Recursion and Human Language (Studies in Generative Grammar)

Recursion and Human Language Studies in Generative Grammar 104 Editors Harry van der Hulst Jan Koster Henk van Riem...

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Recursion and Human Language

Studies in Generative Grammar 104

Editors

Harry van der Hulst Jan Koster Henk van Riemsdijk

De Gruyter Mouton

Recursion and Human Language Edited by

Harry van der Hulst

De Gruyter Mouton

The series Studies in Generative Grammar was formerly published by Foris Publications Holland.

ISBN 978-3-11-021924-1 e-ISBN 978-3-11-021925-8 ISSN 0167-4331 Library of Congress Cataloging-in-Publication Data Recursion and human language / edited by Harry van der Hulst. p. cm. ⫺ (Studies in generative grammar ; 104) Based on presentations at a 2007 conference. Includes bibliographical references and index. ISBN 978-3-11-021924-1 (hardcover : alk. paper) 1. Grammar, Comparative and general ⫺ Syntax ⫺ Congresses. 2. Grammar, Comparative and general ⫺ Phonology ⫺ Congresses. P291.R38 2010 415⫺dc22 2010003502

Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de. ” 2010 Walter de Gruyter GmbH & Co. KG, Berlin/New York Typesetting: RoyalStandard, Hong Kong Printing: Hubert & Co. GmbH & Co. KG, Göttingen ⬁ Printed on acid-free paper Printed in Germany www.degruyter.com

Table of Contents List of authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

Preliminaries Re Recursion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Harry van der Hulst

xv

Part I. Discussing the need for recursion on empirical grounds 1. Piraha˜ – in need of recursive syntax? . . . . . . . . . . . . . . . . . . . . Jeanette Sakel & Eugenie Stapert

3

2. The fluidity of recursion and its implications. . . . . . . . . . . . . . . Marianne Mithun

17

3. Recursion and iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fred Karlsson

43

4. Recursion in conversation: What speakers of Finnish and Japanese know how to do. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ritva Laury & Tsuyoshi Ono

69

5. What do you think is the proper place of recursion? Conceptual and empirical issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Arie Verhagen

93

Part II.

Formal Issues

6. Recursion and the infinitude claim . . . . . . . . . . . . . . . . . . . . . . Geo¤rey Pullum & Barbara C. Scholz

113

7. Just how big are natural languages? . . . . . . . . . . . . . . . . . . . . . D. Terence Langendoen

139

8. Recursion, infinity, and modeling . . . . . . . . . . . . . . . . . . . . . . . Hans-Jo¨rg Tiede & Lawrence Ne¤ Stout

147

9. How recursive is language? A Bayesian exploration . . . . . . . . . Amy Perfors, Josh Tenenbaum, Edward Gibson & Terry Regier

159

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Table of Contents

Part III. Evolutionary Perspectives 10. Was recursion the key step in the evolution of the human language faculty? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Anna Kinsella

179

11. When clauses refuse to be recursive: An evolutionary perspective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ljiljana Progovac

193

12. The use of formal language theory in studies of artificial language learning: a proposal for distinguishing the di¤erences between human and nonhuman animal learners . . . . . . . . . . . . James Rogers & Marc Hauser 13. Over the top – recursion as a functional option . . . . . . . . . . . . Peter Harder

213 233

Part IV. Recursion and the Lexicon 14. Lack of recursion in the lexicon: The two-argument restriction. . Eva Juarros-Daussa`

247

15. Kinds of recursion in Adyghe morphology. . . . . . . . . . . . . . . . Yury A. Lander & Alexander B. Letuchiy

263

16. Recursion and the Lexicon . . . . . . . . . . . . . . . . . . . . . . . . . . . Jan Koster

285

Part V. Recursion outside Syntax 17. A note on recursion in phonology . . . . . . . . . . . . . . . . . . . . . . Harry van der Hulst

301

18. Cognitive grouping and recursion in prosody . . . . . . . . . . . . . . La´szlo´ Hunyadi

343

19. Becoming recursive: Toward a computational neuroscience account of recursion in language and thought . . . . . . . . . . . . . Simon D. Levy

371

20. Recursion in severe agrammatism . . . . . . . . . . . . . . . . . . . . . . Vitor Zimmerer & Rosemary A. Varley

393

Subject index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Language index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

407 417

List of authors Edward Gibson Department of Brain & Cognitive Sciences Massachusetts Institute of Technology Cambridge, MA 02139 USA [email protected] Peter Harder Department of English, Germanic and Romance Studies University of Copenhagen Njalsgade 130, DK-2300 Copenhagen S Denmark [email protected] Marc D. Hauser Depts. of Psychology, Organismic & Evolutionary Biology and Biological Anthropology Harvard University Cambridge, MA 02138 USA [email protected] La´szlo´ Hunyadi Department of General and Applied Linguistics University of Debrecen Egyetem te´r 1. Debrecen, H-4010 Hungary [email protected] Eva Juarros-Daussa` Department of Romance Languages and Literatures State University of New York at Bu¤alo 910 Clemens Hall, North Campus, Bu¤alo, NY 14260-4620 USA ejuarros@bu¤alo.edu

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List of authors

Fred Karlsson Department of General Linguistics PB 24 FI-00014 University of Helsinki Finland [email protected] Anna R. Kinsella Language Evolution and Computation Research Unit, School of Philosophy, Psychology, and Language Sciences, The University of Edinburgh 3 Charles Street, Edinburgh, EH8 9AD, UK [email protected] Jan Koster Department of Linguistics University of Groningen P.O. Box 716 9700 AS Groningen The Netherlands J. [email protected] Yury A. Lander Institute of Oriental Studies, RAS Rozhdestvenka, 12 Moscow 107031 Russia [email protected] D. Terence Langendoen National Science Foundation 4201 Wilson Boulevard, Room 1125 Arlington, Virginia 22230 USA [email protected]

List of authors

Ritva Laury University of Helsinki Department of Finnish Language and Literature PL 3 (Fabianinkatu 33) 00014 University of Helsinki Finland [email protected] Alexander B. Letuchiy Russian Language Institute, RAS Volkhonka, 18/2 Moscow 119019 Russia [email protected] Simon D. Levy Computer Science Department Washington and Lee University Lexington, Virginia 24450 [email protected] Marianne Mithun Department of Linguistics University of California, Santa Barbara Santa Barbara, CA 93106 USA [email protected] Tsuyoshi Ono East Asian Studies 3-31 Pembina University of Alberta Edmonton, AB T6G 2H8 Canada [email protected] Amy Perfors School of Psychology University of Adelaide Level 4, Hughes Building Adelaide, SA 5005 Australia [email protected]

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x

List of authors

Ljiljana Progovac Linguistics Program Wayne State University 5057 Woodward Detroit, MI 48202 USA [email protected] Geo¤rey K. Pullum School of Philosophy, Psychology and Language Sciences University of Edinburgh 3 Charles Street, Edinburgh EH8 9AD Scotland, UK [email protected] Terry Regier Department of Psychology University of Chicago Chicago USA [email protected] James Rogers Earlham College Richmond, IN USA [email protected] Jeanette Sakel University of the West of England Frenchay Campus Coldharbour Lane Bristol BS16 1QY UK [email protected] Barbara C. Scholz School of Philosophy, Psychology and Language Sciences University of Edinburgh 3 Charles Street, Edinburgh EH8 9AD Scotland, UK [email protected]

List of authors

Eugenie Stapert Max Planck Institute for Evolutionary Anthropology, Leipzig Deutscher Platz 6 04103 Leipzig Germany [email protected] Lawrence Ne¤ Stout Department of Mathematics and Computer Science Illinois Wesleyan University P.O. Box 2900 Bloomington, IL 61702-2900 USA [email protected] Josh Tenenbaum Department of Brain & Cognitive Sciences Massachusetts Institute of Technology Cambridge, MA 02139 USA [email protected] Hans-Jo¨rg Tiede Department of Mathematics and Computer Science Illinois Wesleyan University P.O. Box 2900 Bloomington, IL 61702-2900 USA [email protected] Rosemary A. Varley University of She‰eld Department of Human Communication Sciences 31 Claremont Crescent She‰eld S10 2TA UK [email protected]

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List of authors

Arie Verhagen Leiden University Centre for Linguistics (LUCL) Leiden University P.O. Box 9515 2300 RA Leiden The Netherlands [email protected] Vitor C. Zimmerer Department of Human Communication Sciences University of She‰eld 31 Claremont Crescent She‰eld S10 2TA UK [email protected]

Preliminaries

Re Recursion1 Harry van der Hulst ‘‘We hypothesize that FLN only includes recursion and is the only uniquely human component of the faculty of language.’’ (Hauser et al. 2002: 1569) ‘‘If you already know what recursion is, just remember the answer. Otherwise, find someone who is standing closer to Douglas Hofstadter than you are; then ask him or her what recursion is.’’2 ‘‘An apparently new speech disorder a linguistics department our correspondent visited was a¤ected by has appeared. Those a¤ected our correspondent a local grad student called could hardly understand apparently still speak fluently. The cause experts the LSA sent investigate remains elusive. Frighteningly, linguists linguists linguists sent examined are highly contagious. Physicians neurologists psychologists other linguists called for help called for help called for help didn’t help either. The disorder experts reporters SpecGram sent consulted investigated apparently is a case of pathological center embedding.’’3

1. Introduction The present volume is an edited collection of original contributions which all deal with the issue of recursion in human language(s). All contributions (but one4) originated as papers that were prepared for presentation at a conference organized by Dan Everett on the topic of recursion in human 1. I wish to thank the following people for comments on an earlier draft of or ideas contained in this chapter: Jonathan Bobaljik, Marcel den Dikken, Laszlo Hunyadi, Fred Karlsson, Simon Levy, Marianne Mithun, Geo¤rey Pullum, Barbara Scholz and Arie Verhagen. Needless to say that some points that I did not remove from this final version met with strong disagreement. 2. Attributed to Andrew Plotkin (http://en.wikipedia.org/wiki/Recursion). 3. http://specgram.com/CLI.2/03.bakery.disorder.html 4. The exception is chapter 17. In an earlier draft of this introductory chapter I included a section on phonology that I had to remove because it was too long. The reviewers suggested that I turn this section into a separate contribution to this volume, which I did.

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language (Illinois State University, April, 27–29 2007).5 For the purpose of this collection all articles underwent a double-blind peer-review process. The present chapters were written in the course of 2008. The characterization of language as a potentially infinite number of expressions that can be produced with finite means has been noted for a long time, among others by the linguists Panini and Wilhelm von Humboldt. Chomsky’s early work (e.g. Chomsky 1955 [1975]) proposes various ways to build recursive mechanisms into the grammar (cf. below) and since then many linguists have adopted one of these mechanisms, namely a rewrite or phrase structure component which contains recursive rewrite rules or recursive rule sets (cf. below). However, no general agreement seems to exist concerning the empirical status as well as the formal status of this ‘characteristic’ of human languages or the grammars that underlie them. Renewed interest in this subject was sparked by claims made by or attributed to, Hauser, Chomsky and Fitch (2002) which I paraphrase as follows:6 (1) a. b. c. d. e.

Recursion essentially constitutes the innate human language faculty7 Recursion is the sole uniquely human trait of human language Recursion is unique to the language faculty Recursion is universal (i.e. present in all human languages) Recursion is unique to the human mind

As one might expect, all these bold claims are controversial. According to the first claim, language results from several mental faculties whose intersection leads to language, as well as from necessary ‘natural laws’ of some kind that take scope over language (and, presumably many other phenomena). However the recursion faculty (also called the narrow language

5. Dan Everett wishes to thank Bernard Comrie and the Max Planck Institute for Evolutionary Anthropology and the College of Arts and Sciences and the Provost of Illinois State University for financing this conference. 6. There is some uncertainty on what the authors of this article say precisely and di¤erent interpretations can be found in reactions to it. My focus here is on the kinds of claims that linguists have attributed to the article. 7. Together with the so-called interfaces to the sensory-motor system and the conceptual system, it forms the ‘narrow language faculty’. This claim constitutes an interesting and indeed minimalist interpretation of Chomsky’s Innateness Hypothesis which, originally, had it that human are born with a richly articulated universal grammar.

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faculty) is properly contained in this intersection. The second claim adds that all other language-relevant faculties than recursion (which together with recursion make up the broad language faculty) can also be attested in non-human animals, while recursion cannot. Pinker and Jackendo¤ (2005) contest the first claim by pointing to other aspects of language that specifically serve language (being confined to the intersection, which goes against claim a). Thus, for them, the innate language faculty contains more than recursion. They also imply that at least some of these other aspects may also be unique to human minds (which goes against claim b). They also note that recursion seems to play a role in other human cognitive systems such as the ‘mathematical module’, or ‘social intelligence’ which runs against claim c. Hauser, Chomsky and Fitch have responded to their article (Fitch, Hauser and Chomsky 2005) which has sparked a further rebuttal by Jackendo¤ and Pinker (2005). With respect to claim (d), Everett (2005) finds that Piraha˜, a Muran language from the Brazilian Amazon, does not exhibit any recursive structures at the syntactic level. His claim has been called into question in Nevins, Pesetsky and Rodriguez (to appear) to which Everett (2007, to appear) is a response. This claim, which has attracted a lot of attention in the professional literature and in the popular press, has contributed to further interest into the matter of recursion.8 Finally, claim (e) has been called into question by Genther at al. (2006) who report on experiments which show that European starlings can be trained to make a distinction between strings that result from recursive or from non-recursive grammars. These findings, which also gained media attention, have received alternative interpretations (cf. Language Log9; Marcus 2006), notably the idea that making a distinction between anbn and random combination of a’s and b’s may point to an ability to ‘count’ (in itself still a remarkable capacity). In fact, Hauser, Chomsky and Fitch (2002) themselves note that animal navigation capacities can be analyzed as containing recursion, which implies that recursion may not be entirely limited to the human mind. In this volume, the question of recursion is tackled from a variety of angles. It is perhaps fair to say that the conference call invited participants to take a critical stance regarding the claims in, or attributed to Hauser, Chomsky and Fitch (2002) and this is certainly reflected in the present

8. See the discussion on the Edge website (http://www.edge.org/3rd_culture/ everett07/everett07_index.html) 9. http://158.130.17.5/~myl/languagelog/archives/003076.html.

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very interesting collection.10 Some articles cover empirical issues by examining the kinds of structures in languages that suggest recursive mechanisms, focusing on the question to what extent recursive constructions can actually be attested in natural language use. Others focus on formal issues, notably what kind of devices can be used to describe the apparent recursive expressions, and whether the relevant devices have the specific function of making recursion possible or, perhaps lead to recursion as an epiphenomenon. Most articles discuss syntactic phenomena, but a few involve morphology, the lexicon and phonology. In addition, we find discussions that involve evolutionary notions and language disorders, and the broader cognitive context of recursion. In this introductory chapter, section 2 o¤ers a brief discussion of the use of the notion recursion in linguistics and, for the sake of discussion, some further remarks about the role and source of recursion as a morphosyntactic device. Then, in section 3–9 I will review the content of the chapters in the order in which they appear in this volume.11 In some sections I include some additional discussion, particularly in areas which are less well represented in this collection, such as derivational morphology and phonology. Section 10 summarizes what I believe to be the major claims or considerations that are contained in this volume. 2. ‘Recursion as hierarchical grouping’ allows ‘specific recursion’ as a possibility A general problem with the HCF article is that it does not define precisely enough what it means by recursion (cf. Tomalin 2007: 1796). Tomalin (2007) and Parker (2006) clearly show that the concept of recursion and of recursive functions (in linguistics, mathematics and computer science) can be defined in several di¤erent ways. When one gets down to specifics, mathematical formalizations are intricate and inaccessible to most people, including most linguists. In addition, there are di¤erent notions of recursion around and to disentangle their formal di¤erences is, again, largely a 10. Another conference on recursion was held May 26–28, 2009 at the University of Amherst. This conference reflected as less critical view of the centrality of recursion. The centrality of the recursion topic, or the related topic of complexity is further evident from two other conferences that focus on this issue, June 19–20, 2009 and February 24–26, 2010, both in Berlin. 11. The description of the articles’ content is based on abstracts that were provided to me by the authors.

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topic for advanced mathematical minds. Tomalin (2007) presents an overview of the historical background of this notion in generative grammar, pointing to connections to work outside linguistics as well as di¤erent ways in which the notion appears within generative grammar, and, more specifically, within the Minimalist Program.12 He shows how Chomsky, faced with the problem of designing a grammar that could generate an infinite number of expressions with finite means, introduces di¤erent ‘recursive devices’ in di¤erent parts of LSLT (Chomsky 1975 [1955]). In LSLT, chapter 7, it is suggested that a finite set of rewrite rules can be applied more than once. Then in chapter 8 rewrite rules are considered that have the symbol on the left of the arrow also appearing on the right side of the arrow. It is this notion of recursion that became more widely adopted in generative grammar, by Chomsky and others. Thirdly, in chapter 10, the recursive part of the grammar is located in the transformational component where ‘‘the product of a T-marker can itself appear inside the P-base of a T-marker.’’ (LSLT, 516–518; Tomalin 2007: 1793). Tomalin also distinguishes at least five di¤erent notions of recursion and concludes that the type of recursion that HCF refer to (that conforms to the Minimalist Program) is perhaps best characterized as the idea of providing an inductive definition (indeed also called recursive definition) for linguistic expressions. In the MP ‘‘the operations of CHL recursively construct syntactic objects’’ (Chomsky 1995: 226) which means that every syntactic object (i.e. linguistic expression) can be defined in terms of a combination of smaller syntactic objects, with lexical items being the ‘base case’ syntactic objects (that thus terminate a derivation). This characterization of recursion is more general than what most linguists usually have in mind when they define recursion as ‘embedding a constituent in a constituent of the same type’. However, it could perhaps be argued that this latter notion of recursion (which I here will call ‘specific recursion’) is entailed by the more general notion. Let us agree that linguistic expressions (words, sentences) can be analyzed as hierarchically structured object (‘trees’) for which, following LSLT, we can formulate rewrite rules that capture parts of these structures, such as: (2) A % B þ C (often paraphrased as ‘‘An A can consist of a B plus a C’’) 12. Parker (2006) also provides a detailed overview of the way linguists, mathematicians and computer scientists use or define this notion.

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B and C can be atomic units (morphemes in morphology, words in syntax), or they can be combinations themselves (called complex words or phrases). If that latter option is allowed (as it seems to be in linguistic expressions which do have complex words inside (necessarily) complex words and phrases inside phrases) this means that we have rewrite rules of the following sort: (3) a. b.

Phrase % Phrase þ X Word % Word þ X

‘X’ in (3a) can be another phrase or a word, while in (3b) it can be a word or an a‰x. I assume here the idea that X is the head of the phrase to the left of the arrow and will return to the notion of headedness below. The recursive step of an inductive definition, when formalized as a rewrite rule, can be ‘recognized’ by the fact that the symbol on the left of the arrow also occurs on the right. In (3a) and (3b) the identical symbol is ‘word’ or ‘phrase’, respectively. In fact, if the di¤erence between complex words (morphology) and phrases (syntax) is ignored or even denied, there is only one rewrite rule, e¤ectively ‘concatenate’ or, more fashionable: ‘merge’: (4) Linguistic expression % Linguistic expression þ X If we agree that the designation ‘linguistic expression’ literally implies units of the same type (namely the type ‘linguistic expression’) rule (4) meets the classical characterization for recursion: it has the same symbol on both sides of the arrow. When Chomsky says that CHL recursively constructs ‘‘syntactic objects’’ he characterizes such objects as follows (Chomsky 1995: 243): (5) a. b.

lexical items K ¼ {g{a b}}, where a, b are objects and g is the label of K

Starting out with a set of lexical items, the rule in (5b) recursively constructs (binary) units until all members in the ‘numeration’ are dominated by some Kg. With (5a) being the base case that allows the construction to terminate, (5b) is the recursive step (corresponding to 4). Given the ‘definition’ in (5), a complex syntactic object K, if well-formed, can be recursively defined into combinations of (smaller) syntactic objects (which may be complex of simplex). Let us call this notion of recursion here ‘general recursion’. Again, mostly, linguist identify recursion as cases in which a specific rule

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(from a set of rules) is applied (directly, or indirectly) to its own output, but if there is only one rule (i.e., rule 4), every expression that contains another non-basic expression involves recursive application of that rule. However, the more specific understanding of recursion presupposes the idea of linguistic expressions being of a variety of di¤erent categories. Words are nouns, verbs, prepositions etc., while phrases are noun phrases, verb phrases, prepositional phrases, etc. Thus, instead of the rule in (4) we have rules as in (6). (Having linguistic expressions of di¤erent categories allows us to formalize the idea that linguistic expressions have heads that determine the category): (6) a. b.

XPhrase % YPhrase þ X XWord % YWord þ X

This allows cases in which X and Y are identical, which then presents the ‘Russian Doll’ e¤ect: a phrase of type X within a phrase of type X, or a word of type X within a word of type X. The di¤erence between general recursion and specific recursion is exemplified in the following quote from Pinker and Jackendo¤ (2005: 10): ‘‘. . . (As mentioned, HCF use ‘‘recursion’’ in the loose sense of concatenation within hierarchically embedded structures). Recursion consists of embedding a constituent in a constituent of the same type, for example a relative clause inside a relative clause (. . . .). This does not exist in phonological structure: a syllable, for instance, cannot be embedded in another syllable.’’

There is, however, no contradiction between these two characterizations of recursion: the ‘specific recursive case’ is an automatic result of having general recursion, which means there is no need to regard specific recursion as a basic property. What is basic is the possibility of containing non-atomic objects within larger non-atomic objects of the same complexity and thus the idea of unbounded hierarchical structure. In a system of this sort specific recursion occurs unless it would be explicitly blocked. In other words, if phrases are allowed to occur inside larger phrases then finding a noun phrase inside a noun phrase is an expected consequence: (7) NP % NP þ X

(where X ¼ N, the head)

Rule (7) is a specific case of rule (6a). All things being equal, there is no reason to complicate a grammar by blocking rules like (7), especially if expressions occur which seems to be the result of rules like (7). Rule (7) produces direct specific recursion, i.e. a NP which contains a

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NP as one of its daughters. We also expect indirect specific recursion: (8) a. b.

S % NP þ VP VP % V þ S

In this case S contains another S as a granddaughter. The nodes linked in terms of indirect recursion can be separated by an indefinite number of intermediate nodes. Both general and specific recursion are possible because the complex expressions that can be contained in (necessarily) complex expressions are of the same complexity type (although possibly belonging to di¤erent categories). A di¤erent kind of system would result if the general schema for rewrite rules would be as in (9): (9) Phrase nþ1 % Phrase n þ X In this case, self-feeding is excluded because each application introduces a new type of expression. Rewrite rules of this kind, in the more specific form of (10), have been suggested to underlie the so-called prosodic hierarchy (see van der Hulst, this volume): (10) Phrase nþ1 % Phrase n þ Phrase n An indeed, given this rule format, prosodic structure would not be recursive. This also drives home the point that hierarchical structure as such does not entail recursion. In conclusion, general recursion (‘merge’) makes specific recursion a possibility which in turn makes it possible that grammars, being themselves finite, can generate an infinite number of linguistic expressions. In other words, recursive mechanisms are held responsible for the apparent discrete infinity of natural languages in the sense that when languages are thought of as sets of expressions, these sets are infinite. This is what Pullum and Scholz (this volume) call the infinitude claim. The infinitude claim also involves the idea that there is no limit on the potential length of linguistic expressions (‘there is no longest sentence’). However, whether it is ‘true’ that languages cannot be said to have a finite number of expressions is an empirical question, although, as Pullum and Scholz show, linguists generally assume that the infinitude claim is true. And therefore, these linguists design grammars that have recursive mechanisms. Tomalin (2007: 1797–1798) notes that ‘‘if the sole requirement is to generate an infinite number of structures using finite means, then an itera-

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tive, rather than a ‘recursive’, process could accomplish this, and while such a procedure may be less e‰cient than a ‘recursive’ procedure, the basic point is that a requirement for infinite structures using finite means is not itself su‰cient to motivate the use of specifically recursive procedures.’’ In defense of recursion it could be said that iteration does not adequately capture the recursive nature of the semantic structure that syntactic objects are supposed to encode. In other words, one could claim that syntax uses recursion because recursive syntactic structures express complex thoughts which themselves display this kind of combinatorial capacity. Note that, if this is so, then this specific recursive capacity is not unique to (morpho)syntax because it also characterizes our ‘conceptual constellations’ (using this as another term for our ‘thoughts’). The conceptual structure of ‘a bird in a tree on the hill’, which itself displays recursion (indeed specific recursion), if needed to be expressed, ‘inspires’ or ‘drives’ a syntactic system that iconically builds similar structures, i.e. structures that allow complex entities to be part of even larger complex entities. The claim that morphotactics uses recursion to directly express the recursive nature of conceptual structures is controversial for those, like Chomsky, who regard syntax as an autonomous system and as such, the core of human language.13 But autonomous does not have to mean unmotivated (or ungrounded).14 Seeing syntactic recursion in this light allows the possibility that iteration (or indeed other mechanisms such as intonation; cf. below) could be used as conventional ways of expressing recursive conceptual structures. Syntactic recursion (if interpreted realistically, i.e. as forming part of the grammars that people have in their heads) may be the best solution because of the achieved iconic isomorphy between syntactic and conceptual structure, but it need not be the only one. This, indeed, is the essence of Everett’s claim about Piraha˜ (Everett 2005, 2007a,b, 2008). The above reasoning (controversial as it may be) locates the source of recursion in the general recursive structure of the conceptual system. It is sometimes suggested that there is a particular conceptual basis for this kind of conceptual recursion, namely the human theory of mind which suggests a kind of embedding: (11) {I think {that she thinks {that he thinks. . . }}}

13. See Uriagereka (2009) for a defense of the idea that the relationship between syntax and semantics works in the other direction: syntax constructs semantics. 14. The claim that syntactic structure is semantically grounded is central to Anderson’s notional grammar (e.g., Anderson 1997).

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However, it could be said that the conceptual structure ‘a bird in a tree on the hill’ which does not presuppose a theory of mind has the same kind of embedding: (12) {a bird {in a tree {on the hill}}} In this case, however, conceptually, the tree is not contained in the bird, nor is the hill contained in the tree. If anything, the containment runs in the other direction: the hill, as the larger structure, contains the tree and that tree contain the bird. In any event, whether or not the (emergence of a) theory of mind, underlies conceptual recursion, we do not have to make a fuss about conceptual recursion either; it simply results if the conceptual grammar allows hierarchical grouping. If recursion is a side e¤ect of allowing hierarchical grouping that allows units of the same complexity type to occur inside each other, this applies as much to the conceptual grammar as it does to the syntactic grammar.15

3. Types of specific recursion In addition to the distinctions made in the previous section, various types of specific recursion are usually distinguished; cf. Parker 2005 and Kinsella [Parker], this volume, Karlsson, this volume and Verhagen, this volume. An important distinction is that between nested recursion (center-embedding, central embedding, self-embedding) and tail-recursion (the latter covering left-recursion and right-recursion). It is also important to contrast recursion with iteration. Karlsson (this volume) distinguishing six types of iteration (structural iteration, apposition, reduplication, repetition, listing and succession). Let us first illustrate and discuss nested recursion. (13) Nested recursion [ The man [the boy [the girl kissed] hit] filed a complaint] This ‘classical type of example’ is, however, quite atypical of recursion in language because not a single genuine one has ever been attested (Karlsson, this volume). But other cases of nested recursion do occur; cf. below. In 15. Note that if the grammar of ‘conceptual objects’ is recursive and if this ‘conceptual system’ is not seen as part of ‘universal grammar’, recursion cannot be unique to CHL if this system only comprises recursive syntax.

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nested recursion, a constituent occurs ‘in the middle’ of another constituent such that the latter constituent has material on either side of the former constituent, which makes the latter a discontinuous constituent. Centerembedding can be further di¤erentiated in several subtypes (cf. De Roeck at al. 1982; Sampson 2001: 13–14), depending on the degree of identity of the embedded units and the unit that contains it. One degree of centerembedding passes by unnoticed, but two degrees or more are often considered ‘di‰cult’ and Reich (1969), in fact, argued that sentences with center-embedding are ‘ungrammatical’; see also Christiansen (1992). Whether or not this is so, it is true that nested recursion is notoriously di‰cult to process if it exceeds one instance of embedding, although some aren’t all that di‰cult (cf. De Roeck et, al. 1982; Thomas 1995), e.g.: (14) [The fact [that the teenager [who John dates] was pretty] annoyed Suzie] In De Roeck et al. (1982), entitled ‘A myth about center-embedding’, it is reported that spontaneous, and apparently perfectly acceptable cases of multiple center-embedding do exist. Sampson (2001) reports various additional real-life cases such as:16 (15) a. b. c.

[but don’t you find [that sentences [that people [you know] produce] are easier to understand]? [the only thing [that the words [that can lose –d] have in common] is, apparently, that they are all quite common] [The odds [that your theory will be in fact right, and that the general thing [that everybody’s working on] will be wrong,] is low]

The first sentence was constructed by Anne de Roeck and then posed to Sampson as a question after he had just claimed, following the dogma at the time, that multiple center-embedding is rare and di‰cult to process. After having collected several examples in the de Roeck study and in his own later study, Sampson concludes that, although his data are not based on language corpora, multiple central embedding is certainly not ungrammatical and in many cases not that di‰cult to find and understand after 16. Marcel den Dikken (p.c.) notes that all three examples have a copular verb in the root sentences which, perhaps makes them easier than examples with noncopular verbs. He also notes that in (15c) the copular does not agree with its subject, a possible indication that the speaker of this sentence lost track of its structure.

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all. This leaves open the question what the di¤erences are between cases that are not that di‰cult, even having three degrees of embedding, and cases that apparently are, such as the apparently short and simple artificial examples in (16): (16) a. b.

[The man [the boy [the girl kissed] insulted] left] [I met the man [who saw the girl [who left this morning] this afternoon] two minutes ago]

I refer to Thomas (1995) for a review of attempts to narrow down the properties of constructions that pose clear problems and to Karlsson, this volume. Below I return to nested embedding. But first, we turn to tail recursion. (17) Tail recursion a. Left edge (creating a left-branching structure) [[[John’s] sister’s] dog’s] bone was found in the yard b. Right edge (creating a right-branching structure) [This is the car [that hit the boy [who crossed the street]]] We can clearly see that a critical di¤erence between nested and tail-recursion is that the former involves long distance relationships (i.e. relations between two units that are separated by other units), while the latter does not. This di¤erence, according to many, explains why nested recursion is much more di‰cult to process. It is usually said that tail recursion does not pose problems, although it seems to me that (17a) is certainly harder than (17b); cf. Karlsson, this volume. Informally, the di¤erence is that while we can interpret each new relative clause locally as applying to the adjacent noun, (17a) requires us to accumulate the result of each combination so that the genitive ‘s can be interpreted as a property of the steadily growing combination. Returning to nested recursion, as displayed in the sentences in (16), it is often said that such cases involve a string of the form anbn, which can be generated by the context-free grammar in (18): (18) a. b.

S % aSb S % ab

(18) generates a string in which ‘S’ occurs in the middle of a constituent S. However, it is not clear at all that grammars of real languages have rules like (18a). The rule that is responsible for the center-embedding in (16) is the same rule that causes tail-recursion in (17b): (19) NP % NP þ S

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However, the e¤ect of (19) is di¤erent depending on whether it expands an NP that is in subject position or a NP that is in object position. At least in most current syntactic frameworks, there is no mechanism to generate a constituent that is literally in the middle of the constituent that immediately contains it if constituents are always binary (which would disallow rules like 18a). Thus (16a) has something like the following structure: (20)

(15b) on the other hand has the following structure: (21)

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In other words, the bracketing in (16) is incorrect. As shown in (20) the recursive node S does not occur inside any constituent, but rather at the right edge of Noun Phrases. What this means is that there is no special mechanism for center-embedding (such as the rule in 18a). Rather centerembedding results in the following situation: (22) a. b.

A % BþC C % AþC

c.

d.

C is a right hand expansion of A while A is a left hand expansion of C (or vice versa)

Whenever we have two rules that meet the criterion in (22d) we have what is called center-embedding. What this means is that once special recursion is available (which it is once groupings can involve groupings), centerembedding is available too, unless rule pairs that meet criterion (20) would be explicitly blocked. The special feature of center-embedding that makes the relevant constructions hard to process, is that it creates discontinuous (long-distance) relationships between B’s and C’s going from both edges inward. However, it should be noted that this feature is logically independent of centerembedding; see also Verhagen’s contribution to this volume. The structure in (23) has no special recursion, thus no center-embedding, yet it creates three discontinuous relationships. Even though this structure is obviously ungrammatical in English it is so because the head complement relations, all being final, are non-English. One would think that in a language with the appropriate head final structure, an example of this sort could be constructed and that it would pose processing di‰culties, just like selfembedding structures do. Focusing on tail-recursion, several scholars have argued that relevant patterns can be analyzed as instances of iteration (Ejerhed 1982, Pulman

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(23) a.

b.

1986, Parker 2005), and Reich (1969) supports this idea with intonational evidence. Christiansen (1992) draws the conclusion that there are no linguistic phenomena that crucially require recursion if center-embedding is ungrammatical and tail-recursion can be handled with an iterative device.17 However, the claim that center-embedding is ungrammatical as such is wrong since depth 1 certainly is fine as in ‘‘The car I bought cost 1000 dollars’’. Because it is always said that phonology is not recursive, it is perhaps interesting to apply a similar argument in this domain. Assume for the sake of the argument that a word can consist of any number of feet. If true18, there would be an infinite number of possible word forms. However, that does not necessarily require a recursive device. The relevant

17. As just shown, the distinction between self-embedding and tail-recursion may be irrelevant. If specific recursion is blocked (and replaced by an iterative procedure) both phenomena are ruled out. 18. See section 9 and chapter 17 on this matter.

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property can be characterized by a rule schema that can be collapsed into one rule using an abbreviatory device: (24) Word % Foot* In actual fact, however, a more interesting characterization of the phonological structure of words might appeal to a recursive definition: (25) Phonological words (recursive definition) a. Word % foot (base case) b.

Word % Word þ Foot (inductive step)

The two approaches would create di¤erent structures: (26) a.

Iterative definition

b. recursive definition

Both types of representation have in fact been proposed. (24b) has been proposed in Metrical Theory (Liberman and Prince 1977), whereas the flat representation in (26a) has also been proposed (e.g. Halle and Vergnaud 1987) in the guise of so-called bracketed grids. The question is which representation accounts best for the properties of phonological words. (26b), for example, can be said to express di¤erent degree of prominence of feet, about which (26a) has nothing to say. In other words, just like semantic properties may be more adequately expressed in recursive morphotactic structures, phonetic properties may be more adequately expressed in recursive phonotactic structures. These issues are discussed in chapter 17. Even without considering whether the semantic and phonetic substance that underlies morphotactic and phonotactic structure is recursive, we must ask whether the properties of linguistic expressions which suggest that recursive devices are called for must necessarily give rise to these devices. In section 2, I referred to this issue when I said that a recursive structure in morphotactics may be optimal as an expression of the presumed recursive nature of conceptual structures, but this does not mean that morphotactics actually achieves the desired isomorphy in all cases, or, in some languages, at all. It may be that the morphotactics is using an iterative device, which puts a bigger burden on semantic interpretation

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because the recursive semantics now has to be reconstructed from an iterative morphotactic structure. The same applies to phonotactics. Even if one could argue that the phonetic substance is, in some sense, recursive (in fact, however, I will argue in chapter 17 that it probably isn’t), it does not follow that the phonotactics is capable of mimicking this. I briefly return to the question of recursion in phonology in section 9 and more extensively in chapter 17 in this volume. Several authors in this volume indeed explicitly ask whether the apparent recursive morphotactic structures necessarily require a formal recursive characterization. A crucial (although perhaps all too obvious) point that must be born in mind here is that the tactic devices that a linguist proposes (whatever their formal properties) are hypotheses or models for the system that humans have or use to produce and understand expressions (Itkonen 1976, Tiede and Stout, this volume), i.e., if a realist stance is adopted, rather than an instrumentalist stance (cf. Carr 1990 for discussion). These hypotheses/models may involve a formal system that uses recursion but this does not entail that the cognitive tactic system used by real people also has recursion, even if we all agree that the conceptual structure that the morphotactic structures encode is recursive. After all, the data that lead the linguist to suspect that the morphotactic system is recursive may also arise from another kind of system such as iteration, supported by intonation devices; cf. Stapert and Sakel, this volume for some explicit ideas.19 What the above reasoning misses, though, is the point we discussed in section 2 namely that specific recursion is formally available once we admit that the syntax builds hierarchical structures of a certain kind (cf. 6) which is a claim that perhaps most linguists will agree on. And if recursion is free, then self-embedding is, in principle, available, since it uses the same mechanism as tail-recursion. This means that if one wants to question the modeling choice that entails recursion, one would have to reject the idea that the context-free grammars are required for natural languages (assuming that finite state automata are su‰cient).20 However, this being said, we must also accept that constructions that employ specific recursion, espe19. By the same reasoning we can also not take for granted that semantic stu¤, or phonetic stu¤ is or isn’t recursive. That too is a modeling choice. See section 3 for some discussion of the question as to whether the conceptual system allows self-embedding. 20. One could also reject constituent-based grammars and turn to pure dependencybased grammars which have no hierarchical constituent structure.

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cially when leading to center-embedding e¤ects, are clearly avoided in natural languages, since it creates long-distance relationship which call for special computational machinery involving a stack. Whether the causes of this avoidance are ‘dismissed’ as performance factors, seriously studied as processing constraints, or even integrated into the (competence) grammar (if a distinction between ‘competence’ and ‘perfomance/processing’ is maintained) is another matter. I return to these issues, which are also discussed in various chapters in this volume, in the next sections.

4. Discussing the need for recursion on empirical grounds Even though all these formal issues are obviously pertinent, we start this collection with a series of chapters that take an empirical perspective. At the empirical level, the question needs to be raised whether (all) languages display recursive structures since it has been claimed that some languages do not have recursive structures at all, or employ (some kinds of ) recursion very modestly. Also, we need to know what the precise properties of these recursive structures are. Some of these issues were already raised in the previous section. In 1995, the linguist Richard Hudson posted the following question on the Linguist List: Does anyone know of any *empirical* investigations of center-embedding examples (aka self-embedding) such as the following? (1)

The dog the stick the fire burned beat bit the cat.

I’ve found lots of discussions (especially in introductory books – the above example is from Pinker’s ‘The Language Instinct’), but no experimental data (or any other kind of data). There’s no shortage of explanations of the ‘facts’, but there does seem to be a shortage of well-established facts to be explained. (Richard Hudson on Linguist List (4 December 1995).21

Several chapters in this volume provide a di¤erent answer to Hudson’s question than Sampson’s response which I mentioned in the previous section. For languages that have been investigated for the property of recursion using language corpora, it has been found that recursion of more than 21. http://www.linguistlist.org/issues/6/6-1705.html

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one or two steps is far from common. In spoken language, Karlsson (2007a,b; this volume) finds that self-embedding of degree 2 is virtually non-existent (which apparently contradicts Sampson’s admittedly more impressionistic findings). Tail-recursion is not uncommon, especially rightwards, although here actual language data do not show much more than degree 2 recursion. It has of course long been observed that center-embedding of degree 2 and anything higher, even though claimed to be perfectly grammatical (conforming to the design of the linguistic ‘competence’; Chomsky and Miller 1963), is rare.22 This raises the reasonable question how something so marginal can be taken to be so foundational (even definitional as in Hauser, Chomsky and Fitch 2002) for human language. If recursion is a defining feature of human language, as has been claimed, we would expect to find evidence of it in everyday talk, the primary form of language. Chomsky famously asserted that language was not designed to be produced or parsed (understood), meaning that language is not designed to be used as a communication system. Rather it is a system to facilitate thought. Additionally, it is said that language production and parsing belong to ‘performance’ and it is here, as Chomsky claims, that we find the limitations that limit the use of center-embedding. A factor that must be recognized in evaluating the ‘clash’ between the rarity of recursion and its alleged central role in language is that studies of the actual occurrence of recursion focus on specific recursion while Chomsky’s more recent claims about the centrality of recursion seem to emphasize general recursion, i.e. hierarchical grouping. Bearing this point in mind, let us ask, for the sake of discussion, language why should be recursive in the first place. If syntax emerged and exists, primarily, or perhaps exclusively, to facilitate thought, why was recursion required, if we assume that the conceptual system itself had its own syntax (which, I believe, should be an uncontroversial assumption)? Certainly Chomsky does not equate what he calls ‘syntax’ with the ‘syntax of conceptual structures’.23 So, if the two are di¤erent, why does the mind need ‘syntax’ only to duplicate conceptual syntax? What is wrong with the syntax of our conceptual system? This is the point where (most) other 22. Rather than evaluating the degree of embedding, Davis (1995), in particular considers di¤erent types of center-embedding in terms of whether, for example, a relative clause occurs inside a sentential complement, or the other way around. 23. Some authors such as Burton-Roberts (2000) think that Chomsky should. For Burton-Roberts indeed ‘syntax’ is the syntax of thought(s).

