Partitives and Partitivity

The paper offers a broad overview of several structures that fall under the umbrella term of “partitives”. It surveys previous analyses and proposes a treatment based on two null operators, PART% and PARTpro, with different syntactic and semantic properties. The approach is argued to outperform previous theories in its ability to cover conjunctions, mass cases and contrastive differences across Italian and English. Crowd-sourced grammaticality judgments and corpus searches are used to supplement informal judgments and try to shed light on a complex set of facts.


Introduction
In 2016 and 2017 we edited a number of articles on partitives and related constructions, which appeared in a special collection on the topic in the journal Glossa. 1 The present contribution was initially conceived as an introduction to the collection, and as a way to discuss and organize the foundational issues those articles built upon. Along the way, however, the work developed into a full-fledged original theoretical proposal, which is now time to open to public discussion.
We begin with a broad definition of our topic of inquiry. The partitive construction is a noun phrase, like the subject of (1b), which is used to refer to a subset or subpart of another referent, the antecedent, typically one which has been previously introduced in the discourse, as in (1a). The antecedent (in (1a), a simple numeral plus noun-a structure which, following previous literature, we call a quantitative-is picked up by a definite noun phrase inside the bracketed nominal in (1b).
(1) a. [Twenty students] i took the exam. b. [Two of {them i / the students i / these students i }] j⊂i got top grades.
We will refer to the elements in curly bracket in (1b) as the "inner nominals", and to their determiners as the "inner determiners"; the determiner that heads the whole partitive (here, two) will be the "outer determiner".
Partitives have been frequently addressed in the literature, starting from Jackendoff (1968) and especially Selkirk (1977), who gives them the structure of a full noun phrase embedded within another noun phrase. A detailed structural analysis of partitives was offered in Jackendoff (1977), who called Partitive Constraint (PC) the requirement for the inner determiner to be definite, and set the stage for the discussion of three key points which have informed much of the research on the internal structure of these constructions: the possible presence of a phonetically null nominal element N e between the external determiner and the partitive preposition (i.e. three N e of them), the semantic import of the partitive preposition itself (English of, Genitive case in many languages, etc.), and the types of partitive which require proper partitivity, i.e. the necessity for the outer nominal to refer to a proper subpart of the referent of the inner nominal. Directly or indirectly, much of the research that followed has tackled these issues.
While written against this broad research background, the papers collected in the Glossa special collection differed precisely in that, instead of directly addressing issues like those above, they adopt results from previous work (assuming, in particular, the presence of an N e ), and use them to answer problems in gender agreement, differential object marking, quantificational suffixes and floating quantifiers, looking in all cases at languages different from English. This marks, it seems to us, a coming of age of partitive research, as this construction and its properties begin to enter the toolbox of more global linguistic research. The success of this new enterprise can thus be seen as indirect confirmation of the partitive structures and functions on which those works are based.
The present article takes up a complementary role: revisiting some of the background issues, adding a few novel facts and distinctions, and strengthening, if possible, the foundations on which those papers were build. To refine some of the delicate judgments found in the literature on this topic we decided to adopt the methods discussed in Sprouse et al. (2013); Sprouse & Almeida (2017) and use corpus searches, crowd-sourcing and on-line questionnaires 2 to obtain as many judgments as possible for various complex constructions, validating their statistical significance. To simplify, we translated the 1-to-5 judgment given by the informant pool into a more familiar linguistic scale: 1 ≤ ✽ ≤ 2 ≤ ?? < 3 ≤ ? < 4 ≤ √ ≤ 5. Note that the marks refer to the average of all the judgments. Not all the data in the paper were obtained from informant pools: some come from the literature, others were obtained by asking a much smaller number of native speakers (mostly linguists) during the revision stage. To distinguish them, we mark pool judgments by boldfacing and italicizing them (e.g. ✽, ?? vs. *, ??).
The structure of the paper will be as follows. In Section 2 we list a number of "partitivelike" constructions mentioned in the literature, and in Section 2.1 we carry out a preliminary review and exclude some cases from further consideration. Section 3 discusses general issues with the remaining cases, and gives an overview of the previous analyses. Sections 4 and 5 address more peripheral partitive constructions, including the important cases of proportions (Sec. 4.1) and indefinite partitives (Sec. 5). In Section 6 we focus on the structure of the "core" cases, drawing evidence from gender agreement in Italian (Sec. 6.1) and overt raising structures, (the so-called double genitives, in Sec. 6.2). In Sections 6.3 and 6.4 we make a case for a mixed analysis of canonical partitives and double genitives,

The many facets of partitivity
The formal inclusion relation between two sets (A ⊂ B) can be explicitly expressed in natural language in several different ways. At the nominal level, a speaker may simply use different restrictors in an inclusion relation (freshmen⊆students) (2).
(2) Twenty students i from different years took the exam. The freshmen j⊂i did better than last year.
However, if the restrictor remains unchanged, we enter the rich world of part-of constructions, consisting of many different forms. In this section we draw heavily from Jack Hoeksema, who in a seminal 1984 paper and in the introduction to a 1996 collection devoted to this topic attempted a classification of all the English constructions that have a 'subpart/subset'-related semantics. The present list tries to be even more inclusive, though some of the elements in this vast family will later be excluded from our investigation.
A. Canonical partitives (CanonP) partitives introduced by a numeral or a quantity expression (many, few, etc.; "Q-adjectives", in the terminology of Solt 2015), followed by a definite inner nominal introduced by a pronoun, a definite article, a demonstrative or a possessive DP (cf. (1b) above).
(3) Twenty students i from different years took the exam. I spoke with [two of {them i /the students i /these students i /John's students i }] j⊂i .
However, other inner nominals which are apparently definite or at least "strong" in the sense of Milsark (1974) do not work: (4) a. *One of both boys arrived. vs. one of the two boys b. *Three of most boys arrived.
Conjunctions of inner nominals do not work either, even when they are definite: a. *One of this boy and that girl came over. b. *Some of Jack, Marc, Luis and Tom will not come.
The partitives in this section are the ones originally discussed in Jackendoff (1977), and those most frequently addressed in the literature that followed. B. Indefinite Partitives (IndefP) are externally similar to canonical partitives, but with an indefinite inner nominal (6a, b). They are mentioned in Stockwell et al. (1973) and widely discussed in Abbott (1996) and Barker (1998).
(6) a. He ate three of some apples he found on the ground. b. John was one of several students who arrived late. Ladusaw (1982) These examples are a direct counterexamples to Jackendoff's Partitive Constraint (PC)-the requirement for the inner nominal to be (in some sense) "definite", which seems very much active in e.g. (7) (in contrasts with the pseudopartitives discussed below, at [PseudoP]).
A characterization of these indefinite cases seems therefore quite important to achieve a deeper understanding of partitives. C. Proportional Partitives and Percentages (ProporP) they express the subset in terms of a proportion of its total, which can be given in raw form (8), or normalized, as in the case of percentages (9). Both cases can have singular inner nominals (10), in which case they apply to a global mass, or to the mass of each individual object, after its quantifier has taken scope over the proportion operator (like in (10b), interpreted as in (10c)). The examples in (10) come close to constructions containing an overt measure noun, like the biggest part of the house, a meaning which is made explicit in Italian, where the only way to render English most is la maggior parte 'the most part'. Some proportional cases have inner nominals which are indefinite, either plural (11), or singular (12). The latter case seem to be limited to abstract nouns, and does not seem to apply to 'mereological subparts'.
(11) 80% of school children (12) a. Much of theater is improvisation. b. Half of boxing is legwork. (Hoeksema 1996) D. The "Among" construction (AmongP) uses the preposition among in place of of (13). Following Hoeksema 1984, we also refer to it as the "semi-partitive". Note that among partitives can frequently have a second noun before the PP (freshmen in (13)).
(13) Twenty students i took the exam.
Only [five (freshmen) among all these students i ] j⊂i managed to pass.
The distinction between of and among partitives is likely to replay in other languages in terms of Case. Turkish, for instance, has ablative-marked partitives, discussed in von Heusinger & Kornfilt (2017), which seem at least partly equivalent to among constructions (double noun, no PPart, more Case marking variation in the inner nominal, see below) and a Genitive partitive which must contain a single noun (14a), and possibly the special noun tane 'item' (14b) (from von Heusinger & Kornfilt 2017: ex. 17).
(15) (Only) [the most diligent of the freshmen] j⊂i managed to pass.
Note that the definite article is normally not possible in partitives (*the two of the freshmen), while it is obligatory here (compare (15) with (16), where most is an intensifier, not a superlative).
(17) a. I only got two packages of the mail you sent me. b. ?I read two novels of the books you gave me.
If Italian ne 'one(s)' is a pro-NP (see Belletti & Rizzi 1981 in a pre-DP framework, Giusti 1997, Falco & Zamparelli 2016, then cases where ne coexist with a partitive PP, like (18) (from Cardinaletti and Giusti; their judgment) should be analyzed as double noun partitives.
(18) *Ne i ho letti molti t i dei libri che mi hai consigliato. ones I_have read many of_the books that to_me you_have recommended 'I have read many, of the books you recommended.' The question to address here is what determines the higher or lower marginality of such examples, as it emerges from our pooled judgments. G. "Bare partitives" (BareP). Italian has indefinite nominal structures which formally resemble partitives in having the genitive preposition combined with a definite determiner, but lack any external determiner. These forms seem to replace unspecified plural indefinites, when absent (Spanish, which has a plural form of the indefinite article, unos, does not have bare partitives), with a comparable range of meanings.  Chierchia (1998) proposed that they are indeed derived from partitives with a missing external vague numeral (cf. alcuni dei ragazzi 'some of the boys'). The analysis is debated; one obvious problem is that, unlike in other partitive cases, these examples do not presuppose the existence of any external target: the definite semantics is absent (Storto 2003). Zamparelli (2008) points out that the canonical partitive forms in (20a) and (21a)  Note that even if the best analysis of so-called "bare partitives" turns out to be one which excludes them from the partitive family, a question remains: Italian does allow bare nominals in some environments (existentially interpreted verb objects, appositions); but then, why shouldn't these environments also license a "partitive" where the external numeral is missing? We return to this question in Section 9, where we suggest that such cases do exist, but only in the limited environment of appositions. H. Covert partitives (CovertP). These cases have partitive meaning without any overt partitive syntax.
(22) [Ten students] i took the exam. Two j⊂i got top grades.
Obviously, these cases can be linked to the structure of "fuller" partitives only if they covertly display some of the same syntactic or semantic properties. While we think that such properties can be found, we set these cases aside here to address them in depth in a separate paper (Falco and Zamparelli, in progress).
Some additional potential members of the partitive family contain ingredients of the cases seen so far, but present them in non-canonical orders, or add/subtract elements. We list and briefly discuss them for completeness. While this could be a simple case of extraposition, it adds some constraints on the possible structures we want to assume for partitives. J. Inverted partitives (InvertP). Canonical partitives have no noun between the external determiner and the PP, but there are constructions potentially related to partitives which have a noun between the external determiner and the preposition but no noun inside the PP. In English, one example is the so-called double genitive (in (25a), followed by a possible canonical counterpart (b)).  (27), depart from a canonical partitive with a personal pronoun by appending a universal or definite determiner externally (but not, e.g. a demonstrative: *these two of them). Intuitively, they express the proportion of the number of Ns who satisfy some predicate over the total number of Ns, and are thus strictly related to the count cases in (8b), but with a special syntax.

