Quantifier-Specific Usage Patterns Shape Learning—A Corpus Analysis on Universal Quantifiers in English and Dutch Child-Directed Language

Abstract

Quantifiers specify semantic relations between sentence constituents. Due to their abstract meanings, they form a learning challenge for children. This challenge is made more difficult by the fact that different universal quantifiers instantiate slightly different meanings. We investigated what evidence is available in the input that might help children learn the meaning of universal quantifiers by exploring the use of these words in naturalistic child-ambient language in English and Dutch. The cross-linguistic component in this analysis is relevant because languages differ in how they carve up the space of universal quantification. Our analysis revealed language- and quantifier-specific patterns in frequency, variability, and contexts of use. We discuss how these quantifier-specific usage patterns lead to quantifier-specific developmental trajectories and challenges.

Introduction

Children learning language must figure out which words refer to which things in the world, and how to combine these words to convey complex sentence meanings. The construction of sentence meaning requires understanding and producing words with very abstract meanings, like the quantifiers all, some, or none:

• 1. All the beavers are swimming.

•   ∀x[beaver (x) →is – swimming (x)]

In (1), the universal quantifier all specifies that the predicate ‘is-swimming’ applies to every x that is a beaver—anything that is a beaver is swimming. The meaning of all is thus modelled as a semantic relation, represented by the ∀-operator, between ‘beavers’ and ‘is-swimming’. Quantifiers are therefore among the most abstract words in a language. How can children learn these abstract terms?

This question is particularly relevant for universal quantifiers, like all, every, and each. While all these words denote the ‘for all’ (∀) relation, they are not synonymous: Each, for example, highlights individual elements, whereas all emphasises the group as a whole (Champollion, 2017; Gil, 1995; Vendler, 1967). Moreover, languages differ in the lexicalisation of universal quantification (Gil, 1995; Keenan, 2008; Shetreet & Novogrodsky, 2020), so the development of universal quantifiers must be shaped by language-specific factors. In this study, we gained first insights into language-specific patterns of universal quantifier use in English and Dutch. Our goals were exploratory: By exploring their use, frequency, and variability in children’s input, we aimed to predict and explain aspects of the development of universal quantifiers.

Different Universal Quantifiers, Different Meanings

Universal quantifiers are acquired relatively late—even 7 to 8-year-olds are not fully adult-like in their interpretation (see Aravind et al., 2017; Brooks & Braine, 1996; Brooks & Parshina, 2019; Freeman & Stedmon, 1986; Syrett, 2019). One of the challenges that children face is learning the differences between the universal quantifiers (Brooks & Braine, 1996; Syrett, 2019). English, for example, has three of them: each, every, and all. These all operate exhaustively over the set of referents modified by the quantifier (the quantifier’s domain), but they are not synonymous (Champollion, 2017; Gil, 1992, 1995; Knowlton et al., 2022; Vendler, 1967). In particular, each directs attention to the individual members of the quantified domain, while all emphasises the collective domain as-a-whole:

• 2. {Each / All} of the players analysed the match.

In (2), each implies that the players analysed the match individually, while all permits an interpretation in which they analysed the match together. This difference relates to quantifier distributivity—a semantic feature that universal quantifiers may or may not have. Each, a distributive quantifier, forces the separate application of the predicate to each individual in the quantified domain. All, a non-distributive quantifier, also allows the collective application of the predicate to the domain as-a-whole. Therefore, each cannot be paired with collective predicates like to form a line, which require the domain to act together as a group (Champollion, 2016; Dowty, 1986):

• 3. {*Each / All} of the players formed a line.

Every, like each, is a distributive quantifier that cannot be paired with collective predicates:

• 4. *Every player formed a line.

However, there are also cases in which every patterns with all. For example, every and all can express generalisations, while each cannot (Beghelli & Stowell, 1997; Knowlton et al., 2023):

• 5. {Every beaver has / All beavers have / Each beaver has} a tail.

In (5), the use of every and all bears a generic implication (beavers, in general, have tails), while the use of each implies some particular set of beavers. Note that generic expressions can involve distributive predicates, like has a tail. However, generic expressions do not emphasise the distributive application of the predicate, but highlight the shared nature of some property to all instances of a kind (Lasersohn, 2019; see also Knowlton et al., 2023).

So, each, every and all instantiate different ‘flavours’ of universal quantification. Most languages express different flavours of universal quantification (Gil, 1995), but they differ in how universal quantification is lexicalised. For example, Hebrew and (some variations of) Arabic have one universal quantifier, and distributivity is marked morphosyntactically (Fassi Fehri, 2020; Gil, 1995; Shetreet & Novogrodsky, 2019, 2020). On the other end of the spectrum, Malagsy has eight different universal quantifiers, each different in their inherent distributivity (Keenan, 2008).

In this study, we compared English and Dutch, which—despite being closely related—also differ in the lexicalisation of universal quantification. Like English, Dutch has multiple universal quantifiers: alle, al, allemaal, elk and ieder. The first three (alle, al, and allemaal) mean roughly the same, but differ in their syntactic characteristics (which we discuss in the next section). For now, we will collectively refer to these quantifiers as ‘alle-type’ quantifiers. These quantifiers are comparable to English all: They do not strongly individuate, and they are compatible with collective predicates. In contrast, elk and ieder, are distributive quantifiers, like English each or every. However, unlike each and every, which differ in meaning, elk and ieder can be used interchangeably: They do not differ in their inherent individuation, and neither are compatible with collective predicates (Broekhuis & den Dikken, 2012; Haeseryn et al., 1997).

How do children acquire the different universal quantifiers in their native language? Children are known to interpret universal quantifiers in a non-adult-like manner. For example, children up until 8 years old do not discriminate between each and all to the same extent as adults (Brooks & Braine, 1996; Rouweler & Hollebrandse, 2015; see also Syrett, 2019, for review). Moreover, previous work has shown that preschoolers’ interpretation of universal quantifiers is influenced by task demands (Rouweler & Hollebrandse, 2015; Syrett & Musolino, 2016), which can lead to interpretation errors (see Minai et al., 2012; Skordos et al., 2022). Altogether, children seem to acquire an adult-like command of universal quantifiers relatively late in development.

Any comprehensive theory of the development of universal quantification must account for how universal quantifiers appear in children’s everyday input. This claim is uncontroversial: All theories of language, both within nativist and constructivist approaches, agree that children learn language by analysing the language they experience on a daily basis (although theoretical approaches differ in whether this analysis of the input is constrained by innate, domain-specific mechanisms or not). Nevertheless, only a few studies have examined the use of universal quantifiers in children’s input. Knowlton and Lidz (2021) found that each and every are used in distinct contexts: Analysing caregiver language, they observed that every is more often used to quantify over times (e.g. every day), while each is most often used to quantify over individuals (e.g. each piece of fruit). Moreover, the domain of every is more often explicitly restricted than that of each (e.g. every time that we go to the store). These patterns suggest that every is most often used to express generalisations about situations, while each typically quantifies over concrete, specific things. Following up, Knowlton and Gomes (2022) analysed not only every and each but also all. By analysing videos of caregiver–child interactions, they observed that caregivers mostly used every and all to quantify over larger sets of referents while each was mostly used to quantify over a small number of referents. Moreover, for each and all, the set of referents is more often physically present in the context of the utterance than for every. Thus, distinct contexts of use could signal meaning differences between quantifiers.

To our knowledge, research on the use of universal quantifiers in children’s input has been limited to English. However, since universal quantifiers differ cross-linguistically, findings from one language may not generalise to another. In this study, we analysed caregiver language to map the differences and similarities in the use of universal quantifiers in both English and Dutch. However, our focus was not limited to contextual patterns of use; we also examined the role of frequency and variability of universal quantifiers in children’s input.

