1.1 How sentence-to-world pairings underdetermine what any means

What does any mean to an adult, and why might children misanalyze it? Like other polarity-sensitive words (like yet and ever), any leads two lives (Ladusaw, 1979). In one life, any behaves like a Negative Polarity Item (NPI). As an NPI, its appearance is limited to the scope of negation (e.g. I don’t have any cookies), as well as a set of linguistic environments that share certain much-debated properties with negation. These include other ‘downward-entailing’ environments such as the antecedents of conditionals and the restrictors of universals, as well as questions, only, so-called ‘adversative’ predicates, markers of sarcasm, and more (Fauconnier, 1975; 1979; Ladusaw, 1979; Linebarger, 1987; Horn, 1989; 2015; Kadmon & Landman, 1993; Krifka, 1995; Giannakidou, 1998; von Fintel, 1999; Crnič, 2014; i.a.). The meaning of any in all of these contexts corresponds to a kind of indefinite existential quantifier, similar to (and maybe derived from) the meaning of even one (Lahiri, 1998; Chierchia, 2013; 2019). In its other life, any can appear in a restricted set of positive contexts, generally under the scope of modal operators (e.g. Any cookie you want can be yours). In that life, any acts as a Free Choice Item (FCI), and its meaning is generally of a wide-scoping universal (Vendler, 1967; Horn, 1972; Carlson, 1981), though examples of FCI uses with an existential force (Horn, 2000) contribute to a further debate about how best to characterize this second life (Crnič, 2019; van der Auwera, 2024). Outside of either of these two contexts in which any can live, its use is unacceptable to English speakers (e.g. *I have any cookies) and correspondingly virtually unattested in children’s input.

Due to these two lives, linguists have long debated whether any has one meaning or two (Linebarger, 1980; Carlson, 1981; Homma, 1990; Kadmon & Landman, 1993; Dayal, 1998; Giannakidou, 2001, i.a.). Behind this debate is the fact that many uses of any are consistent with multiple different analyses of its meaning. For example, in a negated main clause, any could be interpreted either as a narrow-scoping existential or as a wide-scoping universal. Both would produce the same sentential meaning.

As for the linguist, so too for the child. To analyze any as a narrow-scoping NPI, children may need to notice that it never appears in corresponding affirmative sentences. Indeed, some researchers have suggested that this interpretive ambiguity might explain why any would have a wide-scoping universal FCI meaning in the first place (Ladusaw, 1979; Herburger, 2001; 2023; Kuhn & Maldonado, 2022; 2025). Here, however, we merely highlight this ambiguity as one example of how sentential meanings can underdetermine the lexical meaning of any. We home in on a further interpretive ambiguity, which children must face even if they understand that any cannot appear in an affirmative context.

The ambiguity we focus on is between NPI any and Negative Concord Items (NCIs). NCIs are a class of words that share much of their distribution – but not their meaning – with the NPI life of any (see Herburger, 2001; 2023). They are negative quantifiers (typically meaning ‘nothing’, ‘no one’, or ‘never’) which, when within the scope of another negation, can effectively appear inert; the meaning of the utterance in which they appear is negated just once, not twice. While standard American English does not generally permit negative concord constructions (though see, Blanchette, 2013; 2015), NCIs are common in many varieties of both British and American English (Smith, 2001; Anderwald, 2005), as well as across languages, including Greek, Japanese, Korean, and the Romance family (in French, Spanish, Catalan, Italian, and Romanian; see Robinson & Thoms, 2021, for review). For example, in Romanian, a negative sentence can have two negative operators (a sentential negator and an NCI) that are interpreted as one logical sentential negation (Fălăuş & Nicolae, 2016):

NCI-permitting languages vary with respect to how strictly they require a prior negator to license the occurrence of an NCI. In strict concord languages such as Romanian, NCIs are unlicensed in the absence of negation (Fălăuş & Nicolae, 2016), whereas in non-strict negative concord languages, such as most other Romance languages, NCIs can also occur in the absence of a prior negator pre-verbally. In that case, they contribute a negation themselves (see Giannakidou & Zeijlstra, 2017, for review).

The crux of the learning problem facing children is that under negation, any may look indistinguishable from a negative quantifier in concord with that negation (an NCI; see Figure 1). It is not that any necessarily has the exact same meaning. Rather, its distinctive contribution to a sentence – for instance, as a domain-widener (Kadmon & Landman, 1993) – may not be noticeable in most contexts in which it appears. (3a) and (3b) may not mean exactly the same thing, but they would be hard for a child to tell apart.

Figure 1: Two Aristotelean squares of opposition illustrate three possible mappings from sentential meaning (left) to the lexical meaning of any (right). If a sentence containing any under a negator is correctly understood to have a universal negative meaning (the E corner of the left square), there are three consistent analyses of the lexical meaning of any (three arrows). If the sentence is analyzed as a negative concord construction, the lexical meaning of any would be analyzed as a negator (the E corner of the right square). If the sentence is analyzed with inverse scope (any taking wide scope over not), any would be a universal quantifier or free-choice operator (the A corner of the right square). If the sentence is analyzed with linear scope (not taking wide scope over any), any would be an existential quantifier (the I corner of the right square). Note that two of these analyses yield contradictory lexical meanings (I and E).

