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.’

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.

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).

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

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.

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.

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).

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.

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

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.

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).

(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.

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.

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

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.

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).

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.

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.

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.

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

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.

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

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).

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).

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

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

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

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).

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

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.

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.

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).

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

3.2 Case in nominal ellipsis

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).

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.

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).

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.

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

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).

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.

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).

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.

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

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

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.

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.

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).

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).

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

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

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.

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.

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.

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).

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).

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.

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.

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.

4.1 The inertness of the determiner

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

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).

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

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).

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’.

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.

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.

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.

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).

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

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

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

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

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).

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].

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

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).

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).

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].

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).

bis ‘until’ also combines with directional adverbs.²⁰

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

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

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.

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.

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).

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.

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

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.

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.

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.

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

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.

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.

5.1 [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).

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).

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).

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).

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?