M. Pseudopartitives (PseudoP).
A well-studied construction in which the preposition of is preceded by a relatively small number of semi-functional nominal elements (number, dozen, lot, amount, deal, …) and followed by a bare plural count nominal or a singular mass nominal: (30) a. a number of objections b. a great deal of money In pseudopartitives, the referent of the outer DP is not linked to a previously established antecedent, but rather measured in (vague) units provided by the external semi-functional noun.

Delimiting the inquiry
This variety of ways to express what are after all very similar meanings is impressive, and makes partitivity a delicate topic of inquiry. Due to the competition of different structures with different requirements, judgments can be rather murky. Our strategy to contain the problem is three-pronged: we address the judgment variability by using corpora, pools of informants and significance tests, as described above; we delimit the space of our inquiry by adopting structural consistency within a single language as a criteria, and we use cross-linguistic comparison to further distinguish core aspects of the phenomenon from peripheral ones. Specifically, we take canonical partitives based on definites like (1b) as our reference point-our "core case". Looking within a single language, we make use of classic linguistic tests to highlight major structural differences between the canonical cases and other constructions in the family, excluding (or analyzing as non-partitive) those that seem too different. Looking across languages, we assume that when a language has clear and productive canonical partitives but fails to realize one of the constructions in [IndefP] to [PseudoP], or realizes it with a completely different preposition or Case, this is evidence that the construction at issue is not a "real" partitive, and should presumably be given a different syntactic structure and/or semantic derivation. A case in point is that of pronominal partitives and out-of constructions. In Italian, canonical partitives are completely parallel to the English case, but the literal equivalent of (27) are all severely ill-formed (*i due di noi 'the two of us', *tutti di noi 'all of us' and *c'è solo uno di me 'there is only one of me'). On the other hand, a version of (27a) which respects PPart (uno di noi/loro 'one of us/them') is perfectly well-formed. This suggests that those forms in (27) which violate PPart should actually be regarded as inverted predicational structures, arising from as we all, you two. Indeed, the lack of *you several (possibly connected with the oddness of (ii) in ft. 5) predicts that, while there is a real partitive like (31a), there is no (31b) to match it (Uli Sauerland, p.c.).
(31) a. several of us b. *the several of us The of in (27) would then be a linking element (in the sense of den Dikken 1998 and Martí-Girbau 2010); i.e. the of in the construction (he is) too much of a perfectionist. The interlinguistic contrast follows, since this construction is much more limited in Italian than in English (see *tutti dei ragazzi dormono 'all of the boys sleep').
The same considerations apply in the case of the Italian out-of construction ([Out-ofP]), which uses the preposition su 'over', not di 'of', and prefers the order Num N 'su' Num 3 -again suggesting a derivation different from the one required by a canonical partitive (but perhaps similar to the double genitives of Section 6.2).

(32)
Tre dottori su quattro raccomandano questo dentifricio. three doctors over four reccomend this toothpaste 'Three doctors out of four recommend this toothpaste.' Turning to within-language consistency, Selkirk's (1977) convincing analysis of pseudopartitives ([PseudoP]) in terms of a monoclausal structure give us reasons to exclude them from the partitive family, since all the other structures seen so far appear to distinguish between an inner and an outer DP layer, as in (33).
Selkirk's argument rests on two syntactic tests, the possibility of PP-extraposition in English and the availability of "stacked" relatives. PP extraposition is possible when the PP is selected by a simple relational nouns like review (34a), but impossible when the same noun is embedded in a partitive (34b), and possible again if the noun is embedded inside a pseudopartitive (34c).
(34) a. Two reviews have been reprinted of Helen's first symphony. b. *Two of those reviews have been reprinted of Helen's first symphony. c. A number of reviews have been reprinted of Helen's first symphony.
Her analysis is that in (34b), but not in the other cases, the PP must go through a more complex nominal (a violation of the Complex NP constraint, see Ross 1967: 70). Quantitatives (34a) and pseudopartitives (34c) allow extraposition; this suggests that both have simpler, monoclausal structures. The relative clause test points to the same conclusions. In (35) (where the constituent we bracketed is assumed to be a partitive) the relative clause has two possible scopes: it can apply to the whole set of famous paintings/daffodils, or to the subpart denoted by the whole nominal. In the corresponding pseudopartitive cases, however (36), there is only one scope-the whole set.  Summing up, the monoclausal structures that Selkirk assigns to these cases, translated in the current DP framework as (37), is in contrast with the biclausal structure (33) we are assuming for partitives. 4 (37) [ DP [ DP/MeasureP a dozen/number/lot] (of) NP] We will therefore set aside the cases in [PseudoP] for the rest of the paper, along with the other cases previously excluded: "bare partitives" (no antecedent, so no partitive meaning according to the previous literature), covert partitive (to be discussed elsewhere), the two of us (not partitives at all) and out-of cases (different syntax, not discussed; see Sec. 4 and 5 for related semantic issues). , but the corresponding positive (*the tall of the students) does not? 5. The role of the particle 'of' (or the Genitive case), in contrast with more contentful particles such as among. Of might of course be the source of the partitives meaning itself (see Barker 1998, Zamparelli 1998), but in this case the fact that in many languages and constructions (including, interestingly, the pseudopartitive, where it is often optional: he bought a dozen (of) roses) this particle seems to be completely bleached of meaning is unexpected. 6. The possibility of having count or mass inner nominals, which distinguishes "canonical" and "among" cases ([CanonP] and [AmongP]) from [ProporP].

Partitive Issues
At a more theoretical level, the comparison between canonical partitives [CanonP], double noun partitives [2NounsP] (to the extent they are possible) and inverted partitives in [InvertP] raises a crucial question: do all partitive structures underlyingly contain two nouns (within a DP analysis, two NPs), one of which is typically non overtly realized? If they do, the outmost structure of (canonical) partitives, in (38a), becomes closer to the structure behind three boys (38b); moreover, the double noun makes it easier to explain mismatches in number between the inner and outer determiner (as in one of those boys), but of course the nature of N e (PRO, in Jackendoff; see also Abney (1987: 344)) needs to be addressed. In (ib) the subject is of course a specific number.
If on the other hand the numeral is followed by a simple PP (39) (as proposed in Lobeck 1991;Kupferman 1999;Matthewson et al. 2001;Young Shin 2007 andGagnon 2013), the question is where this PP is attached, and why every numeral must be able to select for either PP or NP. The existence of null nominals inside partitives has been defended on (mostly) syntactic grounds in Giusti (1991), Cardinaletti & Giusti (1990;2006;, but is rejected in Martí-Girbau (2002), and in Martí-Girbau's (2010) dissertation on partitives. This thesis offers a third option: both partitives and quantitatives are seen as cases of nominal predicates which undergo inversion (in the sense of den Dikken 1998;2006), and where the external determiner is raised before a DP or NP, respectively. Of is inserted as a linking element, the nominal equivalent of the copula. Unfortunately, this theory faces the challenge of explaining the facts presented in Section 6, which are problematic for the PP account, and adds a few problems of it's own. 5 For this reason we do not provide an indepth analysis of Girbau's predicational analysis here.
A survey of the literature shows that the issues listed above in [1] to [5] are actually tightly interconnected. Zamparelli (1998)  This structure creates a clash when the inner nominal is a conjunction containing two different inner NPs, solving the coordination problem. Zamparelli assumes that the PP inherits nominal features from the NP in its Spec, so this approach sits somewhat in the middle of the two structures in (38a) and (39). However, if structures with two nouns like (17a) share the structure in (40), with N e overt, an extraposition like (24) (Of the books you gave me, I only read two novels) would break the PP at P′. Barker (1998) links point [4] (the fact that the outer determiner cannot be definite) to point [5], PPart, via the following semantics. Let's assume a lattice-based semantics for plurals à-la Link (1983), with * as the plurality-forming operator, and Sharvy's (1980) Max semantics for the, so that the definite determiner extracts the maximal element within a set of plural individual, and fails if none is present. Partitive of is assumed to be able to extract subpluralities out of a plural individual. Now, saying that the resulting set of pluralities denotes a proper subset of denotation of the inner nominal means saying that its maximal element has been removed; in turn, this entails that a uniqueness presupposition imposed by an outer definite determiner would fail. Assuming for instance, that there are three dogs in the context, we have: 5 Consider for instance Italian. If the source of quantitative adjectives such as parecchi 'several' in a partitive like (ia) is post-nominal, as Martí-Girbau (2010) proposes, one problem is why they cannot remain in this position (ib), unlike nearly all other Romance adjectives. Second, if the nature of the original position is a predication, it is unclear why the English several and other quantitative modifiers are degraded in copular predication (ii). Suppose that that you fed yesterday denotes {a+b, d}, and assume that the modifier is intersected with the denotation of the partitive before the (i.e. Max) is applied (43). Now uniqueness can be reinstated, and the is correctly predicted to be acceptable. Barker, however, has to stipulate proper partitivity (point [3] above). Zamparelli (1998) tries to derive this effect by connecting PPart with the definiteness of the inner nominal, through a subtractive semantics of a special "partitive of": the constituent boys of the boys in (40) would denote * ⟦boys⟧ -Max( * ⟦boys⟧), i.e. the full plurality of boys, minus its maximal element (aka the supremum), which is the denotation of the inner definite nominal (the boys). Zamparelli argues that this semantics is natural in virtue of being the converse of the intersective semantics typical of a relative clause, but this new meaning for of raises questions with respect to point [5] above. The connection between the (im)possibility of an external definite and proper partitivity explains why superlatives, where the adjective introduces an ordering source in the input set, do allow partitives (see item [SuperlP] above). On the other hand, inverted superlative partitives like (26a) are predicted not to allow an external definite any more than any other canonical partitive. In Zamparelli's system, if (26a) is mapped onto the structure in (40) we get (44), with the overt noun in the outer nominal replacing N e and the semantics shown in (44b). In the (b) example the presence of an immediate antecedent (the subgroup of actors who left) is not sufficient to restrict the context to a single pair; the situation seems identical in English, as shown in the glosses. Possessors have an even stronger effect (46).

