The expression of quantity in Oneida: a study in syntactic and semantic variation

2.1 Quantification across languages

To orient readers, we first provide a cursory overview of the structure of Oneida sentences that quantify over objects and how the Oneida structure differs from the more common structure found in other languages. Our discussion is based on extant anthologies of quantification (Bach et al. 1995; Keenan and Paperno 2012; Matthewson 2008; Paperno and Keenan 2017) as well as descriptions of a few other languages to slightly broaden the language sample, in particular Abeillé and Godard (2021) for French (Indo-European), Broadwell (2006) for Choctaw (Muskogean), and Evans (1995) for Kayardild (Tangkic). In all, 48 languages were included in our sample. There were three isolates (Basque, Japanese and Kusunda); the other 45 languages belonged to 26 language families with an overrepresentation of languages from Europe, from the Americas, and the Indo-European family.

When discussing expressions of quantity, three considerations must be kept in mind. First is the part of speech (adjective, determiner, verb, verbal affix, or verbal auxiliary). Second is the grammatical function of those expressions (heads of clauses, heads of determiner phrases, specifiers of nouns, modifiers of nominal or verbal expressions). Third is their semantic type (whether they denote properties of sets – for example, the number of elements in the set – or relations between sets – for example, how many members their intersection has). Of course, within a single language different expressions of quantity can belong to different categories in each of these classificatory dimensions. For example, a few expressions of quantity may be verbs even though most are not; see for example Bruening (2008) for Passamaquoddy (Algonquian) and Evans (1995) for Kayardild (Tangkic). Similarly, in many languages some expressions of quantity can head predicative phrases (including many in English, Solt 2015), while most are heads of determiner phrases or modifiers of nominal expressions. Finally, some scholars analyze cardinal quantifiers as denoting properties of sets while acknowledging that proportional quantifiers semantically denote relations between sets (see, for example, Krifka 1999).

Sentence (2) illustrates a typical way of quantifying objects in Oneida.^[3] The main clause is followed by a verb form based on the root -t- ‘be one’, which incorporates what is being counted, -saheʔt- ‘bean’. As we discuss in Section 8, one can analyze this verb form (and its sisters) either as forming an internally-headed relative clause (skasahé⋅tat can thus more idiomatically be glossed as ‘the bean that amounts to one’) or as one constituent of a clause-combining construction, the main clause being its other constituent. We call roots such as -t- (and verb forms based on such roots) count verbs. (As mentioned in footnote 3, sequences of particles that frequently occur together are translated into English as a unit; for example nʌ kiʔ ok wí⋅ in (2) is translated as ‘right away’.)

Informally, Oneida sentences that contain a quantificational expression and a main verb have the structure represented in (3), where QE stands for quantificational expression. The verb in the quantificational expression typically incorporates a noun stem and it heads a clause that may include a number word (when counting three or more entities). That clause is adjoined to and precedes the main clause in (3), but the reverse order is sometimes possible, as (2) shows (we leave to another venue the pragmatic effect of this infrequent order).

The basic structure of sentences that contain a quantificational expression in other languages is quite different. In the 35 languages included in the Keenan and Paperno two-volume anthology (Keenan and Paperno 2012; Paperno and Keenan 2017), expressions of quantity are typically modifiers of nominal expressions, or they are determiners that either take NPs as complements or are specifiers of nominals, depending on one’s analysis (we focus on these 35 languages as their descriptions are most complete and comparable). This is true even of Chickasaw, where almost all expressions of quantity are verbs (Munro 2017: 132), but where quantifier verbs that are not main predicates bear the morphological hallmarks of nominal modifiers: they bear a switch reference suffix and do not have nominative-marked subjects and therefore can be analyzed as nominal modifiers (Munro 2017: 133; see also Broadwell 2006 for Choctaw, also Muskogean). In other words, in the dominant pattern of all 35 languages, the quantificational expression typically modifies, determines, or specifies the nominal expression that indicates the category of what is being quantified, and the resulting nominal expression combines with the predicate that describes the situation in which these quantified objects participate. We informally represent the typical structure of sentences containing quantificational expressions in other languages in (4). We use the term nominal to remain neutral between a DP or NP analysis of so-called noun phrases.