Frequency, Variability, and Universal Quantifiers

Learning new words and structures is influenced by frequency: There are more learning opportunities for high-frequent forms, and those are therefore generally acquired before low-frequent forms (if all else is equal; Ambridge et al., 2015; Lieven, 2010). Importantly, this claim does not hinge on any theoretical assumptions—most nativist and constructivist accounts of language learning recognise that any theory of language acquisition must be at least sensitive to frequency effects (see Ambridge et al., 2015).

In English, all is more frequent than every, and every is more frequent than each (Deng et al., 2024; Knowlton & Gomes, 2022; Knowlton & Lidz, 2021). So, non-distributive universal quantification is more frequent than distributive quantification—a pattern we expect to replicate in Dutch. Children, therefore, probably acquire non-distributive quantifiers before distributive ones. This prediction is borne out in English by Deng et al. (2024), who observed that all emerges first in children’s spontaneous productions, and by experimental studies that showed that children understand all before every or each (Brooks & Braine, 1996; Ferenz & Prasada, 2002; for some first insights in Dutch, see Drozd & van Loosbroek, 2006; see also Drozd, 2001, for discussion).

The total number of occurrences of a form (token frequency) is not the only relevant metric; the diversity of constructions in which a form appears (type frequency) also affects learning. Children need exposure to different exemplars of the same form to acquire an abstract representation that they can generalise to novel contexts (Ambridge et al., 2015; Behrens, 2009; Jones & Rowland, 2017; Lieven, 2010; Savage et al., 2006; Theakston et al., 2004). If some form has a high type frequency, the child will be exposed to many different exemplars of some form. In this case, the child is given plenty of opportunities to recognise the common form across these exemplars, leading them to rapidly acquire an abstract representation. In contrast, abstraction might take a while for forms with a low type frequency, which children only encounter in a small number of unique exemplars. Now, children are not given much opportunity to generalise across exemplars, leading them to initially store the specific exemplars as fixed, unanalysed ‘chunks’. Only once they have acquired enough chunks with the same form—which might take some time given the low type frequency—children can generalise across these different chunks and form abstract representations (Ambridge et al., 2015; Bannard et al., 2009; McCauley & Christiansen, 2019).

Type frequency is known to influence language development across levels of linguistic analysis (see Ambridge et al., 2015). Taking an example from morphosyntactic development, children rapidly form abstract representations of inflections with a high type frequency, but not of inflections with a low type frequency. Therefore, children rapidly learn that plural nouns can be formed by adding -s in English, which has a high type frequency (Bybee, 1995; Maslen et al., 2004). In contrast, children (and perhaps adults) likely store irregular plural forms (like feet) as unanalysed chunks, because these are associated with a low type frequency (Behrens, 2009; Bybee, 1995).

While type frequency is well-studied in (morpho)syntactic development (Ambridge et al., 2015; Bybee, 1995; Savage et al., 2006; Theakston et al., 2004), its role in learning compositional semantic structure has received less attention. Nevertheless, type frequency almost certainly plays a similar role, because learning compositional semantics also involves the learning of abstract, rule-like structures (Heim & Kratzer, 1998). Universal quantification can be modelled as the abstract structure ∀x → Px (‘for all x, the predicate P applies to x’), which abstracts away from the specific content of x and P (i.e. it is not bounded to specific lexical items). Therefore, children must be presented with various exemplars of universal quantification to map some universal quantifier word onto this abstract representation.

We know little about the type frequency of different universal quantifiers, but they likely differ in their variability due to differences in both semantic and syntactic properties. In our study, we will examine the variability of universal quantifiers in English and Dutch by examining (a) the number of unique lexical items they pair with, but also (b) the different syntactic uses they are associated with.

Table 1 lists the various syntactic uses of English universal quantifiers. Every is syntactically rigid, and serves as a determiner, or as a predeterminer when it precedes a number or another quantifier to indicate regularly occurring events (e.g. every four  weeks, every few days). Each and all are more flexible because they can be used as floating quantifiers or pronouns, in which case the quantifier is not adjacent to its restrictor noun (see also Champollion, 2016, 2017; Doetjes, 1997).

Table 1.

Overview of the Syntactic Uses Associated With the English Quantifiers Each, Every, and All.

Quantifier	Syntactic position	Example
Each	Determiner	Each beaver is building a dam
	Floating (adverbial)	The beavers are each building a dam
	Floating (postnominal)	The beavers are building a dam each
	Pronoun	Each went their own way
Every	Determiner	Every beaver is building a dam
	Predeterminer (before numbers)	Every 4 years
All	Determiner	All beavers are building a dam
	Predeterminer	All the beavers are building a dam
	Floating (adverbial)	The beavers are all building a dam
	Pronoun	All are building a dam
	Post-pronominal object	I’ve seen them all

Note. In the example, the restrictor—the noun that the quantifier modifies—is underlined.

Table 2 lists the various syntactic uses of Dutch universal quantifiers. Elk and ieder can serve as determiners, floating quantifiers, and predeterminers preceding a numeral or another quantifier. ¹ The alle-type quantifiers differ from each other: Alle is a determiner or a predeterminer preceding a numeral, al is a predeterminer (although it cannot precede numerals), while allemaal allows a wider range of syntactic uses. Thus, Dutch universal quantifiers differ in their syntactic behaviour both from one another and from their English counterparts. Moreover, Dutch floating quantifiers can quantify over nouns in both object and subject (Giusti, 1990), while in English, they can only quantify over the subject (expect for all, which can take a post-pronominal object position, see Table 1).

Table 2.

Overview of the Syntactic Uses Associated With the Dutch Quantifiers elk, ieder, alle, al, and allemaal.

Quantifier	Syntactic position	Example
Elk	Determiner	Elke bever bouwt een damElke beaver builds a dam‘each beaver builds a dam’
	Floating	De bevers bouwen elk een damThe beavers build elk a dam‘the beavers are each building a dam’
	Pronoun	Elk ging z’n eigen wegElk went his own way‘each went their own way’
	Predeterminer (before numbers)	Elke twee weken Elke two  weeks ‘every two  weeks’
Ieder	Determiner	Iedere bever bouwt een damIedere beaver builds a dam‘each beaver builds a dam’
	Floating	De bevers bouwen ieder een damThe beavers build ieder a dam‘the beavers are each building a dam’
	Pronoun	Ieder ging z’n eigen wegIeder went his own way‘each went their own way’
	Predeterminer (before numbers)	Iedere twee weken Iedere two  weeks ‘every two  weeks’
Alle	Determiner	Alle bevers bouwen een damAlle beavers build a dam‘All beavers are building a dam’
	Predeterminer (before numbers; see footnote 1)	{Alle honderd / Alle vier de} bevers bouwen een dam{Alle hundred / Alle four the} beavers build a dam‘{All hundred / All four} beavers are building a dam’
Al	Predeterminer	Al de bevers bouwen een damAl the beavers build a dam‘All the beavers are building a dam’
Allemaal	Determiner	Allemaal bevers bouwen een damAllemaal beavers build a dam‘many beavers are building a dam’
	Floating	De bevers bouwen allemaal een damThe beavers build allemaal a dam‘the beavers are all building a dam’
	Pronoun	Hoi allemaal Hi allemaal ‘Hi all’
	Floating over wh-element	Wat heb je allemaal gedaan?What have you allemaal done?‘What kind of things did you do?’