(46)
John's sons and Bill's daughters all came to the party. They made quite a mess playing together, and I must say that … a. *John's of the kids were louder than the others.
In this case, no restriction seems to improve (e.g. *John's of the kids who were at the party). 6 A similar effect is visible with demonstratives: deictic demonstratives do not seem to license partitives (47), but English non-deictic distal demonstratives, which come with an obligatory relative clause, do allow them (48) Those of the inmates who desired it were made members of the congregation, upon the weakly payment of one penny.
(from UKWAC) This shows that partitives block not only the definites with a non-unique restriction, but also those that should be felicitous in virtue of their link to a previous antecedent (in the discourse or in the world). These are the strong/anaphoric type in the classification of Schwarz (2009;; Jenks (2018) (see also Cheng et al. 2017). Since partitives only affect the restriction, it is not immediately clear why this should be the case. Here, we leave the puzzle noted, but not resolved. Note at this point that Barker's and Zamparelli's analyses work only if PPart is a semantic effect. 8  criticize this assumption and propose that proper partitivity should be regarded as purely pragmatic: two of my two eyes would just be a cumbersome way of saying my two eyes, so it is ruled out as redundant. 9 The problem for this position is that we do find pairs such as: (49) a. All of the boys slept. / The boys all slept. b. All of John is underwater. / John is all underwater. c. Both of my eyes are red. / My eyes are both red.
It is reasonable to assume that the first element of these pairs stresses the fact that the predicate applies to the totality of some referent, not anything less. Thus, a purely pragmatic approach would predict that an improper partitive like (50a, b), should just receive a stressed reading as good as the equivalent forms in (49b, c). Yet, the judgments we collected from the informant pool show that the cases in (50) remain marginal.
(50) a. ?Ten of the ten disciples remained. b. ??One of one student remained.
The alternative is that the cases in (49) are structurally different from those (50), since the former are all impossible in Italian and arguably cases of "pivotal of" just like the two of us. In canonical partitives, on the other hand, something enforces proper partitivity at a semantic level. We will return on this issue in Section 5.
With this set of questions in mind, we turn to a more detailed classification of the English data in [CanonP] to [2NounsP], using Italian as a point of reference. We begin with three relatively peripheral cases: proportions, percentages [ProporP] and indefinite partitives [IndefP], to then turn to the case of canonical partitives.
To anticipate, our main proposal is that, in general, the outer nominal of partitives contains a relational noun which introduces partitivity. This noun takes the PP as its complement (51), and can be overt (in proportions) or covert (in most other cases). The covert noun comes in two versions, PART % and PART PRO , both taking crucial semantic information from their specifiers. PART % takes a degree, PART PRO , an invisible pro-NP, which enforces the desired connection between the inner and the outer nominal.

Out-of sentences, proportions and percentages
Proportional partitives and percentages (52) (see [ProporP] above) are semantically quite similar to the out-of construction discussed in the previous section: if 3 doctors out of 4 recommend X, we do not know the total number of doctors any more than with 75% of the doctors recommend X. However, percentages use the P di/of in Italian and English, suggesting, once again, that percentages fall squarely within the partitive family.
(52) …75% dei dottori … …75% of_the doctors … '75% of the doctors' It would be premature, however, to assume that percentages work exactly the same in English and Italian. Revealing inter-and cross-linguistic differences emerge once we consider the possibility for the outer nominal to be definite. In English, a definite article introducing the out-of construction is degraded (53a), even when the percentage reaches totality (i.e. ??the two out of two, in contrast with the totality of doctors), unless of course additional modifiers are present (53b) (the a/b difference is weekly significant, p. < 0.01). Italian behaves identically.
(53) a. ?The two out of three doctors recommend product X.
b. The four doctors out of four who recommended product X will surely also recommend product Y.
But with percentages, the two languages differ sharply. English percentages behave just like out-of: definites are impossible even when they express the totality, unless further modifiers are added (54b) (the ameliorating effect of modifiers noted in Kayne 1994: Chapter 8, Barker 1998, and explained by (43)). 10 Italian percentages of any value, on the other hand, are normally introduced by a definite article, without any need for modifiers (55). 11 If the definite is omitted, as in (56) the result is marked (average judgment 2.5 out of 5, hereafter "2.5/5"; a p.< 0.001 difference). 12 (54) a. ??The {20% / 100%} of the doctors recommend this. b.
The 50% of Americans who don't pay income tax will never be a good revenue source.
(from the Financial Times) of_the doctors recommends 'The {50% / 100%} of the doctors recommends …' (56) ??100% dei dottori raccomanda questo dentifricio. 100% of_the doctors recommends this toothpaste '100% of the doctors recommends this toothpaste.' Corpus searches show that the same effect can be found with proportions that are not percentages, i.e. those based on words such as half, quarter, third, etc. (collectively called denominator nouns, since they provide the denominators of the fraction expressed by the proportion). In English, structures like the num denominator of DP are very infrequent (23 cases, mostly the two halves of DP, vs. 1086 without the), and limited to cases where the whole has a very salient partition, as in (57). (57) a. This is achieved by angling the two halves of the keyboard at 30 degrees to each other. b. The city lies where the rivers Saine and Rhone and the two halves of France -the industrious north and the indulgent south -join. c. … It is divided into the four quarters of the year. 10 The existence of (54b) proves that the deviance of (54a) in English cannot be explained with the idea that "20%" functions as a determiner in English but like a post-determiner in Italian, much as my/mio in the contrast between my dogs and il mio cane 'the my dog'. *The my N is never improved by adding modifiers to N. 11 It should be noted that it is difficult to bring out this effect with on-line grammaticality questionnaires. In Italian, a canonical partitive with a definite scored ✽(1.6/5), which became ??(2.3/5) adding a modifier, but the difference is not statistically significant. We suspect that this could be due to the fact that to see any improvement it is crucial to interpret the modifier at the level of the external DP, out of the scope of the inner definite, i.e. (ib), not (a). This problem, which points to a more general limit of on-line judgments with naive informant pools, is confirmed by the extremely high variance (2.6) in the Italian judgments for the modifier structure.
(i) a. In Italian, on the other hand, the definite pattern is far more common (296 cases with a definite vs. 1058 without in one section of ITWAC), and is applied to cases lacking a clear partition, e.g. (58): (58) Ancora 40 anni fa i tre quarti delle proteine erano di fonte still 40 years ago the three quarters of_the proteins were from source vegetale. vegetable 'Still 40 years ago three quarters of proteins came from vegetable sources.' Since Italian and English do not show any contrast in their possibility of taking definites with canonical partitives (i.e. they both allow them, marginally, only with modifiers), their contrast in the out-of construction and in proportions (percentages i.e. (54a) vs. (55), plus the cases in (58)) shows that both constructions should be treated differently from canonical partitives, but for different reasons: out-of differ in preposition from canonical partitives (and indefinite partitives, see below), but behave identically with respect to definiteness; proportions use the same preposition as canonical partitives, but have diverging patterns with respect to definiteness in the absence of further modifiers-frequent in Italian, excluded in English.
Additional differences can be spotted at a syntactic level: Italian percentages always take singular number and masculine gender, even when the inner noun is feminine (59) (informal judgments). This does not happen in canonical partitives, in Italian as in French, see Sleeman & Ihsane 2016, and Section 6.1). When definites appear in Italian proportions they agree in gender and number with the denominator noun (60), which means that they are typically plural. One could at this point suspect that Italian percentages are idiomatic and non compositional, yet argue that English percentages should still fall under a canonical partitive analysis. This position is ruled out by three additional facts. First, percentages, like all proportional determiners but unlike canonical partitives, can also take mass nominals: {half / most / two thirds / 25%} of the oxygen Second, percentages can be larger than the whole of which they are supposed to be "a part" (62); canonical partitives cannot do this (nor can the out-of construction: ??five doctors out of four is jocular).
(62) His wage must be 133% of the minimum income.
Third, the inner nominal may be a bare plural (or bare mass singular), unlike in canonical partitives: (63) 74% of whites and more than half of Asians (Hoeksema 1996: 10) These facts also hold in Italian, where bare nominals are more restricted than in English. In this case, however, the percentage must be preceded by a determiner (64) (the difference with and without un buon is p. < 0.001; the difference between the determinerless percentage in (64) and in (56) is p. < 0.005).
(64) C'è ✽(un buon) 50% di clienti insoddisfatti di questo prodotto. there is (a good) 50% of customers dissatisfied with this product '(Some) 50% of all customers are not satisfied by this product.' Demonstratives also appear before percentages, e.g. (65), and when they do they are followed three times more frequently by bare inner nominals than by full definite DPs. 13 (65) quell' 80% di spesa per investimenti che gli enti locali that 80% of expenses for investments that the institutions local assicurano … guarantee 'that 80% of investment budget which local institutions guarantee …' Finally, a plural outer determiner is better than no determiner (66), but the difference is only weakly significant (p ≤ 0.01).
(66) ?Due 50% di un salario fanno un salario intero. two 50% of a salary make up a salary whole 'Two 50 percents of a salary make up a whole salary.' Turning to number, in Italian a verb that agrees with a percentage in the singular is much preferred, especially if a definite is present. English has a more mixed agreement: data from UKWAC shows that percentages which embed singular DPs can trigger singular, or more rarely, plural verb agreement (e.g. 18% of the population of the Russian federation […] are not ethnic Russians), while those that embed plural DPs always trigger plural verb agreement.
Taken together, these facts suggest that an analysis spanning (at least) English and Italian would be preferable, provided it can explain their diverging behavior with respect to definiteness. The analysis we want to propose covers all these facts and derives the contrast in definiteness from an independent parameter.