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linguists would say that ‘syntax’ did not emerge to organize our conceptual system, but to express or externalize it (cf. Jackendo¤ 2002). Together with what we call phonology, syntax is a mechanism to relate conceptual structure to utterances that can be produced and perceived. In other words, in this view, syntax (and phonology) did emerge to make communication (or at least, externalization) possible. Putting this issue aside as well, and accepting that syntactic objects are distinct from conceptual objects, we must again ask why it is necessarily the case that syntax is formally set up to allow recursion and thus selfembedding? It is said that syntactic objects with self-embedding are di‰cult to process (in performance), but what warrants their existence in competence (if that distinction is made)? Perhaps, as one might say, the problem is not that humans can’t process self-embedding, but rather that our syntactic system does not have this formal trait to begin with. Conceptually, we can understand self-embedding very easily, for example when it is based on visual information. We can see, and understand a circle that contains another circle which contains another circle and so on. Hence our conceptual system permits self-embedding with no apparent limitation, but, playing the devil’s advocate, one might say that there is no evidence that the syntax can mimic that, and if that is so, and the distinction between competence and performance is accepted, we cannot process it either. We will not try to produce it because the grammar does not deliver the appropriate input to the processing systems, and we cannot parse artificially produced examples because no parse will lead to a result that is syntactically well-formed. Clearly, we cannot here resolve all these issues, but I remind the reader that this line of reasoning does not take into account that specific recursion and thus self-embedding come for free once one admits that grammars generate hierarchical objects with groupings inside groupings of the same complexity. Although, as we have just experienced, empirical and formal issues are di‰cult to separate sometimes (among others because ‘data’ always imply an analysis of some sort), the following five chapters focus on empirical issues. These chapters show that (a) recursive structures are not very common and (b) where apparently occurring they may result from specific templatic constructions involving specific lexical items (often derived from clearly non-recursive constructions) rather than abstract recursive mechanisms. Karlsson reports that multiple nested syntactic recursion of degrees greater than 3 does not exist in written language, neither in sentences nor

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in noun phrases or prepositional phrases. In practice, even nesting of degree 2 is extremely rare in writing. In speech, nested recursion at depths greater than 1 is practically non-existing. Left-branching tail-recursion of clauses is strictly constrained to maximally two recursive cycles. Rightbranching clausal tail-recursion rarely transcends three cycles in spoken language and five in written language. On constituent NP or PP level both left- and right-branching is less constrained (especially in written language), but e.g. left-branching genitives rarely display more than two recursive cycles ([[[Pam’s] mum’s] baggage]). Laury and Ono also supply data on the use of recursion in real speech. However, they first discuss certain methodological problems that arise when one tries to establish the use of recursion in conversation. First, there is the tendency for certain types of main clauses to become grammaticized as discourse particles, in which case it is not clear whether a given item should be counted as a particle or a clause. Secondly, the authors discuss the problematic nature of the category ‘sentence’. In spontaneous spoken language, it is not always possible to tell whether a clausal unit is embedded within another, because conjunctions also have uses as independent discourse particles and also because two speakers may be involved in the production of a single sentence. Both of these problems challenge analysts who try to identify recursion in conversation. The data that Laury and Ono present show that clausal recursion is a strictly limited phenomenon in spoken language. Embedding beyond the depth of two is extremely rare, and the upper limit of clausal embedding is four. Embedding of a clause within a clause of the same type, typically used to illustrate recursion in the literature, is a vanishingly rare phenomenon. In fact, as their data show, speakers of Japanese and Finnish do not seem to be constructing complex clause combinations but rather joining clauses together one at a time. In other words, the authors conclude, recursion appears to be irrelevant to what actual speakers do. They then suggest that a more obvious characterization of clausal embedding is to simply say that speakers know, for example, how to quote, how to identify and describe referents, and how to give reasons, all in the form of one clause combination at a time. They conclude that the nature of clause combining and the limited extent of clausal embedding in ordinary conversation casts doubt on the status of recursion as a defining feature of human language. Recursion, they say, at least as far as Finnish and Japanese are concerned, may be only a linguist’s category, and not supported by the primary form of language. This remark relates to the ques-

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tion raised earlier concerning the distinction between the actual workings of language (which, unfortunately cannot be established objectively) and the way that linguists try to model these mechanisms. Whereas the two previous chapters report on the limited use of recursion in the investigated languages, the chapter by Stapert and Sakel, drawing on their own fieldwork data, tests Everett’s (2005) claims about Piraha˜ having no subordinations or other syntactically recursive structures. They consider possible alternatives for languages to express complex thought and compare their findings from Piraha˜ with discussions in the recent literature (such as the two above-mentioned chapters) on spoken versus written language and formulaic language use. They also consider the possibility that recursive structures could have been borrowed from Portuguese, with which Piraha˜ is in contact. They argue, finally, that complex ideas can be expressed by other means than syntax, and therefore that syntactic recursion may be common (relative to what we learn from the above-mentioned studies), but not universal in human language. Mithun examines a range of complement and adverbial clause constructions which could or have been characterized as displaying recursion in three genetically and distinct languages. Examples of older constructions are drawn from Central Alaskan Yup’ik Eskimo. The Yup’ik constructions are pervasive in speech and deeply entrenched in the grammar, signaled morphologically. Their origins can still be detected, however, in nominalized clauses. The adverbial clauses are marked by subordinating su‰xes descended from case markers. Somewhat younger embedded constructions can be seen in Khalkha Mongolian. A pervasive complement structure, descended from a quotative construction, is marked by a particle homophonous with a non-finite form of the verb ‘say’. This complement construction is no longer restricted to use with utterance verbs like ‘say’; it occurs with a range of other verbs as well. Still, it has not yet been extended to commentative verbs (‘be sad’, ‘be significant’), modals (‘be able’, ‘should’), achievements (‘manage’, ‘try’), or phasals (‘start’, ‘finish’). The author also discusses various adverbial clause markers in Khalkha that are descended from case su‰xes: locative (‘at N’, ‘when S’), instrumental (‘with N’, ‘as a result of S’, ‘in order to S’), and ablative (‘from N’, ‘because of S’). Examples of the youngest embedding constructions are drawn from Mohawk. Mithun says that it may seem that complement constructions have not yet arisen in the language: Mohawk speakers use simple sequences of sentences where speakers of other languages would use embedding. She then addresses the important role of prosody, showing that once prosody is taken into account, clear patterns

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of embedding are easy to identify. Other young complement constructions include demonstratives or definite articles. Again, a consideration of the prosody shows how they originated and evolved, along pathways di¤erent from those usually assumed for complements marked with demonstratives in Germanic languages. Temporal adverbial clauses appear at first to be lacking as well. Mohawk speakers seem to simply add a sentence beginning with a particle ‘at the time, now, then’, where speakers of other languages would use dependent adverbial clauses. Here once more, prosody shows that they are integrated into larger sentences. Mithun concludes that the variability in space and time calls into question the status of recursion as the basic design feature of human language. It suggests instead that recursive structures are epiphenomenal, the product of combinations of a variety of cognitive processes such as the routinization of frequentlyused structure combinations, the reification of events, and the generalization of functions of markers and constructions to ever more abstract contexts. Mithun concludes that recursive structures that occur in human languages are not uniform cross-linguistically, nor are they static within individual languages. This variety indicates, she argues, that recursion may not be the fixed, fundamental, hard-wired property envisioned. Verhagen sets out to characterize the notion of recursion from an empirical perspective and, in so doing, he shows that the role of ‘recursion’ is rather overestimated. He distinguishes between two di¤erent notions that are related but not identical, and that have played a role in di¤erent stages of 20th century theoretical linguistics: (27) a.

b.

‘Di¤erent parts of a phrase may be separated by other (indefinitely long) phrases’, e¤ectively the notion of ‘long distance dependency’. ‘The specification of certain phrases requires the application of a rule to its own output’.

He claims that if (and only if ) both cases occur in combination we have what computer scientists call ‘true recursion’ (i.e. center-embedding), which requires a special kind of computational architecture, in order to keep the intermediate results of the calling procedure in memory while the embedded instance is being executed. If situation (a) does not hold, embedded phrases occur at the ‘edges’ of embedding phrases and processing architecture capable of handling iteration su‰ces, because special architecture to store and retrieve intermediate results is not required (although their description may still involve a recursive rule).

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Using the above distinctions, Verhagen critically examines three phenomena that have been taken as instantiating recursion in the sense of sentential embedding, viz. embedding of adverbial clauses in other adverbial clauses, nonfinite complementation in causative constructions, and longdistance Wh-movement (cf. examples (26a–c) respectively): (28) a. b. c.

[ S Because our flight turned out to be cancelled [ S when we arrived in Madrid]], . . . He made [ S me understand the situation] Whoi did Mary say [ S that John kissed ti ]

On the basis of actual usage data, Verhagen shows that none of these classic cases actually requires a truly recursive specification. Empirically, a system that uses relatively specific templates is at least indistinguishable from one using general recursion, and is in some respects even more adequate (which has obvious consequences for the issue whether recursion can have been a target of selection). He does acknowledge that recursion is relevant for grammar for some ‘pockets’ of rather specific phenomena, adding that it may very well have been produced by cultural evolution (involving literacy) rather than genetic evolution.

5. Discussing the need for recursion on formal and functional grounds The last three mentioned chapters suggest that many apparently recursive constructions may be the result of specific templates (which figure specific lexical items), rather than free-wheeling recursive mechanisms. As mentioned, this raises a question concerning the di¤erence between formal properties of grammars and the languages that they model. In the following five chapters, this issue is discussed from formal and functional perspectives. Pullum and Scholz start out observing that certain remarks in the linguistics literature over the past few years suggest that some linguists think of infinitude (i.e. the infinity of language if thought of as a set of expressions generated by a grammar) as a universal. That is, these linguists, they say, believe that it has been empirically established that there are infinitely many grammatical expressions in human languages, and that we need recursion in grammars in order to account for this. Pullum and Scholz examine the arguments given for the infinitude claim, and show that they depend on an unwarranted assumption: that the only way to

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represent syntactic properties is through a generative grammar with a recursive rule system. They then explore some of the reasons why linguists have been so willing to accept language infinitude despite its inadequate support and its lack of linguistic consequences. These authors suggest that the infinitude claim seems to be motivated chiefly by a lingering adherence to the outdated notion that languages should be regarded as sets. It is not motivated by considerations of the creative aspect of language use, or opposition to associationist psychology, or the putative universality of iterable linguistic structure such as recursive embedding or unbounded coordination (which are probably not universal anyway). Langendoen examines Pullum & Scholz’s argument that there has never been an adequate demonstration for the claim that natural languages contain infinitely many expressions, and concludes that they are correct in asserting that the question remains open. He then proposes a method whereby it can be determined at least under certain conditions whether a language has infinitely many expressions, and finally assesses the claim in Postal & Langendoen (1984) that natural languages contain transfinitely many expressions. As discussed in section 1, Hauser, Chomsky and Fitch (2002) claim that a core property of the human language faculty is recursion and that this property yields discrete infinity of natural languages. On the other hand, recursion is often motivated by the observation that there are infinitely many sentences that should be generated by a finite number of rules. According to Tiede and Stout it should be obvious that one cannot pursue both arguments simultaneously, on pain of circularity. The main aim of their chapter is to clarify both conceptually and methodologically the relationship between recursion and infinity in language. They argue that discrete infinity is not derived, but a modeling choice. Furthermore, many arguments, both for recursion and infinity in language, crucially depend on particular grammar formalisms. Thus, care should be taken to distinguish, on the one hand, whether to derive infinity from recursion or the other way around, and, on the other hand, the role of recursion in language in general from the role of recursion in specific grammar formalisms. Pursuing a similar line of inquiry, Perfors, Tenenbaum, Gibson and Regier state that recursion involves an inherent tradeo¤ between simplicity and goodness–of–fit: a grammar with recursive rules might be simpler than one without, but will predict the sentences in any finite corpus less exactly. As a result, one cannot conclude that any particular grammar or grammatical rule is recursive, given a corpus, without some way to quantify and

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calculate this tradeo¤ in a principled way. They present a Bayesian framework for performing rational inference that enables us to quantitatively evaluate grammars with and without recursive rules and normatively determine which best describe the sentences in a corpus of child-directed spoken English. Their results suggest three main points. First, they suggest that rational principles would favor a grammar with a specific type of recursive rule, even if there are relatively few instances of particular recursivelygenerated sentences in the input. Second, they suggest that the optimal grammar may occupy a representational middle ground between fully recursive and non-recursive. Finally, their results suggest that the optimal grammar may represent subject NPs distinctly from object NPs. According to Harder functional linguists tend to think that recursion as an issue in linguistics is an artifact of a Chomskyan formalism, i.e. from a functionalist point of view, the mathematical properties of models used to describe languages do not automatically qualify as features of real languages. Like everything else, human languages can be simulated by a formal model, but, as we have seen several times, that does not entail that the properties of the model are also properties of the language. However, at the same time, functional linguists do not dispute that languages like English possess syntactic mechanisms that can be formally modeled by recursion. For a functionalist linguist, this then poses the challenge of considering whether recursion has a functional role in language. Recursion, he says, may not be the right way to account for linguistic creativity, but functionalists need to o¤er their own take on the issue – including the question strikingly raised by Piraha˜ (cf. Everett 2005), of what the precise relations are between recursion in culture, cognition and language.

6. Evolutionary Perspectives The HCF paper also addresses the issue of language evolution, a subject that has moved to the center of attention during the last couple of decades, despite Chomsky’s earlier pessimism that anything significant could be said about this subject. By proposing that the innate human capacity for language is not a ‘richly articulated’ mental system (as used to be the case in generative grammar), but a rather minimal system that merely contains a recursive device (in the sense of general recursion; cf. 5), the question of how language came about is considered more manageable by HCF. Human language could have come about abruptly from a simpler

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word-based system (allowing one-word utterances only) because the only thing that is needed is to add a recursive device (cf. Reuland 2009). Hornstein (2009) suggests an even more specific mechanism that made recursion possible: endocentricity or headedness, or what he calls ‘labeling’. Turning back to the rules in (6), while X and Y may be identical (which produces specific recursion), it is usually claimed that X and Z must be identical, which is to say that the category label of a complex syntactic object is projected from one of the daughters, called its head. If a complex word is a noun, one of its daughters must be a noun as well (in derivational morphology this would be a noun-making a‰x, while in compounds it would be simplex or complex word), and if a phrase is a noun phrase it must contain a word of the category noun. According to Hornstein (2009: 59–60) it is the emergence of this specific labeling convention (i.e. projection from the head) which kick started recursion in the evolution of language: (29) a. b.

XPhrase % YPhrase X (e.g., NP % APN) XWord % YWord X (e.g., N % VNaff )

Indeed, it would seem that this rule meets the criterion of being recursive on the understanding that the label of a head and the label of its mother node are strictly identical, which means that we must ignore or eliminate the di¤erence between phrase labels (XP) and word labels (X) and thus replace (28a) by (28b): (30) a. b.

XPhrase % YPhrase X X % YX (e.g., N % AN)

However, by locating recursion in this labeling convention, as Hornstein does, the recursive symbol on the right side of the arrow is the head of the expansion, whereas the usual approach, while accepting the idea of headedness, locates recursion in the dependent (or complement) to the head: (31) a. b.

VP % VPV V % V1V2

If (31b) is the counterpart of (31a), by virtue of eliminating the di¤erence between XP and X, V2 would be the head, while V1 would make the rule recursive (because of its identity to the V to the left of the arrow). In conclusion, it is not clear to me how Hornstein can locate the source of recursion in the head labeling convention, i.e. in endocentricity, if recursion in

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the usual sense results from identity between the symbol on the left and the non-head symbol on the right of the arrow. Taking this one step further we might say that Hornstein’s idea that headedness entails recursion is correct after all, in the sense that endocentricity leads to what I will call recursion following from adjunction. Indeed, when linguists speak of adjunction they refer to a situation in which a head is expanded with a dependent with the result being a category that is identical to category of the head. Normally this means that the resulting category has the same category and the same complexity as the head. In fact, the rule in (19) (NP % NP þ S) was a rule of precisely this sort. Hornstein seems to include the case in which the head is simplex (i.e. lexical category), while the result is phrasal. But by ignoring this di¤erence one might say, then, that headedness entails recursion following from adjunction. However, this kind of recursion di¤ers from the ‘prototypical’ case in which a combination has the same category status as the dependent, which I will call recursion following from subjunction. It remains unclear how the former type of recursion automatically leads to the latter type. Whatever the merit of Hornstein’s suggestion, there can be no doubt that the step from one word utterances to multiword utterances with hierarchical structure (perhaps mediated by a two-word ‘proto-language’) was a crucial step in the development of human language, but it remains questionable whether this is the only property that sets human language apart from other communication systems (cf. Jackendo¤ and Pinker 2005). The evolutionary angle is examined in the following four contributions. Kinsella evaluates the HCF claim that recursion is the one property which sets human linguistic abilities apart from any other system of communication or cognition which she considers to be fundamentally flawed. Like Jackendo¤ and Pinker (2005) she argues that, first, properties of language independent of its recursive nature are unique to the system and, second, recursion is exhibited in domains outside human language. Thirdly, she argues that language works equally well without recursion. Progovac focuses her attention on what she calls a small clause grammar which co-exists, in English, with a sentential grammar. The latter is a robust system of functional projections and structural relationships (tense, case checking, complementizers), while the former does without any such mechanisms, and without a possibility for recursion/embedding. She proposes that this small clause grammar is a vestige/‘‘living fossil’’ of a previous stage of morpho-syntax which utilized no functional categories (which she claims, are necessary for embedding). Her conclusion is that a relevant functional projection/category is necessary to facilitate embedding. She

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argues that if a human grammar with Merge, but without recursion, is possible, then recursion cannot be the defining property of human language, and neither can Merge alone be responsible for all its recursive power (contra the hypothesis in Hauser, Chomsky, and Fitch 2002). This perspective opens up a new way of looking at some puzzling constraints in syntax, including Subjacency. Rogers and Hauser discuss acoustic pattern recognition experiments, often called artificial language learning experiments, which, they claim, hold the promise of providing a method for dissecting the ontogenetic and evolutionary building blocks of the language faculty. In particular, by studying the capacity to acquire specific fragments of linguistic computation in human infants and nonhuman animals, it is possible to determine which psychological processes are available to the developmentally immature human learner and which to humans’ evolutionarily ancestors. They specifically explore the formal mathematical structure of these experiments and develop criteria for their design and interpretation based on the Sub-Regular Hierarchy, a hierarchy of complexity classes which correspond to a hierarchy of cognitive capabilities that are relevant to any faculty that processes acoustic stimuli solely as sequences of events.

7. Recursion and the Lexicon In most articles, specific recursion is treated as a property of syntactic, i.e. sentence-level expressions. The following two articles examine the role of recursion with reference to the lexicon, although the authors take very different perspectives and arrive at seemingly contradictory conclusions. Koster defends a lexicalist approach to recursion in syntax. In a lexicalist framework, syntactic base structures are no longer generated independently of the lexicon but are seen as projections from lexical elements. Chomsky (1981, 31–32) discusses the redundancy problem that arises with lexicon-independent rules: these rules would introduce properties as hierarchical phrase structure organization and recursion, while these elements also exist independently, namely as the projection properties of lexical items. Surprisingly, Koster says, Minimalism reintroduced lexicon-independent structure generation in the form of Merge. This, then, brings back the redundancy problem. As a remedy, Koster proposes to maintain a version of X-bar theory, in which structure-building (with hierarchical organization and recursion) is seen as filling the slots that exist as a matter of lexical projection. Syntactic computation is done on the basis of these lexical-

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cartographic structures and involves the selective, strictly local sharing of properties: by sisters (horizontal) and by daughters and mothers (vertical). By iteration of vertical property sharing (percolation) and in combination with horizontal property sharing, most forms of syntactic construal (including ‘‘movement’’) can be accounted for. In the framework proposed by Koster, recursive Merge is not a rule of grammar, but a characterization of the abstract background capacity that humans built into language by inventing a complex lexicon, as a matter of free, agentive application. In that respect, he claims, language is part of human culture and di¤ers from biological organology, which, clearly, involves non-agentive functionality. Juarros-Daussa’s starting point is the basic fact of argument structure that verbs cannot take more than three core arguments – more precisely, one subject, or external argument, and two objects, or internal arguments, as in the English verb give (32a). Introducing a conceivable additional participant without the help of a lexical preposition (such as for in (32c) below), which contributes its own argument-taking abilities, results in ungrammaticality (32b): (32) a.

[The LinguistList] gave [nice prizes] [to the winners of the challenge]

b.* [The LinguistList] gave [nice prizes] [to the winners] [(to) the students] c. [The LinguistList] gave [nice prizes] [to the winners] [for the students] In her chapter, the above observation is formulated as the Two-Argument Restriction (TAR): ‘‘A single predicate can have at most two internal arguments and one external.’’ The author claims that the TAR is an unrestricted universal (in the sense of Croft 1990) and shows that valencyincreasing operations such as applicative and causative constructions, which present an apparent challenge, do not violate the TAR. She further argues that, since there is no known processing reason not to lexically associate more than three (two) participants to a predicate, the TAR is syntactic in nature, and it is one of a family of architectural constraints that determine and limit possible attainable languages (in this case possible argument structures). Following this idea, she shows that the framework of lexical syntax put forth by Hale and Keyser (2002) is especially suited to derive the TAR. In her proposal, deriving the TAR crucially involves negating the existence of a recursive function in the domain of argument structure.

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8. Recursion and Morphology As traditionally understood, complex words display direct or indirect specific recursion. This can be most easily demonstrated in the domain of compounding. Consider the following compound rules in English (taken from van der Hulst 2008): (33) Compounding N%NN N%AN N%VN

arm - chair green - house jump suit

V%VV V%NV V%AV

break dance steam roll white wash

A%AA A%NA A%VA

red hot nation wide -

In each of the three blocks of rules, the first one meets the criterion of being recursive: the dependent is of the same type as the whole construction. In the area of derivation we also attest recursion: (34) a.

Su‰xation N % N N a¤ friend - ship, child - hood, host - ess, hand - ful N % A N a¤ tall - ness, free - dom, loyal - ist, real - ism N % V N a¤ sing - er, employ - ee, grow - th, inform - ant V % V V a¤ V % N V a¤ victim - ize, beauti - fy V % A V a¤ black - en A % A Aa¤ green - ish A % N Aa¤ boy - ish, wood - en, nation - al, pain - ful A % V Aa¤ read - able, help - ful, harm - less, act - ive

b.

Prefixation N % Na¤ N anti - war, ex - president, super - structure N % Na¤ V N % Na¤ A -

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V % Va¤ V un - do, re - read, mis - align V % Va¤ N en - slave, be - witch V % Va¤ A be - little A % Aa¤ A un - fair, dis - loyal A % Aa¤ N A % Aa¤ V Recursion results not only from rules that are themselves recursive but also from rule sets that form recursive chains which produce indirect recursion: (35)

If even English, with its modest morphology, displays specific recursion, it is to be expected that in polysynthetic languages recursion will play an even greater role in the morphology; cf. Mithun, this volume. Lander and Letuchiy present a survey of various morphological phenomena in Adyghe, a highly polysynthetic language of the Northwest Caucasian family, such as multiple applicatives, multiple propositional operators (e.g., tense markers), and double causatives that all seemingly instantiate recursion. It is argued, however, that the corresponding derivations di¤er in what concerns their ‘recursability’, i.e., their inclination to recursion. Moreover, they propose that the degree to which a derivation is ‘recursable’ correlates with the extent to which a derivation a¤ects the meaning of a stem and the structure of the verb. Since no apparent syntactic restrictions of this kind are found, this suggests that despite the

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existence of morphological recursion, the latter is still somewhat more constrained than recursion in syntax.

9. Recursion and phonology It is quite common to read that phonology is not recursive. To illustrate this point it is often mentioned that, for example, we do not find ‘syllables inside syllables’; cf. the quote from Pinker and Jackendo¤ given earlier. On the other hand, Ladd (1986, 1996) argues that higher-level prosodic structure allows (limited) recursion. I also refer to Wagner (2005, 2007a, 2007b) for extensive discussion of these matters, again with specific reference to higher levels of prosodic organization. Since phonology is somewhat underrepresented in this volume, I included a chapter on this subject in this volume. In this chapter van der Hulst first discusses recursion at lower levels of organization (syllable and foot) showing, contrary to popular belief, that it is possible to think of codas as ‘syllables within syllables’ and, also, once this move is made, to reanalyze feet in terms of recursive syllable structure. Second, he turns to recursion at higher prosodic levels reviewing some of the above-mentioned literature. One central issue that emerges from this discussion is that the kind of data that suggest recursion at higher levels could also be taken as supporting the idea that phonological rules (for example, rules for phrasal accentuation) make direct reference to the recursive syntactic structure, in which case we have no argument for recursion in the prosodic structure as such (cf. Wagner 2007a, 2007b). A second central theme regards the fact that the recursion of prosodic structure itself, if such can de demonstrated to exist, would be caused by (a) adjunction of ‘stray’ units (creating one level of recursion) and (b) by the ‘desire’ to make prosodic structure isomorphic to the syntactic structure which may take the depth of prosodic recursion further. However, in this latter case, as has been argued in Giegerich (1985), recursive structure often tends to be replaced by a flatter structure which is more rhythmic. It would seem, then, that rhythmic forces suppress excessive recursion in phonology or that phonological recursion and rhythm occur at di¤erent levels of representation. Hunyadi introduces the principle of tonal continuity to account for the continuous tonal phrasing of discontinuous structures with nested embedding and suggests that what underlies this cognitive computational process is the bookmark e¤ect. He shows that the computational di¤erence between nested recursion and iteration correlates with their prosodic di¤erence, whereas tail recursion and iteration (which are computationally indistin-

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guishable) also have a similar prosodic realization. Through grouping experiments with (a) abstract visual elements, (b) abstract prosodic elements and (c) actual linguistic utterances Hunyadi shows that speakers use temporal and/or tonal variation to indicate various kinds of grouping and he attributed the underlying principles to more general cognitive strategies because, apparently, they play a role outside language. For temporal variation, recursive embedding is denoted by pre-boundary shortening and de-embedding by pre-boundary lengthening so that for each embedded phrase, the pause preceding it is shorter than the pause following it and that with each level of recursive embedding these respective pauses decrease at the point of embedding and increase at the point of de-embedding. For tonal variation, recursive embedding is denoted by the pre-boundary lowering of the tone and de-embedding by the pre-boundary raising of the tone so that with each level of recursive embedding a given phrase is embedded at a pitch level lower than the previous one. Hunyadi’s paper, specifically his discussion of the principle of tonal continuity relates to Mithun’s paper in that this principle demonstrates that intonation can be used as a mechanism to encode embedding and this, one might argue, does not necessarily presuppose a syntactic embedding mechanism. In other words, semantic center-embedding can perhaps be encoded in terms of intonation alone, which suggests, in line with several other chapters that syntactic recursion, or, specifically, syntactic center-embedding is not the only grammatical device that can be used to encode semantic center-embedding. A final remark about intonation. Intonation is not ‘phonology’. The intonational tune is not merely part of the phonological side of linguistic expressions. Intonational tunes are the product of an intonational grammar which produces intonational expressions that have morphotactic, semantic and phonotactic components; cf. Gussenhoven (1984). As such, the question can be raised whether the intonation grammar displays recursion in its semantic, morphotactic or phonotactic component. I will not explore that issue here.

10. Recursion outside Syntax Finally, the question arises as to the language-uniqueness of recursion. It has been acknowledged that other human cognitive systems also display recursion. In this connection, some mention the numerical system. Chomsky (2005: 6), however, suggests that the numerical system may be the same recursive merge mechanism that is responsible for linguistic expres-

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sions (cf. Tomalin 2007: 1794–5). Others refer to ‘social intelligence’, or more specifically, the other mind capacity as being inherently recursive. Does this mean that recursion is a general cognitive faculty that is used in language, as it is in other cognitive modules? Or is it the case that this more general trait occurs in di¤erent modules as, let us say, homologous traits? The contribution by Levy presents a biologically plausible approach to syntax that treats language as a transduction between propositional meanings and sequences of symbols, conceptualized as a sequential planning task. Recursion emerges as part of a general solution to the problem of transducing the fillers of semantic roles (agent, patient, experiencer, theme) in this manner. His model uses high-dimensional, low-precision vectors of random noise as a plausible stand-in for neural activations. Such vectors support the encoding of semantic role/filler bindings and variable substitutions required for language but (unlike the automata corresponding to traditional grammars) degrade gracefully as more complex representations are encoded. The model thereby o¤ers a plausible account of depth limitations and other psychological phenomena associated with recursion, which are treated as a tangential ‘‘performance’’ issue in traditional grammarbased approaches. The author provides an example of how the model learns a simple grammatical construction from a single instance, avoiding the psychological and biological implausibility of previous neurallyinspired approaches. After describing the relationship of this representational scheme to traditional grammatical categories, he concludes with a discussion of the possible origins of linguistic universals not explained by the model. Zimmerer and Varley show that recursion may be inaccessible to an agrammatic patient in his language, or language-like computations while it is readily available in other cognitive domains. Their report presents data from PR, an agrammatic aphasic patient who shows no signs of processing recursion in his syntactic output and comprehension, but performs well in domains claimed to be recursive, namely mathematics and Theory of Mind. One response to this dissociation might be to claim that PR’s language deficits lie in performance only, linguistic competence being intact. To address this claim, the authors present new data from two artificial grammar learning experiments in auditory and visual modalities. After long exposure to strings of stimuli structured by the grammar AnBn, PR showed an atypical pattern when asked to judge new strings on their correctness. The results suggest that severe aphasia can represent a failure of syntactic competence. It is concluded that in the mature mind, even without syntactic competence, recursion in other cognitive areas is possible.

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11. Final remarks Several general conclusions can be drawn from the collection of chapters in this volume, although these conclusions are not necessarily shared by all authors. First, to formally represent certain linguistic phenomena in terms of recursive devices is a modeling choice. Other modeling choices are possible and should be considered. Second, there is dispute on what the linguistic phenomena are when one does not wish to rely on ‘grammatical intuitions’ which, supposedly, reflect the principles of competence without being cluttered by performance factors. Many linguists adopt a more empirical stance, and insist on inspecting what occurs in actual language use. They then find that the types of constructions that can be modeled in terms of recursive devices are not that common, and, when present, are of limited depth. Third, what I have called specific recursion (A within A) does not have to be regarded as a basic linguistic mechanism. Rather this form of recursion (as is self-embedding) is implicit in a combinatorial system that allows combinations to enter into further combinations. Fourth, it might be argued that morphosyntactic structures display recursion because these structures want to be isomorphic to semantic structure which is inherently recursive. Phonological structures, on the other hand, accommodate phonetic substance which is not inherently recursive but rather rhythmic which induces a flat, non-recursive structure. Nonetheless, phonological structure seems to tolerate limited recursion (competing with rhythmic flattening) in order to increase isomorphy to morphosyntatic (and thus indirectly semantic) structure. Fifth, semantic recursion can be encoded in terms of morphotactic specific recursion, but other mechanisms, such as intonation can also be used to encode semantic embedding. These various points are not conclusions that all authors agree on. Still, these are arguments that the reader will find in this book which, I believe, deserve serious consideration.

References Burton-Roberts, Noel 2000 Where and what is phonology?: A representational view. In Burton-Roberts, N., Carr, P., Docherty, G. (eds.), Phonological Knowledge: Its Nature and Status. Oxford University Press, Oxford, pp. 39–66.

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Christiansen, Morten H. 1992 The (non)necesssity of recursion in natural language processing. Proceedings of the 10th annual conference of the cognitive science society. Indiana University, Indiana: Cognitive Science Society, July/August, 665–670. Chomsky, Noam 1975 The logical structure of linguistic theory. The MIT Press, Cambridge. Massachusetts. 1981 Lectures on government and binding. Foris, Dordrecht. 1995 The Minimalist Program. The MIT Press, Cambridge. Massachusetts. 2005 On Phases. MIT, ms. Chomsky, Noam and George A. Miller 1963 Introduction to the formal analysis of natural languages. In R.D. Luce, R.R. Bush and E. Galanter (eds.), Handbook of mathematical psychology. Vol. II. John Wiley, New York, 269–321. Croft, William 1990 Typology and Universals. Cambridge University Press, Cambridge. Davis, Hugh C. 1995 To Embed or Not to Embed. . . Communications of the ACM (CACM), 38(8): 208–209. De Roeck, Anne, Roderick Johnson, Margaret King, Michael Rosner, Geo¤rey Sampson, and Nino Varile 1982 A Myth about Centre-Embedding. Lingua 58: 327–340. Ejerhed, Eva 1982 The processing of unbounded dependencies in Swedish. In E. Engdahl and E. Ejerhed (eds.), Readings on Unbounded Dependencies in Scandinavian Languages. Almqvist & Wiksell Intl. Stockholm, pp. 99–149. Everett, Daniel 2005 Cultural constraints on grammar and cognition in Piraha˜: Another look at the design features of human language. Current Anthropology 76(4): 621–646. 2007a Cultural constraints on grammar in Piraha˜: A reply to Nevins, Pesetsky and Rodrigues (2007). LingBuzz article archive (http:// ling.auf.net/lingBuzz/000427) 2007b Challenging Chomskyan Linguistics: The Case of Piraha˜. Human Development 50: 297–299. 2008 Don’t sleep there are snakes: life and language in the Amazonian jungle. New York: Pantheon Books/London: Prolile Books. To appear. Piraha˜ culture and grammar: A response to some criticism. Fitch, W. Tecumseh, Marc D. Hauser, and Noam Chomsky 2005 The evolution of the language faculty: Clarifications and implications. Cognition 97: 179–210. Gentner, T. Q., K. M. Fenn, D. Margoliash, and H. C. Nusbaum 2006 Recursive syntactic pattern learning by songbirds. Nature, 440: 1204–1207.

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Giegerich, Heinz J. 1985 Metrical Phonology and Phonological Structure. Cambridge University Press, Cambridge. Gussenhoven, Carlos 1984 On the grammar and semantics of sentence accents. Dordrecht: Foris. Hale, Ken and Samuel Keyser 2002 Prolegomena to a Theory of Argument Structure. The MIT Press, Cambridge, Mass. Halle, M. and J.-R. Vergnaud 1987 An essay on stress. Cambridge, Mass.: MIT Press. Hauser, Marc D., Noam Chomsky, and W. Tecumseh Fitch 2002 The faculty of language: What is it, who has it, and how did it evolve? Science 298: 1569–1579. Hornstein, Norbert 2009 A theory of syntax. Minimal operations and universal grammar. Cambridge: Cambridge Univesity Press. Hulst, Harry van der 2008 Linguistic structures. Kendall/Hunt Itkonen, Esa 1976 The Use and Misuse of the Principle of Axiomatics in Linguistics. Lingua 28: 185–220. Jackendo¤, Ray 2002 Foundations of Language: Brain, Meaning, Grammar, Evolution. Oxford University Press, Oxford. Jackendo¤, Ray and Steven Pinker 2005 The nature of the language faculty and its implications for evolution of language (Reply to Fitch, Hauser, and Chomsky). Cognition 97: 211–25. Karlsson, Fred 2007a Constraints on multiple initial embedding of clauses. International Journal of Corpus Linguistics 12(1): 107–118. 2007b Constraints on multiple center-embedding of clauses. Journal of Linguistics 43(2): 365–392. Kuryłowicz, Jerzy 1952 Uwagi o polskich grupach spo´łgłoskowych. Biuletyn Polskiego Towarzystwa Je˛zykoznawczego 12: 221–232. Ladd, D. Robert 1986 Intonational Phrasing: The Case for Recursive Prosodic Structure. Phonology Yearbook 3: 311–340. 1996 Intonational Phonology. Cambridge: Cambridge University Press. [2nd edition 2008] Liberman Mark and Alan Prince 1977 On stress and Linguistic Rhythm. Linguistic Inquiry 8: 249–270. Marcus, Gary 2006 Startling starlings. Nature 440: 1117–1118.

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Nevins, Andrew Ira, David Pesetsky and Cilene Rodrigues To appear Piraha˜ exceptionality: A reassessment. Parker, Anna R. 2006 Evolution as a Constraint on Theories of Syntax: The Case against Minimalism. PhD Dissertation, University of Edinburgh Peano, G. 1889 Arithmetices principia nova methodo exposita. Opera Scelte 2: 20–55 (Reptinted in Unione Matematica Italiana, 1957–1959. Pinker, Steven and Ray Jackendo¤ 2005 The faculty of language: What’s special about it? Cognition 95: 201–236. Postal, Paul M. and D. Terence Langendoen 1984 The Vastness of Natural Languages. Blackwell, Oxford. Pulman, S.G. 1986 Grammars, Parsers, and memory limitations. Language and Cognitive Processes 2, 197–225. Reich, Peter 1969 The finiteness of natural language. Language 45, 831–843. Reuland, Eric 2009 Language: symbolization and beyond. In R. Botha and C. Knight (eds.). The Prehistory of Language. Oxford: Oxford University Press, 201–224. Sampson, Geofrrey 2001 Empirical Linguistics. London/new York: Continuum Thomas, James Davis 1995 Center-embedding and self-embedding in human language processing. PhD dissertation, MIT. Tomalin, Marcus 2007 Reconsidering recursion in syntactic theory. Lingua 117, 1784– 1800. Uriagereka, Juan 2009 Syntactic Anchors. Cambridge: Cambridge University Press. Wagner, Michael 2005 Prosody and recursion. Ph.D. diss., Massachusetts Institute of Technology, Cambridge, MA. 2007a Prosodic Evidence for Recursion? Ms. Cornell University. 2007b Prosody and Recursion in Coordinate Structures and Beyond. Ms. Cornell University.

Part I.

Discussing the need for recursion on empirical grounds

1. Piraha˜ – in need of recursive syntax?1 Jeanette Sakel and Eugenie Stapert

1. Introduction Since the publication of the article ‘The faculty of language: what is it, who has it and how did it evolve?’ by Hauser, Chomsky, and Fitch (2002) recursion has assumed a prominent place in the discussion of what aspects of our communication system are unique to humans and human language. The hypothesis put forward in that article is that recursion is the only property unique to human language. The entailments of this hypothesis are that recursion would be found in all languages spoken by humans and that a human language that does not use recursive structures would not exist. This claim has provoked a number of reactions, most noticeably Everett (2005), who argues that Piraha˜, the last surviving member of the Muran language family, does not exhibit recursive structures in its syntax, even though it undoubtedly is a language spoken by humans. Piraha˜ is spoken by approximately 450 people in the Brazilian state of Amazonas, in small settlesments along the river Maici. The Piraha˜ live a largely traditional life as hunter-gatherers and rarely seek contact with the outside world. Since the publication of Everett’s (2005) article, there has been an ongoing, mainly web-based, discussion as to whether Piraha˜ exhibits recursive structures, e.g., on LingBuzz by Nevins, Pesetsky, and Rodrigues (2007) and a reply by Everett (2007a), on Language Log by Liberman (2006), Everett (2007b), Sakel’s (2007a) and Slobin’s (2007) Letters to the editor of the journal Human Development and Everett’s reply (2008). The

1. We would like to thank Dan Everett, Nigel Vincent, David Denison, Ted Gibson, Mike Frank, Manfred Krifka, Uli Sauerland, Harry van der Hulst and three anonymous reviewers for comments on earlier versions of this article. We would also like to thank Alison Wray for an inspiring discussion on formulaic language and esoteric communication. This article is based on a presentation at the conference on ‘Recursion in Human Language’ in Normal, Illinois (April 2007).

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issues brought up are far from being resolved. Some of the ambiguity in the present discussion is based on contradictory analyses of Piraha˜ data in two publications by Everett (1986, 2005). Everett’s earlier work (1986) contains an extensive description of embedded clauses in Piraha˜, whereas he rejects the existence of these structures in his more recent work (2005). Due to this discrepancy, researchers who support the hypothesis that Piraha˜ has recursive syntax usually cite data presented by Everett (1986), discarding the new analysis (2005). While the discussion is very focused, few people so far have looked at Piraha˜ language facts other than those given in the two publications by Everett (1986, 2005), comparing them to other indicators as to whether recursion is necessary in a human language. The present article sets out to add new data to the discussion. It is based on our field research among the Piraha˜ and brings together research data from experiments and elicitation, as well as analysis of spontaneous speech.2 We look at first-hand language data in three areas of Piraha˜ grammar which we would expect to be expressed by recursive structures if these existed, and then address our findings in the light of a number of recent findings in linguistics. The article is divided up in the following way: first we will discuss the su‰x -sai, which Everett (1986) reported to be an indicator of embedding, and which features prominently in the recent discussions. We will then look at the other side of the coin and investigate what alternative strategies can be used to express complex situations. Following this, we will address the question whether recursive structures could enter the language through language contact with Portuguese. Finally we will examine our results in the light of recent publications to gain insights into whether recursion is really a necessary notion in human language. This article is a collection of several arguments related to the question whether recursion is necessary in Piraha˜.

2. Our field research was funded by the CHLaSC project (within the EU F6 programme). The fieldwork was facilitated by Dan Everett, who accompanied us to the field, though the research data presented here are entirely our own and based on our own interpretations. Some of the experiments were carried out with Dan Everett as the interpreter, while others were conducted monolingually without his involvement. These settings did not result in any noticeable di¤erences in our language data. We took great care to carry out all experiments as scientifically and objectively as possible.

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5

2. The su‰x -sai The su‰x -sai figures prominently in recent discussions of recursion. Everett (1986: 277) classified it as a nominaliser and an obligatory indicator of embedding in conditional clauses (1986: 264). In his later approach (2005: 21), however, he argues that -sai does not mark syntactic subordination.3 We have studied this marker’s functions, in particular with respect to whether it is an obligatory marker of embedding. We will here look at two very di¤erent constructions in which -sai is used. The first part of our discussion is based on findings by Stapert (2007) and Stapert et al. (in preparation). They tested the functions of -sai experimentally in a sentence repetition task. In this experiment, two clauses representing semantically connected propositions, such as it is raining and I don’t go to the forest were combined. The su‰x -sai was added to either the verb of the first or that of the second clause, cf. (1a) and (1b) and the informants were asked to merely repeat the sentence. Piiboi-bai-sai ti kaha´pi-hiaba. rain-INTENS-SAI 1 go-NEG ‘If it is raining I won’t go.’ b. Piiboi-bai ti kaha´pi-hiabi-sai. rain-INTENS 1 go-NEG-SAI ‘If it is raining I won’t go.’

(1) a.

A total of nine speakers of Piraha˜ – 7 women and 2 men – participated in this language task. In their response, informants attached -sai to the first clause, the second clause, both clauses, or neither of the clauses (cf. 2) independent of the input and with no reported change in meaning or judgement of (un)grammaticality. (2) Piiboi-bai ti kaha´pi-hiaba. Rain-INTENS 1 go-NEG ‘If it is raining I won’t go.’ Out of a total of 39 relevant responses -sai was attached to both clauses in 9 cases, to none in 6, and to one clause – either the rain part or the forest part – in 24 instances4. 3. Everett, p.c., argues that -sai is an old information marker. 4. For a detailed description and analysis of the results of this task see Stapert (2007).

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The alternative in which -sai does not occur in either clause (2) was not part of the input of the experiment. Hence a simple repetition of an ungrammatical sentence from the input is ruled out. This means that the concept can be expressed without the presence of -sai; thus this marker can not be an obligatory marker of embedding. Still unclear, however, is the exact function of -sai in these constructions, but it does not appear to be a marker of subordination, as originally claimed by Everett (1986).5 A related investigation carried out by Sakel and Stapert for the present paper was the analysis of various other constructions with -sai, both in spontaneous speech and elicitation. The results show that -sai occurs most frequently in constructions expressing quotation of the type hi gaisai (3 say-sai) ‘he said’ or ti gai-sai (1 say-sai) ‘I said’. This construction is always followed by direct speech and occurs with great frequency, and indeed in certain discourse contexts in every utterance. While functioning as a quotative in many of these cases, it sometimes appears in contexts that are not directly reportative, cf. (3). (3) Ai hi gai-sai xigihı´ hi xaisigı´aihı´ xaita´hoı´hı´ xoo´. well 3 say-SAI man 3 same sleep forest ‘Well, the same man went to sleep in the forest.’ This example (3) was uttered in the context of elicitation – the story was played out with dolls – where no conversation was directly referred to. Rather than being a quotative, hi gaisai seems to express impersonal reference in this case, such as ‘the Piraha˜ in general do/say this’, detaching the speaker and his responsibility from what is said. The meaning would be ‘one would say it in the following way’. This could point to a possible development away from the mere quotative use of the construction towards a more abstract meaning. Altogether, we can say that hi gaisai and similar constructions function as discourse markers and elements detached from the main content of the clause. Similar claims have been made for constructions in many other languages, including English, cf. Thompson and Mulac (1991) and Thompson (2002) for arguments that I think and I guess have grammaticalised into evidential markers and Hopper (2000) for English pseudoclefts functioning as discourse markers. 5. In the same way as English that, -sai is optional and can be left out. While one could argue that when that is left out in English it is still present in the form of a null complementiser. In Piraha˜ the argument against -sai as a subordination marker is considerably stronger because of the combination of -sai being optional and appearing in di¤erent positions within the clause.

