Questioning Recursion as a Distinctive Feature of Human Language

Introduction

How can we define language? What difference is there between a string of random sounds and a meaningful combination of signs, communicating information between two beings? A first approximation toward a definition of language could be by postulating that language is a way of representing the world in terms of material entities, such as sounds. We might call these entities signs with meaning. While this is a definition of language broadly speaking, we might want to add that such signs can also be systematically combined with each other, resulting in more complex expressions. By adding this aspect, we arrive at a narrower definition that language is a system of signs with combinatory rules.

According to Noam Chomsky, this narrow definition is the basis for what makes human language unique. In more detail, Chomsky argues with Marc Hauser and W. Tecumseh Fitch (2002, abbreviated henceforth as HCF) that humans cannot only combine expressions, but they can do so endlessly by embedding phrases within other phrases. They call this aspect ‘recursion’. According to HCF, this is the distinctive feature that distinguishes human language from communicative systems of animals.

The goal of this essay is to discuss HCF’s claim that recursion is the distinctive property of human language. I begin with outlining recursion and explain in what sense recursion appears to be unique to human language. In the second part of this essay, I present ornithological findings. I introduce how starlings demonstrate recursive understanding by recognizing different grammar types. Finally, I propose the hypothesis that the difference between human language and communicative systems used by animals, such as birds, is rather a matter of quantity than quality.

An Overview of Recursion

Recursive structures are omnipresent in our lives: be it in terms of counting, be it in terms of speaking. Roughly put, recursion can be understood as a function calling upon itself repeatedly. As a first attempt, we might formalize this idea as follows: \(R → R\). But what is more important, this function can even be repeated when additional information is being added. Consider: \(R → R+a\). Such a function provides us with one explanation of how we count. For instance, the rules \(S → 0C\), \(C → C+1\), \(C → ε\) will lead to any natural number, depending on how many times \(C\) is being repeated, until the loop is being terminated with \(ε\). In a similar vein, natural language appears to make extensive use of recursion. This aspect of language is also prominently evident in children’s memory games, such as the ‘My mother went to market’ game where each player must add an item of free choice to the initial phrase, including everything that has previously been said by other players. More complex examples of recursion in language include sentences within sentences. Technically, we can endlessly embed sentences, consisting of subclauses that have additional subclauses and so on. Recursion is one fundamental aspect of how we count or speak, and it is, consequently, part of every other activity or technology that is based on counting and speaking.

According to Michael Corballis (2007), it is important to note that recursion is not mere repetition. He believes that recursion, as the principle is evident in how we speak, allows us to freely choose how things might be combined and embedded within each other. That is, recursive rules do not only allow us to repeatedly add another instance. We also can easily jump to higher numbers, skip intermediate additions, multiply terms. The children’s game that has previously been mentioned might not be the best example illustrating recursion because recursion allows us to add whole sentences, several words, or no element at all.

While this first sketch of recursion explains a central feature of counting and speaking, it is worthy to keep in mind that human beings only use recursion in a limited sense. By observing our day-to-day activities, we see that we will stop counting at some point. Considering language, each layer that is being added to a sentence through recursion makes it harder to follow what has previously been said. This is so because we have cognitive limits. In other words, we can “overstretch [our] working memory”, says Corballis (2007, p. 244).

Recursion as a Distinctive Feature of Human Language

After comparative research in animal communication, HCF (2002) believe that recursion is the distinctive property of human natural language. While different animal species can communicate with each other in a myriad of ways, through alarm calls, by mobbing predators, by asking for help, or by sharing information about valuable food sources, HCF argue that they “lack the rich expressive and open-ended power of human language” (2002, p. 1570). HCF even grant that animals have conceptual representations of the world. However, these concepts appear closely linked to specific functions. Human concepts, on the other hand, are enmeshed in a broader system, without any “straightforward word-thing relationship”, and “can be linked to virtually any [other] concept that humans [] entertain” (Hauser et al., 2002, p. 1576). This difference brings HCF to the conclusion that we “must entertain the possibility of an independently evolved mechanism” (2002, p. 1576). The mechanism that explains the richness and open-ended structure of human natural language lies for the authors in recursion.

With respect to the discussion of recursion in human versus animal language, avian communication is often discussed in more detail (Corballis, 2007; Hauser et al., 2002). For it appears that birds have something like recursion because of their variety of sounds. However, it is argued that birds only have a finite state grammar, that is, a set of limited rules that underlies their communication. The idea of a finite state grammar (also known as regular grammar) consists in restricted combinations of the sort that each rule is determined by the fixed pattern: \(R → aB\) and / or \(R → a\). However, context free or context sensible grammars, which are each more complex respectively, allow either for variations on the right side or variations on both sides of the rule. For this reason, context free grammars can generate expressions of the type \(R → A^n B^n\). It is assumed that this truly allows for the richness of arbitrary combinations that characterizes human language. For the structure of such a grammar can account for center-embedded phrases, such as: ‘I am looking research I need for the essay I must hand in up.’ These constructions would not be possible with a finite state grammar that is confined to a fixed production of binary patterns (see for a visualization of the difference Figure 1).

