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).

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 questionnaires2 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 “partitive-like” 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, which uses a matching analysis with a PRO-NP in the former and NP-movement in the latter; Section 6.5 considers other partitive cases (among-cases, extrapositions) in light of this proposal. Section 7 bolsters the approach using data from coordination, and Section 8 discusses two previous analyses similar to ours. In the last part of the paper we address the case of partitive structures containing two nouns, which we propose should be treated as partitive appositions (Sec. 9). A final section (10) wraps up the paper by giving syntactic trees for the two main structures, and concludes.

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).

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.

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.).

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’ Num3—again suggesting a derivation different from the one required by a canonical partitive (but perhaps similar to the double genitives of Section 6.2).

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).

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

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).

An examination of the remaining cases, [CANONP] to [2NOUNSP], along with their non-canonical order in [EXTRAP] and [INVERTP], reveals a number of important contrasts and one more theoretical issue, all to be addressed. At a data level, we have:

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.

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 and Gagnon 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; 2007), 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 in-depth 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) links the impossibility of coordinate inner nominals to a version of the double-noun idea, show in (40), in which N^e, placed in [Spec,PP], is an invisible copy of the NP within the inner nominal.

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:

Kayne (1994: Chapter 8) and others have observed that when an additional restriction is present, the definite becomes again possible:

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).

At the same time, this approach puts some interesting constraints on the way in which definites link back to their antecedents. Consider for instance (45b) in Italian, uttered right after (a) (informal judgment).

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).

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).7

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; 2013); 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 Ionin et al. (2006) 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:

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.

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.

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.

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.

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

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).

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):

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:

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).

Third, the inner nominal may be a bare plural (or bare mass singular), unlike in canonical partitives:

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).

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

Finally, a plural outer determiner is better than no determiner (66), but the difference is only weakly significant (p ≤ 0.01).

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.

Let’s now turn to consider Indefinite Partitives (case [INDEFP] in Section 2 above), an intriguing case of non-canonical partitives used in Abbott (1996) to reject Jackendoff’s P(artitive) C(onstrain). According to Abbott, virtually all the examples in (85) (unjudged) become acceptable once set in the proper context (e.g. (86), Abbott’s ex.28).

There are two observations to be made about these cases. First, several natural examples came with the word only or just associated to the external determiner. Second, many of the examples provided by Abbott improve with restrictions on the internal nominal: de Hoop (1992) reports the contrast in (87).

Our corpus searches reveal that the vast majority of these cases are of the form CARDINAL of CARDINAL (e.g. All networks fall into one of two categories: source/destination or producer/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.

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) via Choice Functions (CF, see Reinhart 1997; Winter 1997) which yield a (plural) individual, no PC violation arises.20 Such a formulation is in any case desirable to accommodate Ladusaw’s observation about *one of both boys (both boys is not a plural individual, witness *both boys are a couple).

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).

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).

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.

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; 2008), 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.

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).

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).

Again, the contrast holds cross-linguistically—see the equivalent sentences in Italian (133) (p. < 0.0001 for a/c) and German (134) (informal judgments).

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 (135) and e.g. (130b) is p. < 0.01).

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).

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.

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).

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).

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.

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), and that both are acceptable (informal judgments).

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.

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:

If double genitives are partitives in which the inner NP has overtly raised to [Spec,PART^PRO], they should be acceptable only if the extraction can be carried out from each conjunct (in ATB ‘Across The Board’ fashion). Indeed, the following cases seem to be all fine according to informal judgments.

Similarly, in Italian the pro-NP clitic ne can be extracted ATB from a conjunction of “weak” demonstratives.34

Let’s take stock. We have proposed that the null nominal which has been claimed to be present in the outer DP layer of partitives is a relational noun (PART^PRO) which takes of-marked (or equivalent) PPs as its internal argument, and a null PRO-NP (obligatorily coindexed with the inner NP) as its external one. In double genitives, the inner NP has actually moved to [Spec,PART]; this is possible, however, only from inner nominals which allow extractions, yet satisfy the semantic requirements of partitives. This is a narrow window, which leaves in certain types of (arguably, more internal) possessors, superlatives and certain uses of demonstratives with modifiers in Italian. (149a) is thus excluded for English (no extraction out of these definites), while the corresponding partitive (149b) remains possible.

Proportional partitives, on the other hand, have been argued to contain a different relational nominal, PART^%, whose external argument, in Spec, is a degree. Since there is no coindexing with the internal NP, these cases end up being better even with coordinated complements.

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).

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.

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.

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).

One could counter that the problem of (155) is that the upper PP should be obligatorily extraposed (yielding three [of the books] with the red cover), but then the question is why the same does not apply in e.g. I bought five books. The three with a yellow cover are still in the bag. The PRO-matching system seems to fare better in this respect, since it does not use ellipsis, but an element which simply lacks a PF component. It is not clear that such elements can take overt restrictive modifiers, as (156) illustrates for PRO-DP and relative clauses:

Even setting modifiers aside, the PF analysis raises a fundamental question: how should the upper NP books be interpreted in e.g. (157)?

If three in (157) applies to books_i (all of them, yellow or red) it may end up picking three yellow books, disregarding the contribution of the PP. If, on the other hand, three applies to the set defined by the PP, i.e. the red books, then books_i becomes just a syntactic peg for nominal features, devoid of any semantic role. We still need two separate versions of all the determiners which take partitives: one for quantitatives, where they apply to their complement NP (even when invisible, as in (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).

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).

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.

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.

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).

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’.

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).

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 corpus35).

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 double-noun 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).

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.

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.

In the fronted position, of PPs do not seem to differ from among semipartitives, which are nearly perfect in our tests.

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 ablative-marked 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.

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.

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).

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 crowd-sourcing 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.