## 1 Introduction

The topic of this paper is the structure of the German numeral expressions illustrated in (1).

1. (1)
1. a.
1. Um
2. around
1. die
2. the
1. tausend
2. thousand
1. Kinder
2. children
1. saßen
2. sat
1. im
2. in.the
1. Foyer.
2. hall
1. ‘Around one thousand children were sitting in the hall.’
1.
1. b.
1. An
2. on
1. die
2. the
1. siebzig
2. seventy
1. Flüchtlinge
2. refugees
1. sind
2. are
1. erstickt.
2. suffocated
1. ‘Up to seventy refugees suffocated.’
1.
1. c.
1. Gegen
2. against
1. siebzig
2. seventy
1. Flüchtlinge
2. refugees
1. sind
2. are
1. erstickt.
2. suffocated
1. ‘Nearly seventy refugees suffocated.’

I will follow Plank (2004) and refer to such numeral expressions as approximative numerals. They are so-called because these numerals do not specify a unique cardinality but only narrow it down to a certain range of cardinalities. What makes approximative numerals theoretically interesting is the element giving rise to the approximative reading, the so-called approximative modifier. In the examples in (1), the approximative modifier is drawn from the set of local prepositions: um ‘around’ in (1a), an ‘on’ in (1b), and gegen ‘against’ in (1c). Depending on the preposition, the definite determiner die has to be included in the approximative modifier. Omitting die in (1a) and (1b) results in ungrammaticality, whereas adding die in (1c) results in ungrammaticality. Hence in (1a) and (1b), the approximative modifier is an die and um die, respectively, and in (1c) it is gegen. Since the approximative reading cannot be subsumed under the local interpretation of prepositions,1 the question is how to structurally represent such prepositions within the approximative numeral. Based on Dutch, Corver & Zwarts (2006) argue that approximative numerals are PPs, as shown in (2) for the examples (1b) and (1c).2

1. (2)

I argue in this paper that approximative numerals are not PPs. Rather, approximative modifiers are adverbs that are homophonous to a sequence of a preposition with or without the determiner die. The corresponding structures under this approach for (1b) and (1c) are provided in (3).

1. (3)

The structure of approximative numerals as in (1) is hence subsumed under a structure that is independently required, namely one for approximative numerals that contain an adverb as their approximative modifier. Two examples for approximative numerals containing adverbs as approximative modifiers are given in (4), and the corresponding structure for (4b) in (5).

1. (4)
1. a.
1. Ungefähr
2. approximately
1. tausend
2. thousand
1. Kinder
2. children
1. saßen
2. sat
1. im
2. in.the
1. Foyer.
2. hall
1. ‘Around one thousand children were sitting in the hall.’
1.
1. b.
1. Fast
2. nearly
1. siebzig
2. seventy
1. Flüchtlinge
2. refugees
1. sind
2. are
1. erstickt.
2. suffocated
1. ‘Nearly seventy refugees suffocated.’
1. (5)

The paper is structured as follows. I first argue in section 2 that approximative modifiers are attached to the numeral and not to the full DP nor to the DP-internal NP containing the numeral. In section 3, I provide three arguments that show that approximative numerals differ from bona fide PPs but pattern with approximative numerals containing adverbs as their approximative modifier, thereby providing support for a uniform analysis of approximative modifiers as adverbs. In section 4, I argue that in addition to not behaving like PPs, the alleged preposition and the alleged determiner do not behave as prepositions or determiners either, respectively. In section 5, I spell out in more detail the idea that approximative modifiers such as an die ‘up to’ and um die ‘around’ are adverbs and discuss some problems that result from this analysis. In section 6, I discuss the status of approximative modifiers in Dutch and conclude that Dutch in fact has prepositional numerals. The final section, section 7, summarizes the main result.

## 2 The position of the approximative modifier

The purpose of this section is to establish that the approximative modifier is attached to the numeral. Two alternatives suggest themselves. First, the approximative modifier could be directly attached to the DP. Depending on the analysis of the lexical status of the approximative modifier, this either results in a PP or an adverbially modified DP. I will argue that neither option is viable. The second alternative treats the approximative modifier as being attached to the DP-internal NP. I will show that this option is not viable either, irrespective of the lexical status one wishes to assign to the approximative modifier. The three options based on the two alternatives are summarized in (6).

 (6) a. The approximative modifier occupies the head position within a PP that takes the DP containing the numeral and the noun as its complement
 b. The approximative modifier occupies a DP adjoined position
 c. The approximative modifier occupies an NP adjoined position

### 2.1 Phrases containing approximative numerals are not PPs

The first option in (6a) has already been convincingly rejected for Dutch by Corver & Zwarts (2006: 820–821). Based on extraposition, split topicalization, extraction properties of R-pronouns and subcategorization, all which distinguish DPs from PPs, they show that constituents containing approximative numerals always line up in their behavior with DPs, thereby suggesting that they are DPs. Except for split topicalization, which is possible out of PPs in German for some speakers, all these arguments carry over to German. I will only add some more arguments to this conclusion.

The first argument comes from pronominalization. When PPs are pronominalized, the preposition is retained, as can be seen in example (7) for the PP headed by an ‘on’, selected from the verb sich erinnern ‘to remember.’

1. (7)
1. Peter
2. Peter
1. erinnert
2. remembers
1. sich
2. REFL.3
1. √an
2.   on
1. die
2. the
1. siebzig
2. seventy
1. Vasen
2. vases
1. /
2.
1. √an
2.   on
1. sie
2. them
1. / *
2.
1. sie.
2. them
1. ‘Peter remembers seventy vases/them.’

This contrasts with the pronominalization properties of constituents containing an approximative numeral, as shown in (8) with the transitive verb zerbrechen ‘to break,’ which selects a DP object.

1. (8)
1. Peter
2. Peter
1. zerbrach
2. broke
1. √an
2.   on
1. die
2. the
1. siebzig
2. seventy
1. Vasen
2. vases
1. / *
2.
1. an
2. on
1. sie
2. them
1.
1. √sie.
2.   them
1. ‘Peter broke up to seventy vases/them.’

As shown, when the object contains an approximative numeral and is pronominalized, then the objects pronominalize as a regular pronoun, indicating that it is a DP.

The second argument is based on PP-subjects. If constituents containing an approximative numeral were PPs, then they should be unavailable in German in subject position, because German lacks PP-subjects (Plank 2004: 174).

1. (9)
1. Under
2. under
1. dem
2. the
1. Tisch
2. table
1. war
2. was
1. *
2.
1. (es)
2.   it
1. sehr
2. very
1. dunkel.
2. dark
1. ‘Under the table was very dark.’

However, despite the lack of PP-subjects, German does allow constituents containing approximative numerals in subject position, suggesting that they are DPs.

1. (10)
1. An
2. on
1. die
2. the
1. ein
2. one
1. Gramm
2. gram
1. Quecksilber
2. mercury
1. ist
2. is
1. (*es)
2.    it
1. schon
1. tödlich.
2. lethal
1. ‘Up to one gram of mercury is already lethal.’

The third argument is based on verb agreement. If constituents containing an approximative numeral were PPs, one expects them to not trigger verb agreement, since verb agreement is a property of subject DPs only in German. But as the data in (11) show, such constituents do trigger verb agreement when they are subjects, indicating that they are DPs.

1. (11)
1. An
2. on
1. die
2. the
1. zehn
2. ten
1. GästePL
2. guests
1. √kommenPL
2.   come
1. / *
2.
1. kommtSG.
2. comes
1. ‘Up to ten guests come.’

Passivization provides the fourth argument against the idea that constituents containing approximative numerals are PPs. In German, passivization is a property of object DPs. Example (12a) illustrates the active version of a sentence containing the ditransitive verb verabreichen ‘to dose.’ The fact that the direct object containing an approximative numeral can be passivized, as shown in (12b), indicates again that it is a DP.

1. (12)
1. a.
1. Die
2. the
1. Ärzte
2. doctors
1. verabreichten
2. dose
1. ihm
2. him
1. an
2. on
1. die
2. the
1. ein
2. one
1. Gramm
2. gram
1. Quecksilber.
2. mercury
1. ‘The doctors dosed him with up to one gram of mercury.’
1.
1. b.
1. An
2. on
1. die
2. the
1. ein
2. one
1. Gramm
2. gram
1. Quecksilber
2. mercury
1. wurde
2. became
1. ihm
2. him
1. von
2. of
1. den
2. the
1. Ärzten
2. doctores
1. verabreicht.
2. dosed
1. ‘He was dosed with up to one gram of mercury.’

The sentence in (12b) cannot be analyzed as an impersonal passive with the PP moved to SpecCP because when the alleged PP contains a plural noun, verb agreement correspondingly changes to plural, as shown in (13).

1. (13)
1. An
2. on
1. die
2. the
1. zehn
2. ten
1. Tabletten
2. pills
1. wurden
2. became
1. ihm
2. him
1. von
2. of
1. den
2. the
1. Ärzten
2. doctores
1. verabreicht.
2. dosed
1. ‘He was dosed with up to ten pills.’

This contrasts with clear cases of impersonal passives with a PP containing a plural noun, as shown in (14). There the verb sich erinnern ‘to remember’ selecting a PP is passivized. As can be seen, even when the PP contains a plural noun, singular verb agreement is retained.

1. (14)
1. a.
1. Er
2. he
1. hat
2. has
1. sich
2. REFL.3
1. an
2. on
1. die
2. the
1. zehn
2. ten
1. Gäste
2. guests
1. erinnert.
2. remembered
1. ‘He remembered the ten guests.’
1.
1. b.
1. An
2. on
1. die
2. the
1. zehn
2. ten
1. GästePL
2. guests
1. √wirdSG
2.   becomes
1. /*
2.
1. werdenPL
2. become
1. sich
2. REFL.3
1. oft
2. often
1. erinnert.
2. remembered
1. ‘One often remembers the ten guests.’

Moreover, PPs in impersonal passives cannot control a PRO in an infinitival adjunct clause, as shown in (15).

1. (15)
1. *
1. Ohne
2. without
1. PROi
2.
1. etwas
2. something
1. dafür
2. for.it
1. zu
2. to
1. machen,
2. make
1. wird
2. becomes
1. sich
2. REFL.3
1. an
2. on
1. jeden
2. every
1. Gasti
2. guest
1. erinnert.
2. remembered
1. intended: ‘Without doing anything for it, every guest gets remembered.’

But constituents containing an approximative modifier can control a PRO in an infinitival adjunct clause, as shown in (16), indicating that they are proper subject DPs.

1. (16)
1. Ohne
2. without
1. PROi
2.
1. vorher
2. before
1. getestet
2. tested
1. worden
2. become
1. zu
2. to
1. sein,
2. be
1. wurden
2. became
1. an
2. on
1. die
2. the
1. zehn
2. ten
1. neue
2. new
1. Verfahreni
2. procedures
1. angewendet.
2. applied
1. ‘Without having been tested before, up to ten new procedures were applied.’

A fifth argument comes from case marking. If the constituents containing an approximative numeral were PPs, they should be invisible to case marking from the verb. But this is not the case. Consider first the examples in (17).

1. (17)
1. a.
1. Peter
2. Peter
1. hilftDAT
2. helps
1. √Männern
2.   men.DAT
1. /*
2. /
1. Männer.
2. men.ACC
1. ‘Peter helps men.’
1.
1. b.
1. Peter
2. Peter
1. kämpft
2. fights
1. umACC
2. around
1. *
2.
1. Männern
2. men.DAT
1. /
2. /
1. √Männer.
2.   men.ACC
1. ‘Peter fights for men.’

(17a) shows that the object position of the verb helfen ‘to help’ assigns dative case to its object; (17b) shows that um ‘around’ assigns accusative case to its DP-complement. If constituents containing the approximative modifier um ‘around’ occupy the object position of helfen ‘to help’, then dative marking on the noun should be blocked by Minimality: although both the preposition and the verb are licit governors, the preposition is contained within the c-command domain of the verb and is therefore is more local. However, the example in (18) shows that the reverse is the case: dative marking occurs and case assignment by um ‘around’ is blocked.

1. (18)
1. Peter
2. Peter
1. hilftDAT
2. helps
1. umACC
2. around
1. die
2. the
1. zehn
2. ten
1. √Männern
2.   men.DAT
1. /*
2. /
1. Männer.
2. men.ACC
1. ‘Peter helped around ten men.’

In order to account for this, an otherwise unmotivated transparency of PPs for case marking from outside need to be invoked. Under the hypothesis that such constituents are regular DPs, case marking follows neatly.3

The sixth argument comes from coordination.4 On the one hand, a constituent containing an approximative numeral can be conjoined with a DP.

1. (19)
1. Zwanzig
2. twenty
1. Frauen
2. women
1. und
2. and
1. an
2. on
1. die
2. the
1. zehn
2. ten
1. Männer
2. men
1. waren
2. were
1. im
2. in.the
1. Kino.
2. cinema
1. ‘Up to ten men and twenty women were in the cinema.’

On the other hand, two such constituents can be conjoined, as shown in (20).

1. (20)
1. An
2. on
1. die
2. the
1. ein
2. one
1. Gramm
2. gram
1. Quecksilber
2. mercury
1. und
2. and
1. um
2. around
1. die
2. the
1. ein
2. one
1. Milligramm
2. milligram
1. Arsen
2. arsenic
1. sind
2. are
1. schon
1. tödlich.
2. lethal
1. ‘Up to one gram of mercury and up to one milligram of arsenic are already lethal.’

The sentence in (20) features plural verb agreement, similar to the coordination of two singular subject DPs. As the data in (21) show, the grammaticality of (20) cannot be analyzed as coordination of two thematically identical constituents that happen to have a different phrasal status. For this type of coordination is usually not available in German.

1. (21)
1. a.
1. Peter
2. Peter
1. diskutiert
2. discusses
1. (über)
1. ein
2. a
1. Thema.
2. topic
1. ‘Peter discusses a topic.’
1.
1. a.
1. *
1. Peter
2. Peter
1. diskutiert
2. discusses
1. die
2. the
1. Homoehe
2. gay marriage
1. und
2. and
1. über
1. das
2. the
1. Burkaverbot.
2. burqa ban
1. intended: ‘Peter discusses gay marriage and burqa ban.’

The seventh and final argument comes from split topicalization. As mentioned at the beginning of this section, split topicalization is possible with PPs in German for some speakers. Crucially, the preposition has to be retained on both constituents derived from splitting (Fanselow & Ćavar 2002).

1. (22)
1. Mit
2. with
1. Fraueni
2. women
1. hab
2. have
1. ich
2. I
1. nur
2. only
1. mit
2. with
1. schönen
2. beautiful
1. ti
2.
1. getanzt.
2. danced
1. ‘As for women, I danced only with beautiful ones.’

If constituents with an approximative numeral were PPs, their splitting is also expected to result in a repetition of the preposition. But as the data in (23) show, this is not possible: the preposition must not appear at the dislocated constituent.

1. (23)
1. (*An)
2.   on
1. Fraueni
2. women
1. habe
2. have
1. ich
2. I
1. nur
2. only
1. an
2. on
1. die
2. the
1. zehn
2. ten
1. ti
2.
1. gesehen.
2. seen.
1. ‘As for women, I only saw up to ten.’

Under the approach that such constituents are DPs, the non-repetition follows naturally.

### 2.2 Approximative modifiers are not adjoined to DP

Turning to the approach in (6b), according to which the approximative modifier is an adverb adjoined to the DP, DPs containing numerals can be preceded by a quantificational determiner like alle ‘all’ and various elements that are definite.