Semantically, since Barwise and Cooper (1981), quantification over objects is analyzed as involving a relation between the denotation of the nominal (minus the quantificational expression) and the denotation of the VP. Continuing to illustrate with the English sentence in (1b), the quantifiers most and two thirds of relate the set of tires that burned and the set of tires that did not burn. Barwise and Cooper also analyze cardinal numbers as in (1a) as relational – relating the set of tires and the set of things that burned: their intersection has two members – although many current analyses of cardinal numbers, e.g. Krifka (1999) disagree. The proper analysis of cardinal numbers does not matter for our purposes. What is critical is the fact that English quantificational inventory includes quantifiers that relate two sets or entities, which sentences (1b) illustrate.

In Oneida, as mentioned above, the quantificational expression is a verb that usually combines morphologically with the category expression, and the quantificational expression and the verb that describes the situation at issue do not belong to the same clause. Obviously, the structures of quantificational expressions differ markedly between English and Oneida. The issue is whether to this morphosyntactic difference corresponds a semantic or conceptual difference. The answer we will give is Yes: there is a semantic difference in addition to this morphosyntactic difference. Oneida verbal quantificational expressions only express properties of sets (how many members they have), not relations. To continue with our English examples in (1), the fact that the set of tires had two members (a property of that set) can be expressed, but the fact the set of tires that burned was bigger than the set of tires that did not burn (a relation between two distinct sets) cannot. Both English and Oneida have expressions that correspond to English cardinal numbers like one, two, etc. because they can be expressed as properties of a set of objects, i.e. the cardinality of the set. Both languages also include expressions that correspond to all, although in Oneida, universal quantification is a property of sets: the set of objects under discussion is complete. Critically, quantificational expressions that denote relations – in particular proportions – are missing in Oneida: there is no word in Oneida that denotes a two-place predicate for proportions between two sets, nor are there partitive quantifiers such as two of the tires that reference both a set and a subset. Concretely, no quantificational expression like most or three quarters of is present.^[4]

Overall, our analysis shows that Oneida is rather unique in the three-dimensional typology of quantification we just outlined. Morphologically, the part of speech of its quantificational expressions is always or almost always a verb. Syntactically, the verb that denotes the expression of quantity always heads a clause and the nominal expression, when it occurs, is typically incorporated into the verb form. Finally, quantificational expressions always denote properties of sets and never relations between two sets.

2.2 Verbs and nouns

Koenig and Michelson (2010) posit four parts of speech for Oneida: verbs, nouns, kinship terms and particles. Verbs have an inflectional structure that is distinct from nouns. Kinship terms have some of the characteristics of verbs and some of nouns. Particles are uninflected and generally occur in one form only. Here we restrict the description to verbs and nouns. Although we will use terms such as verb and noun for convenience, note that Koenig and Michelson (2020a, 2023) suggest that Oneida morphological parts of speech can be more appropriately characterized in terms of stems that describe situations and stems that describe objects.

A characteristic verb form is given in (5); a characteristic noun form in (6). Verb stems take an aspect suffix while noun stems take a noun suffix.

Both verbs and nouns have pronominal prefixes but the distribution and form of some of the prefixes differ depending on whether the prefix occurs on a verb or a noun. There are three sets of pronominal prefixes: Transitive prefixes which mark two animate arguments and occur only on verbs and kinship terms, and (Intransitive) Agent and Patient prefixes which occur on both verbs and nouns.^[5]

Verbs, but generally not nouns, can occur with one or more prefixes that occur before the pronominal prefixes (see Diaz et al. 2019 for a thorough analysis of these). Three of these – repetitive, dualic, and partitive – occur on count verbs. Verb stems can be derived from other verb stems via prefixes and suffixes. Verb stems are also derived from other verb stems via noun incorporation. Noun incorporation, which is characteristic of several of the quantificational structures, is exemplified by the verb form in (7).

