## Trees and Fields and Negative Polarity

## Abstract

The paper 1 takes as its point of departure a comparison between two kinds of approaches to clause structure, namely tree analyses like the generative analysis and fi  eld analyses like the sætningsskema analysis of Danish of Diderichsen (1946) and many others (or like the topologische Modell analysis of German of Drach 1937 and many others).

The particular difference between the two kinds of analyses which I explore in this paper concerns c-command, which is a relationship between different constituents in a clause. I shall try to show how useful and indispensable c-command is when it comes to accounting for negative polarity items in English, Danish and German, both the more straightforward aspects and the more complex ones, e.g. the so-called NPI-verbs as well as the interaction between NPI-elements and because -clauses.

## 1. Introduction

## 1.1.  Clause structure in tree analyses and in fi  eld analyses

A fundamental difference between various approaches to clause structure is the one between

- tree analyses like the generative analyses that Torben Thrane and I both work with (Thrane 1999, 2003, 2008, 2009, ..., Vikner 1995, 1999a,b, 2007, ...) and
- fi  eld analyses like the sætningsskema analyses of Danish of Diderichsen (1946, 1964) and many others or like the topologische Modell analyses of German of Drach (1937) and many others.

The difference is the extent to which the various parts of the clause are seen

- as boxes inside other boxes , or
- as pearls on a string, one after the other.

It is a question of extent, as neither of the two can be 0% or 100%: Even to Diderichsen (1946), some constituents are inside other constituents (e.g. the object or N is part of the content fi  eld), and even in the generative analyses, some constituents follow other constituents (otherwise trees would only contain mothers and daughters, but no sisters).

The generative tree structure in (1)a is compared to the (simplifi  ed) Diderichsen fi eld model of constituent order in modern Danish, Norwegian and Swedish, as illustrated in (1)b for main clauses and in (1)c for embedded clauses:

1 Thank you to Ken Ramshøj Christensen, Jan Engberg, Eva Engels, Alex Klinge, Ramona Römisch-Vikner, Carl Vikner, Johanna Wood, and to the researchers in the University of Cambridge Project on the Development of Negation in the Languages of Europe (principal investigator: David Willis). Thanks also to the audience at the Conference to Mark the Retirement of Torben Thrane in January 2011, Aarhus, to the audience at the SLK Linguistics Seminar in January 2011, Sandbjerg, and to the students in my various classes on negation. Special thanks to Torben Thrane, for support, inspiration and discussion over the many years since the fi  rst time I took a class with him in the spring of 1980, during my fi  rst year at university.

* Sten Vikner Section for English Department of Aesthetics & Communication Aarhus University DK-8000 Aarhus C sten.vikner@hum.au.dk

39

<!-- image -->

One difference is that in (1)b,c the number of levels and the kinds of constituents that can occur on each level are fi  xed: There are three levels containing three different kinds of constituents, namely clause - fi  elds - slots / sætning - felter - pladser . In other words, the only possible sister of a fi  eld is another fi  eld, and the only possible sister of a slot is another slot. In (1)a, on the other hand, this is not the case at all. It is perfectly possible to have a head (X ° ) and a phrase (XP) as sisters.

Another difference is that (1)a is based on constituents, as supported by constituency tests. In (1)b,c, however, this is not always the case, as constituency tests will show e.g. that part of V may form a constituent together with N.

Please notice that the difference in (1) between tree analyses and fi  eld analyses is NOT one of notation. The tree in (1)a can also be expressed by means of boxes or (or at least square brackets) as in (2)a, and the boxes in (1)b can also be illustrated by means of a tree structure as in (2)b:

## (2) a. [CP [AdvP Nu] [C° har] [IP [DP Torben] [VP [AdvP igen] [VP [VP [V° glemt] [DP piben]] [PP på kontoret]]]]

<!-- image -->

Although I prefer a tree analysis along the lines of (1)a, I willingly admit that fi  eld based models like (1)b,c may have e.g. pedagogical use, as in Conrad et al. (1980:182). Cf. also that it is used in a comparison of Danish and English word order by Davidsen-Nielsen/Harder (2000).

Collapsing the Diderichsen model for the main clause with the one for the embedded clause, as in (1)b,c, was not done by Diderichsen himself but by Platzack (1985:71, fn 5) and Heltoft (1986:108). For more details and many more references, see Bjerre et al. (2008).