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7

3. Alternative strategies to express complex cognitive structures: Mental verb constructions Similar to -sai above, Piraha˜ employs various other strategies to express cognitively complex concepts without making use of syntactic complexity. A striking example is mental verb constructions, such as sentences containing I think or I doubt in English. These are relevant since they always reflect two perspectives: either from two di¤erent people, or between reality and personal experience of one person. Regardless of whether these are two separate propositions or not, which in itself is a much debated issue, we have to do with a cognitively complex situation and many languages choose to encode this in syntactically complex sentences. Still, non-complex ways of coding mental verb constructions are likewise well-attested, e.g., marking for evidentiality by su‰xes. When looking at the data in Piraha˜, we find that there are no separate verbs expressing mental states. Rather, su‰xes corresponding functionally to English mental verbs or adverbs indicating mental attitudes are used. Table 1 brings together some of the mental attitude su‰xes and their functions, as well as their equivalent translations as complex structures or adverbs in English (for a detailed argument on why mental verb constructions and evidential su‰xes are comparable cf. Diessel and Tomasello 2001; Stapert 2009). Table 1. attitude su‰xes in Piraha˜ Verbal su‰x

Function, meaning

Equivalent in English Mental verb

Adverb

-a´ti -haı´ -ha´

Uncertainty

I doubt, I’m not sure

maybe, perhaps

relative certainty

I think, I guess

probably

complete certainty

I know, I bet, I’m sure

definitely, certainly

-sog -hı´ai

Desiderative

I wish, I want, I hope

hopefully

Hearsay

I heard

apparently, allegedly

-sibiga

deductive

apparently, seemingly

-xa´agaha´

observation, matter of fact

I understand, I suspect I get the impression I notice, I see, I’m certain (lit. use)

-bai / -koı´

emphasis, intensifier

I bet, I mean (clarification)

obviously, certainly, for sure

clearly

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Example (4) shows the markers -haı´ ‘relative uncertainty’ and hı´ai ‘hearsay’ added to the verb bog-ai ‘he came’ to express ‘doubt’ and ‘hearsay’ respectively. In examples (5) and (6) the meanings of ‘complete certainty’ and ‘observation’ are added in the same way: (4) Garippı´iru bog-ai-haı´-hı´ai. Brazilian.worker come-ATELIC-DOUBT-HEARSAY ‘(I heard that) the Brazilian worker has probably not come here.’ (5) Hi kaga´ihiai koaba´i-p-a´-ha´ 3 jaguar kill-PERF-REM-COMP_CERT ‘(I’m sure) he shot the jaguar’ (6) Piboi-bai hi kaha´pi-hiab-a´agaha´ Rain-INTEN 3 go-NEG-OBSERV ‘It is raining; (I see) he is not going (to the forest)’ In English the concept of uncertainty can be expressed by the adverb probably, as in the translation of (4), or the entire sentence could alternatively be expressed in a double embedded structure such as ‘someone said that he doubts that the Brazilian worker came here.’ These elements function like evidentials, rather than verbs in expressing probability and source of information without having a separate subject themselves. In this way recursive embeddings in English are very di¤erent from constructions with evidentials in Piraha˜. Compare the recursive sentence in (7a) with the non-recursive equivalent using adverbs with similar functions to the Piraha˜ evidentials in (7b): (7) a. b.

He said that I suspected that the students were hung over. Hearsay perhaps the students are hung over.

Summarising, markers of attitude in Piraha˜ can be analysed as expressing semantically complex structures without syntactic embedding. 4. Language contact The examples we have looked at so far were native Piraha˜ language data. Now, we will turn to elements and morphemes outside of the Piraha˜ system that could be introduced by language contact and that could subsequently introduce recursion into Piraha˜ syntax. The hypothesis is that through intensive language contact with Portuguese, markers and structures of embedding, which are common in Portuguese, could be borrowed into Piraha˜. Our reasoning for this is as follows:

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9

Firstly, elements that mark structures of embedding are frequently borrowed in other contact situations. A typological study of grammatical contact phenomena (Matras and Sakel 2007; Sakel 2007b) concludes that function words such as discourse markers, coordinators and subordinating conjunctions are almost always borrowed in situations where a minority language is in contact with a highly dominant language and with prevailing bilingualism. Indeed, in most of these cases subordinating conjunctions were among the borrowed elements, being taken over wholesale with their form and function. Secondly, the Piraha˜ use many Portuguese lexical elements in their language, even though the community as a whole is predominantly monolingual with only a few older men having rudimentary knowledge of Portuguese. This is surprising as the Piraha˜ have been in contact with outsiders for over 200 years. The loanwords from Portuguese include new concepts such as gahia´o ‘plane’ (from Portuguese avia˜o) and kapı´iga ‘paper’ (from Portuguese papel ), as well as a number of elements that already exist in Piraha˜, but that are frequently used when speaking with outsiders, such as bı´i ‘good’ (from Portuguese bem) or ambora ‘away, let’s go’ (from Portuguese embora). When looking at the syntactic structures, however, there is no evidence that Portuguese has had any influence on the grammar of Piraha˜, as there are no apparent grammatical calques. In a number of cases speakers of Piraha˜ incorporate Portuguese grammatical elements into their language, but this is only the case when making conscious e¤orts to speak Portuguese to foreigners, as in (8). (8) Ai ai aki his-o keeche DM DM here sun-LOC6 hot kwaado aki his-o friio when here sun-LOC cold ai DM ai DM

kaba NEG muito very

keema ai burn DM braako. white

‘It is hot here in the sun. When it is cold here in the sun, you do not burn. (You are) very white.’ (Portuguese elements in bold)

6. Hiso is Piraha˜ for ‘in the sun’ or ‘on the day’, but it is phonologically similar to local Portuguese constructions with fazer ‘to be (in relation to weather). It may hence be a blend of both languages, accommodated by a similar construction in Piraha˜.

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In (8) the speaker makes use of the Portuguese adverbial clause marker cuando ‘when’ (integrated into Piraha˜ as kwaado). Instead of functioning as an adverbial clause marker, however, it appears to be used similar to the Piraha˜ distance marker -so, which expresses that an event is not happening in the immediate context of the utterance.7 In this case, the speaker expresses that it is not cold at the moment of speech. Comparing this example to typical Piraha˜ sentences, the structure is very similar: relations between clauses are established by simple juxtaposition, combined with distance marking when appropriate. Example (8) is thus an instance of insertion of Portuguese material into a grammatical frame that is purely Piraha˜. This is suggestive of the fact that Piraha˜ has not borrowed recursive structures from Portuguese. Increased contact with the outside world in recent years, and hence increased bilingualism could change this, however.

5. Recursion in Piraha˜? Toward an alternative analysis Let us sum up our findings and discuss to what degree we can expect recursion in Piraha˜. Firstly, does Piraha˜ have recursion? Most structures we have looked at so far have given no evidence of being outright syntactically recursive structures. In most cases clauses are linked by simple juxtaposition and relations between them become clear in the discourse context. However, conclusive support of this negative finding would require more evidence than we presently possess. Thus, our conclusions are necessarily tentative. There are a number of markers, such as -sai and -so, that seem to appear in structures parallel to ‘recursive’ structures in other languages, but these are not outright markers of subordination or recursion in the syntactic sense: more often, these markers are expressing semantic cohesion between parts of the discourse. These markers also indicate relations between what is said and the reality of the speech situation, such as the distance marker -so, which expresses a distance to the current reality. Concepts that are expressed recursively in many other languages are marked by a‰xes in Piraha˜, as in the case of mental verb construction. Language contact has likewise failed so far to introduce recursive structures from 7. We do not yet fully understand the exact functions of -so or its distribution. In the same was as -sai, however, it appears to be optional and is not an obligatory marker for embedding.

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11

Portuguese. Hence, we can not say with any confidence that there is – or for that matter is not – recursion in Piraha˜. Instead of saying that recursion is a core characteristic of human syntax, we believe that it is an important feature of human language which is most likely to be present in languages and language varieties that are used to express complex concepts. Let us discuss a number of recent publications in the field to clarify what we mean. 5.1. Spoken language Recursive structures appear to be far less frequent in spoken language than in written language. Mark Liberman discusses this for English in his entry on Language Log in May 2006, citing the following example from Elmore Leonard’s La Brava: (9) What’re you having, conch? You ever see it they take it out of the shell? You wouldn’t eat it. This is a typical example of a variant of spoken language, though paradoxically in this case it is written language imitating spoken language. Nonetheless, it shows that complex and recursive constructions such as ‘if you had ever seen it being taken out of the shell you would not eat it’ can be replaced by paratactic, non-recursive structures in spoken language. That spoken language makes less use of recursion has also been shown for Finnish and Japanese: Laury and Ono (This Volume) present evidence that when recursive structures appear in spoken language they are generally less complicated than in written language. There is often only one degree of recursion in spoken language, while written language can show many di¤erent layers of subordination (cf. also Karlsson 2007). Similar evidence comes from the analysis of informal talk, where clause chains are preferred to embedding (Pawley and Syder 1983). Comparing these findings with our Piraha˜ data, we can argue that since Piraha˜ is a spoken language exclusively, recursion may be unnecessary or at least far rarer than in written language. 5.2. that-omission in relative clauses On top of the decrease in recursive structures we find in spoken language we can also argue for a parallel case that extends to written language. Two recent approaches to that-omission in English restrictive relative clauses claim that the resulting construction is non-recursive. Fox and Thompson (2007: 293) argue that pragmatic-prosodic factors, as well as frequency,

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can lead to a ‘‘monoclausal’’ nature of the combination of relative clause and main clause. These monoclausal combinations are highly formulaic and processed as one, rather than two clauses, and in these cases that is omitted. In a di¤erent approach, Jaeger and Wasow (2007) argue that the more accessible the relativised element is in English non-subject extracted relative clauses, the more likely it is for the relativiser to be omitted. Thatomission usually takes place when the relativised element is given or definite. Hence that is often absent when the content of what is said is predictable. Another parallel case has been reported by Progovac (This Volume), who argues that certain small clauses do not allow for recursion. In this way, English has constructions that have a non-recursive expression and that appear both in spoken and written language. What if such constructions were the default or indeed the only option in another language, such as Piraha˜? Since English relative clauses work equally well in cases with or without overt syntactic marking for recursion, it is possible to imagine a human language that does not need to have recursive structures. 5.3. Esoteric language use More evidence comes from studies of how human language developed. Wray and Grace (2007) distinguish between esoteric vs. exoteric communication, based on Thurston’s (1987) terminology. Esoteric communication is inward-facing, which means that it is used within a well-defined group. In this type of communication comprehension is facilitated as hearers are likely to know what the speaker is going to say in a given situation. This still means that the language can express novel ideas, but the expression of predictable thoughts is a default. Exoteric communication, on the other hand, is outward-facing. Hence, exoteric communication in the definition of Wray and Grace (2007) would range from using a lingua franca to employing one’s local dialect to communicate with somebody unknown. Speakers have to be clear, since hearers are unlikely to predict what the speaker will talk about. This is possible in a language with simple, unambiguous elements that can be combined by unambiguous rules. Hence it is not surprising that the type of linguistic features found in varieties used for esoteric and exoteric communication are very di¤erent: Wray and Grace (2007) discuss how in esoteric communication suppletion and complex semantic structures are frequent, while language varieties used for exoteric communication often show logical and transparent rules

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13

that are also learnable by adult speakers and that are semantically transparent. They argue that human language probably started as a means for esoteric communication and that rule-based grammar is a cultural add-on that evolved with increased necessity for complex negotiations. Many types of communication are exoteric in the complex and globalised world of today. This is most likely to one reason for recursion being very frequent in the world’s languages. The Piraha˜, on the other hand, are an inward-facing group, and their language is only rarely used with outsiders.8 Explicit recursive syntax may thus not be necessary.

6. Conclusion In conclusion, the Piraha˜ structures we have looked at in this paper have shown no evidence of being syntactically recursive. Instead, Piraha˜ appears to make use of juxtaposition and morphological complexity to express complex concepts. Our conclusion is hence very similar to Everett’s analysis (2005). We have discussed a number of constructions in which even syntactically complex languages prefer non-recursive structures to recursive ones. It is possible that what other languages have as an option is the default in Piraha˜. Further support comes from the fact that Piraha˜ is an exclusively oral language. Spoken language and predictable content are exactly the instances in which non-recursive structures are preferred in other languages such as English. Hence, there is no apparent functional need for recursion in Piraha˜ syntax.

References Diessel, Holger and Michael Tomasello 2001 The acquisition of finite complement clauses in English: A usage based approach to the development of grammatical constructions. Cognitive Linguistics 12: 97–141. Everett, Daniel 1986 Piraha˜. In: Desmond Derbyshire and Geo¤rey Pullum (eds.), Handbook of Amazonian Languages I, p. 220–326. Berlin: Mouton de Gruyter.

8. These outsiders are a handful of linguists and missionaries who speak the language to a degree.

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Everett, Daniel 2005 Cultural constraints on grammar and cognition in Piraha˜: Another look at the design features of human language. Current Anthropology 76(4): 621–646. Everett, Daniel 2007a Cultural constraints on grammar in Piraha˜: A reply to Nevins, Pesetsky and Rodrigues (2007). LingBuzz article archive (http:// ling.auf.net/lingBuzz/000427) Everett, Daniel 2007b Challenging Chomskyan Linguistics: The Case of Piraha˜. Human Development 50: 297–299. Everett, Daniel 2008 Dan Everett replies to Slobin and Sakel. Human Development, letters to the editor 50 (6). (content.karger.com/produktedb/ katalogteile/issn/_0018_716x/hde-letters-to-editor-01-09-2008. pdf ). Fox, Barbara A. and Sandra A. Thompson 2007 Relative clauses in English conversation – relativizers, frequency, and the notion of construction. Studies in Language 31(2): 293– 326. Hauser, Marc, Noam Chomsky, and W. Tecumseh Fitch 2002 The faculty of language: What is it, who has it, and how did it evolve? Science 298: 1569–1579. Hopper, Paul 2000 Grammatical constructions and their discourse origins: Prototype or family resemblance? In: Martin Pu¨tz and Susanne Niemeier (eds.) Applied cognitive linguistics: Theory, acquisition and language pedagogy, 109–129. Berlin: Mouton de Gruyter. Jaeger, T. Florian and Thomas Wasow 2008 Processing as a source of accessibility e¤ects on variation. Proceedings of the 31st Berkeley Linguistics Society 169–180. Karlsson, Fred 2007 Constraints on multiple initial embedding of clauses. International Journal of Corpus Linguistics 12(1): 107–118. Liberman, Mark 2006 Parataxis in Piraha˜. Language Log May 19, 2006. (http://itre.cis. upenn.edu/Pmyl/languagelog/archives/003162.html). Matras, Yaron and Jeanette Sakel (eds.) 2007 Grammatical Borrowing in cross-linguistic perspective Berlin: Mouton de Gruyter. Nevins, Andrew Ira, David Pesetsky and Cilene Rodrigues 2007 Piraha˜ exceptionality: A reassessment. LingBuzz article archive. (http://ling.auf.net/lingBuzz/000411). Pawley, Andrew and Frances H. Syder 1983 Two puzzles for linguistic theory: nativelike selection and native-

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like fluency. In: Jack C. Richards, Richard W. Schmidt (eds.) Language and Communication, 191–226. New York: Longman. Sakel, Jeanette 2007a

Sakel, Jeanette 2007b

Slobin, Dan 2007

On Piraha˜ and Everett’s claims about recursion. Human Development, letters to the editor 50 (6). (content.karger.com/produktedb/ katalogteile/issn/_0018_716x/hde-letters-to-editor-12-13-2007. pdf ). Types of loan: Matter and pattern. In Grammatical borrowing, Yaron Matras & Jeanette Sakel (eds.) Grammatical Borrowing in cross-linguistic perspective Berlin: Mouton de Gruyter. Context and comments on Dan Everett’s claims. Human Development, letters to the editor 50 (6). (content.karger.com/produktedb/ katalogteile/issn/_0018_716x/hde-letters-to-editor-01-09-2008. pdf )

Stapert, Eugenie 2009 Universals in language or cognition? Evidence from English language acquisition and from Piraha˜. In: David Gill, Peter Trudgill, Geo¤rey Sampson (eds.) Language Complexity as an Evolving Variable, 230–242 Oxford: Oxford University Press. Stapert, Eugenie 2007 Linguistic theory and fieldwork in interaction: the case of Piraha˜. In: Peter K. Austin, Oliver Bond, David Nathan (eds.) Proceedings of conference on Language Documentation & Linguistic Theory. London: SOAS, University of London. Stapert, Eugenie, Michael Frank, Dan Everett, and Ted Gibson in prep. Embedded structures in Piraha: The expression of relative clauses, possessives and conditionals, manuscript. Thompson, Sandra A. and Anthony Mulac 1991 A quantitative perspective on the grammaticization of epistemic parentheticals in English. In: Elizabeth Traugott and Bernd Heine (eds.) Grammaticalization II, 313–339. Amsterdam: John Benjamins. Thompson, Sandra A. 2002 Object complements and conversation: towards a realistic account. Studies in Language 26(1): 125–164. Thurston, William R. 1987 Processes of change in the languages of north-western New Britain. Pacific Linguistics B99, The Australian National University, Canberra. Wray, Alison and George W. Grace 2007 The consequences of talking to strangers: Evolutionary corollaries of socio-cultural influences on linguistic form. Lingua 117: 543–578.

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Abbreviations 1 3 ATELIC COMP_CERT DM DOUBT EMPH HEARSAY INTENS LOC NEG OBSERV PERF REM SAI

first person third person atelic action/event complete certainty discourse marker expression of doubt emphasis hearsay evidential intensifier locative negation observation perfect remote -sai marker

2.

The fluidity of recursion and its implications

Marianne Mithun 1. Introduction One goal of linguistics is the identification of properties shared by all human languages and no other communication systems. In their muchcited 2002 paper, Hauser, Chomsky, and Fitch proposed a universal: ‘‘FLN (the Faculty of Language in the Narrow sense) only includes recursion and is the only uniquely human component of the faculty of language’’ (2002: 1569). While they provide no explicit definition of recursion, a survey of definitions current in the linguistics and computer science literatures can be found in Parker (2006: 167–190). One that is consistent with much current work in linguistics is that of Pinker and Jackendo¤ (2005: 4), whereby a recursive structure is characterized as ‘‘a constituent that contains a constituent of the same kind’’. Recursive structures are indeed pervasive cross-linguistically. A closer look at the variety of such structures that occur, however, indicates that recursion may not be the fixed, fundamental, hard-wired property envisioned. Much as languages vary in their distribution of structural complexity across the domains of morphology and syntax, they also vary in their distribution of recursion. The most common recursive structures involve noun phrases embedded inside of other noun phrases (the neighbor’s cat’s habits) and clauses embedded inside of other clauses, the type cited by Hauser, Chomsky, and Fitch (Mary believes that S ). As will be seen, such constructions are not uniform cross-linguistically, nor are they static within individual languages. The variability in space and time calls into question the status of recursion as the basic design feature of human language. It suggests, rather, that recursive structures are epiphenomenal, the product of combinations of a variety of cognitive processes. 2. Central Alaskan Yup’ik Languages of the Eskimo-Aleut family contain numerous syntactic constructions containing clause recursion. Examples cited here are drawn from Central Alaskan Yup’ik, a language of southwestern Alaska.

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2.1. Yup’ik complement clauses The single structure cited by Hauser, Chomsky, and Fitch as an example of recursion is complementation: Mary believes that S. Yup’ik counterparts to this English construction are formed with dependent clauses in the Subordinative mood. The Subordinative mood su‰x -lu- on the second verb in (1) marks the clause ‘that you are well’ as dependent. (1) Yup’ik complement counterpart: Elizabeth Ali, speaker p.c. Qanerutelaranka qaner-ute-lar-gar-nka talk-benefactive-habitual-transitive.indicative-1sg/3pl ‘I would tell them assirluten-gguq . . . assir-lu-ten¼gguq be.good-subordinative-2sg¼quotative [that you are well . . . ]’ Although this construction is now deeply entrenched in the grammar, its origin can still be discerned (Mithun 2008). The marker -lu- developed from an old nominalizer that still persists in derived nouns in all of the Eskimo-Aleut languages, though it is no longer productive in that function. (2) Yup’ik nominalizer -lu tamu‘to chew’ kumeg- ‘to scratch’ uig‘to sample, to taste’

tam-lu kum-lu u-lu

‘chin’ ‘thumb’ ‘tongue’

Further confirmation of nominalization as the diachronic source of the Subordinative comes from the shapes of the pronominal endings that occur with this mood. All Yup’ik verbs end in a pronominal su‰x specifying their core arguments: two for transitives and one for intransitives. In the transitive verb qanerutelara-nka ‘I would tell them’ in (1), the pronominal su‰x is -nka ‘I/them’. In the intransitive verb assirlu-ten ‘you are well’, the pronominal su‰x is -ten ‘you’. The pronominal su‰xes that occur with the Subordinative generally match the possessive su‰xes on nouns.

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(3) Yup’ik possessive and pronominal su‰xes Possessive su‰x on noun Pro su‰x on Subordinative verb angya-ten assir-lu-ten boat-2sg/pl be.good-subordinative-2sg ‘your boats’ ‘your wellness’ ¼ ‘that you are well’ The formation of complement clauses by nominalization is not unusual cross-linguistically. This is no accident. The example in (1), ‘I will tell them [that you are doing well]’ was part of a telephone conversation between a sister and her brother, who was away visiting their parents. She asked how things were going, and he responded at length, saying that things were fine, and he was enjoying the daily round of activities. In closing, she promised to pass along his greetings to their friends. The clause ‘that you are well’ in (1) was not an assertion. It was a referential expression evoking a fact established in the preceding discourse. The reification of the situation is reflected in its syntactically nominal expression. 2.2. Yup’ik adverbial clauses Adverbial clause constructions are often cited as examples of clause embedding (Heine and Kuteva 2007, section 5.3.3, inter alia). Such constructions are pervasive in Yup’ik, marked by a variety of mood su‰xes on verbs. One is the Past Contemporative -ller- ‘when in the past’. The example in (4) is from a description of the silent Pear Film. (4) Yup’ik adverbial clause: Elizabeth Ali, Ellinqegcaarluki tlli-nqegcaar-lu-ki put-completely-subordinative-r/3pl atsaq atsaq fruit

speaker p.c. atauciq, atauciq one

igtellerani igte-ller-ani fall-past.contemporative-3sg

ataam tegukii ellirrarluku-ll’ ataam tegu-ke-ii elli-rrar-lu-ku¼llu again take-tr.prtcp-3sg/3sg put-after-subordinative-/3sg¼and ‘He placed them carefully, when one fruit fell, picking it back up and replacing it.’

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The origin of the Past Contemporative construction, like that of the Subordinative, is still discernible (Mithun 2008). The source of this mood su‰x is the past nominalizer -ller-/-lleq, which still persists in the language productively its original function. (5) Yup’ik past nominalizer -ller-/-lleq ayagaya-lleq

‘go, leave’ ‘the one who left’

The identification of this past nominalizer as the source of the Past Contemporative mood marker is confirmed by the fact that the pronominal su‰xes used with it have the same shapes as the possessive pronominals þ locative case endings on nouns. (6) Yup’ik possessed locatives and pro su‰xes on Past Contemporatives Possessed locative noun Past Contemporative verb angy-ani igtellerani boat-3sg/sg.loc fall-past.contemp-3sg ‘at/in his boat’ ‘at its falling’ ¼ ‘when it fell’ The locative case has been extended from simple nouns to nominalized clauses, its function generalized and made more abstract, from marking roles of concrete objects to marking the roles of events. Other dependent mood su‰xes in the language have similar histories. Each development reflects the reification of situations, the treatment of events or states as entities, the generalization of markers from individual words to clauses, and the development of more abstract functions, from denoting physical relationships of objects to indicating abstract relationships among events and ideas.

3. Khalkha Mongolian The Mongolian languages, genetically unrelated to Yup’ik and spoken in another part of the world, show a similar richness of clause combining. Examples cited here are drawn from Khalkha Mongolian. 3.1. Khalkha complement clauses A Khalkha complement construction can be seen in (7).

The fluidity of recursion and its implications

21

(7) Khalkha complement clause: Altanzaya Batchuuluun, speaker p.c. Tegeed so manai xu¨u¨xid u¨r’t n’ nadaas manai xu¨u¨xid u¨r’t n’ nad-aas our son earlier foc me-abl [dandaa qar utas avcˇ o¨go¨o¨cˇ. geǰ] dandaa qar utas av-cˇ o¨g-o¨o¨cˇ geǰ always hand phone take-non.finite give-pol comp quidag baisaÐ cˇin’. qui-dag bai-saÐ cˇin’ beg-hab be-past connector ‘Our son always used to beg me [to buy a cell phone].’ This complement construction is pervasive in Khalkha speech, but its diachronic source is still clear. The complementizer geǰ in (7) is a non-finite form of the verb ge- ‘say’. This construction apparently originated in a quotative construction: ‘He begged me, saying S’. The use of geǰ no longer requires actual speech, but its origins still constrain the contexts in which it occurs. In (8) it appears with a verb meaning ‘think’, and in (9) with ‘plan’. (Example (8) also shows extensive noun phrase recursion, with embedded genitives: the development of the religion of Buddhism of Mongolia.) (8) Khalka complement of ‘think’: Erdenebaatar Erdene-Ochir, sp p.c. E udaa bi this time I MoÐqoliiÐ Burxanii sˇasˇnii burxan-ii sˇasˇin-ii MoÐqol-iiÐ Mongolia-gen Buddha-gen religion-gen of Mongolia of Buddha of religion tuxai, delgerliin delger-l-iiÐ tuxai spread-nzr-gen about of the spread about boqa zereg jarij geǰ bodoǰ bain. boqa zereg jari-ǰ geǰ bodo-ǰ bai-na small level talk-nz comp think-non.finite be-non.past ‘This time I’m thinking [that I’ll talk a little about the development of the religion of Buddhism of Mongolia].’

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(9) Khalkha complement of ‘plan’: Altanzaya Batchuuluun, speaker Manai eeǰ aav manai eeǰ aav our mother father [gurvaÐ gurvaÐ three

xojr aÐxnaasaa xojr aÐxn-aas-aa two first-abl-rfl.poss

xuxedtei boln geǰ] xuxed-tei bol-no ge-ǰ child-com be-fut comp

jiro¨o¨so¨o¨ to¨lo¨vlo¨o¨gu¨i jiro¨o¨so¨o¨ to¨lo¨vlo¨o¨-gu¨i never plan-neg ‘At first my mother and father never planned [that they would have three children].’ The complementizer geǰ is not yet used in all contexts in which complementizers appear in other languages. Of the matrix predicate types listed in Noonan’s (2007) classification, geǰ appears with utterance predicates (such as ‘say’, ‘tell’, ‘report’, ‘promise’, ‘ask’, etc.), predicates of propositional attitude (‘believe’, ‘think’, ‘suppose’, ‘assume’, ‘doubt’, ‘deny’), pretence (‘imagine’, ‘pretend’, ‘fool’), knowledge and its acquisition (‘know’, ‘discover’, ‘realize’, ‘forget’, ‘see’, ‘hear’), fear (‘fear’, ‘worry’, ‘be anxious’), desire (‘want’, ‘wish’, ‘desire’), manipulatives (‘command’, ‘order’, ‘ask’, ‘allow’), and immediate perception (‘see’, ‘hear’, ‘watch’, ‘feel’), but not with what Noonan terms commentatives (‘be sad’, ‘be sorry’, ‘be odd’, ‘be significant’), with modals (‘be able’, ‘be obliged’, ‘can’, ‘ought’, ‘should’, ‘may’), achievements (‘manage’, ‘chance’, ‘dare’, ‘remember to’, ‘happen to’, ‘get’, ‘try’, ‘forget to’, ‘fail’, ‘avoid’), or phasals (‘start’, ‘begin’, ‘continue’, ‘keep on’, ‘finish’, ‘stop’, ‘cease’). The current limits are exactly what would be predicted on the basis of the diachronic source of the complementizer in a verb of saying. The development of verbs meaning ‘say’ into complementizers is of course not uncommon cross-linguistically (Heine and Kuteva 2002: 261–165). The Mongolian particle has not been generalized as far as complementizers from similar sources in some other languages, nor has it become as abstract. 3.2. Khalkha adverbial clauses Khalkha also shows pervasive use of adverbial clauses. One type can be seen in (10), from a description of the same silent Pear Film seen by the Yup’ik speaker cited in (4).

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(10) Khalkha adverbial clause: Erdenebaatar Erdene-Ochir, sp p.c. Tegeed [neg liir then one pear then one pear ‘Then [when one pear tern-iig that-acc that he took it basket).’

qazar unx-ad] ground.loc fall-loc on ground when it fell fell to the ground],

av-aad take-sequential took and and (rubbed it with his bandana and put it into his

The origins of this temporal adverbial construction can also still be discerned. The adverbial su‰x -ad has the same shape as the locative case su‰x that appears on nouns. (11) Khalkha locative case on nouns: E. Erdene-Ochir, sp p.c. sagsan-d-aa liir xuraa-ǰ basket-loc-rfl.poss pear collect-non.finite in his own basket pear collecting ‘he was collecting pears in his basket’

bai-saÐ be-past was

Other case su‰xes have developed into markers of other kinds of adverbial clauses. (12) Khalkha generalization of cases to adverbial clause markers Locative ‘at NP, when S’ Instrumental ‘with NP, by means of NP/S, as a result of, in order to S’ Ablative ‘from NP/S, because of NP/S As in Yup’ik, the adverbial clause constructions developed when speakers extended the use of case su‰xes from nouns to clauses, generalizing their functions from marking the roles of concrete objects to marking those of more abstract entities: events and states.

4. Mohawk In contrast with Yup’ik and Khalkha, Mohawk appears to show a surprising absence of embedded clauses. All Mohawk clauses are finite and can

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stand on their own as fully grammatical sentences. The usual formal features that identify embedded clauses in other languages, such as complementizers, omission of coreferential arguments, and non-finite verb forms, do not normally appear in their Mohawk counterparts. 4.1. Mohawk complement clauses Mohawk counterparts of all types of complement constructions distinguished by Noonan (2007) seem to consist of sequences of independent sentences. Example (13) was later translated by the speaker with an English object complement construction, but both Mohawk clauses are perfectly grammatical sentences on their own: ‘He didn’t know it. It happened thus.’ (13) Mohawk sequence of clauses: Kaia’tita´hkhe’ Jacobs, speaker p.c. Iah ki’ the´: tehoterie`n:tare’ iah ki’ the´: te-ho-ate-rien’tar-e’ not in.fact at all neg-m.sg.pat-middle-know-stative not in fact at all did he know (it) na’a´:wen’ne’. na’-a-w-en’n-e’ partitive-factual-n-fall-prf so it happened ‘In fact he didn’t know [what happened].’ The sentence in (14) was translated with an English subject complement. (14) Mohawk sequence of clauses: Cecelia Peters, speaker p.c. Enta`:’on enieka´ria’ke’ tere´ntsho. w-enta’-on en-ie-karia’k-e’ terentsho n-be.necessary-stative fut-indef.agt-pay-prf trente.sous it is necessary one will pay quarter ‘It is necessary [that one pay a quarter]’ ¼ ‘One has to pay a quarter.’ But most language use does not take place under conditions of silence. As soon as the intonational dimension is added, further structure emerges. Both (13) and (14) were pronounced under a single intonation contour, beginning with a high pitch reset and descending to a final fall only at the end of the second clause. These intonation patterns can be seen in the pitch traces in (13’) and (14’).

The fluidity of recursion and its implications

(13)’

25

Mohawk complement construction

‘In fact he didn’t know what happened.’ (14)’

Mohawk complement construction

‘One has to pay a quarter.’ Contrasts are easy to hear between constructions like these and sequences of separate sentences. The sentence in (15) below, ‘He told him to go home’, was pronounced as a single intonation unit, with a high pitch peak on the accented syllable of the first word/clause wahohro´:ri’ ‘he told him’ and much lower peak on the accented syllable of the second word/ clause: aonsahahte´n:ti’ ‘he should go home’. The syntactic cohesion of the two clauses is echoed in the use of the third person pronominal in the second clause ‘he should go home’, indicating indirect speech, rather than a second person ‘you should go home’. (15) Mohawk single sentence: Charlotte Bush, speaker p.c.

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Wahroro´:ri’ wa-ho-hrori-’ factual-m.sg/m.sg-tell-prf he told him

aonsahahte´n:ti’. a-onsa-ha-ahtenti-’ opt-rep-m.sg.agt-leave-prf he should go home

‘He told him to go home.’ Example (16), by contrast, contains two independent sentences, with a full fall in pitch at the end of the first and a pitch reset at the beginning of the second. The two are further separated by a pause. The syntactic separation of the sentences is reflected in the use of the first person pronominal in the second clause ‘for me to plant’, indicating direct quotation, rather than a third person ‘for him to plant’. (The second sentence also contains a complement of its own.) (16) Mohawk sequence of two sentences

Wahari’wano´n:ton’, wa-ha-ri’w-anonton-’ factual-m.sg.agt-matter-ask-prf ‘He asked, ‘‘Enwa´:ton’ ’’ wahe`n:ron’ en-w-aton-’ wa-ha-ihron-’ future-n-be.possible-prf factual-m.sg.agt-say-prf it will be possible he said ‘‘Would it be possible’’, he said, ‘‘ke`n: entie´ntho’.’’ ken: en-k-ientho-’ here future-1sg.agt-plant-prf here I will plant ‘‘for me to plant here?’’’

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27

Intonation structure is not a simple mirror of syntactic structure: the two often operate in parallel, but they can also diverge to express di¤erent distinctions (Mithun 2006). The prosodic integration does, however, reflect a cognitive integration, which presumably underlies syntactic integration as well. The integration seen in the prosody is consistent with the status of the second clause in each sequence as a referring expression. Definiteness is not obligatorily distinguished in Mohawk, but there is a particle ne that can indicate that the following nominal is identifiable to the listener from previous reference in the discourse: ‘the aforementioned’. The Pear Film mentioned earlier opens with a man in a tree picking pears. A Mohawk speaker first introduced the pears without ne, since they were new to her listeners. (17) Mohawk absence of ne: Kaia’tita´hkhe’ Jacobs, speaker p.c. Ka´tshe’ ka´hi rahia´kwahs. ka-tshe’ ka-ahi ra-ahi-akw-ahs n-jug n-fruit m.sg.agt-fruit-pick-hab ‘He was picking pears.’ The pear picker repeatedly climbs down out of the tree and dumps the pears into baskets, then climbs back up. A boy comes along on a bicycle and, unobserved, steals one of the baskets. As he rides away, he hits a stone and falls, scattering the fruit. Three other boys come along and help him up. At this point the fruit, now familiar to the audience, is preceded by ne. (18) Mohawk ne with noun: Kaia’tita´hkhe’ Jacobs, speaker p.c. A’the´:rakon sahonne´ta’ ne ka´hi. a’ther-akon sa-hon-net’a-’ ne ka-ahi basket-place.inside rep.factual-m.pl.agt-insert-prf the n-fruit ‘They put the fruit back into the basket.’ The same particle ne occurs before complement clauses under exactly the same discourse conditions. It precedes complement clauses referring to events presumed to be identifiable to the audience from prior mention. Two Mohawk speakers were discussing a translation project. One expressed hope that it might be finished before Christmas. The other gave the response in (19). The anticipation of the final product was already an integral part of the conversation at this point, so the complement clause ‘to see what it will be like’ was preceded by ne. (This particle cliticizes to a following vowel-initial word.)

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(19) Mohawk ne with clause: Charlotte Bush, speaker p.c. Ne´: ki’ ni: tewakhsterı´henhs ne: ki’ ne¼ı`:’i te-wak-hsterihen-hs that in fact the I duplicative-1sg.pat-hurry-hab it is in fact myself it hurries me nakatka´htho’ ne¼a:-k-at-kahtho-’ the optative-1sg.agt-middle-see-prf the I would see it ni: tsi oh ni: tsi oh how so how

nenio´hton’ n-en-io-ht-on-’ partitive-fut-n.pat-be.so-prf

wa´hi’. wahi’ tag

‘It hurries me [the for me to see [how it will be]] you know.’ ¼ ‘I’m in a hurry to see what it will be like, you know.’ Similar behavior can be seen with demonstratives kı´:ken ‘this’ and thı´:ken ‘that’. Both can appear with nouns, as would be expected. Recall that the Mohawk speaker cited in (17) first introduced the pears without any preceding particles. As he worked, the pear picker stowed the pears in an apron pocket. At this point the speaker used the proximal demonstrative kı´:ken to refer to the pears, which had just been mentioned in the immediately preceding discourse. (20) Mohawk kı´:ken ‘this’ with noun: Kaia’tita´hkhe’ Jacobs, sp p.c. Tho ki’ iehre´ta’s tho ki’ ie-hr-et’a-s there in.fact translocative-m.sg.agt-insert-hab kı´:ken ka´tshe’ ka´hi. kı´:ken ka-tshe’ ka-ahi proximal n-jug n-fruit ‘[He was wearing something like a bag] and he was putting these pears in there.’ The demonstratives also appear before clauses, where they serve exactly the same function, situating the events denoted by the clauses as proximal or distal in space, time, or discourse. The pear picker climbed down from the tree periodically to transfer the pears into his three baskets. On one trip down, he noticed that a basket was missing.

The fluidity of recursion and its implications

(21) Mohawk kı´:ken before complement: Kaia’tita´hkhe’ Waha´ttoke’ kı´:ken wa-ha-at-tok-’ kı´:ken factual-m.sg.agt-middle-notive-prf proximal he noticed this

29

Jacobs, sp p.c. te´keni khok te´keni khok two only two only

tesewa’the´:raien te-se-w-a’ther-a-ien-’ duplicative-repetitive-n-basket-lie-stative two were basket lying ne ne the the ‘He

kahenta`:ke.’ ka-hent-a’ke n-field-place ground place noticed [this there were only two baskets on the ground].’

When asked later about her use of kı´:ken ‘this’ here, this speaker replied that the demonstrative referred to the fact of there being only two baskets. The proximal form was chosen because the man was noticing this fact as he looked at the baskets right before him. On another occasion, two other speakers were reminiscing about life during the 1930’s. One mentioned an old man, long since dead. This speaker’s use of the distal thı´:ken ‘that’ was appropriate for the distant time. (22) Mohawk thı´:ken ‘that’ with nominal: Tiorhakwe´n:te’ Dove, sp To´ka’ ni:se’ se`:iahre’, to´ka’ ne ´ı:se’ s-ehiahr-’ maybe the you 2sg.agt-remember-prf thike´n:– that Watia’ksne’ke´nha’. Watia’ksne’¼kenha’ name¼decessive ‘Maybe you remember that guy, the late Watia’ksne’.’ A bit later, the same speaker used the distal demonstrative before a clause, referring to an event at the same time in the past.

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(23) Mohawk distal thı´: ‘that’ before clause: Tiorhakwe´n:te’ Dove, sp To´ka’ ken enhsehia`:rake’ thi: toka’ ken en-hs-ehiahr-ak-’ thiken maybe Q future-2sg.agt-remember-cont-prf that wahshakonahskwawı´hon wa-hshako-nahskw-awi-hon factual-m.sg/3pl-domestic.animal-give-distr ‘Maybe you remember [that he (the government) used to give away livestock].’ (These demonstratives have not developed into complementizers comparable to English that. These Mohawk demonstrative constructions originated in a di¤erent source structure and di¤er syntactically, semantically, and prosodically from English that complements. Details are in Mithun 2006, in press). None of these particles, ne ‘the aforementioned’, kı´:ken ‘this’, or thı´:ken ‘that’, occurs before an independent sentence in isolation: they occur only before the kinds of clauses that could be identified as complements on semantic or intonational grounds. Their contexts of use have been generalized from simple nouns to clauses, indicating that the referents of these clauses, like those of nouns, are identifiable, proximal in space, time, or discourse, or distal. Their presence confirms that the clause is not an independent predication, but rather a referring expression. Mohawk thus contains complement constructions after all, but at an early stage of development. The construction is distinguished in three ways: 1) by coreference between a core argument of the first clause and the entire second clause, 2) by a single prosodic contour, and 3) by the fixed order of the clauses. The cross-linguistic tendency for heavy arguments to be postposed has become crystallized, with the complement always following the matrix. 4.2. Mohawk adverbial clauses Mohawk also contains constructions translated as adverbial clauses. Some of the most common types are temporal clauses set o¤ by the particle o´:nen. (24) Mohawk temporal adverbial clause: Watshennı´:ne’ Sawyer, sp p.c. Nek tsi o´:nen tiakwaristı´:ia’ke ne ok tsi o´:nen i-a’-t-iakwa-rist-iia’k-’ but when tloc-factual-dv-1.pl.excl.agt-metal-cross-prf

The fluidity of recursion and its implications

31

kwa´h ki: isto`n:ha saion’we´:sen’ne. kwah ki: o-sto`n¼ha sa-io-on’wesen-’n-’ quite this n-little¼dim rep.factual-n.pat-be.pleasant-inch-prf ‘But when we crossed the border we felt a little better again.’ The particle o´:nen also occurs pervasively in independent sentences meaning ‘at the time’, ‘now’, or ‘then’. (25) Mohawk o´:nen ‘now’: Josephine Horne, Charlotte Bush, sp p.c. JH To: ken nitiako´:ien’ o´:nen? to: ken ni-t-iako-ien’ o´:nen how.many Q partitive-cisloc-f.pat-have now ‘How old is she now?’ ´ :nen ki’ CB O iakoierı´:ton tsa´:ta niwa´hsen. o´:nen ki’ iako-ierit-on tsiata ni-w-ahs-en now in.fact f.pat-complete-st seven prt-n-be.ten-st ‘She’s now seventy.’ ´ :nen ki’ JH En:. O ieio´he’ naiotorı´shen. en: o´:nen ki’ ie-io-he’ na-io-at-orish-en yes now actually tloc-n-be.time prt-n.pat-mid-rest-st ‘Yes. It’s time for her to retire now.’ One might be tempted to conclude that since o´:nen can be used as a temporal adverb without relational syntactic meaning as in (25), examples like (24) are simply sequences of independent sentences with the same adverb: ‘But then we crossed the border. We felt better again.’ There is, however, evidence that these are conventionalized constructions, complex sentences with embedded clauses. Like the complement constructions seen earlier, these constructions are pronounced under a single intonation contour, without an intermediate fall or pitch reset. (24)’

‘But when we crossed the border we felt better again.’

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Temporal clauses may precede the matrix clause as in (24), or follow it as in (26), without implying an iconic sequence of events as they would in separate sentences. The sentence in (26) does not mean that it was pleasant and then people would cook. (26) Mohawk temporal adverbial clause: Awenhra´then Deer, speaker Ion’we´:sen’s ki’ thı´:ken io-on’wes-en¼’s ki’ thı´:ken n.pat-be.pleasant-stative-distr in.fact that o´:nen enthatikho´n:ni. o´:nen en-t-hati-khw-onni-’ o´:nen future-cislocative-m.pl.agt-meal-make-prf ‘In fact it used to be nice when they would cook.’ Furthermore, adverbial clauses, like complement clauses, can be preceded by particles like ne ‘the’, provided that the events referred to are identifiable to the listeners. The speaker cited in (27) had just been describing the di‰culty some children were having as they kept trying to saddle a horse. (27) Mohawk temporal adverbial clause with ne ‘the’: A. Deer, sp No´:nen enhonte’nie´n:ten ne o´:nen en-hon-ate-’nienten’ the when future-m.pl.agt-middle-try-prf sok tenka´:ta’ne’. sok t-en-ka-t-a’n-’ then duplicative-future-n.agt-stand-inch-prf ‘When they would try, it would stop.’ Finally, the translations provided by speakers confirm the fact that these constructions are interpreted not as sequences of separate, independent sentences, but rather as single, complex sentences, routinized constructions. The fact that we can identify a lexical source for the subordinating marker o´:nen is not surprising. As is well known, the most frequent sources of grammatical markers are lexical items (a tendency already noted by Gabelentz (1891) and Meillet (1912), and the object of the extensive work on processes of grammaticalization over the past several decades). The survival of uses of a particular form with lexical meaning in some contexts does not preclude its development of a grammatical function in others.

