1 Introduction
Our specific goal in this chapter is to use experimentation developed in acquisition work to identify the presence of self-embedding recursion in Pirahã.Footnote 1 Our broader goal, in concert with other chapters in this volume, is to jointly explore formal theoretical issues and extend experimental methodology to indigenous languages. We shall provide evidence that recursive self-embedding is present in Pirahã PPs and explore the consequences for the larger tapestry of recursive structures in human language in general. As a result, we reconsider the provocative claim by Everett (Reference Everett2005, Reference Everett2009, Reference Everett2012) that Pirahã lacks recursive syntactic structures altogether, showing that this view most likely results from a misunderstanding about the underlying grammatical system of Pirahã.
1.1 Broader Questions
There are broader issues entailed in the type of research described here:
(a) What is self-embedding in the larger context of recursive operations?
(b) How can a mathematical theory of grammar become visible to researchers in a language whose grammar is not fully understood?
(c) Can we reliably engage with such issues despite the necessity of translation and the presence of cultural differences?
(d) Can we apply a common methodology across a variety of indigenous languages and a variety of self-embedding constructions?
Our work is essentially just a step in this larger quest.
1.2 Experimental Fieldwork
Large challenges exist in doing fieldwork on isolated languages. It is not straightforward to obtain acceptability judgments from monolingual speakers without a writing system, relying mostly on uneasy translations. Yet it is very much like scientific inquiry elsewhere. In astronomy, observations can be severely clouded by limits on visibility. In biology, the extraordinary diversity in the physical environment of organisms, from the microscopic to the macroscopic, can be daunting. Our environmental challenge in discovering grammars may be less severe than in biology: it can be largely overcome once known experimental methods are imported into the inquiry. By utilizing stories and picture choice experimentation, we can create sharp pragmatic contrasts that allow us to highlight minimal pairs. This approach avoids subtle and frequently inconsistent grammaticality judgments.Footnote 2
In general, we find not a contradiction but a refinement of results when informal judgment, as well as truth-functional experiments and on-line approaches, are jointly explored. We see this approach as a harbinger of future work throughout linguistics.
1.3 Abstract Principles and Fieldwork
The claim that sophisticated, abstract Universal Grammar (UG) principles could be quickly and directly visible in a new language may seem very surprising. Half a century of painstaking and subtle explorations of intuitions of grammaticality have been needed to isolate distinctive characteristics of human grammar, such as the cyclic rules, Logical Form, barrier constraints on movement, and underlying parametric patterns (Baker Reference Baker2001). As a result, one might expect that each new isolated grammar produces an equal challenge that would take decades before an appropriate analysis succeeded. However, we believe that the opposite expectation emerges when scientific principles are fully clarified: if a UG principle can be expressed with formal precision, we should be able to isolate it easily in a new language.
In fact, recursion can be signaled by visible surface identity in morphemes, like –’s in ‘John’s friend’s hat’ or –er in ‘coffee-maker-maker,’ or specific prepositions like (de– in Romanian or –no in Japanese). Therefore, it is an excellent candidate for this expectation.
1.4 Overview of Recursion
Two meanings of recursion stand out in the literature in linguistics, derived from work in mathematics and computer science (Graffi Reference Graffi, Busà and Gesuato2015):
| (1) | Recursion as an iterative operation of Merge on words, and |
| (2) | Recursion as self-embedding of structures. |
There can be little doubt that the formation of every phrase requires the recursive algorithm of Merge or an equivalent formal operation that combines elements and operates upon its own output.Footnote 3 Therefore, this fundamental form of recursion must be universal for every structure identified as human language.
As for self-embedding, it is easily spotted in English PPs (the dog next to the cat next to the horse), possessives (John’s friend’s hat), adjectives (the second green ball), compounds (coffee-maker-lover), or in derivational morphology (re-re-reread), as well as in embedded sentences and in relative clauses.
It is well known that not every form of embedding is found in every language (Hale Reference Hale, Kinkade, Hale and Werner1975; Evans and Levinson Reference Evans and Levinson2009). So the question arises: which forms are found where? Tightly coordinated use of experimental materials developed in English (Pérez-Leroux et al., this volume), Japanese (Terunuma and Nakato, this volume), Portuguese (Maia et al., this volume), and Spanish, Dutch, and German have shown the presence of self-embedding not only with adults but also with children for both common (relative clauses) and rare (possessive) structures.