The differences between the two approaches is not just found in the discussion of Danish and the other Scandinavian languages, it is also very prominent in the discussion of e.g. German and Dutch. Also here both tree analyses and fi  eld analyses have a considerable number of advocates.

A generative tree structure of German is found in (3)a, followed by the simplifi  ed fi eld model /topological model analyses of German main and embedded clauses in (3)b,c. For more details and more references, see Wöllstein-Leisten et al. (1997) or any of the recent editions of the Duden grammars (e.g. Fabricius-Hansen et al. 2005:879).

<!-- image -->

As far as English is concerned, fi  eld analyses are not that common, in fact they mainly occur when English is compared to either German or Scandinavian, e.g. Diderichsen (1953) and Hartvigson (1969). However, even though fi  eld analyses are thus rather scarce, this does not mean that all analyses of English clause structure employ a tree analysis. In fact, a great many analyses of Eng- lish employ something rather close to a fi  eld analysis, where most constituents of the clause (e.g. subject, verb, indirect object, object, subject predicate, object predicate, adverbial) are seen as being on the same level, like pearls on a string. Such analyses include Quirk et al. (1985), Preisler (1997), Bache/Davidsen-Nielsen (1997) and Hjulmand/Schwarz (2010).

## 1.2.  C-command

In the tree analyses of generative grammar, frequent reference is made to the relation 'C-command':

- (4)
- C-command:

X c-commands Y if and only if

a. all constituents that contain X also contain Y,

b. neither X nor Y dominates the other.

In other words: if you can get from X to Y in the tree by taking one step upwards and then climbing downwards the rest of the way, then X c-commands Y.

C-command may be used to make a number of different generalisations, e.g. concerning where refl  exive pronouns may and may not be used -- as described e.g. in my MA-dissertation, which was supervised, incidentally, by a certain T. Thrane (Vikner 1985).

C-command is also crucial to generalisations of the following apparently universal type: A pronoun and a DP may not be coreferential if the pronoun c-commands the DP.

- (5) En. a. Torben said that he was retiring. NAME C-COMMANDS PRONOUN, COREFERENCE POSSIBLE

b.

He said that Torben was retiring.

PRONOUN C-COMMANDS NAME,

COREFERENCE

IM

POSSIBLE

<!-- image -->

Such generalisations would seem much more diffi  cult to formulate within fi  eld model analyses. In a Diderichsen model, (1)b,c, (2)b, the subject would only c-command other elements inside the nexus fi  eld, but it would not c-command the object itself, (22), nor any elements inside an object clause, (6).

In this article, I want to show, with illustrations from the area of negation and negative polarity items, that the generative version of c-command illustrated in (4)-(6) is very useful and that e.g. a purely linear rule would not be able to make the right distinctions.

First, however, we need to consider negative polarity items in detail.

## 2. Negative polarity items (NPIs)

## 2.1.  Assertive vs. nonassertive vs. negative items

Quirk et al. (1985: 782) gives the following list of items that fall into one of three groups that they call assertive, nonassertive or negative items.

| Assertive      | Nonassertive          | Negative            |
|----------------|-----------------------|---------------------|
| some           | any                   | no / none           |
| something      | anything              | nothing             |
| somebody       | anybody               | nobody              |
| someone        | anyone                | no one              |
| somewhere      | anywhere              | nowhere             |
| sometimes      | ever                  | never               |
| already        | yet                   |                     |
| still          | any more / any longer | no more / no longer |
| too            | either                | neither             |
| to some extent | at all                | not at all          |

Assertive items do not change the polarity of a clause (i.e. whether a clause is negative or positive). This can be shown by means of tag questions: If a clause is negative, its tag question has to be positive, and vice versa:

- (8) En. a.

<!-- formula-not-decoded -->

- (9) En. a.

```
Torben just bought some books, didn't he? b. * Torben just bought some books, did he?
```

Negative items turn a positive sentence into a negative one:

<!-- formula-not-decoded -->

- (11) En. a.

```
* Torben didn't buy "Pride and Prejudice", didn't he? b. Torben didn't buy "Pride and Prejudice", did he? * Torben bought no books this week, didn't he? b. Torben bought no books this week, did he?
```

Nonassertive items do not change the polarity of a sentence either, but they require the sentence to be negative (certain other contexts work as well: questions, conditional clauses, comparatives, superlatives, ...):

```
(12) En. a. * Torben bought any books this week, didn't he? b. Torben didn't buy any books this week, did he?
```

Quirk et al.'s (1985:782) nonassertive items in (7) are part of what is otherwise known as ' negative polarity items ' ( NPIs ).