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33

5. Cross-linguistic variation in recursive structures As seen in the preceding sections, Yup’ik, Khalkha, and Mohawk all contain syntactic structures that involve recursion, but their constructions are not identical to each other in function. The Yup’ik Subordinative is broader and more general than English complement constructions: it is used extensively to indicate syntactic and discourse cohesion, as in (4) above: ‘He placed them [subordinative] carefully, and when one fell, he picked it up, placing it [subordinative] in the basket’. The Khalkha geǰ construction, on the other hand, is used more narrowly than English complementation, limited to situations involving words or thoughts. There are also cross-linguistic di¤erences in the density of recursion in particular areas of syntactic structure. Some languages show productive recursion in noun phrases, with multiple levels of embedding, as in the Khalkha example in (8): ‘This time I’m thinking that I’ll talk a little about [the development [of the religion [of Buddhism [of Mongolia]]]].’ Others show little if any noun phrase recursion, expressing similar ideas in di¤erent structures. A Yup’ik speaker opened her description of the Pear Film with the sentence in (28). It contained three appositive nominals, each with an Ablative case su‰x marking its syntactic role in the matrix. (28) Yup’ik appositive noun phrases: Elizabeth Ali, speaker p.c. Qalarteqatartua, qalarte-qatar-tu-a speak-fut-intransitive.indicative-1sg I will speak watua uumek, watua una-mek just.awhile.ago this-abl just awhile ago about this one tarenramek tangllemnek. tarenraq-mek tangerr-lleq-mnek picture-abl see-past.nzr-1sg/sg.abl about picture about my seen one ‘I am going to speak about this picture I have just seen.’ Adding appositive nominals could in principle open the way to infinitely long sentences, but such constructions are actually examples of iteration rather than recursion. Parker (2006: 181) characterizes the di¤erence as follows.

34

Marianne Mithun Simply put, the di¤erence between iteration and recursion is this: the former involves mere repetition of an action or object, each repetition being a separate act that can exist in its entirety apart from the other repetitions, while the latter involves the embedding of an action or object inside another action or object of the same type, each embedding being dependent in some way on the action/object it is embedded inside.

The Hauser, Chomsky, and Fitch proposal pertains to recursion. In Mohawk, relationships among entities are not usually expressed in noun phrases at all. (29) Mohawk: Skawe´nnati Montour, speaker p.c. ´ :nen ken o´nhte’ O now Q perhaps rontate’ken’oko`n:’a, ron-atate-’ken’¼okon’a 3pl-rfl-be.siblings¼distr they are siblings to each other roie`n:’a. ro-ien’¼’a m.sg/m.sg-have as o¤spring¼dim he has him as o¤spring ‘Maybe it’s his brother’s son.’ Some languages show recursion in morphological structure, while others do not. The Yup’ik verb in (30) shows what is termed ‘indirect recursion’ (Heine and Kuteva 2007: 265–6). The past tense su‰x appears twice in the word, but it was not applied directly to its own output. (30) Yup’ik indirect recursion: George Charles, speaker p.c. Ayallrunillruat. ayag-llru-ni-llru-a-t go-past-say-past-transitive.indicative-3pl/3sg ‘They said he had left.’ The past stem ayag-llru- ‘left’ first served as the input to the derivation of a new stem, ayagllru-ni- ‘say left’, which in turn served as the base for the second application of the past tense su‰x. The Khalkha verb in (31) shows what is termed ‘direct recursion’ (Heine and Kuteva 2007: 265). The causative -uul was applied directly to a stem formed by a previous application of the same su‰x.

The fluidity of recursion and its implications

35

(31) Khalkha direct recursion: Erdenebaatar Erdene-Ochir, sp p.c. jav ‘go’ jav-uul ‘send’ (cause to go) javuul-uul ‘have (someone) send’ (cause to send) bi bi

zaxia javuulsaÐ. zaxia javuuluulsaÐ.

‘I sent a letter.’ ‘I had (somebody) send a letter.’

The recursive structure was not built up on a single occasion, through simple iteration of a su‰x. The complex stem jav-uul first became established as a lexical unit: javuul ‘send’. The causative -uul was then added to this stem as a whole. The idiosyncratic meaning of the first derived form persists in the second: the verb javuuluul means ‘have someone send’, not ‘cause to cause to go’. Recursive structures may be pervasive but they are far from homogenous in distribution or nature cross-linguistically. They occur in both morphology and syntax, but not in every language. They occur in noun phrases and clauses, but again not in all languages. Some recursive structures, like the noun phrase recursion seen in Mongolian, are the result of what Harder (this volume), citing Pinker and Bloom (1990: 724) and Parker (2006: 5.5.3), describes as ‘top down’: successive specification is added to already existing constituents, resulting in an ever finer level of precision of description. Others, like that seen in complementation, are the result of what Harder describes as ‘bottom-up’ construction: a situation may be first asserted in a predication, as in the Yup’ik ‘I am fine’, then later reified and referred to in a new predication ‘I will tell them [that you are doing fine]’. Information conveyed by embedding in some languages is conveyed by iteration in others. When the Mohawk speaker described the Pear Film, she used the complement construction in (32). (32) Mohawk complementation: Kaia’tita´hkhe’ Jacobs, sp p.c. Sok kı´:ken raksa`:’a so this boy wa`:rehre’ he thought Iah ki’ na:’ the´: thaha´ttoke’ ki: iah ki’ na`:’a the´:nen th-a:-ha-attok-’ kı´: not in fact guess at all contr-opt-m.sg.agt-notice-prf this

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osto`n:ha ia´:khawe’ ki: rao`:hi. oston¼ha i-a:-k-haw-’ kı´:ken rao-ahi little¼dim tloc-opt-1sg.agt-carry-prf this m.sg.al.poss-fruit ‘So this boy thought, ‘‘I guess he wouldn’t notice [that I took a little of this fruit].’ Describing the same film, the Mongolian speaker used a series of adverbial clauses. (33) Mongolian adverbials: Erdenebaatar Erdene-Ochir, speaker p.c. Tegeed ter duguitai xu¨u¨xed xaǰuuqaar n’ neg teg-eed ter dugui-tai xu¨u¨xed xaǰuu-qaar n’ neg do.so-seq that circle-com child side-inst foc one zo¨ro¨x gesnee, uh zo¨r-o¨x ge-sen-ee, uh pass-infinitive say-past-rfl hes ter ter that

xu¨nii xu¨n-ii person-gen

liir xuraaǰ baiqaag xaraad, liir xuraa-ǰ bai-qaa-g xar-aad pear collect-non.finite be-prog-acc see-seq sagstai liiru¨u¨d, ter gazar sags-tai liir-u¨u¨d ter gazar basket-com pear-pl that ground liiru¨u¨diig sagstai sags-tai liir-u¨u¨d-iig basket-com pear-pl-acc tegeed teg-eed thus-seq

ter ter that

deer baigaa deer bai-gaa above be-prog

xaraad xar-aad see-seq

xu¨Ð xu¨Ð person

o¨o¨riig n’ aÐzaaraagu¨i boloxoor ter- xu¨u¨xed ter xu¨u¨xed o¨o¨r-iig n’ aÐzaar-aa-güi bol-ox-oor self-acc foc notice-rfl-neg become-inf-inst that child ter liiriig n’ ter liir-iig n’ that pear-acc foc

xulqailǰ xulqai-l-ǰ theft-verbalizer-non.finite

baiqaa bai-qaa be-prog

The fluidity of recursion and its implications

jum jum thing

37

sˇig baiaÐ. sˇig bai-saÐ like be-past

‘Then, it looked like when the child with the bicycle was about to pass by, having seen the man collecting the pears, having seen the pears being in the baskets, that pears with the baskets were on the ground, since the man didn’t notice him, the child was stealing the pears.’ 6. The dynamism of the recursive constructions The constructions that exhibit recursive structure are not static within languages. The most commonly cited examples of recursion in syntax, the type mentioned by Hauser, Chomsky, and Fitch, are complement constructions. The Yup’ik Subordinative construction is deeply embedded in the grammar, marked by verbal su‰xes, but we can still trace its origin in clause nominalization. The Khalkha geǰ construction developed through the generalization of a quotative construction. It is not as advanced in its development as the Yup’ik Subordinative, nor is it used in the same wide range of contexts: it still shows the full formal structure of direct quotation and is restricted to contexts involving words or thoughts. The Mohawk complement construction shows an even earlier stage of development. There is no complementizer, no omission of coreferential arguments, and no reduction in finiteness. The clausal integration is often marked only intonationally. Still, the status of the complement clause as a referring expression rather than an independent predication is confirmed by its ability to be preceded by a determiner. Adverbial clause constructions show similar variability in their origins and stages of development. Yup’ik Past Contemporative clauses (‘when in the past’) have their source in nominalized clauses inflected for locative case. The Khalkha counterpart shows a similar development through the extension of the locative case su‰x from nouns to clauses. The source of the corresponding Mohawk temporal adverbial clause construction can still be traced as well, but it developed in a di¤erent way and is less deeply integrated into the grammar, marked just by the particle o´:nen ‘at the time’ and intonation. The fact that we can see the origins of these embedded clause structures should not be taken as evidence that the languages lacked recursion at an earlier stage. Each of these languages in fact shows evidence of the earlier existence of complex sentence constructions.

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As is well known, the most common sources of a‰xes are full lexical items. The Eskimo-Aleut languages contain a wealth of modern morphological formations that are apparently descended from complex sentence constructions, like -ni- ‘say’ in the Yup’ik example in (30) above: ‘He said that he had left.’ The Mongolian languages also show morphological formations suggestive of earlier complement constructions, like the causatives based on the su‰x -uul seen in (31): jav-uul ‘cause to go’ ¼ ‘send’. The Iroquoian languages also show traces of earlier complex sentence constructions in their morphologies. Among the derivational su‰xes on verbs are applicatives which add a core argument, such as an instrument, a beneficiary, or a location. One of the instrumental applicative su‰xes is -hst. (34) Mohawk Instrumental Applicative iera’wistakarha’tho´hstha’ ie-ra’wist-a-karha’tho-hst-ha’ one-pancake-linker-flip-inst.applicative-hab ‘one pancake flips with it’ ¼ ‘spatula’ The source of this su‰x persists in the modern Iroquoian languages as the verb root -hst ‘use’, as in Tuscarora kı´hstha’ and Mohawk ka´tsha’ ‘I use it’. After a complement construction has emerged, it can continue to evolve. When the Mohawk speaker cited earlier first began describing the pear picker in the Pear Film, she included two short, barely audible words: ´ı:kehre’ ‘I think’ and o´nhte ‘perhaps’. Both still function in other contexts as matrix verbs, but here they are reduced to barely audible discourse particles, no longer restricted to a position immediately before a complement clause. (35) Mohawk nascent discourse particles: Kaia’tita´hkhe’ Jacobs, speaker Kı´:ken ro´n:kwe, this man kwah kwah just just

´ı:kehre’ ka´tshe’ k-ehr-’ katshe’ 1sg.agt-believe-st jug I believe jug

ka´hi kahi fruit fruit

o´nhte, a:-w-aht-e opt-n.agt-be.so-st it could be so

rahia´kwahs. ra-ahi-akw-ahs m.sg.agt-fruit-pick-hab he fruit picks ‘This man, I guess, was perhaps just picking fruit.’

The fluidity of recursion and its implications

39

Such gradience in evolving forms is of course common cross-linguistically. A well-known example is the English you know (Thompson 2002).

7. The notion of recursion as the essence of human language Recursive structures, in which one constituent is embedded inside of another of the same type, are pervasive cross-linguistically, perhaps more pervasive than might first appear. But as we have seen, they are neither homogenous across languages nor static within them. The variation and gradience suggest that recursion is not the basic, hard-wired feature proposed. Recursive structures are in a sense epiphenomenal, the products of a host of cognitive abilities. Among these is an ability to integrate elements of what is understood as a larger idea into a larger, coherent structure. We saw this in the prosodic integration of sequences of clauses under a single intonational contour. Another is the capacity to reify events, to refer to situations as entities. We saw this in the formation of complement constructions from nominalized clauses in Eskimo-Aleut. Another is the capacity for abstraction, seen in the expansion of Mongolian quotative constructions to complement constructions involving thoughts and intentions. Still another is the capacity for generalization, seen in the extension of case markers from nouns to clauses in the formation of adverbial clause constructions. Yet another is the ability to routinize patterns, so that constructions need not be created anew each time they are used. Such routinization is behind the continuing evolution of certain complement constructions into discourse markers, as in Mohawk. It is also behind the chunking of morphologically complex stems into lexical units, which can in turn serve as the basis for subsequent derivational processes, as in the Khalkha causative ‘go-cause’ ! ‘send’; ‘send-cause’ ! ‘have send’. In the end, the logical possibility of infinitely long sentences is neither the goal of speakers nor the essence of language. It is an artifact of a view of language as a mathematical system instead of the continually evolving product of human cognitive abilities.

Abbreviations abl ¼ ablative, acc ¼ accusative, agt ¼ grammatical agent, cisloc ¼ cislocative, comp ¼ complementizer, dim ¼ dimunitive, distr ¼ distributive, dv ¼ duplicative, excl ¼ first person exclusive, f ¼ feminine gender, foc ¼ focus, fut ¼ future, gen ¼ genitive, inst ¼

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instrumental, loc ¼ locative, m ¼ masculine, mid ¼ middle, n ¼ neuter, neg ¼ negative, nz ¼ nominalizer, pat ¼ grammatical patient, prf ¼ perfective, prog ¼ progressive, r ¼ coreferential 3, rfl ¼ reflexive, seq ¼ sequential, transloc ¼ translocative

References Gabelentz, Georg von der 1891 Die Sprachwissenschaft: ihre Aufgaben, Methoden und bisherigen Ergebnisse. Leipzig: Weigel. Harder, Peter This volume. Over the top-recursion as a functional option. Hauser, Marc D., Noam Chomsky, and W. Tecumseh Fitch 2002 The faculty of language: What is it, who has it, and how did it evolve? Science 22:298.5598: 1569–1579. Heine, Bernd and Tania Kuteva 2002 World Lexicon of Grammaticalization. Cambridge, UK: Cambridge University Press. Heine, Bernd and Tania Kuteva 2007 The Genesis of Grammar: A Reconstruction. Oxford, UK: Oxford University Press. Meillet, Antoine 1912 L’e´volution des formes grammaticales. Scientia 12/26 (Milan). Reprinted 1951 in Linguistique historique et linguistique ge´ne´rale, 130–148. Paris: C. Klincksieck. Mithun, Marianne 2006 Threads in the tapestry of syntax: Complementation and Mohawk. In Jacqueline Bunting, Sapna Desai, Robert Peachey, Christopher Straughn, Zuzana Tomkova´ (eds.), Papers from the Forty-second Meeting of the Chicago Linguistics Society, 213– 238. Chicago: Chicago Linguistic Society. Mithun, Marianne 2008 The extension of dependency beyond the sentence. Language 83.69–119. Mithun, Marianne 2009 Re(e)volving complexity: Adding intonation. In T. Givo´n and Masayoshi Shibatani, (eds.), Syntactic Complexity: Diachrony, Acquisition, Neuro-cognition, Evolution, 53–80. Amsterdam/Philadelphia: Benjamins. Noonan, Michael 2007 Complementation. In Timothy Shopen (ed.), Language Typology and Syntactic Description. 2nd ed, 52–150. Cambridge, UK: Cambridge University Press.

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Evolution as a constraint on theories of syntax: The case against Minimalism. Ph.D. diss, Department of Linguistics, University of Edinburgh. Pinker, Stephen and Raymond Jackendo¤ 2005 The faculty of language: What’s special about it? Cognition 95: 201–236. Thompson, Sandra 2002 ‘‘Object complements’’ and conversation: Towards a realistic account. Studies in Language 26.1: 125–164.

3.

Syntactic recursion and iteration

Fred Karlsson

1. Introduction1 The nature and origin of syntactic recursion in natural languages is a topical problem. Important recent contributions include those of Johansson (2005), Parker (2006), Tomalin (2006; 2007), and Heine and Kuteva (2007). Syntactic recursion will here be discussed especially in relation to its cognate concept of iteration. Their basic common feature is plain structural repetition: ‘‘keep on emitting instances of the current structure, or stop’’. Their main di¤erence is that recursion builds structure by increasing embedding depth whereas iteration yields flat output structures which do not increase depth. My focus here is on the types of recursion and iteration, and on what empirically determinable constraints there are on the number of recursive and iterative cycles of application. Recursion comes in two subtypes, nested recursion (¼center-embedding) and tail-recursion, the latter covering left-recursion and right-recursion. There are six functionally di¤erent types of iteration: structural iteration, apposition, reduplication, repetition, listing and succession. It will be empirically shown that multiple nested syntactic recursion of degrees greater than 3 does not exist in written language, neither in sentences nor in noun phrases or prepositional phrases. In practice, even nesting of degree 2 is extremely rare in writing. In speech, nested recursion at depths greater than 1 is practically non-existing, thus partly confirming an early hypothesis of Reich (1969). Left-branching tail-recursion of clauses is strictly constrained to maximally two recursive cycles. Right-branching clausal tail-recursion rarely transcends three cycles in spoken language and five in written language. On constituent level both left- and rightbranching is less constrained (especially in written language), but e.g.

1. I thank three anonymous referees for valuable comments and suggestions for improvement.

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left-branching genitives rarely recurse more than two cycles ([[[Pam’s] mum’s] baggage]).

2. Types of sequential arrangement There are many types of rules and restrictions on the sequential arrangements of words, constituents and clauses. Most important in any language are the principles of basic linearization of obligatory elements. These are word order restrictions and tendencies governing the arrangements of grammatical elements and simple canonical constituents, clauses and larger structures, e.g. (for English typical pragmatically unmarked declarative sentences): – a grammatical subject precedes its main verb, – a grammatical object follows its main verb, – a subcategorized locative adverbial follows it main verb. This obligatory basic linearization of word classes, constituents, heads and dependents, grammatical functions etc. defines the co-occurrence and word-order properties of the grammatical elements and constructions. This core grammar is the foundation of the optional complexity-introducing types of sequential arrangement such as iteration and recursion. Every natural language has basic linearization principles which also determine its classification in word order typologies. These rules are mostly local and simple precedence statements. A special type of basic linearization is that of lexicalized multiword expressions: phraseology (1) and lexical bundles (2), i.e. expressions frequent in a certain register (Biber et al. 1992: 993): (1) you know (2) I was going to Every language has lexicalized multiword expressions, at least lexical bundles. Most languages have semantically non-compositional idioms and phraseology (however, Piraha˜ is claimed by Dan Everett, p.c., to have no idioms nor lexical bundles). Minimal canonical structures may be optionally elaborated by free modification, e.g. by adding adjectival or genitival premodifiers to nouns, intensifiers as premodifiers to adjectives, free adjuncts to verbs, and noncomplement clauses subordinate clauses to main clauses:

Syntactic recursion and iteration

– – – – – –

45

a determiner precedes its nominal head, a determiner precedes an adjectival modifier of the same head, an adjectival modifier precedes its nominal head, a case-marked genitival NP precedes its nominal head, an if-clause prefers initial embedding position, a when-clause may be embedded initially or finally.

There are also information-packaging principles such as inversion, preposing, postposing, extraposition, and ‘‘fat things last’’, which interact with the principles of basic linearization and free modification, adapting the orders of canonical arrangements to fit textual and pragmatic needs. These three mechanisms together define grammatically well-formed and situationally appropriate sentences such as (3). (3) Nat’s fat cat sat on the mat when it spat out a rat. Recursion and iteration are also types of sequential arrangement, but layered on top of basic linearization, free modification and informationpackaging by invoking repetition: ‘‘keep on emitting instances of the current structure, or stop’’. Their main di¤erence is that recursion builds structure by increasing embedding depth whereas iteration yields flat output structures, repetitive sequences on the same depth level as the first instance. Recursion and iteration are the main topics of this paper and they will here be analyzed in conformance with Wilhelm von Humboldt’s insightful early agenda: (4) ‘‘Ist aber auch die [grammatische] Freiheit an sich unbestimmbar und unerkla¨rlich, so lassen sich dennoch vielleicht ihre Gra¨nzen innerhalb eines gewissen ihr allein gewa¨hrten Spielraum au‰nden; und die Sprachuntersuchung muß die Erscheinung der Freiheit erkennen und ehren, aber auch sorgfa¨ltig ihren Gra¨nzen nachspu¨ren.’’ (von Humboldt 1836: 81; italics added/FK) ‘Even if [grammatical] freedom in itself would be impossible to determine and explain, it might still perhaps be possible to find its limits within the confines of a certain latitude reserved for it, and language study must recognize and respect the phenomenon of freedom, but also carefully try to determine its limits.’ In this spirit, it is relevant to ask both what types of recursion and iteration there are, and what empirically determinable constraints (if any) there are on the number of repetitive cycles in both recursion and iteration. I first turn to iteration.

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3. Six types of iteration On both formal and on functional (partially semantic, partially psycholinguistic) grounds, six types of iterative sequential arrangement can be distinguished: 1) structural iteration, 2) apposition, 3) reduplication, 4) repetition, 5) listing, and 6) succession. They all concatenate elements without additional depth-increasing structure building. The latter feature distinguishes them from recursion, which creates hierarchic structures governing the linear strings it produces, typically by repeatedly subordinating an element to another instance of the same type. 3.1. Structural iteration The most important type of iteration is structural iteration which is overwhelmingly most frequent. It has no clear semantic task and this too sets it o¤ from the other five types of iterative sequential arrangement which are functionally motivated special cases. The main manifestation of structural iteration is coordination, with or without explicit conjunctions. The gist of coordination and all other types of structural iteration is ‘‘optionally add an instance of the same structural type as the current one, with (syndetically) or without (asyndetically) a coordinating conjunction’’. Prototypical structural iteration works much like the Kleene star, ‘‘*’’, in formal language theory. All major constituent types (NP, AP, PP etc.), grammatical functions (subject, object, adverbial etc.) and clause types (relative clauses, ifclauses, infinitive clauses etc.) may be iteratively coordinated, on the same level of structure. Also many free modifiers may be iteratively coordinated, e.g. adjectival modifiers (but not determiners) and case-inflected genitival NPs as premodifiers of nominal heads. It is thus an inherent property of grammatical elements and construction types whether they are iterative, recursive or neither or both. By far the two most important and frequent iterative structures are coordination of clauses in sentences and of NPs in clauses. There are no bounds on the number of constituent-level conjuncts, or on how many coordinated clauses there may be in a single sentence. For example, in Hermann Broch’s (1961: 138–144) novel Der Tod des Vergil there is a 1077-word sentence extending over six pages, with 81 finite and 38 nonfinite clauses, and several hundred instances of coordination on modifier, constituent and clause level. By contrast, observe that depth-increasing recursion with multitudes

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47

(e.g. 100, or even 10) of successively embedded subordinate clauses never is the central mechanism underlying such unusually long sentences. Thus, the maximal clausal embedding depth of Broch’s gigantic sentence is a modest 3, and this is reached only once. In this sentence there are only two instances of subordinate clauses at depth 2. To pick another example, consider the famous chapter of Ulysses where Joyce describes the stream of consciousness of Molly Bloom in eight huge paragraphs without punctuation. One sentence is 12,931 words long. The first ten pages of this chapter (Joyce 1934: 723–732; 5,500 words) contain one instance of recursive final (right-branching) clausal embedding reaching depth 6 (‘‘F’’ ¼ final, the numbers as in F-2 indicate embedding depth): (5) [ . . . she said yes [F-1 because it grigged her [F-2 because she knew [F-3 what it meant [F-4 because I used [F-5 to tell her a good bit of [F-6 what went on between us . . . ]]]]]]] (Joyce 1934 [1922]: 729) But such depths are very untypical. The abnormal length of Joyce’s 12,931-word sentence is caused by extensive use of coordination. One more indication of the prevalence of iterated coordination is the fact that the conjunction and or its equivalent is one of the most common words in many languages. Clause chaining is another variant of iterative clause linkage, closely related to asyndetic coordination. Likewise, certain types of verb serialization are basically iterative in nature (Sebba 1987: 111). 3.2. Apposition Appositions are typically iterated NPs on the same level of depth. Their defining feature is mutual coreference. This property sets appositions o¤ from coordination as a special, semantically motivated type of iteration. (6) is a genuine fivefold Swedish appositive structure (coreferential nominal heads in boldface). (6) Ej la˚ngt da¨rifra˚n sitter ett fo¨rema˚l fo¨r ma¨ngdens ka¨rleksfulla not far away sits an object for crowd’s loving hyllning, ovation Henrik Gabriel Porthan Henrik Gabriel Porthan, akademiens yppersta la¨rare, Academy’s most magnificent teacher

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den fosterla¨ndska ha¨fdaforskningen fader, the national historical research’s father en man som gaf sitt namn a˚t ett helt tidehvarf i va˚r a man who gave his name to a whole epoch in our kulturhistoria. cultural history ‘Not far away sits the object of the loving ovation of the crowd, Henrik Gabriel Porthan, the most magnificent teacher of the Academy, the founder of national history, a man who gave his name to a whole epoch in the history of our culture.’ The number of cycles in iterated apposition is unconstrained but numbers in excess of a handful are rare. This property too sets apposition o¤ from structural iteration for which the number of cycles is truly unconstrained and easy to document by concrete examples. 3.3. Reduplication Syntactic reduplication, often called repetition, is a motivated type of iteration, where a word (normally a content word) is repeated in order to express meaning modulations such as intensification, augmentation, repetition, diminution, or iterative or continuative action. Usually the construction is asyndetic, but it may be syndetic as well, especially with adverbs, comparatives, and verbs. Here are some originally Swedish examples from Lindstro¨m (1999), in direct translations all of which qualify equally as idiomatic English (and all of which can be found on the internet): (7) a. There were cars cars cars. b. a long long way c. small small creatures d. much much better e. played better and better f. came closer and closer g. They walked and walked and walked. In his corpus-based study of syntactic reduplication in 1.7 million words of spoken and written Swedish, Lindstro¨m (1999) noted the predominance of reduplicated pairs with two identical terms. Triples are rare, quadruples extremely rare. Therefore reduplication is indeed the most apt term for this type of iteration. The incidence of asyndetic reduplication (without conjunctions) in Swedish is one per 3000 words, higher in spoken than in written language, and of syndetic reduplication one per

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5000 words. Of 620 Swedish instances of reduplication only five were triples. These are clear preferences. On the other hand, they do not strictly rule out longer chains (which are easy to attest e.g. by googling). 3.4. Repetition, listing, succession The iterative concept of plain repetition (or repeat, in the terminology of Biber et al. 1999: 1055) concerns the special, psycholinguistically motivated case of speech planning. The speaker repeats (often involuntarily) some word or syntagm, especially words belonging to closed grammatical classes, in order to gain time to complete planning the message. The outcomes of such repetitions are formally ungrammatical. (8) a. b.

Yeah, it, it, it is it’s it’s it’s it’s good. (Biber et al. 1999: 1055) And and / if if if you know they had none at all. (British National Corpus, FMD 321)

The corpus data of Biber et al. show that the likelihood of the repetition decreases sharply with the number of words repeated. The vast majority of examples contain a single repeat. There are extremely few instances of three or more repeats. Listing (enumeration) is an iterative mechanism predominantly used in restricted lexical taxonomies, see (9a) and (9b): (9) a. b. c.

Smith, Brown, Jones . . . Monday Tuesday Wednesday . . . one two three . . .

A special kind of listing is succession (9c), which underlies numerosity (Heine and Kuteva 2007: 271). Given any number n, the successor function enables production of n þ 1. Repetition, listing and succession of course have no limits. 4. Syntactic recursion: historical and conceptual background Heine and Kuteva (2007: 264–266) discuss several important conceptual distinctions relating to recursion: direct recursion (modeled by rules like A ! AB) vs. indirect recursion (A ! B, B ! A), counting recursion (yielding AABB) vs. mirror recursion (yielding ABBA), and simple recursion (with only once application cycle) vs. productive recursion (with an unlimited number of cycles). The di¤erence between nested recursion and tailrecursion is the most important one from the viewpoint of the present paper. Nested recursion and tail-recursion have often been presumed to be

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unrestricted (or productive in Heine and Kuteva’s terminology). For tailrecursion this is by and large true, but in Humboldt’s spirit (1) it will be demonstrated below that there are quantitative constraints especially on nested syntactic recursion of clauses, noun phrases and prepositional phrases. The use of nested and tail-recursive rules in grammatical description is ancient because such rules were formulated already around 400 BC, in Pa#n¸ini’s Sanskrit grammar (Bhate and Kak 1993: 79) and in Tholkaappiyar’s Tamil grammar (Baladunarman, Ishwar, and Kumar 2003). In recent linguistic theory recursion was reintroduced around 1950, probably first by Bar-Hillel (1953), under influence from the theory of recursive functions in mathematical logic (Tomalin 2006: 64). In Chomsky’s PhD dissertation (1975 [1955–1956]) recursion is discussed in several connections, e.g. as the source of sentential infinity and as for its proper locus in the grammar. However, Chomsky’s (1956: 65; 1957: 21–23) original published claims concerning the alleged unconstrainedness of nested recursion in English syntax are sketchy and rely only on examples invented by Chomsky himself. It is surprising to note that prior to the current millennium the deeper nature and the various types of recursion in natural languages have not been discussed at great length in any brand of grammatical theory (however, see Halliday 1963 for an early exception). Parker (2006) surveys the prevailing conceptual and terminological variation. Table 1 provides an overview of some relevant concepts and terminology in a mainly generative and computational framework. Table 1. Basic conceptualization and terminology of recursion. Type of rewrite rule (a, b A 0)

Mode (orientation) of recursion

Relation to iteration

Linguistic term

A!A a

left-recursion

left-branching ¼ initial embedding

A!a A

right-recursion

A!a A b

nested recursion

tail-recursion ¼ convertible to iteration2 tail-recursion ¼ convertible to iteration full-blown recursion, not convertible to iteration

right-branching ¼ final embedding nesting, centerembedding

2. Tail-recursion is always convertible to simple iteration (Aho, Sethi, and Ullman 1986: 53).

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A standard view of recursion in the formal sciences is the top-down one that a function is recursive if it is defined in terms of successively simpler versions of itself such that a termination condition (variably called the baseline, base case, or degenerate case) guarantees the process to halt. A recursive function is not well-formed if its termination is not guaranteed (Brookshear 2007: 246). A well-formed recursive procedure is designed to test for the termination condition before requesting further cycles of activation. Material introduced by any lower recursive cycle is always contained (embedded) in the material introduced by the immediately higher cycle. Every applicative cycle increases the recursive depth by 1. Thus, the depth of sentence (5) is 6. The typical generative-linguistic conception of recursion on the contrary emphasizes that syntactic recursion lacks termination conditions: this is the very property that guarantees the infinity of sentence length and structural elaboration. Nested recursion (center-embedding) is recursion par excellence. A nested structure Xn is embedded within a structure of the same type, Xn1, with non-null material (excluding subordinating conjunctions, cf. endnote 3) of Xn1 both to the left and to the right of Xn. Nested recursion consumes memory resources and presupposes storage of pending material and return addresses on a stack in order to secure proper unwinding. This sketchy description is equally true of human language processing and its counterparts in formal language theory and computational linguistics. Nested recursion of precisely the same type of element (e.g. two relative clauses, two if-clauses, two NPs) is called self-embedding. Formally, leftrecursion and right-recursion can always be converted to iteration, i.e. to repetition (one more cycle) of the same procedure, without anything pending on the stack (Aho, Sethi, and Ullman 1986: 53). Structures like ‘‘if if if S1, then S2, then S3, then S4’’, i.e. counting recursion (Christiansen and Chater 1999: 168) were introduced into the public theoretical discussion already by Chomsky (1956: 65) and claimed to be unrestricted as for recursive depth. For reasons mentioned in endnote 3, such sentences are here regarded as initially-embedded, not as centerembedded. Karlsson (2007a) demonstrated that there is a strict empirically determinable quantitative constraint on repeated initial embedding of clauses, viz. (10) to be discussed shortly. A final note is in order concerning the ontological nature of recursion. Halliday (1963: 85–13) is clear on interpreting recursion as an integral part of language structure. A structural element is repeated in depth, a series of such elements thus forming a progression. This ontological commitment also is at the heart of generative grammar, where recursion has

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always been regarded as the very structural feature that caters for the presumed infinity of language (i.e., a category on the left-hand side of a rewrite rule reoccurs on the right-hand side, cf. Table 1). But there are other views. For Linell (2005: 75), in spoken interaction long utterances with multiple embeddings are emergent results of local decisions of moving from one turn-constructional unit to another. They are not part of the grammar per se. The grammar contains just a core syntax plus methods for moving to the next turn-constructional unit. Similarly, Harder (2006) treats recursion as a semantic and functional option of use, a possibility allowed by the whole system, arising as a more or less epiphenomenal consequence or side e¤ect when a functional upgrading operation such as reusing a that-clause after reporting verbs happens to concern a structural type that is already present in the input. Clausal recursion as such is not built into the fabric of grammar. Heine and Kuteva (2007: 265) opt for an intermediate agnostic position. According to them, recursion is not a property of language but rather the product of a theory designed to describe language structure: ‘‘. . . we are not maintaining that language, or language structure, has recursion but rather that there are certain properties to be observed in language that can appropriately be described in terms of a construct [of formal recursion]’’. These views need not be fully contradictory. Properties of languages can be described by formal mechanisms without necessarily renouncing the ultimate functional motivation of the properties. Allowing multiple (even if not fully unconstrained) right-recursion in core grammar seems to be more or less equivalent to Linell’s basic embedding patterns þ methods for moving to the next turn-constructional unit. On the other hand, every theoretical concept is a hypothesis about a phenomenon in some more or less real world and the question whether the concept properly represents the ‘‘God’s-truth Ding an sich’’, or is a plain ‘‘Hocus Pocus construct’’, in the sense of Householder’s (1952) famous and much-debated distinction, can be left open for philosophical discussion.

5. Constraints on clausal recursion Clausal embedding recursion means repeated embedding of clauses in initial, central or final position of the superordinate clause. Initially-embedded clauses (IEs) have either nothing to their left, or a subordinating

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conjunction of the superordinate clause.3 Center-embedded clauses (CEs) have superordinate clause constituents to their left (other than subordinating conjunctions) and right. Final embeddings (FEs) have no material rightwards that immediately belongs to the superordinate clause. IE and FE manifest tail-recursion, CE is nested recursion. Karlsson (2007a; 2007b) has empirically established constraints, quantitative limits and qualitative restrictions, on clausal embedding recursion in many European languages. His data were (i) complex sentences in the British National Corpus (BNC), the Brown corpus, and the LOB corpus, (ii) computerized extraction of complex embedding patterns in Finnish, German, and Swedish, and (iii) consultation of 100þ corpus-based syntactic and stylistic descriptions of European languages, especially Latin and older variants of German. Here (10-14) are some constraints operational in many European languages (at least in Danish, English, Greek, Finnish, Latin and Swedish). ‘‘I’’ stands for initial clausal embedding, ‘‘C’’ for clausal center-embedding, and the raised exponent expresses maximal degree of embedding of a sentence, e.g. I2 is double initial embedding. Expressions like C-2 indicate type and embedding depth of individual clauses. ‘‘-w’’ is short for ‘‘written language’’ and ‘‘-s’’ for ‘‘spoken language’’. (10) I2 max: the maximal degree of initial clausal embedding is 2; 100 instances found, as in (15). (11) Qualitative I2-constraints: Double initial clausal embedding strongly prefers a) written language, b) an if-clause as higher embedding, c) a sentential subject, i.e. a what-clause as lower embedding, and d) finiteness. See (15). (12) C3 max-w: in written language, the maximal (very rare) degree of multiple clausal center-embedding is 3; thirteen instances retrieved, (16). (13) C2 max-s: in spoken language, the maximal (very rare) degree of multiple clausal center-embedding is 2; only two instances retrieved, (17). 3. Note that I follow Quirk et al. (1989: 1037) in interpreting clauses like I-2 in sentence (15), embedded immediately after a subordinating or coordinating conjunction, as initially-embedded rather than as center-embedded. The main argument is that subordinating and coordinating conjunctions are not syntactically as tightly integrated and real constituents in their clauses as ordinary full constituents (and relative pronouns) are.

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(14) Only-postmodifying-self-embedding: only postmodifying (i.e. typically relative) clauses allow self-embedding (16, 17). (15) [[I-1 If [ I-2 what he saw through security] did not impress him] Tammuz . . . ] (BNC) (16) a. Der Ritter von Malzahn, dem der Junker sich als einen Fremden, der bei seiner Durchreise den seltsamen Mann, den er mit sich fu¨hre, im Augenschein zu nehmen wu¨nschte, vorstellte, no¨tigte ihn . . . b. Der Ritter von Malzahn, Main the rider from Malzahn dem der Junker sich als einen Fremden whom the Junker himself as a stranger der bei seiner Durchreise den seltsamen Mann, who upon his journey the unusual man den er mit sich fu¨hre, whom he with himself would bring in Augenschein zu nehmen wu¨nschte, by appearance to judge wanted vorstellte, introduced no¨tigte ihn . . . forced him . . .

C-1 C-2 C-3 C-2 C-1 Main

‘The rider from Malzahn, to whom the Junker introduced himself as a stranger, who upon his journey wanted to judge by appearance the unusual man whom he would bring with himself, forced him . . .’ (Heinrich von Kleist, Michael Kohlhaas) (17) [A lot of the housing [C-1 that the people [C-2 that worked in New Haven] lived in] was back that way.] (Reich and Dell 1976) No genuine triple initial embeddings nor quadruple center-embeddings are on record, suggesting that I2max and C3max-w are firm restrictions on respectively left-branching clausal tail-recursion and nested clausal recursion. Only some 130 double center-embeddings were retrieved among the tens of millions of words checked. The overall rarity and the numerous constraints on multiple IE and CE prompt the conclusion that multiple clausal initial and center-embeddings are not fully recursive at least in the European languages here considered, if ‘‘fully recursive’’ is taken to mean that ordinary language use would provide instances of multiple initial

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clausal embedding or nesting degrees beyond the confines of I2 max and C3 max-w. Of special importance is the fact that multiple nested (¼fully productive) clausal recursion (i.e. multiple center-embedding) is practically absent from ordinary spoken language, as stipulated by constraint (13) C2max-s. Multiple nesting cannot therefore reasonably be considered a central design feature of language, as claimed by Hauser, Chomsky, and Fitch (2002).4 On the contrary, empirical facts prove that Reich (1969) and Reich and Schu¨tze (1991) were on the right track in claiming that the limit on clausal nesting is 1. This is practically true for spoken language, whereas written language allows two cycles and extremely marginally three. C3max-w and Only-postmodifying-self-embedding taken together license triple relative self-embedding, as in (16). Final clausal embedding is less constrained but not totally unregimented. In an extensive empirical study Karlsson (ms.) found evidence in several European languages for a tendency called F3-5max: (18) F3-5 max: Syntactically simple genres (such as most of spoken language and some of written language) avoid final clausal embedding in excess of degree 3, complex genres in excess of degree 5. As sentence (19) from the Brown corpus with eight finally-embedded clauses shows, F3-5 max may be overstepped. Thus, it is a stylistic preference. (19) [ . . . it seems . . . [F-1 that . . . it is unlikely [F-2 to bear much relation . . . to the . . . need of [F-3 ensuring . . . [F-4 that there may be adequate opportunity given to the sta¤ [F-5 to do [F-6 what they can [F-7 to get the man [F-8 to stand again . . .]]]]]]]]] 6. Constraints on NP and PP recursion Surprisingly little empirical work has been done even on much-researched languages like English and German on the recursive potential of basic phrases, especially NPs and PPs, to which I here confine myself. The definition of a noun phrase in this context is that its head is a noun or a pronoun, to the exclusion of clauses, infinitives and similar structures. Furthermore, I do not here treat the case of indirect multiple NP and PP 4. This is further support for Pinker and Jackendo¤ ’s (2005) criticism of Hauser, Chomsky, and Fitch’s (2002) claim.

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recursion arising through embedding of clauses as postmodifiers of head nouns in NPs. Such clauses may of course contain further NPs and/or PPs. All examples below are genuine and emanate from the extensive corpus studies mentioned in Section 5. As for multiple center-embedding of NPs and PPs (which could also be called self-embedding, as they invoke the same types of constituents), the most complex instances found of both are of degree 3. The German 19thcentury specimen of legal language (20) contains one instance of both NP3 and PP3 (Engel 1922: 327). Successive levels of indentation show increasing depth of embedding (in this and later examples). Please note that indentation is not supposed to reflect constituent structure in detail. Material at the same level of indentation is at the same embedding depth (and normally belongs to the same constituent). The rightmost column indicates embedding depth borders (e.g. the first PP-2 marks the start of the PP at depth 2, the second PP-2 marks its end). (20) a. Das Gericht wolle erkennen, der beklagte sei schuldig, mir fu¨r die von mir fu¨r ihn an die in dem von ihm zur Bearbeitung u¨bernommenen Steinbruche bescha¨ftigt gewesenen Arbeiter vorgeschossenen Arbeitslo¨hne Ersatz zu leisten. b. Das Gericht wolle erkennen, der beklagte sei schuldig, mir . . . The court might rule the defendant is guilty to me . . . fu¨r die PP-0; NP-0 for the von mir PP-1a; NP-1a by me fu¨r ihn PP-1b; NP-1b for him an die PP-1c; NP-1c for the in dem PP-2; NP-2 in the von ihm PP-3a; NP-3a by him zur Bearbeitung u¨bernommenen PP-3b; NP-3b to run had taken over Steinbruche PP-2; NP-2 quarry bescha¨ftigt gewesenen Arbeiter PP-1c; NP-1c employed have been workers vorgeschossenen Arbeitslo¨hne Ersatz zu leisten. PP-0; NP-0 prepaid salaries remuneration to pay

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‘May the court rule that the defendant remunerate me for the salaries prepaid by me on his behalf to the workers that were employed in the quarry that he had taken over to run.’ Sentence (20) involves clauses that have been nominalized to premodifying adjectival participles and which carry along their original complements as dependents of the participle in the form of PPs with their requisite NPs. In (20) the PP-0 and NP-0 (fu¨r) die . . . Arbeitslo¨hne ‘(for) the . . . salaries’ at basic level (depth 0) are interrupted by a nominalization (von mir . . . vorgeschossenen ‘by me . . . prepaid’), where the PP-1c and NP1c (at the same depth as PP-1a, NP1-a and PP-1b, NP-1b) (an) die . . . Arbeiter ‘(for) the . . . workers’ (nested PP and NP recursion, degree 1) are interrupted by another nominalization (in dem . . . gewesenen ‘in the . . . been’). This nominalization contains the further nestings PP-2 and NP-2 (in) dem . . . Steinbruche ‘(in) the . . . quarry’ (nested PP and NP recursion, degree 2), interrupted by a third nominalization (von ihm . . . u¨bernommenen ‘by him . . . overtaken’), which contains no less than two more nested PPs and NPs, at depth 3, PP-3a and NP-3a von ihm ‘by him’ and PP-3b and NP-3b zur Bearbeitung ‘to run’. Sentence (21), from Kaseler Zeitung 1.5.1889, also manifests triple nested recursion of prepositional phrases and noun phrases. As for NPs, the nesting sequence is [die . . . [der . . . [das . . . [dem Kloster] Hospiz] Insel] Badereisenden]. (21) a. Fu¨r die nach der durch das von dem Kloster Loccum erbaute Hospitz in weiteren Kreisen bekannt gewordenen Insel Langeoog kommenden Badereisenden hat sich . . . b. Fu¨r die PP-0; NP-0 For the nach der PP-1; NP-1 after the durch das PP-2; NP-2 through the von dem Kloster Loccum PP-3; NP-3 by the monastery Loccum erbaute Hospitz PP-2; NP-2 built hospital in weiteren Kreisen bekannt gewordenen Insel Langeoog PP-1; NP-1 in larger circles known become island Langeoog kommenden Badereisenden hat sich . . . PP-0; NP-0 coming seaside guests has REFL

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‘For the seaside guests coming to the island Langeoog which has become known to larger circles through the hospital built by the Loccum monastery there has . . .’ Of course triple center-embedding of NPs and PPs as in (20) and (21) is extremely convoluted and rare and confined to restricted, formal, stylistically marked, older (obsolete?) genres of writing. It must be emphasized that no genuine examples of triple nesting of PPs and NPs are at hand from the twentieth (not to speak of the twenty-first) century. Even double center-embedding of NPs and PPs is utterly rare so one more genuine example deserves presentation. Here (22) is an Ancient Greek NP from Plato’s The Sophist.5 (22) a. ta` ga`r teˆs toˆn polloˆn psycheˆs o´mmata b. ta` ga`r NP-0 DET because teˆs NP-1 DET toˆn polloˆn NP-2 DET of many psycheˆs NP-1 soul’s o´mmata NP-0 eyes ‘because the eyes of the soul of many’ Insofar as this small corpus (20, 21, 22) can be trusted, the favourite locus of multiple center-embedding of NPs and PPs seems to be after the determiner in the NP. Two quantitative constraints (where again ‘‘-w’’ is short for ‘‘written language’’) can be postulated at least for several European languages: (23) NP3 max-w: In written language, the maximal (very rare) degree of multiple center-embedding of NPs is 3. (24) PP3 max-w: In written language, the maximal (very rare) degree of multiple center-embedding of PPs is 3. Multiple nesting of PPs presupposes the same amount of nested NPs. PPs and NPs thus form a peculiar tightly bonded recursive pair of layered nestings. No genuine examples are at hand of nested NP3s (with nouns or pronouns as headwords) that would not involve at least one PP. 5. This example was helpfully provided by Martti Leiwo.

