Linguistic representation of Number
Given the pivotal role that numbers play in our lives, understanding how children acquire numerical concepts and how they learn to express these concepts through the medium of language represents an important goal for Cognitive Science. Our work work in this domain brings together two independent lines of research on numerically quantified expressions (NQE) (e.g. two balloons, three dogs).The first stems from work in Linguistics and proposes to account for the meaning and formal properties of such expressions. The second comes from the study of language development and asks when and how children acquire the number vocabulary. Until recently, these approaches, represented by work in theoretical Linguistics and developmental Psychology, have had little influence on each other.
For example, developmental psychologists have traditionally assumed that NQE have an ‘exact’ meaning. In other words, the idea is that a phrase like two apples means exactly two apples, which seems to make a lot of intuitive sense. However, for many years, the standard analysis in Linguistics held that a phrase like two apples literally means at least two apples (i.e., two apples or more) (e.g., Horn, 1972). This discrepancy and its implications were initially investigated by Papafragou and Musolino (2003) and Musolino (2004). Since then, a number of additional studies designed to experimentally probe the meaning of NQE have emerged with implications for both theory and acquisition (e.g., Hurewitz et al., 2006; Huang, Snedeker, and Spelke, submitted; Barner and Bachrach, 2010).
Another illustration of the disconnect described above is that developmental psychologists have focused almost exclusively on how children learn the principles underlying counting. However, mastering the properties of NQE extends far beyond learning how to count. For example, children have to figure, among many other things, that sentences involving two interacting NQE, like Three boys are holding two balloons, can have at least 4 possible readings! Take a look at Musolino (2009) who has investigated this phenomenon experimentally and discussed its implications for language acquisition.
Language in individuals with Williams Syndrome
Over the past 20 years, Williams Syndrome (WS) has received considerable attention from scholars interested in the structure and development of the human mind. The main reason is that this rare genetic disorder represents a natural experiment which suggests a potential dissociation between language and other aspects of cognition. Indeed, WS is often described as being characterized by relatively spared linguistic abilities in the face of serious deficits in other cognitive domains such as space and number. WS has thus been cited as evidence supporting the kind of modular view of mental architecture advocated most famously by Jerry Fodor and Noam Chomsky (Anderson, 1998; Bikerton, 1997; Piatelli-Palmarini, 2001; Pinker 1994).
However, these conclusions remain highly controversial, as does the status of linguistic abilities in this disordered population. In order to shed some light on these issues, Barbara Landau and I have begun to systematically investigate knowledge of complex syntactic and semantic structures in this disordered population Musolino, Chunyo and Landau, 2010; Musolino, Chunyo, and Landau in preparation). In one of our studies, we investigated knowledge of core syntactic and semantic principles in individuals with WS focusing on the logico-syntactic properties of expressions such as negation and disjunction (i.e., or)(Musolino, Chunyo, and Landau, 2010. See also, Musolino and Landau, 2010, for a response to a commentary on our study).
Here, we tested knowledge of syntactic relations such as scope and c-command, semantic relations such as entailment relations and DeMorgan’s laws of propositional logic, and the relationship between these two set of principles. These principles are at play in sentences like (2) and (3) below. When or occurs in the scope (i.e. c-command domain) of negation, as in (2), the interpretation of these two elements is governed by one of DeMorgan’s laws of propositional logic (i.e., not (p or q) = (not p) and (not q)) and the sentence receives a conjunctive (i.e., ‘neither’) interpretation. When or does not occur in the scope of negation, as in (3), we get a disjunctive interpretation (i.e., ‘either and possibly both’).
(2) The clown who is holding a flower will not be given a jewel or a coin (conjunctive)
(3) The monkey who is not asleep will get bananas or a ball (disjunctive).
What we found that in spite of mental retardation and an altered genetic potential, individuals with WS interpret sentences like (2) and (3) in a way that demonstrates that knowledge of the abstract linguistic principles described above is present and engaged in this population, just as it is in typically developing and mature individuals. These results have implication for competing accounts of language development in WS, as well as for the relevance of WS to the study of cognitive architecture and development.