Note. The restrictor—the noun that the quantifier modifies—is underlined. The example is first given in Dutch, then a word-by-word translation, and then a meaning translation in English. In these meaning translations, elk and ieder are translated to each, but note that each is not a direct translation (see section ‘Different universal quantifiers, different meanings’).

Note that Table 2 includes two forms of elk and ieder: elk/elke and ieder/iedere. These grammatically singular quantifiers inflect for the restrictor noun’s grammatical gender when used as a determiner. Preceding neuter nouns, the bare stem elk/ieder is used (e.g. elk/ieder varken; ‘every pig’). Preceding common nouns, -e is added (e.g. elk e /ieder e bever; ‘every beaver’). As floating quantifiers, the bare stem is used regardless of the grammatical gender of the restrictor noun (e.g. De bevers hebben elk/ieder geslapen; ‘The beavers have each slept’). In this case, the restrictor is plural, and plural forms are alike for both genders. This also explains why the quantifiers alle, al, and allemaal do not inflect according to gender, as they are grammatically plural.

So, universal quantifiers differ in their syntactic distribution in both English and Dutch. Children must extract the abstract meaning from these different uses of universal quantifiers and learn which quantifier is allowed in which syntactic positions. Moreover, assuming that variability of a form affects development (Ambridge et al., 2015), these syntactic differences should lead to quantifier-specific developmental patterns. We will map out variability in children’s input, predicting that syntactically flexible quantifiers (all and each in English; elk, ieder and allemaal in Dutch) are more variable than rigid ones (every in English; alle and al in Dutch). The more interesting question, however, is whether this variation is comparable across the syntactically flexible quantifiers. Moreover, the syntactic use of the quantifier can also affect meaning.

The Interaction Between Syntax and Meaning: Weak all

An underexplored property of universal quantifiers is the ‘weak’ use allowed by English all and Dutch al and allemaal. These quantifiers permit a non-universal reading in certain contexts, unlike each or every:

• 6. There are all kinds of animals at the zoo.

•   ≈ ‘There are various types of animals at the zoo’

•   ≠ ‘The zoo has each type of animal’

In (6), all enforces (non-universal) plurality, comparable to various. A first intuition might be that all is used hyperbolically in such cases, which can also drive non-universal interpretations of other universal quantification (e.g. They have every kind of animal at the zoo might express a similar meaning as (6)). However, this explanation does not hold. De Vries (2019) argued that such hyperbolic use of universal quantifiers can be ‘admitted’: They have every kind of animal at the Australia Zoo! Well, not polar bears, but still, I’ve never seen so many different animals. Weak uses of all cannot be admitted (*They have all kinds of animals at the Australia Zoo! Well, not polar bears. . .). This suggests that weak all is inherently non-universal, making admissions infelicitous. ²

So, when does all trigger a weak, non-universal interpretation? De Vries (2019) argued that the interpretation of all depends on the givenness and definiteness of the quantified domain. When all quantifies over a definite domain of specific elements known to the speaker and interlocutor, all evokes ‘strong’ universal quantification (see (7)). When all quantifies over a novel, indefinite domain, all evokes ‘weak’ semantic plurality (see (8)).

• 7.  This part of the test contains ten questions, when you’ve finished all these questions, you can continue to the next part.

• 8. Some person called me to ask me all these questions.

This explains why all evokes a strong reading in floating position, since floating all requires a definite noun phrase in its restrictor (see (9) and (10)), which refer to specific, known things.

• 9. The beavers were all outside.

• 10. ??Beavers all have a tail.

The distinction between strong and weak uses of all persists cross-linguistically (De Vries, 2019). In Dutch, the predeterminer al behaves similarly to English all: It evokes a strong reading when quantifying over a definite domain of known entities (see (11)), and a weak reading when quantifying over a novel, indefinite domain (see (12)).

• 11. Al deze dieren zijn ontsnapt.

•   All these animals are escaped.

•   ‘All these animals have escaped.’

• 12. Heb je dat boek met al die dieren?

•   Have you that book with all those animals?

•   ‘Have you got that book with all those animals?’

Allemaal evokes a strong or weak reading depending on its syntactic position. As a determiner, allemaal takes a bare noun in restrictor and evokes a weak interpretation:

• 13. Er zitten allemaal bevers in het bos.

•   There sit all beavers in the woods

•   ‘There are many beavers in the woods’.

As a floating quantifier allemaal requires a definite noun phrase in its restrictor, triggering a strong interpretation (De Vries, 2019):

• 14. De bevers zitten allemaal in het bos.

•   The beavers sit all in the woods.

•   ‘The beavers are all in the woods’

However, there seems to be an exception, floating allemaal can also quantify over wh-items. In this case, the domain of quantification is indefinite, and this construction evokes a weak reading (see also Beck & Rullmann, 1999):

• 15. Wat heb je allemaal gedaan op vakantie?

•   What have you all done on holiday?

•   ‘What kind of things have you done on your holiday?’

Note that Dutch alle always triggers a strong universal interpretation, so there are important meaning differences between the alle-type quantifiers related to their syntactic differences.

So, all (English) and al/allemaal (Dutch) systematically trigger non-universal readings in specific contexts, unlike other universal quantifiers. Children need to learn this systematic variability in the use of universal quantifiers. Previous research has given little attention to the (development of) weak uses of all (but see Smits, 2010). A complementary goal of this study is to explore the prevalence of weak uses of all in children’s everyday input in English and Dutch.

The Present Study

We explored the use of universal quantifiers in children’s everyday input in Dutch and English by analysing naturalistic, adult-produced, child-ambient utterances. In this analysis, we first investigated the frequency and variability of each quantifier by calculating type and token frequency, as well as coding for the syntactic use of each quantifier. This allowed us to form initial predictions on how frequency and variability impact development for each quantifier.

We then investigated how contextual patterns of use could signal quantifier-specific meaning. Following Knowlton and Lidz (2021) and Knowlton and Gomes (2022), we coded each utterance for the semantic category of the quantified domain (e.g. individuals, times, locations). Knowlton and colleges observed that, in English, every mostly quantifies over times, while each and all are mostly used to quantify over individuals—which could signal quantifier-specific meaning differences. We will replicate this exploration in English, and test how this pattern persists in Dutch.

A third, complementary goal was to examine the prevalence of weak uses of all (in English), al and allemaal (in Dutch). Finally, we conducted a data-driven exploration into the nature of the predicates co-occurring with different universal quantifiers. Since universal quantifiers differ in distributivity, they differ in how they interact with predicates. In this part of the analysis, we explored whether, and how, the predicates could signal quantifier-specific meaning.

Method

Corpora

We selected British-English and Dutch corpora with naturalistic caregiver–child interactions involving typically-developing children from CHILDES (MacWhinney, 2000) (Table 3). The English sample contained roughly 1.7 million adult-produced utterances, and the Dutch sample contained roughly 311,000 adult-produced utterances.

Table 3.

Overview of the Selected Corpora.