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What about the present-day limits on multiple NP- and PP-nesting, especially in spoken language? The weirdness of the above genuine obsolete German examples from the nineteenth century, and the total absence of similar genuine contemporary examples, certainly indicates that the current limit is below 3. On the other hand it is clear that at least NP-nesting at depth 1 is a living option for example in Finnish (25). (25) a. ta¨ma¨ edellisen hallituksen ehdotus 6 b. ta¨ma¨ this.DET.NOM.SG edellise+n previous.A+GEN.SG hallitukse+n government.N+GEN.SG ehdotus proposal.N.NOM.SG

NP-0 NP-1 NP-1 NP-0

‘this proposal by the previous government’ Native intuitions tell that NP-1 in (25) could be interrupted by another short NP inflected in the genitive case and still remain grammatical and acceptable: (26) a. ta¨ma¨ edellisen pa¨a¨ministeri Lipposen hallituksen ehdotus b. ta¨ma¨ NP-0 this.DET.NOM.SG edellise+n NP-1 previous.A+GEN.SG pa¨a¨ministeri NP-2 Prime Minister.N.NOM.SG Lippose+n NP-2 Lipponen.N+GEN.SG hallitukse+n NP-1 government.N+GEN.SG ehdotus NP-0 proposal.N.NOM.SG ‘this proposal by the previous government (led by) Prime Minister Lipponen’ 6. The NP (25) can be verified by googling on the internet.

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As a tentative generalization I therefore submit (27), where ‘‘-s’’ is short for ‘‘spoken language’’: (27) NP2 max-s: in spoken language, the maximal (very rare) degree of multiple center-embedding of NPs is 2. Conclusive resolution of this issue, including the limits of PP-nesting in speech, must await additional detailed corpus study of a su‰cient number of languages. As for left-recursion on constituent level, prepositional phrases by their very nature do not have it. NPs are left-recursive, in the form of repeated genitives, where the previous genitive modifies either the subsequent one or the combination of this and the head noun – this is submodification and stacking, respectively, in the terminology of Huddleston and Pullum (2003: 446–447). This feature distinguishes recursive genitives from iterated phrases, which are structurally parallel. The Brown, LOB and ICEGB corpora (3 million words) show that submodifying genitives are rare, brief, and semantically restricted (28a, 28b, 28c). Only some 20 instances were found of submodifying genitive chains of depth 2. Stacked genitives are even rarer. (28) a. b. c.

Hilary’s lawyer’s secretary Burnside’s horse’s belly Pam’s mum’s baggage

Left-recursive open-endedness on constituent level emerges in formal written genres of Finnish where there is a productive construction based on nominalization of verbs and multiple NPs inflected in the genitive or oblique cases. As in (20) and (21), the nominalized verbs act as premodifying adjectival participles in NPs, with their original complements as properly case-inflected dependents of the participle. The postpositional phrase in (29) comes from a regulation adopted by the Finnish government. There are five left-recursive NPs inflected in the genitive case, several of which have adjectivized verbs with their own left-branching case-inflected NPs as dependents or premodifiers, creating an overall depth at word level of 11. (29) a. valtion virkamiehelta¨ virallisesti vaadittavasta kielitaidosta annetun lain ta¨yta¨nto¨o¨npanosta annetun asetuksen 7 pyka¨la¨n 1 momentin mukaan

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valtio+n state+GEN.SG virkamiehe+lta¨ o‰cial+ABL.SG vaadi+tta+va+sta require+PSS+PCP+ELA.SG kielitaido+sta language proficiency+ELA.SG anne+tu+n give+PSS.PCP+GEN.SG lai+n law+GEN.SG ta¨yta¨nto¨o¨npano+sta implementation+ELA.SG anne+tu+n give+PSS.PCP+GEN.SG asetukse+n regulation+GEN.SG 7 seventh+GEN.SG pyka¨la¨+n paragraph+GEN.SG 1 first+GEN.SG momenti+n subsection+GEN.SG mukaan according_to ‘according to subsection 1 of paragraph 7 in the regulation which was issued concerning the implementation of the law which was issued concerning the language proficiency which is required of a state o‰cial’

Right-recursion of phrase-level constituents is most productive in the interplay between multiple PPs and NPs contained in one another in postmodifying structures such as (30). No clear upper limits are in evidence but recursive PPs in excess of degree 5 are rare. However, the complex (genuine) Swedish NP (31), again from a regulation issued by the Finnish government, contains no less than ten right-recursive PPs, labelled a, b, c . . . in (31b), and headed by the prepositions om ‘concerning’, av ‘of ’, and i ‘in’.

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(30) [in the soil [on the slopes [of the rock [by the river [in . . . ]]]]] (31) a. statsra˚dets fo¨rordning om a¨ndring av ikrafttra¨dandebesta¨mmelsen i statsra˚dets fo¨rordning om a¨ndring av ikrafttra¨dandebesta¨mmelsen i statsra˚dets fo¨rordning om a¨ndring av statsra˚dets fo¨rordning om utveckling av landsbygden7 b. statsra˚d+et+s government+DEF+GEN.SG fo¨rordning regulation om a¨ndring (a) concerning change av ikrafttra¨dandebesta¨mmelse+n (b) of implementation decision+DEF.NOM.SG i (c) in statsra˚d+et+s government+DEF+GEN.SG fo¨rordning regulation om a¨ndring (d) concerning change av ikrafttra¨dandebesta¨mmelse+n (e) of implementation decision+DEF.NOM.SG i (f ) in statsra˚d+et+s government+DEF+GEN.SG fo¨rordning regulation om a¨ndring (g) concerning change 7. The source of (31a) is Asetus/Fo¨rordning 778/2004 and the Finnish original is: Valtioneuvoston asetus voimaantulosa¨a¨nno¨ksen muuttamisesta valtioneuvoston asetuksessa maaseudun kehitta¨misesta¨ annetun valtioneuvoston asetuksen muuttamisesta annetun valltioneuvoston asetuksen voimaantulosa¨a¨nno¨ksen muuttamisesta.

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av (h) of statsra˚d+et+s government+DEF+GEN.SG fo¨rordning regulation om utveckling (i) concerning development av landsbygd+en ( j) of rural area+def.nom.sg ‘the government’s regulation concerning change of the implementation decision in the government’s regulation concerning change of the implementation decision in the government’s regulation concerning change of the government’s regulation concerning the development of rural areas’8

7. Conclusion No evidence for nested syntactic recursion of degrees greater than 3 is at hand, neither on clause level nor on phrase level. Two interesting questions cannot be addressed here: Why is the maximal degree 3 and not 2, 7 or some other number? Why is the maximal degree the same on phrase and clause level? Motivated answers to these questions would presuppose careful consideration of referent processing and short-term memory capacity restrictions which transcend the scope of this contribution. The extant examples of nesting of degree 3 and even those of degree 2 are so few, convoluted, and almost exclusively confined to written language as to practically falsify the hypothesis of the importance of unlimited syntactic nesting (multiple center-embedding), thus also confirming the experimental results of Christiansen and Chater (1999) achieved by connectionist modeling concerning the marginality of multiple center-embedding. No more than two spoken instances of double clausal center-embedding have been documented (Karlsson 2007b). Double NP and PP 8. One referee aptly remarks that the English translation of this NP ‘‘is completely Martian, and nothing like anything that would ever be produced by even the most constipated English-speaking bureaucrat. It sounds like an insane utterance!’’

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center-embedding have, to the best of my knowledge, not been recorded in speech at all. Thus, in speech, nested recursion in the domains of clauses and constituents is for all practical purposes confined to just one cycle, degree 1, which is what Heine and Kuteva (2007: 268) call simple (as opposed to productive) recursion. Karlsson (2009) demonstrates in philological detail that multiple nesting arose along with the advent of written language. This is also compliant with known psychological facts: multiple nesting taps short-term memory resources and such resources are more readily available in writing and reading than in real-time speaking and listening. Multiple tail-recursion is real both in its rightwards and leftwards manifestations especially in written language, but not fully unconstrained, as shown above e.g. for multiple left-branching of clauses (I2 max) and for genitives (triple genitive chains are extremely rare). One more interesting question will be left open here as for its proper explanation: Why is clausal left-branching strictly constrained to two cycles, but left-branching of certain premodifiers (such as nominalized participle constructions) is not? In the invitation to the April 2007 recursion conference organized by Dan Everett at the University of Northern Illinois, a complex sentence by the late Cli¤ord Geertz was singled out in the call for papers, with the implication that this sentence (32a) is particularly relevant for the conference topic. (32b) is the precise analysis of this sentence in terms of clause structure (C ¼ finite center-embedded, F ¼ finite finally-embedded, f ¼ non-finite finally-embedded). (32) a. The notion that the essence of what it means to be human is most clearly revealed in those features of human culture that are universal rather than in those that are distinctive to this people or that is a prejudice that we are not obliged to share . . . b. The notion that the essence of what it means to be human is most clearly revealed in those features of human culture that are universal rather than in those that are distinctive to this people or that is a prejudice that we are not obliged to share . . .

Main C-1 C-2 f-3 F-2 F-2 F-1 f-2

The analysis shows that (32b) complies with all constraints on clausal embedding outlined in Section 5, in particular with the constraints

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C3 max-w, F3-5 max and Only-postmodifying-self-embedding. There is a double center-embedding in (32b), where the lower center-embedding C-2 contains a further non-finite final embedding f-3 (the infinitive construction to be human). The upper center-embedding C-1 contains two more final embeddings F-2 þ F-2. The predicate complement a prejudice contains two more final embeddings, F-1 þ f-2. No NPs nor PPs in (32b) violate NP3 max-w, PP3 max-w, nor NP2 max-s. Thus, Geertz’s sentence is structurally interesting, but fully compliant with all the constraints on clausal and phrasal recursion outlined in this paper.

References Aho, Alfred V., Ravi Sethi, and Je¤rey D. Ullman 1986 Compilers. Principles, Techniques, and Tools. Reading, Mass.: Addison-Wesley Publishing Company. Baladunarman, I., S. Ishwar, and R. Sanjeeth Kumar 2003 Context-free grammar for natural language constructs. An implementation for Venpa class of Tamil poetry. In: The Sixth International Tamil Internet Conference and Exhibition With the Theme ‘‘IT for Education in Tamil’’. Available at http://www. infitt.org/ti2003/papers/19_raman.pdf. Bar-Hillel, Yehoshua 1953 On recursive definitions in empirical science. 11th International Congress of Philosophy 5: 160–165. Amsterdam: North-Holland. Bhate, Saroja, and Subhash Kak 1993 Pa#n¸ini’s Grammar and Computer Science. Annals of the Bhandarkar Oriental Research Institute 72: 79–94. Also available at http://www.ece.lsu.edu/kak/bhate.pdf. Biber, Douglas, Stig Johansson, Geo¤rey Leech, Susan Conrad, and Edward Finegan 1999 Longman Grammar of Spoken and Written English. London: Longman. Brookshear, J. Glenn 2007 Computer Science. An Overview. Ninth edition. Boston etc.: Pearson Addison Wesley. Broch, Hermann 1961 Der Tod des Vergil. Darmstadt: Moderner Buch-Club. Chomsky, Noam 1956 On the limits of finite-state description. MIT Research Laboratory of Electronics, Quarterly Progress Report 41: 64–65. Chomsky, Noam 1957 Syntactic Structures. The Hague: Mouton.

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Chomsky, Noam 1975 [1955–1956] The Logical Structure of Linguistic Theory. New York and London: Plenum Press. Christiansen, M. H., and N. Chater 1999 Toward a connectionist model of recursion in human linguistic performance. Cognitive Science 23: 157–205. Engel, Eduard 1922 Deutsche Stilkunst. 30th edition. Vienna & Leipzig: Ho¨lderPichler-Tempsky A-G. Halliday, M.A.K. 1963 Class in relation to the axes of chain and choice in language. Journal of Linguistics 2: 5–15. Harder, Peter 2006 Recursion in a functional-semantic grammar. In: Timo Haukioja (ed.), Papers on Language Theory. Publications in General Linguistics 10: 67–105. Turku: University of Turku. Hauser, Marc D., Noam Chomsky, and W. Tecumseh Fitch 2002 The faculty of language: What is it, who has it, and how did it evolve? Science 298: 1569–1579. Heine, Bernd, and Tania Kuteva 2007 The Genesis of Grammar. A Reconstruction. Oxford: Oxford University Press. Householder Jr., Fred W. 1952 Review of Harris, Zellig S., 1951, Methods in Structural Linguistics. International Journal of American Linguistics 28: 260–268. Huddleston, Rodney, and Geo¤rey K. Pullum 2003 The Cambridge Grammar of the English Language. Cambridge: Cambridge University Press. Humboldt, Wilhelm von ¨ ber die Verschiedenheit des menschlichen Sprachbaues und ihre 1836 U Einfluss auf die geistige Entwickelung des Menschengeschlechtes. Berlin: Druckerei der Ko¨niglichen Akademie der Wissenschaften. Johansson, Sverker 2005 Origins of Language. Constraints on Hypotheses. Amsterdam: John Benjamins Publishing Company. Joyce, James 1934 [1922] Ulysses. New York: Random House Inc. Karlsson, Fred 2007a Constraints on multiple initial embedding of clauses. International Journal of Corpus Linguistics 12 (1): 107–118. Karlsson, Fred 2007b Constraints on multiple center-embedding of clauses. Journal of Linguistics 43 (2): 365–392. Karlsson, Fred 2009 Origin and maintenance of clausal embedding complexity. In:

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Geo¤rey Sampson, David Gil, and Peter Trudgill (eds.), Language Complexity as an Evolving Variable, 192–202. Oxford: Oxford University Press. Karlsson, Fred (ms.)

Multiple final embedding of clauses. University of Helsinki: Department of General Linguistics.

Lindstro¨m, Jan 1999 Vackert, vackert! Syntaktisk reduplikation i svenskan. Studier i nordisk filologi 77. Helsingfors: Svenska Litteratursa¨llskapet. Linell, Per 2005 The Written Language Bias in Linguistics. Its Nature, Origins and Transformations. London: Routledge. Parker, Anne R. 2006 Evolving the narrow language faculty: was recursion the pivotal step? In: Angelo Cangelosi, Andrew D. M. Smith, and Kenny Smith (eds.), The Evolution of Language: Proceedings of the 6th International Conference (Evolang 6), 239–246. London: World Scientific. Pinker, Steven and Ray Jackendo¤ 2005 The faculty of language: What’s special about it?. Cognition 95: 201–236 Quirk, Randolph, Sidney Greenbaum, Geo¤rey Leech, and Jan Svartvik 1972 A Grammar of Contemporary English. London: Longman. Reich, Peter A. 1969 The finiteness of natural language. Language 45: 831–843. Reprinted in Fred Householder (ed.), Syntactic Theory 1. Structuralist, 238–272. Harmondsworth: Penguin. Reich, Peter A., and Gary S. Dell 1977 Finiteness and embedding. In: R. J. Di Pietro and E. L. Blansett Jr. (eds.), The Third LACUS Forum 1976, 438–447. Columbia, S.C.: Hornbeam Press. Reich, Peter A., and Carson T. Schu¨tze 1991 Syntactic embedding: What can people really do? In: Barbara Brunson and Tom Wilson (eds.), Toronto Working Papers in Linguistics 11 (1)–11 (2): 91–97. Sebba, Mark 1987 The Syntax of Serial Verbs. An Investigation into Serialisation in Sranan and Other Languages. Amsterdam/Philadelphia: John Benjamins Publishing Company. Tomalin, Marcus 2006 Linguistics and the Formal Sciences. The Origins of Generative Grammar. Cambridge: Cambridge University Press. Tomalin, Marcus 2007 Reconsidering recursion in syntactic theory. Lingua 117: 1784– 1800.

4.

Recursion in conversation: What speakers of Finnish and Japanese know how to do

Ritva Laury and Tsuyoshi Ono

1. Introduction In their article in Science (2002), Hauser, Chomsky & Fitch (HCF, hereafter) advance a provocative hypothesis that recursion is the only uniquely human component of the faculty of language. That is, HCF in essence proposes that recursion is an innate capacity possessed by all humans which accounts for the central aspects of what human language is like, and in fact what makes it specifically human. There has since been much discussion over this hypothesis both in print and on the internet. In our view as discourse linguists, this hypothesis is seriously flawed at the very least. That is, although HCF assumes that recursion is the defining component of the human language faculty, our experience of closely examining actual human speech leads us to suggest that recursion explains very little of actual human language behavior. In fact, we strongly feel that to evaluate the recursion hypothesis it is necessary to verify that recursion is real for human speech. We will do just that in this article.1 Specifically, we will examine the recursion hypothesis based on clause combining in Finnish and Japanese conversational data. Our rationale behind adopting this approach was that since everyday conversation is the most fundamental form of human language, if recursion is indeed central to human language, as HCF claims, then we should be able to find some manifestation of it in our data. Alternatively, if we find little evidence of recursion in our data, the status of the recursion hypothesis has to be questioned since it would mean that it is a descriptively inadequate hypothesis. That is, in our view, an extremely rare incidence of examples in everyday language use to which recursion might be relevant seriously weakens the HCF

1. One very common research thread in the field is mathematical modeling of recursion. Again, our position is that the first step should be to establish that recursion is an actual human trait.

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hypothesis that recursion is the defining property of human language. It should also be pointed out that much of the investigation into the recursion hypothesis, a universal hypothesis, has been based solely on English and a few other Indo-European languages. For this reason, we felt it important to apply our methodology to two non-Indo-European languages to see if they exhibit similar patterns (see also Everett, 2005, this volume, on Piraha˜, another non-Indo-European language). Below, as a way of presenting our data and methodology, we will first discuss the analytical di‰culties in studying clausal recursion in conversational data. We will then show that even with a very liberal definition of recursion, there are clear limits to it in everyday conversation. We further conclude that multiple embedding is a result of looking at human language as an atemporal object. That is, we find that in ordinary language use, speakers combine clauses one at a time, as already suggested by Pawley & Syder 1983 and Chafe 1988, and that the internal structure of the foregoing material does not seem to be an issue to them. In fact, we suggest that the evocation of the concept of recursion is not necessary to account for the patterns of clause combining in our data, and that our data give no reason to assume that recursion, specifically infinite recursion, is a defining property of human language. Our data consist of approximately five hours of transcribed audiotapes of conversation in Finnish (from corpora collected at the University of Helsinki and the University of Turku2) and five hours of conversation in Japanese (from corpora collected at the University of California, Santa Barbara and University of Arizona3). For our quantitative analysis, in order to provide a good representation of our target populations, we took a random sample consisting of approximately 1000 clausal units from each language, from which we coded all clause combinations, labeling each clause as either a matrix clause or a type of subordinate clause (adverbial, complement, or relative clause), and we coded the depth and 2. The Finnish corpus consists of audiotaped telephone and face-to-face conversations transcribed for and housed in the Conversation Analysis archive at the Department of Finnish, University of Helsinki. Some of the conversations used were originally audiotaped for the Turku spoken language project (see Suojanen 1985). The transcripts have been slightly simplified: for transcription symbols used, see Appendix. 3. The Japanese corpus consists of audiotaped face-to-face and telephone conversations collected and transcribed by researchers at the Universities of California (Santa Barbara) and Arizona and currently housed in Spoken Discourse Research Studio at University of Alberta.

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direction of embedding for each clause. Our qualitative analysis is more inclusive; we also examined examples found in our data which are not included in the counts.

2. Problems with analyzing embedding in conversational language In analyzing our data, we had to deal with two major problems: the nondiscreteness of linguistic categories and the problematic status of the concept of ‘sentence’ in spoken language. Before we give the main results of the current study, we would like to review these problems in order to allow 1) the reader to properly interpret the type of data we will be dealing with and, we hope, 2) those interested to further pursue this line of research. 2.1. Non-discreteness of categories In actual language use, linguistic categories are non-discrete (Hopper & Thompson 1980, 1984; Langacker 1987, 1991; Hopper 1998) due to the fact that language is constantly changing as it adapts to functional needs. One example of this is the cross-linguistic tendency for certain clause types, clausal markers, and predicates to grammaticize into particles and/ or discourse markers (e.g., I think in English (Scheibman 2003, Ka¨rkka¨inen 2003), iu ‘say’ in Japanese (Suzuki 1999), kato ‘look’ in Finnish (Hakulinen & Seppa¨nen 1992), kedo ‘although’ in Japanese (Nakayama and Ichihashi-Nakayama 1997). This causes problems when one has to make coding decisions. Consider the following examples. The first example comes from a conversation where coworkers are discussing a colleague who is not present. Example (1) Kahvikutsut (Turku spoken language corpus, C-134) 1 EK: tia¨da¨k sa¨a¨ et ha¨n on pyyta¨ny mult know-2SG-Q 2SG COMP 3SG be ask-P.PPLE 1SG-ABL kerran anteeks once apology ‘(Do) you know that s/he has apologized to me once 2

kuule ja siit on muutama pa¨iva¨ aikaa. hear-2SG.IMP and 3SG-ELA be a.few day time-PRT listen and it was only a few days ago.’

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3 JS: a¨la¨:. NEG-2SG.IMP ‘[You] don’t [say] (You’re kidding!)’ ((SEGMENT OMITTED)) 4 EK: tieda¨k sa¨ ma¨[a¨ olin ih]an ha¨mma¨styny know-2SG-Q 2SG 1SG be-PST-1SG quite surprised ‘You know I was really surprised’ 5 X:

[a¨la¨::] NEG-2SG.IMP ‘[You] don’t [say]. (You’re kidding!)’

6 EK: kuule etta¨(.) ha¨nes on tapahtunu: o¨o¨hh oikee hear-2SG-IMP COMP 3SG-INE be happen-P.PPLE PTC really siis (0.7) [su[u:ri PTC great ‘listen that in her there’s been really a great 7 JS:

[suuri ‘great’

8 IW: [just ‘just’ (.) 9 EK: suuri muu- muutos juu:. great change PTC great change yeah.’ In this example, EK uses the expressions tia¨da¨k sa¨(a¨) ‘do you know’ and kuule ‘listen’ twice each. The verbs tieta¨a¨ ‘know’ and kuulla ‘hear’ are full complement-taking verbs in Finnish, but they also function as particles or ¨ stman adverb-like fixed expressions similar to the English you know (O 4 1981) and I think (Thompson 2002 , Ka¨rkka¨inen 2003, Scheibman 2003; see also Sakel & Stapert, this volume, on similar expressions in Piraha˜). It is not always clear which of the two use types one is dealing with. In line 1, tia¨da¨k sa¨a¨ ‘do you know’ is followed by the complementizer et(ta¨)

4. Important evidence for the particle-like functioning of these expressions is that they can and do freely ‘float’ in a sentence; see, for example, Thompson 2002 for examples and discussion.

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‘that’ and another clause, and thus line 1 is analyzable as a main clause followed by a complement clause (although see Laury 2006, Seppa¨nen & Laury 2007, Laury & Seppa¨nen 2008). However, kuule ‘listen’ in line 2 is not followed by a complement clause, but rather a clause coordinated with the preceding clause with the conjunction ja ‘and’. For that reason, and also because Finnish complement clauses follow their main clauses (Korhonen 1993), kuule is here best analyzed as a particle. The second use of tieta¨a¨ ‘know’, tieda¨k sa¨ ‘(do) you know’ in line 4, is much less main-clauselike than the one in line 1. The pronoun is less stressed and shorter, and the complementizer is missing, although one is normally used in all contexts of finite clausal complementation in Finnish. In line 6, kuule ‘listen’ is followed by an etta¨-initial complement clause. However, kuule does not seem to function here as a complement-taking predicate either. A better analysis would be to consider it here as a particle. The etta¨-initial clause following kuule in lines 6 and 9 is more plausibly, for semantic as well as syntactic reasons, meant as a complement of the clause following tieda¨k sa¨ ‘do you know’, ma¨a¨ olin ihan ha¨mma¨styny ‘I was really surprised’ in line 4. If tieda¨k sa¨ in line 4 is a main clause, we should code the utterance in lines 4, 6, and 9 as an instance of two levels of final embedding (a main clause followed by two complement clauses, the second of which would be embedded within the first one), but if we consider tieda¨k sa¨ a particle, then we have one level of final embedding. The coding decision is essentially arbitrary. For the purpose of this study, we have adopted a maximal definition of embedding and coded this and similar combinations as two levels of final embedding. Consider a similar example from Japanese. In this excerpt, the speaker is recounting an event of talking with a homeless person. Example (2) Homeless 1

shumi de yatten no ka ttsutara hobby as doing NOM Q say:COND ‘When (I) said ‘are (you) doing it (being homeless) as (a) hobby’,

2

shumi de yatteru tteta yo hobby as doing say:PAST FP (he) said ‘(I) am doing that as (a) hobby’ ’

The two utterances end with ttsuta and tteta, reduced forms of a combination of quotative complementizer te and the past tense form of the verb ‘say’ yutta (‘said that . . .’). In these forms, morpheme boundaries are becoming opaque. Further, ttsuta and tteta are produced along with the

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preceding utterance without a pause. For these two reasons, one might suggest that these forms simply mark the preceding utterance as a quote, rather than functioning as full-blown complementizers followed by main clauses or complement-taking predicates. It is, in fact, well known that the ‘say’ verb grammaticizes into a quotative marker cross-linguistically (as in Japanese; Suzuki 1999). In (2), should ttsuta and tteta be considered complementizers with full verbs or quotative particles? In this project, we coded them as verbs in order to capture as many potential levels of embedding as possible. That is, our coding was quite inclusive because we wanted to be careful about dealing with a hypothesis that has been getting quite a bit of attention in the field. Both of these examples thus demonstrate that categories in actual use are not discrete due to the on-going change of human language, which makes our job as analysts very di‰cult and results in many arbitrary coding decisions. This is also an important factor one has to take into account when interpreting our quantitative results. 2.2. The problematic status of the category ‘sentence’ in spoken language Previous studies have shown that in spontaneously produced spoken language, sentence boundaries, even clausal boundaries, are di‰cult to determine, for example when speakers add material (‘increments’ Ford, Fox & Thompson 2002; Couper-Kuhlen & Ono 2007) to already completed clausal utterances. Such expansions of syntactically complete structures can be fitted to what they precede, or they may reanalyze the preceding syntax (e.g., added ‘quotationalizing’ main clauses in Japanese, Tanaka 2001). In fact, the idea of the sentence may be a ‘linguist’s category’, based on written language (Linell 2005) and constructed examples. Sentences do not really present a clear gestalt in speech, although clauses emerge quite clearly as a unit (Helasvuo 2001, Iwasaki & Ono 2001, Thompson & Couper-Kuhlen 2005, Thompson 2006; see also Crystal 1980, Ikola et al 1989, Miller 1995). Consider the following examples from Finnish and Japanese. In example (3), Missu has just said that she has registered for the university. Example (3) Pa¨a¨nsa¨rky (U. of Helsinki Finnish dept. corpus Sig 113_2a1) mi(h)ta¨ ma¨ shain 1 Missu: ja to ta, arvaa and PTC guess.2SG-IMP what-PRT 1SG get-PST-1SG tieta¨a¨.h know-1INF ‘And guess what I found out.’

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2 Kaaka: >no?,[h< PTC ‘What?’ 3 Missu: [.mmthh<Paltamosta.h> (0.2) meia¨n (.) P-ELA 1PL-GEN ‘From Paltamo my 4

tota: (.) m:ummun naapuri?h (.) >jonka kanssa ma¨ PTC grandma-GEN neighbor REL-GEN with 1SG um grandma’s neighbor with whom I

5

oon< lapsena leikkiny ¼Tiina Valkiajoki?h be-1SG child-ESS play-P.PPLE T. V. played with as a child. Tiina Valkiajoki.’

6 Kaaka: [tulee sinne kans [(>opiskeleen<.) come-3SG there also study-ILL ‘Is coming to study there too.’ 7 Missu: [.hhhhh [>nii.< PTC ‘Yeah.’ In lines 3–5, Missu produces a complex NP, including a relative clause, which she finishes prosodically in line 5. After completing the NP, she adds an appositive proper name, Tiina Valkiajoki. In line 6, Kaaka produces a predication which is syntactically fitted to either of the NPs produced by Missu in lines 3–5. The status of line 6 with respect to lines 3–5 is not entirely clear. Speakers do frequently produce NPs which have no syntactic a‰liation with any neighboring clausal units (so-called ‘free NPs’; see Tao 1996 for Chinese, Helasvuo 2001 for Finnish). The option of continuing with, for example, a new clause containing a pronoun coreferential with the NPs in lines 3–5 is open to Missu at the end of line 5 (see e.g. Auer 2005). Given this, do lines 3–6 form a ‘sentence’? Does the relative clause in lines 4–5 constitute an instance of ‘center embedding’? We have not coded it as such, but the decision not to code clause combinations involving two speakers is an arbitrary one. Our next example comes from a Japanese conversation about playing baseball at the high school level.

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Example (4) Bukatsu 1 U: regyuraa wa kore mo dame jan. regular TOP this also bad TAG ‘(becoming) a starting player, it’s also bad, isn’t it? (I can’t be a starting player)’ 2 M: . . .[un] ‘mhm’ 3 U: [chuu]gakkoo kara yatteru yatsu ga [iru kara]. junior.high.school from do:STAT guy GA exist so ‘because there are guys who have been playing from Junior High School’ 4 M: [un un] ‘mhm mhm’ The utterance in line 1 is a clear complete single clause sentence with a final pitch pattern followed by a pause. The speaker adds another utterance ending with kara ‘because’ in line 3. Please note that kara is originally a conjunctive particle but it has been suggested to be becoming a final particle (Kokuritsu Kokugo Kenkyuujo 1960; Iguchi 1998). So the question is: Is the added utterance an adverbial reason clause ending with kara, forming a sentence with the utterance on line 1? Or is it an independent sentence ending with the final particle kara? In other words, an ongoing categorical change makes the coding decision for (4) essentially arbitrary. We should note that in coding our data, we were extremely inclusive in coding clause combinations as cases of embedding in order to not exclude any possible cases; we coded the kara-clause on line 3 in (4) as an adverbial reason clause associated with the main clause on line 1.

3. Major findings 3.1. Quantitative findings In the Finnish conversational data, there were 997 clauses5 altogether. Table 1 shows the absolute numbers of clause combinations at di¤erent

5. Only finite clauses were counted. That is, we did not include participial or infinitival constructions as clauses in our counts.

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depths found in the data, and the percentage of these types of clause combinations calculated as a percentage of the total number of clauses in the data: Table 1. Depth of embedding in the Finnish conversational data 146 depth of one embeddings

14.6%

27 depth of two embeddings

2.7%

6 depth of three embeddings

0.6%

4 depth of four embeddings

0.4%

(of the total number of clauses)

These figures show that embedding at a depth of more than two was extremely rare in the Finnish data. The most common type of embedding was at a depth of one (clause combinations consisting of just one subordinate or embedded clause combined with a main clause). Furthermore, and consistent with Karlsson 2007a and 2007b, and Karlsson & Sinnema¨ki 2007, who studied embedding depth in mostly written data from several European languages, including Finnish, there were no clause combinations with a depth of more than four found in the data. This shows that clausal embedding is not unlimited in either spoken or written data. These findings on embedding depth are also consistent with Ikola et al. (1989), a study based on a large dialect interview corpus consisting of 166,262 sentences. Although Ikola et al. found eighteen instances of embedding at a depth of greater than four, those instances were vanishingly rare, given the size of the corpus. Thus, their findings were consistent with ours. Ikola et al. also note, as we do, that the notion of the sentence is problematic for spoken language, and present several examples illustrating why that is so. They further note that all cases of embedding at a depth of more than four from their data are questionable, as it is not clear what is embedded within what in such complex clause combinations (1989: 23). This is a point we will also illustrate below. In our data, and also consistently with Karlsson (2007a & b) and Karlsson & Sinnema¨ki (2007), there were also no cases of more than two relative clauses or adverbial clauses embedded within one another. Even embeddings at the depth of two were limited in number. There were only six cases of two consecutive adverbial clauses, five cases of two consecutive complement clauses, and one case of two relative clauses in a row. Three of these twelve cases were quite marginal and open to interpretation. In particular, in two cases, it seemed clear that the successive complement clauses and relative clauses were not embedded within each other, but

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rather were modifying the same main clause or head noun, but without an overt coordinator. Only one case involving a sequence of three complement clauses embedded within each other was found. In keeping with the typological nature of Finnish as a predominantly right-branching language, most embedded clauses in our data followed their main clauses. There were nine adverbial clauses in the data which preceded their main clauses, but only one initial sequence of two adverbial clauses was found (and even that one was suspect, as shown below, in Example (5). There was one case of center embedding, at the level of one. In the Japanese conversational data, there were 1029 clauses altogether. In these data, there were: Table 2. Depth of embedding in the Japanese conversational data 145 depth of one embeddings

14.1%

48 depth of two embeddings

4.7%

13 depth of three embeddings 6 depth of four embeddings

1.3% 0.6%

(of the total number of clauses)

Replicating the Finnish findings, embedding in Japanese at a depth greater than two was very rare. In fact, we found no clear examples of clause combinations with a depth of more than four. And there were no cases of more than two of the same type of clauses embedded within one another in this data. Further there were 10 cases of two adverbials, three cases of two complement clauses, and one case of two relative clauses embedded within one another. These figures show that embedding is clearly limited in Japanese. Finally, our Japanese data highlights the typological feature of Japanese as a left-branching language; embedded clauses were most typically found to precede their main clause, as shown in (2). However, examples such as (4), where embedded clauses can be interpreted to follow their main clause, were not uncommon in the data (Ono and Suzuki 1992; Ono 2006). To summarize, one general finding of our study is the scarcity of multiple embedding (at most four levels) in conversational data in both Finnish and Japanese (consistent with Karlsson 2007a, 2007b, Karlsson & Sinnema¨ki 2007 for written Finnish, and Ikola 1989 for spoken Finnish). The figures also show that approximately 80% of the clauses in our Finnish and Japanese data showed no embedding at all. We also found that embedding follows the typological tendency of each language, so that

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Finnish uses predominantly a ‘main clause first’ strategy, while Japanese, uses a ‘main clause last’ strategy. Embedding of more than two of the same type of clause within each other is also extremely rare (only one case consisting of three successive complement clauses in Finnish). The limitations in the depth of clausal embedding may be a result of a cognitively-based processing di‰culty (Miller 1956, Chafe 1994, Gibson 1998, Cowan 2001, Davis 2001). As suggested by Auer (2005: 27), even on the production side, ‘memory for form is shorter than memory for content’, and therefore, ‘speakers do not usually succeed in keeping ongoing syntactic projects alive for a very long time.’6 It might also be the case that clausal embedding beyond a certain number (e.g., four) is something which speakers of these languages have not experienced in their linguistic life and have not produced since there has not really been a need for it. It is simply not a linguistic practice speakers engage in, which undermines the validity of recursion as a component of the faculty of language. 3.2. Clausal embedding is a local, one-clause-at-a-time phenomenon We suggest, based on our data, that in conversational language, examples which might look like instances of recursion are actually created through local operations, and what seems to be more relevant/central to speakers than syntax is semantic processing. That is, clause linkages are made one at a time in conversation. Consider the following three examples. In the first example, Tiina, who is giving rides to an event to a group of people, is negotiating the departure time with Mallu, suggesting that Mallu come earlier than she has suggested herself 7. Example (5) La¨hto¨aika (U. of Helsinki Finnish dept. corpus Sig 112-1b3) 1 Mallu: o<[kyl me oltas tulos]sa; ‘We really are coming’ 2 Tiina: [ni et jos te<,] ‘So like if you,’ (0.5)

6. Auer’s points are reminiscent of the insights gained from early psycholinguistic studies; see, e.g. Bever (1976). 7. Ritva Laury would like to thank Ilona Herlin and Maria Vilkuna for discussing their insights regarding this example with her.

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3 Tiina: niij jos te oisitte halunnu tulla so if 2PL be-COND-2PL want-P.PPLE come-1INF ai:kasemmin early-CMP ‘So if you had wanted to come earlier 4

sitte ku, (.) .hhh ku tota noin #m# > " tai then when when PTC PTC or then when because like um or

6

sillee ku mum pita¨a¨ kumminki katov vieda¨ like.that when 1SG-GEN must anyway PTC take-1INF ihmisia¨ people-PRT like that because I have to anyway you see take people

7

mun sinne nii se on silleen nii ja¨mpti et there so 3SG be like.that so exact COMP 1SG-GEN there so it is so exact like that that I

8

[siella¨.< pita¨s seittema¨lta¨ ollas should-COND seven-ABL be-1INF there should be there at seven’

Potentially, we have here a case of two levels of embedding before the main clause in line 7, se on silleen niin ja¨mpti ‘it’s so exact like that’, and one level of embedding (the extraposed clause et mun pita¨s seittema¨lta¨ olla siella¨ ‘that I should be there at seven’) after the main clause, as illustrated below: jos te oisitte halunnu tulla ai:kasemmin sitte ku mum pita¨a¨ kumminki katov vieda¨ ihmisia¨ sinne nii se on silleen_nii ja¨mpti et mun pita¨s seittema¨lta¨ ollas siella¨.< if you had wanted to come earlier then because I have to anyway you see take people there so it is so exact like that that I should be there at seven However, semantically, this analysis does not make sense. The jos ‘if’ clause in line 3 is not a precondition for Tiina’s exact timing, and thus not subordinate to the main niin ‘so’ -initial clause in line 7. On the other hand, the ku ‘because’ clause in line 6 expresses a cause both for Tiina’s

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wish, expressed in the jos-clause, for Mallu to arrive earlier (Tiina has to take (other) people too) as well as the cause for her having to be on time (a fact expressed in the niin-clause). In fact, Tiina is expressing a polite wish or directive in the jos ‘if’ -clause, (‘if you would like to come earlier’), and then provides the reason for making the request in the following ku ‘because’ clause. The ku-clause has double status as an account to the clause that precedes it (as a speechact causal; Sweetser 1990) and the reason for the one that follows it (a content causal), as shown below: Can you maybe come earlier because I have to take people it is so exact that I have to be there at seven In other words, the kun ‘because’ clause has two main clauses, the one preceding it and the one following it. Each one of these linkages is arrived at independently, as the utterance proceeds (observe the dysfluency in lines 2 and 4 as Tiina is formulating her delicate request). The linkages are made one at a time, not with the whole structure in mind. Therefore, even though we might consider the utterance as an instance of two levels of initial embedding and one level of final embedding (the last et-clause is a complement to the niin-clause), considering the semantics of the utterance and especially its emergence in time, we can see that for the speaker, this is not the case. Similar examples are reported in German (Franck 1985), and Japanese (Mori 1999 and Iwasaki & Ono 2001). Consider also the following example from our Japanese data, where M restates her utterance by quoting it. Example (6) Party 1 M: kiite yo yappari sa are kara sa denwa kakattekite listen FP after.all FP that from FP telephone ring ‘Listen! After all, the phone call came since then’ 2 K: doko kara? where from ‘From where?’ 3 M: tte yuu ka koko denwa kaket- kaketekite sa that say or here telephone call- call FP ‘Rather (than saying that), (they) called here and

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futari tsuika tte itta ja nai two addition that said TAG requested two additions (for the party) didn’t they?’

5 K: un un un ‘hm hm hm’ 6 M: aitsura konakatta n da yo those.guys didn’t.come NOM COP FP ‘Those guys didn’t come’ 7 K: nani sore! what that ‘What!’ M has just came back from a party which she organized. She starts recounting an earlier event on line 1, but K doesn’t follow, as seen on line 2. M immediately restates it by quotationalizing (Tanaka 2001) or reframing her original utterance as a quote with tte yuu ka ‘(I) say . . . or . . . ’ (a complementizer tte with a ‘say’ verb yuu, followed by a conjunction ka ‘or’). K understands it this time, as seen on line 5. This embedding operates locally. That is, the addition of the main clause on line 3 was not planned and takes place when M finds that K does not follow her original utterance. It should be noted, however, that as the translation ‘rather,’ provided on line 3, might suggest, the added main clause tte yuu ka ‘(I) say . . . or . . . ’ may have been lexicalized into a discourse marker which is used to restate the previous utterance (Ono 2006). That is, there is a scenario in which this example doesn’t involve embedding at all: the connection between the utterances on lines 1 and 3 is not syntactic but more semantic/pragmatic. We find this analysis to be highly likely, but adopting it would result in a further reduction of the already small number of examples of embedding in our data. For this reason, we coded this example as involving embedding. This is significant particularly in light of the fact that examples similar to this are numerous in our data, but even with our inclusive coding, we still have a hard time finding examples in our data for which the concept of recursion might be evoked, again weakening the status of the recursion hypothesis. A similar process is found even across speakers.8 The wife and the husband are discussing meals. 8. Please note that, as we stated earlier, clause combinations produced by more than one speaker were not coded in this article. We are presenting this example simply because it gives a clue as to what might be linguistically happening when Japanese speakers combine clauses.

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Example (7) Burokkorii 1 B: sukiyaki wa ashita de sukiyaki TOP tomorrow and ‘Sukiyaki is tomorrow and 2

nanka mottekuru no wa kyoo desho? something bring NOM TOP today COP bringing something (potluck) is today, isn’t it?’