In this volume, Franchetto, working on Kuikuro, Lima and Kayabi on Kawaiwete, Amaral and Leandro on Wapichana, and Maia et al. on Karajá apply virtually identical or comparable materials on recursive locative PPs. Even though the tests have varied from non-chronometric acting-out tests applied to a single subject to direct on-line measures obtained with many subjects, all this work presents gratifyingly comparable results, showing the existence of self-embedding in these less-studied languages. Is it possible that Pirahã is a completely different language, banning any form of self-embedding? While Everett, based on his fieldwork, denies the presence of all forms of self-embedding, independent evidence first gathered by Sandalo in 1991 from informants, discussed below, runs directly counter to his claims. Moreover, Sandalo’s data fall together with Sauerland’s and Rodrigues et al.’s contributions (this volume) for recursively embedded sentential complementation in Pirahã, and with further work by Salles (Reference Salles2015) on self-embedded possessive nominal phrases.
At any rate, it is the full panoply of results within a language, using a variety of methodologies, that produces the kind of empirical robustness that science traditionally seeks. To capture all these facts, we need a more refined representation of recursion varieties.
2 Recursion Types
The universal form of Merge has been defined by Chomsky (Reference Chomsky2013) in the following terms:
| (3) | Merge (α,β) = {α,β} |
| Recursive Merge: T (α,β) → {T [α,β]} |
That is, recursive Merge refers here to a structure-building algorithm where only set formation ({α,β}) is combined, without a built-in label assigned to nodes.
In this recursive procedure, every step in structure-building is an operation of Merge that takes as its input (α and β) two lexical items and merges them, delivering as its output a more complex object ({α,β}). In the next step, Merge may take a new phrase as input and combine it with the complex object formed in step 1.Footnote 4
When we turn to self-embedding recursion, it is easy for us to conceive it in terms of node labels, which abstractly are maximal projections, represented as XP or YP, projected from heads, as X or Y. From there, we can differentiate three types of structures with rules that operate upon labelled nodes. Each entails a different formal representation, although their ideal formal representation will no doubt undergo further evolution. Snyder and Roeper (Reference Roeper and Snyder2004) and Roeper (Reference Roeper2011), building upon work in computer science, have identified Direct Recursion (DR) and Indirect Recursion (IR). Roeper and Oseki (this volume) have further divided Direct Recursion into Direct Unstructured Recursion (= Conjunctive) (DUR) and Direct Structured Recursion (DSR).Footnote 5
DUR delivers a conjunction, which can be generated in accordance with the rewriting rule in (4a):
| (4a) | Direct (conjunctive) Recursion: X → X (and X) |
The signature characteristic of DUR can be represented as in (1) and it is interpreted as conjunction or “and.”
Everett (Reference Everett2005) calls this elementary form “parataxis,” and claims that all phrases in Pirahã are interpreted in this straightforward way. Arsenijević and Hinzen (Reference Arsenijević and Hinzen2012)Footnote 6 suggest that this default form actually lies outside of grammar itself and it applies to every structural level (XP-level, sentence-level, word-level).Footnote 7 Classic evidence for this kind of structure comes from forms like (4b), where order has no interpretive effect and little evidence of binary structure is present:
| (4b) | John, Bill, Susan, and Fred arrived |
A second form of recursion, Indirect Recursion, involves an extra derivational step, or an extra rewriting rule (5):
| (5) | X → Y Z |
| Z → W (X) |
According to this, a category Z may emerge from the combination of other categories. In this second step of the derivation, X, created in step 1, is optionally re-introduced, resulting in a structure with self-embedding or “mutual recursion” in some accounts. The core forms of self-embedding in grammar are expressed through IR because they entail interpretive dependencies. An interesting case for the present discussion is DP-PP recursion (6), where PPs are introduced within DPs, creating a loop:
| (6) | Indirect Recursion |
| DP → D NP | |
| NP → N PP | |
| PP → P DP |
This can produce forms like (7) (marking the maximal projections: DP, NP, PP):
| (7) | a. | The jar on the shelf in the closet in the kitchen |
| b. | [DP the [NP jar [PP on [DP the [NP shelf [PP in [DP the [NP closet [PP in [DP the [NP kitchen]]]]]]]]]]] |
In (7), we have a cascade of referential DPs containing a NP with a PP specifying the reference of the DP. This means that the DP the jar is defined by the PP on the shelf, and the shelf is defined by the PP in the closet, which is further defined by the PP in the kitchen. The significant fact here is, ultimately, the complex way in which recursion controls reference or interpretation dependencies. Pérez-Leroux et al. (this volume) provide discussion of the syntax/semantics interface entailed by this type of structure.
