Language as a mechanism for reasoning about possibilities

(a) Theories of language acquisition and the interaction of language and thought

On classic theories of language acquisition, the process of learning one's native language consists of mapping incoming speech onto pre-existing, universal conceptual categories [15–18]. Such theories make specific assumptions about how mental representations interact with language. Specifically, it is assumed that the mental representation of a concept precedes the emergence of the corresponding linguistic term in child language and, thus, linguistic achievements rely on cognitive achievements, which are assumed to develop in a universally fixed order. The cross-linguistically stable order children learn spatial locatives, which reflects the order they develop the corresponding spatial concepts, is a case in point [19–21].

Although the classic view is widely acknowledged, other accounts suggest that, for specific phenomena, the relation between language and cognition might be reversed to some extent, and language itself might be providing input to cognition [22–27]. On such views, language acts as an ‘augmenter’ to cognition, whereby linguistic representations combine with nonlinguistic representations to enable performance in tasks that could not be performed with one representation alone [26,28]. Examples of such phenomena include acquiring mental state verb syntax and developing the ability to reason about other people's beliefs [22,29], learning the counting sequence and developing exact representation of large numbers [24,30,31], and using relational language to facilitate relational reasoning [25]. The common denominator in all these phenomena is that they concern highly abstract concepts that are hard to learn from observation alone, while the corresponding linguistic constructions contain clear cues (e.g. special syntactic and semantic properties) that could provide the scaffolding for developing mature conceptual representations.

In this paper, we explore the idea that language might be playing a similar role in the case of possibility reasoning. The domain of possibility is an excellent candidate for studying interactions of language and thought, as possibilities are by definition non-actual (e.g. they may never be materialized) and, thus, not directly observable in the physical world. Instead, a domain of human experience where possibilities can be observed is language, as numerous linguistic expressions exist to mark propositions as possible or necessary [32]. Examples of such expressions include lexical categories such as adverbs (e.g. Maybe/possibly/probably, Paul is guilty), nouns (e.g. There is a strong possibility that Paul is guilty) and adjectives (e.g. It is necessary that Paul is guilty), functional categories such as modal verbs (e.g. Paul must/should/might/may/could be guilty), or grammatical constructions such as conditionals (e.g. If these are Paul's fingerprints, then Paul is guilty). Although it is often assumed that language might be a critical mechanism for possibility reasoning, we currently lack a detailed account of how linguistic (i.e. semantic) representations and non-linguistic (i.e. conceptual) representations of possibility interact during development. Our goal is to integrate research from both conceptual and linguistic domains to begin shedding light onto such processes.

(b) Empirical focus

Our discussion centres around a specific type of possibility reasoning: reasoning about disjunctive beliefs. Representing disjunctive beliefs requires the representation of two states of affairs as possibly true or possibly false [5,33]. Evidence that young children can reason about disjunctive beliefs has been explored through tasks that target a simple logical inference, the disjunctive syllogism: if presented with two possibilities (A or B), and one of them is subsequently excluded (not A), one deduces that the alternative possibility necessarily has to hold (therefore B).

This reasoning process was chosen because: (a) in recent years, disjunctive syllogism has been studied extensively with various populations, and (b) it presents clear correlates between conceptual and linguistic representations. At a conceptual level, the syllogism requires the representation of the logical relations of disjunction and negation: the two possibilities need to be represented as dependent on each other, linked by the relation of disjunction (A or B), while the elimination of one of these possibilities should lead to the representation of a negative premise (not A). At the same time, the syllogism requires the representation of the modal concepts of possibility and necessity: the two states of affairs need to be considered simultaneously and be represented as merely possible (could be in A or could be in B), while, once one of these states of affairs is ruled out, the alternative becomes necessarily true (it is not in A, therefore it must be in B). At a linguistic level, these concepts may be encoded in logical connectives and particles such as or and not, epistemic adverbs such as possibly, necessarily or epistemic modal verbs such as can/could/may and must/should/have to. These correspondences facilitate the comparative investigation of linguistic and non-linguistic developmental trajectories.

The paper is organized as follows. In §2 and §3, we summarize evidence on how children reason by the disjunctive syllogism and how they acquire the corresponding logical and modal language. In the final section (§4) we sketch a proposal for the interaction of language and thought in the domain of possibility.