Since children cannot know a priori whether their variety of English has NCIs, they must be prepared to consider the possibility. And being so prepared, children could mistake the meaning of any under negation for the meaning of an NCI no. To make matters worse, noticing that any does not appear in corresponding affirmative constructions like (3c) would not disabuse the child of their misanalysis, because that distribution is still consistent with any being an NCI. In a strict NC language, an NCI would never appear without a negation either, but even in a non-strict NC language, NCIs would not appear postverbally in constructions like (3c) without some other negative element to license them (see Giannakidou & Zeijlstra, 2017).

To make matters even worse for the child, in at least some non-strict NC languages, the licensor for a postverbal NCI need not be a negation. Other downward-entailing and non-veridical environments – including questions, the antecedents of conditionals, and the restrictors of universals – can license NCIs just like they do NPIs (Giannakidou, 1998; Herburger, 2001). For instance, in Italian, postverbal NCIs are unlicensed in an affirmative assertion as in (4a), but can be used in a corresponding polar question as in (4b) without any other negative element. Again, this is just the same environment that would license an NPI with the meaning of any, and again it produces an indistinguishable sentential meaning.¹ Strikingly, in non-veridical contexts like these, the NCI itself is also bleached of its negative meaning; the question is a positively – not a negatively framed – polar question (Zanuttini, 1991; Giannakidou, 1998). Indeed, this is one reason Herburger (2001) suggests that NCIs themselves are systematically ambiguous between an existential and a negative meaning.

If children are open to the possibility of a word like nessuno appearing in their language, then figuring out what any means becomes that much harder. Questions, conditionals, and universals are just the sort of contexts that would be expected to distinguish an NPI from an NCI – only the NCI might start acting like an NPI! Although, to our knowledge, there is no one language in which questions, conditionals, and universals all license NCIs, each of these environments is a licensor in some language. That means that children, who have yet to learn which licensors are exclusive to NPIs in their particular language, cannot be sure that a word that is dependent on either one or more of these licensors is an NPI and not an NCI. The learner’s situation is not just malevolent, it’s absolutely devilish.

To be sure, there do exist contexts that distinguish any from an NCI. The same evidence that convinces linguists that any is not actually a negative quantifier could, if it were available, also convince the child. First, in its other life as an FCI, any appears without a wider-scoping negation, in which case it does not act as a negation itself but rather as either a universal or an existential (Horn, 2000; Crnič, 2019; van der Auwera, 2024). Maybe children, like some linguists, posit that any is ambiguous between its free choice meaning(s) and its meaning under negation. But at least prima facie, FCI uses of any should count for the child as evidence against the NCI hypothesis. (4a) and (4b) do not have the same sentential meanings.

Even in its life as an NPI, there are cases where understanding the sentential meaning should be sufficient to distinguish any from an NCI. An NCI in the same environment would either be unacceptable in a strict-NC language, or else would contribute a semantic negation to the meaning of the sentence in a non-strict one, which would yield the wrong sentential meaning; compare (5a) and (5b).

Moreover, in both strict and non-strict concord languages, NCIs can be used as single-word fragment answers to questions, in which case they clearly express a negative quantifier. In English, any in the same position (i.e. What do you want? Anything / When can we go? Anytime) would never have a negative meaning. Finally, although both NPI any and certain NCIs can appear in the antecedents of conditionals, in the restrictors of universals, and in questions – as well as under negation – their distributions are not entirely the same. The licensing of NCIs by negation appears to be subject to a locality constraint, while NPI any can be licensed at longer distances and within islands (see Giannakidou & Zeijlstra, 2017 for a review).

The problem for English-learning children is that all of this disambiguating evidence is rare. In a corpus analysis of child-directed speech, Tieu (2013; 2015) found that sentential negation is by far the most common licensor of any, appearing in approximately 80% of utterances in which any is used. That is, at least about 80% of the uses of any that children hear are ambiguous between an NPI and an NCI interpretation. In contrast, Tieu found that any was only used as an FCI in 1–4% of its appearances, varying across the children whose input she examined. The remainder of cases are NPI uses with other licensors than negation, some of which might in principle disambiguate any from an NCI, as in (6) above. But consider that children also have to be open to the possibility that there really is an NCI in their language. For example, consider Japanese, a strict NC language, which has the NCI nanimo (meaning ‘nothing’). Sano et al. (2009) found that in over 160,000 tokens of child-directed Japanese, which included 56 tokens of nanimo, children did not hear a single piece of evidence that could distinguish nanimo from an NPI.

In sum, children face the dual challenge of differentiating between these two classes of words – NCIs and NPIs – even as they simultaneously have to work out whether their language uses negative concord constructions at all. And they must do this with evidence that ranges from rare to nonexistent in their early input.

1.2 What do children think any means?

If much of the distribution of any in children’s input underdetermines its meaning, then children might learn to expect and reproduce this distribution – only producing NPI any where it is licensed – before they have figured out whether any has the meaning of an existential or of a negation. Consistent with this possibility, Tieu’s (2013; 2015) corpus analysis of 26 British and American children found that by age 3, they produced very few unlicensed instances of NPI any (<3%). Sentential negation was the most frequently produced licensor (around 95%). At the same time, most of these children did not produce FCI any at all, and those who did produced it as an NPI significantly earlier. Thus, even as young children overwhelmingly used any within the scope of negation – more often, even, than they heard it used that way in their input – it is unclear if they were treating any as an NPI or an NCI.