## 2.2.  Negative polarity items are not just idiomatic expressions

The adverbial expression En. at all / Da. overhovedet / Ge. überhaupt is a negative polarity item (NPI), as it would seem to need a negative element to be possible (or a question/conditional/comparative ...). However, at fi  rst glance one might simply think this dependence on negation comes from at all being part of the idiomatic expression not ... at all :

- (13) En. a. * Torben understands Icelandic at all.
- b. Torben does not understand  Icelandic at all.
3. Da. c. * Torben forstår islandsk overhovedet.
- d. Torben forstår ikke islandsk overhovedet.
5. Ge. e. * Torben versteht überhaupt

Isländisch.

- f. Torben versteht überhaupt nicht Isländisch.

But this would predict the following to be ungrammatical, as there is no not :

- (14) En. a. * Some students in this class understand Icelandic at all.
- b. No students in this class understand Icelandic at all.
3. Da. c. * Nogle studerende på det her hold forstår islandsk overhovedet.
- d. Ingen  studerende på det her hold forstår islandsk overhovedet.
5. Ge. e. * Einige Studenten in diesem Seminar verstehen überhaupt Isländisch.
- f. Keine  Studenten in diesem Seminar verstehen überhaupt Isländisch.
- (15) En. a. * Torben understands one of the Baltic languages at all.
- b. Torben understands none of the Baltic languages at all.
9. Da. c. * Torben forstår et af de baltiske sprog overhovedet.
- d. Torben forstår ingen af de baltiske sprog overhovedet.
11. Ge. e. * Torben versteht überhaupt eine von den baltischen Sprachen.
- f. Torben versteht überhaupt keine von den baltischen Sprachen.
- (16) En. a. * Torben sometimes speaks German at all.
- b. Torben never speaks German at all.
15. Da. c. * Torben taler nogle gange tysk overhovedet.
- d. Torben taler aldrig

tysk overhovedet.

- Ge. e. * Torben spricht überhaupt ab und zu Deutsch.
- f.
- Torben spricht überhaupt nie Deutsch.

The idiomatic expression hypothesis would run into even bigger problems with examples that are not negative in any way at all, like yes / no -questions, as such examples only display part of the idiom not at all , and therefore should be impossible:

- (17) En. a. Does Torben understand Icelandic at all?
- b. Does Torben not understand Icelandic at all?
3. Da. c. Forstår Torben overhovedet
4. islandsk?
- d. Forstår Torben overhovedet ikke islandsk?
6. Ge. e.
7. Versteht Torben überhaupt Isländisch?
- f. Versteht Torben überhaupt nicht Isländisch?

## 2.3.  English and Danish NPIs

Here are a few English NPIs (in addition to the nonassertive items from (7) above):

- (18) all that +

adj/adv a red cent stand (as verb) bat an eyelid bother to do something budge an inch do a thing about something drink a drop give a damn about something hold a candle to someone move a muscle say a word about something see a living soul sleep a wink

Here are two lists, (19) and (20), of negative polarity items in Danish -- the result of a quick check of the electronic version of NuDansk Ordbog (Appel et al. 2002). In the fi  rst list, (19), the NPIs can be used both in negated clauses and in questions or conditionals:

- (19) a. Arguments

nogetsomhelst

skyggen af noget en snus / spor / en stavelse / et suk (money only) en hvid / en klink / en rød reje / en rød øre

en brik / en bønne / en disse / en dyt / en døjt / en flyvende fis / et hak / et klap / et kuk / et kvidder / et kvæk / en lyd / en meter / et muk / en pind / et pip / en pløk / en skid /

- b. Adjectives / Adverbs

nævneværdig(t)

synderlig(t)

- c. Place Adverbials

nogen steder

nogetsteds

- d. Time Adverbials

nogensinde

endnu

på noget tidspunkt

- e. Measure adverbials

overhovedet på nogen måde i mindste måde

i det hele taget

så meget som ....