1. (24)
1. a.
1. alle
2. all
1. zwanzig
2. twenty
1. Gäste
2. guests
1. ‘all the twenty guests’
1.
1. b.
1. die drei Frauen
2. ‘the three women’
1.
1. c.
1. meine zwei Kinder
2. ‘my two kids’
1.
1. d.
1. Peters zwei Jobs
2. ‘Peter’s two jobs’

All of these elements occur in the DP-domain, that is, in D° or SpecDP. Now if approximative modifiers were adverbs adjoined to DP, they are predicted to precede the elements from (24). But the data in (25) show that approximative modifiers necessarily follow them.

1. (25)
1. a.
1. alle
2. all
1. an
2. on
1. die
2. the
1. hundert
2. hundred
1. Gäste
2. guests
1. /*
2.
1. an
2. on
1. die
2. the
1. alle
2. all
1. hundert
2. hundred
1. Gäste
2. guests
1. ‘all the up to hundred guests’
1.
1. b.
1. die
2. the
1. an
2. on
1. die
2. the
1. zehn
2. ten
1. Frauen
2. women
1. /*
2.
1. an
2. on
1. die
2. the
1. die
2. the
1. zehn
2. ten
1. Frauen
2. women
1. ‘the up to ten women’
1.
1. c.
1. meine
2. my
1. an
2. on
1. die
2. the
1. tausend
2. thousand
1. Bücher
2. books
1. /*
2.
1. an
2. on
1. die
2. the
1. meine
2. my
1. tausend
2. thousand
1. Bücher
2. books
1. ‘my up to thousand books’
1.
1. d.
1. Peters
2. Peter’s
1. an
2. on
1. die
2. the
1. tausend
2. thousand
1. Bücher
2. books
1. /*
2.
1. an
2. on
1. die
2. the
1. Peters
2. Peter’s
1. tausend
2. thousand
1. Bücher
2. books
1. ‘Peter’s up to thousand books’

Moreover, adverbs that do modify DPs like schon ‘already’ or sogar ‘even’ attach to DP and precede elements that are definite.

1. (26)
1. a.
1. Schon
1. /
2.
1. sogar
2. even
1. alle
2. all
1. zwanzig
2. twenty
1. Gäste
2. guests
1. im
2. in.the
1. Nebenraum
2. side.room
1. machen
2. make
1. Arbeit.
2. work
1. ‘Already/even all the twenty guests in the side room cause a lot of work.’
1.
1. b.
1. Schon
1. /
2.
1. sogar
2. even
1. die
2. the
1. zehn
2. ten
1. Frauen
2. women
1. machen
2. make
1. Lärm.
2. noise
1. ‘Already/even the ten women make noise.’
1.
1. c.
1. Schon
1. /
2.
1. sogar
2. even
1. meine
2. my
1. tausend
2. thousand
1. Bücher
2. books
1. haben
2. have
1. ihn
2. him
1. beeindruckt.
2. impressed
1. ‘Already/even my thousand books impressed him.’
1.
1. d.
1. Schon
1. /
2.
1. sogar
2. even
1. Peters
2. Peter’s
1. zwei
2. two
1. Bücher
2. books
1. haben
2. have
1. ihm
2. him
1. gefallen.
2. impressed
1. ‘Already/even Peter’s two books impressed him.’

### 2.3 Approximative modifiers are not adjoined to NP

Lastly, the approach in (6c), according to which approximative modifiers are adjoined to NP, makes wrong predictions about the scope of approximative modifiers. As is well-known, adjectival modifiers can take scope over NP-internally conjoined material.

1. (27)
1. Ich
2. I
1. habe
2. have
1. attraktive
2. attractive
1. Frauen
2. women
1. und
2. and
1. Männer
2. men
1. gesehen.
2. seen
1.  ‘I saw attractive women and men.’
2. =I saw [attractive women] and [men].
3. =I saw [attractive [women and men]].

But approximative modifiers – be they adverbs or alleged prepositions – lack the wide scope reading where they take scope over both conjuncts and only allow the reading where they take narrow scope over the first conjunct.5

1. (28)
1. a.
1. An
2. on
1. die
2. the
1. 300
2. 300
1. Demonstranten
2. protesters
1. und
2. and
1. 10
2. 10
1. Randalierer
2. rioters
1. wurden
2. became
1. festgenommen.
2. arrested
1.       ‘Up to 300 protesters and 10 rioters were arrested.’
2.     =[up to 300 protesters] and [10 rioters] were arrested
3. =/=[up to [300 protesters and 10 rioters]] were arrested
1.
1. b.
1. Ungefähr
2. approximately
1. 300
2. 300
1. Demonstranten
2. protesters
1. und
2. and
1. 10
2. 10
1. Randalierer
2. rioters
1. wurden
2. became
1. festgenommen.
2. arrested
1.     ‘Approximately 300 protesters and 10 rioters were arrested.’
2.    =[approximately 300 protesters] and [10 rioters] were arrested
3. =/=[approximately [300 protesters and 10 rioters]] were arrested

The unavailability of the wide scope reading is unexpected if approximative modifiers were adjoined to NP. For if that were possible, they should be able to adjoin to an NP resulting from the coordination of two NPs. Since the approximative modifier c-commands the two conjoined NPs, it should consequently be able to take scope over both NPs, as shown in (29).

1. (29)

The unavailability of the wide scope reading therefore argues against the idea that the approximative modifier occupies an NP adjoined position as shown in (29). The absence of this reading, however, follows neatly from a structure where the approximative modifier is adjoined to the numeral, as shown in (30).

1. (30)

In (30), the approximative modifier only c-commands the numeral, hence only scopes over this numeral, so that the wide scope reading for (28) is excluded, as desired. In this respect, approximative modifiers behave like adverbs that modify adjectives.6

1. (31)
1. Sehr
2. very
1. schöne
2. handsome
1. Männer
2. men
1. und
2. and
1. attraktive
2. attractive
1. Frauen
2. women
1. haben
2. have
1. uns
2. uns
1. begrüßt.
2. greeted
1.     ‘Very beautiful men and attractive women welcomed us.’
2.    =[very beautiful men] and [attractive women] welcomed us
3. =/=[very [beautiful men and attractive women] welcomed us

This similarity is expected because under the analysis that the approximative modifier is adjoined to the numeral, both (31) and (28) feature a structure where the adverb is attached too low to take wide scope. The structure of the subject-internal coordination structure of (31) is given in (32) and should be compared with (30).7

1. (32)

## 3 Approximative numerals are not PPs

The previous section established that approximative modifiers are attached to the numeral. In this section I will argue that approximative modifiers are not prepositions and hence that the resulting approximative numerals are not PPs either. Rather, approximative modifiers that look like prepositions are adverbs adjoined to the numeral. Therefore, approximative numerals are adverbially modified numerals. In total I will present three arguments against the idea that approximative numerals are PPs. They are all of the same form. I will present properties of bona fide PPs and show that approximative numerals containing approximative modifiers that look like prepositions behave differently vis-à-vis these properties. I will then show that the behavior of approximative modifiers is identical to that of clear cases of approximative modifiers that are adverbs, pointing to a uniform analysis of approximative modifiers.

### 3.1 PP splitting

The first difference between bona fide PPs and approximative numerals concerns the splitting of PPs by focus particles, expressions such as zum Beispiel ‘for example,’ and parentheticals. By parentheticals, I refer to clause-like expressions indicating the attitude of the speaker or the subject, such as glaube ich ‘I think’ or so wird behauptet ‘it is claimed.’ In bona fide PPs, focus particles, zum Beispiel, and parentheticals can split up PPs and appear between the preposition and its complement.8

1. (33)
1. a.
1. focus particles splitting up PPs
1.
1.
1. Ich
2. I
1. habe
2. have
1. mal
2. once
1. eine
2. a
1. Frage
2. question
1. an
2. on
1. nur
2. only
1. die
2. the
1. Frauen
2. women
1. unter
2. under
1. uns.
2. us
1. ‘Here is a question for only the women among us.’
1.
1. b.
1. zum Beispiel splitting up PPs
1.
1.
1. Die
2. the
2. city
1. kann
2. can
1. den
2. the
1. Auftrag
2. order
1. an
2. on
1. zum
2. for
1. Beispiel
2. example
1. einen
2. a
1. lokalen
2. local
1. Anbieter
2. company
1. vergeben.
2. give
1. ‘The city can place the order with a local company.’
1.
1. c.
1. parentheticals splitting up PPs
1.
1.
1. Peter
2. Peter
1. denkt
2. thinks
1. an
2. on
1. denke
2. think
1. ich
2. I
1. die
2. the
1. Frauen.
2. women
1. ‘Peter has in mind the women, I think.’

Whatever the precise position for parentheticals, zum Beispiel ‘for example’, and focus particles inside PPs turns out to be, it can be observed that such expressions can split up PPs as shown in (34).

1. (34)

If approximative numerals were PPs, it is predicted that they can equally be broken up, as shown in (35).

1. (35)

However, the examples in (36) show that this prediction is not borne out: none of these elements can split up approximative numerals, providing the first piece of evidence against the idea that approximative numerals are PPs.9

1. (36)
1. a.
1. focus particles not splitting up approximative numerals
1.
1.
1. *
1. Er
2. he
1. hat
2. has
1. an
2. on
1. nur
2. only
1. die
2. the
1. zehn
2. ten
1. Menschen
2. people
1. getötet.
2. killed
1. intended: ‘He killed only up to ten people.’
1.
1. b.
1.
1. zum Beispiel not splitting up approximative numerals
1.
1.
1. *
1. Peter
2. Peter
1. hat
2. has
1. an
2. on
1. zum
2. for
1. Beispiel
2. example
1. die
2. the
1. hundert
2. hundred
1. Frauen
2. women
1. geküsst.
2. kissed
1. intended: ‘Peter kissed up to hundred women for example.’
1.
1. c.
1.
1. parentheticals not splitting up approximative numerals
1.
1.
1. *
1. Peter
2. Peter
1. hat
2. has
1. an
2. on
1. denke
2. think
1. ich
2. I
1. die
2. the
1. hundert
2. hundred
1. Frauen
2. women
1. geküsst.
2. kissed
1. intended: ‘Peter kissed up to 100 women, I think.’

The impossibility of (36) is crucially not due to some constraint banning the splitting expressions from appearing inside a complex numeral. In (37), the splitting expressions appear after the approximative modifier and the sentences are perfectly grammatical.

1. (37)
1. a.
1. focus particles splitting up numerals
1. Er
2. he
1. hat
2. has
1. an
2. on
1. die
2. the
1. nur
2. only
1. zehn
2. ten
1. Menschen
2. people
1. getötet.
2. killed
1. ‘He killed only up to ten people.’
1.
1. b.
1. zum Beispiel splitting up numerals
1. Peter
2. Peter
1. hat
2. has
1. an
2. on
1. die
2. the
1. zum
2. for
1. Beispiel
2. example
1. hundert
2. hundred
1. Frauen
2. women
1. geküsst.
2. kissed
1. ‘Peter kissed up to hundred women for example.’
1.
1. c.
1. parentheticals splitting up numerals
1. Peter
2. Peter
1. hat
2. has
1. an
2. on
1. die
2. the
1. denke
2. think
1. ich
2. I
1. hundert
2. hundred
1. Frauen
2. women
1. geküsst.
2. kissed
1. ‘Peter kissed up to 100 women, I think.’

The alternative analysis treating approximative numerals as adverbially modified numerals predicts both the contrast between (33) and (36) as well as the contrast between (36) and (37). As for the first contrast, it follows from the fact that approximative qualifiers are adverbs. Since adverbs are monolexical, they simply cannot be split up. This is completely parallel to bona fide adverbial modifiers of numerals, which cannot be split up either.

1. (38)
1. a.
1.
1. focus particles not splitting up adverbs
1.
1.
1. *
1. Er
2. he
1. hat
2. has
1. un
2. ap
1. nur
2. only
1. gefähr
2. proximately
1. sechzig
2. sixty
1. Hot
2. hot
1. dogs
2. dogs
1. gegessen.
2. eaten
1. intended: ‘He ate only approximately sixty hot dogs.’
1.
1. b.
1.
1. zum Beispiel not splitting up adverbs
1.
1.
1. *
1. Peter
2. Peter
1. hat
2. has
1. un
2. ap
1. zum
2. for
1. Beispiel
2. example
1. gefähr
2. proximately
1. hundert
2. hundred
1. Frauen
2. women
1. geküsst.
2. kissed
1. intended: ‘Peter kissed up to hundred women for example.’
1.
1. c.
1.
1. parentheticals not splitting up adverbs
1.
1.
1. *
1. Peter
2. Peter
1. hat
2. has
1. un
2. ap
1. denke
2. think
1. ich
2. I
1. gefähr
2. proximately
1. fünfzig
2. fifty
1. Hot
2. hot
1. dogs
2. dogs
1. gegessen.
2. eaten
1. intended: ‘Peter approximately ate 50 hotdogs, I think.’

The second contrast, that between (36) and (37), follows from the structure the alternative analysis assigns to approximative numerals, as shown in (39) for example (37a).

1. (39)

Since the adverb an die ‘up to’ and the numeral sechzig ‘sixty’ form separate constituents, the splitting expressions can appear in-between them. Importantly, this analysis also correctly predicts that focus particles, zum Beispiel ‘for example’, and parentheticals are fine after approximate modifiers that are clearly adverbs.10

1. (40)
1. a.
1. focus particles splitting up numerals
1. Er
2. he
1. hat
2. has
1. höchstens
2. at.most
1. nur
2. only
1. zehn
2. ten
1. Menschen
2. people
1. getötet.
2. killed
1. ‘He killed only at most ten people.’
1.
1. b.
1. zum Beispiel splitting up numerals
1. Peter
2. Peter
1. hat
2. has
1. ungefähr
2. approximately
1. zum
2. for
1. Beispiel
2. example
1. hundert
2. hundred
1. Frauen
2. women
1. geküsst.
2. kissed
1. ‘Peter kissed at most 100 women for example.’
1.
1. c.
1. parentheticals splitting up numerals
1. Peter
2. Peter
1. hat
2. has
1. ungefähr
2. approximately
1. denke
2. think
1. ich
2. I
1. hundert
2. hundred
1. Frauen
2. women
1. geküsst.
2. kissed
1. ‘Peter kissed approximately 100 women, I think.’

### 3.2 Case in nominal ellipsis

#### 3.2.1 Emergence of inflectional case marking under nominal ellipsis

The second argument against treating approximative numerals as PPs comes from case marking of numerals. In contrast to adjectives, numerals are not case marked when their NP complement contains an overtly realized noun (the subscript on the verb indicates the case it assigns to its object).

1. (41)
1. a.
1. Peter
2. Peter
1. trafACC
2. met
1. *
2.
1. schön
2. beautiful
1. /
2.
1. √schöne
2.   beautiful.ACC
1. Frauen.
2. women
1. ‘Peter met beautiful women.’
1.
1. b.
1. Peter
2. Peter
1. trafACC
2. met
1. √fünf
2.   five
1. /*
2.
1. fünfe
2. five.ACC
1. Frauen.
2. women
1. ‘Peter met five women.’
1. (42)
1. a.
1. Peter
2. Peter
1. begegneteDAT
2. met
1. *
2.
1. schön
2. beautiful
1. /
2.
1. √schönen
2.   beautiful.DAT
1. Frauen.
2. women
1. ‘Peter met beautiful women.’
1.
1. b.
1. Peter
2. Peter
1. begegneteDAT
2. met
1. √fünf
2.   five
1. /*
2.
1. fünfen
2. five.DAT
1. Frauen.
2. women
1. ‘Peter met five women.’