Evidence from children’s own production suggests that at least some children really may have misanalysed any as an NCI. Davidson (2020) points out that in Tieu’s (2013) analysis of child speech, most of children’s errors in using any were in utterances that the children intended to have a negative meaning.

Sarah (Brown corpus, age 2;10)

*MOT: that’s to make orange juice (.) squeeze the oranges for orange juice for babies.

*CHI: me?

*MOT: yeah.

*CHI: I want any.

%com: negative meaning

*MOT: you don’t want any !

(Transcript 33, Line 410)

Maybe this child intended to include a higher negator, but made a speech error and omitted it. Or maybe this child misanalysed any as a negative quantifier, and thought they could use it to convey a negative meaning without a higher negator.

Evidence from comprehension studies is likewise inconclusive, but consistent with the possibility that different children commit to different analyses of what any means (Xiang et al. 2006; Tieu & Lidz, 2016). Tieu and Lidz (2016) used a truth-value-judgement task in which children and adults saw a character searching for and finding different kinds of stars in a scene, but failing to find one particular kind, the fuzzy stars. A puppet then described the scene by saying the character “can’t find any stars”. All adults – and most children – rejected this description, interpreting NPI any as quantifying over a wider domain of stars, and so the puppet as saying, in effect, that the character did not find even one kind of star (which was false). But a third of children accepted the puppet’s description. Tieu and Lidz quote some of these children’s justifications for their responses, and argue that they are consistent with treating any as quantifying over the same domain as a plain indefinite; that is, with treating any as an NCI, in concord with the wider-scoping negation. For instance, one child who agreed with the puppet that the character “can’t find any stars” justified this response by pointing to the still-lost fuzzy stars in the image and saying, “Cause they’re all the way up there”. Tieu and Lidz report that this subset of children gave both the same truth-value judgments and similar justifications for their responses to “can’t find any stars” as both they and adults gave to “can’t find stars” – or as both might have given to “can’t find no stars” in a negative concord language. Still, a negative concord language was not tested here, nor was children’s understanding of any in an affirmative context, which could disambiguate the meaning of an existential from a negation. It is possible either that these children analyzed any as an NCI, or that they analyzed it as an NPI but did not understand its domain-widening, even-one-like, property.

What about children’s comprehension and production of any in questions? Tieu (2013) reports that questions are the second most frequent licensor of NPI any in children’s input after negation, making up 16–30% of NPI any tokens, depending on the child. This should give children good evidence that any is licensed in questions. Indeed, Tieu (2010) found that there is a high correlation and no evidence of lag between when children start producing any under negation and in questions. But as we have been emphasizing, adult-like production of an NPI does not entail adult-like comprehension. Moreover, as the case of nessuno shows, NCIs may act NPI-like in questions too. Establishing that children distinguish any from an NCI in a question requires testing their comprehension in a way that specifically distinguishes any from some masquerading NCI, which is no easy feat. While there is, to our knowledge, one study of how children understand questions containing any, it does not quite address this issue. Thornton (1995), tested 10 children (3;06–4;11) on questions in which a negation was either higher or lower than any:

Thornton found that children pointed to the turtle that hadn’t bought an apple in response to (7a) 93% of the time, and to the turtle(s) that had bought an apple in response to (7b) 85% of the time. Note, however, that a child who thought any means no_NCI might respond exactly the same way. Consider again the case of nessuno. Consider moreover what the questions are about. The question in (7a) asks about those turtles that did not buy an apple, and those are the turtles children point to. The question in (7b) asks about turtles who did buy an apple, and children point to those. Children might respond the same way no matter what they think any means, as long as they independently understand which turtles are under discussion.

1.3 Negative concord and double negation

A closely related set of studies show that English-speaking children prefer a negative concord interpretation of sentences containing two negations (Thornton et al. 2016). When presented with a sentence as in (5), three to five-year-old English-speaking children overwhelmingly preferred the negative concord interpretation in (5a), whereas adults from the same speech community preferred the double negative interpretation in (5b) (Thornton et al. 2016).

These results have been replicated in German-speaking, Italian-speaking, Japanese-speaking, and Afrikaans-speaking children, with studies finding that children prefer negative concord interpretations of sentences containing two negations more than adults do, across both languages that have negative concord constructions, and those that do not (Sano et al. 2009; Nicolae & Yatsushiro, 2020; Moscati, 2020; White et al. 2023). Artificial language learning tasks have also shown that English-speaking adults find it significantly harder to learn a double negation language compared to a negative concord language (Maldonado & Culbertson, 2021).

One interpretation of this pattern is that NCI analyses of unfamiliar function words that appear under a negator may be cross-linguistically preferred, not just by young children, but also by adults. An alternative explanation is that the preference for a negative concord interpretation reflects the processing difficulty and higher cognitive demands imposed by double negation (Corblin, 1996), especially in children (Jou, 1988), and especially given that negative quantifiers may pose additional interpretive challenges for children relative to positive quantifiers (Katsos et al. 2016; Moscati 2024).

How children interpret any bears on whether the negative concord interpretation of double negation is more likely to be a processing failure or a lasting linguistic analysis. If children treat any as equivalent to no_NCI in affirmative contexts, that would indicate that they have analyzed it as part of a negative concord construction in its more typical appearances under a wider-scoping negation. If this NCI analysis is available for any under a negation, it may likewise be available for an actual negator in the same position. This would raise the possibility that children may initially be biased to assume that they are in a negative concord language. We will return to this possibility in the discussion.