With this snapshot of Oneida morphology as background, we move on to the constructions Oneida countenances to quantify over objects.

3.1 Exact cardinal quantifiers

There are several verb constructions that are used to quantify over objects depending on their number: one, two, or three or more. In the constructions that count one or two objects a verbal prefix identifies the exact number; in the constructions that count three or more, an expression external to the verb form further specifies the number. Some verbs are restricted to either animate or inanimate entities, while others are used for both animate and inanimate entities. It is interesting that the kinds of distinctions typically seen in languages in which quantification is done via determiners and nominals are found also in Oneida, where quantification is done via verbs. Languages commonly distinguish singular, dual, and plural number on the noun, the determiner, the adjective, or any combination of these, and often animacy is encoded in nouns. Both number and animacy are relevant in Oneida too, but in Oneida it is the specific count verbs, and the verbal prefixes, that encode the number and animacy of the counted entities.

3.2 Vague cardinal quantifiers

A frequently attested vague quantifier is the word e⋅só⋅ ‘a lot, much, many, very’. E⋅só⋅ is based on the verb root -eso-, which can occur with verbal inflectional prefixes, but inflected forms are relatively infrequent and it is usually treated as a particle. E⋅só⋅ also occurs very often as a quantifier over situations or as an expression of degree, but in the extract in (24) it quantifies over the number of cars.

Otherwise large quantities are expressed by verb forms built on stems that, in themselves, may not include the meaning of quantity. The stem -nakl(e)- ‘reside, dwell’, can occur with an incorporated noun specifying the category of the quantified object, as in the extract in (25). (In its quantification function, -nakl(e)- is restricted to inanimate objects.) The stems -eʔtowanʌ-, literally ‘big pile’, and -ityohkwanʌ-, literally ‘big group’, are both based on the root -owanʌ-/-kwanʌ- ‘be big, be large’ and are used for inanimate (26) and animate (27) objects, respectively.

Small vague quantities are expressed by the particle ostúha ‘a little’, or by a count verb in combination with the particle tóhkaʔ ‘a few’, or by a count verb plus kok (probably from kʌʔ ‘certain, small’ plus ok ‘only’). Examples of each of these are given in (28)–(29).

3.3 Universal quantifiers

Akwekú ‘all, every, the whole of’, based on the verb root -kweku- ‘the whole of, entire’, can be roughly translated into English as ‘every’ or ‘all’, depending on the context. It is used for both inanimates (30) and animates (31). (See Michelson and Doxtator 2002 for examples of inflected verb forms of -kweku-.)

Although akwekú is aptly translated into English as ‘all’ or ‘every’, it is important to keep in mind that it is better literally glossed as ‘the whole of, entire’, as suggested by the nominalized word ohutsyakwekú ‘the whole world’ with the incorporated noun -hutsy-’ ‘land, earth’, or predicative uses of -kweku where it is best translated as ‘together, altogether’ (see (55) in Section 7 or Michelson and Doxtator 2002: 501). Thus, the root of the verb form akwekú should be glossed as ‘be complete’ and the proto-patient argument in (30) and the proto-agent argument in (31) are more literally translated as ‘the entire/complete amount/set of (money, those who left)’.

Also corresponding roughly to English ‘every’ are forms of the count verbs -ke- ‘amount to’, -i- ‘make up the total of’, and -u- ‘be a certain amount’ with the translocative, the dualic, and optionally the partitive prepronominal prefixes, and usually together with the emphatic particle kwáh ‘just, quite’. An example is the sentence in (32). This structure is used also for the meaning ‘all kinds of’ as in (33).

As with akwekú, the English translation should not be taken to be the literal gloss of what is expressed in Oneida. What is literally expressed is a little harder to be sure of as the combination of the translocative and dualic prefixes (and optionally the partititive prefix) seems idiomatic in this case, at least synchronically, as already noted in Lounsbury (1953: 48). One possible guess is that the translocative, which can indicate a distant location, and the dualic, which can indicate multiplication of parts, combine to express something like ‘all of the parts of the extension of’ so that nyaʔtekanúhsake in (32) is best glossed as ‘what amounts to all the parts of the extension of house’.

