Logical nativists contend that human languages and their learners exhibit deep-seated regularities. Many of these regularities, or core linguistic principles, pertain to logical expressions, including both the basic meanings of logical expressions and the interpretations given to combinations of these expressions. Because core linguistic principles are candidates for innate specification, they are expected to meet the diagnostics of innateness. These diagnostics can, in turn, be used to distinguish the logical nativist approach from the experience-based approach. Let us briefly review these features.

First, linguistic phenomena governed by core linguistic principles are expected to be universal. Second, core linguistic principles are expected to range over several phenomena, including ones that may appear on the surface to be unrelated. If abstract principles pertain to clusters of facts that appear to be unrelated on the surface, then these principles provide a unique testing ground to distinguish the logical nativist approach from the experience-based approach, such as the constructivist model discussed in Chapter 2. Because the experience-based approach postulates shallow linguistic representations, it follows that the experience-based approach and logical nativism make radically different empirical predictions about the nature of language, and about the language acquisition process. For one thing, core linguistic principles are expected to be evident in children’s language as soon as they can be tested, even where children lack decisive evidence for them in the primary linguistic data.

English and Mandarin Chinese are typologically distinct languages, yet they share several core linguistic properties. These core properties govern the assignment of interpretations to logical expressions, individually and in combination. For example, both English and Mandarin have downward-entailing expressions. Downward-entailing expressions are important in teasing apart the alternative accounts of language acquisition, because such expressions tie together clusters of linguistic properties, including fixing the interpretation of disjunction. Both English and Mandarin possess logical expressions that are similar in meaning to the corresponding expressions in logic, including the inclusive-or interpretation of disjunction, to cite just one example. The inclusive-or interpretation of disjunction serves as the basic meaning of disjunction in classical logic and forms the basis for the logical entailments in de Morgan’s laws. The previous chapter reviewed several experimental investigations of children’s knowledge of the syntactic and semantic constraints on the interpretation of disjunction words (English or and Mandarin huozhe). The findings from these investigations demonstrated that, in responding to sentences with disjunction, children acquiring English and Mandarin (and Japanese) initially assigned interpretations that coincide with the laws of logic.

If downward entailment is an innate property of human languages, then we would expect downward-entailing expressions to also manifest another of its characteristic properties, both within and across languages, namely the licensing of negative polarity expressions such as any, ever, and at all, and their counterparts in other languages. Although the licensing of negative polarity items and the conjunctive entailment of disjunction appear to be unrelated, we observed in Chapter 1 that these linguistic phenomena are really variations on a theme, which explains why they are both associated with the class of downward-entailing expressions. The prediction that these expressions form a natural class in human languages has been confirmed, both within and across languages. In the present chapter, we report the findings of experimental investigations of children’s competence in producing and understanding polarity-sensitive items. As noted, polarity-sensitive items can be partitioned into negative polarity items, such as English any, and positive polarity items, such as English some. We review what we have found out from experimental investigations of the acquisition of both kinds of polarity-sensitive items. We begin with a brief discussion of their linguistic behavior in adult languages.

Child language acquisition proceeds without the benefit of the vast array of data available to linguists. In developing linguistic analyses, linguists consider many kinds of evidence that are not available to children, including cross- linguistic data, as well as both positive and negative evidence (i.e., the kinds of sentences that are ungrammatical in a particular language). These data permit linguists to disconfirm hypotheses, and formulate better ones. Despite the lack of cross-linguistic data and negative evidence in children’s experience, by the time they have reached their fourth birthday, every normal child has mastered many, perhaps most, of the linguistic and logical principles that have been uncovered by linguists and logicians over the past few decades of research.

The principles children master in the first few years of life include non-trivial generalizations. For example, we have seen that downward-entailing operators tie together clusters of apparently unrelated linguistic phenomena in particular languages, like English, and we have seen that the same phenomena are governed by downward- entailing operators in other languages around the globe. We have also seen that, although these phenomena appear unrelated at first glance, it turns out that, upon closer scrutiny, these phenomena are related at a deeper level of analysis. In the absence of an alternative account of these regularities – i.e., lacking a learning-theoretic account of how young children come to know these phenomena – it seems reasonable to conclude that humans are innately endowed with the universal principles and parameters of grammar, and that children only acquire languages that conform to these principles and parameters. Furthermore, many of these principles and parameters involve logical expressions and their interactions. So it is reasonable to suppose that logical principles and parameters (e.g., scope parameters) are part of the innate genetic endowment of the species.