- f. Verbs

behøve (with infinitive only)

døje

fordrage

orke

- g. Full VPs

falde nogen ind at ... finde hoved og hale på/i noget fortænke nogen i noget have en jordisk chance have noget at skulle have sagt kimse ad noget lade noget sidde på sig lade sig mærke med noget se en hånd for sig skulle nyde noget tro sine egne øjne vokse på træerne være at foragte

være helt appelsinfri være med nogens gode vilje være nogens afdeling være nogens kop te være noget at rafle/tale om være noget galt i at ... være nogen ben i noget være på talefod være så dårligt/slemt være til at blive klog på være tilfældet at ...

være rigtig klog / være vel forvaret

In the second list of negative polarity items in Danish, (20), the NPIs can be used in negated clauses but for some reason, they are not so good in questions or conditionals:

## (20) a. Adjectives (inside arguments)

det mindste

det fjerneste

## b. Adverbial

heller

## c. Full VPs

give fem flade øre for noget give noget ved dørene have en trevl på kroppen have opfundet den dybe tallerken have opfundet det varme vand have opfundet krudtet have tone i livet krumme et hår på nogens hovede kunne gøre en kat fortræd kunne tage/snuppe/udstå noget lægge fingrene imellem lægge skjul på noget

lukke et øje løfte en finger sige noget to gange stikke op for bollemælk tro nogen over en dørtærskel ville røre noget med en ildtang være bleg for at ... være lutter lagkage være mange sure sild værd være tabt bag af en vogn være til at stå for være ved sine fulde fem

## 2.4.  Licensing of NPIs requires c-command

The negative polarity element must be c-commanded by the licenser, e.g. by the negative element (see e.g. Fromkin 2000: 223, 404, though see Hoeksema 2000 for certain problems with this analysis).

The subject c-commands the object, but the object does not c-command the subject. Therefore a negative subject can license an NPI-object, but a negative object cannot license an NPI-subject:

## (21) En. a. No one  understood anything.

b.

* Anyone understood nothing.

Da. c.

Ingen

forstod nogetsomhelst.

- d. * Nogensomhelst forstod ingenting.

<!-- image -->

For the purposes of this article 2 , I will simply assume that sentential negation has the same position in the tree as any other sentential adverbial. This has the following consequences for c-command:

2 For a much more detailed discussion of negation in Danish and other languages, including the position of negation, see Christensen (2005, e.g. pp. 28 & 38ff), and also Christensen (2008).

<!-- image -->

The subject position (IP-spec) is not c-commanded by the negation, (24)a,d, but the position of the logical subject ('the associate') in there -constructions is, (24)b,e.

- (24) En. a. * Because anybody wasn't
- b. Because there
- c. * Because there was
4. Da. d. * Fordi nogensomhelst ikke stod
- e. Fordi der
- f. * Fordi der

```
standing outside the door, ... wasn't anybody standing outside the door, ... anybody standing outside the door, ... uden for døren , ... ikke stod nogensomhelst uden for døren , ... stod nogensomhelst uden for døren , ...
```

The negative polarity element can also be licensed by a negative element in a different clause, provided there is c-command:

- (25) En. a. * Because Torben thought that I would ever understand it, ... b. Because Torben didn't think that I would ever understand it, ... c. * Because Torben ever thought that I would not understand it, ... Da. d. * Fordi Torben troede at jeg nogensinde ville forstå det, ... e. Fordi Torben ikke troede at jeg nogensinde ville forstå det, ... f. * Fordi Torben nogensinde troede at jeg ikke ville forstå det, ... Ge. g. * Weil Torben geglaubt hat, dass ich es jemals verstehen würde, ... h. Weil Torben nicht   geglaubt hat, dass ich es jemals verstehen würde, ...
- i. * Weil Torben jemals geglaubt hat, dass ich es nicht verstehen würde, ...

A topicalised object is not c-commanded by the negation (i.e. the situation that counts is the one after movement of the object from the object position to topic position in CP-spec, cf. (23)):

(26) En. a. Torben had not met a living soul

- b. * A living soul Torben had not met c. Not  a living soul had Torben met Da. d. Torben havde ikke mødt en levende sjæl. e. * En levende sjæl havde Torben ikke mødt. f. Ikke en levende sjæl  havde Torben mødt. Ge. g. Torben hatte keine Menschenseele getroffen. h.   *  Eine Menschenseele hatte Torben nicht getroffen.
- i. Keine Menschenseele hatte Torben getroffen.

