COCA) (229) Only this time, we went to her condo instead of mine. (COCA)

(230) Only this time, we'll leave the saw at home and instead carry a red bandanna to stake our claim -- we'd hate for Theo to think his mom and dad don't know what they're doing. (COCA)

(231) Only this time, he got more than " Amen " in response. (COCA) (232) Only last week, he had left a flyer in her mailbox. (COCA) (233) Only two months previously he had become the hero of the North when his 100,000-strong army took Atlanta after a grueling summer campaign, effectively saving the incumbent President Abraham Lincoln from defeat in the autumn presidential elections. (COCA) (234) Only an hour ago he'd told them that raising his daughter had been the best thing he'd ever done, but he'd neglected to mention an important detail. (COCA) (235) Fortunately, he was a fast reader, and only four hours later he reached the last word. (COCA) (236) Martinez's ERA has risen from 2.34 to 3.04 over his last seven starts, only two of which he has won, … (COCA)

Of the above cases, we argue that in the first 5 cases, the meaning is not ‘no other than x is y’, but it seems to be functioning like the conjunction ‘but’. This could be possible because but is used to show contrast, which is closely related to the meaning of only, which expresses a contrast between the denotation of the focused constituent and the domain of alternative values to that constituent. The next 4 cases, (231) – (235), also have a non-negative meaning, more specifically ‘as recently as’, which blocks any possible subject- auxiliary inversion. The last case seems to be of the meaning ‘no other than x is y’, although its embeddedness might have an influence on the non-inversion that occurs. This brief corpus research, though the sample size is very limited (i.e. 1000 results analyzed), gives us an indication that cases of preposed only-phrases that do not trigger subject-auxiliary inversion occur infrequently. Of those that do occur, most cases seem to either have a non-negative meaning such ‘as recently as’ or be cases where only behaves like the conjunction ‘but’, which seems to be similar to a topic. This indicates that cases of (focalized) preposed only-phrases with the negative meaning ‘no other than x is y’ (i.e. corpus data from the main analysis) that do not trigger inversion could be considered as ungrammatical or marginal, although a more thorough corpus research would be needed to confirm this.

4.2.4.4. DE quantifiers: rarely Similar to only, a (very limited) corpus research has been performed to uncover the frequency of preposed downward entailing QPs that do not trigger inversion. Using the ‘collocates’ search function, the downward entailing quantifier rarely was entered as the ‘collocate’ that precedes (up to 4 words) a combination of any personal pronoun (using the _pp* tag), immediately followed by any verb (using the _v* tag). This should

provide us with at least some cases of preposed rarely without subject-auxiliary inversion. The entry resulted in 218 results in BNC; these were analyzed and 7 cases of preposed rarely-phrases without subject-auxiliary inversion were identified. These are presented in (237) – (243).

(237) Rarely sexy, it is nevertheless far spunkier than Ambition. (BNC) (238) Although rarely defined, it is often on the lips of the members, so that the phrase,' I don't want to seem disloyal, but...' will often preface even the mildest internal criticism of any of the systems of policing. (BNC) (239) More rarely, I watched them diving in the sea for sea urchins or other easy prey. (BNC) (240) Rarely, they may propagate in an oral direction. (BNC) (241) They are usually adapted for cutting or crushing the food and frequently also for defence; more rarely they are modified into sickle-like or stylet-like piercing organs. (BNC) (242) Rarely, they might talk more coherently, but what is said is seldom sensible. (BNC) (243) Rarely, it may even be unreasonable to select you for redundancy on the basis of length of service, for instance if doing so entails retaining another employee past retiring age when you are much younger and still have plenty to offer. (BNC)

With regard to the above cases, we argue that in cases (237) and (238), rarely is part of a topic. As it is thus in SpecTopP, it does not have scope over the clause and subject-auxiliary inversion cannot occur. Cases (239) – (243) are arguably ungrammatical/marginal, as in all of these cases rarely seems to scope over the auxiliary and can be replaced by a version in which the comma is removed and in which rarely does give rise to subject-auxiliary inversion. In COCA, the same search entry resulted in the error “All of the "slots" in your multi-word search string occur more than 40,000,000 times in the corpus”. As such, specific personal pronouns had to be used. As most cases that were identified for BNC occurred with the personal pronouns it and they, these two were used, resulting in 286 results for it and 285 results for they. These were all analyzed; which resulted in 4 hits for it (244) – (247) and 6 hits for they (248) – (253).