3 A: u:n to omou kedo mhm that think but ‘mhm I think (so) but’ In lines 1–2, B lists upcoming meal plans, which she asks her husband A to confirm. A on line 3 produces a complement marker to and the verb omou ‘think’. That is, A turns B’s utterance on lines 1–2 into a quote ‘I think that . . .’. However, if you simply combine the utterances in lines 1–3, the outcome is awkward: ?sukiyak wa ashita de sukiyaki TOP tomorrow and nanka mottekuru no wa kyoo desho to omou kedo something bring NOM TOP today COP that think but This awkwardness comes from the fact that the combined utterance involves both an element which solicits the addressee’s confirmation about the upcoming events and another which asserts the speaker’s own understanding or belief. That is, the clause on line 2 involves a form desho ‘isn’t it’, whose function is similar to the English tags and solicits A’s confirmation while the clause on 3 involves the verb omou ‘(I) think’, which asserts A’s understanding or belief. Yet, in actual spoken discourse, utterances like this are constantly produced; they don’t seem to be what some people call ‘‘performance errors’’. What is conveyed by the utterance on line 3 of (7) is A’s belief or understanding that sukiyaki is tomorrow and potluck is today; A’s expression of belief or understanding is only about a certain portion of B’s utterance in lines 1–2 ‘sukiyaki is tomorrow and potluck is today’, what might be called ‘proposition’. In other words, we observe that speakers operate with the local semantic connection, not syntax: clauses are connected one at a time based on semantics/pragmatics, and the specific syntactic structure within foregoing material might be irrelevant or even invisible to speakers (cf. Auer 2005). With this new understanding, the small number

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of examples with more than one level of embedding should be characterized as involving a series of combinations of two clauses at a time, locally, giving infinite recursion the status of a theoretical device without empirical reality.

4. Conclusion Our data suggest that recursion is at best a very limited phenomenon in spoken Finnish and spoken Japanese. This casts serious doubt on the status of the recursion hypothesis. The supporters of the hypothesis would undoubtedly suggest that our findings simply pertain to performance, not the recursion capacity itself. That is, one might argue that there is surely a recursion component, since one can very easily create examples which involve multiple levels of embedding and that performance factors such memory and attention limit the actual application of the mechanism.9 Typically, those holding such a view will ask: how can one access grammatical representation (knowledge) by examining discourse data (performance)? However, we challenge those who take such a view to first prove that data constructed for linguistic analysis actually capture the spoken language ability, the target of investigation in the field of linguistics. In fact, in no other scientific field do data created by the researchers themselves, who are more than familiar with the goal of research, count as data.10 On the other hand, actual discourse data is not only authentic in the sense that it is not created by the researcher, but it is also certain to have at least

9. Similar views were expressed when we gave a preliminary version of our paper at the Recursion Conference. 10. Some might argue that we cannot really abandon the findings from the study of constructed examples particularly because that is the gist of research in the field for the past several decades. We are sympathetic to the time and e¤ort which has been put into that line of research. However, it still has to be pointed out that we are ultimately responsible for meeting a minimum requirement in scientific inquiry where researchers themselves are not the provider of the data. We do recognize that so-called intuition can be a target of scientific inquiry. But again, in such an endeavor, data has to be provided by speakers who are not researchers themselves, and obviously until demonstrated as such, intuition cannot be assumed to reflect spoken language ability (‘‘competence’’).

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some connection to actual grammatical knowledge.11 In fact, discoursebased investigations have shown evidence for a direct connection between actual usage and the grammar of human language (e.g. Bybee 2006; Du Bois 1987). At the same time, however, we would like to stress that we are not denying the reality of recursion in constructed data. Rather, we are claiming that we have not seen any evidence which suggests that recursion is a central aspect of human speech. So, for instance, we are more than happy to entertain ideas in which recursive behavior in constructed data is part of written language, and in fact, developed alongside literacy, which involves a relatively slow reflective process, rather similar to the process of constructing linguistic examples (see also Karlsson 2007a, b): that is, recursion may be a specific adaptation to communicative needs in a particular type of language use, but not the only uniquely human component of the language faculty, unlike what HFC assumes. To sum up, we would like to suggest that it is not warranted to base a model of human language on constructed data. We suggest instead that from actual speech data, it is clear that speakers know how to quote, how to conceptualize events based on the semantics of verbs, how to modify nouns, and in general how to link clauses with various relationships. However, they seem to do so one clause combination at a time, since spoken language is fundamentally a temporal phenomenon. Recursion is not a new idea. Several decades after its conception its reality is being questioned for the first time with overwhelming evidence that it has little to do with what actual speakers know and do. Further, despite its self-claimed theoretical importance, neither has the recursion hypothesis attracted the type of interdisciplinary research e¤orts which HCF advocates.12 Perhaps this is a good point in the history of the field to abandon the idea of recursion as a defining feature of human language, and instead to engage in collective interdisciplinary e¤orts to determine what actual human traits are by studying what speakers do in their everyday linguistic life. That undoubtedly would a¤ord the field with opportunities to propose descriptively adequate, falsifiable hypotheses, which will constitute significant steps toward the understanding of real human language. 11. A debate concerning some of these issues is found in a series of discussion notes which appeared in the March issue of Language (2005), which includes reviews of Newmeyer (2003) and his response. 12. The interdisciplinarity which HCF advocates is highly selective.

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References Auer, Peter 2005

Projection in interaction and projection in grammar. Text 25 (1): 7–36. Bever, Thomas G. 1976 The influence of speech performance on linguistic structure. In: Thomas G. Bever, Jerrold J. Katz, and D. Terence Langendoen (eds.) An integrated theory of linguisticability, 65–88. New York: Crowell. Hakulinen, Auli, and Eeva-Leena Seppa¨nen 1992 The Finnish kato: from verb to particle. Journal of Pragmatics 18: 527–549. Bybee, Joan 2006 From usage to grammar: the mind’s response to repetition. Language 82 (4): 529–551. Chafe, Wallace 1994 Discourse, Consciousness and Time. Chicago: University of Chicago Press. Couper-Kuhlen, Elizabeth and Tsuyoshi Ono (eds.) 2007 Turn Continuation in Cross-Linguistic Perspective, special issue of Pragmatics 17 (4). Crystal, David 1980 Neglected grammatical factors in conversational English. In: Sidney Greenbaum, Geo¤rey Leech, and Jan Svartvik (eds.) Studies in English Linguistics in honour of Randolph Quirk, 153– 166. London: Longman. Du Bois, John W. 1987 The discourse basis of ergativity. Language 63 (4): 805–855. Everett, Daniel L. 2005 Cultural constraints on grammar and cognition in Piraha˜: Another look at the design features of human language. Current Anthropology 46 (4): 621–646. Franck, Dorothea 1985 Sentences in conversational turns: A case of syntactic ‘double bind’. In: Marcelo Dascal (ed.), Dialogue: An Interdisciplinary Approach, 233–245. Amsterdam: John Benjamins. Hauser, Marc D., Noam Chomsky and W. Tecumseh Fitch 2002 The faculty of language: What is it, who has it, and how did it evolve?. Science 298: 1569–1579. Helasvuo, Marja-Liisa 2001 Emerging syntax for interaction. Noun phrases and clauses as a syntactic resource for interaction. In: Margaret Selting and Elizabeth Couper-Kuhlen (eds.), Studies in Interactional Linguistics, PAGES. Amsterdam: John Benjamins.

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Hopper, Paul. J. 1998 Emergent grammar. In: Michael Tomasello (ed.), The New Psychology of Language: Cognitive and Functional Approaches to Language Structure, 155–175. Mahwah, NJ: Lawrence Erlbaum. Hopper, Paul and Sandra A. Thompson 1980 Transitivity in Grammar and Discourse. Language 56 (2): 251– 299. Hopper, Paul and Sandra A. Thompson 1984 The Discourse Basis for Lexical Categories in Universal Grammar. Language 60 (4): 704–754. Iguchi, Yoko 1998 Functional variety in the Japanese conjunctive particle kara ‘because’. In: Toshio Ohori (ed.), Studies in Japanese grammaticalization: Cognitive and discourse perspectives, 99–128. Tokyo: Kurosio. Ikola, Osmo, Ulla Paloma¨ki, and Anna-Kaisa Koitto 1989 Suomen murteiden lauseoppia ja tekstikielioppia [Syntax and text grammar of Finnish dialects.] Helsinki: Suomalaisen Kirjallisuuden Seura. Iwasaki, Shoichi, and Tsuyoshi Ono 2001 ‘Sentence’ in spontaneous spoken Japanese discourse. In: Joan Bybee & Michael Noonan (eds.), Complex Sentences in Grammar and Discourse, 175–202. Amsterdam: John Benjamins. Karlsson, Fred 2007a Constraints on multiple initial embedding of clauses. International Journal of Corpus Linguistics 12 (1): 107–118. Karlsson, Fred 2007b Constraints on multiple center-embedding of clauses. Journal of Linguistics 43 (2): 365–392. Karlsson, Fred, and Kaius Sinnema¨ki 2007 Ms. Constraints on final embedding of clauses. Department of General Linguistics, University of Helsinki. Korhonen, Riitta 1993 Buts about Conjunctions: A syntactic study of conjunction expressions in Finnish. Helsinki: Suomalaisen Kirjallisuuden Seura. Ka¨rkka¨inen, Elise 2003 Epistemic Stance in English Conversation. Amsterdam: John Benjamins. Kokuritsu Kokugo Kenkyuujo [National Language Research Institute] 1960 Hanashi kotoba no bunkei (1): Taiwa shiryoo ni yoru kenkyuu. [Analysis of spoken language (1): Study based on dialogue data] Tokyo: Shuuei Shuppan. Laury, Ritva 2006 On Subordination, Finnish-style: Questioning the category of finite clausal complements in spoken Finnish. In: Mickael Suo-

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minen, Antti Arppe, Anu Airola, Orvokki Heina¨ma¨ki, Matti Miestamo, Urho Ma¨a¨tta¨, Jussi Niemi, Kari K. Pitka¨nen, and Kaius Sinnema¨ki (eds.), A Man of Measure. Festschrift in Honour of Fred Karlsson on his 60th Birthday, 310–321. Turku: The Linguistic Association of Finland. Laury, Ritva, and Tsuyoshi Ono 2005 Data is data and model is model: You don’t discard the data that doesn’t fit your model! Language 81 (1): 218–225. Laury, Ritva, and Eeva-Leena Seppa¨nen 2008 Clause combining, interaction, evidentiality, participation structure, and the conjunction-particle continuum: the Finnish etta¨. In: Ritva Laury (ed.), Crosslinguistic Studies of Clause Combining. The multifunctionality of conjunctions (Typological Studies in Language 80), 153–178. Amsterdam: Benjamins. Linell, Per 2005 The Written Language Bias in Linguistics. London: Routledge. Miller, George A. 1956 The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review 63 ( ): 81–97. Mori, Junko 1999 Negotiating Agreement and Disagreement in Japanese: Connective Expressions and Turn Construction. Amsterdam: John Benjamins. Nakayama, Toshihide, and Kumiko Ichihashi-Nakayama 1997 Japanese kedo: Discourse genre and grammaticization. In: Homin Sohn and John Haig (eds), Japanese/Korean Linguistics 6, 607–618. Stanford: CSLI Publications. Newmeyer, Frederick J. 2003 Grammar is grammar and usage is usage. Language 79 (4): 682– 707. Ono, Tsuyoshi 2006 Postpredicate elements in Japanese conversation: Nonmodularity and panchrony. In: Timothy J. Vance and Kimberly Jones (eds.), Japanese/Korean Linguistics 14, 381–391. Stanford: CSLI Publications. Ono, Tsuyoshi, and Ryoko Suzuki 1992 Word order variability in Japanese conversation: Motivations and grammaticization. Text 12 (3): 429–445. Parker, Anna 2006 Evolution as a Constraint on Theories of Syntax: The Case against Minimalism. Ph.D. thesis, University of Edinburgh. ¨ stman, Jan-Ola O 1981 You know: A Discourse-Functional Approach (Pragmatics and Beyond II:7). Amsterdam: John Benjamins.

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Pawley, Andrew, and Frances Syder 1983 Natural selection in syntax: Notes on adaptive variation and change in vernacular and literary grammar. Journal of Pragmatics 7 (5): 551–79. Scheglo¤, Emanuel A. 1979 The relevance of repair to syntax-for-conversation. In: Talmy Givo´n (ed.), Discourse and Syntax (Syntax and Semantics 12), 261–286. New York: Academic Press. Scheibman, Joanne 2003 Point of View and Grammar. Structural patterns of subjectivity in American English conversation. (Studies in Discourse and Grammar 11). Amsterdam: John Benjamins. Seppa¨nen, Eeva-Leena, and Ritva Laury 2007 Complement clauses as turn continuations: Syntax, prosody and interactional functions of the Finnish et(ta¨)-clause. Pragmatics 17 (4): 553–572. Suojanen, Matti K. (ed.) 1985 Mita¨ Turussa puhutaan. Raportti Turun puhekielen tutkimuksesta. [What are they saying in Turku: A report on the Turku spoken language project]. (Turun puhekielen projektin julkaisuja 3, Turun yliopiston suomalaisen ja yleisen kielitieteen laitoksen julkaisuja 23). Turku: University of Turku. Sweetser, Eve 1990 From etymology to pragmatics. Cambridge: Cambridge University Press. Tanaka, Hiroko 2001 The implementation of possible cognitive shifts in Japanese conversation: Complementizers as pivotal devices. In: Margaret Selting and Elizabeth Couper-Kuhlen (eds.), Studies in Interactional Linguistics, 81–109. Amsterdam: John Benjamins. Tao, Hongyin 1996 Units in Mandarin conversation. Amsterdam: John Benjamins. Thompson, Sandra A., and Elizabeth Couper-Kuhlen 2005 The clause as a locus of grammar and interaction. Discourse Studies 7 (4–5): 481–505. Thompson, Sandra A. 2002 ‘Object complements’ and conversation: towards a realistic account. Studies in Language 26 (1): 125–164. Thompson, Sandra A. 2006 What are clauses for? Understanding grammar in terms of social action. Plenary address, Linguistic Society of America Annual Meeting.

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Appendices Transcription symbols . , ? here : >< hh .hh @ (0.3) (.) ¼ [ ] ( ) (( ))

falling intonation level or slightly falling intonation rising intonation emphasis lengthening of the sound talk inside is done with a faster pace than the surrounding talk audible exhalation audible inhalation laughter syllabe (e.g. ‘ha’) silences timed in tenths of a second silence shorter than 0.2 seconds no silence between two adjacent utterances utterances starting simultaneously point where overlapping talk stops talk not discernible transcriber’s comments

Glossing symbols 13 ABL ACC ADE CLT CMP COND COMP COP DET FP GEN INE INF INS 1INF

ablative accusative adessive clitic comparative conditional complementizer copula determiner final particle genitive inessive infinitive instructive 1st infinitive

13. In the Finnish glossing, present tense and nominative case are considered default and are not marked.

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NEG NOM PASS PAST PL PPLE PST PRT PTC Q STAT TAG TOP

negation nominalizer passive past plural participle past partitive particle question stative tag topic

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5.

What do you think is the proper place of recursion? Conceptual and empirical issues

Arie Verhagen

1. Introduction1 The ‘‘recursion-only-hypothesis’’ tentatively put forward by Hauser, Chomsky, and Fitch (2002) – henceforth: HCF – holds that ‘‘recursion’’ might be the only component of the Faculty of Language in the Narrow sense (‘‘FLN’’), with ‘‘narrow’’ being defined as: Neither shared by other organisms, nor shared by other cognitive capacities than the faculty of language, so being both unique to humans and unique to language at the same time2. This suggestion has generated many responses, from students both of human cognition and of animal behavior. Especially the latter responded not only to HCF, but also to Fitch and Hauser (2004); although published two years after HCF itself, this article had already been invoked by HCF (1578, col.1) as a study suggesting some empirical support for the hypothesis, so it is understandable that the scientific community took the two as directly linked. Fitch and Hauser showed that cotton-top tamarins could easily master regularities in certain strings of sounds that were

1. I would like to thank Dan Everett for organizing a stimulating conference, and him as well as Peter Harder, Jan Koster, Bob Ladd, and Marianne Mithun for stimulating discussions at the conference. Thanks are also due to Carel ten Cate and Jelle Zuidema for discussions on some evolutionary and formal issues, that allowed me to – hopefully – find suitable formulations for what I wanted to say in these areas. Three anonymous reviewers provided useful feedback on the first draft, which led to a number of changes and additions. But as usual, I am solely responsible for any remaining errors. 2. In HCF, ‘‘FLB’’ – ‘‘B’’ standing for ‘‘Broad sense’’ – comprises all capacities an organism must possess in order to be said to have language. So FLB includes FLN by definition, and also much more that is, in one form or another, also used in at least one other cognitive domain, present in at least one nonhuman animal, or both. Notice that FLN may be empty, under this definition (cf. Fitch, in press, who also provides some other clarifications).

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defined by a finite state grammar (FSG); these strings were of the type (AB)n (A and B representing two classes of sounds di¤ering in some salient respect), and the animals could learn to distinguish legitimate from illegitimate strings, as defined by this grammar. But what they could not learn, apparently, was to distinguish legitimate from illegitimate strings as defined by a phrase structure grammar (PSG); in this case, legitimate strings were of the type AnBn, thus involving center-embedding introducing long-distance dependencies (Fitch and Hauser 2004: 378). Although they do not use the term ‘‘recursive’’ itself, it is clear that Fitch and Hauser (2004) are in fact referring to this property, since the term is used for exactly the same phenomenon in HCF (1577, col. 3), and since it is graphically illustrated by means of figure 1, showing nested embedding of pairs of AB in each other in the second case, as opposed to the non-embedding structure for strings of the type (AB)n.

Figure 1

It was the idea that animals are intrinsically incapable of processing ‘‘recursive’’ structures conceived in this way that was addressed by Gentner et al. (2006). Using exactly the same types of grammars to construct their own stimulus materials, they showed that European starlings were capable of learning the regularity in AnBn patterns, i.e., to distinguish legitimate from illegitimate strings as defined by this grammar, and they thus concluded that at least this non-human species has the capacity to acquire a recursive grammar. Given the character of HCF’s ‘‘recursion-only-hypothesis’’, this conclusion naturally generated a considerable amount of interest and discussion as well.3 The reason is that this line of research promises to provide 3. Something that did not receive much attention, even though Gentner et al. are quite explicit about it, is the fact that there was much individual variation in the performance of the birds: Only 4 out of 11 individuals learned to do the

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part of the answer to the question what makes human language so special and powerful as compared to animals’ communicative abilities. However, there is an issue that we should take into account before any such comparison can be made at all, viz. the question whether ‘‘recursion’’ is sensibly identified with long-distance dependencies, for the purpose of testing a hypothesis about a biologically and cognitively unique characteristic of language. Fitch and Hauser (2004: 378, col. 3), in line with HCF, assume so, despite the fact that they acknowledge that center-embedded structures are ‘‘less common in human language than other (e.g., rightbranching) structures’’; they write: ‘‘This PSG thus provides the ideal grammar for the empirical issue addressed by this study’’. The argument is essentially that there is ‘‘a broad consensus in linguistics and machine learning that PSGs are more powerful than FSGs and that grammars above the FSG level are, minimally, a crucial component of all human languages’’ (col.1), and that the AnBn grammar is a minimal PSG. However, as argued by Zuidema (2005), the observation that all FSGs (to which animal communication systems are generally assumed to belong) are included in the set of PSGs and that human languages are beyond the power of FSGs only suggests that precisely this boundary corresponds to an evolutionarily relevant step, but it is not at all clear that this is actually the case. First, there are many PSGs that bear little or no resemblance to human linguistic systems; ‘‘[n]atural languages are [ . . . ] constrained in many ways (e.g., semantics, learnability) that have nothing to do with the Chomsky Hierarchy’’. Second, the idea of evolution ‘‘climbing the Chomsky Hierarchy’’ suggests that more formal power than FSG is hard to get, but it is actually extremely easy (Zuidema 2005: 50). So it is still necessary to raise the question formulated above: How much sense does it make to identify ‘‘recursion’’ with long-distance dependency, or more to the point: What sense of ‘‘recursion’’ is useful in the light of empirically sound generalizations concerning the structure of human linguistic utterances? Most of the remainder of this article is concerned with this question; the discussion will involve both conceptual and empirical considerations. What we will task well, and 2 never showed any progress. Moreover, an extremely high number of trials was needed, though the birds depended on their performance for their food. Thus, the task was apparently very di‰cult, and the results suggest that the capacity for recursive processing had to be learned and was not biologically given a priori, such that it only had to be ‘‘triggered’’ by exposure to stimuli; in that case, one would not expect so much variation despite a large amount of training.

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see is that it makes little sense to view recursion as a property at the global level of a language’s grammar as a whole; it is much better viewed as a ‘‘local’’ property of certain subparts of a grammar. 2. Di¤erent formulations in 20th century linguistics The role of recursion to account for long-distance dependencies goes back to Chomsky’s initial work on formal models for the description of grammar. To make the point that a natural language cannot be described by means of a Finite State (‘‘Markov’’) model, Chomsky (1957) drew attention to English sentences of the following form: (1)

(i) (ii) (iii)

If S1, then S2. Either S3, or S4. The man who said that S5, is arriving today.

In such sentences, a dependency between two elements exists, though they can be indefinitely far apart: ‘‘between the interdependent words, in each case, we can insert a declarative sentence S1, S3, S5, and this declarative sentence may in fact be one of ([1]i–iii)’’ (22), i.e., the kind of process HCF allude to when they write (1577): ‘‘Natural languages go beyond purely local structure by including a capacity for recursive embedding of phrases within phrases, which can lead to statistical regularities that are separated by an arbitrary number of words or phrases.’’ But in Chomsky (1965), the primary role of recursion is to account for the property of productivity: ‘‘The infinite generative capacity of the grammar arises from a particular formal property of these categorial rules, namely that they may introduce the initial symbol S in a line of a derivation. In this way, the rewriting rules can, in e¤ect, insert base Phrase-markers into other base Phrase-markers, this process being iterable without limit.’’ (142). This role for recursion is also present in HCF, but then at the beginning of the article (1571): All approaches agree that a core property of FLN is recursion, attributed to narrow syntax in the sense just outlined. FLN takes a finite set of elements and yields a potentially infinite array of discrete expressions. [ . . . ]. The core property of discrete infinity is intuitively familiar to every language user. Sentences are built out of discrete units [ . . . ]. There is no longest sentence (any candidate sentence can be trumped by, for example, embedding it in ‘‘Mary thinks that . . .’’), and there is no non-arbitrary upper bound to sentence length. [ . . . ] At a minimum, then, FLN includes the capacity of recursion.

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There is indeed a connection between these two roles of recursion: Arbitrary long-distance dependency (recursion role 1) implies that the length of a sentence is unbounded (thus there is no longest sentence) and this in turn implies an infinite number of sentences; and similarly, a mechanism for embedding phrases/sentences in other phrases/sentences also implies that there is no longest sentence, and thus an infinite number of sentences (recursion role 2). But does the fact that these two mechanisms produce the same result of unboundedness mean that they are identical, as the use of the term ‘‘recursion’’ for both cases suggests? Obviously, unbounded long distance dependency implies the existence of embedding (phrases within other phrases of the same type). But is this a relation of equivalence? Is this implication bi-directional? In other words: Does embedding of sentences imply the existence of long-distance dependencies? Another question relates to a presupposition in both of Chomsky’s formulations: Is it truly the case that all instances of the category S (i.e., any phrases categorized as ‘‘sentences’’) can be embedded in each other? This question concerns the proper level of abstraction of a recursive analysis of some linguistic construct. I will begin by addressing this latter issue, as it is also relevant for a discussion of the first one. 3. Roles and types of recursion, and their empirical counterparts 3.1. Adverbial subordinate clauses The first construction invoked by Chomsky (1957) to illustrate long-distance dependency in English concerns an adverbial clause type (if . . . then). But contrary to Chomsky’s suggestion, it is practically impossible to embed an if . . . then construction in itself, or, for that matter, in either . . . or, in ordinary English (while such constructs are run-of-the-mill in computer programming): ??If

if it rains, then they will cancel the match, then I will not buy a ticket. (3) ??Either if Federer won, then Nadal lost, or the Wimbledon finals have not taken place yet.

(2)

There seems to be a quite general restriction: Center-embedded clauses cannot be headed by the same conjunction as the embedding clause. For example, 109 (¼about 1%) of the over 10,500 subordinate clauses in the Dutch Eindhoven corpus contain another, center-embedded clause, and of these, only 1 has the same conjunction as the embedding clause:

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(4) [Als jij haar [als je thuis kwam] waarschijnlijk vriendelijk en blij tegemoet kwam,] waren haar goede voornemens weer op de loop. ‘[When/While you, [when you came home,] were probably nice and friendly,] her good intentions were gone again’ Notice that the content of the relation marked by the two instances of als is not entirely the same; the first is more or less concessive, the second purely temporal. These observations have a natural interpretation in terms of the assumption that human memory, unlike a computer, does not work with basically arbitrary addresses, but is rather content-driven. Interrupting the processing of some construct requires that the intermediate result be correctly retained in memory for processing to be resumed later, and this is much more problematic when the interrupting sequence has the same kind of content. Example (5), the English equivalent of one of the Dutch corpus sentences, also illustrates this: (5) (6)

Because our flight turned out to be cancelled when we arrived in Madrid, we missed our connecting flight in New York. ?? Because

our flight was cancelled because the Spaniards were on strike, we missed our connecting flight in New York.

Embedding a temporal relation in the middle of a causal one leads to a much better sentence (5) than embedding a causal relation in another causal one (6). A more radical, but arguably simpler and better way of putting it, is to say that, for the cognitive system, cases like (5) do not involve recursion at all, because the embedding and the embedded sequences are actually not of the same category, and hence the whole sentence does not satisfy the elementary definition of recursion: That a constituent is embedded in another one of the same type. If it is the embedding of a temporal relation into a clausal one that a cognitive system has to process in (5), then this does not involve two constituents of the same type. This is in fact a much more general issue, as we will see. Let me explain here why usage data like the ones just considered are particularly relevant in the present context, which involves a discussion of evolutionary issues. In this context, it is important to keep in mind that it is only through behavior that a cognitive trait can interact with the environment, so it is only through behavior that such a trait can be selected for (give an organism an advantage). So if an organism with an alleged language-related cognitive trait T is indistinguishable in linguistic usage from one without T, then there is no evidence that T has been selected

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for (it does not have to be selected against, either, of course), and thus there is no explanation why it should have become dominant in the population. In other words: Then there is no reason to assume that the emergence of T is part of the explanation of the evolution of language as we encounter it today. For the adverbial clauses under consideration, this seems to make sense: Since strictly recursive adverbial clauses (involving embedding of the same type of clause in itself) do not have to be produced or processed, a verbally communicating organism without the capacity to embed adverbial clauses of type X into themselves will be indistinguishable from one with that capacity in actual linguistic usage; in a sense, there will not really be opportunities to use the capacity to some advantage in the linguistic environment, and thus it will not increase in frequency in the population.4 Of course, this does not mean that the same 4. In principle, if the same behavior could be produced using less resources (energy, time), due to the presence of recursion, than without recursion, then it may also be a target of selection. For instance, a grammar with recursion may be smaller in size, requiring less memory space, while still describing the same language; or it may be learnable in a smaller amount of time. This costadvantage is certainly operative in evolutionary processes, a prime example being conspicuous signals that are indicative of the health or fitness of an individual (in competition or sexual attraction), where individuals that are able to produce them at lower costs have an advantage (albeit with subsequent loss of value of the signal as a consequence). While such a mechanism cannot be excluded a priori, the fact that it is possible in principle does not undo the relevance of the point about observable behavior. For one thing, it should be demonstrated separately that, for instance, reduced grammar size provides an advantage in terms of memory load, as this depends on the way memory works and the availability of memory capacity (which is quite impressive in humans, to say the least), and on potential additional disadvantages elsewhere. In the case of ‘‘true recursion’’, in particular, a well known problem is that although the statement of a rule may itself be very simple, processing requires a ‘‘push down stack’’ to store intermediate results of computations for a potentially indefinite amount of time and an indefinite number of times, which produces costs for working memory that may not outweigh the benefits for long term memory; the fact that such structures are actually very di‰cult to process for humans, suggests that at least this kind of recursion is not hardwired into us (I will return to this in the conclusions). Secondly, and most importantly in the present context, e¤ects of traits in terms of behavior interact more directly with the relevant environment and have a more directly observable e¤ect than cost e¤ects, so the former should always be considered as prime candidates when considering the question whether the trait in question can have been the target of selection.

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conclusion also holds for other alleged areas of grammar where recursion has been claimed to be operative; each should be investigated in its own right. 3.2. Recursive non-finite clauses? One such area is that of causative constructions, since these are mostly analyzed as involving an embedded S, albeit an infinitival one. Consider the English and Dutch examples (7) and (8). (7) He made me understand the situation. (8) De sergeant liet de rekruten door de modder kruipen. The sergeant let the recruits through the mud crawl ‘The sergeant had/made the recruits crawl through the mud.’ These are usually analyzed as in (9), expressing the linguistic generalization that the recruits has the same role with respect to crawl as a fullblown subject has in a finite clause with crawl as its main verb: (9) [S The sergeant made [S the recruits crawl through the mud ]] Considering usage again, this analysis predicts that in a particular corpus, the ratio of transitive and intransitive embedded non-finite Ss is the same as for embedded finite clauses. After all, analyzing the embedded phrase in (9) as an S amounts to assigning it the same grammatical status as a tensed sentence, essentially claiming that the value of the feature finiteness is irrelevant to its syntactic category. If finite and non-finite phrases are indeed of the same syntactic category, then one should expect that the overall distibution of subtypes of the category (such as transitive vs. intransitive) is the same within a particular corpus, since the subtypes should also be indi¤erent to the feature of finiteness. So, given that a causative clause has one additional argument (the subject of the matrix verb), the ratio of three- to two-participant causative clauses should be the same as that of transitive to intransitive finite clauses. However, in the Dutch Eindhoven corpus, the actual ratios are 10% three-participant causatives to 90% two-participant ones, while the transitive-intransitive ratio is 40%–60%. This is not only a very big di¤erence, the 10% three-participant clauses is also about the same as the portion of ditransitive clauses (mainly events of transfer) within the set of monoclausal transitives.

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Not only does this suggest that the representation in (9) might be ascribing an overdose of structural complexity to causatives. So far I have not found actual cases of causatives embedded in causatives, i.e., sentences like the constructed examples in (10) and (11); and as a matter of fact, these are at least strange, too: (10)

??John

(11)

??Deze

let me make his son understand the situation.

opmerking deed de sergeant de rekruten door de modder laten kruipen. ‘This remark made the sergeant have the recruits crawl through the mud’5

Another piece of linguistic evidence that causatives share more properties with monoclausal structures than with biclausal ones (cf. Kemmer and Verhagen 1994, Verhagen and Kemmer 1997), is the fact that the selection of expressions marking the role of the causee (the alleged subject of the alleged embedded clause) operates at the level of the combined predicates, not at the level of either one of the two hypothetical clauses. Consider the Dutch example (12). (12) Je mag die brief aan niemand laten lezen. You may that letter to nobody let read ‘You must not let anybody read that letter.’ The preposition aan is used in simplex sentences to mark indirect objects as recipients (typically with give). Here it marks nobody in precisely that way. But neither laten (‘let’) nor lezen (‘read’) selects a recipient role; it is the combination let read that does. Again, all this indicates that the actual categories used by the cognitive system to process causative structures are of di¤erent types (presumably, a very limited set of grammaticalized, auxiliary-like causal predicates on the one hand, and a more open class of result predicates on the other). So they are not of the same type, and embedding one in the other therefore does not actually constitute recursion. And in any case, an individual lacking the capacity to embed causatives recursively would be indistinguishable, in practice, from one having it, so the fact that it is possible to analyze

5. Notice that these constructed cases have di¤erent causal verbs, in order to avoid the ‘‘content-restriction’’ alluded to in the previous section.

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these structures as biclausal does not provide evidence for the presence of recursion in the biologically given, universal faculty of language. 3.3. Finite complements and tail-recursion The prototype of syntactic recursion, also invoked by HCF, is complementation: Embedding of an arbitrary tensed sentence in a matrix of the type ‘‘Mary thinks/says/knows that . . .’’. Unlike the non-finite complements of causatives, these actually can be embedded in each other; it is not hard to find instances like (13) in actual texts. (13) This gentleman thinks that I do not know it is a doll. Arguably, this is directly related to the fact that complementation expresses a kind of content that is itself recursive, viz. perspective-taking, a cognitive capacity – putting oneself in someone else’s shoes, thus ascribing to them one’s own cognitive capacities, including perspective taking – that implies recursivity (cf. Verhagen 2005: 98–99). At the same time, it is important to notice that the general capacity to embed complement clauses in other complement clauses develops gradually during language acquisition. Children start out with using highly fixed phrases like I think . . ., I guess . . ., you know . . ., Look . . ., each with its own specific function in managing the triadic relationship between themselves, their interlocutors and some object of shared attention (Diessel and Tomasello 2001; Tomasello 2003). It is only later, with increasing linguistic experience, that they generalize it to a pattern, or rule, for embedding clauses into clauses. Children do not start making complex sentences by combining the simplex clause types they have acquired at a certain point, rather they start adding certain initially di¤erent fixed elements to their utterances, out of which a pattern for complex sentences ultimately emerges as a generalization. In fact, the fixed expressions and their specific interactional functions remain available, and continue to play a prominent role into adulthood especially in spontaneous conversation, where they account for the vast majority of ‘‘complementation sentences’’ (Thompson 2002). It is especially in writing (printed public texts) that the operation of a generalized pattern for complementation can be observed. In Verhagen (2005: 102–104), it is shown that the four most frequent complement taking predicates account for only about 25% of complement constructs in newspaper texts, while predicates with a token frequency of 1 or 2 account for as much as 50%. In contrast, in Thompson’s (2002) conversational

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data, the four most frequent predicates account for over 80% of the data, with a single verb, think, accounting for over 50%. While the type-token ratio in the conversational data is .26, it is .59 in the newspaper texts. It seems reasonable to assume that it is to a large extent the process of learning to read and write that is responsible for the increase in people’s linguistic experience that allows generalized embedding of complements (beyond just tagging relatively fixed expressions onto other clauses) to become a productive process, especially by causing the type-frequency (the number of di¤erent lexical items occupying the same slot in a pattern) of complement taking predicates to increase in people’s linguistic experience (cf. Bybee 1995 for the relation between type-frequency and productivity). Thus, it is proposed in Verhagen (2005: 111) that the knowledge of complementation constructions of an adult speaker of Dutch can be (partially) represented as the construction network in figure 2:

Figure 2

Initial fixed expressions (‘‘I think’’, etc.) are still available for processing, and in fact well entrenched (indicated by the bold lines). But generalized versions (e.g., the verb think) are also available on the basis of experience with similar but somewhat di¤erent instances, and ultimately also an abstract pattern (at the top of figure 2), on the basis of experience with different forms occurring in formally and functionally similar environments. But while actually instantiated, the type of recursion allowed in complementation clearly does not produce center-embedding. Rather it involves what is known as tail-recursion, which does not require the special memory requirements (a ‘‘stack’’, to maintain intermediary results when processing must be interrupted) that is needed for processing centerembedding (the latter is also known as ‘‘true recursion’’). So here we have an empirical answer to the first question raised in Section 2: Embedding of

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one S in another certainly does not necessarily produce center-embedded structures, so the two roles for which recursion has been invoked in Chomsky (1957) and (1965) respectively, and in HCF at the same time, certainly do not entail one another. However, complementation is assumed to be the domain of a particular phenomenon that has received much attention in theoretical linguistics and that does seem to produce long-distance dependencies, viz. Whmovement. This is what I will turn to as a final case (cf. Section 3.3.5 of Verhagen 2005 for a more detailed account). 3.4. Long-distance Wh-movement Consider examples (7) and (8) (Chomsky’s (1977) examples (32) and (10)). (14) Who did Mary say that John kissed t. (15) Who did Mary hope [ S that Tom would tell Bill [ S that he should visit t ]] We seem to have very clear cases here of displacement. The element Who in (14) is the object of kissed, but it is not included in the clause of which kissed is the main verb, so it seems to pose a computational challenge: How do language users manage to interpret the role of the Wh-element when it is not included in the same unit that determines this role? The challenge is even larger, it seems, when one realizes, in view of (15), that the number of clauses between the elements to be connected may be indefinitely large (so the phenomenon indeed appears to instantiate true recursion). However, when looking at actual linguistic usage again, it soon becomes clear that utterances containing apparently displaced Wh-elements share quite a few other specific properties as well. For example, 10 out of the 11 instances in the Brown Corpus have think as complement taking verb (the other one is say), and 9 have a second person pronoun as its subject, i.e., a reference to the addressee of the question; cf. (16). (16) What do you think I did with them? That there is indeed a high degree of lexical and grammatical specificity of long-distance Wh- sentences is strongly confirmed when we look at a larger corpus, in this case a whole year (1995) of the Dutch newspaper de Volkskrant. In this corpus, we do find some more examples with other verbs than denken, e.g., willen (‘want to’) in (17), and other subjects than second persons, such as Mayor and Aldermen in (18).

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(17) Waar wil je dan dat ik het over heb? Where want you then that I it about have ‘What do you want me to talk about then?’ (18) Wat What zullen will

denken think denken think

B en W dat onze burgers Mayor and Aldermen that our citizens van zo’n dure buitenlandse reis? of such-a expensive foreign trip

‘What do Mayor and Aldermen think that our citizens will feel about such an expensive trip abroad?’ Still, the verb denken (‘think’) and second person subjects are strongly favored. Denken accounts for 34 of the 43 instances; the other verbs are willen (‘want to’), zeggen (‘say’), and vinden (‘find, believe’). Second person accounts for 36 of the 43 cases; the other subjects are third person pronouns, definite noun phrases, and a first person pronoun. Thus, there is clear evidence for the entrenchment of a specific template for prototypical ‘‘Wh-extraction’’ in Dutch that has the form given in (19).6 (19) [Wh . . . – denk- pron2nd dat . . . ] In fact, the entrenchment of this template seems to be stronger than that of many idiomatic expressions. The frequencies of the verbs and the subject types di¤er dramatically from their overall frequency in the corpus, and the corpus does not contain ‘‘Wh-extraction’’ cases that di¤er from (19) in more than one respect. Also, a few of the 7 subjects that are not grammatical second persons, are demonstrably referring to the addressee of the question, so conceptually still second persons (including the case of a first person matrix subject; cf. Verhagen 2005: 129–131); for example, (18) was uttered by a city council member while addressing Mayor and Aldermen. It is also clear that the other verbs occurring in this pattern are the most basic verbs of communication, volition, and ‘‘opinion’’ (vinden). Thus, the patterns licensing all cases are minimal, less well entrenched, extensions from the prototype template in (19).7 And so far, I have not been able to find examples like (15) in actual usage. 6. Its English counterpart could be [Wh . . . do pron2nd think . . . ] (cf. Dąbrowska 2004, chapter 9). 7. Indeed, it is conceivable that some instances of use, at least for some speakers, are direct extensions from the prototype, constructed ad hoc, rather than licensed by independent templates.

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Consequently, actual instances of patterns that are usually analyzed as combinations of abstract pieces of structure (i.e., clauses) and involving apparent violations of the boundaries between these abstract structural units, turn out to be produced and understood on the basis of a much more specific template. The lexically specific part denk je (‘do you think’) exactly parallels the part I think in the ‘‘complement taking’’ formulaic templates underlying children’s early complementation-like utterances, and those found in spontaneous conversation (cf. Section 3.4). It marks the subjectivity of the person whose mind is being ‘‘put on stage’’: The speaker’s (I think) in the case of assertions, the addressee’s ( you think) in the case of questions (Verhagen 2006). The template thus occupies a similar ‘‘low-level’’, well-entrenched position in the network of complementation constructions (cf. figure 3).

Figure 3

Actual constructs such as (16)–(18) are not the result of combining abstract clausal structures (from the top of this network), embedded in each other. Low-level templates inherit properties of higher nodes in the network, but can have additional properties as well; thus, specific properties of lower-level templates do not as such license inferences about properties of the more abstract nodes in the network. Again, it appears that for the cognitive system, the embedding of a clause in this template involves di¤erent categories, not categories of the same type, hence it does not amount to recursion. Again, an individual lacking the capacity for clausal recursion but equipped with this memorized specific question-forming template would be indistinguishable in actual linguistic usage from an individual with the recursive capacity.

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4. Conclusions Summarizing, we have first of all found that it is necessary to keep di¤erent aspects and di¤erent types of recursion well distinct, and investigate each of them separately. The general point is that the behavior of one kind of phenomenon that can be put in the very general rubric of ‘‘recursion’’ does not predict the behavior of other phenomena that have been put into the same rubric. The identity-requirement for recursion is not easily met in actual linguistic phenomena, indicating that this rubric may simply be too general for many descriptive and explanatory purposes. Hence the necessity for keeping di¤erent types and aspects apart, both conceptually (e.g. true and tail recursion) and analytically: Di¤erences between linguistic phenomena that may be claimed to exhibit recursivity (e.g. adverbial clauses, complementation, Wh-movement) are as important for explaining their actual properties as this point of similarity, if not more so. By the same token, a general conclusion of the type ‘‘Recursion is irrelevant in natural language’’ is not licensed by the present considerations either. Recursive phenomena exist, and can be an important feature of specific parts of the grammar of a language. Complementation, as expressing perspective-taking, is such a part. Other areas that come to mind are those of referential specification (e.g., by means of relative clauses), or of locating something in space (‘‘zooming in’’ by means of prepositional phrases of the same type embedded in each other). Second, there are some important consequences for views of the evolution of language, grammar in particular. It is clear that built-in general recursion cannot have given verbally communicating organisms an advantage. Present day language use does not provide evidence that there has been a selective pressure in our evolutionary past favoring a variant with a general recursive syntactic capacity such that it became more and more frequent in the population over subsequent generations. There is no reason to assume that the capacity for recognizing centerembedding patterns (true recursion) is built into humans, just us there is no reason to do so for starlings (cf. footnote 3). In fact, it is well known that processing center-embedded structures is generally hard for humans. In view of the content-restriction on center-embedding, it is perhaps not even clear a priori that all humans would be equally able to recognize the purely formal regularity that at least some of Gentner et al.’s starlings were capable of picking up. It is also quite telling that one of the clearest types of actual, general

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syntactic linguistic recursion – complementation – is not immediately available to children, but needs time and experience to develop. I have suggested that the development of literacy in an individual’s life may play an important role in the general complementation pattern becoming a productive rule, since it is especially through the interaction with texts that the type frequency of this pattern increases dramatically in a person’s linguistic experience. Following this line of thought, the hypothesis suggests itself that it may very well also have been the development of writing systems, and their spreading through human populations, that created the basis for the evolution, i.e., the cultural evolution, of general recursion in this area of the grammars of the languages involved. Literacy, especially reading, leads to communication between larger numbers of individuals and thus contributes to an increase in variation in linguistic experience, especially if it is wide-spread in a population. Moreover, writing, as an external representation of linguistic utterances, provides individuals with an extension of their memory, and thus also facilitates the recursive use of grammatical patterns (not only ‘‘true’’ recursion).8 A parallel with the number system is useful here. As is well known, recursion in our number system is a product of cultural evolution. The development of the place-value system, including the invention of zero which made it possible to distinguish between 11, 101, and 110, was a gradual process. Each step simplified the task of performing calculations on paper (rather than with an abacus). Ultimately, once the recursive number system was in place, it expanded the cognitive abilities of its users, partly by providing the basis for the invention of more dimensions of numbers (negative numbers, infinity, rational numbers, etc.), partly by allowing routinization and internalization. Surely, we do not want to say that the recursive number system (and its ramifications) has been part of all humans’ cognitive make-up for millennia before it was ‘‘discovered’’ a few centuries ago, when it became possible to start using it (in those parts of the world that had access to the discovery . . . ). The only view that makes sense is that recursivity is a truly new property, having emerged on the basis of still the same basic cognitive capacities; these happen to apply to new circumstances also emerging from cultural evolution and therefore give rise to truly novel results, not present in the original state of the organism. 8. A specification of some mechanism that actually produces recursive use from a non-recursive initial state of grammars is still required, of course. This issue is taken up in Verhagen and Zuidema (in prep.).