I shall now try to show that the c-command condition on NPI-licensing is necessary, and that it cannot be replaced by a precedence condition 3 . Consider fi  rst a set of examples where the NPI a word is both c-commanded and preceded by the licenser:

```
(27) a. En. Earlier nobody tried to understand a word during the classes b.  Da. Tidligere forsøgte ingen at forstå et ord i timerne c. Ge. Früher hat niemand versucht im Unterricht ein Wort zu verstehen
```

Consider now a set of examples where the NPI is preceded but not c-commanded by the licenser, because the negation is inside the PP in topic position:

```
(28) a.  En.  * [Not long ago] I tried to understand a word during the classes b.  Da.  * [For ikke ret lang tid siden] forsøgte jeg at forstå et ord i timerne c.  Ge.  * [Vor nicht langer Zeit] habe ich versucht im Unterricht ein Wort zu verstehen
```

If precedence was suffi  cient as a condition on NPI-licensing, (28) should have been grammatical. 4

## 2.5.  Licensing of NPI-verbs

Now I want to look at a special kind of NPIs where c-command might seem not to be required, NPI-verbs.

The fi  rst NPI-verbs we shall examine are need in English (not the lexical verb need , but the auxiliary need , i.e. the need that takes an infi  nitive without to ) and its corresponding verbs in Danish and German, behøve / brauchen (only  when  they  embed  an  infi  nitive),  see  (29).  When need/behøve / brauchen take a DP-object, they are not NPI-verbs, see (30).

In none of (29)a,c,e do the NPI-verbs seem to be c-commanded by the negation. Nevertheless I think that these verbs need to be licensed by e.g. a negation, as shown by the ungrammaticality of (29)b,d,f. Instead, it must suffi  ce for the licensing of NPI-verbs that the base position of the NPIverb is c-commanded by a licenser (i.e. the NPI-verb must be c-commanded by a licenser before the verb undergoes movement to the left):

```
(29) En. a. Maybe Torben need not read these books. b. * Maybe Torben need read these books. Da. c. Måske behøver Torben ikke læse de her bøger. d. * Måske behøver Torben læse de her bøger. Ge. e. Vielleicht braucht Torben diese Bücher nicht zu lesen. f. * Vielleicht braucht Torben diese Bücher zu lesen.
```

3 Although the c-command condition on NPI-licensing may in principle also be applied within one of the fi  eld analyses, as in (1)b,c, (2)b, or (3)b,c, it would give completely wrong predictions: E.g. the subject would be c-commanded by the negation, something shown in (24)a,d not to be the case, as negation does not license an NPI-subject. This means that the fi  eld analyses would have to have a different condition on NPI-licensing, and here an option would be to refer to precedence instead, but as shown in (28), this would not give the right predictions either.

4 To give a complete picture, let me point out a complicating factor. There is a contrast between (28) and (i) below, even though both contain a negation inside a topic: In (i), the NPI is (again) both preceded and c-commanded by the licenser, because here not what is negative is not just the negation but the entire topic - as can be shown e.g. by tag questions or by the English subject-auxiliary inversion in (i)a:

```
(i) a.  En. [At no point in time] did I try to understand a word during the classes b.  Da. [På intet tidspunkt] forsøgte jeg at forstå et ord i timerne c.  Ge. [Zu keiner Zeit] habe ich versucht im Unterricht ein Wort zu verstehen
```

- (30) En. a. Maybe Torben does not need  these books.
- b. Maybe Torben needs these books.
3. Da. c. Måske behøver Torben ikke de her bøger.
- d. Måske behøver Torben de her bøger.
5. Ge. e. Vielleicht braucht Torben diese Bücher nicht.
- f. Vielleicht braucht Torben diese Bücher.

Constituent negation inside the object does not c-command the NPI-verb (here stand / fordrage / abkönnen ),  not  even  when this  verb  is  in  its  base  position,  (31)a,c,e,  as  opposed  to  (31)b,d,f, which do not contain any NPI-verb at all:

```
(31) En. a. * Torben can stand [not vodka but whisky]. b. Torben might drink [not vodka but whisky]. Da. c. * Torben kan fordrage [ikke vodka men whisky]. d. Torben kunne drikke [ikke vodka men whisky]. Ge. e. * Torben kann [nicht Wodka sondern Whisky] ab. f. Torben könnte [nicht Wodka sondern Whisky] trinken.
```

The NPI-verbs (or at least their base positions) must be c-commanded by a licenser, e.g. the sentential negation:

- (32) En. a.
2. Torben can't stand vodka. b. * Torben can stand vodka. Da. c. Torben kan ikke fordrage vodka. d. * Torben kan fordrage vodka.. Ge. e. Torben kann Wodka nicht ab. f. * Torben kann Wodka ab.