(244) Rarely done well, it is one of our chief obstacles in securing happiness and satisfaction in singing. (COCA) (245) Too rarely it is considered that patients may want to be reminded of their humanity. (COCA) (246) Very rarely, it can be a sign of something more serious, like an intestinal problem or hypothyroidism, so if it gets bad enough that there's bleeding, it's a good idea to see the doctor. (COCA)

(247) Rarely, it happens, which is why only the bravest of these cowards get drafted for this job; by their standards, Potts is a daredevil. (COCA)

(248) Rarely, they may also cause: # * Interstitial nephritis * Nephrotic syndrome # * Acute renal failure # * Acute tubular necrosis. (COCA) (249) Although rarely, they can sometimes injure nerves or cause pulmonary embolisms. (COCA) (250) Rarely smiling, they keep their heads low and move carefully among the throngs of kids scrambling to wash plates under a running tap. (COCA) (251) Rarely, they glimpsed the flame-red tail of a fox shooting by, or the monstrous, glorious form of a pileated woodpecker. (COCA) (252) Rarely, they opt for an associate's degree. (COCA) (253) Very rarely they surprise us. (COCA)

With regard to the above cases, we argue that in cases (244) and (250), rarely is part of a topic; in SpecTopP, it does not have scope over the clause and SAI does not occur. All other cases are arguably ungrammatical/marginal; similar to those in BNC, rarely seems to scope over the auxiliary or verb. These cases can all be replaced by a version in which the comma is removed and in which rarely does give rise to SAI.

4.3. Conclusion Initially, a general overview of the (expected) analysis that was to be applied to all types of QPs was provided; some cases where a preposed consituent is ambiguous (i.e. it can occur as either a focus or a topic) were then discussed, noting the differences in meaning and in structure between the topicalized and the focalized versions of the constituent. After studying some cases of subject-auxiliary inversion (from both corpora) of the different types of (preposed) QPs according to Rizzi’s split CP, it was argued that all QPs that were examined can be analyzed as proposed by Haegeman (2000b), i.e. they move to the specifier position of FocP, from where SAI is triggered to satisfy the NEG-criterion. The auxiliary, which carries the matching [NEG]-feature thus moves leftward to Foc° to achieve the right spec-head configuration. It was shown that all fronted SAI- triggering QPs can be preceded by a topicalized constituent as well, suggesting that these QPs are indeed hosted by SpecFocP. For each type of quantifier, it was then argued that it is indeed the NEG-criterion that applies. For anti-additive/antimorphic QPs, the application of the NEG-criterion is evident. In the case of downward