An analysis of proportions and percentages
Let's start from the case of proportions with denominator nouns (quarter, thirteenth, etc.). We will assume that the structure is (67) 13 Demonstratives plus percentages and bare nominals are well attested also in English (i). We thank an anonymous reviewer for pointing out to us the relevance of these cases.
(i) This 1% of public servants in Whitehall effectively drives most of what happens. 14 As it will be clear later, the numeral is inserted as the argument of an (often, null) operator. This is a limited variation on the idea, put forth in Krifka (2003), that numerals should be seen as arguments of nouns, and contrasts with the analysis given in  to two hundred people, where two is argued to be a numeral head in the main DP spine, taking the NP hundred as its complement. Our proposal to explain the Italian/English difference in the presence of definite articles crucially rests on the assumption that tre in i tre quarti di 'the three quarters of' is in Spec, and not in the position it normally occupies (see later, the discussion around ex. (74)).
From [Spec,NP], we take the cardinal numeral to be able to transmit its formal features to the DP layer above it, thus licensing a null Det head (in an alternative formulation, CardP is moved to [Spec,D 0 ] where it licenses this empty category, but is 'reconstructed' to [Spec,NP] for interpretation, see (68)).
We assume that the complement PP has the same denotation as the definite inner nominal, i.e. a plural individual, and that "≤" is the plural individual nonempty subpart relation (see Link 1983). The semantics of denominator words like quarter will make use of a discretizer: a measuring function amount, from objects and measuring units to numbers (69). When applied to pluralities formed with count nouns the unit defaults to the atomic item measure.
(69) [amount(x,u)] <e<en>> = amount of x measured in unit u (70) gives the semantics for the expression in (67a), assuming that ⟦of the people⟧ = ⟦the people⟧ = a. 15 Note that using ≤ as the subpart relation means that proper partitivity is (correctly) inactive in these cases (so, three thirds of the people is semantically well-formed, and usable in the appropriate pragmatic contexts).
"the set of plural individuals which are subparts of the people and whose amount, measured by unit u, is three quarters the amount of the people" Now the presence or absence of an external definite determiner follows from the wellknown observation that Italian, like all European Romance languages but unlike English, requires a definite article to give a DP a kind denotation (71a vs. b) (Contreras 1986;Longobardi 1994). In certain cases, the definite can also yield a pure indefinite existential interpretation (72) (Zamparelli 2002). We propose that the definite found in Italian proportions is precisely this kind of "generic article". (i) one third of the ten participants Since 10 is not divisible by 3, (i) seems to entail the existence of participant pluralities whose by-item measure is 3.3̅ . This might be desirable in some special cases (especially averages, see e.g. the average family has 1.2 children, Kennedy & Stanley 2009), but it is not usually a welcome result. Three solutions seem possible: (i) using a different measure function (e.g. height in two thirds of the four buildings are underwater); (ii) adding a presupposition that the measure of the pluralities in the set must be an integer (so, (i) becomes infelicitous) or (iii) approximating the pluralities in the set to the closest integer (so that (i) ends up referring to 3 participants). We will not take a stand on these possibilities here.
In English and Italian, any attempt to use a "normal" definite with denominator nouns is blocked by the same effect that blocks definites with canonical partitives (see ex. (41)): the lack of a unique/maximal element in the set taken by the definite. We suggest that, like English bare plurals, the "generic definites" in (71) and (72) do not require a (extensional) set of objects with a maximal element, so they are not excluded. In those proportional cases where the denominator noun refers to contextually specific portions (e.g. in (57), the left and right side of the keyboard, the four seasons, etc.), a unique/maximal element can be formed and extracted by the regular definite determiners, which thus remain possible, in English as in Italian, in these special circumstances.
Romance generic definites are normally incompatible with the insertion of a numeral before the noun: the DP in (73) has no kind reading, and can only apply to a specific set of ten rhinos (say, those still alive in 2006), thus barring kind-level predicates like are very rare, practically extinct, etc. Longobardi (1994) proposes that this happens because the numeral, a head in the main DP line (74), blocks the abstract movement of N to D needed for the kind reading to emerge.
(73) i dieci rinoceronti bianchi settentrionali the ten rhinoceros white Northern 'the ten Northern white rhinos' In the structure we are giving to proportions, repeated in (75)  This analysis now makes an interesting prediction. In Romance, just as in English, the use of a singular generic definite determiner is quite limited: with some approximation, it can only be applied to well-established, non-modified natural kinds (Carlson 1977;Dayal 2004). Since a wounded tiger is not in this category, the oddness of (76) follows.
If the Italian definite seen with proportions is a case of generic article, we expect that when the denominator noun is count singular (forcing any determiner to appear in the singular, due to agreement) this "generic definite" should become impossible (assuming, that is, that un quarto 'one quarter' is more like wounded tiger than like tiger). The only remaining strategy to license the whole DP is movement of the singular indefinite un (or of its formal features, depending on one's favorite theory of "reconstruction") to D, as illustrated in (68). This is indeed what happens: excluding the irrelevant ordinal meaning (the fourth person in a sequence), (77) behaves just like English (54b) in requiring a modifier, and contrasts with the plural case in e.g. (58). 16 (77) a. Il quarto del gruppo ??(che hai visto) è qui. the sng quarter of_the group (that you_have seen) is here 'The quarter of the group (that you have seen) is here.' b. L' un tredicesimo del totale ??(che deve essere messo da parte) the one thirteenth of_the total (that must be set aside) deve poi essere riportato alla fine.' must then be recorded at_the end 'The one thirteenth of the total (that must be set aside) must then be recorded at the end.' The case of percentages is conceptually not different from that of proportions (25% of the people just means one quarter of the people), but with a syntactic twist: the symbol "%", read "percent", is a less likely candidate for a nominal head meaning hundred. Moreover, the fact that here the Italian accompanying determiner is always singular requires a slightly different analysis.
We propose that percentages contain an abstract relational noun, written PART % , which in Spec position takes the value "card%" (the phrase formed by the numeral card and the "%" sign, tentatively marked AdvP/PP due to the presence of the morpheme per-'by') (78). PART % bears the syntactic features +n (nominal) and +mass; in Italian, it is has no gender feature, so it takes +masc (the canonical default value, in this language). The semantics for the example 10% of the people (with ⟦of the people⟧ = ⟦the people⟧ = a) is given in (79). 17 Note that here the card element that was able to license a DP in (68)  (1/10) = λeλx∃u[x≤e ∧ amount(x,u) = amount(e,u)×1/10] e. ⟦10% PART % of the people⟧ = λx∃u[x≤a ∧ amount(x,u) = amount(a,u)×1/10] "the set of plural individuals which are subparts of the people and whose amount, measured by unit u, is 1/10 th of the amount of the people" Let's see how the syntactic behavior of the construction follows from (78). When the nominal relational element is present, the verb agrees in number with it, rather then with the plurality generated by the percentage; the result is singular. Licensing the whole DP by means of the cardinal in [Spec,%], as in (68) is not an option (possibly because it would involve a left-branch subextraction of CardP), except in special non-argumental cases, where the whole DP layer might be missing (see ft. 12). Plural external determiners at the DP layer are also out, since PART % is +mass; singular indefinites are apparently possible, but they apply to the overt measure (i.e. to 50 in the example (66)), yielding an approximative meaning (cf. the translation of (64): some 50%). 18 Modifying an amount is indeed a characteristic behavior of the singular indefinite article when combined with an abstract mass nouns, see (80) (Tovena 2001 Like in proportions, the presence of an external definite determiner in Italian but not in English follows from the parameter regulating the distribution of "generic definite" articles, this time with mass nouns. The contrast seen in (54a) vs. (55) (i.e. the widespread use of a singular definite in Italian percentages vs. its absence in English) can now be reduced to the contrast in (81).
(81) a. ✽(La) democrazia è spesso problematica. the democracy is often problematic '(*The) democracy is often problematic.' b. Ho appena visto *(la) democrazia in azione. I_have just seen the democracy in action 'I have just seen (?the) democracy in action.' In Italian, determinerless examples such as (56), to the extent they are possible in argumental position (see ft. 12 for the non-argumental position) can be treated as cases where the overt percentage is reinterpreted as a quantity expression akin to many, so that the construction is coerced into the mold of a canonical partitive, whose structure is discussed in Section 6 below. Now the verbal agreement can be plural, and an external determiner becomes impossible unless modification is added (much as in (42), the two of the dogs that …).
The fact that in Italian determiners become obligatory when the complement is a bare nominal (as in (64), (65)) suggests that such cases should be analyzed as pseudopartitives, much like a number of objections or this low number of participants. As well-known, this construction requires the element before P to be +n (witness *many/*200 of objections); the only element capable of delivering this feature is the relational noun PART % which in turn forces the presence of an overt determiner, which can be the generic definite article in Italian, but not in English (following the pattern in (81)). In other terms, the presence of a bare inner nominal blocks any possibility to interpret the construction as a canonical partitive. 19 Additional evidence for PART % comes from its role in explaining the (non) acceptability of nominals introduced by most with collective predicates like gather or disperse, noted in van der Does (1993) (see Dobrovie-Sorin 2015).
When most takes a noun directly, the resulting nominal does not combine with collective predicates (82); but if an (apparent) partitive is formed, everything works (82b).
(82) a. Most soldiers {*gathered / *dispersed / were here}. b. Most of the soldiers {gathered / dispersed / were here}. 19 Remembering that of can be missing in pseudopartitives (a dozen (of) roses), we suggest that the case of non conservative proportions (ia) studied by Ahn & Sauerland (2017) are also pseudopartitives, or anyway measure phrases. Interestingly, their Italian correspondents must place the percentage inside a PP when in argument position (ib).
(i) a. The company hired 30% WOMEN.
b. La compagnia ha assunto *(al) 30% donne. the company has hired (at the) 30% women 'The company hired 30% women.' Taking the lead from the Italian sole translation for most, in (83), we propose that in (82b) most is not a determiner, but again, an argument of the abstract relational mass noun PART % (cf. the collocation for the most part). (84) shows that the overt noun part is fully compatible with cumulativity; so is, we propose, its cover counterpart.