(a) Negation

Investigations of children's naturalistic speech across languages have revealed that negation terms are among the earliest terms children produce, emerging, on average, at around 15 months of age [44–47]. However, children's early negation words do not express denial (i.e. logical negation), but rather conceptually simpler functions of negation such as rejection and non-existence [44–46]. Denial negation was found to emerge in children's speech several months later, during their third year of life [44–47].

Comprehension studies with English-speaking children have qualified this timeline by providing more detailed evidence for when children understand denial negation [42,47,48]. In these studies, using variations of the reasoning by elimination paradigm, 2-year-olds searched for a reward between two locations (A or B), after hearing a negative sentence (e.g. The toy is not in A). Only after 27 months of age did children understand the negative sentence (as indicated by successful searches in the unmentioned location); 20- and 24-month-olds did not. Importantly, this timeline was replicated even when children were asked to infer the location of the reward in more complex reasoning tasks. As already discussed, success in 2-location paradigms is compatible with the possibility that children do not engage in deductive reasoning but are simply eliminating options [14]. On such interpretations, it is unclear whether children who showed successful understanding of negation in 2-location paradigms interpreted the negative sentence (e.g. The toy is not in A) as conveying denial (logical) negation (i.e. not A) or as conveying a less abstract concept of negation, such as non-existence (i.e. A is empty). However, it was shown that 27-month-old children were also successful in search tasks that involved reasoning over three and four locations and required children to combine verbal and visual information to reach a logical conclusion [42]. This flexibility in using negative sentences in logical reasoning suggests that by 27 months of age children interpret negation words as having a truth-functional (logical) meaning. Given that this is roughly the age at which children begin to succeed in non-linguistic reasoning by disjunction (which requires the application of a logical concept of negation) [14], the converging evidence from search tasks shows that, in terms of negation, the development of the logical (truth-functional) concept and the acquisition of the corresponding linguistic terms go hand in hand.

Interestingly, recent findings from more diverse experimental paradigms and speakers of languages other than English suggest that children may comprehend negative sentences at an even younger age. For instance, in a recent study using a word-learning eye-tracking paradigm, French-speaking children showed evidence of comprehending negative sentences at 18 months of age [49]. Although this earlier success is most likely due to the lower cognitive demands of the word-learning task (which did not involve logical reasoning but simply matching a sentence with the appropriate referent) rather than the different linguistic background of the children, it is possible that semantic differences in negation constructions across languages may affect acquisition trajectories (e.g. see [50] for evidence that 18-month-old (but not 15-month-old) Hungarian-speaking infants comprehend sentences with both denial and non-existence negation markers in 2-location search tasks). Even though it is not clear whether such paradigms provide definite proof that children possess an understanding of denial negation this early or of a simpler concept, they are in accordance with findings from the non-linguistic domain showing that children can succeed in non-linguistic 2-location search tasks as early as 17 months of age (but not earlier) [51], thus reinforcing our conclusion that, in terms of negation, linguistic and non-linguistic representations develop at a similar pace. Currently, more systematic cross-linguistic investigation with children younger than age 2 and with a variety of paradigms (not just search tasks) is needed to clarify the exact age different types of linguistic and non-linguistic negation become available to human language and thought.

(b) Disjunction

Disjunction in natural language is often expressed as a connective (such as the English or), which coordinates two syntactic units of the same type. Disjunction can receive multiple interpretations. For example, the sentence The woman ordered sushi or pizza, can have an inclusive interpretation (i.e. the woman ordered only sushi, only pizza or both) or an exclusive interpretation (i.e. the woman ordered only sushi or only pizza but not both). On standard linguistic accounts, the semantic meaning of or is inclusive, and the exclusive interpretation is derived through pragmatic inference [52,53]. For example, if a speaker uses the sentence mentioned above, the speaker typically implies that the woman ordered only sushi or only pizza, because if she had ordered both, then it would be more felicitous to use the stronger connective and (i.e. The woman ordered sushi and pizza).