A third form of recursion involves linked or “stacked” PPs or relative clauses and has been called feature-sharing by Chomsky (Reference Chomsky2013). Roeper and Oseki (this volume) call it DUR because it is formed in accordance with the rules in (6), in which a category PP emerges from merging a PP with a *PP, but the result involves referential dependencies and structural domination. This is best illustrated through VP recursion
(notation adapted from traditional Kleene* system):
| (8) | Direct Structured Recursion: |
| VP → V DP (PP*) | |
| PP* → PP (PP*) | |
| PP → P DP |
It is evident in cases of phrases describing motion following a path:
| (9) | a. | The ball rolled down the stairs into the street into the gutter into a hole |
| b. | Stand the chair up in the living room in the corner on the small rug |
It can also generate examples like (10) with order opposite to (7):
| (10) | Put the jar in the kitchen in the closet on the shelf |
Notably these forms allow wh-extraction, which requires c-command:
| (11) | a. Where did you say you put the jar in the kitchen in the closet? |
| → On the second shelf |
(10) and (11) involve a series of locative interpretations dependent upon each other, and is, therefore, not conjunctive, as it would be for (12), where conjunction would allow multiple jars to be placed:
| (12) | Put a jar in the kitchen and in the closet and on the shelf |
Therefore, DUR behaves syntactically and semantically differently from DSR, as in (13):
| (13) | Direct Structured Recursion through linked PPs: |
The PP* shares the [+LOC feature] and represents one argument of the verb ‘put.’ It also reflects the direction of motion and the fact that a single action of putting is usually entailed. That is, one does not first put the jar in the kitchen, then move it into the closet, and then move it onto the second shelf.
IR
through DP, however, is the more common form:
| (14) | Indirect Recursion through DP: |
| [DP [PP [DP [PP [DP [PP]]]]]] |
Or a more fully expanded DP:
| (15) | [DP [NP [PP [DP [NP [PP [DP…]]]]]]] |
Roeper and Oseki (this volume) show very early spontaneous use of PP recursion in language acquisition, which suggests that it is less difficult for a child to recognize it. Maia et al. (this volume) also observe that DUR is a more accessible default form, which does not exclude the presence of Indirect Recursion.
3 Pirahã Recursion
Now we have to adjust our structures to account for the left-branching nature of DP-PPs in Pirahã. The structures run the opposite way, but with the same relations:
| (16) | gata hio apo hoai |
| can inward match box | |
| ‘The match box is in the can’ |
Based on the example in (16), where hio apo likely represents a complex preposition akin to English into, we could represent the internal structure of the DP in (16) as in (17):
| (17) | Head-final NP constructions in Pirahã |
What would happen to the internal structure of the construction if Pirahã accepted multiple PP embedding? The example above suggests that should Pirahã speakers be able to understand multiple embedded PPs under DUR, then sentences like the one in (18) would be preferred over IR, as it is along the acquisition path from DUR to DSR to IR. The left-branching reverses the order: ‘coin on paper on chair on board’ to ‘on board on chair on paper coin’:
| (18) | tabo apo tiapapati apo kapiiga apo gigohoi |
| board on chair on paper on coin | |
| ‘The coin on the paper on the chair on the board’ |
Notice that the sentence in (18) allows for a representation following the Indirect Recursion example presented in (15) above for English. The main distinction would be based on the fact that Pirahã is a head-final language, which would give us the structure in (19):
| (19) | PP Indirect Recursion in Pirahã |
This also allows PP DUR with the implied conjunctive ‘and.’ If PP DSR is available in Pirahã, then speakers would be able to interpret DPs like those in (20), with the structure in (21):
| (20) | kapiiga apo tiapapati apo tabo apo gigohoi |
| paper on chair on board on coin | |
| ‘The coin on the board on the chair on the paper’ |
| (21) | PP Direct Structured Recursion in Pirahã |
We should, therefore, seek all three forms of recursion in Pirahã, although it is conceivable that Indirect (and, consequently, Structured) Recursion might be less evident, since it seems to be rarer among languages in general. Nevertheless, as we shall see, there are indications that they are all present. It might be that Pirahã blocks some forms of IR, as so many languages do. For instance, it is impossible to have recursive possessives in German (of the type, ‘John’s friend’s father’s house’), but Franchetto (this volume) and Lima and Kayabi (this volume) find them in Kuikuru and Kaiweiwete, respectively. Pirahã also allows recursive possessive DPs as shown in Salles (Reference Salles2015), who collected data containing three levels of self-embedding within possessive DPs. Can we predict where this type of recursion will be found? It is not obvious where one should look, and in fact any language might have a form of syntactic recursion never seen before. For Pirahã, in addition to sentence recursion, PP recursion is a natural choice to investigate.