entailing QPs, which are seen as ‘weaker’ negators, it seems likely as well. In the case of nonmonotonic QPs, a “negative-like meaning” implies the application of the same mechanism. As such, concrete arguments for the presence of either an overt or a covert syntactic negative feature in all three types of QPs were presented. The presence of such a negative feature would then require the satisfaction of the NEG-criterion when such a QP is focalized. It would also account for the distribution of NPIs and positive question tags. For anti-additive/antimorphic QPs, there is an overt syntactic negative marker (i.e. the negative morpheme not); in the case of downward entailing QPs, evidence was provided for a covert syntactic negative feature (in the form of NPI licensing, positive questions tags, either-licensing, split scope readings and even some typological evidence). Lastly, for nonmonotonic QPs, it was argued that these also contain a covert syntactic negative feature. Initially the semantics of only were looked at, which revealed that only-phrases (and arguably also exactly-phrases) consist of a positive presupposition (i.e. the prejacent) and a negative assertion (i.e. the annex; set of untrue alternatives to the focussed constituent). They also satisfy the property of Strawson decreasingness, which was explained to be similar to monotone decreasingness. Eventually, the syntactic behavior of only was investigated. Its negative behavior was evidence by its capability of triggering SAI, licensing NPIs and having split scope readings; some typological evidence was provided as well. There were, however, some exceptions (e.g. question tag test; too/either tag; so/neither tag; ‘negative appositive tag’). To account for these, it was argued that these tests which indicate an affirmative sentence apply only to the prejacent, which is affirmative, and not the annex, which is negative. Some exceptions were elaborated on as well. For nothing, it was argued that the majority of instances were non-negative; in these cases it behaves like (and has the structure of) a type Z vulgar minimizer. These cannot license NPIs, trigger negative fronting, have a ‘negative appositive tag’ or trigger positive question tags. In the case of the numeral zero, it was argued that it behaves much like other numerals insofar that it does not easily scope out of VP. For cases of preposed only without inversion, it was argued that they were either non-negative and/or served as a topic. Lastly, for cases of preposed rarely without inversion, it was argued that they were either a topic or that they are ungrammatical/marginal and can be replaced with a version in which they do give rise to SAI.

Conclusion

The current literature on quantifiers makes a distinction between upward entailing (UE) quantifiers, downward entailing (DE) quantifiers and nonmonotonic quantifiers. Of these, DE quantifiers are subdivided into (merely) DE quantifiers and anti-additive/antimorphic quantifiers. Regarding their behavior when situated in sentence-initial position, anti-additive/antimorphic QPs, DE QPs and nonmonotonic QPs all show the capability of giving rise to subject-auxiliary inversion. A corpus research was performed in BNC and COCA to test the frequency of SAI patterns for the different types of preposed QPs. The anti-additive QP never resulted in many cases of SAI, while the DE QPs rarely, seldom, and few resulted in a fair number of cases of SAI. Some exceptions, however, were that nothing (anti-additive QP) and zero (DE QP) resulted in almost no cases of SAI; while only (nonmonotonic QP) resulted in the highest number of cases of SAI. Exactly only occurred in interrogative constructions, in which the wh-phrase already accounts for the inversion pattern. It is assumed that negation is the underlying factor that triggers inversion. In the case of anti- additive/antimorphic QPs, the negation is present in both their meaning and their form; DE QPs also contain negation, although merely in their meaning and not in their form. Only, on the other hand, is not marked negative as such, as it is nonmonotonic and does not contain a morphological mark of negation; it does, however, have a ‘negative-like meaning’ similar to ‘no other than x is y’. Due to their ‘negative’ meaning and the inversion patterns they trigger, it was thus hypothesized that there is a covert syntactic negative feature present in downward entailing QPs and nonmonotonic QPs. It was thus assumed that a negative feature within all three types of quantifiers is responsible for triggering the inversion pattern. An explanation for how this occurs was then provided using Haegeman’s NEG-criterion. The NEG-criterion states that when a negative constituent (i.e. it contains a feature of negation) is preposed (due to a [focus] feature) and takes sentential scope (i.e. in SpecFocP), it triggers subject-auxiliary inversion due to the need of a spec-head configuration with an X-[NEG]. As it is assumed that this X-[NEG]-feature is on T°, the auxiliary (or tense) thus moves leftward to Foc° to achieve this spec- head configuration and thus satisfy the NEG-criterion. As the auxiliary moves to a head position to the left of the subject, subject-auxiliary inversion occurs. Besides cases of subject-auxiliary inversion with the above (‘negative’) quantifiers, there are also cases where such a “negative constituent” does not give rise to subject-auxiliary inversion when preposed. As such, a distinction had to be made between focalization and topicalization. In some cases, these mechanisms can occur with an (ambiguous) constituent that superficially looks the same in both cases. When

such a constituent is negative and is focalized, it has sentential scope and there is thus sentential negation. Due to this, subject-auxiliary inversion is triggered, as in (55), reiterated here.