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Finally, as to the proper place of recursion, I have argued that this should not be thought of as a single spot in the grammar of a language, let alone in language. Rather, as far as grammar is concerned, it is to be found in di¤erent forms and with di¤erent constraints, in di¤erent ‘‘niches’’, associated with a particular kind of content. As far as domains of evolution are concerned, the proper place of recursion is definitely not only to be sought in genetic evolution, but (at least) also in cultural evolution. Both points, especially taken together, imply that we should actually expect a considerable amount of variation to occur, in individuals, in populations, and through historical time, since the conditions leading to recursivity of certain patterns – linguistic experience for generalization, functional content favoring recursive expression, memory capacity, cultural-environmental conditions providing means of external representation – are not equally available everywhere all the time. It seems to me that the reality of linguistic usage actually fits this picture rather well.

References Bybee, Joan 1995

Regular morphology and the lexicon. Language and Cognitive Processes 10: 425–455.

Chomsky, Noam 1957 Syntactic Structures. The Hague: Mouton. Chomsky, Noam 1965 Aspects of the Theory of Syntax. Cambridge, MA: The MIT Press. Chomsky, Noam 1977 On wh-movement. In: Peter W. Culicover, Thomas Wasow, Adrian Akmajian (eds.), Formal Syntax, 71–132. New York, etc.: Academic Press. Da˛browska, Ewa 2004 Language, Mind, and Brain: Some Psychological and Neurological Constraints on Theories of Grammar. Edinburgh: Edinburgh University Press. Diessel, Holger and Michael Tomasello 2001 The acquisition of finite complement clauses in English: A corpus-based analysis. Cognitive Linguistics 12: 97–141. Fitch, W. Tecumseh in press Three meanings of ‘‘recursion’’: Key distinctions for biolinguistics. In: R. Larson, V. Deprez, and H. Yamakido (eds.), The Evolution of Human Language: Biolinguistic Perspectives. Cambridge: Cambridge University Press, 2009.

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Fitch, W. Tecumseh and Marc D. Hauser 2004 Computational constraints on syntactic processing in a nonhuman primate. Science 303: 377–380. Gentner, Timothy Q., Kimberley M. Fenn, Daniel Margoliash and Howard C. Nusbaum 2006 Recursive syntactic pattern learning by songbirds. Nature 440: 1204–1207. Hauser, Marc D., Noam Chomsky, W. Tecumseh Fitch 2002 The faculty of language: What is it, who has it, and how did it evolve? Science 298: 1569–1579. Kemmer, Suzanne and Arie Verhagen 1994 The grammar of causatives and the conceptual structure of events. Cognitive Linguistics 5: 115–156. Thompson, Sandra A. 2002 ‘‘Object complements’’ and conversation: towards a realistic account. Studies in Language 26: 125–164. Tomasello, Michael 2003 Constructing a Language. A Usage-Based Theory of Language Acquisition. Cambridge, MA/London: Harvard University Press. Verhagen, Arie 2005 Constructions of Intersubjectivity. Discourse, Syntax, and Cognition. Oxford: Oxford University Press. Verhagen, Arie 2006 On subjectivity and ‘long distance Wh-movement’. In: Angeliki Athanasiadou, Costas Canakis and Bert Cornillie (eds.), Subjectification: Various Paths to Subjectivity, 323–346. Berlin/New York: Mouton de Gruyter. Verhagen, Arie and Suzanne Kemmer 1997 Interaction and causation: causative constructions in modern standard Dutch. Journal of Pragmatics 27: 61–82. Verhagen, Arie and Willem H. Zuidema in prep. A gradual route to recursion in natural language. Zuidema, Willem H. 2005 The major transitions in the evolution of language. Ph.D. dissertation, University of Edinburgh.

Part II.

Formal Issues

6.

Recursion and the infinitude claim*

Geo¤rey K. Pullum and Barbara C. Scholz

1. Infinitude as a linguistic universal In a number of recent works, linguists have portrayed the infinitude of sentences in human languages as an established linguistic universal. Lasnik 2000 asserts, in the opening chapter of a textbook based on his introductory graduate syntax lectures: (1) Infinity is one of the most fundamental properties of human languages, maybe the most fundamental one. People debate what the true universals of language are, but indisputably, infinity is central. (Lasnik 2000: 3) This is not a statement about the use of idealized infinitary mathematical models in theoretical science. It is about alleged ‘‘fundamental properties of human languages’’ themselves. Epstein and Hornstein (2004), a letter originally submitted for publication in Science but ultimately printed in Language, is yet bolder: (2) This property of discrete infinity characterizes every human language; none consists of a finite set of sentences. The unchanged central goal of linguistic theory over the last fifty years has been and remains to give a precise, formal characterization of this property and then to explain how humans develop (or grow) and use discretely infinite linguistic systems.

* The authors are grateful for the support of fellowships at the Radcli¤e Institute for Advanced Study in 2005–2006, during which some of the ideas set out here were conceived. A much earlier version of the paper was to have been presented at the conference on Recursion in Human Languages at Illinois State University in April 2007, but air travel problems prevented that, so the ideas presented here did not have the benefit of comments by the conference participants. We are very grateful to Julian Bradfield, Gerald Gazdar, Harry van der Hulst, Andra´s Kornai, Gereon Mu¨ller, Paul Postal, and four referees for comments on earlier drafts. These people should certainly not be assumed to agree with what we have said; the views presented here are ours alone, as are any and all errors.

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Here again, ‘‘discrete infinity’’ (which we take to mean denumerable infinity in sets of discrete elements such as symbol strings) is claimed to be a feature of ‘‘every human language’’, as if one by one they had all been examined by scientists and checked for discrete infinitude. Yang (2006: 103–104) takes up this theme in a popular book. After a rather confusing equation of recursion with reproduction (‘‘Language . . . has the ability of self-reproduction, or recursion, to use a term from mathematics: a phrase may beget another phrase, then another, then yet another’’), plus an assertion that ‘‘There is no limit on the depth of embedding’’, and an assertion that prepositional phrase modifiers may be added ‘‘. . . ad infinitum’’, he remarks: (3) Recursion pops up all over language: many have argued that the property of recursive infinity is perhaps the defining feature of our gift for language. (A footnote here refers the reader to Hauser et al. (2002), whose claims about recursion as the defining property of human language have been widely repeated; see Pinker and Jackendo¤ (2005) for further discussion.) Remarks such as these represent infinitude as a fact about languages, which contrasts with views that were current fifty years ago. Chomsky (1957b: 15) simply remarks that a grammar projects from a finite corpus to ‘‘a set (presumably infinite) of grammatical utterances’’, the infinite cardinality of the projected set being treated as a side consequence of the way the theory is set up. This is precisely in line with the views of his doctoral supervisor, Zellig Harris, who stated in the same year: Although the sample of the language out of which the grammar is derived is of course finite, the grammar which is made to generate all the sentences of that sample will be found to generate also many other sentences, and unboundedly many sentences of unbounded length. If we were to insist on a finite language, we would have to include in our grammar several highly arbitrary and numerical conditions – saying, for example, that in a given position there are not more than three occurrences of and between N. (Harris 1957: 208)

Harris’s point is that a grammar should not include arbitrary numerical stipulations with no function other than to block coordinations from having unboundedly many coordinates. It is better, he proposes, to accept the consequence that the grammar generates unboundedly many sentences longer than any found in the corpus providing its evidential basis.

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It is of course a familiar feature of science that idealizing assumptions are made, and that the idealized models have characteristics that are strictly false of the phenomena under study. Sometimes, for example, finite systems are modeled as infinite if that simplifies the mathematics. This is clearly what Harris is alluding to. And it is desirable, provided it does not result in distortion of predictions in finite domains, and it does enhance elegance in theories. But contemporary linguists, particularly when writing for broader audiences such as beginning students, scientists in other fields, and the public at large, are treating infinitude as a property of languages themselves. This shift of view appears to stem from a kind of argument for infinitude that begins with observed facts about human language syntax and draws from them a conclusion concerning infinite cardinality. 2. The Standard Argument The argument that linguists have most relied upon for support of the infinitude claim is actually a loose family of very similar arguments that we will group together and call the Standard Argument. Versions of it are rehearsed in, for example, Postal (1964), Bach (1964), Katz (1966), Langacker (1973), Bach (1974), Huddleston (1976), Pinker (1994), Stabler (1999), Lasnik (2000), Carnie (2002), and Hauser et al. (2002). The Standard Argument starts with certain uncontested facts about the syntactic structure of certain classes of expressions. It draws from these the intermediate conclusion that there can be no longest expression. The infinitude claim then follows. For concreteness, here as throughout much of the paper, we limit ourselves to English illustrations of the relevant kinds of syntactic facts. A few representative examples are given in (I). (I)

Syntactic facts I exist is a declarative clause, and so is I know that I exist, and so is I know that I know that I exist; came in and went out is a verb phrase coordination, and so is came in, turned round, and went out, and so is came in, saw us, turned round, and went out; very nice is an adjective phrase, and so is very very nice, and so is very very very nice; and so on for many other examples and types of example.

It is not controversial that a huge collection of facts of this sort, showing grammaticality-preserving extensibility of various types of expression, could

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be presented for many di¤erent languages. References to (I) in what follows are intended to refer to some suitably large collection of such facts. The intermediate conclusion that purportedly follows from facts like those in (I) is presented in (II): (II) The No Maximal Length claim (NML) For any English expression there is another expression that is longer. (Equivalently: No English expression has maximal length.) Some linguists give a stronger claim we can call NML+, which entails (II): They claim not just that for any expression a longer expression always exists, but that starting from any arbitrary grammatical expression you can always construct a longer one that will still be grammatical, simply by adding words. NML+ is never actually crucial to the argument, but we note various appearances of it below. The ultimate conclusion from the argument is then (III): (III) The Infinitude Claim The collection of all grammatical English expressions is an infinite set. Presentations of the Standard Argument utilizing (I)–(III) in various forms can be found in large numbers of introductory texts on linguistics. Langacker (1973), for example, asserts (II) as applied to English, in both its weaker and its stronger form (he seems to o¤er NML+ as an explication of why NML must be true), and concludes (III), with an additional claim appended: (4) There is no sentence to which we can point and say, ‘Aha! This is the longest sentence of the language.’ Given any sentence of English (or any other language), it is easy to find a longer sentence, no matter how long the original is . . . The set of well-formed sentences of English is infinite, and the same is true of every other language. (Langacker 1973: 30) The parenthetical remark ‘‘or any other language’’, claiming a universalization of (III) to all human languages, does not, of course, follow from the premises that he states (compare the similar remark by Epstein and Hornstein in (2)). Bach (1974: 24) states that if we assent to (II) – which he gives as NML+ – then we must accept (III):

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(5) If we admit that, given any English sentence, we can concoct some way to add at least one word to the sentence and come up with a longer English sentence, then we are driven to the conclusion that the set of English sentences is (countably) infinite. (1974: 24) (The parenthesized addition ‘‘countably’’ does not follow from the premises supplied, but we ignore that.) Huddleston (1976) (making reference to unbounded multiple coordination rather than subordination facts) also asserts that if we accept (II) we must accept (III):1 (6) to accept that there are no linguistic limits on the number of clauses that can be coordinated within a sentence is to accept that there are no linguistic limits on the number of di¤erent sentences in the language, ie that there is a (literally) infinite set of well-formed sentences. (Huddleston 1976: 7) Stabler (1999: 321) poses the question ‘‘Is the set of linguistic structures finite? ’’ as one of the issues that arises in connection with applying formal grammars to human languages, and answers it by stating that (II) seems to be true, so we can conclude (III): (7) there seems to be no longest sentence, and consequently no maximally complex linguistic structure, and we can conclude that human languages are infinite. A more recent discussion in Hauser, Chomsky and Fitch (2002: 1571) a‰rms that human languages have ‘‘a potentially infinite array of discrete expressions’’ because of a ‘‘capacity’’ that ‘‘yields discrete infinity (a property that also characterizes the natural numbers).’’ They proceed to the rather surprising claim that ‘‘The core property of discrete infinity is intuitively familiar to every language user’’ (we doubt this), and then state a coordination redundantly consisting of three di¤erent ways of expressing (III):

1. Standard generative grammars cannot account for multiple coordination with unbounded branching degree. They enforce an undesired numerical upper bound on the number of coordinate daughters a node can have. The point is irrelevant to our theme here, so we henceforth ignore it; but see Rogers (1999) for a very interesting non-generative approach.

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(8) There is no longest sentence (any candidate sentence can be trumped by, for example, embedding it in ‘Mary thinks that . . .’), and there is no non-arbitrary upper bound to sentence length. Other passages of a broadly similar character could be cited. We now proceed to critique the argument that they all hint at.

3. How the Standard Argument fails All the linguists quoted in (4)–(8) seem to be concentrating on the step from (II) to (III), which is trivial mathematics. Under the traditional informal definition of ‘infinite’, where it simply means ‘not finite’ (a collection being finite if and only if it we can count its elements and then stop). As Dretske (1965: 100) remarks, to say that if a person continues counting forever he will count to infinity is coherent, but to say that at some point he will have counted to infinity is not. So (II) and (III) are just paraphrases. The claim is that counting the expressions of a language like English could go on forever, which is all that ‘infinite’ means. It is the inference from (I) to (II) that should be critically examined. Linguists never seem to discuss that step. What licenses inferring NML from certain syntactic properties of individual English expressions? 3.1. Not inductive generalization, nor mathematical induction To begin with, we can dismiss any suggestion that the inference from (I) to (II) is an inductive generalization – an ampliative inference from a statement about certain individuals to a statement about all the members of some collection. An example of inductive generalization on English expressions – and a justifiable one – would be to reason from English adjective phrases like very nice, very very nice, very very very nice, and so on, to the generalization that repeatable adverb modifiers in adjective phrases always precede the head. But inferring that the collection of all possible English adjective phrases has no longest member is an entirely di¤erent matter. The conclusion is not about the properties of adjective phrases at all. It concerns a property of a di¤erent kind of object: It attributes a size to the set of all adjective phrases of a certain form, which is very di¤erent from making a generalization about their form. A di¤erent possibility would be that (II) can be concluded from (I) by

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means of some kind of mathematical argument, rather than an inductive generalization from linguistic data. Pinker (1994: 86) explicitly suggests as much: By the same logic that shows that there are an infinite number of integers – if you ever think you have the largest integer, just add 1 to it and you will have another – there must be an infinite number of sentences.

This reference to a ‘‘logic that shows that there are an infinite number of integers’’ is apparently an allusion to reasoning by mathematical induction. Arguments by mathematical induction use recursion to show that some property holds of all of the infinitely many positive integers. There are two components: A base case, in which some initial integer such as 0 or 1 is established as having a certain property P, and an inductive step in which it is established that if any number n has P then n þ 1 must also have P. The conclusion that every positive integer has P then follows. However, it follows only given certain substantive arithmetical assumptions. Specifically, we need two of Peano’s axioms: The one that says every integer has a successor (so there is an integer n þ 1 for every n), and the one that says the successor function is injective (so distinct numbers cannot share a successor).2 Pinker’s suggestion seems to be that a mathematical induction on the set of lengths of English expressions will show that English is an infinite set. This is true, provided we assume that the analogs of the necessary Peano axioms hold on the set of English expressions. That is, we must assume both that every English expression length has a successor, and that no two English expression lengths share a successor. But to assume this is to assume the NML claim (II). (There cannot be a longest expression, because the length of any such expression would have to have a successor that was not the successor of any other expression length, which is impossible.) Thus we get from (I) to (II) only by assuming (II). The argument makes no use of any facts about the structure of English expressions, and simply assumes what it was supposed to show. 2. The Axiom of Mathematical Induction, despite its suggestive name, is not relevant here. It states that if a set contains 1, and contains the successor of every member, then all the positive integers are members. The point is to rule out non-standard models of arithmetic, where there are additional o¤-the-scale integers, unreachable via successor. The two axioms mentioned in the text are su‰cient to guarantee an infinity of integers.

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3.2. Arguing from generative grammars A third alternative for arguing from (I) to (II) probably comes closest to reconstructing what some linguists may have had in mind. If facts like those in (I) inevitably demand representation in terms of generative rule systems with recursion, infinitude might be taken to follow from that. The enormous influence of generative grammatical frameworks over the past fifty years may have led some linguists to think that a generative grammar must be posited to describe data sets like the ones illustrated in (I). If in the face of such sets of facts there was simply no alternative to assuming a generative grammar description with recursion in the rule system, then a linguistically competent human being would have to mentally represent ‘‘a recursive procedure that generates an infinity of expressions’’ (2002: 86–87), and thus (II) would have to be, in a sense, true. There are two flaws in this argument. The less important one is perhaps worth noting in passing nonetheless. It is that assuming a generative framework, even with non-trivially recursive rules, does not entail NML, and thus does not guarantee infinitude. A generative grammar can make recursive use of non-useless symbols and yet not generate an infinite stringset. Consider the following simple context-sensitive grammar (adapted from one suggested by Andra´s Kornai): (9) Nonterminals: Start symbol: Terminals: Rules:

S, NP, VP S They, came, running S ! NP VP VP ! VP VP NP ! They VP ! came / They ___ VP ! running / They came ___

The rule ‘‘VP ! VP VP’’ is non-trivially recursive – it generates the infinite set of all binary VP-labelled trees. No non-terminals are unproductive (incapable of deriving terminal strings) or unreachable (incapable of figuring in a completed derivation from S). And no rules are useless – in fact all rules participate in all derivations that terminate. Yet only two strings are generated: They came, They came running. The structures are shown in (10).

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(10)

No derivation that uses the crucial VP rule more than once can terminate. Thus recursion does not guarantee infinitude. One might dismiss this as an unimportant anomaly, and say that a proper theory of syntactic structure should simply rule out such failures of infinitude by stipulation. But interestingly, for a wide range of generative grammars, including context-sensitive grammars and most varieties of transformational grammar, questions of the type ‘Does grammar G generate an infinite set of strings?’ are undecidable, in the sense that no general algorithm can determine whether the goal of ‘‘a recursive procedure that generates an infinity of expressions’’ has been achieved. One could stipulate in linguistic theory that the permissible grammars are (say) all and only those context-sensitive grammars that generate infinite sets, but the theory would have the strange property that whether a given grammar conformed to it would be a computationally undecidable question.3 One important point brought out by example grammars like (9) is that you can have a syntax that generates an infinitude of structures without thereby having an infinitude of generated expressions. Everything depends on the lexicon. In (9) only the lexical items They, came, and running are allowed, and they are in e¤ect subcategorized to ensure that came has to follow They and running has to follow came. Because of this, almost none of the rich variety of subtrees rooted in VP can contribute to the generation of strings. Similarly, the syntax of a human language could allow clausal complementation, but if the lexicon happened to contain no relevant lexical items (verbs of propositional attitude and the like), this permissiveness would be to no avail. However, there is a much more important flaw in the argument via generative grammars. It stems from the fact that generative grammars 3. For various well-behaved theories of grammar the infinitude question is decidable, however. These include context-free-equivalent theories such as GPSG (Gazdar et al., 1985) and the formalization of ‘minimalist’ grammars developed by Stabler (1997).

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are not the only way of representing data such as that given in (I). There are at least three alternatives – non-generative ways of formulating grammars that are mathematically explicit, in the sense that they distinguish unequivocally between grammatical and ungrammatical expressions, and model all of the structural properties required for well-formedness. First, we could model grammars as transducers, i.e., formal systems that map between one representation and another. It is very common to find theoretical linguists speaking of grammars as mapping between sounds and meanings. They rarely seem to mean it, because they generally endorse some variety of what Seuren (2004) calls random generation grammars, and Seuren is quite right that these cannot be regarded as mapping meaning to sound. For example, as Manaster Ramer (1993) has pointed out, Chomsky’s remark that a human being’s internalized grammar ‘‘assigns a status to every relevant physical event, say, every sound wave’’ (Chomsky 1986: 26) is false of the generative grammars he recognizes in the rest of that work: Grammars of the sort he discusses assign a status only to strings that they generate. They do not take inputs; they merely generate a certain set of abstract objects, and they cannot assign linguistic properties to any object not in that set. However, if grammars were modeled as transducers, grammars could be mappings between representations (e.g., sounds and meanings), without regard to how many expressions there might be. Such grammars would make no commitment regarding either infinitude or finitude. A second possibility is suggested by an idea for formalizing the transformational theory of Zellig Harris. Given what Harris says in his various papers, he might be thought of as tacitly suggesting that grammars could be modeled in terms of category theory. There is a collection of objects (the utterances of the language, idealized in Harris 1968 as strings paired with acceptability scores), whose exact boundaries are not clear and do not really matter (see Harris 1968: 10–12 for a suggestion that the collection of all utterances is ‘‘not well-defined and is not even a proper part of the set of word sequences’’); and there is a set of morphisms defined on it, the transformations, which appear to meet the defining category-theoretic conditions of being associative and composable, and including an identity morphism for each object. In category theory the morphisms defined on a class can be studied without any commitment to the cardinality of the class. A category is characterized by the morphisms in its inventory, not by the objects in the underlying collection. This seems very much in the spirit of Harris’s view of language, at least in Harris 1968, where a transformation is ‘‘a pairing of sets . . . preserving sentencehood’’ (p. 60).

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Perhaps the best-developed kind of grammar that is neutral with respect to infinitude, however, is a third type: The purely constraint-based or model-theoretic approach that has flourished as a growing minority viewpoint in formal syntax over the past thirty years, initially given explicit formulation by Johnson and Postal (1980) but later taken up in various other frameworks – for example, LFG as presented in Kaplan (1995) and as reformalized Blackburn and Gardent (1995); GPSG as reformalized by Rogers (1997); HPSG as discussed in Pollard (1999) and Ginzburg and Sag (2000). The idea of constraints is familiar enough within generative linguistics. The statements of the binding theory in GB Chomsky (1981), for example, entail nothing about expression length or set size. (To say that every anaphor is bound in its governing category is to say something that could be true regardless of how many expressions containing anaphors might exist.) Chomsky (1981) used such constraints only as filters on the output of an underlying generative grammar with an X-bar phrase structure base component and a movement transformation. But in a fully model-theoretic framework, a grammar consists of constraints on syntactic structures and nothing more – there is no generative component at all. Grammars of this sort are entirely independent of the numerosity of expressions (though conditions on the class of intended models can be stipulated at a meta-level). For example, suppose the grammar of English includes statements requiring (i) that adverb modifiers in adjective phrases precede the head adjective; (ii) that an internal complement of know must be a finite clause or NP or PP headed by of or about; (iii) that all contentclause complements follow the lexical heads of their immediately containing phrases; and (iv) that the subject of a clause precedes the predicate. Such conditions can adequately represent facts like those in (I). But they are compatible with any answer to the question of how many repetitions of a modifier an adjective can have, or how deep embedding of content clauses can go, or how many sentences there are. The constraints are satisfied by expressions with the relevant structure whether there are infinitely many of them, or a huge finite number, or only a few. 3.3. Interim summary We have made four points so far. First, the inference from (I) to (II) is not a cogent inductive (ampliative) generalization. Second, it can be represented as a deductive argument (a mathematical induction on the integers) only at the cost of making it completely circular. Third, requiring that

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human languages be modeled by generative grammars with recursive rule systems does not in fact guarantee infinitude. And fourth, it is not necessary to employ generative grammars in order to model the data of (I) – there are at least three other kinds of fully explicit grammars that are independent of how many expressions there are. Of course, linguists certainly have the right to simply assume (III) – or equivalently (II) – as an axiom. But it is quite hard to see why they should want to. This would be an unmotivated axiom with no applications. It neither entails generative grammars with recursion nor is entailed thereby. With no consequences for linguistic structure, and no consequences for human knowledge of linguistic structure, it would appear to be an unnecessary excrescence in syntactic theory (and incidentally, one that is not first-order expressible).

4. The stubborn seductiveness of infinitude If the Standard Argument for infinitude fails so clearly, and the property itself has no discernible applications in linguistics, the question arises of why the conclusion of the argument has been so seductive to so many linguists. We briefly consider four factors that seem to have contributed to linguists’ eagerness to believe in language infinitude despite its singular inertness in actual linguistic practice. 4.1. The notion that languages are collections There can be no doubt that one factor tempting linguists to accept infinitude is the ubiquitous presupposition that a language is appropriately given a theoretical reconstruction as a collection of expressions. This is not an ordinary common-sense idea: Speakers never seem to think of their language as the collection of all those word sequences that are grammatically well-formed. The idea of taking a language as a set of properly structured formulae stems from mathematical logic. Its appearance in generative grammar and theoretical computer science comes from that source. It is alien to the other disciplines that study language (anthropology, philology, sociolinguistics, and so on).4 4. The notorious assertions that begin Montague (1970a) and Montague (1970b), to the e¤ect that there are ‘‘no important theoretical di¤erence between natural languages and the artificial languages of logicians’’, were shockingly at

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The source of the idea that a language is a collection of word sequences lies in early generative grammar, with its emphasis on processes of derivation and its origins in the theory of recursively enumerable sets of symbol sequences. It placed an indelible stamp on the way linguists think about languages. It has even survived direct rejection by Chomsky (1986: 20¤ ), where the term ‘E-language’ is introduced to cover any and all views about language that are ‘‘external’’ to the mind – not concerned with ‘Ilanguage’ (languages construed as ‘‘internal’’, ‘‘individual’’, and ‘‘intensional’’). ‘E-language’ covers all sorts of traditional views such as that a language is a socially shared system of conventions, but also the mathematical conception of a language as an infinite set of finite strings. Chomsky’s dismissal of the notion of infinite sets of sentences as irrelevant to modern linguistics leaves no place at all for claims about the infinitude of languages. Chomsky dismisses the study of sets of expressions (e.g., weak generative capacity studies) for ‘‘its apparent uselessness for the theory of language.’’ But questions of cardinality only sensibly apply to the conception of language that Chomsky rejects as useless. It is hard to see any application for mathematical results on infinite sets in the study of a biological object like a brain component. Linguists and philosophers who follow Chomsky’s terminology assert that they study ‘I-language’ rather than ‘E-language’. But the view of languages as collections has persisted anyway, even among those who purport to believe it atavistic. If a language is a set of expressions, it has to be either finite or infinite; and if taking it to be finite is out of the question, then (if it is finitely describable at all) it can only be a computably enumerable infinite set. But these are conditional claims. The infinitude claim depends crucially on a prior decision to stipulate that a language has to be a set. Chomsky comes quite close to expressing the alternative view that we urge when he includes ‘‘intensional’’ in his characterization of ‘I-language’. The goal of a grammar is not to reconstruct a language extensionally, as a collection containing all and only the well-formed expressions that happen to exist; rather, a grammar is about structure, and linguistic structure should be described intensionally, in terms of constraints representing the form that expressions share. That does not require that we regard any variance with the views of most linguists in 1970. And Montague does not appear to regard the mere availability of infinitely many expressions as significant fact about natural languages anyway: that is not what he was intending to emphasize.

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particular set, finite or infinite, as the one true set that corresponds to a particular grammar or stands as the unique theoretical representation of a particular human language. Linguists’ continued attraction toward the idea that languages are infinite is thus at least in part an unjustified hangover from the extensional view adopted by mathematical logicians in the work that laid the mathematical foundations of generative grammar (on which see Scholz and Pullum 2007). 4.2. The phenomenon of linguistic creativity A second factor that encourages linguists to believe that human languages are infinite sets stems from a presumed connection between linguistic creativity and the infinite cardinality of languages. Note, for example, this statement by Chomsky (1980: 221–222): . . . the rules of the grammar must iterate in some manner to generate an infinite number of sentences, each with its specific sound, structure, and meaning. We make use of this ‘‘recursive’’ property of grammar constantly in everyday life. We construct new sentences freely and use them on appropriate occasions . . .

He is suggesting that because we construct new sentences, we must be using recursion, so the grammar must generate infinitely many sentences. Note also the remark of Lasnik (2000: 3) that ‘‘The ability to produce and understand new sentences is intuitively related to the notion of infinity.’’ No one will deny that human beings have a marvelous, highly flexible array of linguistic abilities. These abilities are not just a matter of being able to respond verbally to novel circumstances, but of being capable of expressing novel propositions, and of re-expressing familiar propositions in new ways. But infinitude of the set of all grammatical expressions is neither necessary nor su‰cient to describe or explain linguistic creativity. To see that infinitude is not necessary (and here we are endorsing a point made rather di¤erently in the philosophical literature by Gareth Evans 1981), it is enough to notice that creating a verse in the very tightly limited Japanese haiku form (which can be done in any language) involves creation within a strictly finite domain, but is highly creative nonetheless, seemingly (but not actually) to an unbounded degree. Over a fixed vocabulary, there are only finitely many haiku verses. Obviously, the precise cardinality does not matter: The range is vast. A haiku in Japanese is composed of 17 phonological units called morae, and Japanese has roughly

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100 morae (Bill Poser, personal communication), so any haiku that is composed is being picked from a set of phonologically possible ones that is vastly smaller than 10017 ¼ 1034 (given that phonotactic, morphological, lexical, syntactic, semantic, pragmatic, and esthetic considerations will rule out most of the pronounceable mora sequences). This set is large enough that competitions for haiku composition could proceed continuously throughout the entire future history of the human race, and much longer, without a single repetition coming up accidentally. That is part of what is crucial for making haiku construction creative, and gives the poet the experience of creativity. The range of allowable possibilities (under the constraints on form) should be vast; but it does not need to be infinite. Indeed, language infinitude is not only unnecesary but is also insu‰cient for linguistic creativity. For mere iterable extension of expression length hardly seems to deserve to be called creative. Take the only recursive phrase structure rule in Syntactic Structures (Chomsky 1957b, where embedding of subordinate clauses was accomplished di¤erently, by generalized transformations), quoted above: The rule ‘‘Adj ! very Adj’’. If that rule is included in a generative grammar that generates at least one string where some lexical item appears as an expansion of Adj, then the set of generated strings is infinite. Over the four-word vocabulary {John, is, nice, very}, for example, we get an infinite number of sentences like John is very, very, very, very, . . . , very nice. Infinitude, yes, under the generative idealization. But creativity? Surely not. Repetitiveness of this sort is widely found in aspects of nature where we would not dream of attributing creativity: A dog barking repeatedly into the night; a male cricket in late summer desperately repeating its stridulational mating call over and over again; even a trickle of water oozing through a cave roof and dripping o¤ a stalactite has the same character. All of them could be described by means of formal systems involving recursion, but they provide no insight into or explication of the kind of phenomena in which human linguistic creativity is manifested. 4.3. The critique of associationist psychology We conjecture that a third factor may have had some influence on linguists’ enthusiasm for infinitude. A prominent feature of the interdisciplinary literature that arose out of the early generative grammar community was a broad attack on such movements as associationism and Skinnerian behaviorism in 20th-century psychology. A key charge against such views

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was that they could never account for human linguistic abilities because they conceived of them in terms of finite behavioral repertoires and could never explain how humans could learn, use, or understand an infinite language. Asserting the infinitude claim might thus have had a rhetorical purpose in the 1950s. The point would have been to stress that the dominant frameworks for psychological research at that time stood no chance of being able to model human linguistic capacities. We say only that we ‘‘surmise’’ that such a rhetorical strategy ‘‘may have had some influence’’, because in fact instances of the strategy being explicitly pursued are thin on the ground. Chomsky (1957b: 26–27n) does point out that the examples of axiomatic grammars provided by Harwood (1955) ‘‘could not generate an infinite language with a finite grammar’’, but not in connection with any psychological point. In his critique (Chomsky, 1957a) of the psycholinguistic proposals of Hockett (1955), who gave (pp. 7–8) an illustrative stochastic generative grammar of ‘select one word from each column’ form, inherently limited to a finite number of outputs, Chomsky does not mention infinitude, but concentrates on the stochastic aspects of the proposal. And he ignores infinitude when citing the remarks of Lashley (1951) about how ‘‘any theory of grammatical structure which ascribes it to direct associative linkage of the words of the sentence, overlooks the essential structure of speech’’ (Chomsky 1958: 433). It is just as well that infinitude was rarely used as a stick with which to beat associationism, because such a strategy would be entirely misguided. To see why, note that associationist psychology can be mathematically modeled by grammars generating sets of strings of behavioral units (represented by symbols), and the relevant grammars are the ones known as strictly local (SL) grammars (see Rogers and Pullum 2007, and Rogers and Hauser, this volume, for a review of the mathematics). SL grammars are nothing more than finite sets of n-tuples of (crucially) terminal symbols. If n ¼ 2 a grammar is a set of bigrams, as used in various contemporary connectionist systems and speech recognition programs, and we get the SL2 languages. The ‘Wickelphones’ of Rumelhart and McClelland 1986 are trigrams, and characterize the SL3 languages. The SL class is the union of the SLn sets of grammars for all n b 2. Bever, Fodor and Garrett (1968: 563) claim to provide a formal refutation of associationist psychology by pointing out (correctly) that SL grammars are not adequate for the description of certain syntactic phenomena in English. They stress the issue of whether non-terminal symbols are allowed in grammars, and remark that associationism is limited to ‘‘rules defined over the ‘terminal’ vocabulary of a theory, i.e., over the vocabu-

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lary in which behavior is described’’, each rule specifying ‘‘an n-tuple of elements between which an association can hold’’, given in a vocabulary involving ‘‘description of the actual behavior’’. SL grammars have precisely this property of stating the whole of the grammar in the terminal vocabulary. They cite a remark by Lashley (1951) which in e¤ect observes that SL2 cannot even provide a basis for modeling the behavior seen in typing errors like typing ‘Lalshey’ for ‘Lashley’. However, no matter what defects SL grammars might have, an inability to represent infinite languages is not one of them. Bever et al. tacitly acknowledge this, since they nowhere mention infinitude as a problem. We make this point because Lasnik (2000: 12) claims that the finitestate conception of grammar ‘‘is the simplest one that can capture infinity’’, and this is a mistake. The infinite set we just alluded to above, containing all strings of the form ‘John is (very)* nice’, is easy to represent with an SL2 grammar. (Using ‘z’ to mark a left sentence boundary and ‘y’ to mark a right boundary, the bigrams needed are: ‘z John’, ‘John is’, ‘is nice’, ‘is very’, ‘very very’, ‘very nice’, and ‘nice y’.) Insofar as associationist psychology and connectionist models of cognition are theoretically reconstructible as (possibly stochasticized) varieties of SL2 grammars (or SLk grammars, for any fixed k), they are entirely untouched by the infinitude claim. The putative infinitude of languages has no more consequences for these research programs than it does for other theories of grammar, or for linguistic creativity. It should be kept in mind, in any case, that if creative sentence production is the topic of interest, the use of subordination considered to be typical (and educationally prized) in educated written Standard English is actually quite rare in real-life colloquial language use. Pawley and Syder (2000) argues that clausal subordination hardly occurs at all in spontaneous English speech. Quite a bit of what might be taken for on-the-fly hypotaxis is in fact fill-in-the-blanks use of semi-customizable schemata containing subordination (It depends what you mean by ___ ; I can’t believe ___ ; etc.). Active spontaneous management of clause subordination in colloquial speech may be rather rare in any language. It should not be too surprising if in some preliterate cultures the resources for it are entirely absent from the grammatical system. 5. Finite human languages? The quotations from Langacker (1973) and Epstein and Hornstein (2004) in (4) and (2) baldly assert that infinitude holds for every human language.

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And Lasnik (2000), Hauser et al. (2002), and Yang (2006) hold that infinitude, which they take to be a direct consequence of recursion in grammars, is a central and fundamental aspect of human language. We have argued that such claims are not well supported, either directly or indirectly. As a side consequence of the stress on language infinitude and recursion, a controversy has recently emerged about the Amazonian language Piraha˜, stimulated primarily by the assertion in Everett (2005) concerning its lack of both recursive hypotaxis and syndetic coordination. But Everett’s claims should not surprise anyone who has a thorough acquaintance with syntactic typology. Similar properties have been attributed to many other languages, in diverse families. Collinder (1960: 250–251, in a chapter contributed by Paavo Ravila) states the following about Proto-Uralic (PU) and many of its modern descendants: In PU there was no hypotaxis in the strict sense of the word. The sentences were connected paratactically, and in the absence of conjunctions, the content determined the mutual relations of the sentences. In PU, as in the Uralic languages spoken today, the subordinate clauses of the IndoEuropean languages had as counterparts various constructions with verb nouns . . .

But this di¤ers very little from what has often been said about Australian Aboriginal languages. They show remarkably little evidence of subordination, with hardly any real indication of recursion, no finite clause complements at all, and no syndetic clause coordination. One should not be misled by the fact that structural representations showing clauses embedded within clauses in Dyirbal appear in Dixon (1972: 147–220). These are purely theoretical posits, suggested by the kinds of derivations that were assumed for English sentences at the time he was writing. Full clausal hypotaxis is never encountered in the derived structures, and the examples given seem highly paratactic, with English glosses like ‘‘Man told woman: Light fire: Find girls’’ (1972: 165). Moreover, Dyirbal has no syndetic coordination: there are no equivalents of words like and, or, and but. Things are similar with Wargamay: although Dixon (1981: 70) has a section headed ‘complement clauses’, the examples given are not complements at all; all are clearly non-finite adjunct phrases of result or purpose. There are no finite subordinate clauses, and Dixon o¤ers no indications of any kind of recursion.

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Derbyshire (1979) describes the Amazonian language Hixkarya´na (in the Cariban family, unrelated to Piraha˜), and similar syntactic characteristics emerge. Hixkarya´na has no finite complement clauses, hence no indirect speech constructions or verbs of propositional attitude. According to Derbyshire, ‘‘Subordination is restricted to nonfinite verbal forms, specifically derived nominals’’ or ‘‘pseudo-nominals that function as adverbials’’, and ‘‘There is no special form for indirect statements such as ‘he said that he is going’. . .’’ (p. 21). (There is a verb meaning ‘say’ that allows for directly quoted speech, but that does not involve subordination.) Hixkarya´na has nominalization (of an apparently non-recursive kind), but no clausal subordination. Derbyshire also notes (1979: 45) the absence of any ‘‘formal means . . . for expressing coordination at either the sentence or the phrase level, i.e. no simple equivalents of ‘and’, ‘but’ and ‘or’.’’ Givon (1979: 298) discusses the topic in general terms and relates it to language evolution, both diachronic and phylogenetic. He claims that ‘‘diachronically, in extant human language, subordination always develops out of earlier loose coordination’’, the evidence suggesting that it ‘‘must have also been a phylogenetic process, correlated with the increase in both cognitive capacity and sociocultural complexity’’, and he observes: there are some languages extant to this day – all in preindustrial, illiterate societies with relatively small, homogeneous social units – where one could demonstrate that subordination does not really exist, and that the complexity of discourse – narrative is still achieved via ‘‘chaining’’ or coordination, albeit with an evolved discourse-function morphology . . .

Other works, more recent but still antedating Everett, could be cited. For example, Deutscher (2000, summarized in Sampson 2009) claims that when Akkadian was first written it did not have finite complement clauses, though later in its history it developed them. We are not attempting an exhaustive survey of such references in the literature. We merely note that various works have noted the absence of iterable embedding in various human languages, and for some of those it has also been claimed that they lack syndetic sentence coordination (that is, they do not have sentence coordination that is explicitly marked with a coordinator word, as opposed to mere juxtaposition of sentences in discourse). Languages with neither iterable embedding nor unbounded coordination would in principle have just a finite (though very large) number of distinct expressions, for any given finite fixing of the lexicon – (though

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saying that there are only finitely many sentence presupposes that we have some way of distinguishing sentences from sentence sequences; this is by no means a trivial codicil, but let us assume it). The suggestion that there might be finite human languages, then, did not suddenly emerge with Everett’s work in 2005. It is implicit in plenty of earlier linguistic literature. No one should think that finiteness in this sense would imply some sort of inferiority for the speakers of the language, or their linguistic or cognitive abilities, or their linguistic creativity. As we argued earlier, there is no necessary link between infinitude and linguistic creativity, since for creativity the number of possible expressions needs only to be very large – it does not need to be infinite. Nor should anyone think that finiteness of the set of sentences would imperil either the claimed semantic universal that all human languages have what Katz (1978) called ‘e¤ability’ (the property of having resources for expression of all propositions) or the closely related claim of universal intertranslatability (that any proposition expressible in one language is also expressible in all others). These universal claims may be false – we take no stand either way on that – but they would not be falsified by the mere existence of some human language with only finitely many sentences. A language that can express multiple thoughts in a single sentence is not thereby required to do so. Complex sentences involving can be reexpressed in sequences of syntactically simpler sentences. For example, I think you realize that we’re lost and we should ask the way contains a coordination of finite clauses serving as a complement within a clausal complement, but it could be re-expressed paratactically (Here are my thoughts. You realize our situation. We’re lost. We should ask the way). Such re-expression transfers the (semantic) complexity of the content of the di¤erent clauses from the sentence level to the paragraph level. Absence of syntactic embedding and coordination resources in a language that calls for certain content to be expressed multisententially rather than unisententially is not the same as rendering a thought inexpressible or untranslatable. Just as absence of syntactic support for infinitude claims about some language does not imply anything demeaning about its speakers, neither does it threaten the research program of transformational-generative grammar. Generative linguistics does not stand or fall with the infinitude claim. Overstatements like those in (1) or (2) can be dismissed without impugning any research progam. We argued at the end of § 3.2 above that generative rule systems with recursion do not have to be used to represent

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the syntax of languages with iterable subordination; but that does not mean it is an error to use generative rule systems for describing human languages or stating universal principles of linguistic structure. Whether it is an error or not depends on such things as the goals of a linguistic framework, and the data to which its theorizing aims to be responsive (Pullum and Scholz 2001, 2005).

6. Concluding remarks Infinitude of human languages has not been independently established – and could not be. It does not represent a factual claim that can be used to support the idea that the properties of human language must be explicated via generative grammars involving recursion. Positing a generative grammar does not entail infinitude for the generated language anyway, even if there is recursion present in the rule system. The remark of Lasnik (2000: 3), that ‘‘We need to find a way of representing structure that allows for infinity’’, therefore has it backwards. It is not that languages have been found to be infinite so our theories have to represent them as such. Language infinitude is not a reason for adopting a generative grammatical framework, but merely a theoretical consequence that will (under some conditions) emerge from adopting such a framework. What remains true, by contrast, is Harris’s claim (1957: 208) ‘‘If we were to insist on a finite language, we would have to include in our grammar several highly arbitrary and numerical conditions.’’ No such arbitrary conditions should be added to grammars, of course. Ideally grammars should be stated in a way that insists neither on finitude nor on infinitude. It is a virtue of model-theoretic syntactic frameworks that they allow for this.