(83)
La maggior parte dei soldati si radunò. the main part of the soldiers gathered 'Most of the soldiers gathered.' Part of the soldiers {gathered / dispersed}.
To summarize this section, we have proposed that percentages and proportions differ from canonical partitives in containing a relational nominal element, overt in proportions, covert in percentages, whose syntactic properties dictate a different behavior even in languages where the behavior of canonical partitives does not differ. Some of their special properties follow from the possibility to reclassify some cases of percentages as pseudopartitives or as canonical partitives.
As discussed above, proper partitivity in not enforced in our semantics, thus freely allowing 100% of the people (cf. four out of four doctors). The partitivity does not come from the Case marker di/of, but from the semantics of a special class of nouns, in agreement with an analysis put forth in Chierchia (1998). The inner nominal could contain any constituent whose semantics returns a single plural individual, a point which will be important when we discuss the coordination effects, in Section 7.
(85) a. three of some men Abbott (1996: ex.24) b. many of all women c. several of no books d. two of too many acquaintances e. several of twenty of his roses that were sick f. few of many questions (86) a. I know you have too many acquaintances, but you only need to bring two of them. Two of too many acquaintances is still only two. b.
[…] I am sure that each student only answered few of many questions that he might have been able to get with a little thought. ducer/consumer). Indeed, cases introduced by some, many and all were rather very low in the crowd-sourcing task, while cases introduced by a numeral fared better (89) (the difference between (88a) and (89a) is highly significant). Note that (89a vs. b) does not support de Hoops' judgment, though the difference did not come out as statistically significant in the crowd-sourced data.
(88) a. ??Some of many soldiers died. b. ✽ Most of some say that the Earth is flat. c. ??All of many soldiers died. d. ??Some of all apples were rotten. e. ??Some of twenty soldiers died.
(89) a. John was one of several students. b. ?John was one of several students who arrived late. c. ?Speaking of acquaintances, only two of many came to the party.
Barker (1998: Section 2) capitalizes on the presence of a strong restrictor to argue that the internal nominal in these cases is specific in context and must thus denote a plural individual. Barker cites I found an even prime as another example where an indefinite has the same model-theoretic referent as a definite, and points out that cases such as *I hurt two of half of my fingers, which entail the existence in context of additional relevant elements, make the partitive unacceptable.
If the PC is recast in a purely semantic version (90), and specific indefinite are interpreted as in (91)
(91) a. If I expel two students that cheated in my exam I will be criticized. b. ∃f[expel(I,f(student_who_cheat) → criticized(I)] 'There is a certain method to chose individuals such that if I expel two individuals chosen by this method from the set of exam-cheating students, I will be criticized.' One potentially problematic aspect of Barker's proposal is that the inner nominals in indefinite partitives may contain determiners like many or several, which do not pass another classic test of specificity, the possibility of scoping out of strong islands. For instance, (92a) has the wide scope made explicit in (92b) only when D is a simple cardinal (three) but not when it is most or a vague amount modifier (many, few, several) (Liu 1990;Zamparelli 2005).
(92) a. If you see {three / many / few / several / most} people with red hats, let me know. b. There are D people with red hats such that, if you see them, you let me know.
If wide scope is connected to the possibility of denoting an individual (Fodor & Sag 1982), or of being under a Choice Function bound from outside the conditional, then the Q-adjectives that yield clause-bound indefinites must be quantificational (see, indeed, an analysis along these lines in Solt 2015).
In conclusion, appealing to specific indefinites might be a valid solution for some of the cases pointed out by Abbott, but this solution might not extend to other cases (for instance, to the contested case with several).
An additional possibility, suggested by the presence of just/only, is that some indefinite partitives may actually be focus constructions, based on quantities. This means that while the communicative goal of a canonical partitive is to show that some entities are part of a larger, contextually salient group, the focus of some indefinite cases would be to contrast two quantifiers in a Horn scale: the actual amount of entities to which some predicate applies, given by the external determiner, and the larger number to which it might have applied, given by the internal one. If this idea is on the right track, only one of four students came would end up having the informal semantics in (93) (with one and four in a Horn scale, four a stronger value than one).
(93) a. One student came in world w b. It is not true that four students came in w c. There are worlds w′ accessible from w such that four students came in w′ (i.e. four students might have come) This fits with the fact that numeric partitives with no inner determiner like ✽three of apples were rotten are severely ill-formed in any context, since bare plurals are not specific and their "null" determiner is not focusable. Leaving a formal rendering of (93) and it compositional derivation for future work, we tentatively conclude that indefinite partitives might be seen as a combination of two strategies: one in which the inner nominal denote a plural individual much like a definite (but without a presupposition that the hearer should be able to identify the referent) and one which overlaps in function with the out of construction (but without out), contrasting an actual and a possible or expected amount. In Italian, where the preposition su 'over' is used for out-of cases like one doctor out of four, the same preposition can be used in a subset of non-definite partitives given by Abbott (e.g. solo uno su quattro controesempi possibili 'only 1 over 4 possible counterexamples'), blurring the distinction between the two constructions.

The internal structure of canonical partitives
As we have seen, one of the structures proposed for partitives involves an empty nominal category, marked N e , before the partitive PP: The analysis of proportional partitives we have proposed in the previous section sees N e as a null relational noun, PART % , which takes the partitive PP as its argument. There is however strong evidence that this structure does not fit all partitives, and in particular, that is should not be adopted without considerable modification for canonical cases like many of the boys (witness the impossibility of *many% of the boys). In the next sections we will defend a "matching" version of the structure in (94) where N e contains an empty proform coindexed with the inner NP (NP2 in (94)). This coindexing makes it a variant of the movement approach adopted in Zamparelli (1998;, while overcoming some of its defects. Though unpronounced, the upper nominal is semantically active.
There are two main arguments in favor of this structure: the pattern of gender agreement between the outer determiner and the inner noun, and "double genitives", where the outer NP is actually a raised copy of inner one. A third crucial consequence of the analysis-the ill-formedness of some coordinated inner nominals-will be taken up later, in Section 7.

Agreement patterns in Italian
The relevance of gender to make the case for the existence of a null nominal category in partitives was pointed out already in Sleeman & Kester (2002). Cardinaletti & Giusti (2006: §3.3.4) discuss the fact that in French partitive constructions introduced by a quantifier cannot present mismatches in gender: In an analysis in which a copy of filles is present after the outer determiner, as in (96), the impossibility of agreement mismatches reduces to the ungrammaticality of un fille 'a M.Sng daughter F.Sng (see Sleeman and Ishane, 2016 §4 and 5, for a technical implementation). Note that, crucially, we do not want number features to be copied as well, or (96) would be ungrammatical due to the number mismatch in *une filles (we also don't want (96) to refer to a granddaughter-this semantic problem will have to wait till Section 6.4; see the discussion around ex. (121)).
(96) une fille F.Sng de mes filles F.Pl In (95), however, semantics is a strong confound: un could be impossible not for grammatical reasons, but because it is a masculine pronoun which refers to (a subpart of) a group of females-the antecedent of the partitive. A better test should use human plural nouns that have a single grammatical gender but comprise either man or women, such as persone F 'people' or partecipanti M 'participants', in Italian. Sleeman & Ihsane (2016) analyze the situation in French and conclude that gender mismatch may be allowed (especially in superlatives) only when the mismatched quantifier is masculine, the default form. Here we report on Italian, which seems at first glance more permissive: mismatches like (97) seem fairly acceptable in both directions, and they are robustly represented in web searches with human nouns (though not with animals), even if the matching case is far more common. 21 (97) a. ?Una dei partecipanti era arrivata molto presto. one F.Sng of_the participants M.Pl was arrived F.Sng very early 'One of the participants arrived very early.' b. ?Uno delle persone era arrivato molto presto. one M.Sng of_the people F.Pl was arrived M.Sng very early 'One of the people arrived very early.' In the plural, however, a gender mismatch is much less tolerated (98) (the difference between the fem-masc mismatch in (97a) and (98a) is p. < 0.001).
(98) a. ✽Alcune dei partecipanti sono arrivate molto presto. some F.Pl of_the participants M.Pl are arrived F.Pl very early 'Some of the participants arrived very early.' b. ✽Alcuni delle persone sono arrivati molto presto. some M.Pl of_the people F.Pl are arrived M.Pl very early 'Some of the people arrived very early.' The general preference for gender matching supports a double noun structure in canonical partitives, and the existence of masc-fem mismatches like (97b) (informal judgment) could perhaps be tolerated on account of the default nature of masculine gender in French and Italian. But the fact that gender mismatches go in both directions and depend on number clearly calls for an explanation.

Double genitives as inverse partitives
The possibility of a hidden double-noun structure in partitives would obviously be strongly boosted by constructions with a partitive meaning but where the outer noun is overt. Double genitives, 22 [InvertP], introduced in Section 2 seem to fit the bill. Indeed, Kayne (1994: Chapter 8) and Barker (1998) already regard these cases as "inverted partitives" (as we listed them in our initial review of the partitive family). 23 (99) a. two books of John's b. a relative of mine Like canonical partitives, double genitives display PPart: it is odd to say ??a mother of John's, ??a nose of mine. 24 Building on Kayne's idea that (100) involves fronting of a subpart of the inner nominal, Zamparelli (1998) argued that both partitives and double genitives involved raising the inner NP to a position to the right of the outer determiner (two). Partitives would then spell out only the foot of the chain, double genitives, only the head. Zamparelli linked the two orders in (99) to the two orders found in the "kind construction": a car of this kind/this kind of car. Note that this raising structure would have to apply even in cases like two of them. This is unproblematic, if we adopt Elbourne's (2005) structure for pronouns, which makes them hidden definite descriptions with an invisible restrictor: Italian has a broader range of constructions similar to (100b). (102) (originally discussed in Cardinaletti & Giusti 1990) has a demonstrative as the inner determiner. 25 Inverted superlative partitives (103) were mentioned in Section 2, item [SuperlP].
(102) a. due amici i di quegli amici i che porti sempre a casa two friends of those friends that you_bring always home 'Two of those friends you always take home' b. due amici i di quelli amici i che porti sempre a casa two friends of those friends that you_bring always home 'Two friends of the kind you always take home' (103) a. due vini i dei vini i migliori two wines of_the wines best 'Two of the best wines' b. due vini i dei vini i migliori two wines of_the wines best 'Two wines of the best' In an approach that does not posit an identity between the inner nominal and the noun after the outer determiner, the parallel between the cases in (a) and those in (b) is lost. Of course, this is a shortcoming only if we have convincing evidence that (a) is indeed a variant of (b). But this position has come under attack.
One problem, noted in McCawley (1988) and rediscovered in Storto (2000), is that English double genitives allow only a subset of the types of possessive relations which canonical partitives allow. Thus, (104) shows that "small" DP possessors which express a modifier relation (place and especially time) worsen when inverted (p < 0.001 for time, (104b)); (105) shows that leaving a numeral after the possessor in the lower DP degrades only the inverted order; (106), modeled after an example in Storto (2005), shows that possessive relations which are assigned by the context (here, the patient of the attack event) are worse in double genitives than in the corresponding partitives (the difference is shared by McCawley and other native speakers we asked, but it was not statistically significant for our naive informant's pool).
(104) a. (i) One of Rome's hills has a spring.
(ii) ?One hill of Rome's has a spring. 25 As discussed in Zamparelli (1998), these demonstrative are non-deictic, and tend to have a qualitative, kind-oriented meaning (see also Cardinaletti & Giusti 2007: Section 3.3). If the inner demonstrative has no modifiers it takes a negative connotation (e.g. that lousy kind), as in (i), where ne has been extracted from after the demonstrative: (i) Di stupidaggini i , ne i ha fatte di quelle! of silly_things, one(s) he did of those 'He did such silly things!' A possibly better translation of (102)b is 'two friends of the kind you always bring home'. See ft. 34 for further remarks.
b. (i) One of yesterday's lectures was boring.
(105) ??A novel of Jack's two was made into a movie.
(106) Two distinct groups of dogs attacked Jack and John. a. Unfortunately, one of John's dogs turned out to be rabid. b. ?Unfortunately, one dog of John's turned out to be rabid.
These distinctions show that the differences between double genitives and canonical partitives cannot be a matter of spell out-which of the two copies gets pronounced. However, other possibilities remain open. Far from undermining the link between double genitives and partitives, we believe that these facts point to a way for refining it. Consider for a moment the alternatives. The hallmark of double genitives is a simple possessor not followed by a noun. But this is only possible when the context presents an overt noun whose content can be identified with the missing one: out of the blue, (107) cannot be understood as Mozart's music is played a lot (note that Mozart is still played a lot can metonymically get precisely this meaning).
This strongly suggests that, if double genitives are not a case of raising, they must be cases of nominal ellipsis, on the model of (108).
But in English, nominal ellipsis has none of the restrictions reported above. (109) shows that "modifier" possessors are fine; (110) is fine both in subject and object cases; (111) (contrasting with (105) at p. < 0.001), shows that stranded numerals are fine in ellipsis contexts.
(110) Two distinct groups of dogs attacked Jack and John.
a. John's dogs turned out to be rabid, while Jack's didn't. b. I had to check John's dogs for rabies, while my colleague checked Jack's.
(111) John's four novels may be bestsellers, but Jack's two are masterpieces.
Thus, in an ellipsis account, the restrictions noted for double genitives remain a mystery. What we really need is a movement-based account of double genitives that can also explain them. Zamparelli (1996: Pg.136) proposed that possessors may occupy a higher or a lower position in the DP spine (say, [Spec,DP], preferably, or [Spec,NumP], in special cases; see Cheng et al. 2017), and that the presence of a numeral in Num (as in John's two wishes) forces the possessor to occupy the higher position. Suppose that double genitives are indeed derived by moving the inner nominal to the outer DP. To move overtly, however, the edge of the inner DP, a phase in the system of Chomsky (2001;, must be unoccupied (112). 26