Thus far, there are no known criteria for what links recursive structures in a given language, but it is very noticeable that, although English has both left and right-branching recursion, Romance languages with SVO structures appear to favor right-branching, while languages with SOV structure allow more left-branching recursion. The question of whether different forms of recursion are linked typologically and along the acquisition path is the next frontier in this research.
3.1 Naturalistic Examples of PP Recursion in Pirahã
During fieldwork, Sandalo collected examples like (22) that immediately suggest that Pirahã allows recursive PPs. (22) is a description provided by a Pirahã speaker for a scenario in which a pen is placed inside a small paper boat, which is placed inside a bigger paper boat.Footnote 8
| (22) | kapiiga ko kapiigatoi xihi-aip-aáti kapiiga ko kapiiga |
| paper inside pencil store-downward-unexpectedly paper inside paper | |
| ho-áop-aáti | |
| aux-impefective-unexpectedly | |
| ‘(You are putting down) pencil inside paper inside paper’ |
This example contains two verbal forms: a main verb xihi ‘put’ and an auxiliary ho-áop-aáti.Footnote 9 The main verb root, xihi, is inflected by two morphemes: a directional morpheme (downward) and a morpheme indicating ‘unexpected.’ It is the auxiliary verb that carries inflection related to tense (imperfective), as in other languages: for example, Basque. The presence of only one tense morpheme suggests that there is only one sentence with a postpositional phrase embedded under another. Therefore, with respect to PP recursion, Pirahã might not be different from other Brazilian native languages, for instance Kaingang, which seems to allow PP recursion as well.Footnote 10, Footnote 11
| (23) | Kãkénh tá runja kãki lata ki krẽkufár vyn kỹ pó ki |
| canoe on bucket inside can in fish grab thn rock in | |
| krẽkufár rẽ fi | |
| fish near put | |
| ‘Grab the fish in a can inside a bucket in the canoe then put (it) near the fish in the rock’ |
One might imagine that examples like (23) are not spontaneously found in Pirahã, as this type of complex sentence may overload the parser. Thus, in order to verify the availability of examples like this in Pirahã, we ran two experimental pilot studies. Two monolingual native speakers of Pirahã were tested: Iapohen Pirahã, who is about 40 years old, and Iaoá Pirahã, who is about 20 years old.Footnote 12 These two speakers participated in our research in two different venues: in July 2012 at the University of Campinas/Brazil and in August 2013 at the Federal University of Rio de Janeiro/Brazil.Footnote 13 Given the small amount of speakers we had access to and the fact that we did not have a controlled experimental set-up, our experiments should be understood as pilot studies.
In these experimental pilots, we worked with picture description (experiment 1) and acting-out routines (experiment 2).