When the complement NP is elided, case marking on the numeral is optionally licensed.11

1. (43)
1. a.
1. Ich
2. I
1. trafACC
2. met
1. zehn
2. ten
1. Frauen,
2. women
1. aber
2. but
1. Peter
2. Peter
1. nur
2. only
1. fünfe _.
2. five.ACC
1. ‘I met ten women, but Peter only five.’
1.
1. b.
1. Ich
2. I
1. begegneteDAT
2. met
1. zehn
2. ten
1. Frauen,
2. women
1. aber
2. but
1. Peter
2. Peter
1. nur
2. only
1. fünfen _.
2. five.DAT
1. ‘I met ten women, but Peter only five.’

What is important for the discussion of the status of the approximative numeral is that case marking of the numeral under nominal ellipsis is unaffected by the presence of an approximative modifier. As (44) illustrates, the approximative modifier um die ‘around’ does not interfere with dative case marking on the numeral.

1. (44)
1. a.
1.
1. Ich
2. I
1. begegneteDAT
2. met
1. umACC
2. around
1. die
2. the
1. zehn
2. ten
1. Frauen,
2. women
1. aber
2. but
1. er
2. he
1. nur
2. only
1. um
2. around
1. die
2. the
1. fünfen _.
2. five.DAT
1.
1. b.
1. *
1. Ich
2. I
1. begegneteDAT
2. met
1. umACC
2. around
1. die
2. the
1. zehn
2. ten
1. Frauen,
2. women
1. aber
2. but
1. er
2. he
1. nur
2. only
1. um
2. around
1. die
2. the
1. fünfe _.
2. five.ACC
1. ‘I met around ten women, but he only around five.’

The reason this observation is important is that it points to the following generalization.

 (45) In nominal ellipsis, case marking on the numeral is determined by the verb.

This generalization is a problem for the analysis of approximative numerals as PPs. Consider the simplified structure in (46) for the numeral from (44a), where strike-through indicates ellipsis.

1. (46)

No matter how the PP is eventually combined with the NP, what is apparent is that the PP defines a separate case marking domain. So what the structure in (46) predicts is that if case marking appears on the numeral, then it is determined by the preposition. Since um ‘around’ assigns accusative case, the numeral should show up with accusative case under nominal ellipsis. But this is precisely not what happens, as (44b) shows. Instead, the case on the numeral is determined by the verb. This indicates quite strongly that the numeral is not part of a separate case domain and hence not part of a PP either. Importantly, the generalization in (45) is of course no problem for the analysis of the approximative numeral as an adverb, as shown in (47).

1. (47)

The reason that this structure is compatible with the generalization in (45) is that the presence of an adverb does not define a separate case marking domain since adverbs don’t assign case. The adverb will hence be invisible to whatever case marking demands the numeral is subject to. Moreover, as correctly predicted by this analysis, case marking is not affected by the presence of an approximative modifier that is clearly an adverb.

1. (48)
1. a.
1. Ich
2. I
1. trafACC
2. met
1. fast
2. nearly
1. zehn
2. ten
1. Frauen,
2. women
1. aber
2. but
1. er
2. he
1. nur
2. only
1. fast
2. nearly
1. fünfe _.
2. five.ACC
1. ‘I met nearly ten women, but he only nearly five.’
1.
1. b.
1. Ich
2. I
1. begegneteDAT
2. met
1. fast
2. nearly
1. zehn
2. ten
1. Frauen,
2. women
1. aber
2. but
1. er
2. he
1. nur
2. only
1. fast
2. nearly
1. fünfen _.
2. five.DAT
1. ‘I met nearly ten women, but he only nearly five.’

#### 3.2.2 Case marking vs. empty nouns

An anonymous reviewer points out that the argument just developped crucially hinges on the assumption that the suffixes -e and -en in (43), (44) and (48) are inflectional suffixes and hence directly belong to the numeral. However, there are alternative approaches such as those developed by Corver & van Koppen (2009; 2011) according to which such suffixes are not inflectional suffixes but exponents of empty nouns. If this line of reasoning is adopted for the data in (43), (44) and (48), then the argument loses its force. Since the empty noun is outside the c-command domain of the preposition, it is outside its case assignment domain, too, cf. (49).

1. (49)

But there are two arguments in favor of the view that the relevant suffixes are inflectional.

The first argument in favor of an analysis in terms of inflection is that numerals follow the inflectional paradigm of the determiner ein ‘a’ in German. The determiner ein ‘a’ follows one of the following three paradigms: strong, weak, and mixed.

1. (50)
1. a.
1. einerstrong
1. Einer
2. a.STRONG
1. hat
2. has
1. was
2. something
1. gesagt.
2. said
1. ‘Someone said something.’
1.
1. b.
1. eineweak
1. Der
2. the
1. eine
2. a.WEAK
1. Mann
2. man
1. hat
2. has
1. etwas
2. something
1. gesagt.
2. said
1. ‘The one man said something.’
1.
1. c.
1. einmixed
1. Ein
2. a.MIXED
1. schöner
2. handsome
1. Mann
2. man
1. hat
2. has
1. etwas
2. something
1. gesagt.
2. said
1. ‘A handsome man said something.’

The strong form is shown in (50a), which is used when ein ‘a’ is free standing. (50b) illustrates the weak form, which is used if ein ‘a’ follows a determiner with strong inflection. (50c) finally illustrates the mixed form, which is used if ein ‘a’ is used as determiner in the nominative case; in that case, the following adjective bears strong inflection. In case of nominal ellipsis, each of the three forms is licensed, depending on the position of ein ‘a’ and the amount of elided material.

1. (51)
1. a.
1. Mir
2. I.DAT
1. gefiel
2. liked
1. ein
2. a
1. schöner
2. handsome
1. Mann
2. man
1. und
2. and
1. ihr
2. she.DAT
1. gefiel
2. liked
1. auch
2. also
1. einer _.
2. a.STRONG
1. ‘I liked a handsome man and she also liked one.’
1.
1. b.
1. Mir
2. I.DAT
1. gefielen
2. liked
1. alle
2. all
1. Männer
2. men
1. aber
2. but
1. ihr
2. she.DAT
1. gefiel
2. liked
1. dieser
2. this
1. eine _.
2. a.WEAK
1. ‘I liked all men and she liked this one.’
1.
1. c.
1. Mir
2. I.DAT
1. gefiel
2. liked
1. ein
2. a
1. schöner
2. handsome
1. Mann,
2. man
1. aber
2. and
1. ihr
2. she.DAT
1. gefiel
2. liked
1. ein
2. a.MIXED
1. hässlicher _.
2. ugly
1. ‘I liked a handsome man but she liked an ugly one.’

Now compare the behavior of ein ‘a’ with numerals such as vier ‘four’.

1. (52)
1. a.
1. vierestrong
1. Viere
2. four.STRONG
1. haben
2. have
1. was
2. something
1. gesagt.
2. said
1. ‘Four people said something.’
1.
1. b.
1. vierweak
1. Die
2. the
1. vier
2. four.WEAK
1. Männer
2. men
1. haben
2. have
1. etwas
2. something
1. gesagt.
2. said
1. ‘The four men said something.’
1.
1. c.
1. viermixed
1. Vier
2. four.MIXED
1. schöne
2. handsome
1. Männer
2. men
1. haben
2. have
1. etwas
2. something
1. gesagt.
2. said
1. ‘Four handsome men said something.’
1. (53)
1. a.
1. Mir
2. I.DAT
1. gefielen
2. liked
1. drei
2. three
1. Männer,
2. men
1. aber
2. but
1. ihr
2. she.DAT
1. gefielen
2. liked
1. viere _.
2. four.STRONG
1. ‘I liked three men but she liked four.’
1.
1. b.
1. Mir
2. I.DAT
1. gefielen
2. liked
1. die
2. the
1. drei
2. three
1. Männer,
2. men
1. aber
2. but
1. ihr
2. she.DAT
1. gefielen
2. liked
1. die
2. the
1. vier _.
2. four.WEAK
1. ‘I liked the three men but she liked the four.’
1.
1. c.
1. Mir
2. I.DAT
1. gefielen
2. liked
1. drei
2. three
1. alte
2. old
1. Männer,
2. men
1. aber
2. but
1. ihr
2. she.DAT
1. gefielen
2. liked
1. vier
2. four.MIXED
1. junge _.
2. young
1. ‘I liked three old men but she liked four young ones.’

As the comparison between (50)/(51) and (52)/(53) makes clear, the strong, weak, and mixed forms of vier ‘four’ are used in the same contexts as the strong, weak, and mixed forms of ein ‘a’. The strong form is used when the numeral is freestanding (52a and 53a). The weak form is used after determiners with strong inflection (52b and 53b). And finally, the mixed form is used when the numeral is used as a determiner (52c and 53c). The only difference between numerals such as vier ‘four’ and ein ‘a’ is that the mixed and the weak form of numerals are syncretic. Importantly, that numerals follow an inflectional pattern is completely unexpected under the view that the endings are exponents of empty nouns, but it trivially follows from an analysis where they are inflectional suffixes.

The argument just developed only works if one accepts that the suffix appearing on freestanding ein ‘a’ in (50a) and (51a) is inflectional, that is, that einer ‘one’ has the structure in (54).

1. (54)

If one denies this and again follows Corver & van Koppen (2009; 2011), then possibly the suffix -er on einer ‘one’ is an exponent of an empty noun, too, so that (50a) and (51a) have the following structure.

1. (55)

Then the parallelism between ein ‘a’ and numerals such as vier ‘four’ shows nothing about inflection. Here the second argument comes in. If the examples in (50a) and (51a) really have the structure in (55), then one predicts that the suffix -er should attach to any possible host. For example, -er is also expected to appear on phrases in SpecDP, such as possessors. So the following structure is predicted to also be available.12

1. (56)

But this is not the case. Crucially, the suffix -er never attaches to prenominal possessors (cf. Roehrs 2006: 285).

1. (57)
1. Mir
2. I.DAT
1. gefällt
2. like
1. Stefans
2. Stefan’s
1. Rechner,
2. computer
1. aber
2. but
1. ihr
2. she.DAT
1. gefällt
2. liked
1. Guidos/**Guidoser
2. Guido’s
1. _ mehr.
2. more
1. ‘I like Stefan’s computer but she likes Guido’s computer more.’

The behavior of prenominal possessors is a problem for the view that -er is not inflectional because nothing excludes phrases as hosts. In fact, not only is not excluded, Corver & van Koppen make use of structures where the host is phrasal (Corver & van Koppen 2011: 383). But if -er is inflectional, the ungrammaticality of (57) is a trivial consequence of the fact that inflection is a property of noun-related heads only in German (nouns, determiners, adjectives, numerals) but never of phrases.13

In sum, the analysis of the suffixes in (50a) and (51a) as exponents of empty nouns instead of inflectional suffixes is hard to motivate for German.

### 3.3 Stacking

The third problem for the idea that approximative numerals are PPs comes from the observation that approximative numerals allow stacking of approximative modifiers. That is, two or more approximative modifiers can be attached to the numeral. This is illustrated in (58).

1. (58)
1. a.
1. Ich
2. I
1. füttere
2. feed
1. ihn
2. him
1. jeden
2. every
1. Tag
2. day
1. um
2. around
1. die
2. the
1. an
2. on
1. die
2. the
1. hundert
2. hundred
1. Gramm
2. gram
1. Rindfleisch.
2. beef
1. ‘I feed him every day with approximately up to 100g beef.’
1.
1. b.
1. Mein
2. my
1. Baby
2. baby
1. hatte
1. jeden
2. every
1. Tag
2. day
1. immer
2. always
1. an
2. on
1. die
2. the
1. um
2. around
1. die
2. the
1. vierzig
2. fourty
2. degrees
1. Fieber.
2. fever
1. ‘My baby had up to approximately 40°C fever every day.’

Since under Corver & Zwarts’ (2006) approach approximative modifiers are heads of PPs, stacking of approximative numerals has to involve multiple PPs. There are three strategies to implement this idea technically, and all three turn out to be unsatisfactory.

The first strategy is to assume that stacked approximative modifiers involve a recursive PP structure.

1. (59)

In (59), the lower PP is a complement to the determiner of the complement DP of the higher PP. The problem with this structure is that it is otherwise unattested in the grammar of German. There are no other instances of a structure in German where a determiner selects for a PP, casting doubt on the appropriateness of this structure. An anonymous reviewer points out that if viewed from an antisymmetry perspective (Kayne 1994), PP-modifiers necessarily instantiate such a structure. Consider (60), adopted from Kayne (2005: 52).

1. (60)

I agree on this, but (59) and (60) still differ in one crucial aspect: in (60), the SpecPP is obligatorily filled by the NP, whereas in (59), the SpecPP-position has to remain obligatorily empty. As shown in (61) and (62), raising vierzig ‘fourty’ to the specifier of the embedded PP, which is fully parallel to the raising of man in (60), results in ungrammaticality.

1. (61)
1. (62)
1. *
1. an
2. on
1. die
2. the
1. vierzig
2. fourty
1. um
2. around
1. die
2. the
1. intended: ‘up to around forty’

The second strategy is again to assume a recursive structure, but one where the inner PP is the complement to an empty N°.

1. (63)

Although PPs selected by N°s are attested in German, the precise configuration in (63) is not attested. There is no N° that is both empty and requires a PP-complement. But this is required to make (63) work. Otherwise approximative modifiers themselves are expected to function as numerals, contrary to fact, cf. (64).

1. (64)
1. a.
1. *
1. Peter
2. Peter
1. hat
2. has
1. an
2. on
1. die
2. the
1. Ø
2.
1. Männer
2. men
1. gesehen.
2. seen
1. *‘Peter saw up to men.’
1.
1. b.
1. *
1. Ich
2. I
1. habe
2. have
1. um
2. around
1. die
2. the
1. fünf
2. five
1. Männer
2. men
1. gesehen,
2. seen,
1. und
2. and
1. Peter
2. Peter
1. an
2. on
1. die
2. the
1. Ø
2.
1. Frauen.
2. women
1. intended: ‘I saw around five men, and Peter up to five women.’

Example (64b) is particularly telling because it shows that the relevant N° must not be empty, even when discourse given and hence available for ellipsis. An anonymous reviewer points out that partitive structures (Jackendoff 1977) instantiate structures where an empty N° requires a PP-complement.

1. (65)

I disagree that partitives provide independent support for the structure in (63). On the one hand, the empty noun position in partitives can, but need not, be empty, contrary to the empty noun position in (63). Witness the contrast between (66a) and (66b).

1. (66)
1. a.
1.
1. drei
2. three
1. Verdächtige
2. suspects
1. von
2. of
1. den
2. the
1. fünf
2. five
1. Verdächtigen
2. suspects
1. ‘three suspects out of the five suspects’
1.
1. b.
1. *
1. Wir
2. we
1. haben
2. have
1. an
2. on
1. die
2. the
1. vierzig
2. fourty
1. um
2. around
1. die
2. the
1. vierzig
2. fourty
1. Männer
2. men
1. gesehen.
2. seen
1. intended: ‘We saw up to approximately fourty men.’

On the other hand, there are serious problems with the idea that the empty N°-position in partitives is syntactically empty. Rather, the empty noun arguably results from the ellipsis of a lexical noun. Evidence for this comes from selectional restrictions. The quantifier element in partitives in German need not be a numeral, it can also be a container noun, similar to pseudo-partitives (a glass of water). Some container nouns are possible as a quantifying element only with a restricted set of nouns.

1. (67)
1. ein
2. a
1. Teller
2. plate
1. Suppe/*
2. soup
1. Brühe
2. broth
1. ‘a portion of soup/broth’

The contrast observed in (67) carries over to partitives.

1. (68)
1. Ich
2. I
1. hätte
1. gern
1. einen
2. a
1. Teller
2. plate
1. von
2. of
1. der
2. the
1. Suppe/*
2. soup
1. Brühe.
2. broth
1. ‘I’d like a portion of soup/broth.’

The contrast in (68) follows trivially under the ellipsis approach. The corresponding structures for (68) are provided in (69).

