Reflections on Recursion

Recursion is an important aspect of human language, and a core part of the notion of Universal Grammar (UG). Recursion is the ability to string together a potentially infinite regress of embedded sentences, which are functionally limited only by human memory and cognitive processing power. Evans and Levinson (E&L) cite Hauser et al. (2002) who say that recursion is “the only uniquely human component of the faculty of language.”

Recursion is typically defined with reference to constituent structure, wherein a certain type of constituent is embedded within another of the same type (Pinker & Jackendoff 2005), cited by E&L. For example, English may recursively embed prepositional phrases within other prepositional phrases: ‘the horse in the barn’ -> ‘the horse in the barn in the dark’ and so forth. However, more recent research by Levelt (2008), cited by E&L, suggests that because dependency structures, like constituent structures, are generated “by rule,” recursion can occur equally well with dependency structures as well.

Chomsky, using the language of formal mathematics, posited that recursion could only be generated by a phrase-structure grammar (PSG), wherein rules are constructed by individual constituents, each of which can be itself broken down into two other constituents, “as in ‘If A, then B,’ where A itself could be of the form ‘X and Y,’ and ‘X’ of the form ‘W or Z.'” (E&L).

Further study has shown non-human animals (in this case, tamarin monkeys) are capable of grasping at least some level of finite state grammar (FSG), which Chomsky holds would be insufficient to generate the potentially infinite recursion of human language, but those same animals are unable to “grasp the patterning in PSG-generated sequences” (E&L). Some suggest that PSG is the locus of unique human language.

E&L, however, disagree, and show evidence of human languages that allegedly do not possess recursivity at all. They cite data from the complex polysynthetic language Bininj Gun-wok (Evans 2003a, p. 633), showing a lack of embedding at the syntactic level. Instead, the evidence suggests that embedding, if it exists at all in Bininj Gun-wok, takes place at the morphological level. They assert that the maximum embedding permitted is only one level – a far cry from the theoretically limitless embedding postulated by Chomsky and others as a fundamental part of human language. They go on to offer counter-examples from Kayardild, which also seems to permit only a single layer of embedding.

E&L then go further still, with data drawn from Everett (2005) on the Amazonian language Piraha, showing a total absence of embedding at all – even local sign languages apparently show an absence of recursive embedding (Meir et al., in press), cited by E&L. Thus, E&L conclude that these distinct counter-examples suggest that recursive embedding cannot be a fundamental property of inherited grammar, and must instead be a product of other human cognitive processes that may or may not surface in language.

Margoliash and Nusbaum (M&N), in their reply to E&L, assert that linguistics, as a subset of “organismal biology,” must take into account results from evolutionary biology and animal sciences. They suggest that E&L have succeeded on the first count, but failed on the second, and thus M&N offer further perspective on recursion from studies of starlings.

First, M&N relate E&L’s discussion of recursive embedding to Fitch & Hauser’s (2004) study of tamarins, wherein the monkeys failed to distinguish PSG-generated structures (as above). However, they go further, discussing a Gentner et al. (2006) study of starlings, wherein the birds were able to learn not only FSG sequences, as tamarins could, but PSG sequences as well.

M&N suggest that the starlings performed better at “complex vocal processing behaviour” because they are songbirds, and “excellent mimics.” Thus, there is a functional correlation between vocal processing and vocal production behaviours in starlings, which may extend to humans and other animals. M&N critique E&L for failing to address this particular point in detail, instead opting to cite the single counterexample of the tamarins and leave it at that. M&N also point to a study by Marler & Tamura (1964) that showed “rapid changes in learned vocal patterns within non-human species,” which E&L also fail to mention.

Overall, M&N are supportive of E&L’s efforts, and cite evidence that it should be pushed further to include a greater range of experimental data “rooted in … evolutionary biology.” These studies and others will help point the way to the truly inherent mental structures for language, of the human species, and others.

Works Cited:

Evans, N. (2003a) Bininj Gun-wok: A pan-dialectal grammar of Mayali, Kunwinjku and
Kune. 2 vols. 2003a., Pacific Linguistics.

Evans, N. & Levinson, S. (2009) “The myth of language universals:
Language diversity and its importance for cognitive science.” Behavioral and Brain Science, vol. 32, pp. 429-492.
Everett, D. L. (2005) Cultural constraints on grammar and cognition in Piraha˜. Another look at the design features of human language. Current Anthropology 46:621–46.

Fitch, W. T. & Hauser, M. D. (2004) Computational constraints on syntactic processing in a nonhuman primate. Science 303(5656):377–80.

Gentner, T. Q., Fenn, K. M., Margoliash, D. & Nusbaum, H. C. (2006) Recursive syntactic pattern learning by songbirds. Nature 440(7088):1204–1207.

Hauser, M. D., Chomsky, N. & Fitch, W. T. (2002) The faculty of language: What is it, who has it and how did it evolve? Science 298(5598):1569–79.

Levelt, W. J. M. (2008) Formal grammars in linguistics and psycholinguistics, vol.1-3. Benjamins.

Margoliash, D., Nusbaum, H. (2009) Animal comparative studies shouldbe part of linguistics. Behavioral and Brain Science. pp. 458-459.

Marler, P. & Tamura, M. (1964) Culturally transmitted patterns of vocal behavior in sparrows. Science 146 (3650):1483–86.

Meir, I., Sandler, W., Padden, C. & Aronoff, M. (in press) Emerging sign languages. In: Oxford handbook of deaf studies, language, and education, vol. 2, ed. M. Marschark & P. Spencer. Oxford University Press.

Pinker, S. & Jackendoff, R. (2005) The faculty of language: What’s special about it? Cognition 95:201–36.