1.4 The present study

In this study, we investigate directly what children think any means. Given that children almost never produce unlicensed any, do they also assign any the same meaning as adults by the age at which they begin saying it? If not, do they sometimes confuse any with a negator, consistent with the majority of its distribution in their input and the meanings of the sentences in which it appears on a negative concord analysis?

To answer these questions, we test how children interpret any in an affirmative context, in the absence of a wider-scoping negation. We use two picture-choice comprehension tasks to do this. In one task, we investigate how children interpret any in a free choice context, in which it is licensed in adult speech. In the other, we test how the same children interpret any in an affirmative sentence, where it is unlicensed. We look for correspondence in children’s interpretation across tasks as a way of identifying a potential sub-group of children who might consistently interpret any as a negator.

In using an ungrammatical sentence as a probe of what children think any means, we do not assume that children think this sentence is acceptable. Rather, based on Tieu’s (2013; 2015) finding that children almost never produce any in such sentences themselves, we think these children probably know that these sentences are unacceptable – no matter what they think any means. Nevertheless, their interpretation of any in such sentences may differ from adults and between younger and older children. In that case, comparison to appropriate controls can inform whether different interpretations stem from different reactions to ungrammaticality or from differences in what these children think any means.

In each task, in order to probe what children think any means, we compare children’s and adults’ interpretation of any to their interpretation of three other target words: some, no, and a nonce word. We also present each of these words in both an affirmative and a negative context. Prior research has found that 2-year-olds interpret some as an existential quantifier both in affirmative sentences (Barner et al. 2009) and under negation (Feiman et al. 2019). Comparing children’s responses to any and their response to some tests whether they interpret any the same way as an existential. Similarly, children interpret no as a negative quantifier at least by age 3 (Nordmeyer & Frank, 2014), so that children’s responses to no provide a reference for how children would respond if they interpret any the same way as a negator. Our central hypothesis is that some children – unlike adults – may interpret any like no and unlike some in affirmative contexts. Trials in which no is itself within the scope of another negator test participants’ interpretation of double-negated sentences, allowing us to replicate prior findings that English-learning children tend to interpret the second negation as semantically null negative concord (Thornton et al. 2016).

Finally, nonce words, such as dax or blick, probe how children respond to a word appearing in the same position as any when they don’t know what the word means. Although it is common to assume that children who are confused will choose randomly between all available options, it is possible that children have baseline preferences, priors, or biases that favor certain choices, or that the process of trying to make sense of an unknown word would itself lead them to pick certain options more often than others, possibly in a context-sensitive manner. Children’s responses to a nonce word in the same position as any should provide an empirical estimate of these factors both generally and at different ages, serving as an improved baseline measure that plays a similar function to a “chance” rate of responding.

2.1 Ethics and consent

Ethical approval was obtained from the Institutional Review Board at Brown University (1809002208).

2.2 Participants

We tested 20 adults and 106 children across five age groups: 2-year-olds (N = 20, M_age = 2;5, SD = 6.8 months, 5 boys), 3-year-olds (N = 22, M_age = 3;6, SD = 2.9 months, 7 boys), 4-year-olds (N = 23, M_age = 4;4, SD = 3.3 months, 7 boys), 5-year-olds (N = 20, M_age = 5;4, SD = 3.1 months, 14 boys), 6-year-olds (N = 21, M_age = 6;6 months, SD = 4.2 months, 7 boys). We had planned to test 20 children per age group, but scheduled a few additional participants and included all the data. All children were reported by their caregivers to be typically developing monolingual English speakers who were exposed to fewer than ten hours of another language per week. Caregivers received a $5 online gift card as compensation. Sixteen additional children were tested but excluded for failing to complete all tasks. Adults were recruited through Amazon Mechanical Turk and children were recruited from the Brown University Developmental Labs’ participant database. Written consent to participate was obtained from all children’s caregivers, as well as verbal assent from children over 6 years of age.

2.3 Design

All participants took part in two picture-choice comprehension tasks, the ‘Crayon Task’ and then the ‘Liquid Task’, always in that order. These tasks assessed participants’ interpretation of any outside of the scope of a preceding negation. In the Crayon Task, the use of any was meant to be acceptable on a Free Choice interpretation. In the Liquid Task, any was used postverbally in an upward entailing context where a Free Choice reading is unavailable, and where it is unlicensed for adult speakers. So that responses on the Crayon Task could not be affected by any confusion on unlicensed Liquid Task trials, the Crayon Task was always administered first.

In both tasks, participants heard different target words in determiner position within the critical utterance (some, dax/blick, any, no), both with and without a preceding negation to create a downward- or upward-entailing environment, respectively. This produced a 4 (Target Word) X 2 (Environment) design. Trials were blocked into upward-entailing and downward-entailing environments, with the order of the blocks and the order in which target words appeared within-block counterbalanced between participants within each age group.