1. (69)
1. a.
1.
1. Ich
2. I
1. hätte
1. gern
1. einen
2. a
1. Teller
2. plate
1. Suppe
2. soup
1. von
2. of
1. der
2. the
1. Suppe.
2. soup
1. ‘I’d like a portion of soup/broth.’
1.
1. b.
1. *
1. Ich
2. I
1. hätte
1. gern
1. einen
2. a
1. Teller
2. plate
1. Brühe
2. broth
1. von
2. of
1. der
2. the
1. Brühe.
2. broth
1. intended: ‘I’d like a portion of broth.’

Since an elided copy of Suppe ‘soup’ and Brühe ‘broth’ is contained within the partitive expression, this noun has to satisfy the selectional restriction of the container noun Teller ‘plate’. But whereas the noun Suppe ‘soup’ is compatible with Teller ‘plate’, Brühe ‘broth’ is not (cf. 67).

The third strategy treats the higher PP as adjoined to the lower PP, which defines the real approximative numeral.

1. (70)

Even though this type of adjunction structure does not pose a general problem, the specific structure is again unattested. For there is no empty N° in German that only occurs in PPs that are adjoined to another PP. As shown in (71), if the empty N° appears in the lower PP, ungrammaticality results.

1. (71)
1. *
1. Peter
2. Peter
1. hat
2. has
1. an
2. on
1. die
2. the
1. fünf
2. five
1. um
2. around
1. die
2. the
1. Ø
2.
1. Männer
2. men
1. gesehen.
2. seen
1. intended: ‘Peter has seen up to approximately five men.’

An anonymous reviewer points out that empty nouns inside a PP that is adjoined to another PP are attested in path structures (Jackendoff 1990; Williams 1994).

1. (72)
1. [PP [PP
1. Von
2. from
1. meinem
2. my
1. Ø]
2.
1. [PP
2.
1. bis
2. until
1. zu
2. to
1. deinem
2. your
1. Haus]]
2. house
1. sind
2. are
1. es
2. it
1. nur
2. only
1. drei
2. three
1. Minuten.
2. minutes
1. ‘From my to your house takes only three minutes.’

But the two structures cannot be compared, for three reasons. First, the empty noun in path structures is not required, contrary to approximative numerals; witness the contrast in (73).

1. (73)
1. a.
1.
1. [PP [PP
1. Von
2. from
1. meinem
2. my
1. Haus]
2. house
1. [PP
2.
1. bis
2. until
1. zu
2. to
1. deinem
2. your
1. Haus]]
2. house
1. sind
2. are
1. es
2. it
1. nur
2. only
1. drei
2. three
1. Minuten.
2. minutes
1. ‘From my house to your house takes only three minutes.’
1.
1. b.
1. *
1. Wir
2. we
1. haben
2. have
1. an
2. on
1. die
2. the
1. vierzig
2. fourty
1. um
2. around
1. die
2. the
1. vierzig
2. fourty
1. Männer
2. men
1. gesehen.
2. seen
1. intended: ‘We saw up to approximately fourty men.’

Second, in path structures either of the two noun positions can be empty, contrary to approximative numerals. Compare (74) with (71).

1. (74)
1. [PP [PP
1. Von
2. from
1. meinem
2. until
1. Haus]
2. house
1. [PP
2.
1. bis
2. until
1. zu
2. to
1. deinem
2. your
1. Ø]]
2.
1. dauert
2. takes
1. es
2. it
1. nur
2. only
1. drei
2. three
1. Minuten.
2. minutes
1. ‘From my house to yours takes only three minutes.’

Third, in path structures both positions can remain empty, again contrary to approximative numerals, as the contrast in (75) shows.

1. (75)
1. a.
1. [PP [PP
1. Von
2. from
1. meinem
2. mine
1. Ø]
2.
1. [PP
2.
1. bis
2. until
1. zu
2. to
1. deinem
2. yours
1. Ø]]
2.
1. dauert
2. takes
1. es
2. it
1. nur
2. only
1. drei
2. three
1. Minuten.
2. minutes
1. (talking about houses) ‘From mine to yours takes only three minutes.’
1.
1. b.
1. *
1. Peter
2. Peter
1. hat
2. has
1. an
2. on
1. die
2. the
1. Ø
2.
1. um
2. around
1. die
2. the
1. Ø
2.
1. Männer
2. men
1. gesehen.
2. seen
1. intended: (talking about the quantity ‘40’) ‘Peter saw up to approximately 40 men.’

Strikingly, the analysis of approximative modifiers as adverbs adjoined to numerals runs into no problems. The examples in (58) with stacking simply involve two adjoined adverbs.

1. (76)
1. a.
1.
1. b.

There are three benefits of this multiple adjunction analysis. First, multiple modifiers are independently attested, for example in the domain of adjectival modifiers (the beautiful young woman). Second, this analysis correctly captures that the different orders of the two modifiers an die ‘up to’ and um die ‘around’ correspond to two different readings, due to their different c-command relations. The two examples from (58) are repeated in (77) for convenience.

1. (77)
1. a.
1. Ich
2. I
1. füttere
2. feed
1. ihn
2. him
1. jeden
2. every
1. Tag
2. day
1. um
2. around
1. die
2. the
1. an
2. on
1. die
2. the
1. hundert
2. hundred
1. Gramm
2. gram
1. Rindfleisch.
2. beef
1. ‘I feed him every day with approximately up to 100g beef.’
1.
1. b.
1. Mein
2. my
1. Baby
2. baby
1. hatte
1. jeden
2. every
1. Tag
2. day
1. immer
2. always
1. an
2. on
1. die
2. the
1. um
2. around
1. die
2. the
1. vierzig
2. fourty
2. degrees
1. Fieber.
2. fever
1. ‘My baby had up to approximately 40°C fever every day.’

The reading of (77a) is that the amount of beef is around an upper limit of 100 gram. The reading of (77b) is that the amount of fever goes up to an amont of approximately 40°C. Now these two readings differ. The first reading says that the amount of beef is always around 100 gram but never much lower or much higher than that. For example, 80 gram is not within the range of possible amounts. Under the second reading, the maximum amount of fever is also around 40°C or a bit higher (say, 40.2°C). What is possible under the second reading however is that the amount of fever is much lower than 40°C, say 38°C. All that is required is that the relevant amount still satisfies the definition of fever (that is, 30°C are excluded). In a nutshell, the first reading defines both an upper and a lower limit, the second reading only a higher limit.

The third (although not exclusive)14 benefit of this analysis is that approximative modifiers that clearly are adverbs can be stacked with aproximative modifiers that look like prepositions.

1. (78)
1. a.
1. Ich
2. I
1. füttere
2. feed
1. ihn
2. him
1. jeden
2. every
1. Tag
2. day
1. ungefähr
2. approximately
1. an
2. on
1. die
2. the
1. hundert
2. hundred
1. Gramm
2. gram
1. Rindfleisch.
2. beef
1. ‘I feed him every day with approximately up to 100g beef.’
1.
1. b.
1. Mein
2. my
1. Baby
2. baby
1. hatte
1. jeden
2. every
1. Tag
2. day
1. immer
2. always
1. an
2. on
1. die
2. the
1. ungefähr
2. approximately
1. vierzig
2. fourty
2. degrees
1. Fieber.
2. fever
1. ‘My baby had up to approximately 40°C fever every day.’

Before turning to the next section, let me add that the problems posed by stacking are not specific to the idea that approximative numerals are PPs. They carry over to any approach that treats the relation between the approximative modifier and the numeral it belongs to as one of complementation. Consider for concreteness the idea that approximative numerals in German are structurally parallel to approximative numerals in French (thanks to an anonymous reviewer for raising this possibility), illustrated in (79).

 (79) quinzaine ‘around fifteen’ = quinze ‘fifteen’ + -aine ‘around’ vingtaine ‘around twenty’ = vingt ‘twenty’ + -aine ‘around’ centaine ‘around one hundred’ = cent ‘hundred’ + -aine ‘around’

According to Kayne (2005: 15–18; 2010: Chapter 3), the suffix -aine occupies the head position of a functional projection and attracts the numeral to its specifier. Transposing this idea to approximative numerals in German, one could suggest that approximative modifiers occupy the same head position as -aine, but given their non-affixal status do not trigger movement of their complement nominal to their specifier position. Alternatively, one could suggest that the relevant head position is empty and approximative modifiers are base-generated in the specifier position, thereby blocking movement of the numeral to that position. The two analyses are shown in (80).

1. (80)
1. a.
1.
1. b.

However, the two structures are as inadequate as the previous proposals when it comes to stacking. The first structure, (80a), allows the following structure to be assigned to stacked approximative modifiers.

1. (81)

The problems with this structure are basically identical to the ones the structure (70) poses. Only ad hoc conditions can guarantee that, first, both NumP’s must not be filled simultaneously (cf. 73b), that, second, both positions cannot be empty simultaneously (cf. 75b), and that, third, only NumP2 but not NumP1 can remain empty (cf. 71). No such ad hoc conditions are required under the analysis that approximative numerals are adverbs.

The two structures in (80) also allow the following structure to be assigned to stacked approximative modifiers.

1. (82)

Although this structure doesn’t face the problems the structure in (81) faces, it faces complications when it comes to issues of selection. In order to capture the very fact that stacking is possible, one has to assume that approximative heads select either NumP’s or other phrases containing an approximative head. No such double selection is required under the view that approximative modifiers are adverbs and hence adjoin. To solve this problem, two solutions suggest themselves. First, one could assume that the relevant functional heads for approximative modifiers are always present but can remain inactive (by not filling the specifier position, for example). This view, however, faces the problem that the order of approximative modifiers is simply not fixed (cf. 58), whereas the order of functional projections is fixed. Crucially, the relevant ingredient to derive different orders, namely movement, is unavailable in this case because the specifier positions are already filled. If one allows multiple specifiers, this problem disappears but then a new problem pops up: the relevant movement step must never move NumP alone, for otherwise the numeral is expected to occur between approximative modifiers, contrary to fact (cf. 62b). Second, an anonymous reviewer suggests that the selectional relation between the functional head and the numeral is one of s-selection, that is, all that X2° in (82) selects is some phrase containing a numeral. Then the intervening X1P is invisible, “as in the case where a verb s-selects a particular property of its object noun (say, animacy).” The problem I see with this approach is that it massively overgenerates. It basically predicts that any functional projection can intervene between X2° and the numeral in (82). But this is not the case: neither can a DP intervene (*an die die/diese zwanzig ‘up to the/these twenty’) nor a PP (*an die mit zwanzig ‘up to with twenty’). So eventually this structure too requires ad hoc assumption to capture the stacking behavior of approximative numerals. The alternative analysis, however, which treats them as adverbs does not only not require ad hoc constraints to capture stacking, it in fact predicts stacking.

## 4 Approximative modifiers do neither contain a determiner nor a preposition

I have so far argued that approximative numerals containing approximative modifiers that look like prepositions never behave like PPs but always pattern with numerals modified by an adverb. In this section, I will investigate the internal make-up of approximative modifiers that look like prepositions and argue that despite appearance, they do neither contain a determiner nor a preposition.

### 4.1 The inertness of the determiner

Corver & Zwarts (2006: 823, fn. 11) mention the following contrast, noted by Gertjan Postma.15

1. (83)
1. a.
1. *
1. de
2. the.COM
1. /
2.
1. √het
2.   the.NEUT
1. miljoen
2. million.NEUT
1. ‘the million’
1.
1. b.
1.
1. rond
2. around
1. √de
2.   the.COM
1. /*
2.
1. het
2. the.NEUT
1. miljoen
2. million.NEUT
1. mensen
2. people
1. ‘around one million people’

The problem this contrast poses is that the numeral miljoen ‘million’ is lexically specified for neuter gender (cf. 83a) but that this gender specification is overwritten to common gender when appearing as an approximative numeral (cf. 83b). Corver & Zwarts (2006: 823, fn. 11) acknowledge the problem and suggest that “it could be that de is chosen under the influence of the plural noun mensen”. According to this idea, the definite article in the approximative numeral in (83b) agrees with the plural noun mensen ‘people.’ Since the plural form of the definite article is also de ‘the’, the occurrence of de ‘the’ is captured. This idea is sketched in (84).

1. (84)

What I want to argue is that this solution is not viable and the contrast in (83) is part of a much bigger problem, namely that the determiner in approximative numerals is inert and hence syntactically invisible. There are two arguments that the alleged determiner is not a determiner.

The first argument is that the solution offered by Corver & Zwarts (2006) for the contrast in (83) cannot be correct. For there are cases where there is no possible source that could possibly determine the shape of the determiner. Consider the following contrasts from German.16

1. (85)
1. a.
1.
1. Ich
2. I
1. nehme
2. take
1. täglich
2. daily
1. an
2. on
1. die
2. the
1. ein
2. one
1. Gramm
2. gram
1. Magnesium
2. magnesium
1. zu
2. to
1. mir.
2. me
1. ‘I ingest up to 1g magnesium each day.’
1.
1. b.
1. *
1. der
2. the.MASC
1. /*
2.
1. die
2. the.FEM
1. /
2.
1. √das
2.   the.NEUT
1. Gramm
2. gram
1.
1. b’.
1. *
1. der
2. the.MASC
1. /*
2.
1. die
2. the.FEM
1. /
2.
1. √das
2.   the.NEUT
1. Magnesium
2. magnesium
1.
1. c.
1.
1. die
2. the.PL
1. *
2.
1. Magnesium
2. magnesium
1. /*
2.
1. Magnesiums
2. magnesiums
1. /*
2.
1. Magnesia
2. magnesia
1. /*
2.
1. Magnesien
2. magnesia
1. (86)
1. a.
1.
1. Plank (2004: ex. 32b)
1. Manche
2. some
1. von
2. of
1. ihnen
2. them
1. können
2. can
1. um
2. around
1. die
2. the
1. ein
2. one
1. Pfund
2. pound
1. heben.
2. lift
1. ‘Some of them are able to lift around a pound.’
1.
1. b.
1. *
1. der
2. the.MASC
1. /*
2.
1. die
2. the.FEM
1. /
2.
1. √das
2.   the.NEUT
1. Pfund
2. pound
1.
1. c.
1.
1. die
2. the.PL
1. *
2.
1. *Pfund
2. pound.SG
1. /
2.
1. √Pfunde
2.   pound.PL

The a-examples illustrate two grammatical cases of an approximative numeral containing the approximative modifiers an die ‘up to.’ The b-examples show that the alleged determiner die ‘the’ cannot be the singular feminine form of the definite article because neither Gramm ‘gram’ nor Magnesium ‘magnesium’ in (85), nor Pfund ‘pound’ in (86) is feminine. And the c-examples also show that die ‘the’ cannot be the plural form of the definite article either because none of the three nouns is plural. Moreover, as (85c) shows, Magnesium ‘magnesium’ in German is a singulare tantum and hence doesn’t even possess a plural form. So bascially there is simply no noun in (85) and (86) that could specify the morphological shape of the alleged determiner die ‘the’ within the approximative numeral an die ‘up to’. This casts doubt on the overall idea of Corver & Zwarts’ (2006) proposal that one is dealing with a regular determiner in approximative qualifiers such as rond de ‘around’ or an die ‘up to.’

An anonymous reviewer suggests that die ‘the’ alternatively forms a complex numeral with ein ‘one’ as shown in (87).

 (87) an [die ein] Gramm/ Pfund

The shape of the determiner then follows trivially from the inherent gender feature of the numeral ein ‘one’: numerals in German all bear feminine gender, so die ‘the’ would agree with ein ‘one’.

 (88) an [diefem einfem] Gramm/ Pfund

The problem with this idea is that an die ‘up to’ also occurs in contexts where a numerical expression is present that does not contain a numeral and hence no source for the gender feature on die ‘the’. What I have in mind are elements such as zig ‘umpteen’ or etlich ‘many.’ These elements are simplex approximative numerals, that is, elements that inherently specify an approximate value but disallow an accompanying numeral.