Language	Corpus	Country a	Number of children	Age range	Number of adult utterances
British-English	Edinburgh	Scotland	47	0;9	82,532
	Forrester	England	1	1;0–3;2	9007
	Gathercole/Burns	Scotland	12	3;0–6;4	13,423
	Howe	Scotland	16	1;6–2;1	8900
	Korman	England	6	0;1–0;4	13,272
	Lara	England	1	1;9–3;3	96,254
	Manchester	England	12	1;8–3;0	361,075
	MPI-EVA-Manchester	England	4	1;8–3;2	567,248
	Nuffield	England	76	0;11	13,116
	Sekali	England	2	0;9–5;0	97,344
	Thomas	England	1	2;0–4;11	363,499
	Tommerdahl	England	23	2;6–3;6	13,568
	Wells	England	32	1;6–5;0	30,609
Dutch	Groningen	Netherlands	7	1;5–3;7	180,255
	Utrecht	Netherlands	2	2;3–3;1	35,498
	SchlichtingVanKampen	Netherlands	4	3;5–5;3	18,892
	Van Kampen	Netherlands	2	1;6–6;0	59,096
	Gillis	Belgium	1	0;11–1;11	12,931
	De Houwer	Belgium	4	4;8–4;11	4252

Note. The corpora were retrieved from the CHILDES database (Beaupoil-Hourdel, 2015; Bol, 1995; Elbers, 1985; De Houwer, 2003; Gathercole, 1986; Howe, 1981; Korman, 1984; Ota et al., 2018; Forrester, 2002; Gillis, 1984; Maslen et al., 2004; McGillion et al., 2017; Rowland & Fletcher, 2006; Schlichting, 1987; Theakston et al., 2001; Tommerdahl & Kilpatrick, 2013; van Kampen, 2009; Wells, 1981).

a

We are not aware of any differences in the use of universal quantifiers between English and Scottish varieties of English or between Belgian and Netherlandic varieties of Dutch.

Utterance Selection

The data processing pipeline is outlined in Appendix 1. Utterances were extracted and annotated using CLAN (V 07-Nov-2022 11:00; MacWhinney, 2000). First, we extracted all adult-produced utterances to quantify the total of adult-produced language. Second, we extracted utterances with universal quantifiers: all, each and every in English, and elk(e), ieder(e), al, alle, and allemaal in Dutch. We also extracted included compounds everywhere, everybody, everyone, and everything in English and iedereen (‘everyone’) in Dutch. The frequency of these terms is relevant because of their universal force. Compounds were excluded from subsequent analyses, which focused on free-standing universal quantifiers.

In English, we filtered all-utterances by removing utterances with the homonymous adverb (e.g. The dog is all wet!; see Buchstaller & Traugott, 2006). ³ Moreover, all was far more frequent than each and every. Therefore, we randomly selected a subsample of all utterances for a balanced analysis. This random selection was biased for corpus size, meaning that the selection included more utterances from larger corpora.

In Dutch, allemaal was far more frequent than the other quantifiers. We therefore selected a random subset of allemaal utterances, proportionate to corpus size. Moreover, al is homonymous with the temporal adverb al (‘already’), which we manually filtered out (n = 3075) before coding.

Finally, we removed incomplete utterances, repetitions of the previous utterance (including child-produced), misspellings in which the quantifier is part of a compound (e.g. every where), and utterances with idiomatic uses of the quantifier. ⁴

Frequency Analysis

First, we conducted a frequency analysis in which we calculated the token frequency of each quantifier in our sample prior to utterance removal. All other analyses were carried out on our final subsample of utterances. As a proxy for type frequency, we counted the number of unique words that immediately followed the quantifier in our subsample (extracting a bigram). Although there are other possible conceptualisations of type frequency, extracting these bigrams is an efficient, automated way to gain initial insights into a quantifier’s surface-level variability.

For Dutch al, we counted the second word after the quantifier since al, a predeterminer, is always followed by a closed-class word (e.g. determiners, possessives), while the second word following al is the restrictor noun. Counting the immediate rightward-adjacent word would therefore be an underestimation of al’s productivity. For ease of explanation, we nevertheless refer to the combination of al and the second following word as ‘bigrams’.

We calculated the type-token ratio of each quantifier by dividing the number of unique bigrams by the total number of utterances: A high type-token ratio indicates a high degree of variation.

Coding Analysis

Second, we conducted a coding analysis, in which we annotated the utterances in our subsample for the following (see Table 4 for examples):

Table 4.

The Coding Scheme of our Coding Analysis.

Category	English example	Dutch example
Which type of entities is quantified over?
Objects	all pieces, each biscuit	alle stukjes, elk koekje
Individuals	all adults, every dog	alle volwassenen, elke hond
Times	each day, every time	elke dag, elke keer
Events	each kiss, every step	elke kus, elke stap
Locations	every corner, every playground	elke hoek, elke speeltuin
Mass nouns	all the water, all the food	al het water, al het eten
Abstract entities	every word, all the colours	elk woord, al de kleuren
Anaphoric demonstratives	Have you seen all this?	Heb je dit allemaal gezien?
What is the syntactic position of the quantifier?
Determiner	all cars, each hand	alle auto’s, elke hand
Predeterminer	all the ducks, all your crayons	al de eendjes, al jouw krijtjes
Prenumber	all five women, every two weeks	alle vijf vrouwen, elke twee weken
Floating a	We’re all tired.	We zijn allemaal moe.
Floating over wh-elements	NA	Wat heb je allemaal gedaan?
Pronoun	all in a pile, each of the flowers	allemaal op een stapel, elk van de bloemen
Floating (postnominal)	You can have a biscuit each.	Jullie mogen een koekje elk.
Is the quantifier used as the head of a partitive construction?
Yes	Each of the flowers	Elk van de bloemen
No
Is the quantifier used as a strong or as a weak quantifier? (English all, Dutch al and allemaal)
Strong quantifier	all the dogs, the people are all on the street	al de honden, de mensen zijn allemaal op de straat
Weak quantifier	all these animals (indefinite), all sorts of things	al die beesten (indefinite), allemaal dingen

Note. The Dutch translations are word-by-word translations of the English ones. Note again, however, that these translations do not imply that the quantifiers used are direct translations of each other.

a

For floating quantifiers modifying the subject noun, we distinguish between floating quantifiers that take the typical adverbial position, and postnominal quantifiers. For floating quantifiers modifying the object noun (grammatical in Dutch), we do not make such a distinction.

1. What is the syntactic use of the quantifier? We distinguished between determiner, predeterminer, prenumber, floating, postnominal, pronoun, and floating over wh-elements. We also coded whether the quantifier appeared in a partitive frame, as this construction might signal a part-whole relation (Bloom & Wynn, 1997).

2. What is the semantic category of the quantified domain? We distinguish between individuals, ⁵ times, mass nouns, locations, events, abstract entities, and anaphoric demonstratives.

3. Does the quantifier trigger a strong or a weak interpretation? We coded utterances with English all and Dutch al and allemaal for whether the quantifier required a strong universal reading or a weak non-universal plural reading.

Results

Frequency Analysis

English

The English sample contained 28,019 utterances with all, 606 utterances with each, and 942 utterances with every, which made up 1.8% of the adult-produced utterances in the sample. Note that percentage includes adverb all, so the percentage of utterances with a universal quantifiers is even lower. In addition, there were 264 utterances with everyone, 873 with everybody, 1245 utterances with everything, and 520 utterances with everywhere. After data clean-up, our sample contained 523 utterances with each and 695 utterances with every, and for a balanced sample, we randomly selected 601 utterances with quantifier all for subsequent analyses.

The bigram analysis (Figure 1) revealed that all appeared in 134 unique bigrams (type-token ratio: 0.22), every appeared in 109 unique bigrams (type-token ratio: 0.16), and each appeared in 163 unique bigrams (type-token ratio: 0.31).

Figure 1.

The universal quantifiers every, each and all in English differ in the diversity of words that co-occur with them in the rightward position, with each and all being more variable than every according to this metric. Note, however, that all is mostly followed by closed-class determiners, and therefore, this figure shows a conservative estimate of the true productivity of all.

Note that all was mostly followed by determiners or possessives (Figure 1), due to the common use of all as a predeterminer. In this case, all is followed by a closed-category word, similar to Dutch al (see section ‘Frequency analysis’). We therefore counted the number of unique words in the second slot following all, which revealed 268 unique bigrams (type-token ratio 0.45; Figure 2).