2.4 Materials

2.4.1 Crayon Task

The Crayon Task consisted of 8 trials. In each trial, participants saw two boxes of crayons on opposite sides of the screen (see Figure 2). Elmo always appeared in the top left of the screen, and a different Sesame Street character (“Elmo’s friend”) appeared centered above the two boxes on each trial. The researcher introduced Elmo’s friend by name, after which Elmo would say what his friend wants. Participants were asked to give each friend the crayon box they want by pointing to the box that Elmo describes. Then the experimenter (or the adult participant themselves) clicked on Elmo, causing his mouth to animate and produce a pre-recorded sentence in a voice different from the experimenter’s:

“[Name] [wants/doesn’t want] a box with [some/any/dax/no] [color] crayons”

Figure 2: An example display of one trial in the Crayon Task. In this trial, participants would be introduced to Elmo’s friend Grover, and then see a video of Elmo saying, “Grover wants a box with any green crayons.”

Participants were asked, “Which crayon box should we give to [Name]? Can you point to it?” To record children’s responses, the caregiver was asked to report which side of the screen the child pointed to (indicating left or right without re-describing the crayon box) and the experimenter clicked on the corresponding box.

Critically, one of the crayon boxes contained multiple crayons of the color that Elmo mentioned, varying along a spectrum (e.g. light green and dark green). In the upward-entailing sentences, in which Elmo says what color his friend “wants”, this box matched a Free Choice interpretation of any, with the variation in colors supporting the use of any to include potentially non-prototypical cases.

Trials were grouped into blocks by upward- and downward-entailing environment (i.e. wants vs doesn’t want), to avoid alternating between affirmative and negative sentences and ease the processing load of negation for younger children (see Reuter et al. 2018). For counterbalancing between participants, trials were ordered into four lists. One pair of lists had the UE sentences first, and the other pair had the DE sentences first. Crossed with these pairs, three target words (some/any/no) appeared in two different pseudo-random orders, always in the same order for both blocks within a list. Dax was always the final target word within each block, to avoid any confusion that might be caused by a nonce quantifier on preceding trials. Within each block, each color (red, green, blue, purple) was mentioned once.

Across all lists, each character always made the same request. For example, Grover always ‘wants any green crayon’. The box containing the mentioned color was always presented on the same side for a given experimental item. Each character and item appeared once per list. Across items, each side (left or right) was the ‘correct’ response for 50% of trials (excluding dax trials, for which there is no ‘correct’ response). This resulted in the mentioned color appearing on the right-hand side on one out of the four trials within each block. The lists were assigned to participants in ascending order within each age group. Appendix A shows the lists.

2.4.2 Liquid Task

At the start of this task, participants were told that they would help Elmo find his friends. The task consisted of 8 trials. On each trial, participants were presented with three images of identical characters with different volumes of liquid: an empty container, a small volume, or a large volume (see Figure 3). The researcher then introduced the characters: “Let’s see which one of these [girls/boys] is Elmo’s friend. Look at what all these [girls/boys] have.” and pointed to each container with the cursor, in order from left to right. “All of these [girls/boys] look the same, but only one of these [girls/boys] is Elmo’s friend, [Name].” Elmo would then animate and describe his friend, with a pre-recorded voice different from the experimenter’s:

Elmo: [Name] [has/doesn’t have] [any/dax/no/some] [liquid].

Figure 3: An example display of one trial in the Liquid Task. Participants would be told that while all these boys look the same, only one of them is Elmo’s friend John. Elmo would then say, “John has any water,” and participants would be asked, “Which one of these boys is Elmo’s friend John?” Unlike in the Crayon Task, the appearance of any was unlicensed in the affirmative trials.

The experimenter then asked the participant, “Which one of these [boys/girls] is Elmo’s friend [Name]?” and invited them to point. As in the Crayon Task, the child’s caregiver reported where the child pointed, and the researcher recorded the caregiver’s report (left, middle, or right). For adults, no experimenter was present and the instructions were written out. Adults were asked to click on the character themselves.

As in the Crayon Task, trials in the Liquid Task were grouped into block by entailment environment (UE vs. DE; i.e. has vs. doesn’t have). Each trial showed a new character, who was given a new name. There were four different kinds of liquids (water, juice, tea, milk), each of which was used twice during the task, once per block. Each character’s name, appearance, and the kind of liquid they had was held constant across lists (e.g. John was always the boy with the green shirt, and always had water).

For counterbalancing between participants, trials were ordered into four lists. As in the Crayon Task, one pair of lists had the UE sentences first, and the other pair of lists had the DE sentences first. Crossed with these pairs, three target words (some/any/no) appeared in two different pseudo-random orders, with the same order for both blocks within a list. Blick was always the final target word within each block. We used blick instead of dax so that children would not assume that the nonce word had the same meaning in both the Crayon and the Liquid Task. The lists were assigned to participants in ascending order within each age group. Appendix B shows the lists.

2.5 Procedure

Children took part in the study online over Zoom video-call with their caregiver and an experimenter present. The experimenter shared their own screen with the participant, and advanced through a Qualtrics survey that displayed the experiment.

Adults completed both tasks on Qualtrics on their own, using a modified version of the same survey form. Adults were told the truth – that they were responding to questions designed for children in order to compare children’s language comprehension to theirs. Before starting the study, adults completed three additional sound-check trials, in which they pressed an on-screen button to play audio of one spoken word and were asked to write that word into a textbox in order to advance. For adults, all of the instructions that the experimenter would give verbally were written on the screen instead, and audio/video recordings of Elmo automatically played when advancing to a new trial. Adults were instructed that they could replay the audio and video of Elmo within each trial by clicking on him.

