The Structure of ILCs on the ‘Inverse’ Reading: High NP-Adjunction

In section 2.4.2, it was pointed out that the behaviour of jeweils-DPs parallels that of ILCs

on the ‘inverse’ reading. It follows that the syntactic structure that gives rise to this

reading of ILCs is of particular interest to the analysis of jeweils-DPs. Below, it will be

argued that the structure of ILCs on the ‘inverse’ reading is the underlying structure of both constructions.

38 _{See Hartmann & Zimmermann (2002), who distinguish between postnominal genitive complements to verb}

nominalisations (and other relational expressions), as in (ia), and postnominal genitive modifiers that are adjoined to NP, as in (ib):

(i) a. die Zerstörung der Stadt b. der Verein des Präsidenten the destruction theGEN cityGEN the team theGEN presidentGEN

‘the destruction of the city’ ‘the team of the president’

The authors argue that a semantic and syntactic distinction into N-complements and NP-modifiers accounts for the observable differences between the constructions concerning their interpretation and distribution.

39 _{The derivation proceeds as follows:}

(i) a. [[ QPP in every basket]] = λx. ∀z [basket’(z) Æ in’(x,z)]

b. [[ NP apple in every basket]] = λx. apple’(x) ∧∀z [basket’(z) Æ in’(x,z)]

The full structure for the ‘inverse’ reading of ILCs is given in (85): (85) a. [DP D0 [NP [NP one [NP apple]] [QPP in every basket]]]

b. DP

D0 _NP

NP QPP

one NP in every basket

apple

The structure in (85) differs from (84) in the adjunction site of the postnominal QPP. In (85), the QPP is adjoined higher than the numeral/indefinite expression and therefore takes scope over it at surface structure. No LF-movement is required for scope reasons (but see fn.36). Another important point is that the analysis in (85) treats the sequence of

numeral one and NP apple as a single constituent, in contrast to the LF-movement

analysis.

Above, it was argued that the difference in syntactic structure is semantically conditioned. A closer look at ILCs reveals that ‘inverse’ readings with ILCs

predominantly show up with a restricted list of prepositions, among which we find in,

from, and on. Typically, these prepositions do not allow for a sensible ‘surface’ reading,

as witnessed by (86). What these prepositions have in common is that they specify the local position or origin of an entity. It lies in the nature of things that entities above the atomic level usually do not occur at more than one place simultaneously, or come from more than one place. It follows that surface readings of ILCs with these prepositions are perceived as strange. With prepositions that allow for a sensible ‘surface’ reading (e.g. with to or about), ‘inverse’ readings are hard, if not impossible, to get (cf.87).

(86) Some man from / inevery city fell ill.

#Some man who came from / lived in every city fell ill. (87) Some trip to every city was fantastic.

a. ‘There was some trip directed to every city which was fantastic.’ b. ??’For every city x, there was some trip to x which was fantastic.’

The data in (86) and (87) suggest that the syntactic structure in (85) is freely generated only in those cases in which the modifier structure in (84) gives rise to an implausible

interpretation.40 _{In my view, the change in syntactic structure is effected by a change in}

the meaning of the postnominal QPP. The meaning change ensures the derivation of a meaningful interpretation after all. It turns the QPP in (85) from a property-denoting expression (here: the property of being in every basket) of type <et>, into a generalised quantifier (cf. Barwise & Cooper 1981) over pluralities of type <<et,t>,t> The generalised quantifier denotes a property of sets, or the set of plural properties such that every basket contains an individual that has this property.41

40 _{In contrast, the generation of the “inverse” structure must be licensed by additional discourse factors for ILCs}

with a meaningful “surface” reading. This accounts for the difficulty to get “inverse” readings with sentences such as (87).

41 _{It thus turns out that the label ‘QPP’ is not just a convenient abbreviation, but is meaningful at least in the case}

In order to see how this works, consider a situation with three baskets which all

contain two apples, three pears, and one cucumber. In this scenario, the expression in

every basket denotes the three properties of being a set of two apples, of being a set of three pears, and of being the singleton set of one cucumber. Each of these properties is instantiated by one individual in each basket in the situation indicated.

The generalised quantifier interpretation of QPPs in ILCs is formalised in (88). (88) [[in every basket]] = λP<et,t>. ∀z [basket’(z) →∃X [P(X) ∧ *in’(X,z)]]

The expression in (88) takes the property of pluralities P denoted by the numeral NP as its semantic argument. The entire expression is true in a given situation if every basket in that

situation contains an element from the set denoted by the numeral NP.42 _{Turning back to}

(85), the expression is true if every basket contains an element from the set of singleton sets of apples. Note that the expression in (88) introduces an additional existential quantifier in the nuclear scope (cf. Heim 1982) of the universal quantifier. The presence of this existential quantifier formally captures the fact that ILCs on their “inverse” readings often have the flavour of asserting the existence of an individual. This is made clear by the

paraphrase of (85): In every basket, there IS an apple such that…We will encounter more

instances of double quantification in chapter IV where the interpretation of jeweils is

discussed.