Figure 2.

For all we counted the number of unique words in the second position following it. Since all is often used as a predeterminer, this number would produce a closer estimate of the true productivity of all. This type-token ratio suggests that all is paired with a diverse set of words (note the small range on the x-axis).

Altogether, all is the most frequent universal quantifier and combines with a diverse set of words. Every is the second most frequent universal quantifier but often appears in the same few phrases: Only two words (time and day) account for nearly half of all utterances with every. Each is the least frequent quantifier and is combined with a relatively diverse set of words.

Dutch

The Dutch sample contained 652 utterances with alle, 112 utterances with elk, 117 utterances with ieder, 3007 utterances with allemaal, and 305 utterances with (quantifier) al, which made up 1.3% of the adult-produced utterances in the sample. In addition, there were 117 utterances with iedereen (‘everyone’). After data clean-up, our sample contained 107 utterances with elk and 57 utterances with ieder. We randomly selected 110 utterances with alle, 110 utterances with allemaal, and 110 utterances with al.

The bigram analysis (Figure 3) revealed that alle appeared in 71 unique bigrams (type-token ratio: 0.65), allemaal appeared in 71 unique bigrams (type-token ratio: 0.65), ieder appeared in 20 unique bigrams (type-token ratio: 0.35), and elk appeared in 32 unique bigrams (type-token ratio: 0.30). Figure 3 suggests that the use of ieder is more restricted than that of elk, but we refrain from interpreting this difference due to the small sample. Finally, al appeared in 81 unique bigrams (type-token ratio: 0.74; Figure 4).

Figure 3.

Note. The Dutch universal quantifiers alle and allemaal are being paired with a larger set of unique words than elk and ieder (note that relative large range on the x-axis).

Figure 4.

For al, a predeterminer, we counted the number of unique words in the second subsequent position. The type-token ratio suggests that al is paired with a diverse set of words (note the small range on the x-axis).

Altogether, the alle-type quantifiers are more frequent than elk and ieder, with allemaal being particularly high-frequent. The alle-type quantifiers also combined with a diverse set of words. Elk and ieder, on the other hand, were less frequent and combined with a small set of unique words: A large proportion of the elk and ieder utterances involved elke/iedere keer (‘every time’) and elke/iedere dag (‘every day’).

Coding Analysis

What is the syntactic use of the quantifier?

In English (Figure 5), every was the most syntactically rigid, and primarily functioned as a determiner. Each was mainly a determiner but also appeared as a pronoun and floating quantifier. All primarily functioned as a predeterminer but also served as a determiner, pronoun, or floating quantifier. Additionally, all appeared as the head of a partitive in 20 utterances (3% of all-utterances) and each in 55 utterances (11% of each-utterances). Note that every cannot be the head of a partitive.

Figure 5.

The proportion of occurences of all, every, and each, split up across syntactic positions. All and each both occur in various syntactic positions, while every is syntactically rigid and mainly occurs in the same syntactic context.

In Dutch (Figure 6), al was the most rigid syntactically, and virtually only used as a predeterminer. Alle, elk, and ieder were most often used as determiners, though elk and ieder also served as pronouns and floating quantifiers in a few cases. Allemaal, finally, is far more variable syntactically, and occurred as a floating quantifier, as a pronoun, and as a determiner. None of the Dutch universal quantifiers served as the head of a partitive in our sample (even though partitives are grammatical with elk or ieder).

Figure 6.

The proportion of occurences of al, alle, allemaal, elk, and ieder, split up across syntactic positions. Allemaal occurs in various syntactic positions, while all other analysed quantifiers are more syntactically rigid, and mostly occured in the same few positions.

What is being quantified over?

In English (Figure 7), all and each were mostly used to quantify over individuals, whereas every was mostly used to quantify over times (replicating Knowlton & Gomes, 2022; Knowlton & Lidz, 2021). Moreover, mass nouns—although infrequent—were virtually only quantified by all.

Figure 7.

The proportion of occurences of all, every, and each, split up based on what is being quantified over. All and each are both mainly used to quantify over individuals, while every is mainly used to quantify over times.

In Dutch (Figure 8), the alle-type quantifiers primarily quantified over individuals, although there were also some differences among the alle-type quantifiers: Of the three, al is most paired with mass nouns, while allemaal showed most variability altogether. Elk and ieder primarily quantified over times.

Figure 8.

The proportion of occurences of al, alle, allemaal, elk, and ieder, split up based on what is being quantified over. The alle-type quantifiers are mainly used to quantify over individuals, while elk and ieder are mainly used to quantify over times.

All/Al/Allemaal: Is the quantifier used as a strong quantifier?

In English, all required a strong interpretation in 91% of utterances (n = 545) and a weak interpretation in 9% (n = 56). In Dutch, al was strong in 64% of utterances (n = 70) and weak in 46% (n = 40). Allemaal was strong in 45% of utterances (n = 49) and a weak in 55% (n = 61).

Nature of the Predicate

Universal quantifiers differ in their distributivity, and therefore in their interaction with predicates (Champollion, 2017). We explored the types of predicates paired with each quantifier, by examining the utterances in our corpus that had the form of a subject-predicate sentence where universal quantifier modified the subject (English: n = 152 for all, n = 173 for each, and n = 38 for every; Dutch: n = 21 for al; n = 41 for alle, n = 30 for allemaal; n = 6 for elk, and n = 9 for ieder). After a first exploration of these utterances, we coded them for whether they were copular constructions and whether the predicate contained another quantifier. We will motivate these categories below but note that this part of the analysis is exploratory, and that these two coding categories were not defined a priori.

Copular Constructions

Copular constructions describe a common feature shared by all members of the quantified domain, like in (16).

• 16. *MOT: Every painting you do is blue.

•         Manchester corpus (Nicole, 030003.cha)

These constructions emphasise the common property of the quantified domain (e.g. the ‘blueness’ of every painting), rather than individuating the domain. Therefore, copular constructions might be more common with all or every than with each in English, and with alle-type quantifiers than with elk or ieder in Dutch.

In English, 49% of all utterances, 37% of every utterances, and 12% of each utterances were copular constructions. In Dutch, 43% of al utterances, 39% of alle utterances, 43% of allemaal utterances, 33% of elk utterances and 0% of ieder utterances were copular constructions (but note the small number of elk and ieder utterances included in this analysis).

Quantified Predicates

When a universal quantifier is paired with another quantifier in the predicate, a systematic ambiguity emerges. In this case, the scope of both quantifiers can be assigned in two ways (Ruys & Winter, 2011):

• 17. *MOT: [. . .] each page has a story about the animal.  Thomas corpus (020823.cha)

•   a. For each page, there is a potentially different story.  each > a ⁶

•   b. There is a single story that is on each page.  a > each

Scope assignment is guided by several (extra-)linguistic factors (see Anderbois et al., 2012; Kurtzman & MacDonald, 1993), but for our purposes, it is important that distributive quantifiers have a stronger tendency to take wide scope over the predicate than non-distributive ones (Feiman & Snedeker, 2016; Ioup, 1975). In this case, the referent expressed in the predicate covaries with respect to the individual members of the (universally) quantified domain in subject (Dotlačil, 2010; Fodor, 1982; Ioup, 1975). For example, interpretation (17a) introduces as many stories as there are pages. This one-to-one correspondence could highlight the distributive application of the predicate, and therefore each might occur particularly often with a quantified predicate in English, and elk and ieder in Dutch.