(55) Not even ten years ago could you buy a house for less than 50k. (Büring 2004: 4-5) ‘Even 10 years ago, you could not buy a house for less than 50k’ [not even [PP [DP 10 years] ago]

When the negative constituent is topicalized, there is no sentential negation but local or constituent negation. The negation thus has scope over the adverbial only, while the rest of the sentence is semantically and syntactically affirmative, as in (54), reiterated here.

(54) Not even ten years ago you could buy a house for less than 50k. (Büring 2004: 4-5) ‘Less than 10 years ago, you could buy a house for less than 50k.’ [PP [DP not even 10 years] ago]

Although a difference in meaning is clearly distinguishable by using a paraphrase (provided below both examples), the difference also lies in their structure (also provided below both examples) and information structure (respectively introducing “new information” and “old information”). Relating the difference between these two to Rizzi’s split CP, they also sit in different projections. Focalized constituents are in SpecFocP; topicalized constituents are in SpecTopP. As such, it seems to be that if subject-auxiliary inversion is triggered by a preposed QP, this preposed QP meets two criteria. Firstly, it is a focalized constituent (i.e. it has a [topic] feature) and can thus have scope over the sentence; secondly, it contains a [NEG]-feature and thus the NEG-criterion has to be satisfied. These two criteria were then applied to a sample of the corpus data. Initially, all examples were applied to Rizzi’s split CP, which revealed that all analyzed cases go into SpecFocP and are thus focalized. The application of the NEG-criterion was then analyzed; it was argued that either an overt or a covert syntactic negative feature is present in all three types of QPs. As such, evidence for such a negative feature, which would enforce the satisfaction of the NEG- criterion, was provided for all three types of QPs. Firstly, anti-additive/antimorphic QPs are negative in meaning and in form, as these contain a morphological mark of negation; as such, they also show negative syntactic behavior. Secondly, for DE quantifiers a covert instance of negation was argued due to their negative syntactic behavior, their downward monotonicity, as well as some typological support. Lastly, the nonmonotonic quantifier only was examined. It was argued that it contains a covert syntactic negative feature. Arguments for this come in the form of its ‘negative-like meaning’ (i.e. the associated negated set of

alternatives to the focused constituent), (some) syntactically negative behavior, as well as some typological support. Lastly, some exceptions had to be addressed. In the case of nothing, it was argued that it has some non-negative instances in which it behaves (and has the structure of) a type Z vulgar minimizer. For zero, a possible explanation was provided in which it behaves like other numerals, which do not easily scope out of VP and thus prevent quantifier raising. In the case of preposed only, some cases that did not trigger subject- auxiliary inversion were found; these were argued to serve as a topic and/or the meaning of only was argued to be different (i.e. non-negative; e.g. ‘as recently as’, ‘but’). For preposed rarely without inversion, it was argued that in some cases it serves as a topic; in other cases, it was argued that the non-inversion was ungrammatical and could easily be replaced by a sentence in which inversion does take place. Based on these findings, it can thus be concluded that, even with constituents that are not marked negative as such, like only, there are numerous arguments to assume the presence of a (covert) negative feature. As this negative feature is present in anti-additive/antimorphic QPs, downward entailing QPs and nonmonotonic QPs, the NEG-criterion applies; when they are focalized in sentence-initial position (due to the [focus] feature), all three types of QPs trigger subject-auxiliary inversion due to the need of a spec-head configuration with the auxiliary (i.e. it moves to Foc°), which carries the matching [NEG]-feature. Further research is needed on the specific meaning and/or structure of those cases of preposed ‘negative’ QPs that do not give rise to subject-auxiliary inversion. More specifically, one could look at the difference between focalized only-phrases such as “only yesterday” in sentences in which they either do or do not trigger subject-auxiliary inversion, as these constructions differ in meaning. The question then is why exactly the only-phrase does not seem to entail a negative assertion (i.e. annex) in cases where inversion does not take place.