The acquisition of disjunction presents a particularly complex puzzle. Studies on children's spontaneous speech demonstrate that or emerges in child language at around age 3 [54–57]. However, from production data alone, it is not always clear what meaning of disjunction children have in mind. Some corpus studies have shown that exclusive interpretations are more frequent in both the input that children receive and their own production, thus suggesting that children may have access to the exclusive interpretation very early on [57,58]. Nevertheless, comprehension studies demonstrate that children have persistent difficulties with exclusive interpretation during preschool years [59–64]. For instance, numerous studies demonstrate that although adults reject statements involving disjunction in contexts where the stronger alternative and is true (e.g. Every boy chose a skateboard or a bike, when the boy chose both objects), thus showing an appreciation of the exclusive interpretation of disjunction, 3- to 6-year-old children tend to accept them [62–64]. These findings are taken to suggest that children are more ‘logical’ than adults, as they have an appreciation of the inclusive semantics of the logical operator of disjunction, but they have issues with the exclusive inference of disjunction, owing to pragmatic difficulties [65].

In sum, children's acquisition patterns indicate that, although disjunction emerges early in children's speech (at around age 3), mature understanding of disjunction undergoes significant development for years later. Children's persistent problems with the exclusive interpretation of disjunction are in accordance with findings from children's reasoning by the disjunctive syllogism, showing that children—although not at ceiling—pass the task at around age 3 in trials where one location is shown to be empty (not A, therefore B) [14,42] but fail until age 5 in trials where one location is shown to contain a reward and the alternative location also has to be excluded (A, therefore not B) [43]. Although, in principle, in the disjunctive syllogism, the relation ‘or’ in the premise ‘A or B’ can be inclusive (at least one of A and B is true) or exclusive (exactly one of A and B is true), search tasks require exclusive disjunction, as only one location contains the reward. When children see that one location is empty (not A), the conclusion that the reward is in the alternative location within the pair (therefore B) is predicted by both an inclusive and an exclusive interpretation of the ‘or’ relation. However, when children see that one location contains the reward, the conclusion that the alternative location within the pair needs to be excluded (A, therefore not B) is consistent only with an exclusive interpretation of disjunction (figure 2).

(c) Epistemic modals

Epistemic modals express what is possible or necessary given the available evidence [32,66,67]. For example, the sentence The keys could be on the kitchen table is used when the available evidence suggests that it is possible that the keys are on the kitchen table, while the sentence The keys have to be on the kitchen table is used when there is evidence from which it necessarily follows that the keys are on the kitchen table.

Research on the acquisition of modal verbs in English has demonstrated that children spontaneously produce modal verbs at around age 2, but these early uses express root (i.e. non-epistemic) meanings such as ability or obligation, while epistemic uses of modals arise at around age 3 [68–72]. Different explanations could account for the later emergence of the epistemic meaning of modals. On a conceptual explanation, the later emergence of epistemic modals is due to the complexity and metarepresentational nature of the underlying concepts of possibility and necessity, as well as young children's more general difficulty to reason about the contents of other people's minds [69,71,73]. If so, children cannot map modal terms to epistemic meanings, because the related concepts are not yet available to them.

On a grammatical explanation, at least part of children's difficulty with epistemic modals is the fact that they require more elaborate grammatical structure than root modals [72]. If so, the concepts of possibility and necessity may already be in place, but children cannot yet use them because they lack grammatical capacity. This view is supported by the fact that epistemic adverbs such as maybe and probably, which express epistemic meanings but are semantically and syntactically less complex than modal verbs, emerge in children's speech in adult-like contexts at around age 2, a year earlier than epistemic modals [74–77]. Although such data suggest that some preliminary understanding of possibility might be available to children early on, naturalistic production data do not provide sufficient information about the concepts that children possess.