An analysis of double genitives
When a numeral is present, the possessor is forced into the high position, at the edge of the DP (113), but now this position hinders NP extraction. This obtains the contrast between (105) and (111)

A matching theory of canonical partitives
While the various restrictions of double genitives can be addressed, we believe, in a raising analysis, the fact that none of them applies to canonical partitives casts doubts on a simple raising theory like Zamparelli's (1998), which sees "canonical" and "inverted" partitives (e.g. the examples in (100), (102) and (103) above) as simple spell-out variants. This approach predicts that, across languages, it should be possible to overtly extract the inner NP out of definites and even demonstratives. In actual fact, constructions like the (b) variant of (102) or (103) are marginal or impossible in languages where (a) is perfect (English is one example: *Two people of the tallest, *A wine of the best). 28 In addition, the reason why in the canonical partitive case languages should spell-out the foot and not the head of the movement chain remains mysterious. Last but not least, Zamparelli's movement-to-[Spec,of] analysis does not solve the syntactic problem raised by the side-by-side existence of quantitatives and partitives: most determiners would have to select either for NP or PP (abstracting away from intermediate functional projections). What is needed is a theory that preserves the advantages of the raising analysis-the idea that there is a match between the inner nominal and an invisible element to the left of the preposition-without treating partitives as cases of covert NP movement. We believe that our proposal for canonical partitives can achieve this goal.
26 See Fiengo & Higginbotham 1981;Campbell 1996 for discussion and different approaches to this problem in relation to the "Specificity Condition" on extraction. 27 Some speaker we consulted found the variant two children of Jacks's four grammatical, with contrastive focus on four. We suggest that this might be a case closer to out-of "partitives". In such cases, the PP may be preposed.
(i) (out) of John's *(FOUR), I bought THREE books. 28 In Italian, we find semi-lexicalized cases of ne extraction (where ne is a pro-NP) out of distal demonstratives, as in (i), but not from other cases (on the meaning of demonstratives in (102) and (i), see footnote 25).
(i) Ne ha fatte di {quelle! / *queste! / *quelle laggiù}. them he_has done of {those! / these! / those over_there} 'He did such (naughty) things!' Suppose that in partitives the outer determiner selects a null relational element part pro , which hosts in its specifier a pro-NP, equivalent to a null version of the Italian clitic ne or English pro-NP one (see Falco & Zamparelli 2016 for a full treatment of these elements). part pro , in turn, selects for the of PP. In canonical partitives, the PRO in [Spec, part pro ] is coindexed with (i.e. cataphorically controlled by) the NP 2 in the inner nominal (114).
Let's review some features of this proposal. First, both partitives and quantitatives contain a nominal element and have the same structure, so there is no need to assume that D or Num select for NP in quantitatives and for PP in partitives. Second, the fact that the determiners which support partitives are those which allow null-nominals constructions (witness the contrast between each and every in (115)) is no longer a coincidence: in partitives, the null nominal is PART pro . We propose that, unlike PART % , PART PRO is not mass and can be freely singular or plural, compatibly with the number specification it gets from PRO.
(115) a. When the kids came, {each / *every} got a gift.
(null nominal) b. When the kids came, {each / *every} of them got a gift. (partitives) Next, let's reconsider the Italian agreement facts presented in (97) and (98): gender mismatches between the outer determiner and the inner nominal are more or less tolerated, but not when the outer determiner is plural. In the theory we are proposing, gender features in the upper nominal are normally inherited via PRO in [Spec,part pro ] (possibly via part pro itself, assuming that it does not have gender features of its own). But PRO can inherit a smaller or larger set of grammatical features from the inner NP, by coindexing-we suggest-with a larger or smaller nominal portion of the inner DP. To spell out the idea, suppose that gender is contributed either by a Gender projection which is adjacent to the NP proper and inserted from the lexicon along with it (116a) (cf. Harris' 1991 notion of "Word Marker", but also to the Classifier Phrase proposed for many classifier languages, see e.g. Cheng & Sybesma 1999;Simpson 2005), or delivered by the same phrase that contributes plurality, tagged PlP here, (116b) (this second structure, defended in Di Domenico, 1997 is probably an option only for those animate nouns with a semantically interpretable gender, e.g. Italian ragazz-o/a 'boy/girl'). Number, on the other hand, is always realized in the projection higher than NP, and is independent from it (see Either configurations in (116) make it possible for PRO to target a noun with its gender (by coindexing with GendP or PlP) or, in more marked cases, without it (by coindexing with just the NP). The singular mismatching case can thus receive the structure in (117a): PRO targets NP, the DP formal gender features are not copied on PRO, the gender of the outer D reflects the semantics of the referent (its biological sex; recall that gender mismatches are restricted to humans, where grammatical gender is interpretable) and its singular number is a default value for number. When the outer D is plural, however, it must agree with PART/PRO, which must in turn obtain fully specified number features by coindexing with Pl(ural)P (117b). But now the gender features from the inner nominal are carried along, blocking the possibility of mismatched gender, as we saw in (98) In Zamparelli (1998), the internal NP was moved to the Spec of a PP headed by a "residue head", a head which subtracts the semantic of its complement (a maximal plural individual) from that of its specifier (a semilattice). This derived PPart at the cost of an unusual semantics for of. Here the preposition of reverts to being a simple Case assigner with the semantics of an identity operator, and the "residue" semantics is transfered to PART PRO (118), which combines first with PRO (denoting a plural property), then with the definite complement (denoting its maximal element), subtracts the second from the first ("P-x" in (118)) and uses the result as the new nominal restrictor (i.e. λy[P-x(y)]).
In double genitives, on the other hand, [Spec,PART PRO ] hosts an actual movement copy of the inner NP. Just like PRO-NP, the overt NP denotes a property and the semantics works exactly as in the last line of (119).
It is now easy to show that the partitive PP is not a complement of the raised nominal by simply picking raised nominals which have complements of their own, like director of immigration services in (120).
(120) a. Your director of immigration services made an awful mess.
b. This [director of immigration services] i of yours t i made an awful mess.
This defuses the possible objection that (121a, b) cannot have a covert structures which is similar to (121c) (with one of the two friends replaced by a PRO-NP or a trace).
(121) a. two of John's friends b. two friends of John's c. two friends of John's friends The objection now has no force, since (121a) means something very different from (121c): in (121c) the PP is the object of the upper friends, while in (121a) the PP is an object of PART PRO , not of PRO coindexed with friends. Likewise, of John's in (121b) is not an object of the raised friends. In (120), the argument of the noun director is of immigration services, which has raised along with it to the Spec position to the left of the PP of yours. 29 Positing an empty nominal element at the core of partitive semantics leads to the expectation that this element might be overt in some languages. A concrete possible candidate for PART PRO is the Turkish "classifier-noun" tane we saw in (14b), and which might be realized overtly as a way to support number and Case morphology (when this noun is missing, the same morphological markers appear on the numeral, see (14a)).