Finally, the free relative expression (kwáh) tsiʔ nikú ‘what amount, how much’ is often translated into English as ‘all’ or ‘every’ (especially in temporal contexts) although, yet again, the literal gloss is not an exact correspondent of the universal quantifier which the translation of (34) includes.

5.1 Most, least

There is no real equivalent for English ‘most’. In recorded texts where the context or subject matter requires the use of many quantificational expressions, in particular those that describe growing and preparing tobacco (requiring two people tying three leaves into a certain number of bundles, with so many sticks, etc.), there are no examples. When asked about the equivalent of English ‘most’, Michelson’s collaborators expressed a certain surprise that expressions that correspond to the concept ‘most’ do not exist, instead providing the sentences below, with remarks such as “I suppose the only way you can say that is …”.

One possible strategy for inanimate objects relies on vague cardinal quantification over events (‘often’) and allows listeners or readers to infer quantification over entities from the kind of relations between number of events and number of entities participating in events that is well-known since Obenauer (1983). This strategy is illustrated in sentence (39).

Another strategy is to use a vague cardinal quantifier roughly equivalent to ‘a lot’ as in (40).

Yet another strategy relies on hedging the universal quantifier akwéku as illustrated in sentence (41).

But, the closest translation of most N when N denotes a category of animate entities involves the stem that means literally ‘large crowd’ (42), discussed in Section 3.2.

The conclusion we can draw from these different ways of trying to express proportionality is that none of them involves relational predications. They involve expressions that quantify over events or describe properties of sets (vague cardinal numbers, hedged universal quantifiers), or expressions that denote scalar predicates (small quantity, large crowd).

5.2 Half

The previous section showed that instead of a term literally expressing what English most expresses, Oneida uses expressions that are more aptly translated as often, large quantity, or almost all. There is one seemingly proportional quantificational expression in Oneida, a verb form that is aptly translated as ‘half’, -ahsʌnʌ- ‘be the middle of’. But, in fact, the Oneida form does not denote a proportion between the numbers of members of two sets (as English half the spectators), but rather a quantity that is midway between two quantities, zero and one. The extract in (43) exemplifies the literal, spatial use of the root -ahsʌnʌ- ‘be the middle of’. This example makes clear that a particular point or region in space is included in the denotation of this root.

The example in (44) illustrates how the same root has metaphorical uses where it expresses ‘half’, i.e. a quantity that is in the middle of a unit interval. Critically, as in the literal examples, the notion of ‘half’ included in the metaphorical meaning of the root is treated as a quantity rather than a proportion (a position on the clock or watch), as befits its locative literal origin. The expression is thus on a par with roots that express cardinal quantification (see Section 3).

Expressions such as tshaʔtewahsʌnʌ́ skatshé⋅tat ‘half a bottle’ or tshaʔtewahsʌnʌ́ wá⋅yeke’ tsiʔ nikú i⋅wát ‘She ate half of what (candies) is in there’ (i.e. half the dish of candies) aptly illustrate the metaphorical link between the middle of a spatial region and half of a quantity that quantificational uses of -ahsʌnʌ- rely on. Crucially, metaphorical uses of -ahsʌnʌ- do not involve two sets whose cardinalities are compared.^[12]

5.3 Partitivity

Just as there are no proportional quantifiers similar to English most in Oneida, partitive quantificational expressions such as two of the rabbits are conspicuously absent: there is no way of expressing within a nominal subset-superset relations, just as there is no way of expressing something like English most. In particular, nominal partitive expressions do not exist in Oneida.^[13] Below is an interesting example that illustrates how the absence of constructions that can semantically express partitivity (and, by extension, proportionality) does not necessarily restrict what can be conveyed, as partitivity may be conveyed pragmatically, i.e. through intended inferences on the part of listeners and readers. The following is an excerpt from a story developed by the late Mercy Doxtator for use in her grade school classroom at the Standing Stone School at the Oneida Nation of the Thames.