Each co-occurred with another quantifier in predicate in 81% ⁷ of utterances, compared to 34% for every and 3% for all. In Dutch, elk co-occurred with another quantifier in predicate in 50% of utterances and ieder in 66%, compared to alle in 12%, allemaal in 10%, and al in 0%. Notably, the majority of doubly-quantified each, elk and ieder utterances were possessive constructions like (18) ⁸ (61% of each, 66% of elk, and 83% of ieder utterances).

• 18. *FAT: I need some help again.

•   *FAT: it’s Christmas.

•   *FAT: and my kittens each have two presents.

•   *FAT: but which are the right ones.

•   *FAT: can you join the presents to the right kittens?

•   MPI-EVA-Manchester corpus (Eleanor, 021103b.cha)

In such contexts, the distributive predicate causes a one-to-one correspondence between each member of the quantifier domain and the possessed item (e.g. each individual kitten has two items), which could be physically perceivable.

General Discussion

Our corpus analysis revealed that the use of universal quantifiers is characterised by quantifier-specific patterns in frequency, variability, and context of use, in both English and Dutch child-directed language. In this General Discussion, we describe the developmental implications of these findings. In sections ‘Quantifier frequency and development’ and ‘Syntactic variation and quantifier development’, we describe how differences in frequency and (syntactic) variability might impact the development of each quantifier. The developmental predictions in these sections concern the question of when and how children map universal quantifiers onto their meanings. We turn to the question of how children come to acquire quantifier-specific meanings in sections ‘Different quantifiers and the domain of quantification’ and ‘Individuation of the domain and distributivity’, in which we discuss how the contexts of use of each quantifier. Finally, in section ‘Weak and strong uses of all’, we briefly discuss our exploration of weak and strong uses of English all and Dutch al and allemaal.

Quantifier Frequency and Development

If all else is equal, children learn high-frequent forms before they learn low-frequent forms (Ambridge et al., 2015). We considered both token and type frequency. Starting with token frequency: Universal quantifiers are generally infrequent in children’s input, appearing in fewer than 2% of adult-produced utterances in both our English and Dutch corpora. Non-distributive quantifiers were more frequent than distributive quantifiers. In English, all was most frequent, followed by every (including the compounds everyone, everybody, everything and everywhere), and then each (replicating Deng et al., 2024; Knowlton & Gomes, 2022). In Dutch, the alle-type quantifiers (particularly allemaal) were more frequent than elk and ieder. Elk was slightly more frequent than ieder, but ieder also occurs as part of the compound iedereen, which was more frequent than elk—however, we refrain from interpreting this difference due to the small number of utterances. Based on these patterns, we predict that children acquire non-distributive quantifiers before distributive quantifiers.

Several studies support this prediction in English. First, experimental studies suggest that toddlers understand all before each in comprehension (Ferenz & Prasada, 2002; see also Brooks & Braine, 1996; Drozd, 2001; for similar findings in (pre)school-aged children). Second, studies on naturalistic child language showed that children first produce all (typically before the second birthday), then every (after the second birthday), and then each at a later stage in development (Deng et al., 2024; see also Roeper, 2007, p. 183). Finally, data from Wordbank, which contains thousands of MacArthur-Bates CDI administrations, show that all enters the child’s productive vocabulary first, followed by every and then each (Frank et al., 2017; Figure 9). We are not aware of similar studies in Dutch: Most existing work in Dutch focussed on preschoolers (who already have initial understanding of alle, elk, and ieder, Drozd & van Loosbroek, 2006; De Koster, 2021; Rouweler & Hollebrandse, 2015), and we are not aware of studies that examined universal quantifiers in Dutch children’s productive vocabulary. Nevertheless, we predict that the onset of acquisition of alle-type quantifiers, particularly allemaal, is earlier than that of elk and ieder. ⁹

Figure 9.

This plot was generated using data from the Wordbank repository (Frank et al., 2017), which contains the data of several thousands of MacArthur-Bates CDI administrations. The plot shows that (a) children produce all earlier than every and each, and (b) more children produced all, then every, and then each.

Distributive quantifiers are likely more frequent than non-distributive ones because their semantics is more restricted. While a strong distributive operator like each is only suitable to talk about sets of individuated referents, non-distributive quantifiers can be used in a range of situations. This observation is not specific to English or Dutch: Non-distributive quantifiers are likely more frequent than distributive quantifiers across languages. Therefore, the prediction that children acquire non-distributive quantifiers first should hold for languages with non-distributive and distributive universal quantifiers (Gil, 1995). Moreover, as we will discuss in section ‘Different quantifiers and the domain of quantification’, the quantifiers every (in English) and elk and ieder (in Dutch) are both commonly used to express generalisations. At least in child-directed language, caregivers probably talk more often about specific referents in the discourse context than express generic thoughts (Bergelson & Swingley, 2013; Coffey et al., 2024). This could explain why every, elk and ieder are relatively low-frequent.

Turning to type frequency, each and all (in English), and alle-type quantifiers (in Dutch) co-occur with many unique words, while every (English) and elk and ieder (Dutch) were used with day (Dutch: ‘dag’) or time (Dutch: ‘keer’) in approximately 50% of analysed utterances. Moreover, Dutch ieder often occurred in the idiomatic phrase in ieder geval (‘in any case’; Footnote 5). Recall that a high type frequency facilitates the construction of abstract representations, while forms with a low type frequency might initially be stored as (unanalysed) chunks (Ambridge et al., 2015; Behrens, 2009; Savage et al., 2006; Theakston et al., 2004). Therefore, children likely form abstract representations for each and all (in English) and the alle-type quantifiers (in Dutch) rapidly after the onset of acquisition, but initially understand every, elk and ieder as part of a chunk (i.e. specific quantifier-noun pairs like every day, every time). ¹⁰ Note that the general prediction that type frequency impacts learning is not bound to any specific language. Therefore, future research is needed to test whether the general distinction between quantifiers with a high type frequency and quantifiers with a low type frequency persists across more languages.

Chunking in universal quantifier development has not been systematically investigated, but some first insights in English support our hypothesis that children initially store every as part of a chunk: First, Roeper (2007, p. 183) studied the naturalistic language of 6 children up to age 5, and found 25 instances of every, with 17 of these occurring in compounds like every time or every day (see also Deng et al., 2024). Second, an experiment by Huang et al. (2010) showed that number development might involve chunking. They trained children who understood one and two but not yet three on the meaning of three. After training, the children’s understanding of three was restricted to the number-noun pairs from training—if the child was trained on three dogs they could reliably interpret three dogs but not generalise three to novel pairs like three cows. We might predict a similar effect in children’s understanding of every, elk, and ieder, in which case children go through a phase in which they understand the phrases every day or every time, but do not yet generalise the meaning of these quantifiers to other quantifier–noun pairs.

Syntactic Variation and Quantifier Development

In the previous section, we hypothesised that greater variability in nouns paired with each quantifier positively impacts development. Universal quantifiers also differ in their syntactic variability: Some are syntactically rigid (every in English; elk, ieder, alle, and al in Dutch), ¹¹ while others are flexible (all and each in English; allemaal in Dutch). It is possible that syntactic variability could negatively impact development by obscuring common underlying meaning, especially given that we know that the consistent appearance of a word in the same grammatical frame can highlight meaning (Fisher et al., 2010; Savage et al., 2006).