Predictions for other partitive structures
We can now observe what happens when we cross double genitives with other members of the partitive family: the proportional partitives studied in Section 2, ([ProporP]), and the among-partitives ([AmongP], Hoeksema's semipartitive). Proportions are impossible as double genitives: (122b) is grammatical, but not with the meanings of (122a) (rather, something like I talked to semi-friends of John's). (122c), where this meaning is not available since friends doesn't take a "fraction" argument, is out.
I talked to half of John's friends. b.
I talked to half friends of John's.
(not a double genitive) c. ??I talked to 50% friends of John's.
Also out, given the characterization of percentages given above, is a structure where the inner noun has moved to [Spec,PART % ]: unlike PART pro , this noun does not take a nominal argument.
Among can more or less freely replace of in most types of partitives, but not in mass partitives (*half among the people), nor, again, in double genitives like (123).
In plural cases like (124) the difference was not so clear-cut, however.
b. ??Two novels among John's have became bestsellers.
Unlike other linguists we have asked, our informant pool did not detect any difference between (124a and b) (note that, due to randomization, the two cases were judged independently). Additional, informal judgments, show that adding a numeral after the possessor in (124b) (e.g. ?Only two novels among John's twenty became best sellers) does not degrade the situation much, suggesting that perhaps (124b) should be regarded as a case of nominal ellipsis (125), and that the more degraded status of (123) could be due to a number mismatch (a friend among John's friends).
(125) two novels among John's (twenty) novels Italian informal judgments show that fra 'among' tolerates the presence of two full nominals in cases which would be impossible with di 'of' partitives (126). The situation is probably identical in English (see Section 9 for similar cases).
(126) due persone {fra / *di} loro two people {among / of} them 'Two people among/*of them' Cardinaletti & Giusti (20062) examined the Italian semipartitives and conclude that among cases are in fact adjuncts, not selected by D or N. 30 von Heusinger & Kornfilt (2017) give an analogous analysis to Turkish ablative-marked partitives (see (175) 30 One could of course wonder if the "partitive" meaning of among is simply a special case of a locative meaning, visible in e.g. (i) (from UKWAC).
(i) Among some papers from Atherton & Clothier we find 2 gallons of egg listed in the ingredients required for dyeing sheep skin. below), but also point out (von Heusinger & Kornfilt 2017: Ft.11) that Turkish has a separate adverbial which more closely resembles from among, and that ablative-marked cases can apparently take mass nouns as inner nominals (127). This could mean that the count semantics of among is orthogonal to its adjunct status, or that (127) should in fact be reanalyzed as a pseudopartitive (cf. English two glasses of wine).
(127) Ali şarap-tan iki bardak iç. Ali wine-Abl two glass drink 'Ali drank two glasses of the wine.' In conclusion, in agreement with previous literature we believe that an adjunct analysis is the best one for tra/among constructions and for Turkish ablative-marked cases. One consequence is that semipartitives should not allow movement of the type used in double genitives; the contrast in (126) follows straightforwardly: in the among case, people is generated in the external position, not moved from somewhere inside the inner nominal. We return to semipartitives in Section 9, where we discuss in more details the possibility of dislocated PPs and doubly-filled partitive nominals.

Coordination
A strong argument in support of a matching analysis of canonical partitives comes from the coordination of definites. Semantically, the conjunction of two definite arguments under a single collective predicate, as in (128), must denote either a plural entity whose atoms are the denotations of the individual definites (i.e. j+m in (128a)), or a generalized quantifier, GQ, whose generator is j+m (i.e. λP[*P(j+m)]). Opinions differ on how to derive these denotations (see e.g. Winter 2001 for discussion), but there is no disagreement on what the final output should be. Thus, if the boy and the girl in question are my best friends, the denotation of the boy and the girl should be the same as that of my two best friends. Yet, surprisingly, while the latter is perfect within a partitive (129a), the former isn't (129b), (130b). The same holds in Italian (131).
(129) a. I am looking for one of my best friends. b. ??I am looking for one of [the boy and the girl]. c. ✽ One of [this boy and that girl] came over.
Some/Two of those 4 boys will not come. b.
{??Two / ✽Some} of Jack, Marc, Luis and Tom will not come.
(131) ✽Conosco bene uno del ragazzo e della ragazza. I_know well one of_the boys and of_the girl 'I know well one of the boys and of the girl.' The quantifier each provides an interesting minimal pair, since it can form partitives with plural definites (132a), appear 'floated' in association with singular definite conjunctions or plural definites (132b), but not form a partitive with a singular definite conjunction (132c) (p. < 0.001 for b/c) (de Hoop 1997).
Each of the two students ate one ice-cream. b.
{John and Mary / the two students} ate one ice-cream each. c. ??Each of John and Mary ate an ice-cream.
(=(132a)) b. {Gianni e Maria / i due studenti} hanno mangiato un gelato ciascuno. This unexpected contrast is unlikely to be due to a general problem with applying of to a coordination (a friend of the baron and the general is after all impeccable). Also, Hoeksema (1996) cites good mass proportional partitives such as Only about half of John and Jacky was visible for the sniper, which were partly confirmed by our informant pools in English (135) and in Italian (136)  The contrast between ??one of John and Mary and half of John and Mary is noted and discussed in Helen de Hoop (1997). She proposes to distinguish the two cases on the basis of a broader divide between number-based and amount-based partitives. Cardinal numerals can introduce only the former (3 of the boys), mass determiners only the latter (much of John), but most determiners (notably, proportional ones like all, most, 20%, one third, half) are ambiguous between the two types, so we get an ambiguity in cases such as (137).
(137) Half of the flowers should now be in the water.
(i.e. 3 out of 6, or the lower part of each flower) De Hoop's (1997) proposal is that the two readings come from a semantic ambiguity in the denotation of the DP embedded in partitives: in number-based cases, the flowers would denote a contextually restricted set of atomic individuals, in amount-based ones, a plural individual whose atomic components are flowers.
One positive feature of this approach is that since the flowers can have the same semantic type as that of the common noun flowers (i.e. <et>), she can explain the existence of both all flowers and all the flowers. Crucially, she proposes that the option to have these different denotation types is open to all definites, but not, apparently, to conjunction: John and Mary can only have the "plural individual" meaning, so this nominal is excluded from number-based partitives, but remains possible in amount-based ones.
This proposal covers the facts, but at the expense of overgeneration. If both flowers and the flowers can be a property (i.e. <et>-type), it is not clear what blocks *{three/many/red} the flowers. 31 In addition, the semantic effect of plurality remains unclear in this system. Worse, without independent motivations, the proposal that conjunction does not have a set denotation is a mere stipulation. De Hoop points to the fact that definites involve contextual restrictions while conjunctions like John and Mary do not, but it is unclear why this should matter for having a set rather than an individual denotation. Moreover, coordinations of two definites (e.g. the boy and the girl) should also have undergone contextual restriction at the level of conjuncts, yet their status in partitives is unchanged. Finally, not all definites require contextual restrictions: the Earth poles has none, and it denotes what the North pole and the South pole denotes, yet the former is allowed in partitives, the latter is not. We conclude that de Hoop's approach is neither viable nor very explanatory.
In the approach pursued in this paper (and in the raising theory from which it derives), the ban on conjunction in canonical partitives comes for free. In the matching theory, partitives crucially contain a PRO (an NP proform) coindexed with the inner NP. The source of the problem is that in conjunctions there are multiple distinct NPs (in the boy and the girl), or none at all (in John and Mary) to which PRO should be simultaneously coindexed.
(138) *one PRO ? part pro of [ the boy i and the girl j ] One could wonder if (138) could not simply be available as a case of split reference, as in John i told Mary j that they i+j should split up. Remember, however, that our PRO is actually closer to an overt NP/GendP/PlP proform like ones: it picks up properties, not individuals. Split reference may be possibly for individuals, but interestingly it is not possible for properties, as shown by the contrast between them and ones in (139).
(139) John wanted [two blue shirts] i and [three gray sweaters] j and Mary bought {them i+j / *four brown ones shirts∪sweaters } (instead).
The same applies to the Italian pro-NP clitic ne: in (140b) ne (object of sei 'six' before movement) cannot mean "martinis and spritz" (see also the English translation).
(140) a. I ragazzi ha bevuto tre martini i , e le ragazze hanno poi the boys have drank three martinis, and the girls have then preso quattro spritz j . taken four spritz 'The boys drank three martinis i ; later the girls took four spritz j .' b. Alla fine, {li i+j ho pagati tutti io / *ne martinis∪spritz ho pagati sei t}.

At_the end, {them have paid all I / ones
I_have paid six } 'At the end {I paid them i+j all / I paid six (i.e. six out of set of martinis and spritz)}' Note that an account which posits a null nominal before PP but does not obligatory coindexes it with the elements inside the inner DP does not predict any problem with coordination (see the discussion in Sec. 8, on alternative double-noun analyses, esp. (158) and (160)). Neither does an approach à la Kupferman, Lobeck, etc., which has no empty outer nominal at all.
Our account predicts that, in principle, the situation might get better if the two inner DPs had restrictors which referred to the same individuals. The test is only feasible in the plural, but indeed, we believe that if in a certain context the singers are the same as the songwriters, (141) is felicitous.
(141) one of the singers and (the) songwriters Natural cases where the NP in the two antecedents is identical are harder to construct, but we believe that (142) can be easily understood as entailing the partitive in (143) On the other hand, our pool informants found that even disjoint plural conjunct like (144) were significantly better than the singular case. Since a potential confound is the possibility of a two-people reading with ellipsis (from one of the boys and one of the girls), we also tested (145), which of course cannot be derived from three of these two boys and three of those two girls. (145) was found to be worse, but not significantly worse than (144) (though still significantly worse than the case of singular conjuncts). 32 The improvement thus remains unresolved.
(144) ?One of the boys and the girls will came over.
(145) ?Three of the two boys and the two girls set up a tent.
As we have seen, mass partitives allow conjoined inner nominals. This is expected, since proportions are based on PART % , which does not have a PRO. The only remaining ingredient to obtain mass proportions is the presence of a count-to-mass type-shift (from an object to its material constituent part), which seems to be independently needed in light of many mass uses of count nouns, well documented in the literature (Pelletier & Schubert 1989).
Here we assume a single such operators (mass), but this is a simplification, since cases like Some of theater is improvisation or Most of cheese is saturated fat (to the extent they are acceptable: our pool raters gave them ?? and ?, respectively) require more abstract types of count-to-mass operators (on which see Zamparelli 2019). 33 De Hoop's flower sentence can thus be rendered as:

Alternative double nominal analyses
Let's now discuss two alternative incarnations of the "covert noun structure" which have been proposed in the literature on canonical partitives. Both posit an outer NP, but do not assume coindexing or movement. Both will turn out to be more problematic than the PRO i … NP i analysis advocated here. Sauerland & Yatsushiro (2004) proposes that partitives have an outer noun which is identical in form to the inner noun, but is not coindexed with it. The upper noun is then deleted at PF under identity of form with the second. As in Barker, Kayne and Zamparelli's previous accounts, double genitives have the same structure, but erase the lower NP.
Since the upper noun is not extracted, this approach, unlike Zamparelli's (1998) NP-movement system, avoids the island status of the inner definite DP. In addition, it explains the status of (150), which seems to be marginal out of redundancy, more than grammar (no PF-deletion has taken place).
(150) ?Three sofas of those sofas you bought.
As observed in Cardinaletti & Giusti (2006), assuming that sofas and couches denote the same objects, (150) is still better than (151), where PF-deletion cannot take place.
(151) *Three sofas of those couches you bought.
On the other hand, since the final structure is a matter of PF, this account predicts that double genitives should have exactly the range of meanings as the corresponding canonical partitives, which we have seen to be incorrect (Section 6.2).
A second problem is the direction of PF-deletion: partitives should have the same status of e.g. (152). But (152) is marginal, at best.
Allowing backward NP ellipsis in partitives is in fact not enough: some amount of cancellation should be obligatory, or we could create examples like (153) (from Martí-Girbau 2002): a partitive structure like two of them, but without an (overt) inner NP which could license the ellipsis of people.
(153) *two people of them Even with a fuller inner DP, a PF account runs into other problems. Imagine a context with 6 books, 3 red and 3 yellow-covered. Now (154) is possible, but (155) is not (see Martí-Girbau 2002 for a similar point).
(154) The three books with a red cover are on the table, the three books with a yellow one, on the shelves.
(155) *I bought three books with a red cover of the books.
One could counter that the problem of (155) (154)), another for partitives, where despite the presence of an (invisible) NP complement, they take their restriction from the PP, as it must happen in (157). Thus, this theory seems to combine PF complexity (backward ellipsis), syntactic complexity (a null NP which violates Full Interpretation) and semantic complexity (a double meaning for most determiners), gaining very little in return. It would, for instance, not explain the conjunction facts we have reviewed, since it should be expected to allow (158).
(158) ??one book of this book and that notebook Let's now consider another possibility. Suppose that the empty category posited by Jackendoff (1977) is not a phonologically empty token of the lower NP, but a maximally underspecified nominal category, meaning something like person, object or entity. This is suggested as a possibility in Sauerland & Yatsushiro (2017), and is implicit in various syntactic accounts of partitives, e.g. Sleeman & Kester (2002), or even Jackendoff's own account. A partitive such as I saw two of the boys/two of the boxes would end up being semantically equivalent to (159).
(159) a. I saw two [persons] of the boys. b. I saw two [objects] of the boxes.
Where person/object are abstract nominals with no phonetic form. This approach would ease the PF problem of backward ellipsis, but not the semantic problem discussed above, which leads to a double version for all determiners. In addition, it would not explain the conjunction facts: (160) would be a perfectly viable form.
(160) I saw one person of the boy and the girl.
Last but not least, this approach would have to face the fact that while (150), three sofas of those sofas you bought, seems redundant more than ungrammatical, (161) seems outright out (as a partitive), despite the fact that each of the bracketed nouns fits the bill for an overt version of the maximally general nominal meaning in (160).
In this respect, the "same NP" view embodied by (150) seems in fact better, but still more problematic than our PRO-matching analysis.

An analysis of partitives with two overt nouns
It is important to point out, at this stage, that while (161) is bad, there are well-formed partitive-like cases where two overt nouns are present. Some have the order of canonical partitives (162); in others the PP has been fronted (163).
(162) a. I only got two packages of the mail you sent me. b. ?I read two novels of the books you gave me.
(163) a. Of the mail you sent me, I got only two packages. b. Of the books you gave me, I only read two novels.
Cases like (162) were discussed in Cardinaletti & Giusti (2006), and judged ungrammatical for Italian (their ex. (120b)). However, the crowd-sourced English data show that they range from completely acceptable to slightly marginal. Cardinaletti & Giusti do observe, however, that extraposed cases like (163) are better in Italian, and that even the order in (162) becomes better if partitive di/of is replaced with tra/fra 'among'.
(164) a. Ho letto solo due romanzi, dei libri che mi hai dato. I_have read only two novels, of_the books that to_me you_have given 'I have read only two novels, of the books you gave me.' b. ?Ho letto solo due libri, dei romanzi che mi hai dato. I_have read only two books, of_the novels that to_me you_have given 'I have read only two books, of the novels you gave me.' The partial acceptability of partitives with two nouns is unexpected, and needs to be addressed, but a preliminary question is how to account for the acceptability contrast between (165a) and (b) (both understood as partitives, both containing two nouns; informal judgments).
(165) a. ??I returned two presents of the books I got for Christmas.
I returned two books of the presents I got for Christmas.
The difference, of course, is that the first has a more general noun (presents) followed by a nominal potentially referring to a subset of the first one (books I got for Christmas), the second has the opposite order. Now, the order <superset, subset> is found elsewhere in language. One example is anaphoric reference, see (166) and (167) The order <superset, subset> is not entirely impossible, but it requires a certain amount of accommodation. A stronger effect in the same direction is found in appositions (a type of nominal adjunct, we assume), as in the following examples with relative clauses (the (a)-cases are once again taken from the UKWAC corpus 35 ).
(168) a. Fruits also contain [ethanol and pectin] i , [antidotes] i which prevent methanol from being metabolized into formaldehyde. b. *Fruits also contain [antidotes] i , [ethanol and pectin] i which prevent methanol from being metabolized into formaldehyde.
(169) a. Specialist advisors will involve developing [basic legal theory or philosophy] i , [disciplines] i that still tend to be somewhat marginalized today. b. *Specialist advisors will involve developing [disciplines] i , [basic legal theory or philosophy] i that still tend to be somewhat marginalized today.
Note that appositive nominals are typically determinerless: apposition is in fact known to license even bare count singulars (e.g. John, vice-president at Exxon)-subject to various language-specific constraints (e.g. uniqueness, animacy). Putting all these facts together, we are now ready to propose that partitive-like doublenoun cases such as (162a) or (165b) are appositional partitives, with the structure shown in (170). In (170) the determinerless partitive constituent [PRO i PART pro of the [mail you sent me] is an apposition of the previous NP. The fact that the order is <subset, superset> now aligns with the corresponding phenomenon in other kinds of appositions, and with the observation that, at least in Italian, the construction improves if there is a pause (a comma, in the instructions given to the informants pool) between the first noun and the PP.
Consider now in this light the paradigm in (171): ne (a clitic, moved to V from below due) is a pro-NP, so the configuration is essentially that of a double-noun partitive. The a/b and the a/c difference is p < 0.0001, b/c is weakly significant (p < 0.01).
(171) a. Ho visto due dei partecipanti. I_have seen two of_the participants 'I have seen two of the participants.' b. ??Ne ho visti due dei partecipanti. Ones I_have seen two of_the participants lit. 'I have seen two ones (=participants) of the participants.' c. ?Ne ho visti due, dei partecipanti. Ones I_have seen two, of_the participants (like above, but with a pause before the PP) 35 Other natural occurring examples are in (i) (i) a. He then found out that he was [an immortal] j , [someone] j who will live forever, unless he is decapitated. b. A reduction in annual leave entitlement by [three to five days] j , [time] j which could be earned back for low sickness absence c. A large number of birds, including many so-called [Neotropical migrants] j , [species] j which breed in North America but go south in the winter.
While our informant pool did not detect a similar contrast in English, some cases can be constructed with demonstratives. Without a pause, (172a) is a normal partitive with the maximality problem we have seen and analyzed in (42) above. As with the, an additional restrictor solves the problem (172b), but so does a pause before the PP, since now the deictic gesture can identify a referent, which is then modified by the partitive apposition.
(172) a. ??I read only those of the books you gave me.
I read only those of [the books you gave me] [that had less than 50 pages].
I read only those (books), of (all) the books you gave me.
(pointing to some books) If these partitive PPs are essentially adjuncts, it is not surprising to see them in dislocated positions (compare President of Exxon Corporation, John could easily afford a private jet.). As we have seen, (173a) is judged nearly perfect, and significantly better than the non-extraposed version in (173b). Note that in contrast with the Italian (171c), the comma does not seem to improve the rating of (173b)-for reasons which remain to be understood.
(173) a. Of the mail you sent me, I got only two packages. b. ??I only got two packages, of the mail you sent me.
In the fronted position, of PPs do not seem to differ from among semipartitives, which are nearly perfect in our tests.
(174) a. Among John's novels, two have became bestsellers. b. Among John's novels, I have liked two.
This is not surprising. If the analysis in (170) is on the right track, the PP (actually, a bare predicate nominal, headed by PART pro ) is an adjunct, so its behavior matches that of among PP adjuncts (see the discussion at the end of Section 6.4). Indeed, Turkish ablativemarked partitives, which are analyzed as adjuncts in von Heusinger & Kornfilt (2017: 12) and have no PPart, routinely contain two overt nouns (175). Unlike in Genitive-marked partitives, the subset (elma 'apple') is free to take Accusative case, depending on specificity.

Conclusions
In this paper we reviewed a number of constructions typically collected under the umbrella of "partitives", arguing that they can be divided in three broad classes.
• Constructions which establish a contrastive comparison between real and potential amounts (the out-of construction two out of four Ns and some indefinite partitives only one of several (possible) Ns); • constructions which express an indefinite whose amount is defined as a proportion of a previous entity (plural, as in half of the children, mass, as in 30% of the butter, or "massified" by a type-shifting operator, as in most of John); • constructions where the indefinite is built from the plural restriction of the inner NP (boys in three of the boys), removing its supremum and thus yielding Proper Partitivity.
We argued that the last two cases are the effect of two distinct silent nominal operators, PART % and PART pro . The first takes a (proportional) amount as its external argument, the second, a pro-NP co-indexed with the internal NP, or, in the case of double genitives, an overt movement copy of the internal NP. Both operators can be overt in special cases (with words like quarter or half, in proportions, possibly with classifier-nouns like tane, in Turkish canonical partitives). The corresponding tree structures (minus any raising of the numeral to D, possibly needed to license the (a) case, see (68)) are in (176).
(176) a. Due to the coindexing between PRO and the inner NP in (176b), canonical partitives cannot take non-identical conjoined complements (though distinct plural conjuncts appear to be better, for reasons that remain to be clarified). Finally, we argued that partitives with two nouns (like two novels of the books I gave you), to the extent they are acceptable, should be analyzed as a quantitative (two books) followed by a determinerless partitive apposition, preferably with a slight pause. Extraposed cases and the similarity with among semipartitives follow from their status of adjuncts.
We assumed that the proliferation of similar and partially overlapping structures can make judgments difficult and potentially inconsistent. To address this issue, we used crowdsourcing to assess the grammaticality of a core subset of our cases, obtaining judgments from up to 117 (self assessed) native speakers (average: 25.6 for English, 22 for Italian). This gave us the possibility to statistically validate some subtle cases (e.g. the difference between simple and conjoined inner nouns), but also gave us results which disagreed with the intuitions of some linguist native speakers we consulted (e.g. the lack of difference between Two among John's books vs. Two books among John's), possibly pointing to limits in the technique (e.g. presentation order, instructions, sentence complexity, gold items) which we hope to address in future work.
Some aspects of the problem of partitivity remain only marginally addressed, first and foremost at a typological level: most of our data come from English and Italian, and the conclusions we reached cannot go much beyond these and related languages. However, we are confident that the general methodological approach (especially the contrastive use of conjunction and overt raising cases like double genitives) can be easily extended to other language families without special difficulties.