1. (89)
1. Peter
2. Peter
1. hat
2. has
1. zig/etliche
2. umpteen
1. (*zwanzig)
2.   twenty
1. Frauen
2. women
1. gehabt.
1. ‘Peter had umpteen (*hundred) women.’

To the extent that approximative modifiers like an die ‘up to’ can combine with such expressions, we see that it is still die ‘the’ that shows up.

1. (90)
1. ?
1. Peter
2. Peter
1. hat
2. has
1. an
2. on
1. die
2. the
1. etliche
2. umpteen
1. Frauen
2. women
1. gehabt.
1. ‘Peter had up to umpteen women.’

In this example, there is no numeral that could determine the shape of die ‘the’, yet the example is possible, although a bit odd. The oddity of (90) cannot be explained by the absence of an accompanying numeral for the determiner. Examples with bona fide adverbs, which do not contain a determiner, are equally odd when modifying simplex approximative numerals.

1. (91)
1. ?
1. Peter
2. Peter
1. hat
2. has
1. fast
2. nearly
1. etliche
2. umpteen
1. Frauen
2. women
1. gehabt.
1. ‘Peter had nearly umpteen women.’

The second argument against Corver & Zwarts’ (2006) analysis of die ‘the’ in an die ‘up to’ as a regular determiner comes from the observation that there are numeral expressions that under Corver & Zwarts’ (2006) view contain two adjacent articles, as shown in (92).

1. (92)
1. Peter
2. Peter
1. hat
2. has
1. an
2. on
1. die
2. the
1. eine
2. one
1. Million
2. million
1. Frauen
2. women
1. geküsst.
2. kissed
1. ‘Peter kissed up to one million women.’

In (92), there are two determiners, die ‘the’ and eine ‘a.’ That eine is really a determiner and not the homophonouns numeral eine ‘a’ is suggested by the fact that eine ‘a’ in (92) can be reduced to ‘ne, which option is only available for determiners but never for numerals.17

1. (93)
1. a.
1. Peter
2. Peter
1. hat
2. has
1. ‘ne
2. one
1. Million
2. million
1. Frauen
2. women
1. geküsst.
2. kissed
1. ‘Peter kissed one million women.’
1.
1. b.
1. Peter
2. Peter
1. hat
2. has
1. ‘ne
2. one
1. Frau
2. woman
1. geküsst.
2. kissed
1. ‘Peter kissed √a/*one woman.’

Crucially, this reduction is also possible when the numeral eine Million ‘one million’ is preceded by an approximative modifier.

1. (94)
1. Peter
2. Peter
1. hat
2. has
1. ungefähr
2. approximately
1. /
2.
1. um
2. around
1. die
2. the
1. /
2.
1. bis
2. until
1. zu
2. to
1. ‘ne
2. one
1. Million
2. million
1. Frauen
2. women
1. geküsst.
2. kissed
1. ‘Peter kissed approximately/up to one million women.’

According to Corver & Zwarts’ (2006) proposal, the structure for (92) then has to be the one in (95).18

1. (95)

The problem with this structure is that it is otherwise not attested: there are no other structures containing two articles that also differ in their definiteness value. The approach that treats approximative modifiers as adverbs runs into no difficulties when faced with the data from this section. The structures for the approximative numerals from (83b), (85a), (86a), and (92) are provided in (96).19

1. (96)
1. a.
1.
1. b.
1.
1. c.
1.
1. d.

Under this approach, the alleged determiner is not a determiner but part of an adverb, so the alleged determiner is correctly predicted not to behave as a determiner.

### 4.2 The inertness of the preposition I

The first piece of evidence that approximative modifiers that look like prepositions do not contain regular prepositions comes from the phonological behavior of the two elements gegen and bis zu in the dialect of the Berlin-Brandenburg area. In Standard German, the two elements are used as prepositions, as shown in (97).

1. (97)
1. a.
1. Peter kämpft gegen Drachen.
2. ‘Peter fights against dragons.’
1.
1. b.
1. Peter
2. Peter
1. läuft
2. runs
1. bis
2. until
1. zu
2. to
1. Marias
2. Maria’s
1. Haus.
2. house
1. ‘Peter runs until Maria’s house.’

In the Berlin-Brandenburg dialect, the two elements are used as prepositions, too, but undergo phonological changes: the initial [g] of gegen is lenited to [j], and the affricate [ts] represented by {z} of zu is changed to [s].

1. (98)
1. a.
1. Peter kämpft [j]egen Drachen.
2. ‘Peter fights against dragons.’
1.
1. b.
1. Peter
2. Peter
1. läuft
2. runs
1. bis
2. until
1. [s]u
2. to
1. Marias
2. Maria’s
1. Haus.
2. house
1. ‘Peter runs until Maria’s house.’

Both gegen and bis zu are also used as approximative modifiers in the standard language.

1. (99)
1. a.
1. Peter
2. Peter
1. hat
2. has
1. gegen
2. against
1. sechzig
2. sixty
1. Hotdogs
2. hot dogs
1. gegessen.
2. eaten
1. ‘Peter ate up to sixty hot dogs.’
1.
1. b.
1. Peter
2. Peter
1. hat
2. has
1. bis
2. until
1. zu
2. to
1. sechzig
2. sixty
1. Hotdogs
2. hot dogs
1. gegessen.
2. eaten
1. ‘Peter ate up to sixty hot dogs.’

The same basically also holds for the Berlin-Brandenburg dialect, with one important difference. When used as approximative modifiers, gegen and bis zu no longer undergo the phonological changes illustrated in (98).

1. (100)
1. a.
1. Peter
2. Peter
1. hat
2. has
1. √[g]/*[j]egen
2.   against
1. sechzig
2. sixty
1. Hot
2. hot
1. dogs
2. dogs
1. gegessen.
2. eaten
1. ‘Peter ate up to sixty hot dogs.’
1.
1. b.
1. Peter
2. Peter
1. hat
2. has
1. bis
2. until
1. √[ts]/*[s]u
2.   to
1. sechzig
2. sixty
1. Hot
2. hot
1. dogs
2. dogs
1. gegessen.
2. eaten
1. ‘Peter ate up to sixty hot dogs.’

This state of affairs is again unexpected for the approach according to which approximative modifiers are prepositions. For whatever phonological process affects the preposition should likewise affect the approximative modifier because the modifier simply is this preposition. So this view provides no basis for an analysis of the contrast between (98) and (100).

The alternative view that approximative modifiers are adverbs does offer an analysis. As for gegen, even though the lenition of [g] to [j] affects many [g]-initial words in the Berlin-Brandenburg dialect, it nevertheless does not affect all words. Witness the contrasts in (101), with the standard version in (101a), and their dialectal variants in (101b).

 (101) a. ganz b. √[j]anz ‘totally’ gaffen *[j]affen ‘to stare’ gib √[j]ib ‘give!’ Gicht *[j]icht ‘arthritis’ Gold √[j]old ‘gold’ Gorilla *[j]orilla ‘gorilla’

These contrasts show that not every syllable-initial [g] is lenited to [j]; rather, it is a lexical property. Since the alternative analysis analyzes the preposition gegen as a word different from the approximative modifier gegen, the contrast between (98a) and (100a) is easily captured: the preposition undergoes lenition from [g] to [j], the approximative modifier does not.

Regarding bis zu, the change from [ts] to [s] only affects word-initial [ts].

 (102) a. Razzia b. *Ra[s]ia ‘razzia’ schätzen *schä[s]en ‘to estimate’ Zahl √[s]ahl ‘number’ bezahlen *be[s]ahlen ‘to pay’ ziehen √[s]iehen ‘to pull’ Erziehung *Er[s]iehung ‘education’

The first two examples show that morpheme internal [ts] is never affected by the change. The last four examples are important because they show that the change affects only word initial [ts] but not morpheme-initial [ts]. This is a problem for the approach treating approximative qualifiers as prepositions because bis zu consists of two words. Whereas the preposition zu ‘to’ marks the direction, the preposition bis ‘until’ indicates completion, cf. (103).

1. (103)
1. a.
1. Peter geht zu der Tür.
2. ‘Peter goes to the door.’ (but maybe Peter never reaches the door)
1.
1. b.
1. Peter
2. Peter
1. geht
2. goes
1. bis
2. until
1. zu
2. to
1. der
2. the
1. Tür.
2. door.
1. ‘Peter goes until the door.’ (Peter necessarily reached the door)

bis ‘until’ also combines with directional adverbs.20

1. (104)
1. Peter geht bis dorthin.
2. ‘Peter goes until there.’

Thus bis ‘until’ takes directional XPs as its complement, irrespective of their category, as shown in (105).

1. (105)

The corresponding structures for (103b) and (104) are provided in (106).

1. (106)
1. a.
1.
1. b.

Now if bis zu as used in (103b) were the same bis zu that is used as an approximative modifier in (99b), then the preposition zu ‘to’ is a separate word. If so, the zu in the approximative modifier is expected to undergo the change from [ts] to [s], contrary to fact. However, under the alternative analysis, bis zu when used as an adverbial modifier is an adverb and has the following structure.

1. (107)

According to this structure, zu is not word initial. Since, as shown in (102), the change from [ts] to [s] only affects word initial [ts], the non-change from [ts] to [s] is captured.

Two anonymous reviewers suggest an alternative for the different behavior of gegen and bis zu in the Berlin-Brandenburg dialect. As is well-known, German possesses fused versions of preposition and determiner, both of the contraction-type, where the preposition is fused with an article (van Riemsdijk 1998), and of the R-pronoun type (van Riemsdijk 1978), where the preposition is fused with a pronoun.

1. (108)
1. a.
1. für
2. for
1. +
2.
1. das
2. the
1.
1. fürs
2. for.the
1. ‘for the’
1.
1.
1. in
2. in
1. +
2.
1. das
2. the
1.
1. ins
2. in.the
1. ‘for the’
1.
1.
1. mit
2. with
1. +
2.
1. dem
2. the
1.
1. mitm (substandard)
2. with.the
1. ‘with the’
1.
1. b.
1. mit
2. with
1. +
2.
1. es
2. it
1.
1. damit
2. with.it
1. ‘with it’
1.
1.
1. für
2. for
1. +
2.
1. es
2. it
1.
1. dafür
2. for.it
1. ‘for it’

The relevant incorporation operation between P° and D° can affect the shape of the preposition. In Afrikaans, for example, the prepositions met ‘with’, tot ‘to’, and vir ‘for’ have distinct forms when they are fused with dat ‘it’ in the formation of R-pronouns (Donaldson 1993: 345–6).

1. (109)
1. met
2. with
1. +
2.
1. dat
2. it
1.
1. daarmee/*daarmet
2. with.it
1. ‘with it’
1.
1. tot
2. to
1. +
2.
1. dat
2. it
1.
1. daartoe/*daartot
2. to.it
1. ‘to it’
1.
1. vir
2. for
1. +
2.
1. dat
2. it
1.
1. daarvoor/*daarvir
2. for.it
1. ‘for it’

Combining these two observations, the alternative analysis that suggests itself is that preposition and determiner obligatorily fuse in approximative numerals. A first result of this is that nothing can intervene between the preposition and the determiner, thereby neatly capturing the data from section 3.1. The second result is that the preposition is blocked from undergoing whatever phonological change it normally can undergo. So the absence of the lenition of [g] to [j] in gegen is the consequence of fusing gegen with an empty D°. Similarly, zu cannot be changed to su because it fuses with bis. Although attractive, this analysis cannot be correct. It crucially relies on the assumption that the preposition and the determiner can fuse in approximative modifiers. But this is in fact impossible. In contrast to Standard German, where die ‘the’ never fuses with prepositions (van Riemsdijk 1998: 653), it does so in the Berlin-Brandenburg dialect.

1. (110)
1. a.
1. Ich
2. I
1. denk’
2. think
1. jeden
2. every
1. Tag
2. day
1. an’e
2. on.the
1. Maria.
2. Maria
1. [an’e = an die]
2.
1. ‘I think of Maria every day.’
1.
1. b.
1. Ich
2. I
1. denk’
2. think
1. jeden
2. every
1. Tag
2. day
1. an’e
2. on.the
1. Eltern.
2. parents
1. [an’e = an die]
2.
1. ‘I think of the parents every day.’
1.
1. c.
1. Ich
2. I
1. lauf’
2. walk
1. um’e
2. around.the
1. Ecke.
2. corner
1. [um’e = um die]
2.
1. ‘I walk around the corner.’

Importantly, die ‘the’ never fuses with um ‘around or an ‘on’ in approximative modifiers.

1. (111)
1. a.
1. *
1. Peter
2. Peter
1. küsst
2. kisses
1. an’e
2. on.the
1. hundert
2. hundred
1. Frauen.
2. women
1. intended: ‘Peter kisses up to hundred women.’
1.
1. b.
1. *
1. Peter
2. Peter
1. küsst
2. kisses
1. um’e
2. around.the
1. hundert
2. hundred
1. Frauen.
2. women
1. intended: ‘Peter kisses approximately hundred women.’

Since fusion is not independently motivated for approximative modifiers to begin with, fusion cannot be responsible for the contrasts observed in (98) and (100).

### 4.3 The inertness of the preposition II

The second piece of evidence against the idea that approximative modifiers that look like prepositions contain a preposition comes from the behavior of um. As a local preposition, it is usually extended to a circumposition.

1. (112)
1. Peter
2. Peter
1. läuft
2. walks
1. um
2. around
1. das
2. the
1. Haus
2. house
1. herum.
2. around
1. ‘Peter walks around the house.’

At first appearance, this looks like a form of doubling (van Riemsdijk 1990; 1998; Brandner 2008) illustrated in (113) and hence not like a circumposition.

1. (113)
1. Peter
2. Peter
1. läuft
2. walks
1. auf
2. up
1. den
2. the
1. Berg
2. mountain
1. herauf.
2. up
1. ‘Peter walks up the mountain.’

But there are two arguments that um … herum is a circumposition and cannot be subsumed under doubling. First, herum in (112) does not indicate movement, in contrast to the doubled prepositions. This can be seen in (114), where um … herum occurs in a stative context.

1. (114)
1. Maria
2. Maria
1. hat
2. has
1. die
2. the
1. Kette
2. necklace
1. um
2. around
1. den
2. the
1. Hals
2. neck
1. herum.
2. around
1. ‘Maria wears the necklace around the neck.’

Second, in contrast to doubled prepositions, the right member herum of um … herum cannot be separated from the rest of the PP.

1. (115)
1. a.
1. dass
2. that
1. Peter
2. Peter
1. auf
2. up
1. den
2. the
1. Berg
2. mountain
1. hat
2. has
1. herauf
2. up
1. laufen
2. walk
1. wollen
2. want
1. ‘that Peter wanted to walk up the hill’
1.
1. b.
1. *
1. dass
2. that
1. Maria
2. Peter
1. die
2. the
1. Kette
2. necklace
1. um
2. around
1. den
2. the
1. Hals
2. neck
1. hat
2. has
1. herum
2. around
1. haben
2. have
1. wollen
2. want
1. intended: ‘that Maria wanted to wear the necklace around the neck’

Now if the element um when used in the approximative modifier um die ‘around’ is simply the local preposition um ‘around’, then it should be possible to replace um in the approximative modifier by um … herum. But this is not possible: herum can neither appear after the numeral nor after the DP.

1. (116)
1. Peter
2. Peter
1. hat
2. has
1. um
2. around
1. die
2. the
1. sechzig
2. sixty
1. <*
2.
1. herum
2. around
1. >
2.
1. Hotdogs
2. hot dogs
1. <*
2.
1. herum
2. around
1. >
2.
1. gegessen.
2. eaten
1. ‘Peter ate approximately sixty hot dogs.