3.2 Pilot Study 1: Teasing Direct and Indirect Recursion Apart
Method: Participants, Materials, and Design
Iaoá and Yapohen Pirahã, our participants, are native speakers of Pirahã with no apparent knowledge of Portuguese. They were exposed to a series of six pictures, like the ones shown in Figure 15.1, and after hearing a sentence in Pirahã (pronounced by one of the experimenters) they were expected to point towards the picture that best fit the description provided in the sentence.Footnote 14
Figure 15.1 Pictures in pilot study 1
Pictures 1 to 6 in Figure 15.1 were borrowed from Maia (Reference Maia2012) and Maia et al. (this volume) and were crucial to this experiment, as they visually describe the following grammatical possibilities:
| i. | No recursivity or coordination of PPs (pictures 3 and 4) |
| alligator on the beach on the stone =/=> not on stone on the beach (picture 3) | |
| =/=> not on stone and beach |
| ii. | Coordination of two PPs (picture 1) |
| alligator on stone on beach => alligator on stone and on the beach |
| iii. | Coordination of three PPs (picture 4) |
| alligator on blanket on stone on beach => on blanket and on a stone and on a beach |
| iv. | Recursivity of two PPs (picture 2) (pictures 1, 2, 4, 5) |
| alligator on stone on beach = alligator is on the stone that is on the beach |
| v. | Recursivity of three PPs (picture 5) |
| alligator on blanket on stone on beach = alligator that is on the blanket that is on the stone that is on the beach |
We started the procedure with lexical elicitations. Each of the objects composing the pictures in Figure 15.1 was first introduced to the speakers, and the corresponding lexical items were elicited. Then, we pointed to each picture and asked the speaker to describe it for us. Note that it was mandatory for this study that a picture representing direct and IR (e.g., pictures 5 and 6) be shown together in contrast to highlight a minimal pair.
Through controlled elicitations, we collected the following target sentences where apo ‘on’ re-appeared with reference to recursive pictures.
| (24) | a. | koxoahai bege apo xaxai apo |
| alligator floor on stone on | ||
| b. | koxoahai bege apo xaxai apo tahoasi apo | |
| alligator floor on stone on mat on |
The second part of our procedure was an interpretation task, which reversed the tasks done in the first procedure. The experimenter pronounced out loud each one of the elicited sentences to the participant, and asked him to show the situation (a picture in Figure 15.1) described by the sentences he heard. This was done sentence by sentence, situation by situation, and the trials were randomly ordered in order to prevent saturation.
If the participant treated the target sentences in (24) as involving conjoined PPs, then he was expected to point towards picture 1 or 4. If, however, the prepositional phrases were treated as a case of self-embedding, then the participant should point towards either picture 2 or 5.
3.3 Results and Discussion
The results of this first experiment suggest that Pirahã speakers are able to process, comprehend, and differentiate ambiguous prepositional phrases. The speaker consistently paired the target sentences with the recursive pictures, as shown in the following:
To describe pictures with coordination, the speaker modified the target sentences, introducing an additional word, piai, a coordinative particle translated as ‘also’ by Everett (Reference Everett1990).Footnote 15
These results clearly show that Pirahã speakers are capable of teasing coordination and recursion apart. It suggests that the target sentences, (24a) and (24b), might not even be ambiguous. If they are, however, the results presented here indicate that: (a) a recursive structure (IR) is available for these sentences; (b) speakers have a preference for treating (24a) and (24b) as containing IR PPs; and (c) the ambiguity is resolved by inserting an overt conjunction, reinforcing a coordinative reading.
In formal terms, we conclude, thus, that Pirahã, similar to English, Portuguese and many other known languages, has both DUR (Direct) and IR.
3.4 Pilot Study 2: Spotting Indirect Recursion
Methods: Participants, Materials, and Design
This test followed test 1. Iaoá was our only participant. The test consisted of an acting-out game, with the participation of two players. The player in charge would give commands that the other had to execute. The picture (Figure 15.2) shows one of the scenarios involved in the activity. Two chairs were placed on the floor, one above a wooden board. There were two cups, one placed on the wooden board, and the other placed on the chair, which was placed on the wooden board.