3.1 Crayon Task

3.1.2 Control trials: dax and some

Figure 4 shows participants’ responses on the Crayon Task, broken down by age group and trial type. To check whether children at different ages could understand and perform the task, we tested whether each year-long age group responded differently to DE than UE trials on some and on dax trials (that is, whether they differentiated wants some from doesn’t want some and wants dax from doesn’t want dax). We tested for an effect of Entailment (UE or DE) for each of these target words separately, and found that two-year-olds were the only group whose responses did not significantly differ between UE and DE environments in response either to some (χ²(1) = 1.13, p = .29) or to dax (χ²(1) = 0.59, p = .44). Given this lack of sensitivity to the difference between positive and negative requests for some and dax, we concluded that two-year-olds’ responses on the critical any and no trials would be uninformative and excluded these children from further analysis on the test trials.

Figure 4: Results of the Crayon Task. The percentage of participants in each age group who chose the Crayon Box with the color mentioned by Elmo for each trial type. Rows correspond to entailment environment: DE (Elmo doesn’t want…) on top and UE (Elmo wants…) on bottom. Facets correspond to the determiner [any/dax/no/some]. Error bars denote one standard error from the mean.

3.2 Liquid Task

The analysis strategy for the Liquid Task was identical to the Crayon Task. In the Liquid Task, the binary DV was whether the participant chose the character with the empty container or not, collapsing “small volume” and “large volume” responses together.

3.2.1 Control trials: blick and some

Figure 5 shows participants’ responses on the Liquid Task, broken down by age group and trial type. As we did for the Crayon Task, we tested whether each year-long age group responded differently to DE than to UE trials when asked who has/doesn’t have some and dax. As in the Crayon Task, we again found that two-year-olds were the only group whose responses did not significantly differ between UE and DE environments in response either to some (χ²(1) = 0.64, p = .42) or to dax (χ²(1) = 0, p = 1). Given their lack of sensitivity to a single negation, we again concluded that two-year-olds’ responses on the critical any and no trials would not be informative, and excluded these children from further analysis.

Figure 5: Results of the Liquid Task. The percentage of each response option (large volume, small volume, or empty) chosen by participants, broken down by age group, target word, and linguistic environment. Rows indicate whether there was negation in the prompt: [doesn’t have] (top), [has](bottom). Facets indicate the target word [any/nonce word/no/some].

To check whether children at different ages could understand and perform the task, we tested whether each year-long age group responded differently to DE than UE trials on some and on dax trials (that is, whether they differentiated wants some from doesn’t want some and wants dax from doesn’t want dax). We tested for an effect of Entailment (UE or DE) for each of these target words separately, and found that two-year-olds were the only group whose responses did not significantly differ between UE and DE environments in response either to some (χ²(1) = 1.13, p = .29) or to dax (χ²(1) = 0.59, p = .44). Given this lack of sensitivity to the difference between positive and negative requests for some and dax, we concluded that two-year-olds’ responses on the critical any and no trials would be uninformative and excluded these children from further analysis on the test trials.

3.3 The interpretation of any across both tasks

The two tasks we used probed what children thought any means when it is not preceded by a negation. The Crayon Task probed children’s interpretation of any in a licensed, free choice context, while the Liquid Task probed their interpretation of any in an unlicensed, affirmative context. Because the same participants completed both tasks, we can ask whether it was the same participants who interpreted any in a non-adult-like way in both cases. Recall that on the Crayon Task, when told that “Elmo wants the box with any [color] crayons”, the non-adult-like response is choosing the crayon box without the mentioned color. On the Liquid Task, the non-adult-like response is choosing the character with the empty container when told that “John has any water”. In both cases, these responses suggest that any was interpreted as a negator. If a child has mis-analyzed any as a negator, that child should give the non-adult-like response on both tasks, not just one of them.

Figure 6 shows the crosstabulation of participants’ responses to affirmative (UE) trials on the Crayon Task and the Liquid Task. A majority (15 out of 21) of the children who interpreted any as a negator in Crayon Task also interpreted it as a negator in the Liquid Task. Conversely, of the children who did not interpret any as a negator in the Crayon Task, only a minority (27 out of 66) interpreted it as a negator in the Liquid Task. This pattern was consistent across ages. It did not hold among 3-year-olds: only 2 of the 6 who treated any as no in the Crayon Task went on to do the same in the Liquid Task. However, 6 out of 7 4-year-olds, 3 out of 4 5-year-olds, and 4 out of 4 6-year-olds did so. Conversely, 5 out of 19 3-year-olds who did not treat any as no in the Crayon Task went on to treat it as no in the Liquid Task. This was true of 5/15 4-year-olds, 8/16 5-year-olds and 9/18 6-year-olds

Figure 6: A mosaic plot, showing the numbers of children across all ages who gave specific combinations of responses to affirmative (UE) “any” trials across both comprehension tasks. Each tile corresponds to a cell in the crosstabulation between the two tasks, and the area of each tile is proportional to the number of children in that cell. Two-year-olds and adults are excluded. Columns indicate the choice of crayon box (with-vs-without the mentioned color); rows and shading indicate choice of character (empty container, small volume, or large volume of liquid). Sum frequencies of each response type for both tasks are printed outside the cells, in the margins.