By contrast, comprehension studies support the conceptual explanation as they demonstrate that before age 7 children have non-adult comprehension of epistemic modals [65,77–81]. An important step in acquiring the meaning of epistemic modals has to do with understanding when possibility and necessity modals are true. In fact, while necessity modals (e.g. must/have to) are true only in necessity contexts (i.e. when an outcome is not just possible but necessary given the evidence), possibility modals (e.g. can, could, may) are true in both possibility and necessity contexts (i.e. when an outcome is possible or necessary given the evidence). Experimental findings show that children often over-accept necessity modals in possibility contexts [65,78,79,82]. In one demonstration [79], 4- to 5-year-old children were presented with scenarios where animals were hidden in different-coloured boxes and heard statements with necessity or possibility modals (e.g. X has to/may be in the blue box). Children were asked if they agreed with the statements or not. Children successfully accepted possibility modals as true in contexts where the location of the animal was uncertain (i.e. when they were presented with two closed boxes), and both possibility and necessity modals in contexts where the location was certain (e.g. when one of two boxes was shown to be empty), in accordance with modal verb semantics. However, children also over-accepted necessity modals in the uncertain context, where the stated location of the animal was simply possible but not necessary. Children seem to have a robust understanding of this semantic distinction at around age 7 [82,83].

These persistent difficulties with processing epistemic modals have been attributed to a broader, conceptual difficulty with maintaining two open possibilities, which children overcome by committing to one outcome, even when there is insufficient evidence to make such a commitment [70,78,79]. Children's protracted difficulties with the meaning of epistemic modals are reminiscent of children's difficulties distinguishing certainty from uncertainty in the search tasks reviewed earlier [14,42,44], and are in accordance with various other developmental findings where children are shown to commit to one outcome when multiple outcomes are possible [6,83,84].

(a) Can language contribute to conceptual change?

Two main aspects of the available evidence are compatible with the view that language might be a contributing factor in the development of logical and possibility concepts. The first concerns irregular acquisition patterns, where the production of a term in adult-like contexts seems to precede mature understanding of the term. Typically, when acquiring language, children comprehend how a word maps onto a concept before they can use this word in speech production. However, a prevalent pattern in the linguistic data we reviewed was that, across phenomena, children produced the different linguistic terms much earlier than the age they understood these terms in comprehension tasks. The acquisition of modal verbs presents a characteristic pattern, with children producing modal verbs with epistemic meanings at around 3 years of age (and epistemic adverbs even earlier) but their semantic understanding of necessity and possibility meanings is non-adult-like until age 7. Such irregular acquisition patterns are puzzling, because, to use a term in speech appropriately, one must understand something about the meaning of the term. Although multiple accounts have been proposed to explain such irregular acquisition patterns [85], it has been suggested that such patterns might be indications of language acquisition contributing to conceptual change [23]. On such accounts, if a specific conceptual distinction is refined by learning the corresponding linguistic (semantic) distinction, then we would expect to see it manifest in children's own language first, while comprehension of the term in someone else's speech would await the full development of the corresponding concept [23]. Under this suggestion, the early emergence of a term in child language and its use in appropriate contexts does not presuppose that the concept is already in place; instead, children who produce a certain term in an adult-like manner may not yet have a fully developed concept but operate on the basis of an immature concept. This view is compatible with classic acquisition theories proposing that children's understanding of linguistic terms may undergo significant conceptual/semantic reorganization [86,87], as well as recent theoretical models of children's possibility reasoning distinguishing early, ‘minimal’ concepts of possibility from mature, ‘modal’ concepts of possibility [5]. On such views, irregular acquisition patterns, as in the case of modals, could be explained by suggesting that the early emergence of modal terms in children's speech might be reflecting a ‘minimal’ understanding of possibility, while the adult-like comprehension of modal verbs might await the development of ‘modal’ concepts of possibility [75].

A second aspect of the reviewed evidence suggesting that language could contribute to conceptual change has to do with the fact that, across languages, logical and modal terms tend to be polysemous and children seem to learn ‘easier’ (i.e. non-logical, non-epistemic) meanings first. Given that logical and possibility concepts are hard to learn from observation alone, polysemy might be providing the workspace for developing such concepts, through extension of the ‘easy’ meanings (as some sort of ‘conceptual bootstrapping’ [88]). Negation is a case in point, as words such as no and not have multiple meanings, each of which seems to be acquired at different time points. As we saw earlier, children first acquire the meanings of rejection and non-existence, which can plausibly be acquired by observation alone (e.g. by seeing others rejecting things or finding a container to be empty). Once these meanings have been mapped onto negation words, children may notice that the same words are also used when the speaker wants to express denial, and that the mere function of this word is to flip the truth value of a proposition. This observation—which is linguistic in nature—could potentially be contributing to the representation of logical (truth-functional) negation in children's mind.