So even though NPI-verbs might seem to be counterexamples to the hypothesis that NPIs require c-command by e.g. a negation, it would seem that they still need a licenser, (29)b,d,f, (32)b,d,f, and that this licenser must c-command the base position of the NPI-verb.

## 2.6.  NPIs and because -clauses

Finally I want to examine another case where c-command might seem to be problematic as a licensing condition for NPIs, namely the interaction between NPIs and because -clauses.

Consider examples of the following type (which are also discussed e.g. in Linebarger (1987), in McCawley (1988: 565), and in Ladusaw (1996: 334):

- (33) a. En.
- b.  Da.
- c. Ge.

```
Torben had not understood my talk Torben havde ikke forstået mit foredrag fordi jeg havde brugt tyske eksempler. Torben hatte meinen Vortrag nicht verstanden,  weil ich deutsche Beispiele verwendet
```

because I had used German examples. hatte.

In spite of what one might think at fi  rst glance, these examples are actually ambiguous. Each of them may describe either

- (34) or (i) the  situation  where  the  use  of  German  examples  had  prevented  Torben  from understanding my talk - after all, he is a professor of English,
2. (ii) the  situation  where  Torben  had  understood  my  talk  for  a  different  reason  than because  of  my  use  of  German  examples.  In  other  words,  the  German  examples were not a problem - after all, he was once a student of Gunnar Bech's - but what really made him understand the talk was that it was about syntax.

Consider now the following examples, which contain an NPI and which lack such an ambiguity:

| (35)   | a.   | En. Torben had not understood a          | thing because I had used German examples.    |
|--------|------|------------------------------------------|----------------------------------------------|
| b.     | Da.  | Torben havde ikke forstået et klap       | fordi jeg havde brugt tyske eksempler.       |
| c.     | Ge.  | Torben hatte nicht die Bohne verstanden, | weil ich deutsche Beispiele verwendet hatte. |

(35) can only be used in the situation described by (34)i, not the one described by (34)ii. This can be shown more clearly if we expand the examples such that only the (34)ii interpretation is possible. Such an expansion is possible for (33), as shown in (36) below, but it is not possible for (35), cf. (37).

| (36) a.   | En.   | Torben had not understood my talk             | because I had used German examples, but because the talk was about syntax.             |
|-----------|-------|-----------------------------------------------|----------------------------------------------------------------------------------------|
| b.        | Da.   | Torben havde ikke forstået mit foredrag       | fordi jeg havde brugt tyske eksempler, men fordi foredraget handlede om syntaks.       |
| c.        | Ge.   | Torben hatte meinen Vortrag nicht verstanden, | weil ich deutsche Beispiele verwendet hatte, sondern weil der Vortrag über Syntax war. |
| (37) a.   | En.   | * Torben had not understood a thing           | because I had used German examples, but because the talk was about syntax.             |
| b.        | Da.   | * Torben havde ikke forstået et klap          | fordi jeg havde brugt tyske eksempler, men fordi foredraget handlede om syntaks.       |
| c.        | Ge.   | * Torben hatte nicht die Bohne verstanden,    | weil ich deutsche Beispiele verwendet hatte, sondern weil der Vortrag über Syntax war. |

A different set of examples of the same effect are the following:

- (38) a. En. Torben had not read the book because he was annoyed.
- b.  Da. Torben havde ikke læst bogen fordi han var irriteret.
- c. Ge. Torben hatte das Buch nicht gelesen, weil er genervt war.
- (39) a. En. Torben had not lifted a finger because he was annoyed.
- b.  Da. Torben havde ikke rørt en finger fordi han var irriteret.
- c. Ge. Torben hatte keinen Finger gerührt, weil er genervt war.

Again, (38) is actually ambiguous and may describe both the situation in (40)i and the one in (40) ii. (39), on the other hand, only describes the one in (40)i and not the one in (40)ii.

- (40) (i) the situation where being annoyed had prevented Torben from reading the book (he needs peace of mind for reading),

or

- (ii) the situation where Torben had read the book for a different reason than because he was annoyed. In other words, it wasn't being annoyed that made him read the book, it was being bored.