Figure 15.2 A scene from pilot study 2 in which the experimenter gives commands to the participant
As in the first test, we started with lexical elicitations. Each of the objects composing the scene above was first introduced to the speakers, and the correspondent lexical items were elicited. Then we executed actions of putting coins in/on different objects present in the scene. This procedure allowed us to elicit target sentences, such as (25), which describes a scene in which a coin is placed inside the cup on top of the wooden board to the left and another coin is placed on the blue chair to the right, and (26), which describes a scene in which a coin is placed inside the cup on the chair on the wooden board.Footnote 16
| (25) | ihiaipati gigohoi kopo ko tiapapati apo piai |
| put coin cup in chair on also |
| (26) | ihiaipati gigohoi kopo ko tiapapati apo |
| put coin cup in chair on |
Once the participant felt comfortable with the game, we changed the scenario to include situations involving three pieces of paper, one sitting on the top of the chair placed on the wooden board, one on the top of the other chair, and another one on the wooden board. This scene allowed us to test the following target sentences:
| (27) | ihiaipati gigohoi kapiiga apo tiapapati apo (piai) tabo apo piai |
| put coin paper on chair on (also) board on also |
| (28) | ihiaipati gigohoi kapiiga apo tiapapati apo tabo apo |
| put coin paper on chair on board on |
These four target sentences are samples of the following type of structures:
| (29) | a. | Coordination of two PPs | (25) |
| b. | Recursivity of two PPs | (26) | |
| c. | Coordination of three PPs | (27) | |
| d. | Recursivity of three PPs | (28) |
In the first part of the game, the experimenter provided the participant with a handful of Brazilian coins, and asked him to put coins in different places. The commands were the target sentences in (25)–(28).
In the second part of the game, the roles of the participants were reversed, and Iaoá became the one in charge. He provided the experimenter with a handful of Brazilian coins and gave him commands about places to put the coins. This procedure allowed us to verify if Pirahã speakers were capable of comprehending and producing structures with multiple levels of PP embedding. Thus, similar to the first experiment, this experiment was originally designed to examine the availability of Direct (Unstructured Recursion) versus Indirect Recursion.
3.5 Results and Discussion
In the first part of the procedure, the speaker had no problem in comprehending and, consequently, executing the commands he heard. Once he understood the game, he was fast in executing all the commands, including those involving two or three embeddings. However, in the second part of the game, when the speaker himself was producing the target sentences, he switched the order of the PPs in the sentence involving recursivity, providing examples like:
| (30) tabo apo | tiapapati | apo | kapiiga | apo | gigohoi |
| board on | chair | on | paper | on | coin |
| ‘The coin on the paper on the chair on the board’ | |||||
| = (put) coin on board on chair on paper = DSR | |||||
In (30) the PPs are computed bottom up, which fits the claim that the lower PP nodes share interpretative features with the upper PP nodes, rather than indirectly modifying DPs. This is then spontaneous evidence of DSR. These results corroborate the first experiment: Pirahã grammar allows DUR, DSR, and IR. These spontaneous data suggest that Pirahã may prefer DUR. This type of recursion is arguably easier for them to produce, just as it seems to be for children (see Roeper and Oseki, this volume).
4 Conclusion
These pilot studies constitute informal, experimental evidence that Pirahã allows recursive syntactic structures of three types. Once again, the speakers who participated in our pilot studies demonstrated no difficulties in comprehending and producing self-embedding postpositional phrases (IR), in contrast to conjunctive, or paratactic, structures, which Everett claimed were the only available structures.
Although Everett’s strong claim (Reference Everett2005, Reference Everett2012) is not upheld, it had the merit of provoking fruitful discussion on Pirahã grammar and recursion in general. Based partly on data published by Everett and Nevins, Pesetsky, and Rodrigues (Reference Nevins, Pesetsky and Rodrigues2009b) developed an interesting cross-linguistic study, showing that Pirahã is in no way exceptional with respect to recursion.
Their work has now initiated new fieldwork beyond this study, as has the work by Sauerland (this volume) for sentential self-embedding and Rodrigues, Salles, and Sandalo (this volume) for self-embedding VPs in control configurations. Silva (Reference Silva2014), looking at constructions with focus and topicalization, points out that movement is possible out of self-embedding/recursive PPs, in contrast with coordinated PPs. Additionally, Salles (Reference Salles2015) demonstrates clear cases of recursive possessive DPs. The studies here and throughout this book demonstrate that the extension of acquisition experimentation to fieldwork is quite straightforward. It has created a new vista of possibilities for experimental fieldwork.
As such, support for UG has emerged from fieldwork with isolated indigenous languages. With such compelling support, we maintain that the same type of complex grammatical phenomena and formal constraints upon them are found in all known languages in the world.