The narrator of (45) sets up a group of children in the first sentence and universally quantifies over that set via the verb form latikwekú, which literally means something close to ‘the set (of children) is complete’ or ‘the entire set of children’. The cardinality of subsets of that set are then expressed in the usual way, using the root -yashe- ‘be together (for animate entities)’ and -i- ‘total’. The fact that the set of children who are facing off is a subset of the set of all children is left to inference. All that is introduced in the second sentence is another set of children of cardinality two so that it is literally paraphrased as something like ‘They [the children] all have skates on (…). Two are facing off (…). Two have on black shirts and three have on white uniforms’ where the fact that the sets of two and three children are subsets of the first set is not part of the semantic representation. The fact that the first set is universally quantified and the second set’s cardinality is two is enough, in context, for listeners and readers to infer that the second set is a subset of the first set. The semantic (or grammatical) inexpressibility of partitivity (and, by extension, proportionality) does not correspond to a pragmatic incommunicability, just as the absence of tense in a language does not entail the inability of conveying temporal relations. Temporal relations (and notions such as past or present) can be communicated via intended inferences (see Bohnemeyer and Swift 2004).

The absence of partitive quantificational expressions is part of a larger lacuna. There is no way of expressing a part-whole relation between two referring expressions within a noun phrase (aside from possessed body part nouns), i.e., no way of expressing things like ‘the top of the table’. Similarly, there is no explicit way of expressing measure phrases such as ‘a pair of shoes’, ‘a bag of potatoes’ or ‘two cups of flour’ within a noun phrase. The excerpt in (10) above illustrates how “disagreement” between the indices of arguments of verbs and of referring expressions within the same sentence or across sentences is used by speakers to convey what measure phrases do in English (see Koenig and Michelson 2019 for a more detailed discussion of “disagreement” in Oneida). What is being obtained in example (10) above is the shoes and what is being counted by the verb form whose root is -ke is pairs, as indicated by the incorporated noun -yan- ‘pair’ as well as the presence of the dualic prepronominal prefix. Similarly in the example (46), what is being counted by -t- (with the repetitive prefix) is the bag, but what costs two dollars is the potatoes. The relation between what is counted (one bag) and what is obtained (a bag containing potatoes) is not explicitly expressed as it is in English (with a measure phrase including “of”, e.g., “bag of potatoes”). Oneida relies on something looser than identity between the index for the bag and that for the potatoes to convey that relation.

The looser than strict co-indexing relation that can exist between the corresponding arguments of -t- and -nolu- in (46) or between the argument counted by the verb -ke- and the incorporated noun in (10) (or between what is counted and what was planted in (29) above) is put to use to convey what cannot be explicitly expressed syntactically.

This is not to say part-whole relations cannot be expressed at all, but few part-whole relations (aside from possessed body-part nouns) can be expressed and they can never be expressed within noun phrases. The few part-whole relations that can be expressed are expressed by verb forms based on the root -ut- ‘be attached’ (which must incorporate a noun), as shown in (47). Note that e⋅só⋅ ‘a lot’ can directly combine with the main verb in this example, as the main verb describes a relation of possession, broadly speaking (see Section 6.2).

6.1 Number words without any count verb

Bare number words can occur with English words or words based on English borrowings, and with other lexicalized forms. For example, in (48) úska ‘one’ occurs with the English word ‘stamp’. The number words úska ‘one’ and tékni ‘two’ sometimes occur with lexicalized forms, usually inflected verbs that cannot be incorporated, which might explain why quantification does not require count verbs in this case. For example, úska yehyatúkhwaʔ ‘one pencil’, literally, ‘one writes with it’. Although we provide an example of a number word occurring without a count verb for completeness, the grammatical status of such examples (their naturalness or frequency) is somewhat uncertain. The only clear and recurring use of number names without count verbs is with verbs describing possession relations, which we now discuss.

6.2 Possession and part-whole relations

Oneida has nominal and verbal possessive constructions. Here we focus on the more relevant verbal constructions. The meaning of the verb root -kaʔte- ‘have many’ entails both possession and quantity. The verb requires patient prefixes, and the possessed entity is expressed either by an incorporated noun, as in (49), or by an external noun.