The view according to which approximative modifiers that look like prepositions gives us no clue as to why there is a contrast between (112) and (116). The alternative analysis treating such modifiers as adverbs does capture the contrast because um in um die ‘up to’ is not a preposition and hence not expected to undergo whatever change the real preposition um ‘around’ undergoes.

## 5 Approximative modifiers as adverbs

The data presented in sections 3 and 4 have shown that approximative modifiers that look like prepositions such as an die ‘up to’, um die ‘around’, bis zu ‘up to’, and gegen ‘around’ do not behave in any respect like PPs. Rather, they show the behavior of approximative modifiers that are adverbs like ungefähr ‘approximately’ and fast ‘nearly.’ The conclusion to draw from this pattern is that approximative modifiers are always adverbs, even if on the surface they look like PPs. The structure for the approximative modifiers illustrated in (117) is given in (118).

1. (117)
1. Peter
2. Peter
1. hat
2. has
1. um
2. around
1. die
2. the
1. /
2.
1. an
2. on
1. die
2. the
1. /
2.
1. gegen
2. against
1. /
2.
1. ungefähr
2. around
1. /
2.
1. fast
2. nearly
1. 60
2. 60
1. Hot
2. hot
1. dogs
2. dogs
1. gegessen.
2. eaten
1. ‘Peter ate approximately/up to/up to/approximately/nearly sixty hot dogs.
1. (118)

So what I ultimately claim is the following.

 (119) In German, approximative modifiers that look like prepositions (um die, an die, bis zu etc.) constitute single lexemes that lack internal structure.

Ignoring the clash with orthographic convention,21 this analysis apparently faces three problems. First, it seems to postulate a completely novel class of adverbs, namely one where an adverb has the surface form of a preposition followed by a determiner. Second, the analysis doesn’t capture that the approximative reading of approximative modifiers that look like prepositions is related to the local interpretation of the preposition they contain. And third, it doesn’t capture that adverbs proper that function as approximative modifiers like ungefähr ‘approximately’ have a much freer distribution than approximative modifiers that look like prepositions. I will discuss each problem in turn and argue that these problems are only apparent.

### 5.1 [P + D] adverbs

The first problem the analysis of approximative modifiers as adverbs faces is that it requires the postulation of a class of adverbs otherwise unattested, namely a class of adverbs that have the surface form ‘preposition + determiner’, which class one anonymous reviewer calls “unusual.” But this problem is not real because similar adverbs outside the domain of approximative modifiers are well-attested in German, cf. (120).

 (120) trotzdem ‘nevertheless’ ← trotz ‘despite’ + demDAT ‘that’ unterdessen ‘meanwhile’ ← unter ‘under’ + dessenGEN ‘that’ überdies ‘furthermore’ ← über ‘over’ + diesACC ‘that’

That these three elements are adverbs and not PPs composed of the preposition plus a determiner is suggested by their morphological and semantic properties.22 As for the morphological properties, the preposition trotz ‘despite’ selects genitive case in present-day German and not dative case. Similarly, the preposition unter ‘under’ is only compatible dative or accusative case (depending on its use as a local or directional preposition) but never with genitive case. Lastly, the form of the demonstrative in überdies ‘furthermore’ is the archaic short neuter form dies ‘this’, which in modern German has been replaced by the long form dieses ‘this.’ Regarding their semantics, unter and über do not have the relevant meaning when used as prepositions. That is, unter when used as a preposition never means ‘during’ nor does über when used as a preposition mean ‘in addition to.’ Therefore, analyzing the elements in (120) as PPs requires idiosyncratic case assignment properties for these PPs only as well as a non-compositional interpretation for unterdessen ‘meanwhile’ and überdies ‘furthermore’. If one analyzes these elements as adverbs, these problems disappear. As no case assignment is invoked, no idiosyncratic case assignment rules are required. And a non-compositional interpretation for lexemes is standard. So adverbs having the surface form of a preposition followed by a determiner do exist in German outside the approximation domain.

Related to this problem, but partly distinct from it, is Corver & Zwarts’ (2006: 823) observation “that adverbs that fulfill the same role as (approximative) prepositions are never accompanied by an article”, illustrated in (121).

1. (121)
1. Er
2. EXPL
1. waren
2. were
1. ongeveer/
2. around
1. hoogstens
2. at most
1. (*de)
2.     the
1. twintig
2. twenty
1. deelnemers.
2. participants
1. ‘There were approximately/at most twenty participants.’

Based on this distribution, Corver & Zwarts (2006: 823) conclude that “the article can be taken as indicating that the numeral functions as the argument of the preposition”. Although I disagree with this conclusion for the reasons laid out in sections 3 and 4,23 the problem nevertheless remains. That is, why is it the case that one never finds adverbs that have the surface form ‘adverb + determiner’ (be it inside or outside the domain of approximation)? The answer to this question in my view is ultimately a diachronic one. As Plank (2004) shows, approximative modifiers that look like prepositions in German did in fact start out as PPs that only recently were reanalyzed as DPs. The relevant change for German is illustrated in (122).

 (122) a. → b.

The reason that approximative adverbs (or adverbs generally) never co-occur with an article is that adverbs never take complements. Therefore, they could never possibly instantiate a structure similar to the one in (122a) and hence never undergo the structural change to (122b). But this change is required to arrive at a structure with an adverb of the surface form ‘adverb + determiner’. Instead, approximative adverbs would directly attach to the numeral.24

### 5.2 Local meaning

The second problem for the view that approximative modifiers that look like prepositions are adverbs is that it doesn’t capture the semantic relationship between the meaning of the modifier and that of the local preposition. For concreteness, consider the approximative modifier über ‘above.’ The local interpretation of the homophonous preposition über is that it defines a region where the complement über takes is at the lower border of that region. When the resulting PP is used as a predicate, the subject is then located inside that region. Being above the clouds means that one is a region where the clouds define lower border. Now as Corver & Zwarts (2006: 824–825) observe, when über is used as an approximative modifier, its meaning is basically identical: über selects a region on the one-dimensional space of natural numbers such that the number über combines with is at the lower border.

In fact, the analysis that treats approximative modifiers such as über as adverbs cannot establish a connection between the meaning of the approximative modifier and that of the homophonous preposition, at least not a synchronic one. But there is of course a diachronic connection. If the change sketched at the end of the previous section 5.1 is on the right track, then the approximative modifier über diachronically results from a re-analysis of a PP with über as its head. The approximative meaning of the preposition was then transferred to the adverb resulting from the re-analysis sketched in (122). So the reason that the meaning of über when used as an approximative modifier resembles the meaning of über when used as a preposition is not that they are synchronically related to each other but that the approximative adverb über is diachronically related to a PP-structure where über is the head of the PP. There are two arguments in favor of a diachronic instead of a synchronic connection.

First, if it is their local meaning that allows prepositions to be used as approximative modifiers, then one fails to account for the curious fact that only a small subset of the many local prepositions can be used as approximative modifiers. In German, only seven local prepositions are used as approximative modifiers: an ‘on’, bis zu ‘up to’, gegen ‘against’, über ‘above’, um ‘around’, unter ‘below’, and nahezu ‘nearly.’ Needless to say that out of those that cannot be used, many are excluded because they are incompatible with the one-dimensional space of natural numbers (for example abseits ‘apart from’, außerhalb ‘outside of’, or durch ‘through’). But there are many others that possess the right semantics, yet cannot be used as approximative modifiers. A partial list is given in (123).

 (123) auf ‘up’, bei ‘at’, diesseits ‘on this side of’, hinter ‘behind’, in ‘in’, jenseits ‘on the far side of’, nach ‘towards’, neben ‘next to’, oberhalb ‘above’, unterhalb ‘beneath’, unweit ‘near’, vor ‘in front of’

Corver & Zwarts (2006: 819) acknowledge this mismatch but their analysis provides no clue as to why there is such a mismatch to begin with. The analysis of such approximative modifiers as adverbs doesn’t face this problem because it simply doesn’t expect a full match between the set of local prepositions and the set of approximative modifiers that look only like prepositions. In addition, the alternative analysis need not be enriched with a filter that blocks prepositions in general to function as approximative modifiers.

Second, subsuming the meaning of approximative modifiers under the meaning of the prepositions they contain is not general enough a solution. For there are still bona fide adverbs that can be used as approximative modifiers. And although these adverbs do not have a local interpretation, they are nevertheless mapped onto the one-dimensional space of natural numbers, too. So whatever mechanism gives the meaning for adverbs as approximative modifiers will also provide the basis for assigning a meaning to approximative modifiers that only look like prepositions. Thus, the alternative analysis presented in this paper relies on a uniform semantic mechanism, namely one for adverbs. The view that takes some approximative modifiers to be adverbs and others to be prepositions requires two mechanisms, one for adverbs and another one for prepositions enriched with a filter blocking any preposition.

### 5.3 A contrast between ungefähr vs. an die

The third problem was first brought to my attention by Yaron McNabb (personal communication, 2015/9/3) and also raised by two anonymous reviewers. As they point out, bona fide adverbs like ungefähr ‘approximately’ differ from approximative modifiers that look like prepositions in that only ungefähr ‘approximately’ can right-adjoin to a DP containing a numeral and extrapose. Witness the contrast between (124) and (125).

1. (124)
1. a.
1.
1. Zwanzig
2. twenty
1. Leute
2. people
1. ungefähr
2. approximately
1. wurden
2. became
1. verhaftet.
2. arrested
1.
1. b.
1.
1. Zwanzig
2. twenty
1. Leute
2. people
1. wurden
2. became
1. verhaftet
2. arrested
1. ungefähr.
2. approximately
1. ‘Approximately twenty men were arrested.’
1. (125)
1. a.
1. *
1. Zwanzig
2. twenty
1. Leute
2. people
1. an
2. on
1. die
2. the
1. wurden
2. became
1. verhaftet.
2. arrested
1.
1. b.
1. *
1. Zwanzig
2. twenty
1. Leute
2. people
1. wurden
2. became
1. verhaftet
2. arrested
1. an
2. on
1. die.
2. the
1. intended: ‘Up to twenty men were arrested.’

As the a-examples show, ungefähr ‘approximately’ can right-adjoin to a DP, whereas an die ‘up to’ cannot. German is verb-second in main clauses, so zwanzig Leute ‘twenty people’ and ungefähr ‘approximately’ have to form a constituent in (124a). The b-examples show that ungefähr ‘approximately’ can extrapose, in contrast to an die ‘up to.’ There are two dimensions of this problem. First, can the analysis according to which some approximative modifiers are adverbs and some are prepositions capture the contrast between (124) and (125)? Second, can the analysis defended here according to which approximative modifiers are all adverbs capture that contrast?

#### 5.3.1 The contrast under Corver & Zwarts’ (2006) analysis

As for the first issue, it depends on the treatment of right-adjunction and extrapostion. If one conceives of these two as rightward movement, then one can easily capture the contrast. For under the PP analysis of the approximative modifiers in (125), an die ‘up to’ doesn’t form a constituent, and is thus unmovable.

1. (126)

However, if one follows Corver & Zwarts’ (2006: 831) analysis of right-adjunction and extraposition as leftward movement plus rightward stranding, then the contrast does not follow. Consider their analysis for (124a), shown in (127).

1. (127)

This structure incorporates two ideas of Corver & Zwarts’ (2006) already alluded to in fn. 2. First, the numeral ungefähr zwanzig ‘approximately twenty’ and the NP Leute ‘people’ the numeral modifies are assumed to form a small clause (XP in 127) such that the modified NP is the subject and the numeral is the predicate of that small clause. On top of that XP, a NumP is projected to whose head Num° the empty head X° of XP adjoins. Second, normally the whole numeral is moved to the specifier of NumP. In (127), however, subextraction out of the numeral takes place, moving only zwanzig ‘twenty’ instead of ungefähr zwanzig ‘approximately twenty.’ If this analysis is applied to approximative modifiers that look like PPs, then one arrives at (128) as a licit structure for (125a).

1. (128)

Based on this structure, one also derives extraposition of an die ‘up to.’ No matter how one wishes to analyze extraposition under a leftward movement plus rightward stranding approach, an die ‘up to’ does form a constituent all of the sudden. Note that the type of movement in (128) violates an independent constraint on movement, namely that extraction out of PPs in German is generally blocked (ignoring R-pronouns). However, the same applies to the structure in (127): adverbs cannot be stranded in German (or Dutch) either.

1. (129)
1. *
1. Schöni
2. handsome
1. ist
2. ist
1. Jan
2. Jan
1. sehr
2. very.
1. ti.
2.
1. intended: ‘Jan is very handsome.’

An anonymous reviewer points out that sehr ‘very’ and ungefähr ‘approximately’ might have a different syntax. Their Dutch counterparts heel ‘whole’ and ongeveer ‘approximately’ differ in their positioning: heel ‘whole’ occupies a head or a specifier position whereas ongeveer ‘approximately’ is an adjunct (Corver 1997). The relevance of this difference is that adjuncts can be stranded, for example quantifiers under quantifier-float.

1. (130)
1. Die
2. the
1. Frauenk
2. women
1. sind
2. are
1. gestern
2. yesterday
1. alle
2. all
1. tk
2.
1. gekommen.
2. come.
1. ‘Yesterday all the women came.’

However, it is not clear whether (124a) is parallel to (130). On the one hand, it is far from obvious that (130) involves simple subextraction because the corresponding base structure is marginally grammatical at best.

1. (131)
1. ???
1. Gestern
2. yesterday
1. sind
2. are
1. alle
2. all
1. die
2. the
1. Frauen
2. women
1. gekommen.
2. come
1. ‘Yesterday all the women came.’

On the other hand, the fully grammatical version of (131) with the non-agreeing form all ‘all’ instead of alle ‘all’ does not allow subextraction.

1. (132)
1. a.
1.
1. Gestern
2. yesterday
1. sind
2. are
1. all
2. all
1. die
2. the
1. Frauen
2. women
1. gekommen.
2. come
1.
1. b.
1. *
1. Die
2. the
1. Fraueni
2. women
1. sind
2. are
1. gestern
2. yesterday
1. all
2. all
1. ti
2.
1. gekommen.
2. come.
1. ‘Yesterday all the women came.’

More importantly, if one considers structures other than Q-float, then one observes that being an adjoined non-agreeing adverbs is not sufficient for stranding. One example is the adjunct genau ‘exactly’. The example in (133a) shows that genau ‘exactly’ attaches to DPs and the example in (133b) shows that it cannot be stranded.

1. (133)
1. a.
1.
1. Genau
2. exactly
1. diese
2. these
1. Frauen
2. women
1. sind
2. are
1. gestern
2. yesterday
1. gekommen.
2. come
1.
1. b.
1. *
1. Diese
2. these
1. Fraueni
2. women
1. sind
2. are
1. gestern
2. yesterday
1. genau
2. exactly
1. ti
2.
1. gekommen.
2. come.
1. ‘Yesterday exactly these women came.’

In sum, the contrast between (124) and (125) doesn’t necessarily favor the view that approximative modifiers come in two flavors.

#### 5.3.2 The contrast under the adverb analysis

This brings us to the second and more important issue of how the analysis defended here according which all approximative modifiers are adverbs can handle the contrast between (124) and (125). The analysis I would like to suggest is that this contrast shows nothing about a distinction between adverbs as approximative modifiers on the one hand and alleged prepositions as approximative modifiers on the other hand. Rather, the contrast derives from an independent factor, namely the number of possible hosts for an adverb. More specifically, I claim that the following descriptive generalization holds.25

 (134) An adverb x can right-adjoin to a DP and extrapose if and only if x has more than one licit host phrase.26

The contrast between the synonymous ungefähr and um die (both ‘around’) shown in (135) and (136), respectively, illustrates this generalization.