Fig. 1: While the finite state grammar would only allow for a fixed pattern of binary addition, the context free grammar allows for center-embedding. This is an adoption of Gentner’s et al.’s figure (2006, p. 1204).

Ornithological Findings Concerning Recursion and Finite State Grammars

There are at least two ways of how one can question the argument that the most developed animals only master a finite state grammar, whereas human beings are capable of processing more complex grammar structures. The first strategy would be to prove that animals can master a context free grammar, too. The second one could probe the power of finite state grammars, which may also account for some degree of recursion.

As to the first strategy, Timothy Gentner and his colleagues (2006) created an experiment with the aim to train starlings recognizing different sound motifs, rattles and warbles, that they had recorded and replayed in front of the birds. The motifs were patterned to resemble either a finite state grammar, creating a string of binary sounds, or a context free grammar with center-embedding. The result from simple tests has been that the starlings could learn to recognize and to differently respond to the different sounds sequences, representing each grammar type. To corroborate their results, they further enlarged the sequences by \(n=3\) and \(n=4\) for their finite \((AB)^n\) and context free \(A^nB^n\) sound structures. Again, the birds were capable of producing different reactions to each of the structures. Gentner and his colleagues also assured that the starlings had no similar reactions to arbitrary patterns. While they leave open the possibility that the birds might have used other cognitive heuristics, such as approximating context free patterns through finite state rules, Gentner and his colleagues conclude from their experiment that “starlings can recognize syntactically well-formed strings, including those that use a recursive centre-embedding rule” (2007, p. 1206).

The caveat to Gentner’s findings points at the second strategy of questioning the limitations of animal communication. At the outset, we should note that recursion appears in finite state grammars because these grammars can reiteratively produce an infinite string of symbols. This has already been recognized by Chomsky (1956; Chomsky & Miller, 1958) in his early papers on finite languages. So the point is not that human natural language is defined by reiterative rules, but by some context free or higher grammar, allowing for greater varieties of recursion. But what if center-embedding could be achieved with the means of a finite state grammar, too? This still is an ongoing research question where syntacticians (Roche & Schabes, 1997; Dacjuk & van Noord, 2002) attempt to represent a more complex grammar through the means of a stricter one. A detailed discussion of this topic would go beyond this essay. However, it is worthy to keep such a possibility in mind when discussing the properties of language(s).

Final Discussion

To conclude, recursion as a reiterative rule cannot be the distinctive property characterizing human natural language because it is possible to loop through finite state grammar rules that have been attributed to animals. Although Chomsky, Hauser, and Fitch (2002) as well as Corballis (2007) speak of ‘recursion’ when singling human language out, it has been evident from the discussion that they have something slightly different in mind that goes beyond the minimal definition of recursion as a self-applicative rule. For them, recursion implies the possibility of grammatically complex structures, allowing center-embedding. For this reason, the essay has additionally discussed the possibility of context free grammars in avian communication by presenting research on starlings. Here, Gentner et al. (2006) offer empirical evidence that starlings can master complex recursive patterns, as in \(R → A^n B^n\) combinations. Therefore, it appears that recursion, neither in its simplest form, nor in its more complex applications, is the distinctive property of human language.

While Gentner et al. (2006) believe that humans are not the only ones having recursion, they also acknowledge that there is a difference between communicative systems of birds and human natural language. Obviously, the number of words and syntactical structures over which birds have command, and which they can process, is more restricted than those of humans. We can assume that the most advanced birds use about 100-200 signals (Ballentine & Hyman, 2021) and might have some basic ordering rules, of which some are even recursive. Therefore, it is fair to say that the difference between species is “quantitative rather than qualitative”, especially with respect to “distinctions in cognitive mechanisms” (Gentner et al., 2006, p. 1206). This conclusion also fits Ray Jackendoff’s and Steven Pinker’s (2005) critique of HCF’s claim that the distinction between animals’ and human beings’ communication systems should rather be gradual than categorical.

When quantitative differences between human language and animal communication are undeniable, we should not forget that human memory is limited, too. In fact, it has been argued by Fred Karlsson (2007) that actual embedding in spoken language is almost absent and that it appears in written discourse only up to three times. While it is common to assume that a certain quantitative difference ought to be explained with a different quality, or with “an independently evolved mechanism”– as HCF (2002, p. 1576) argue – memory limits in humans makes one wonder where we should draw the line between animal language and human language. While human grammars allow for endless center-embedding in principle, it is rarely used. What if bird grammars also allow for center-embedding principally, but we just have not observed it so far?

Another strategy to question recursion in terms of center-embedding as a distinctive property of human language would be to grant that birds only use finite state grammars. However, it would be worthwhile discussing whether these grammars could approximate recursive patterns, such as center-embedding. While there still is need for research on this topic, part of the idea is also driven by the fact that humans’ cognitive capacities are finite. So human natural language might be less context sensible or even less context free in some respects and in that less recursive, as assumed.

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