Bibliography

Barwise, Jon and Robin Cooper (1981). “Generalized quantifiers and natural language”. Linguistics and Philosophy 4, 159-219. Bayer, Josef (1996). Directionality and Logical Form: On the Scope of Focusing Particles and Wh-In-Situ. Dordrecht: Kluwer academic. Beghelli, Filippo and Tim Stowell (1997). “The syntax of distributivity and negation”. In Anna Szabolcsi, ed., Ways of Scope Taking, Dordrecht, The Netherlands: Kluwer. 71-108. Biber, Douglas, Stig Johansson, Geoffrey Leech and Randolph Quirk (2000). Longman Grammar of Spoken and Written English. 3rd edition. Harlow: Longman. Brasoveanu, Adrian, Karen De Clercq, Donka Farkas and Floris Roelofsen (2014). “Question tags and sentential negativity”. Lingua 145, 173-193. Bruening, Benjamin (2015). “Subject auxiliary inversion”. To appear in Martin Everaert and Henk van Riemsdijk, eds., The Blackwell Companion to Syntax, 2nd edition, Hoboken: Wiley-Blackwell. Büring, Daniel (2004). “Negative inversion”. PROCEEDINGS-NELS 35(1). Bylinina, Lisa and Rick Nouwen (2017). “The semantics of ‘zero’”. 18th Workshop on the Roots of Pragmasemantics. Szklarska Poreba, Poland. 2nd-6th of March. Collins, Chris and Paul Postal (2014). Classical NEG Raising. An Essay on the Syntax of Negation. Cambridge (Mass.): MIT Press. Davies, Mark. (2008-.) The Corpus of Contemporary American English: 520 million words, 1990- present. Available online at http://corpus.byu.edu/coca/. Davies, Mark. (2004-). BYU-BNC. (Based on the British National Corpus from Oxford University Press). Available online at http://corpus.byu.edu/bnc/. De Clercq, Karen, Liliane Haegeman and Terje Lohndal (2012). “Medial adjunct PPs in English: implications for the syntax of sentential negation”. Nordic Journal of Linguistics 35, 5–26. De Clercq, Karen (2017). “The internal syntax of Q-words”. manuscript, University of Ghent, Ghent. De Swart, Henriette (2009). Expression and interpretation of negation: an OT typology. Springer Science & Business Media. Erlewine, Michael and Hadas Kotek (2014). “Only as a quantifier”. LING 721 Advanced seminar 1: questions, focus, and friends. Gajewski, Jon R. (2011). “A note on licensing strong NPIs”. Natural Language Semantics 19, 109-148.