More interesting perhaps are verb forms that consist of the stative aspect of a postural verb, usually -yʌ- ‘put, lie’, -ot- ‘stand’, or -ut- ‘be attached’. For example, the verb form lonúhsoteʔ ‘he has a house, his house’ is composed of the masculine singular patient prefix lo-, the incorporated noun -nuhs- ‘house’, the verb -ot- ‘stand’, and the stative aspect ending -eʔ. The possessed entity can be expressed either via an incorporated noun, as in this form, or by an external nominal expression, or both. In the case of these verb forms, a specific number of possessed entities is expressed in one of two ways. One way, exemplified in (50), consists of a count clause and a possessive clause. The count clause may be any of the structures described in Section 3.

The other way is exemplified in (51) (see Koenig and Michelson 2021 for details) (The example in (51) is from an omitted part of a conversation published in Michelson et al. 2016). In this case there is no count clause. Instead the possessive verb is prefixed with the dualic (for two possessed entities) or the partitive (for three or more possessed entities) and an external expression, such as a number word, specifies the quantity of possessed entities. What is interesting about this structure is that, just as with the count verb -ke- ‘amount to’, it is the dualic prefix that specifies ‘two’ and the partitive plus external expression that specifies more than ‘two’. Even though the verb root in (51) does not include a notion of quantity, restrictions on the quantity of what is possessed (two vs. three or more) are encoded via a prepronominal prefix, just as in the case of count verbs. (Note that this alternative structure is not available for just one possessed entity.)

Part-whole relations involving body parts or parts of houses employ the same structure as this second possessive structure. The verbs -ut- ‘be attached’, -kahlut- ‘be an opening’ (etymologically -kahl- ‘eye’ plus -ut- ‘be attached’), and -ot- ‘stand’ occur with an incorporated noun that denotes the enumerated body part or house part (e.g. wall, window, door), and with the dualic or partitive prefixes. Inalienably possessed body parts require the Agent category of pronominal prefix.

8.1 Quantificational expressions and Oneida inflectional morphology

The upshot of our analysis of Oneida quantification is that it denotes properties of sets rather than relations between sets. In this section, we provide morphological evidence that supports this claim as well as our contention that there is no true equivalent of words like English most.

Recall that each Oneida noun and verb form must include a pronominal prefix. Prefixes reference up to two animate arguments. Inanimate arguments are not referenced; verbs that only have inanimate arguments (or no argument at all in the case of weather verbs) bear a default third person singular prefix, whether the argument is singular or plural.^[14] Thus, shakoyaʔtaha⋅wí⋅ ‘he was carrying them’ in (57) (repeated from (22)) includes the pronominal prefix shako-, which references both the third person masculine singular proto-agent argument and the third person proto-patient argument of the verb.

This general morphological property of Oneida inflection is of particular relevance to the issue of the semantic type of count verbs. If some of the verbs used to quantify over objects denoted relations between two sets, we would expect these verbs to bear Transitive pronominal prefixes when what is counted is animate. This is because the relational theory of quantifiers analyzes sentences like (58) as relating two sets, the set of students and the set of people who left. Since both sets are denoted by properties predicated of humans, both arguments of the relation should be referenced on the corresponding verb in Oneida.

But this is not the case. This is already illustrated by the count verb in example (57) which bears an Intransitive pronominal prefix in contrast to the Transitive main verb pronominal prefix. But consider now examples (59), repeated from (27) above, and (60). Example (59) illustrates the structure that is the best approximation of English proportional quantifiers and (60) the best approximation of English universal quantifiers.