The hypothesis that the presence of a consistent grammatical frame facilitates meaning detection (known as syntactic bootstrapping) is supported by Wellwood et al. (2016). Their experiment showed that 4 and 5-year-old children interpreted a nonword as quantity-based when it was used as a determiner, and as quality-based when it was used as an adjective. In English and Dutch, syntactically rigid quantifiers predominantly served as determiners (except for Dutch al, which is a predeterminer), so syntactic bootstrapping could facilitate meaning detection. Here, it is relevant to note that previously, Bloom and Wynn (1997) hypothesised that the partitive construction (e.g. each of the beavers) also acts as a syntactic bootstrap that highlights a part-whole relationship. Syrett et al. (2012), however, showed that partitive constructions often convey non-quantity relations (e.g. back of the room). Our corpus contained few partitive constructions in English and none in Dutch, making the partitive construction a weak and language-specific cue to meaning at best.

If syntactic consistency is an advantage, then syntactically flexible quantifiers might pose a developmental challenge because children must detect common meaning across varied syntactic constructions. Moreover, these quantifiers can appear in floating or pronominal constructions in which they are non-adjacent to their restrictor. This long-distant dependency could obscure the semantic relation between the quantifier and its restrictor, leading to incorrect interpretations. For example, Deng et al. (2024) hypothesised that children might misinterpret floating quantifiers in English as quantifying events (following Philip, 1995). Under this hypothesis, children interpret a sentence like The beavers each build a dam as ‘each event involves a beaver building a dam’ rather than ‘each beaver build a dam’. Floating quantifiers often occupy the adverbial slot, typically used to modify verb phrases, so they may promote such incorrect restrictions of the quantified domain.

Few studies have tested how syntactic flexibility affects the development of universal quantifiers. Deng et al. (2024) analysed the spontaneous language of 10 English-speaking children (aged 1;2-5;2) and found that determiner and floating uses of all and each emerged around the same time. This suggests that an early acquisition of the syntactic flexibility of all and each. This does not contradict our prediction that syntactic flexibility poses a learning challenge: Our hypothesis concerns the detection of meaning, and production data cannot confirm whether children have fully developed meaning representations of determiners and floating quantifiers. In fact, Deng et al. themselves hypothesised that floating uses could reflect misinterpretations in which the quantifier quantifies over events. Thus, further research is needed, particularly in a cross-linguistic setting: Our hypothesis is not language-specific, and syntactic flexibility is thus expected to be a learning challenge for all languages with syntactically flexible quantifiers.

Different Quantifiers and the Domain of Quantification

The frequency and variability of universal quantifiers do not tell us how children learn each quantifier’s specific meaning. To that end, we examined the different patterns of use of each quantifier. This analysis was inspired by Knowlton and Lidz (2021), who observed that the meaning differences between different universal quantifiers have the downstream effect that caregivers use different quantifiers to quantify over different types of things. Their analysis on each and every in English child-directed language showed that caregivers used each primarily to quantify over individuals and every to quantify over times. Our analysis replicated this finding in English and showed that—in this respect—all patterns with each (replicating Knowlton & Gomes, 2022), and that a similar distinction holds in Dutch: Alle-type quantifiers mostly quantify over individuals, while elk and ieder mostly quantify over times.

Knowlton and Lidz (2021) linked the distinction between quantifying over individuals and times to genericity versus specificity: Every is commonly used to express generalisations. Generic domains can consist of individuals (or kinds, e.g. Every beaver is a mammal), but caregivers more often generalise over situations. We observed this in our corpus as well, for example in (19).

• 19. *TUR: every time someone walks by she runs out to see who it is

•   Korman corpus (staples, 16.cha)

An example like (19) does not express that some property (‘she runs out to see who it is’) applies to a specific set of times, but generalises that the property applies to every possible moment someone walks by, including future ones. ¹² In contrast, each presupposes specific, salient referents and therefore resists generalisations (Garton, 1983; Knowlton et al., 2023). While specific domains can consist of times (as in (20)), caregivers more often talk about specific individuals—perhaps because they are talking about things in the surrounding world (see also Knowlton & Gomes, 2022).

• 20. *MOT: I’ll leave that big hand on the twelve and each time we turn the page and we turn the hour you move the little on round.

•   Thomas corpus (030119.cha)

Our English analysis extends Knowlton and Lidz (2021) by showing that all, like each, is also primarily used to quantify over individuals (replicating Knowlton & Gomes, 2022). This is interesting because each and all evoke different representations: Each individuates the domain, while all groups together the domain as-a-whole (Champollion, 2017; Dowty, 1986). We will return to this difference in the next section, but for now, note that both representations presuppose that the domain is specific. The attribution of predicates to distinct individuals or to a group as-a-whole presupposes a predefined set. In contrast, generics do not quantify over specific groups of individuals but highlight common properties shared by all instances of a kind (which cannot act individually or together; see Lasersohn, 2019). ¹³

Two- and three-year-olds already distinguish between generic and specific referents (Gelman et al., 2008, 2015; Gelman & Raman, 2003). At this age, children also produce their first universal quantifiers (Deng et al., 2024; Roeper, 2007). Since they have the conceptual system in place, children might initially map every to generic domains and all/each to specific domains. Some first support comes from children’s naturalistic productions: Recall that children’s first productions of every are often in the phrases every time or every day, while their use of all is more productive (Deng et al., 2024; Roeper, 2007). This finding might suggest that children understand that every is suited for generalising over situations early on (even if their understanding of every is initially limited to these specific quantifier-noun pairs). To our knowledge, however, the generic/sensitive contrast in the development of universal quantifiers has not been experimentally investigated. Most previous experimental work compared children’s understanding of different universal quantifiers in the same context, typically involving (easily depictable) specific sets of individuals (Brooks & Braine, 1996; Ferenz & Prasada, 2002; Rouweler & Hollebrandse, 2015).

Our Dutch analysis also showed a distinction between quantifying over times and over individuals: Elk and ieder primarily quantified over times, and the alle-type quantifiers primarily quantified over individuals. Therefore, Dutch-speaking children likely map elk/ieder on generic domains and alle-type quantifiers on specific domains early on. However, elk and ieder are not completely equivalent to English every. In some cases, they act more like English each, distributively attributing properties to specific individuals:

• 21. Ernst en Maike hebben er ieder één in hun schoen gehad

•   ‘Ernst and Maike have each had one in their shoe’

•   SchlichtingVanKampen (Carl, 031005.cha)

Thus, the development of universal quantifiers must be influenced by language-specific cues and properties. Dutch-speaking children must navigate the subtle distinctions between elk and ieder. Again, their sensitivity to the generic/specific contrast could act as a scaffold: When quantifying over specific referents, elk and ieder induce an individualised representation. In addition, syntactic structure could signal meaning: Elk and ieder can serve as floating quantifiers, in which case they modify definite noun phrases or proper nouns. Since these noun phrases refer to specific, known referents, floating quantifiers effectively rule out generic interpretations. As described in section ‘Syntactic variation and quantifier development’, little is known about children’s command of floating quantifiers. Therefore, we cannot form any specific predictions about when children distinguish floating elk/ieder from determiner elk/ieder. However, previous work has shown that children learn that definite noun phrases refer to specific things around age 2.5 (in English and Dutch; Gelman et al., 2010; Rozendaal & Baker, 2008; van Hout et al., 2010), which likely facilitates the representation of the quantified domain as specific.

Finally, a separate hypothesis is that domains of individuals should be easier to represent than domains of times, because individuals are more imageable. Children typically learn imageable words earlier than less imageable ones (Bergelson & Swingley, 2013; Bird et al., 2001). Therefore, the quantified domains of all and each in English and the alle-type quantifiers in Dutch, which primarily quantify over individuals, are predicted to be easier to represent. Moreover, domains of individuals can be physically co-present (see also Knowlton & Gomes, 2022), which enables richer contextual cues or explicit feedback on quantifier meaning:

• 22. *CHR: wat gaat ge nu met de doos doen?