1. (135)
1. a.
1.
1. ungefähr
2. approximately
1. das
2. the
1. dümmste
2. most stupid
1. Argument
2. argument
1. [host = DP]
2.
1. ‘the approximately most stupid argument’
1.
1. b.
1.
1. Peter
2. Peter
1. hat
2. has
1. ungefähr
2. approximately
1. getanzt.
2. danced
1. [host = VP]
2.
1. ‘Peter did something that approximately resembles dancing.’
1. (136)
1. a.
1. *
1. um
2. around
1. die
2. the
1. das
2. the
1. dümmste
2. most stupid
1. Argument
2. argument
1. [host = DP]
2.
1. intended: ‘the approximately most stupid argument’
1.
1. b.
1. *
1. Peter
2. Peter
1. hat
2. around
1. um
2. around
1. die
2. the
1. getanzt.
2. danced
1. [host = VP]
2.
1. intended: ‘Peter did something that approximately resembles dancing.’

(135) shows that ungefähr ‘approximately’ can attach to hosts other than numerals, whereas um die ‘around’ cannot, as (136) reveals. According to the analysis in (134), the contrast between (124) and (125) is not one about adverbs vs. prepositions. It therefore predicts that one should find approximative modifiers that are bona fide adverbs that cannot right-adjoin to DP and extrapose, and that one should find approximative modifiers that look prepositions that can right-adjoin to DP and extrapose. In fact, both predictions are confirmed. As for the first prediction, the adverbs rund and so (both ‘around’) cannot right-adjoin to DPs nor extrapose, as shown in (137).

1. (137)
1. a.
1. *
1. Zwanzig
2. twenty
1. Leute
2. people
1. rund
2. round
1. /
2.
1. so
2. so
1. wurden
2. became
1. verhaftet.
2. arrested
1.
1. b.
1. *
1. Zwanzig
2. twenty
1. Leute
2. people
1. wurden
2. became
1. verhaftet
2. arrested
1. rund
2. round
1. /
2.
1. so.
2. so
1. intended: ‘Approximately twenty men were arrested.’

Importantly, these two adverbs cannot combine with hosts other numerals either.27

1. (138)
1. a.
1. *
1. rund
2. round
1. /
2.
1. so
2. so
1. das
2. the
1. dümmste
2. most stupid
1. Argument
2. argument
1. [host = DP]
2.
1. intended: ‘the approximately most stupid argument’
1.
1. b.
1. *
1. Peter
2. Peter
1. hat
2. has
1. rund
2. round
1. /
2.
1. so
2. so
1. getanzt.
2. danced
1. [host = VP]
2.
1. intended: ‘Peter did something that approximately resembles dancing.’

As for the second prediction, there is one approximative modifier that looks like a preposition that can right-adjoin to DP and extrapose, namely nahezu ‘nearly’, as shown in (139) and (140).

1. (139)
1. a.
1. ?
1. Zwanzig
2. twenty
1. Leute
2. people
1. nahezu
2. nearly
1. wurden
2. became
1. verhaftet.
2. arrested
1.
1. b.
1. ?
1. Zwanzig
2. twenty
1. Leute
2. people
1. wurden
2. became
1. verhaftet
2. arrested
1. nahezu.
2. nearly
1. ‘Nearly twenty men were arrested.’
1. (140)
1. a.
1.
1. nahezu
2. nearly
1. das
2. the
1. dümmste
2. most stupid
1. Argument
2. argument
1. [host = DP]
2.
1. ‘the nearly most stupid argument’
1.
1. b.
1.
1. Peter
2. Peter
1. hat
2. has
1. nahezu
2. nearly
1. getanzt.
2. danced
1. [host = VP]
2.
1. ‘Peter did something that comes close to dancing.’

Incidentally, closely related elements can differ with respect to their potential to right-adjoin to DP and to extrapose, like etwa and in etwa (both ‘around’).

1. (141)
1. a.
1. Zwanzig
2. twenty
1. Leute
2. people
1. in
2. in
1. etwa
2. around
1. /*
2.
1. etwa
2. around
1. wurden
2. became
1. verhaftet.
2. arrested
1.
1. b.
1. Zwanzig
2. twenty
1. Leute
2. people
1. wurden
2. became
1. verhaftet
2. arrested
1. in
2. in
1. etwa
2. around
1. /*
2.
1. etwa.
2. around
1. ‘Approximately twenty men were arrested.’
1. (142)
1. a.
1. in
2. in
1. etwa
2. around
1. /*
2.
1. etwa
2. around
1. das
2. the
1. dümmste
2. most stupid
1. Argument
2. argument
1. [host = DP]
2.
1. ‘the approximately most stupid argument’
1.
1. b.
1. Peter
2. Peter
1. hat
2. has
1. in
2. in
1. etwa
2. around
1. /*
2.
1. etwa
2. around
1. getanzt.
2. danced
1. [host = VP]
2.
1. ‘Peter did something that approximately resembles dancing.’

So it is the possibility to attach to more than one host that correlates with the availability to right-adjoin to DPs and to extrapose. Whatever the ultimate reason for this correlation might turn out to be, it undermines the analysis that it is the status of the approximative modifier as an adverb or as an alleged preposition that correlates with the greater distributional flexibility. For there are bona fide adverbs that cannot right-adjoin to DP or extrapose and there are approximative modifiers that like prepositions that can right-adjoin to DP and extrapose. Hence the flexibility cannot be taken as argument for a separate treatment of approximative modifiers containing adverbs and those that look like prepositions.

## 6 A note on Dutch

### 6.1 The status of approximative numerals in Dutch as PPs

The discussion has so far centered on German exclusively. Since Corver & Zwarts’ (2006) paper is mainly concerned with Dutch, the question is of course whether the analysis of approximative modifiers as adverbs can be adapted for Dutch. To the extent that I can overlook the relevant evidence, the answer is negative. Although the original arguments Corver & Zwarts (2006) gave are inconclusive in my view, there are new ones that provide conclusive evidence that Dutch does in fact have prepositional numerals. Let me start with the three arguments Corver & Zwarts (2006: 822–823) provided and then move on to the new ones.

#### 6.1.1 Corver & Zwarts’ (2006) old arguments

The first argument Corver & Zwarts (2006) discuss is that similar to real prepositions, approximative modifiers that look like prepositions select a definite article. This contrasts with bona fide adverbs functioning as approximative qualifiers, which never take the definite article.

1. (143)
1. a.
1. Er
2. EXPL
1. waren
2. were
1. rond
2. around
1. (de)
2.   the
1. twintig
2. twenty
1. deelnemers.
2. participants
1. ‘There were around twenty participants.’
1.
1. b.
1. Er
2. EXPL
1. waren
2. were
1. tegen
2. against
1. *
2.
1. (de)
2.   the
1. twintig
2. twenty
1. deelnemers.
2. participants
1. ‘There were close to twenty participants’
1. (144)
1. Er
2. EXPL
1. waren
2. were
1. ongeveer/
2. around
1. hoogstens
2. at most
1. (*de)
2.   the
1. twintig
2. twenty
1. deelnemers.
2. participants
1. ‘There were approximately/at most twenty participants.’

This argument is inconclusive because of the seven true prepositions that allegedly function as approximative modifiers in German, only two select the definite article; all other forbid it.

1. (145)
1. a.
1. An
2. on
1. /
2.
1. um
2. around
1. *
2.
1. (die)
2.   the
1. zwanzig
2. twenty
1. Leute
2. people
1. kamen.
2. came
1. ‘Up to/around twenty people came.’
1.
1. b.
1. Bis
2. until
1. zu
2. to
1. /
2.
1. nahezu/
2. nearly
1. über
2. over
1. /
2.
1. gegen
2. against
1. /
2.
1. unter
2. under
1. (*die)
2.     the
1. zwanzig
2. twenty
1. Leute
2. people
1. kamen.
2. came
1. ‘Up to/nearly/more than/up to/less than twenty people came.’

In addition, the argumentation is problematic on its own (cf. fn. 23) and the exclusion of (144) probably has the diachronic explanation suggested at the end of section 5.1.

The second argument they provide is that approximative modifiers can be complex.

1. (146)
1. Er
2. EXPL
1. waren
2. were
1. in
2. in
1. de
2. the
1. buurt
2. neighborhood
1. van
2. of
1. de
2. the
1. twintig
2. twenty
1. deelnemers.
2. participants
1. ‘There were close to twenty participants.’

They then state that “expressions like in de buurt van do not make sense as adverbs, of course”. This argument tacitly assumes that it is fine for prepositions to be complex but not for adverbs. But I see no principled reason why preposition are allowed to be complex but not adverbs.2829

Their third argument is that approximative numerals that look like PPs allow modifiers that only attach to PPs.

1. (147)
1. Ergens
2. somewhere
1. /
2.
1. iets
2. something
1. /
2.
1. ruim
2. above
1. in
2. in
1. de
2. the
1. twintig
2. twenty
1. deelnemers
2. participants
1. hebben
2. have
1. zich
2. REFL.3
1. aangemeld.
2. registered
1. ‘Approximately/around/way over twenty participants registered.’

This argument is inconclusive because the relevant modifiers in (147) are not genuine PP-modifiers.30 On the one hand, ruim ‘way over’ is compatible with numerals quite general, cf. (148).

1. (148)
1. voor
2. for
1. ruim
2. above
1. dertig
2. thirty
1. klanten
2. clients
1. ‘for more than thirty clients’

On the other hand, ergens ‘somewhere’ and iets ‘around’ can also combine with adverbs.

1. (149)
1. a.
1. Vandaag
2. today
1. voel
2. feel
1. ik
2. I
1. me
2. me
1. al
1. iets
2. something
1. beter.31
2. better
1. ‘I feel already a little bit better today.’
1.
1. b.
1. Zijn
2. his
1. beenderen
2. remains
1. liggen
2. lie
1. ergens
2. somewhere
1. hier
2. here
1. begraven.
2. buried
1. ‘His remains are buried somewhere here.’

#### 6.1.2 New arguments

There are nevertheless three new arguments kindly provided by Norbert Corver (personal communication, 2017/2/23), two of which in my view convincingly show that in Dutch, approximative modifiers that look like prepositions in fact project a PP. The first argument he gives is that approximative modifiers that look like prepositions disallow stacking, in contrast to German (cf. 58) as expected under the view that they project a PP (cf. section 3.3).

1. (150)
1. *
1. tegen
2. against
1. de
2. the
1. over
2. above
1. de
2. the
1. dertig
2. thirty
1. deelnemers
2. participants
1. intended: ‘up to more than 30 participants’

The second argument comes from Right Node Raising. Right Node Raising can apply to approximative modifiers that look like prepositions but not to adverbs, again as expected under an analysis where they project a PP.

1. (151)
1. a.
1. Jan
2. Jan
1. heeft
2. has
1. tegen
2. against
1. _,
2.
1. en
2. and
1. Marie
2. Marie
1. heeft
2. has
1. over
2. over
1. de
2. the
1. dertig
2. thirty
1. vrienden.
2. friends
1. ‘Jan has close to thirty friends, and Marie has more than thirty friends.’
1.
1. b.
1. *
1. Jan
2. Jan
1. heeft
2. has
1. min
2. at least
1. _,
2.
1. en
2. and
1. Marie
2. Marie
1. heeft
2. has
1. hoog-stens
2. highest
1. dertig
2. thirty
1. vrienden.
2. friends
1. intended: ‘Jan has at least thirty friends, and Marie has at most thirty friends.’

Dutch contrasts sharply with German, where Right Node Raising cannot apply to approximative numerals that look like prepositions.

1. (152)
1. *
1. Peter
2. drinks
1. trinkt
2. around
1. um
2. around
1. _,
2.
1. aber
2. but
1. Maria
2. Maria
1. sicher
2. certainly
1. nur
2. only
1. an
2. on
1. die
2. the
1. zehn
2. ten
1. Bier.
2. beer
1. intended: ‘Peter drinks around ten beers, but Maria certainly only up to ten beers.’

There is a third argument that possibly indicates that they are PPs: parentheticals can appear between the preposition and the definite article.

1. (153)
1. ??
1. Er
2. EXPL
1. waren
2. were
1. rond
2. around
1.
1. pak
2. grab
1. ‘m
2. him
1. beet
2. PRT
1.
1. de
2. the
1. twintig
2. twenty
1. deelnemers.
2. participants
1. ‘There were about, I guess, twenty participants.’

It is not fully clear, however, whether (153) really involves splitting. rond de ‘around’ has a variant without de ‘the’ (Corver & Zwarts 2006: 823). Coupled with the observation from the previous subsection about the difference between etwa ‘around’ and in etwa ‘around’, it might be the case that rond ‘around’ is different from rond de ‘around’, namely that rond ‘around’ is an adverb attaching to the DP containing the numeral. Then, de ‘the’ belongs to twintig deelnemers ‘twenty participants’ so that it is not rond de ‘around’ that is broken up. So data from approximative modifers that look like prepositions other than rond de ‘around’ is required before one can draw any firm conclusion from (153).

### 6.2 Why Dutch (still) possesses prepositional numerals

The two arguments illustrated in (150) and (151) show that Dutch in contrast to German possesses prepositional numerals. What could be responsible for this difference between Dutch and German? The relevant clue to answer this question comes from an observation made by Plank (2004). Consider again the change approximative numerals underwent in German in (154).

 (154) a. → b.

Regarding this change, Plank (2004: 183) notes the following:

 (155) “It is only in the twentieth century […] that [approximative modifiers that look like prepositions] with definite articles have begun to appear in syntactic contexts where they are externally assigned case […]”

As external case assignment implies the change from PP to DP shown in (154), the structural reanalysis from (154a) to (154b) is a relatively recent one. On the assumption that (i) approximative modifiers that look like PPs have been existing for the same time in Dutch as in German and that (ii) the change from PP to DP that German underwent was only possible after some 400 years, Dutch could not have possibly been undergone that change. The reason that German underwent the change from (154a) to (154b) was to resolve the conflict between case assignment by the preposition and external case assignment by the predicate. Whereas in earlier stages, case assignment by the preposition outranked external assignment, in the 19th century external case assignment started to outrank case assignment by the preposition. However, Dutch lost its case system already at the end of the 18th century (Donaldson 1983). Since due to the loss of case marking there was no conflict between the case marking requirements of the preposition and that of the position the PP appeared in, the change that resolved this conflict was never required. In other words, due to the existence of only a single case form for nouns, the DP inside the PP was trivially compatible with the requirements of external case marking. So no conflict arose and no re-analysis was needed.

If this analysis is on the right track, it implies that prepositional numerals in Dutch are real PPs, that is, it’s not the numeral that is merged with the preposition but the whole DP containing the numeral. But if this is true, then how can this be made compatible with the evidence provided by Corver & Zwarts (2006: 820–821) that these PPs behave like DPs? The most promising route to take in my view can be found in the work by Hornstein & Uriagereka (2002). They suggest that the by now common mechanism of reprojection (Donati 2006; Cecchetto & Donati 2015; Blümel 2017), whereby the label of a constituent changes in the course of the derivation, applies at the interface to LF. Their analysis is based on the behavior of subject quantifiers. Syntactically, subject quantifiers are subject arguments and hence specifiers. Semantically, however, they are predicates and therefore heads. What they suggest is that the label of the clause changes when sent to LF. Before LF, the clause is a TP where the subject quantifier is a specifier. At LF, the clause is a QP and the subject quantifier is the head of the structure. So a sentence as Most men like beer has the two structures in (156).

1. (156)

This captures that quantifiers behave as arguments syntactically but as predicates semantically. Transposing this idea to prepositional numerals in Dutch, one could suggest that the label of the nominal containing a prepositional numeral changes. Before LF, the DP provides the label, whereas at LF, the preposition provides the label, as shown in (157).