And again this can be shown more clearly if we expand the examples such that only the (34)ii interpretation is possible. Such an expansion is possible for (38), as shown in (41) below, but it is not possible for (39), cf. (42).

| (41)   | a. En.   | Torben had not read the book          | because he was annoyed, but because he was bored.     |
|--------|----------|---------------------------------------|-------------------------------------------------------|
|        | b. Da.   | Torben havde ikke læst bogen          | fordi han var irriteret, men fordi han kedede sig.    |
|        | c. Ge.   | Torben hatte das Buch nicht gelesen,  | weil er genervt war, sondern weil er gelangweilt war. |
| (42)   | a. En.   | * Torben had not lifted a finger      | because he was annoyed, but because he was bored.     |
|        | b. Da.   | * Torben havde ikke rørt en finger    | fordi han var irriteret, men fordi han kedede sig.    |
|        | c. Ge.   | * Torben hatte keinen Finger gerührt, | weil er genervt war, sondern weil er gelangweilt war. |

Presumably, the two interpretations (i.e. (34)i vs. (34)ii, and (40)i vs. (40)ii) differ crucially with respect to whether the because -clause is negated:

- In the (i) -interpretations, the because -clause is not negated (it gives a valid reason for why something did not happen). This is because it is outside the scope of negation, i.e. it is not c-commanded by not - hence it must be higher in the structure than negation (and therefore this is also the only interpretation available when the because -clause is fronted).
- In the (ii) -interpretations, the because -clause is part of what is negated (it gives an invalid reason for why something happened). This is because it is inside the scope of negation, i.e. it is c-commanded by not - hence it must be lower in the structure than negation.

This analysis is supported by the fact that only in the (ii)-interpretations may there be an NPI inside the because -clause itself. The examples in (43) where the NPI the least bit is inside the because -clause thus require the (ii)-interpretations, and therefore they are only really good when this is spelled out, as in (44) (and therefore they also do not allow fronting of the because -clause):

| (43)   | a.   | En. ?                                               | Torben had not skipped my talk because he was the least bit tired.                     |
|--------|------|-----------------------------------------------------|----------------------------------------------------------------------------------------|
|        | b.   | Da. ? Torben havde ikke pjækket fra mit foredrag    | fordi han var det mindste træt.                                                        |
|        | c.   | Ge. ? Torben hatte meinen Vortrag nicht geschwänzt, | weil er im Geringsten müde war.                                                        |
| (44)   | a.   | En. Torben had not skipped my talk                  | because he was the least bit tired, but because he had heard it before.                |
|        | b.   | Da. Torben havde ikke pjækket fra                   | mit foredrag fordi han var det mindste træt, men derimod fordi han havde hørt det før. |
|        | c.   | Ge. Torben hatte meinen Vortrag nicht geschwänzt,   | weil er im Geringsten müde war, sondern weil er ihn schon gehört hatte.                |

But even if the (ii)-interpretation has the because -clause inside the scope of negation, this does not explain why the (ii)-interpretation is not available in (35) and (39), i.e. it does not explain the ungrammaticality of (37) and (42), which are the expanded version of (35) and (39). Under both interpretations, (i) and (ii), the NPI in (35) and (39) must be taken to be c-commanded by not .

In the extensive literature on this question, there are two kinds of approaches, but they agree that what is special about the (ii)-interpretation is that it is a case of focussing negation, with the focus on the because -clause.

One approach to why (ii)-interpretation is not available in (35) and (39) (and thus also to why (37) and (42) are ungrammatical) is syntactic in nature, and says that when the because -clause is itself c-commanded by negation, it disturbs the licensing of the NPI (e.g. a thing in (37)). As the because -clause is itself c-commanded by negation and c-commands the NPI, it intervenes in the licensing. For the exact details of such an account, I refer to Linebarger (1987), Guerzoni (2006: 372), and for defence of the idea that focus elements can be interveners, I refer to Kim (2002). A different example of an intervention effect is given in Vikner (1995: 22) and repeated here:

```
(45) Da. a. Hvad for  nogen studerende har du inviteret? b. Hvad har du inviteret for nogen studerende? What (for any students) have you invited (for any students) (= 'Which students have you invited?') (46) Da. a. Hvad for  nogen studerende har du ikke inviteret? b. * Hvad har du ikke inviteret for nogen studerende? What (for any students) have you not invited (for any students) (= 'Which students have you not invited?')
```

If there is no negation present, it is both possible to front the entire what for students , (45)a, and to front just what , (45)b, the latter perhaps being more colloquial, but nevertheless defi  nitely possible. If negation is present, however, it is still possible to front the entire what for students , (46)a, but it is now not possible to front just what , (46)b. (46)b is an example of an intervention effect, as ikke is c-commanded by what and c-commands for students .