The verb form nikʌtyohkwanʌ́ includes the third person feminine-zoic/neuter singular Intransitive prefix kʌ- and the verb latikwekú includes the third person masculine plural Intransitive prefix lati-. Verbs that best approximate English proportional or universal quantifiers thus seem to take a single semantic argument and to denote a property of a set of animate entities rather than a relation between two sets of animate entities. If the verbs in count clauses related two sets, we would expect the verb in example (59) (or in (42) above) to include either the Transitive prefix yo- referencing both sets (as the members of both sets are animate) or a reflexive prefix, and the verb in example (60) to include the Transitive prefix luwati- or the reflexive prefix. Neither is the case, supporting the observation that Oneida does not include translations for most and that the encoding of universal quantification does not involve a relational quantifier.

8.2 Oneida clauses and functional completeness

The previous section provided corroborating morphological evidence that Oneida verbs that quantify over objects denote properties of sets and do not express relational proportional quantifiers or partitives. Is the absence of verbs that express relational quantificational concepts an accidental gap? We do not believe it is. It is predicted given broadly agreed upon analyses of the syntax of clauses in Iroquoian. Iroquoianists from Mithun (1986) to Baker (1996) agree that most or all external phrases are not selected by verbs. Koenig and Michelson (2012, 2014, 2015a) further argue that the absence of syntactic selection is due to the absence of morphosyntactic argument structure and, more generally, syntactic features. So in a sentence like (61), the noun phrase laoto⋅kʌ́⋅ is not selected by the verb. It combines with a fully saturated verb and the relation between the verb and the noun phrase is strictly semantic: the index of the noun phrase is identified with a semantic argument of the predicate denoted by the verb. Otherwise put, the nominal laoto⋅ kʌ́⋅ ‘his axe’ does not saturate the proto-patient argument of ʌhahyoʔthi⋅ yáteʔ ‘he sharpened it’. It merely specifies further the category of the entity being sharpened. For reasons of space we cannot detail their arguments. Suffice it to say that none of the evidence that justifies a representation of argument structure and argument selection (morphological or syntactic) is present in Oneida: nouns and verbs do not have obligatory dependents, there is no valence alternation, there is no evidence of syntactic or morphological processes that reference grammatical functions (no antipassives, inverses, middles, passives or switch reference), no syntactic coindexing (reflexives and reciprocal are strictly morphological operations on semantic arguments), no conjunction reduction construction or constraints on relative clause formation (Keenan and Comrie 1977). Although scholars do not necessarily agree with every aspect of their analysis, Koenig and Michelson’s overall view of the relation between external nominals and verbs is common in work on Iroquoian. For our purposes, the details of various scholars’ analysis matter little; what is of relevance are the facts that verb forms are fully saturated and external nominals (or clauses) neither select nor are selected by these verb forms.^[15]

If verbs in Oneida are fully saturated (correspond to complete functional complexes; Chomsky 1986: 15, 87), neither main verbs nor verbs expressing quantificational concepts select for clauses headed by the other. The absence of syntactic selection between the main verb and the verb of the count clause makes it impossible for the latter to denote a relational quantificational concept. Going back to examples (1b), repeated below, assessing whether a certain proportion of tires burned requires comparing the sets of tires that burned and the set of tires that did not burn. For a count clause verb to express proportions, the denotation of the main clause (or part of it) should be “visible.” Since the proportion pertains to the tires that burned (or did not burn), the putative relational verb needs to “see” the meaning of the main verb. The functional completeness of verbs makes this impossible.

Furthermore, if main verbs are fully saturated (functionally complete), they denote truth-values, not sets. Their semantic type is therefore incompatible with the requirement of a putative relational count verb. The consensus view of the syntax of Oneida thus supports and explains the morphological evidence that verbs expressing quantification do not denote relations between sets: verbs do not select for external phrases and main verbs are already fully saturated, i.e. do not denote sets, but a truth-value.

If neither the count clause nor the main verb selects for the other, the question is how the two in the typical excerpt in (63) are related. Two syntactic analyses of the co-occurrence of count clauses and main clauses are possible and we currently do not have data to distinguish between them.

Under one analysis, count clauses form internally-headed relative clauses and the relative clause functions as a referring expression and is connected with the relevant main verb’s argument position just as other combinations of verbs and referring expressions. Sentence (64) exemplifies internally-headed relative clauses in Oneida.