Similarly, epistemic meanings of modal verbs might be developing from the ‘easier’, root meanings, which are acquired earlier. In fact, ambiguity between root and epistemic meanings in a single class of modals is a widespread cross-linguistic phenomenon [68,89,90]. Some semantic theories argue that epistemic meanings of modals are related to root meanings through metaphorical extension [91,92]. For example, the root meaning of may (e.g. You may go now) expresses the existence of a potential but absent barrier in the ‘physical world’, while its epistemic meaning (e.g. He may be at work) expresses a barrier of reasoning in the speaker's ‘mental world’ [92]. On such views, children may be able to learn root meanings of modals though observation, and then they can extend these meanings to the more abstract, epistemic domain, through metaphorical mapping. Thus, polysemy of logical and modal terms may provide a critical workspace for learning the ‘harder’, more abstract meanings. This view is in accordance with recent accounts of word learning, demonstrating that polysemy, rather than a barrier, is highly beneficial for language acquisition [93,94], and that knowledge of the ‘easy’ meaning of a word (i.e. referring to concrete entities/properties/actions) can pave the way for learning its ‘harder’, more abstract meaning [95].

(b) Does language facilitate logical reasoning?

To our knowledge, one study provides evidence for language effects on thought in logical reasoning during development. In this study by Grigoroglou et al. [42], children performed a linguistic version of the Mody & Carey [14] 4-cups paradigm, in which instead of seeing that one cup was empty, 2.5- and 3-year-old children heard a negative statement (e.g. There is no coin in the red cup) and were asked to reason about the location of the reward (figure 1). Findings showed that, in this linguistic version of the task, 2.5-year-olds, who were shown to fail in the non-linguistic version, passed the task. This finding indicates that verbal negation somehow facilitated children's logical reasoning. However, the linguistic 4-cups paradigm by Grigoroglou et al. involved more than one modification of the non-linguistic Mody & Carey paradigm, making it difficult to isolate the exact manipulation that led to improved performance in 2.5-year-olds. Specifically, in Grigoroglou et al., before the test trials, children received two additional training trials, which were a linguistic version of the 2-cups task, where children had to reason about the location of the coin between two cups after hearing a negative sentence. It is possible that 2.5-year-olds' success was due to the additional training in reasoning by exclusion rather than to language.

On-going research directly tests this possibility [96]. In this study, 2.5-, 3- and 4-year-old children perform the non-linguistic version of the 4-cups task, similarly to Mody & Carey [14], but are also provided with additional training trials in the 2-cup paradigm, similarly to Grigoroglou et al. [42]. Crucially, in this additional training, children are provided with either a verbal cue (i.e. a negative statement) or a visual cue (i.e. seeing that one cup is empty) indicating emptiness. Results thus far show that only 2.5-year-olds who received the linguistic training passed the disjunctive syllogism task [96]. Although further experimentation is needed to clarify the exact mechanism that drives improved performance, two explanations are possible. On one explanation, the improvement in 2.5-year-olds is due to the modality of the evidence from which children construct the logical representation. Children consider verbal evidence as more reliable than visual evidence [97,98]; therefore, the verbal clue might have increased children's certainty about the premise ‘not A’ and subsequently the conclusion (therefore B) [42]. Alternatively, hearing logical language could be inviting children to encode logic-like representations in a more detailed way than visual information does, by activating the relevant semantic structure (similarly to findings about how the presence of relational language (e.g. spatial prepositions) facilitates relational reasoning [25]; see also [99] for similar evidence with causal language and causal reasoning). On this view, receiving the negative proposition verbally gave children more direct access to the relevant premise 'not A’ compared with when the same premise had to be constructed from visual evidence of 'emptiness’, thus providing them with a 'head start’ in the inferential process. This view predicts that, given a more complex reasoning task, not just 2.5-year-olds but also older children could benefit from hearing logical language. Furthermore, if the effect of language on logical reasoning is induced by activating the relevant semantic structure that supports logical representations, we would expect to see differences in logical reasoning based on the type of linguistic cue provided to children. Future work could test these predictions.