Reinterpreting the QPP as a generalised quantifier over pluralities may look artificial at first sight, especially since the process of reinterpretation is not a compositional semantic operation. It is not possible to construe the quantifier meaning from the ‘basic’ meaning of the QPP, which is a property. The inclusion of a non-compositional procedure into the semantic component is a weakening of the semantic premise of strict compositionality from chapter I.3. However, there is independent evidence that supports the assumption that QPPs can be reinterpreted in the described manner. In English and German, semantic (or: variable) binding of a pronoun is possible with QPs that are embedded inside a PP. An example from English is given in (89a). The apparent structural

configuration between semantic binder and semantic bindee is given in (89b).43

(89) a. In no cityi have I found anybody who loves iti.

b. [PP in QPi] … iti.

The problem is that the QP-binder does not c-command the pronoun in (89b), as it should if semantic binding is licensed under c-command only (Heim & Kratzer 1998:262ff.). The

negative quantifier no was chosen in order to exclude the possibility of Quantifier Raising

of the QP at LF. As argued in Beghelli (1995), negative QPs do not undergo such

movement to take clausal scope at LF.44

42 _{Observe that the semantic type of the NP is <t> on the revised analysis, i.e. the NP is assumed to denote a}

proposition. The existence of proposition-denoting nominal arguments is argued for in chapter IV.4.1.2. The semantic analysis of ILCs is sketched in chapter IV.7.

43 _{Notice that a blind application of the reinterpretation in (88) to the QPP in (89) gives the implausible result}

that in no city there is anything which is loved by somebody who I found. The difference between (89) and the basket-example above is due to the event modifying nature of the QPP in (89). See fn.46 on how to reinterpret event modifying QPPs .

44 _{As witnessed by the impossibility of inverse scope of the prepositional object over the direct object in (ia), and}

the impossibility to license a negative polarity item in a structurally higher position in (ib).

(i) a. I showed something to nobody. b. *I showed anything to nobody. *‘There is nobody to which I showed anything.

In principle, there are two ways out of the dilemma. First, one could take the PP-layer

to be invisible for c-command in this particular case (a syntactic stipulation).45 _{The fact}

that the phenomenon in (89) appears to hold for prepositions in general argues against this solution. The question arises why the otherwise strict conditions on c-command should be weakened to such an extent in the case of prepositions.

The second way out of the dilemma is to assume that the (quantified) PP is reinterpreted as a generalised quantifier and binds the pronoun under c-command as in (90).

(90) QPPi… iti.

This is the solution advocated here. The prepositional phrase and its QP-complement are reinterpreted as a quantified prepositional phrase that can bind the pronoun under c-

command.46 _{I take (89a) as independent evidence for the interpretation of PPs as}

quantifier expressions.

Given that the PP on the ‘inverse’ reading is interpreted as a quantified expression, its structural position as the topmost NP-adjunct follows directly. In general, modifying adjuncts do not change the semantic type of the modified constituent. Normally, modifiers

combine with a set-denoting expression of type <et>, say the head noun apple in (85),

giving a set-denoting expression of type <et>. To give a concrete example, modification

of the noun apple with the modifying adjective red is accompanied by a semantic

mapping from the set of all apples to the set of red apples. Before and after modification, we have to do with sets of entities. Modification restricts the initial set to a subset. The

same holds for modification with numerals. Modification of the plural noun apples (type

<et,t>) with the numeral adjective two will restrict the set of all pluralities of apples (i.e. pluralities of two, three, four, five etc. apples) to the set which comprises only groups of two apples (type <et,t>). In any event, the resulting type is the same as the input type. In contrast, generalised quantifiers take expressions of type <et> or <et,t> (i.e. set-denoting expressions) as their input and map these onto truth-values (type <t>). It follows that the application of a generalised quantifier to a set-denoting expression bleeds the possibility of modification of this set at a later stage because expressions of the resulting type <t> are not of the right type to undergo further modification (the right type being <et> or <et,t>). It follows that expressions denoting a generalised quantifier will always be adjoined higher than modifier-denoting expressions, if both are adjoined to the same syntactic category.

Applying these considerations to the case of ILCs with ‘inverse’ readings, only the syntactic configuration in (91a) is interpretable. In (91b), application of the generalised quantifier before the numeral blocks the latter from combining with the NP-denotation.

I thank Eddy Ruys for suggesting the choice of a negative quantifier.

45 _{This approach is taken by Giorgi & Longobardi (1991) in response to DP-internal PPs that seem to be}

transparent (i.e. no barriers) for c-command.

46 _{The presence of an event argument (see the discussion of events in chapter IV.1) forces the QPP to denote a}

function from relations into truth-values (type <eet,t>). The value of the QPP in (89a) is given in (ia), that of the rest of the clause after λ-abstraction over the pronoun’s index in (ib). Functional application of (ia) to (ib) gives (ic), which adequately captures the truth-conditions of (89a):

(i) a. [[in no city]] = λR. ¬∃x [city’(x) ∧∃e R(x)(e) ∧ in’(e,x)]

b. [[have I found anybody who loves iti]] = λyλe. ∃z [I have found z in e and z loves y]

c. [[in no city have I found anybody who loves iti]] =

(91) a. NP<t> b. * NP???

NP<et,t> QPP<<et,t>,t> AP<et,t> NP<t>

in every basket one

AP<et,t> NP<et,t> NP<et,t> QPP<<et,t>,t>

one apple apple in every basket

This way, we have arrived at a semantic motivation for the structure in (85). The postnominal QPP in ILCs is adjoined above the numeral adjective because of its semantic status as a quantified expression.