The other approach to why (ii)-interpretation is not available in (35) and (39) (and thus also to why (37) and (42) are ungrammatical) is semantic in nature. Focus creates a series of alternatives (see Rooth 1992 and many others), cf. e.g. the focussing negation reading of (47)a, where focus is on this morning , and where the alternatives all have the form (47)b:

```
(47) En. a. Peter didn't arrive in Aarhus this morning b. Peter arrived in Aarhus at some point in time X,  X
```

- z this morning

(The following is strongly simplifi  ed, for a much more detailed analysis see e.g. Meier 2001). It would seem that whereas normal negation licences any NPI that it c-commands, focussing negation only licenses an NPI which is inside the focus (i.e. inside the because -clause in (35) and (39)).

This is unexpected, given that a focussing negation c-commands much more than what is inside the focus. What is crucial here is that in the case of focussing negation, the alternatives are all positive, cf. that although (47)a is negative, the alternatives are all positive, (47)b.

The alternatives to the focus readings of (35) and (39) thus do not contain any negation, and therefore the NPI in these alternatives would not be licensed:

- weil ich deutsche Beispiele verwendet hatte,

```
(48) En. a. * Torben had not understood a thing because I had used German examples, ... he had understood a thing because the talk was about syntax. Da. b. * Torben havde ikke forstået et klap fordi jeg havde brugt tyske eksempler, ... han   havde forstået et klap fordi foredraget handlede om syntaks. Ge. c. * Torben hatte nicht die Bohne verstanden, ... er hatte die Bohne verstanden, weil der Vortrag über Syntax war.
```

```
(49) En. a. * Torben had not lifted a finger because he was annoyed, ... he had lifted a finger because he was bored. Da. b. * Torben havde ikke rørt en finger fordi han var irriteret, ... han   havde rørt en finger fordi han kedede sig. Ge. c. * Torben hatte keinen Finger gerührt, weil er genervt war, ... er hatte einen Finger gerührt, weil er gelangweilt war.
```

If, on the other hand, the NPI is inside the focus, there is no problem, because what is inside the focus is absent from the alternatives, and then it does not matter that there is no negation in the alternatives.

```
(50) En. a. Torben had not skipped my talk because he was the least bit tired, ... he had skipped my talk because he had heard it before. Da. b. Torben havde ikke pjækket fra mit foredrag fordi han var det mindste træt, ... han   havde pjækket fra mit foredrag fordi han havde hørt det før. Ge. c. Torben hatte nicht meinen Vortrag geschwänzt, weil er im Geringsten müde war, ... er hatte meinen Vortrag geschwänzt, weil er ihn schon gehört hatte.
```

Although I have not been able to present a defi  nite analysis of because -clauses, I hope to have shown some of the properties that such an analysis must have, and in particular how any analysis of because -clauses (like any other analysis of anything to do with NPI) must make reference to c-command.

## 3. Conclusion

The objective of this paper was mainly to illustrate a particular difference (concerning the availability of c-command) between two kinds of approaches to clause structure, namely tree analyses like the generative analysis that Torben Thrane and I both advocate and fi eld analyses like the sætningsskema analysis of Danish of Diderichsen (1946) and many others (or like the topologische Modell analysis of German of Drach 1937 and many others).

Having said this, I hope that at least the fi  rst part of my paper also illustrated that these approaches have a number of properties in common. I continue to believe that syntacticians would be well advised to look further than the surface of the different formal and functional approaches. Despite the occasionally polemic tone, the various approaches actually have much in common, and they have a lot to learn from each other's insights.

All syntacticians, regardless of theoretical persuasion, are ultimately interested in explaining language data. Given the complex subject matter of the discipline, we need all the help we can get, and therefore none of us can afford to ignore the results reached within 'the opposite camp'.

The particular difference between the tree analyses and the fi  eld analyses that was explored in this paper concerned c-command, a relationship between different constituents, which as far as I can see can only be formulated in a tree analysis and not in a fi  eld analysis. The question must therefore be how necessary and useful a tool like c-command is, and here I tried to show that it is indeed extremely useful when it comes to accounting for negative polarity items in English, Danish and German, both the more straightforward aspects presented in 2.1-2.4 and the more tricky ones concerning NPI-verbs, section 2.5 and NPI-elements and because -clauses in section 2.6.

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