Gast, Volker (2005). “Towards a typology of focus quantifiers”. 6th annual meeting of the Association for Linguistic Typology. Padang, Sumatra. 23rd of July. Gast, Volker (2013). “At least, wenigstens and company. Negated universal quantification and the typology of focus qiantifiers”. In Kook-Hee Gil, Stephen Harlow and George Tsoulas, eds., Strategies of Quantification, Oxford: Oxford University Press. 101-122. Haegeman, Liliane (1995). The syntax of negation. Cambridge: Cambridge university press. Haegeman, Liliane and Raffaella Zanuttini (2014). “Negative heads and the neg criterion”. In Richard S. Kaybe, Thomas Leu and Raffaella Zanuttini, eds., An Annotated Syntax Reader, Oxford, UK: Wiley- Blackwell. 263-276. Haegeman, Liliane (2000a). “Inversion, non-adjacent inversion and adjuncts in CP”. Transactions of the Philological Society 98, 121–160. Haegeman, Liliane (2000b). “Negative inversion, negative inversion and the split CP”. In Laurence R. Horn and Yasuhiko Kato, eds., Negation and Polarity, Oxford: Oxford University Press. 29-69. Haegeman, Liliane (2006). Thinking syntactically. Oxford: Blackwell. Horn, Laurence (1989). A Natural History of Negation. Chicago: University of Chicago Press. Huddleston, Rodney and Geoffrey K. Pullum (2002). The Cambridge grammar of the English language. Cambridge: Cambridge University Press. Isac, Daniela (2004). “Focus on Negative Concord”. In Reineke Bok-Bennema, Bart Hollebrandse, Brigitte Kampers-Manhe and Petra Sleman, eds., Romance Languages and Linguistic Theories 2002, Amsterdam/Philadelphia: John Benjamins Publishing Company. 119-140. Jackendoff, Ray S. (1972). Semantic interpretation in generative grammar. Cambridge (Mass.): MIT press. Kang, Seung-Man (2014). “Focus and inversion in English”. Studies in English Language & Literature 40, 235-252. Klima, Edward (1964). “Negation in English”. In Jerry Fodor and Jerrold Katz, eds., The Structure of Language, Englewood Cliffs, New Jersey: Prentice-Hall. 246–323. Ladusaw, William (1980). Polarity sensitivity as Inherent Scope Relations. New York: Garland Publishing. Lasnik, Howard (1972). Analyses of negation in English. MIT diss. Indiana University Linguistics Club. Martinková, Michaela (2010). “Subject-operator inversion in sentence with fronted only”. In Roman Trušník, Katarína Nemčoková and Gregory Jason Bell, eds., Theories and Practice: Proceedings of the Second International Conference on English and American Studies, Czech Republic: Tomas Bata University. 65-78. May, Robert (1985). Logical form, Its Structure and Derivation. Cambridge (Mass.): MIT Press. McCawley, James (1998). The syntactic phenomena of English. Chicago: University of Chicago Press

Neeleman, Ad and Reiko Vermeulen (2011). “Interpreting focus under negation.” Paper presented at the Annual Conference of the Linguistics Association of Great Britain, Salford, 7th-10th of September. Nishiguchi, Suyimo (2003). “Non-monotonic negativity”. Proceedings of 17th Pacific Asia Conference on Language, Information and Computation (PACLIC 17). Penka, Doris (2011). Negative indefinites. Oxford: Oxford University Press. Peters, Stanley and Dag Westerståhl (2006). Quantifiers In Language and Logic. Oxford: Clarendon press. Progovac, Ljiljana (2005). Negative and positive polarity: A binding approach. Cambridge University Press. Reinhart, Tanya (2006). “Scope shift with numeral indefinites”. In Liliane Tasmowski and Svetlana Vogeleer, eds., Indefiniteness and Plurality, Aktuell/Linguistics Today Series, Benjamins. 291-310. Rizzi, Luigi (1990). Relativized Minimality. Cambridge (Mass.): MIT Press Rizzi, Luigi (1996). “Residual verb second and the Wh criterion. In Adriana Belletti and Luigi Rizzi, eds., Parameters and Functional Heads. Essays in Comparative Syntax, Oxford and New York: Oxford University Press. 63-90. Rizzi, Luigi (1997). “The fine structure of the left periphery”. In Liliane Haegeman, ed., Elements of grammar, Dordrecht: Kluwer. 281-337 Rudanko, Juhani (1980). “Towards a description of negatively conditioned subject operator inversion in English”. English Studies 58, 348-59. Rullmann, Hotze (2003). “Additive particles and polarity”. Journal of semantics 20, 329-401. Van der Wouden, Ton (1997). Negative contexts. Collocation, Polarity, and Multiple Negation. London and New York: Routledge. Veselovská, Ludmila (2011). “Inversion and fronting in English: a cartography of discourse in a generative framework”. Czech and Slovac Linguistic Review, 53-72. Von Fintel, Kai (1999). “NPI licensing, Strawson entailment and context dependency”. Journal of Semantics 16, 97- 148. Quirk, Randolph, Sidney Greenbaum, Geoffrey Leech and Jan Svartvik (1985). A Comprehensive Grammar of the English Language. London: Longman. Zwarts, Frans (1998). “Three types of polarity”. In Fritz Hamm and Erhard Hinrichs, eds., Plurality and Quantification, Dordrecht: Kluwer. 177-238.