1. (157)

The pre-LF structure derives that they occur in DP-positions only, the post-LF structure captures that they behave like PPs interpretation-wise.

## Conclusion

To conclude, I argued in this paper that expressions such as an die ‘up to’ used as approximative modifiers in numeral expression in German like an die zehn Bier ‘up to ten beer’ are directly attached to the numeral, and that such expressions are not PPs in German. Although they look like prepositions, they don’t behave like prepositions but pattern with adverbs modifying numerals.

## Abbreviations

3 = third person, ACC = accusative, COM = common gender, DAT = dative, FEM = feminine gender, MASC = masculine gender, MIXED = mixed declension class, NEUT = neuter gender, PL = plural, REFL = reflexive pronoun, SG = singular, STRONG = strong declension class, WEAK = weak declension class

## Notes

1. This claim is a bit simplified; I will return to this issue in section 5.2. [^]
2. Corver & Zwarts (2006: 828) make two additional assumptions about the structure of NPs modified by a numeral. The first concerns the status of numerals. Whereas I analyze them as modifiers, Corver & Zwarts (2006) analyze them as predicates of the NP modified by that numeral. The second concerns the phrasal status of the numeral+NP constituent. For Corver & Zwarts (2006), the resulting constituents are NumPs whereas for me they are NPs. As both issues are orthogonal to the topic of this paper, namely the internal structure of approximative numerals, I chose to leave out the phrasal status of numeral+NP constituents and to label numerals as NUM in order to make no commitment about their internal make-up. [^]
3. The determiner surfaces as die, which is the nominative and accusative form, and not as den, the dative plural form. This follows both from my analysis that an die ‘up to’ is an adverb and hence fixed in its shape, as well as from Corver & Zwarts’ (2006) analysis that an die ‘up to’ projects a PP containing only the numeral, because via Minimality the preposition blocks case assignment from outside. [^]
4. An anonymous reviewer points out that the argument makes use of the idea that coordination is based on categorial identity of the two conjuncts, even though problems with this approach are well-known (Sag et al. 1985). I agree with the reviewer that this approach is problematic. I nevertheless claim that coordination is a problem for the view that the constituents under discussion are PPs. There are three routes to the problem of the categorial non-identity of conjuncts that have been taken in the literature. None of these routes is satisfactory to deal with the fact that an alleged PP can be conjoined with a DP. The first invokes relational identity instead of categorial identity (Dik 1968). This approach doesn’t help because it requires PPs to be licit subjects to start with, but as shown in (9), this is not the case, so that the grammaticality of (19) remains a problem. The second approach demands both conjuncts to be independently compatible with the position occupied by the coordinate structure (Sag et al. 1985). This approach doesn’t work either because it directly clashes with the contrast in (21). According to the third approach, only the categorial feature of the first conjunct has to be compatible with the position of the position occupied by the coordinate structure (Progovac 1998a; b; Johannessen 1998; Zhang 2009). However, reversing the order of the two conjuncts in (19) doesn’t affect the grammaticality of the sentence, contrary what is expected under this approach. [^]
5. The unavailability of the wide scope reading becomes especially clear under corrective focus. It is possible to give the correction in (i) to (28a) and (28b), but it is impossible to give the correction in (ii).
 (i) No, it were exactly 300 protesters. (ii) #No, it were exactly 10 rioters.
I do not wish to exclude that approximative modifiers such as ungefähr ‘approximately’ never adjoin to NP in any other languages. In Dutch, the sentence corresponding to (28b) does have a wide scope reading (Norbert Corver, personal communication, 2017/2/23), as does its Greek equivalent with πɛρίπου (Vasiliki Koukoulioti, personal communication, 2017/5/27). But at least in German, they do not adjoin to NP. [^]
6. To be more precise, what is important is that the wide scope reading is not entailed by the meaning of (31); it is of course nevertheless compatible with it. [^]
7. Similar to the label NUM (cf. fn. 2), I chose the label ADJ in order to make as few as possible commitments about the structure of adjectives and the way they combine with nominals. [^]
8. Originally claimed to be impossible (Bayer 1990), focus particles have been shown to be able to occur between a preposition and its complement in German (Hoeksema & Zwarts 1991; Reis 2005; Bouma et al. 2007). [^]
9. An anonymous reviewer suggests that the contrast between (33) and (36) could be due to an obligatory incorporation operation affecting the preposition and the determiner in approximative numerals, which then blocks intervening elements. I return to this suggestion in section 3.5. [^]
10. An anonymous reviewer observes that PP-structures cannot be generally split up. In Dutch, for example, the focus particle zelfs ‘even’ cannot appear between the preposition and its complement.
1. (i)
1. <Zelfs>
2. even
1. naar
2. in
1. <?*
2.
1. zelfs>
2. even
1. de
2. the
1. kerk
2. church
1. gaat
2. goes
1. Jan
2. Jan
1. iedere
2. every
1. week.
2. week
1. ‘John goes every week even to the church.’
Ignoring that the German equivalent of this sentence is grammatical, the observation that PPs cannot be split up across the board does not affect the argumentation. For the argument only says that whatever element can appear between a preposition and its complement in bona fide PPs should also be able to appear between the alleged preposition and its complement in the relevant approximate numerals. This does neither entail nor necessitate that anything can appear between a preposition and its complement. [^]
11. Case marking on numerals also re-appears under split topicalization, cf. (i), which is well-known for its morphological regeneration effects (van Riemsdijk 1989).
1. (i)
1. Fraueni
2. women
1. hab
2. have
1. ich
2. I
1. nur
2. only
1. fünfe
2. five.ACC
1. ti
2.
1. getroffenACC.
2. met
1. ‘As for women, I only met five.’
[^]
12. Conceiving of this movement as a form of local dislocation (Embick & Nover 2001), -er attaches to XP at the level of PF. The intervening D° head does not block this movement because local dislocation affects string-adjacent elements. [^]
13. An anonymous reviewer suggests that the ungrammaticality of (57) is compatible with Corver & van Koppen’s (2011) approach if one assumes some Spell out constraint that either bans two inflectional elements or a linear sequence of two weak elements. As for the first constraint, it is at odds with the fact that the presence of two inflectional endings in German usually doesn’t cause any trouble. For example, the noun Männern ‘men.DAT’ contains both the plural morpheme -er and the case morpheme -n. The second constraint is at odds with the fact that a sequence of two weak elements, for example two weak object pronouns, is otherwise licit in German.
1. (i)
1. Ich
2. I
1. hab’s’m
2. have’it’him
1. gesagt.
2. told
1. ‘I told it to him.’
One argument in favor of an analysis of ‘s ‘it’ and ‘m ‘him’ as weak object pronouns comes from the observation that both are banned from the preverbal position in a verb second clause, similar to Dutch (Zwart 1997).
 (ii) a. * ‘s hab ich ihm gesagt. b. * ‘m hab ich es gesagt. it have I him told him have I it told ‘I told it to him.’ ‘I told it to him’
[^]
14. An anonymous reviewer observes that if adverbs are analyzed as adjuncts, then the data in (78) also follow from Corver & Zwarts’ (2006) analysis: the adverb ungefähr ‘approximately’ is adjoined to the numeral in (78a) but to NP in (78b). I agree but Corver & Zwarts’ (2006) analysis wrongly predicts that the adverb ungefähr ‘approximately’ can also adjoin to the DP selected by the preposition an ‘on’.
1. (i)
1. *
1. Ich
2. I
1. kenne
2. know
1. an
2. on
1. ungefähr
2. approximately
1. die
2. the
1. hundert
2. hundred
1. Frauen.
2. women
1. ‘I know approximately around a hundred women
For reasons laid out in section 3.1, my analysis predicts the ungrammaticality of (i). [^]
15. An anonymous reviewer doubts that rond het miljoen ‘around one million’ is ungrammatical, noting that it is attested and concludes from this that the determiner is not inert. As for the grammaticality of this expression, I cannot judge because I’m not a native speaker of Dutch. Regarding the reviewer’s conclusion that this invalidates my argument for the inertness of the determiner, I strongly disagree. As Corver & Zwarts (2006: 823) observe, the definite article in rond de ‘around’ is facultative, that is, rond ‘around’ alone is also fine as an approximative modifier. But then, rond het miljoen ‘around one million’ simply features the bare version rond ‘around’ directly attached to the numeral het miljoen ‘one million’. Support for this analysis comes from the observation, made by another anonymous reviewer, that rond de ‘around’ can also attach to the numeral een miljoen ‘one million’, giving rise to rond de een miljoen ‘around one million.’ [^]
16. I ignore in my discussion the problem that the definite article does not c-command the noun to which the numeral belongs at any point in the derivation (cf. the structures in 2 and 3). Given standard assumptions that the agreement controller has to be c-commanded by the element with unvalued features, the agreement features of the noun are outside the search domain of the definite article, so that the noun could never provide the number features for the definite article. [^]
17. Numerals upwards from and including Million ‘million’ seem to feature an obligatory determiner, whereas those below Million ‘million’ seem to feature an optional one.
 (i) a. * (eine) Million/Milliarde/Billion ‘one million/billion/trillion’ b. (ein)hundert/tausend ‘one hundred/thousand’
But the forms in (ib) are no longer determiners. First, no reduction to ‘n as in (93) is possible with the numerals from (ib).
 (ii) * ‘n hundert/’n tausend Frauen ‘a hundred/a thousand women’
Second, een(e), the form of ein(e) ‘a’ in the Berlin-Brandenburg dialect, is available for the numerals from (ia) but not for the ones from (ib).
 (iii) √eene Million/*eenhundert/*eentausend ‘one million/one hundred/one thousand’
[^]
18. An anonymous reviewer calls it “misleading” to claim that under Corver & Zwarts’ (2006) proposal the structure for (92) has to be (95) “because eine Million in their proposal would be a numeral.” But such a solution is not available for Corver & Zwarts (2006) because the overall conclusion they draw in their paper is that “that there is no separate syntactic category of numerals” and that “words like four and twenty behave in all sorts of respects as nouns” (Corver & Zwarts 2006: 833). [^]
19. An anonymous reviewer points out that (96d) presents a problem for my analysis because if the determiner projects, then (96d) is incompatible with the result from section 2.2, namely that approximative modifiers are not attached to DPs. This problem is only a minor one. On the one hand, the internal structure of numerals is irrelevant to the topic of this paper (cf. fn. 2). On the other hand, assume for the sake of the argument that eine Million ‘one million’ is indeed a DP. This will not affect the result from section 2.2 because the DP eine Million ‘one million’ and the DPs investigated in section 2.2 differ from each other in that only the latter are arguments of predicates. So the hypothesis rejected in section 2.2 must then be re-phrased as “the approximative modifier is an adjunct to an argument.” [^]
20. I ignore that bis can unexpectedly also combine with locational adverbs, like bis hier ‘until here’ and bis dort ‘until there.’ Possibly these expression contain the elided directional marker hin. [^]
21. Orthography is never a good indicator for wordhood. Already within the narrow domain of approximative modifiers that look like prepositions, inconsistencies are observed. Whereas bis zu ‘up to’ is written as two words, the closely related item nahezu ‘nearly’ is written as a single word. [^]
22. There are other elements for which this is not so clear, like außerdem ‘furthermore’, zudem ‘furthermore’, währenddessen ‘meanwhile’, and stattdessen ‘instead.’ [^]
23. In general, I find the argumentation based on co-occurrence restrictions dubious. In German the adverb etwa ‘around’ functioning as an approximative modifier can optionally be preceded by the element in, which looks like the preposition in ‘in.’
1. (i)
1. (In)
2.  in
1. etwa
2. approximately
1. zwanzig
2. twenty
1. Leute
2. people
1. kamen.
2. came
1. ‘Approximately twenty people came.’
According to Corver & Zwarts’ (2006) argumentation, this indicates that etwa ‘around’ has to be an article. First, the example in (i) cannot feature stacking of two approximative modifiers because the element in itself is bad as an approximative modifier in German.
1. (ii)
1. *
1. In
2. in
1. zwanzig
2. twenty
1. Leute
2. people
1. kamen.
2. came
1. ‘Around twenty people came.’
Second, in ‘in’ cannot be an adverb modifying etwa ‘around’ because the adverb corresponding to in is drin(nen). Third, the preposition in ‘in’ in German is only compatible with DP-complements, in contrast to other preposition (for example bis, cf. 104). Hence etwa ‘around’ can only be an article. But this clashes with the overall syntactic behavior of etwa ‘around.’ So co-occurrence data show little about the categorial status of approximative modifiers. [^]
24. Possibly, this diachronic scenario also explains why one only finds the article die ‘the’ in approximative modifiers that look like prepositions in German. Suggesting a much more elaborate structure, the determiner would take an empty noun AMOUNT as it complement, to which a small clause of the form ‘numeral + noun’ is attached, in the spirit of Corver (2001) and Corver & Zwarts (2006). Since the German word Menge for AMOUNT is feminine, the feminine version of the definite article is chosen, which is die ‘the.’ Lastly, as to why only the definite determiner occurs in the relevant approximative modifiers, cf. Plank (2004: 180). [^]
25. I leave it to future research whether and how this generalization can be derived from independent principles of grammar. [^]
26. The restriction to a unique type of host is not unknown. In English, very when used as a degree adverb can only attach to adjectives and adverbs derived from them (Huddleston & Pullum 2002: 532–533). [^]
27. Importantly, so in (137b) and (138b) illustrates the adverb so meaning ‘approximately’ and not the adverb so meaning ‘in that manner’. [^]
28. An anonymous reviewers questions an analysis of in de buurt van ‘close to’ as an adverb because it would be “strange to have an adverb that ends with a preposition that is usually never intransitive.” But at least in German, there are plenty of adverbs that end in a preposition that is never intransitive.
 (i) anbei ‘enclosed’ ← an ‘on’ + bei ‘at’ durchaus ‘by all means’ ← durch ‘through’ + aus ‘out of’ hingegen ‘by contrast’ ← hin ‘towards’ + gegen ‘against’ immerzu ‘always’ ← immer ‘always’ + zu ‘to’ nebenan ‘next door’ ← neben ‘next to’ + an ‘at’ zuvor ‘earlier’ ← zu ‘to’ + vor ‘before’
[^]
29. I deliberately remain silent about the precise structure of in de buurt van ‘close to’ as this is not at stake. What is at stake is whether one allows a complex structure for elements that are standardly taken to have a monolexical structure only. If one does so for prepositions, then one can also allow it for adverbs, irrespective of how the resulting structures eventually look like. [^]
30. I do not wish to claim that ruim ‘way over’, ergens ‘somewhere’, and iets ‘around’ are unconstrained regarding their hosts. All I say is that PPs do not define the relevant restriction on their hosts. [^]
31. An anonymous reviewer points out that beter ‘better’ is maybe an adverbially used adjective, which analysis is suggested by the presence of the comparative morpheme -er. If true, this doesn’t affect my argument that iets ‘a little bit’ is not a modifier restricted to PPs. However, I am unconvinced that comparative formation is a sufficient criterion for adjectivehood because there are also genuine adverbs that form a comparative. For example, the German adverb oft ‘often’ has a comparative form öfter ‘more often’. Analyzing oft ‘often’ as an adverbially used adjective is precluded by the fact that it can never be used as an adjective in German. [^]

## Acknowledgements

I wish to thank the audience of the workshop “The Syntax and Semantics of Numerals” at SLE 2015 in Leiden for their challenging questions. I hope I managed to adequately answer them in this paper. I also wish to thank three anonymous reviewers whose comments improved the content of this paper. Special thanks go to Norbert Corver for his comments and the stimulating discussions about numerals, adverbs, and PPs.

## Competing Interests

The author has no competing interests to declare.

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