To assess the reliability of this pattern – whether certain children consistently interpreted any as a negator in both tasks – we tested whether children who gave the non-adult-like response on one task were more likely to give the non-adult-like response on the other. We restricted the data to 3- to 6-year-old children’s responses to UE any trials, and used a logistic mixed effects regression, with their probability of choosing the empty container on the Liquid Task as the DV, and that child’s choice of the crayon box (with vs without the mentioned color) in the Crayon Task, the child’s age, and the interaction between them as fixed effects. This revealed a significant association between children’s response to UE any trials across tasks (χ²(1) = 7.82, p = .005), a marginal effect of age (χ²(1) = 3.54, p = 0.06), and no significant interaction (χ²(1) = 2.12, p = 0.15).

Was this association specific to any? It is possible, for example, that some children systematically either chose or avoided choosing whatever was mentioned (the mentioned crayon color, the mentioned kind of liquid) in both tasks, perhaps in cases where they didn’t understand what the target word meant. To investigate this possibility, we also tested whether children’s responses to UE nonce word trials (dax and blick) on one Task similarly predicted their responses to UE any trials in the other Task. We used the same logistic regression as above, only with the data restricted to UE dax Crayon trials and UE any Liquid trials. This revealed no significant association in the has any trial in the Liquid Task and the wants dax trial on the Crayon Task (χ²(1) = 0.43, p = .51), and no significant effect of age (χ²(1) = 0.01, p = .92), or interaction (χ²(1) = 0.02, p = .89). We repeated the same procedure with UE any trials as the prediction and UE blick trials as the DV, and again found no association between the “wants any” trial in the Crayon Task and the “has blick” trial in the Liquid Task (χ²(1) = 1.93, p = .16), and no significant effect of age (χ² (1) = 2.38, p = .12) or interaction (χ²(1) = 0.31, p = .58).

In sum, a subset of children appeared to persistently respond to affirmative statements with any as if it meant no. The same children did not respond the same way to a word they did not know, suggesting that their responses were not the result of confusion or uncertainty, but a genuine misanalysis.

4.1 Does representing the licensing conditions of an NPI depend on representing its meaning?

Our findings indicate that not all children comprehend the existential meaning of any by the age at which they produce any only in grammatically licensed utterances. At the same time, Tieu (2015) found that children do not produce any with all of its possible licensors. While any is licensed by a negator around 80% of the time children hear it in their input, children themselves use a negator 95% of the time they say any. This is consistent with some children assigning any an adult-like meaning, but others analyzing any as a strict negative concord item, which – unlike NPI any – can be licensed only by a negation and not by other downward entailing environments. This means that the finding that children almost never produce unlicensed any may not actually indicate that they have mastered the licensing conditions of its life as an NPI.

This raises an important further question about the link between the licensing conditions and the meanings of NPIs. Most theories derive the licensing requirements of any from the combination of its semantics – for example, as a domain-widener (Kadmon & Landman, 1993) or as equivalent to ‘even one’ (Lahiri, 1998; Chierchia, 2013; 2019) – and the semantics of downward-entailing environments (Fauconnier, 1975; Ladusaw, 1979; von Fintel, 1999). A natural interpretation of all accounts of this kind is that speakers should know the licensing requirements of any by virtue of knowing its meaning. A natural extension is that children should learn the licensing requirements of any by virtue of learning its meaning (Tieu & Lidz, 2016).

Our findings suggest an alternative possibility: that children learn what any means by first observing and reproducing its distribution, and then hypothesizing candidate lexical meanings that would be consistent with the meanings of sentences in which any has appeared. In the case of any, some children may (correctly) generalize across the distribution and hypothesize that any is an NPI, while others may (incorrectly) generalize across the same distribution and hypothesize that any is an NCI, and it may be surprisingly late until they encounter data that can arbitrate between these possibilities. If children can only acquire the adult-like meaning of any from hypotheses about its distribution, that would entail that children represent at least part of the distribution and licensing conditions of any prior to – indeed, as a prerequisite to – representing its meaning. Could it be possible to represent all of the licensing requirements of any without representing its meaning?

The answer may turn on an empirical point that future studies may test. Do all children who make the right generalization about the full range of licensors do so only after they have homed in on the adult-like meaning for any (or on whatever component of that meaning actually drives the licensing requirements)? Such a pattern would be expected under an account in which the grammatical distribution and the semantic properties are part of the same system (e.g. Chierchia, 2013). Alternatively, are there some children who master the full range of licensors for any – beyond just negation – prior to mastering its meaning? For example, these children could conceivably continue to posit a negative meaning for any while learning it is licensed in the scope of only, the antecedents of conditionals, and so on. Such a pattern would suggest that children’s acquisition of well-formedness is independent from mastery of the meaning, and specifically that representing the full grammatical distribution of an NPI does not depend on knowing what it means.

It is important to note that even if it turns out that children can learn the full range of licensing requirements of NPI any without knowing its meaning, that would not mean that there is no principled link from the meaning to the distribution. One possibility might be that the distribution is dependent on the semantics diachronically through language change, driven by the semantic knowledge of adult speakers. For example, Herburger (2023) argues for a compatible view, on which the semantic contribution of NPIs to the conditions of NPI-licensing is strictly diachronic. On her account, speakers for whom any is a weak existential use it to convey strong meanings in downward-entailing contexts. The more adult speakers use any in this way to the exclusion of others, the more likely child learners are to infer that any is restricted to these environments. At the same time, the same learners would be free to infer different lexical meanings for any – from a semantically null and redundant negator, to a narrow-scoping existential, to a wide-scoping universal. This may explain why any, along with many other NPIs, appear to lead multiple lives, with systematically different meanings in downward-entailing contexts versus in restricted classes of upward-entailing ones (see also, Kuhn & Maldonado, 2022; 2025).