Kʌʔ niyaká⋅ literally means ‘she is little’ but is used in (64) to refer to somebody who is little, hence its translation as ‘the little one’. Koenig and Michelson (2014) analyze such structures as involving a type-shifting construction from a situation description to an object description. Under an internally-headed relative clause analysis, the relation between the count clause and the main clause is identical to that between all referring expressions and verbs: the index of the referring expression is identified with the index of a semantic argument of the verb (see Koenig and Michelson 2014, 2015a for details).

Under another analysis, count clauses and main clauses form a clause-combining construction, and the co-indexing of an argument of the count clause verb and the main verb is simply part of the definition of the construction. Koenig and Michelson (2014) provide the sentence in (65) as an example of such a clause-combining construction and subsequent work has shown the construction to be more widespread than previously thought.

Both analyses ensure the proper identification of indices and we leave it to future work to determine if one analysis should be favored. As a formal analysis of the two constructions is beyond the scope of this paper, we only provide an informal representation of both analyses in Figure 1 (see Koenig and Michelson 2020b for a formal analysis of the internally-headed relative clause analysis). In both analyses, the count clause verb heads a clause and has an argument co-indexed with an argument of the main verb, but the internally-headed relative clause analysis additionally maps the count clause’s situation description (a statement about the cardinality of the set being discussed) into a description of that set. As should be clear, nothing critical for our semantic point hinges on choosing between these two syntactic analyses, and both analyses are independently motivated within Oneida.

Figure 1:

Two possible analyses of the syntax of quantification in Oneida.

8.3 Oneida-style quantification and expressibility

The absence of proportional quantifiers in Oneida does not prevent quantificational expressions that denote properties of sets to be truth-conditionally evaluated via the conceptual use of proportions. To illustrate the distinction we are after, consider the English sentence (66a) and two possible denotata for the class, an advanced graduate class with about 15 students in it and a large undergraduate class with about 100 students. Speakers might consider (66a) to be true if, say, eight out of the 15 registered students attended the first class in person, while if only eight students attended the large undergraduate class in person, (66a) would be judged false. Speakers’ truth-theoretic evaluation of (66a) involves computing some kind of proportion of the set of students in each class, just as most in (66b) does.

Truth-theoretic proportionality is not specific to the adjective large. It applies to words like frequency which can receive either an absolute or relative interpretation in sentence (67) or to crowd in sentence (68).

The fact that the evaluation of sentences such as (66a) or (68) may involve proportionality does not mean these words denote relational predicates. Quantificational expressions denoting one-place predicates over sets can be truth-conditionally evaluated via the computation of proportions without proportionality being expressed as a relation between two sets. We distinguish between representationally proportional quantifiers and truth-conditionally proportional quantifiers. Representationally proportional quantifiers explicitly denote a relation between two sets; truth-conditionally proportional quantifiers denote properties of sets, but the evaluation of the truth of the proposition containing the quantifier involves computing a proportion. Note that truth-conditional proportionality may not just be a property of expressions like large, frequency, or crowd; it might be a property of scalar predicates in general, as Hong (2021) shows in her experimental study of tall (see Schmidt et al. 2009 for a similar suggestion in a broader context): tall objects for Hong’s participants were the k tallest objects (where k is a certain proportion of the set of all objects in the context set).^[16] The closest translation of English most into Oneida are words that can be roughly paraphrased as ‘large crowd’ (kʌtyohkwanʌ́ in (42)). We therefore expect a truth-conditionally proportional interpretation to be possible for these verbs. And indeed it is. Proportionality is thus part of Oneida’s conceptual repertoire. But, Oneida does not have representationally proportional quantifiers, because Oneida does not have the morphosyntactic means to express proportions. It can only convey proportionality through the evaluation of one-place predicates in a way similar to English scalar adjectives. A corollary of the absence of representationally proportional quantifiers in Oneida is that it does not have as rich a set of quantifiers as languages like English have, because set/subset or other set-theoretic relations cannot be expressed syntactically (see Keenan and Stavi 1986 for the richness of English quantifiers).