•   What are you going to do with the box?

<. . .>

• *CHR: nog een boek insteken?

• Putting another book in?

<. . .>

• *CHR: alle boekjes erin.

• All books in the box.

• Gillis corpus (011001.cha)

• Note: English translation is not verbatim.

Thus, caregivers use all and each and the alle-type quantifiers mostly to quantify over individuals. Domains consisting of individuals are (a) likely easier to represent (compared to domains consisting of times), and (b) lend themselves for specific feedback on quantifier meanings. These properties could further facilitate the meaning detection of all, each, and alle-type quantifiers.

Individuation of the Domain and Distributivity

Universal quantifiers differ in their tendency to individuate the domain (Vendler, 1967): English all and Dutch alle-type quantifiers group the quantified domain, while each, and in some cases elk and ieder, emphasise the individual members of the domain. Our analysis revealed several cues in the input that could facilitate learning whether (and to which degree) a quantifier individualises the domain of quantification. First, only English all and the Dutch alle-type quantifiers quantify over mass nouns, which cannot be broken into atomic parts (Champollion, 2017). Therefore, pairing with mass nouns could signal a collective bias. Children grasp mass noun semantics early on (at or before the age of three; Barner & Snedeker, 2006), which could aid early learning. Moreover, since mass nouns generally only pair with non-distributive quantifiers across languages (Doetjes, 1997; Gil, 1995), this cue likely generalises cross-linguistically.

Second, quantifier-specific differences in individuation can also be signalled by the predicates co-occurring with each quantifier, due to differences in distributivity (Champollion, 2020; Dowty, 1986). We therefore explored which predicates were commonly paired with each quantifier. This exploration firstly showed that all and every occurred more often in copular constructions than each (see (23) and (24)). Likewise, Dutch alle-type quantifiers appeared more often in copular constructions than elk and ieder (although this pattern is tentative due to the small sample size).

• 23. These are all suitable for babies.

•   Thomas corpus (021107.cha)

• 24. Every day is a bad hair day.

•   Thomas corpus (020930.cha)

Copular constructions accentuate some common property of the quantified domain. For example, even though the predicates in (23) and (24) are distributive, these sentences do not emphasise the individual application of the predicate, but the shared nature of the predicated property (see also Knowlton et al., 2023).

Our predicate exploration secondly revealed that English utterances with each and Dutch utterances with elk and ieder relatively often occurred with another existential or numerical quantifier in the predicate (as in (25)).

• 25. So we’ll each get a piece of bread

•   Gathburn corpus (53.cha)

In such constructions, the referent denoted by the predicate can covary with the separate members of the quantified domain in a one-to-one correspondence (Dotlačil, 2010), which could even be physically perceivable at the time of the utterance. This explicit one-to-one relation between the individual members of the quantified domain and the predicate could facilitate the detection of each, elk and ieder as distributive quantifiers that impose a separate application of the predicate.

Existing work suggests that children’s understanding of each’s distributivity emerges late. For example, Brooks and Braine (1996) found that even 7-year-olds accept sentences with each in collective contexts (see Rouweler & Hollebrandse, 2015, for similar findings in Dutch). Based on our data-driven exploration, we cannot make specific predictions about when children understand that each (or elk/ieder) evokes distributivity. However, our analysis suggests that children likely map all and each onto different representations at the onset of development, but the general onset of acquisition of each might be protracted because this term is low-frequent. Thus, findings like those from Brooks and Braine may reflect a general delayed acquisition of each, not just of its distributive meaning (which is likely also true for elk/ieder in Dutch).

So, predicates could signal the degree to which a quantifier individuates the quantified domain. Future work is encouraged to identify other relevant properties of the predicate and investigate when and how children could pick up on such meaning cues. In the next—and final—section, we will shift our attention to another aspect of quantifier meaning: strong and weak uses.

Weak and Strong Uses of all

English all and the Dutch al and allemaal can express weak semantic plurality and strong universal quantification. A strong interpretation is required when the domain of quantification is definite and specific. A weak interpretation is required when the quantified domain is indefinite and non-specific (De Vries, 2019). Note that a non-specific, indefinite domain introduces a novel set of entities in the discourse, which is distinct from a generic domain discussed in section ‘Different quantifiers and the domain of quantification’.

Our analysis revealed that weak uses of all/al/allemaal are not uncommon, particularly in Dutch. Therefore, children must learn when to assign a strong or weak interpretation to these quantifiers. Let’s consider Dutch allemaal first, by far the most frequent quantifier in our Dutch analysis. We coded allemaal as weak in 55% of utterances. For allemaal, meaning relates to syntax. As a floating quantifier or pronoun, allemaal universally quantifies over a specific domain of referents (syntactically marked by a definite noun phrase or proper noun)—except for when allemaal floats over a wh-element, in which case the domain is indefinite. As a determiner, allemaal enforces semantic plurality over a novel, indefinite domain (De Vries, 2019). Children learning allemaal must learn its interaction with syntax, and their knowledge of definite noun phrases (which emerges around 2.5 years; Rozendaal & Baker, 2008), could support this learning.

Turning to English all and Dutch al, we coded English all as weak in 9% of utterances and Dutch al as weak in 36% of utterances. Syntax does not serve as a strong cue for the interpretation of these terms, since they trigger a weak interpretation when they modify indefinitely used demonstratives (e.g. Why are you asking me all these questions?)—which superficially resemble definite demonstratives (e.g. Once you’ve answered all these questions, you can leave). Instead, navigating strong versus weak all and al requires pragmatic inferencing. When the domain of quantification is specific, all and al instantiate universal quantification. When the quantifier introduces a novel domain, al or all enforces semantic plurality. Children display knowledge of the distinction between known referents and referents before the age of two (see Moll et al., 2007; Rubio-Fernández, 2024), which could facilitate the interpretation of al or all early in development.

So, the distinction between weak and strong all/al/allemaal depends on syntax and/or pragmatic inferencing. These quantifiers could therefore form an interesting testing ground on how children integrate semantic, pragmatic, and syntactic information in quantifier interpretation.

Conclusion

Our corpus analysis on universal quantifiers in English and Dutch adult-produced, child-ambient language firstly showed that (a) non-distributive quantifiers are more frequent than distributive quantifiers, and (b) universal quantifiers differ in their variability. In both languages, there were quantifiers that paired with many possible words and quantifiers that mostly appeared in a few phrases (e.g. every in every time and every day). Moreover, quantifiers differ in their syntactic flexibility. These differences in frequency and variability almost certainly affect learning.

In addition, usage patterns signal quantifier-specific meaning. In both languages, we observed a distinction between quantifiers mostly used to quantify over specific individuals, and quantifiers mostly used to express generalisations (replicating Knowlton & Lidz, 2021). Since children distinguish specific referents from generic expression early on, they could pick up on this cue for quantifier-specific meaning. Moreover, the predicates commonly paired with quantifiers could signal whether the quantifier individuates the quantified domain.

Finally, we explored weak uses of the English quantifier all and the Dutch quantifiers al and allemaal. This analysis showed that weak readings are particularly ubiquitous in Dutch, and children require pragmatic cues to assign the intended interpretation.

Altogether, our corpus analysis indicates that different universal quantifiers are associated with distinct patterns of use, which we predict leads to quantifier-specific development of the specific semantic and syntactic properties of each universal quantifier. Further experimental work is encouraged to test the developmental predictions posed in this paper. Moreover, since the expression of universal quantifiers differs cross-linguistically, we particularly encourage future work to investigate which predictions posed in this paper might generalise across languages.