4.2 Do children assume their language uses negative concord?

That some children misanalyse any as a negative concord negator offers a unique insight into a long-standing puzzle: why it is that, across languages, children tend to interpret double-negated constructions as if they only had one negation, including in languages that use both concord and double negation constructions, and even in languages that do not have negative concord at all (Sano et al. 2009; Thornton et al. 2016; Moscati, 2020; Nicolae & Yatsushiro, 2020; White et al. 2023). One proposal is that processing double negation is too hard for children, either because the operation is too cognitively demanding or too confusing pragmatically (Jou, 1988). Another proposal is that independent of any difficulty understanding double negation, children may be predisposed to analyze a second negator as being in semantic concord with the first (Nicolae & Yatsushiro, 2020).

Our results support the latter possibility, that children tend to assume their language has negative concord by default. The fact that any is not a negator, and yet some children misanalyse it as such, suggests that children’s tendency to interpret two negation words as a single negation does not actually depend on the second word being a negator. If children interpret a polarity sensitive word as an NCI when it is not actually a negator, then that interpretation cannot depend on any difficulty they might have with processing double negation. Consistent with this, we find that children’s tendency to interpret two negation words as one sentential negation actually increases with age, even as the difficulty of a single negator declines. While 3- and 4-year-olds struggle with a single negation, 5- and 6-year-olds interpret single negations just like adults do, but interpret double negation in an even less adult-like way. The processing difficulty of negation appears to dissociate, across development, from the tendency to interpret two negation words as one logical negation, again suggesting that the former is the result of a learning bias that favors an NC grammar and only strengthens with age.

Such a bias may well be functional. After all, children who are learning languages with negative concord need to learn the NCIs they encounter, and to analyze them as NCIs rather than NPIs. Although NPIs and NCIs share licensors beyond negation, there are other environments (e.g. the scope of only) which license NPIs, but not NCIs. This means that the distribution of NCIs – especially in strict-NC languages – is close to a subset of the distribution of NPIs. As with other cases of learning problems that have this structure, a bias to assume the narrower hypothesis may allow learning both hypotheses given the evidence. If all the evidence is consistent with two hypotheses, a learner should pick whichever hypothesis does not predict additional unobserved evidence (a kind of ‘size principle’; e.g. Xu & Tenenbaum, 2007).

Of course, in the case of any, the available evidence is not entirely consistent with both hypotheses. Recall Tieu’s (2013; 2016) finding that in about 20% of its appearances in the input of the children she studied, any was either used as an NPI licensed by something other than a negation (~15%), or had a free choice interpretation. This distribution should prevent children from analyzing any as a strict negative concord item, which would always require a licensing negator (though maybe it does not prevent all children; see the example from Davidson, 2020, in the introduction). On the other hand, distinguishing any from a non-strict NCI may not be possible on syntactic grounds, given this input. It may require further understanding that the speaker does not intend to be negating anything. For example, in a context in which children are being offered cookies, they might need to figure out that, “You can have any cookie you like” is not intended as a prohibition. Or in a context in which they are asked, “Which vegetables do you want?”, they may need to figure out that answering with any will not get the same response as saying none. Maybe it is by trying to use or interpret any in these sorts of cases that children figure out that it is not a negator. A further speculation is that the difference between the majority of children in our study who interpreted any as an existential and that minority who interpreted it as a negator is just whether they have heard (or paid attention to) some sufficient amount of these sorts of cases. This is just what we would expect if children learn the meanings of non-referential, hard words like any by making inferences about their meanings from their distributions, as in syntactic bootstrapping. Indeed, any may be just one example of a much more general phenomenon – the difficulty of pinning down the meaning of an abstract word when its distribution is consistent with multiple candidate meanings. The reason some children may confuse any for an NCI may not be far from the reason many adults think that ambivalent means indifferent, that penultimate means ultimate, and so on.

All this is currently just speculation. As our study did not collect data regarding our participants’ linguistic input, we cannot know what exposure children in our study had to actual negative concord constructions. While negative concord constructions are absent from standard English, it is possible that some of the children in our sample may have been exposed to NCIs in their input from adult English speakers, especially in less formal and highly emphatic contexts (e.g. He doesn’t want nothing to do with you!). Nor can we know what specific distribution of any these children had actually heard, and specifically how much they had heard any in non-negated environments, such as in conditionals, questions, and universals. Studies of how individual differences in the linguistic input that children hear match up with changes in their comprehension may help to uncover how children attain the adult semantics of any and why some children misanalyse the meaning of any through to age 6 while others do not.

Additionally, while we focused on how English-speaking children learn the meaning of any, children in NCI-permitting languages have to learn both NPIs like any and actual NCIs, and keep them separate. Given our results, an open question is whether the presence of actual NCIs in the input helps to learn the meaning of NPIs by providing a contrast, or whether it hinders, by providing another similarly distributed, potentially ambiguous word to learn. A clear direction for future research is to investigate how our findings relate to both strict and non-strict NC languages.

Appendix A – Crayon Task conditions

Side with the box containing the mentioned color: Left (lighter shade) OR Right (darker shade)

Appendix B – Liquid Task conditions