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Katz, Jerrold J. 1966 The Philosophy of Language. New York: Harper and Row. Katz, Jerrold J. 1978 E¤ability and translation. In F. Guenthner and M. GuenthnerReutter, eds., Meaning and Translation: Philosophical and Linguistic Approaches, 191–234. London: Duckworth. Langacker, Ronald W. 1973 Language and Its Structure. New York: Harcourt Brace Jovanovich, second ed. Lashley, Karl 1951 The problem of serial order in behavior. In L. A. Je¤ress, ed., Cerebral Mechanisms in Behavior, 112–136. New York: Wiley. Lasnik, Howard 2000 Syntactic Structures Revisited: Contemporary Lectures on Classic Transformational Theory. Cambridge, MA: MIT Press. Manaster Ramer, Alexis 1993 Towards transductive linguistics. In Karen Jensen, George E. Heidorn, and S. D. Richardson, eds., Natural Language Processing: The PLNLP Approach, 13–27. Dordrecht: Kluwer Academic. Montague, Richard 1970a English as a formal language. In Bruno Visentini, ed., Linguaggi nella Societa` e nella Tecnica, 189–224. Milan: Edizioni di Comunita`. Reprinted in Thomason (ed.) 1974. Montague, Richard 1970b Universal grammar. Theoria 36: 373–398. Reprinted in Thomason (ed.) 1974. Pawley, Andrew and Frances Syder 2000 The one clause at a time hypothesis. In Heidi Riggenbach, ed., Perspectives on Fluency, 163–191. Ann Arbor: University of Michigan Press. Pinker, Steven 1994 The Language Instinct. New York: William Morrow. Pinker, Steven and Ray S. Jackendo¤ 2005 What’s special about the human language faculty? Cognition 95 (2): 201–236. Pollard, Carl 1999 Strong generative capacity in HPSG. In Gert Webelhuth, JeanPierre Koenig, and Andreas Kathol, eds., Lexical and Constructional Aspects of Linguistic Explanation, 281–297. Stanford: CSLI Publications. Postal, Paul M. 1964 Underlying and superficial linguistic structure. Harvard Educational Review 34: 246–266. Pullum, Geo¤rey K. and Barbara C. Scholz 2001 On the distinction between model-theoretic and generative-enu-

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merative syntactic frameworks. In Philippe de Groote, Glyn Morrill, and Christian Retore´, eds., Logical Aspects of Computational Linguistics: 4th International Conference, number 2099 in Lecture Notes in Artificial Intelligence, 17–43. Berlin: Springer Verlag. Pullum, Geo¤rey K. and Barbara C. Scholz 2005 Contrasting applications of logic in natural language syntactic description. In Petr Hajek, Luis Valdes-Villanueva, and Dag Westerstahl, eds., Proceedings of the 13th International Congress of Logic, Methodology and Philosophy of Science. London: KCL Publications. Rogers, James 1997 ‘‘Grammarless’’ phrase structure grammar. Linguistics and Philosophy 20: 721–746. Rogers, James 1999 The descriptive complexity of generalized local sets. In HansPeter Kolb and Uwe Mo¨nnich, eds., The Mathematics of Syntactic Structure: Trees and their Logics, number 44 in Studies in Generative Grammar, 21–40. Berlin: Mouton de Gruyter. Rogers, James and Geo¤rey K. Pullum 2007 Aural pattern recognition experiments and the subregular hierarchy. To appear in UCLA Working Papers in Linguistics. Rumelhart, David and J. L. McClelland 1986 On learning the past tenses of English verbs. In J. L. McClelland and D. E. Rumelhart, eds., Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Volume 2: Psychological and biological models, 216–271. Cambridge, MA: MIT Press. Sampson, Geo¤rey 2009 A linguistic axiom challenged. In Language Complexity as an Evolving Variable. Oxford: Oxford University Press. Scholz, Barbara C. and Geo¤rey K. Pullum 2007 Tracking the origins of transformational generative grammar. Journal of Linguistics 43: 701–723. Seuren, Pieter A. M. 2004 Chomsky’s Minimalism. Oxford: Oxford University Press. Stabler, Edward 1997 Derivational minimalism. In Christian Retore´, ed., Logical Aspects of Computational Linguistics, LACL ’96, number 1328 in Lecture Notes in Artificial Intelligence, 68–95. Berlin: Springer Verlag. Stabler, Edward 1999 Formal grammars. In Robert A. Wilson and Frank C. Keil, eds., The MIT Encyclopedia of the Cognitive Sciences, 320–322. Cambridge, MA: MIT Press. Yang, Charles 2006 The Infinite Gift. New York: Scribner.

7.

Just how big are natural languages?

D. Terence Langendoen

1. The question of natural language infinity The assumption that natural languages are comprised of an infinite set of expressions is widely held, and viewed as a characteristic that must be accounted for by any theory of natural language.1 Pullum & Scholz (2005, 2009) have recently argued, however, that no adequate demonstration for natural language infinity (NLI) has ever been made and that the cardinality of the set of all the expressions in a language is not important for the formulation of grammars for natural languages (2005: 497). In this section, I examine their argument against the claims for NLI and conclude that they are correct in asserting that the question of NLI remains open, though perhaps not exactly for the reasons they provide. However I do not agree with them about the lack of importance of the question of NLI, and in the remainder of the paper attempt to show how it might be answered. Pullum & Scholz (2005: 495) threw down the gauntlet when they asserted that ‘‘[c]ontrary to popular belief, it has never been shown that natural languages have infinitely many expressions’’. They contend that what they call the Master Argument for language infinity is the basis for all the putative demonstrations of NLI, and that it fails because it is either unsound or begs the question. They also note that their point is not new, but a paraphrase of an argument that Paul Postal and I published some 25 years ago (Langendoen & Postal 1984: 30–35). Since Paul and I went on to make an even stronger claim about how many expressions a natural language has, namely that it has transfinitely (i.e. more than denumerably infinitely) many, I find myself in the somewhat odd position of having

1. I thank three anonymous reviewers, who convinced me that the original version of this paper needed a major overhaul. This material is based in part upon work that was supported while I was serving at the National Science Foundation. Any opinion and conclusions are those of the author and do not necessarily reflect the views of the National Science Foundation.

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argued that NLI is correct, but also of having helped formulate an argument that purports to deny that anyone has ever shown that it is correct. Pullum & Scholz (2009) elaborate on this point by showing that NLI cannot be established by any of a variety of arguments for infinite size, such as inductive generalization or mathematical induction. Similarly, it cannot be established by a reductio ad absurdum of the form (1)–(3): (1) Assume that natural languages have at most finitely many finitely large expressions; (2) Show that the assumption together with other known properties of natural languages leads to a contradiction, namely that all expressions have an upper bound on size, but that there is at least one larger one; and (3) Conclude that natural languages must have infinitely many expressions. The success of the reductio argument depends on identifying the correct known properties. As Pullum & Scholz (2005, 2009) point out, the known property that is typically appealed to in arguments for NLI is the existence of operations that iteratively increase the size of expressions and that in doing so preserve well-formedness. Certainly, as they also point out, if a language is closed under one or more of those operations, so that they are genuinely recursive, not just iterative, it is infinite. However from the fact that one’s grammatical model is closed under such an operation, it does not follow that the language it models is. Without a demonstration of closure under a particular operation for the language itself, the issue of the correctness of NLI remains open. In formulating our argument for NLI, Postal and I asserted that English and other natural languages are closed under two iterative size-increasing operations; however, whether we were successful in demonstrating it is also open to question. I return to that issue in Section 3. In the next section, I consider a way of determining whether a natural language is infinite and conclude that it is possible for some natural languages to be infinite while others aren’t.

2. Determining the size of natural languages Determining the size of a natural language requires projecting beyond what is known about it from the direct evidence we have at hand. Our direct evidence comes in the form of judgments about particular expressions: whether they are grammatical in that language, whether they have

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such-and-such conditions of use in that language, etc. For any natural language L, let Lj represent the finite set of expressions known to belong to L on the basis of such direct evidence. Given that Lj provides indirect evidence for genuinely recursive size-increasing operations, standard generative models project a denumerably (countably) infinite set Ly of ‘possible’ members of L. By not distinguishing the models from the language, proponents of such models conclude that L ¼ Ly and so is infinite. As noted above, that conclusion may be correct, but an argument is still needed to show that the models do not overgenerate. In the absence of such an argument, all we can conclude is that L lies somewhere between Lj and Ly, and so may be either finite or infinite. The question we now face is this: Q1. How far can we project membership in L beyond Lj with a reasonable degree of certainty? One promising approach is to attempt to identify on the basis of Lj those expressions L⌂ that are needed by speakers of L, since it is reasonable to assume that L contains every expression that its speakers will ever have occasion to need. Taking this approach, we then ask: Q2. What do people need from the languages they speak? It is clear that a large finite set of expressions will su‰ce to satisfy the expressive needs of anyone with finite temporal and physical resources, i.e. everyone. However it is appropriate to abstract away from those resource limitations to ask what people might need if those limitations were removed. The simplest and most striking answer to this question was given by Sapir (1949 [1924]: 153), who contended that every natural language has the property of ‘‘formal completeness’’, thereby providing ‘‘a complete system of reference’’ for human experience, on analogy with numerical and geometric systems of reference for quantity and space, so that for any of its speakers, ‘‘no matter how original or bizarre his idea or fancy, the language is prepared to do his work’’.2

2. Von Fintel & Matthewson (2008: 142–146) consider Sapir ‘formal completeness’ thesis to be a forerunner of Katz’s (1976) ‘e¤ability’ thesis for natural languages – that every language is capable of expressing every meaning. If they are right about this, it would not be inappropriate to refer to the e¤ability thesis as the ‘Sapir-Katz hypothesis’. However Sapir’s thesis explicitly relates a language’s expressive power to speaker’s need in a way that Katz’s does not. On the other hand, Katz considers e¤ability the defining characteristic of natural languages, whereas Sapir simply considers formal completeness ‘‘[t]he outstanding fact’’ about them.

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Although Sapir’s answer is a simple one, it is not immediately clear how to apply it to the problem under consideration, except perhaps by exploiting his mathematical analogy, which he says ‘‘is by no means as fanciful as it appears to be’’. Since the analogous systems are all complete in the sense that they are closed under the relevant operators, e.g. addition for arithmetic, it seems reasonable to construe formal completeness to mean that linguistic systems are comparably closed under the relevant operators.3 If we accept Sapir’s formal completeness hypothesis as just interpreted as the basis for identifying membership in L⌂, our question next becomes: Q3. What is the size of the set of expressions that is closed under the relevant operators? Having noted above that closure under iteratively size-increasing operations results in an infinite set, it would appear that the answer is just that. For example, from the occurrence of tautocategorial embedding – Pullum & Scholz’s (2005) example of an iterative size-increasing operation that preserves well-formedness in English – in members of Lj together with the judgment that the operation is needed for L to do the expressive work for its speakers, L⌂ is closed under that operation, and is thereby infinite. However I also interpret Sapir’s hypothesis as consistent with the view, argued for by Everett (2005), that the expressive needs of one linguistic community can di¤er from that of another, since the languages that meet those di¤erent needs can nevertheless all be formally complete. If for example the community speaking language P does not need the ability to refer to distant ancestors, whereas the one speaking language Q does, P ⌂ may still be formally complete in Sapir’s sense, being analogous, say, to an arithmetic system over the set of positive integers, with Q ⌂ analogous to one over the full set of integers. One can even imagine the community speaking P to have such limited expressive needs that P⌂, though formally complete, is finite, analogous to an arithmetic system over the set of positive integers modulo some large, but finite number. For example, imagine that speakers of P need no more expressive resources than a (possibly large, but finite) set of k simple a‰rmative sentences and the operations of negation, conjunction and disjunction defined 3. Starting from the assumption of NLI, Hauser, Chomsky & Fitch (2002: 1571) consider natural language to be ‘‘directly analogous to the natural numbers’’ but nothing like formal completeness or closure figures in their account of human linguistic capacity.

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over them. Then the smallest language P ⌂ that is closed under these operk ations is much larger, but still finite, having 22 members, in which there is exactly one expression for each logically distinct member of P ⌂. Of course P may be larger, allowing for paraphrase, but the method proposed here for determining whether P is infinite would not lead to a definite conclusion one way or the other.

3. Can natural languages be bigger than denumerably infinite? The starting point for Postal’s and my argument for NLI is not much different from the hypothetical example in the previous paragraph. Instead of a finite set of simple a‰rmative sentences as the base of operations for P, it proposes an infinite set P0 based on closure over a single iterative tautocategorial embedding operation. Granted that this starting point begs the question of establishing NLI, we had a di¤erent concern, namely to show that natural languages are not merely denumerably infinite but transfinite in size. The only operation we considered over this base was conjunction, and we asserted that P is closed under that operation, by which we meant the condition in (4) (an update of the starting point for our Closure Principle for Coordinate Compounding), in which the absence of a final member of the list of expressions in the antecedent is critical; it indicates that there is no finite bound on the number of conjuncts in members of P. From (4) it follows that P has nondenumerably many expressions. (4) If p1, p2, . . . are in P0, then their conjunction is in P. Our argument for (4) was based not on consideration of expressive need, but rather on economy of description: The simplest empirically adequate grammatical account of conjunction does not limit the number of unconjoined expressions that can be conjoined, so (4) is to be preferred to any account that does limit it, for example to a finite number of conjuncts.4 Moreover, if we think of conjunction in P as logical rather than grammatical, then (4) can be recast as a valid entailment schema as in (5), where p1, p2, . . . is a possibly infinite sequent. 4. Conjoined expressions can also be members of a conjunction, but not recursively so (Langendoen 1998), so for convenience they are left out of the formulation in (4). If the antecedent list in (4) is construed as the members of a set, it also does not provide for conjuncts to be repeated.

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(5) p1, p2, . . . p1 & p2 . . . However despite its elegance, our argument has not convinced many linguists of its correctness, even among those who uncritically accept NLI.5 There are, I believe, two reasons for this. One is the entrenched dogma, as Pullum & Scholz (2005) put it, that every expression in a natural language is a finitely-sized object; see also Dale (1996) and Hintzen & Uriagereka (2006). The other is that no convincing need has been identified for infinitely-sized expressions. Pullum & Scholz (2005: 497) make the best case that I am aware of for the usefulness of infinitely-sized expressions, namely for characterizing the notion of mutual belief, citing the work of Schi¤er (1972) and Joshi (1982).6 Postal and I did not stop at (4) in our formulation of the principle of closure under conjunction, but went on to propose that for every nonempty, nonsingleton set of expressions of a natural language, it contains a conjunctive expression having every member of that set as a conjunct, from which it follows that natural languages are proper classes, making them too large to be considered sets. However in the absence of a need for expressions of a size greater than that of the denumerably-infinitelylong conjunctions characterized by (4), I conclude that they are not part of L⌂ for any natural language L.7

4. Conclusion Determining the size of a natural language is not as easy as simply declaring that there is no longest expression in any language and saying as a 5. Though it has found some resonance in computer science; see for example Zeitman (1993). 6. Uriagereka (2005) considers, but does not formalize, the possibility that the attachment of disjuncts, the class of adjuncts that do not scope over one another, gives rise to infinitely-sized expressions, and perhaps more interestingly, to infinitely large forms of interpretation expressible with finite phonologies. Even if all that is correct, it still remains to be seen whether a need for them can be identified. 7. Pullum & Scholz (2005: 498, n. 15) give as a reason for not characterizing natural languages as proper classes the fact that the closure principle that leads to that result is unstatable as a Model-Theoretic Syntax constraint. If I read them correctly, the weaker closure principle in (4) is also unstatable, but there is another way in that framework for admitting denumerably infinitelysized expressions.

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result ‘‘Clearly it’s denumerably infinite’’, and we may be grateful to Pullum & Scholz (2005, 2009) for pointing that out. The greatest di‰culty is in finding and agreeing upon a basis for determining whether a language is closed under one or more of its iterative size-increasing operations, and if so how. If the basis for doing so is whether the results of the operations are needed by the community of speakers of that language, as I have suggested, following Sapir, there is still room for dispute about which operations should be counted, and about what conclusion to draw if it should turn out that there are no such operations in a particular language. The question of whether the sets of expressions of particular natural languages are finite, denumerably infinite or nondenumerably infinite (of the cardinality of the real numbers) remains open. Furthermore, given that the question of the size of natural languages remains a matter of dispute, we need to look more deeply at the relation between natural languages and mathematical systems than simply the parallel between the enumeration of their members (expressions on the one hand and integers on the other, for example), as Sapir did when he developed the notion that natural languages are formally complete.

References Dale, Russell Eliot 1996 The theory of meaning. Ph. D. diss., Philosophy Program, Graduate Center of the City University of New York. https:// webspace.utexas.edu/deverj/personal/test/theoryofmeaning.pdf (accessed 2007-04-01). Everett, Daniel L. 2005 Culture constraints on grammar and cognition in Piraha˜: Another look at design features of human language. Current Anthropology 46: 621–646. Hauser, Marc, Noam Chomsky, and W. Tecumseh Fitch 2002 The faculty of language: What is it, who has it, and how did it evolve? Science 298: 1569–1579. Hintzen, Wolfram, and Juan Uriagereka 2006 On the metaphysics of linguistics. Erkenntnis 65: 71–96. Joshi, Aravind 1982 Mutual beliefs in question-answer systems. In: Neil Smith (ed.), Mutual Knowledge, 181–197. London: Academic Press. Katz, Jerrold 1976 A hypothesis about the uniqueness of natural languages. In: Steven Harnad, Horst Steklis, and Jane Lancaster (eds.), Origins

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and Evolution of Language and Speech ¼ Annals of the New York Academy of Sciences 280: 33–41. Langendoen, D. Terence 1998 Limitations on embedding in coordinate structures. Journal of Psycholinguistic Research 27: 235–259. Langendoen, D. Terence, and Paul Postal 1984 The Vastness of Natural Languages. Oxford: Blackwell. Pullum, Geo¤rey, and Barbara Scholz 2005 Contrasting applications of logic in natural language syntactic description. In: Petr Ha´jek, Luis Valde´s-Villanueva, and Dag Westerstha˚l (eds.), Logic, Methodology and Philosophy of Science 2003: Proceedings of the 12th International Congress, 481–503. London: KCL Publications. Pullum, Geo¤rey, and Barbara Scholz 2009 Recursion and the infinitude claim. This volume. Sapir, Edward 1949 Reprint. The grammarian and his language. In: David Mandelbaum (ed.), Selected Writings of Edward Sapir in Language, Culture and Personality, 150–159. Berkeley: University of California Press. Original edition, American Mercury 1: 149–155, 1924. Schi¤er, Steven 1972 Meaning. Oxford: Clarendon Press. Uriagereka, Juan 2005 Adjunct space? Paper presented at the Prospects for Dualism Conference, Amsterdam. von Fintel, Kai, and Lisa Matthewson 2008 Universals in semantics. The Linguistics Review 25: 139–201. Zeitman, Suzanne 1993 Somewhat finite approaches to infinite sentences. Annals of Mathematics and Artificial Intelligence 8(1–2): 27–36.

8.

Recursion, infinity, and modeling

Hans-Jo¨rg Tiede and Lawrence Ne¤ Stout

1. Introduction Hauser, Chomsky, and Fitch (2002) claim that a core property of the human language faculty is recursion and that this property ‘‘yields discrete infinity’’ (2002: 1571) of natural languages. On the other hand, recursion is often motivated by the observation that there are infinitely many sentences that should be generated by a finite number of rules. It should be obvious that one cannot pursue both arguments simultaneously, on pain of circularity. The main aim of this paper is to clarify both conceptually and methodologically the relationship between recursion and infinity in language. We want to argue that discrete infinity is not derived but a modeling choice. Furthermore, many arguments, both for recursion and infinity in language, crucially depend on particular grammar formalisms. Thus, care should be taken to distinguish, on the one hand, whether to derive infinity from recursion or the other way around, and, on the other hand, the role of recursion in language in general from the role of recursion in specific grammar formalisms.

2. Linguistics as modeling While it may not be the standard view of linguistics, it is clear that to the extent that linguistic theories, i.e. grammars, aim to capture human knowledge of language, these theories are formal models. In fact, grammars in the generative tradition are symbolic models, as opposed to, say, connectionist models or dynamical systems (Clark 2001). The fact that generative linguistics employs symbolic models has a crucial impact on the role of recursion and infinity, as we shall see. The object in modeling is not to gain a perfect representation of an empirical reality, but rather to focus on simpler structures which give

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useful information about that more complicated reality. Models are, by their nature, abstractions. Certain features of the object to be modeled are retained, while others are not. Decisions about how to model need to be made both for verisimilitude and for ease in handling the model. An overly complex model of a more complex situation only leaves us more confused. Things we can say about the model should give information about the empirical reality, but we should not confuse the model with the reality. In particular, we need to be careful to distinguish the assumptions we make in our modeling decisions from their consequences. Certain, completely standard, assumptions underlie the construction of grammars: First, we are concerned with grammaticality of sentences. We assume that sentences can be modeled as finite sequences of symbols and that languages can be modeled as sets of such strings, either finite or infinite. Second, we attempt to model linguistic competence in judging acceptability, an ideal judgement free from performance errors. Another important assumption that is commonly made is that grammars should be finite, since we are modeling human knowledge of language which has to be represented in a finite medium: the brain. Our grammars are symbolic models producing formal languages. We hope they tell us something useful about the mental processes which produce natural languages. All of these assumptions have been commonly made in the generative approach to grammar since its inception (Chomsky 1957, 1965). However, not enough care has been taken in linguistics to identify features of grammatical theories as modeling choices and to distinguish modeling assumptions from their consequences. Furthermore, many of these modeling choices have been challenged. For instance, Langendoen and Postal (1984) challenge the assumption that sentences should be modeled as strings of finite length. Itkonen (1976: 214) questions whether the purpose of constructing natural language grammars is comparable to the purpose of constructing formal grammars: ‘‘Is it, or should it be, the purpose of a grammar to generate sentences which are so complex that not even the best linguist, unaided by formal machinery could utter or understand them? In my opinion the answer is definitely ‘No’.’’ At the beginning of their analysis of the role of ‘‘embedding recursion’’ in grammars and how it might have arisen, Heine and Kuteva state that Recursion is not a property of language but rather the product of a given theory designed to describe or account for language structure; given an appropriate theory, one might argue that language is no more recursive than, say biological reproduction, or some other natural phenomenon.

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Accordingly, when using this term we are not maintaining that language, or language structure, has recursion but rather that there are certain properties to be observed in language that can appropriately be described in terms of a construct of the form proposed [ . . . ] (Heine and Kuteva 2007: 265)

However, in our opinion, the latter two criticisms fail to make the distinction between models and what they model su‰ciently clear. What matters in modeling is that the choices made give us a lens through which to understand what we are modeling. The above mentioned assumptions have consequences: since the set of strings of finite length on a finite alphabet is at most countably infinite, our model can only give at most a countable infinity of grammatical sentences. Not all possible languages can be generated by finite grammars, since there are more formal languages than grammars. If we assume that the natural language is infinite and decide that that should also be true of our formal model, there will be constraints on the grammar which is to produce that formal language: it must have some process which can be extended indefinitely to keep producing more grammatical sentences. One such process is recursion. The information we can gain by empirical study of languages either through field work or corpus studies will always be incomplete. We can ask for judgments to get data about competence and we can use performance data to see what is produced in the natural language. The following table gives a sketch of how the empirical reality is (or might be) represented in the formal model: Empirical Reality

Model

Natural Languages

Formal Languages (Sets of finite strings)

Knowledge of Language (Competence)

Grammars

Performance

Derivations of bounded length

Figure 1: Relationship between empirical reality and models in linguistics.

The basic grammar formalism employed here is that of context-free grammars, which generates a set of strings over some symbols. For an

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introduction to formal language theory in the context of linguistics, see (Partee, ter Meulen, and Wall 1990). The set of all strings over some set of symbols, V , is denoted by V . A context-free grammar (CFG) is specified in terms of two sets of symbols, the terminal and non-terminal symbols, VT and VN , respectively, a designated member of VN , usually denoted by S, the start symbol, and a finite set of rules of the form A!w

with A 2 VN and w 2 ðVT [ VN Þ . We say )G when G derives in a finite number of steps. The language of a CFG G, LðGÞ, is defined as LðGÞ ¼ fw j S )G wg where w consists only of terminal symbols. The set of all languages generated by CFGs, the context-free languages, is denoted by CFLs. We can distinguish the weak generative capacity of a grammar formalism, the string sets generated by a grammar formalism, from its strong generative capacity, the sets of structural descriptions, trees in the case of CFGs, assigned to those strings. Thus, the weak generative capacity of CFGs are the CFLs (by definition), while the strong generative capacity of the CFGs are the so-called local tree languages (Thatcher 1967). There has been a significant amount of debate about whether CFGs are good models of grammar. While much of the early criticism of CFGs was found to be flawed (Pullum and Gazdar 1982), it was eventually shown by Shieber (1985) that there are natural languages that cannot be modeled as CFLs. Nevertheless, CFGs are used extensively in computational linguistics because they can be parsed e‰ciently (Aho and Ullman 1972) and because they can be used to model other languages, particularly English, reasonably well (Gazdar et al. 1985; Rogers 1998). Furthermore, some of the problems of CFGs, although not the one outlined by Shieber, are due to their strong generative capacity. Thus, there are several grammar formalism that, while retaining the weak generative capacity of the CFGs, extend them with respect to their strong generative capacity, for instance certain categorial grammars like the Lambek Calculus (Tiede 2003) or formalisms that operate on trees. 3. Recursion and Infinity There is little disagreement that most natural languages can be analyzed as containing recursive structures, i.e. trees containing nodes that dominate nodes with the same label, as in Figure 2.

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Figure 2. Recursive tree structure

However, recursive structures are distinct from recursion which is a process. Recursion is a process with which infinitely many items can be generated using finitely many symbols. For CFGs, there is a close connection between generating recursive structures and generating infinitely many strings. Intuitively, any CFG generating the tree above will generate infinitely many trees, simply by repeatedly using the rule A ! B3 B4 after the rule B3 ! A B5 and so on. Furthermore, there is no way to constrain CFGs so that they can generate recursive structures without admitting infinitely many structures. Formally, a CFG G is recursive when A )G uAv. The close connection between recursive CFGs and infinite languages is shown by the following theorem which follows from a simple application of the pumping lemma for CFLs: Theorem 1. Let G be a CFG. L(G) is infinite i¤ for some A 2 VN ; u; v; w; x; y 2 VT S )G uAv A )G xAy A )G w (with j xy j> 0). It should be noted that the relationship between recursive structures and infinity is not universal, that is, it depends on the grammar formalism employed. Grammar formalisms operating on trees can generate fully recursive structures with only bounded recursion. While grammars operating on trees may seem exotic, given that much of linguistic theory in the last 30 years has been concerned with well-formedness conditions on trees, formalizing such theories naturally makes use of tree based formalisms (see e.g. (Rogers 1998)).

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We formalize trees using terms over an alphabet, such as f ðgða; bÞÞ. In this example, the symbol f has an arity of 1 and g has an arity of 2. A ranked alphabet is a finite set of symbols, each of which has some fixed arity. There are di¤erent, equivalent ways of defining the regular tree languages. We will use regular tree grammars. For an overview of tree automata theory, see (Ge´cseg and Steinby 1997). A regular tree grammar is specified in terms of two alphabets, the terminal and non-terminal symbols, VT and VN , respectively, a designated member of VN , usually denoted by S, the start symbol. The di¤erence to CFGs is that the terminal symbols are ranked. Finally, regular tree grammars consist of a finite set of rules of the form A!t where t is a term over VT and VN . Example 1: Since regular tree grammars are probably rather unfamiliar to the reader, we give an example of a regular tree grammar that generates a tree language for a CFL that no CFG could generate for it. The grammar is for the language of palindromes with trees that are labeled with the same label, c. Although, there are technically three di¤erent symbols named c, one of unary, binary, and ternary arity, respectively.The grammar consists of the following rules: S ! cðaÞ j cðbÞ j cðcðaÞ; cðaÞÞ j cðcðbÞ; cðbÞÞ j cðcðaÞ; S; cðaÞÞ j cðcðbÞ; S; cðbÞÞ In a regular tree grammar, symbols of non-zero arity are labels of internal tree nodes, thus would be represented as non-terminals in a CFG, while the symbols of zero arity would be the terminals of a CFG. This grammar generates the tree cðcðaÞ; cðcðbÞ; cðbÞÞ; cðaÞÞ for example. However, no CFG can generate this tree language, since any node labeled with c can be rewritten with either an a or a b, thus such a CFG would also generate, say, cðcðaÞ; cðcðaÞ; cðbÞÞ; cðaÞÞ which is not generated by the regular tree grammar.

y

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Now, we turn to an example of a recursive tree generated without recursion in the grammar. Example 2: A regular tree grammar can generate a single recursive structure, disallowing longer ones, as follows: S ! b1 ðb2 ; aðb3 ðaðb6 ; b7 Þ; b5 Þ; b4 ÞÞ This grammar generates precisely the (recursive) tree at the beginning of this section, but no other. Of course, it should be noted that a regular tree grammar generating infinitely many trees uses recursion on its non-terminals, just like CFGs. The di¤erence is simply that regular tree grammars have a more complex set of terminals at its disposal, or, put another way, that CFGs are poor at generating trees (Rogers 1997). y Since, nevertheless, for context-free grammars, recursion and infinity are so closely related, if our model assumes one, the other can be derived. The question now is which should be assumed and which should be derived.

4. Deriving Infinity or Assuming Infinity? According to Hauser, Chomsky, and Fitch (2002), a core property of the human language faculty is recursion and this property ‘‘yields discrete infinity’’ of natural languages (2002: 1571). Thus, they claim that infinity is a derived property. However, the main reason that is usually given for assuming recursion is to model linguistic productivity, i.e. the ability to produce longer and longer sentences. But that uses infinity to justify recursion, which is circular (Pullum and Scholz 2001). Given that there are more infinite formal languages than grammars, deriving infinity is actually less interesting than trying to find a grammar that generates a given language. Instead of assuming recursion to derive infinity, we want to propose that infinity is an assumed modeling choice. Assuming an infinite model does not imply that natural languages actually are infinite, just as modeling natural languages as sets of strings does not imply that natural

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languages are sets of strings. There are three main reasons why we believe that infinity should be assumed: linguistic productivity, the systematicity requirement for symbolic models, and grammar conciseness. 4.1. Linguistic Productivity As we mentioned above, linguistic productivity, the proper containment of one phrase within another of the same syntactic category, is a fairly uncontroversial claim about human languages. Of course, linguistic productivity only implies an infinite model if it is unbounded. While there are reasons to believe that linguistic productivity may be bounded by performance considerations, say, ruling out sentences that take longer than 100 years to generate, such considerations do not give a least upper bound. Assuming a finite model would in fact give a least upper bound, which does not appear to be empirically justifiable. 4.2. Systematicity To some extent, this argument for assuming infinity simply amounts to the observation that, if we want to use symbolic models, as opposed to, say, connectionist ones, finite languages are uninteresting. Given a finite language fw1 ; . . . ; wn g, we can trivially generate it with the following grammar: S S

! w1 .. .

! wn

Notice, however, that this argument depends on the assumption that we model grammars symbolically. Connectionist models are frequently employed to learn finite sets (Clark 2001). 4.3. Grammar Conciseness The last, and in our opinion most important, reason for assuming infinity was originally put forward by Chomsky in 1956: In general, the assumption that languages are infinite is made for the purpose of simplifying the description. If a grammar has no recursive steps [ . . . ] it will be prohibitively complex – it will, in fact, turn out to be little better than a list of strings [ . . . ] (Chomsky 1956: 115–116, emphasis added)

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Chomsky’s observation was formalized by Savitch, employing the following definition: Definition 1. Let L be a finite language, and let n be the length of the longest string in L. L is essentially infinite with respect to a grammar formalism if: 1. there is a grammar G that generates an infinite superset of L, 2. if w 2 LðGÞ and jwj n, then w 2 L, 3. if LðG 0 Þ ¼ L, then jGj < jG 0 j. where jwj denotes the length of w and jGj denotes some size measure of grammars, such as the number of rules. The intuition behind this definition is that a language is essentially infinite if any grammar that generates it is larger than some grammar that generates an infinite superset of it. The purpose of part 2 of the definition is to rule out the trivial superset consisting of all strings. Using this definition, Savitch (1993: 21) was able to prove the following theorem. Theorem 2. For any ‘‘reasonable’’ grammar formalism, there exist infinitely many essentially infinite languages. It would take us too far afield to spell out how ‘‘reasonable’’ is defined in this context, except to say that it so broadly defined that it includes almost all formal grammars considered in formal language theory and formal linguistics. Details can be found in (Savitch 1993). It should be noted that essentially infinite is defined with respect to a given grammar formalism. There are languages that are essentially infinite with respect to one grammar formalism, but not with respect to another. It is an interesting question whether formal languages used to model natural languages are essentially infinite with respect to certain grammar formalisms. This result, together with Chomsky’s remark, can be used to suggest that recursion may be a mechanism to reduce grammar size for natural languages. Even if the natural language being modeled is finite, we may assume an infinite model, so that we can construct a smaller, recursive grammar. Thus, ‘‘finite’’ may not be a trivial notion for symbolic models if we are interested in grammar size. However, we may end up with a grammar that overgeneralizes by generating strings that are ‘‘too long to be grammatical.’’ As in all modeling situations, the process of abstraction produces something di¤erent than the phenomenon being modeled, and so this mismatch is in fact well motivated by concern for grammar size.

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5. Conclusions The study of syntax in linguistics is a process of making formal symbolic models of aspects of natural languages. While we expect good models to provide us with an understanding of the empirical reality being modeled, we should not confuse properties of the model with properties of the reality being modeled. Infinity of the formal language is a modeling choice. We have given reasons why it should be an assumption and not a conclusion. Even if the formal language is infinite, the natural language it models may not be. In context-free grammars recursion in the grammar and infinity in the formal language generated are equivalent. The choice to use recursion (and hence an infinite model) may be a mechanism to reduce grammar size for natural languages. Even if the natural language being modeled is finite, we may assume an infinite model, so that we can construct a smaller, recursive grammar. Thus deciding between finite and infinite languages is not trivial for symbolic models if we are interested in grammar size. However, we may end up with a grammar that overgeneralizes by generating strings that are ‘‘too long to be grammatical.’’ References Aho, Alfred and Je¤rey Ullman 1972 The Theory of Parsing, Translation, and Compiling. Englewood Cli¤s: Prentice Hall. Chomsky, Noam 1956 Three Models for the Description of Language. IRE Transactions on Information Theory 3: 113–124. Chomsky, Noam 1957 Syntactic Structures. The Hague: Mouton Publishers. Chomsky, Noam 1965 Aspects of the Theory of Syntax. Cambridge, MA: MIT Press. Clark, Andy 2001 Mindware: An Introduction to the Philosophy of Cognitive Science. New York: Oxford University Press. Gazdar, Gerald, Ewan Klein, Geo¤rey Pullum, and Ivan A. Sag 1985 Generalized Phrase Structure Grammar. Cambridge, MA: Harvard University Press. Ge´cseg, Ferenc and Magnus Steinby 1997 Tree Languages. In: Grzegorz Rozenberg and Arto Salomaa (eds.), Handbook of Formal Languages, Vol. 3, 1–68. Berlin: Springer.

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Hauser, Marc D., Noam Chomsky, and W. Tecumseh Fitch 2002 The Faculty of Language: What Is It, Who Has It, and How Did It Evolve? Science 298 (5598): 1569–1579. Heine, Bernd and Tania Kuteva 2007 The Genesis of Grammar: A Reconstruction. New York: Oxford University Press. Itkonen, Esa 1976 The Use and Misuse of the Principle of Axiomatics in Linguistics. Lingua 28: 185–220. Lambek, Joachim 1958 The Mathematics of Sentence Structure. American Mathematical Monthly 65: 154–169. Langendoen, D. Terence and Paul M. Postal 1984 The Vastness of Natural Language. Oxford: Blackwell Publishers. Partee, Barbara H., Alice ter Meulen, and Robert E. Wall 1990 Mathematical Methods in Linguistics. Dordrecht: Kluwer Academic Publishers. Pentus, Mati 1997 Product-Free Lambek Calculus and Context-Free Grammars. The Journal of Symbolic Logic 62 (2): 648–660. Pullum, Geo¤rey and Gerald Gazdar 1982 Natural Languages and Context-Free Languages. Linguistics and Philosophy 4 (4): 471–504. Geo¤rey K. Pullum and Barbara C. Scholz 2001 On the Distinction between Model-Theoretic and GenerativeEnumerative Syntactic Frameworks. In: Philippe de Groote, Glyn Morrill, and Christian Retore´ (eds.), Logical Aspects of Computational Linguistics, 17–43. Berlin: Springer. Rogers, James 1997 Strict LT2 : regular :: local : recognizable. In: Christian Retore´ (ed.), Logical Aspects of Computational Linguistics, 366–385. Berlin: Springer. Rogers, James 1998 A Descriptive Approach to Language Theoretic Complexity. Stanford, CA: CSLI Publications. Savitch, Walter J. 1993 Why it might pay to assume that languages are infinite. Annals of Mathematics and Artificial Intelligence 8 (1–2): 17–25. Shieber, Stuart 1985 Evidence Against the Context-Freeness of Natural Language. Linguistics and Philosophy 8 (3): 333–343. Thatcher, James W. 1967 Characterizing Derivation Trees of Context-Free Grammars through a Generalization of Finite Automata Theory. Journal of Computer and System Sciences 1 (4): 317–322.

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Tiede, Hans-Jo¨rg 2003 Proof Theory and Formal Grammars: Applications of Normalization. In: Benedikt Lo¨we, Wolfgang Malzkom, and Thoralf Ra¨sch (eds.), Foundations of the Formal Sciences II, 235–256. Dordrecht: Kluwer.

9.

How recursive is language? A Bayesian exploration

Amy Perfors, Joshua B. Tenenbaum, Edward Gibson, and Terry Regier

1. Introduction One of the most notable features of human language is its capacity to generate a potentially infinite number of possible sentences. Because such a capacity must result from an underlying generative mechanism (a grammar) that is recursive in some way, many linguists have concluded that recursion must be a fundamental, possibly innate, part of the language faculty (Chomsky 1957). Some have gone further and claimed that the core mechanism underlying recursion is the only part of language that is specific to humans (Hauser, Chomsky, and Fitch 2002). While the latter, stronger claim is contested (Pinker and Jackendo¤ 2005), the former has been largely accepted for decades. However, recent work on Piraha˜, a language spoken in the Amazon basin, suggests that there may be a language that does not in fact contain any recursion in its phrase structure whatsoever (Everett 2005). The empirical claim about Piraha˜ is the subject of much debate (Nevins, Pesetsky, and Rodrigues 2007; Everett 2007), and an essential key to resolving the debate is to be able to objectively determine whether Piraha˜ is better described by a grammar with recursive elements or by one without. But what does it mean to say that one grammar constitutes a ‘‘better description’’ of a language than another? In this article we argue that this question cannot be answered for any particular language without a rigorous, quantitative, and principled mechanism for comparing grammars with respect to linguistic corpora. We propose such a method and demonstrate its e‰cacy by applying it to a corpus of child-directed speech in English. Our results suggest that simple rational principles support the inference of a specific set of recursive phrase structures in English, even if few sentences in the corpus contain multiple embeddings resulting from multiple expansions of those productions. The method yields several

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insights about the possible role, nature, and learnability of recursion in language, and may ultimately be applicable to addressing the case of Piraha˜. 1.1. Measuring recursion A grammar is recursive if it contains at least one rule whose expansion can eventually involve a call to itself. There are three main types of recursion: left-branching, right-branching, and center embedding. The first two types of recursion occur in both finite-state (FS) and context-free grammars (CFGs), but center embedding exists only in grammars capable of representing phrase structure: that is, grammars whose formal complexity is at least equivalent to that of a CFG. A phrase of depth n results from a recursive rule that is expanded n times. For instance, the following centerembedded sentences are generated by self-embedding NPs with relative clauses. (1) (a) (b) (c)

The cat eats [depth 0] The cat that the dog chased eats [depth 1] The cat that the dog that the boy petted chased eats [depth 2]

Human learners have di‰culty parsing sentences with multiple center embeddings (Miller and Chomsky 1963; Marks 1968; Bach, Brown, and Marslen-Wilson 1986), probably due to performance factors such as limitations on working memory (Chomsky 1956; Miller and Chomsky 1963; Gibson 1998; Weckerly and Elman 1992). It is in principle possible that this particular English grammatical rule is not truly recursive: as long as there are no sentences with more than n embeddings, a grammar with n non-recursive rules would also parse the language. Indeed, work by Christiansen and Chater (1999) suggests that it may not be necessary to assume unbounded recursion in the grammar in order to qualitatively explain aspects of human performance. How might a linguist or a child attempting to acquire the proper grammar determine whether a grammar, or a particular grammatical rule, is recursive? The standard argument that grammars of natural language must contain recursion dates back to Chomsky (1957), who pointed out that natural language appears to have the property of discrete infinity: it is composed of discrete basic elements (words) which can be combined to produce apparently infinitely many sentences. An infinite set can only be generated from a finite grammar if the grammar contains some form of recursion. But is it true that natural language is infinite? After all, there are no infinitely long sentences, and only a finite number of sentences

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have ever been uttered. Since any finite language may be captured by a finite grammar without recursive rules, why believe that grammars of natural language have recursive rules? The standard reason is simplicity: a non-recursive grammar capable of generating natural language would be very large, since it would require additional sets of rules for each additional depth of recursive expansion. Any evaluation metric that favors shorter (i.e., simpler) grammars should therefore prefer a grammar with recursive rules over one with non-recursive rules.1 This simplicity-based argument is reasonable, but not airtight: it is qualitative, not quantitative, based on our intuitions about how much more complex a grammar with non-recursive instead of recursive rules would be. The complexity of a grammar would increase with each additional rule, and how many non-recursive rules would be necessary depends on the precise sentences in the corpus. Furthermore, it is the tradeo¤ between the complexity of a grammar and how well that grammar explains the observed sentences that is important – not its complexity alone. If choosing the simplest grammar were the only consideration necessary, a learner would always favor the grammar that can generate any sentence whatsoever. Such a grammar is maximally simple since it contains no rules constraining how the terminal symbols may be combined, but we would obviously like to rule it out. This suggests that a rational learner should evaluate a grammar with respect to how precisely it predicts the sentences observed as well as its simplicity. All else being equal, a grammar that generates sentences not present in the observed language should be dispreferred relative to one that does not. Unfortunately, recursive productions hurt the fit of a grammar on any finite corpus, since they will always predict sentences that are not observed. The fewer sentences in the corpus that result from multiple expansions of recursive rules, the more a grammar with recursive rules, relative to one without, will overgeneralize, since it predicts very long sentences that are never actually used. Thus, recursion involves an inherent tradeo¤ between simplicity and degree of fit: while a grammar with recursive rules might be shorter and 1. When we speak of evaluating a grammar, we presume unless stated otherwise that it is evaluated with respect to a finite corpus of sentences of the language, and relative to all of the (infinitely many) grammars that can generate the sentences in that corpus. Grammars that cannot generate the sentences may be eliminated on that basis. The corpus is assumed to contain positive evidence only.

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simpler than one without, it will also fit any finite set of sentences less precisely. Furthermore, both the degree of complexity and the degree of fit of the grammar depend on the precise nature of those sentences. As a consequence, we cannot conclude on a priori grounds that any grammar for natural language must contain recursion. While that may be a reasonable starting assumption, it might not be true in all cases, whether for a specific language (e.g., Piraha˜) or for a specific rule or set of rules (e.g., centerembedded relative clauses in English). In order to evaluate these specific cases it is necessary to quantify degrees of simplicity and fit, as well as to calculate the tradeo¤ between the two in a principled and rigorous way. How can we perform such a calculation? Traditional approaches to formal language theory and learnability are unhelpful because they presume that a learner does not take either simplicity or degree of fit into account (Gold 1967). A Bayesian approach, by contrast, provides an intuitive and principled way to calculate the tradeo¤ between a grammar’s simplicity (prior probability) and its degree of fit to a corpus (likelihood). Such an approach is consistent with Chomsky’s formulation of the problem of language learning, which presumes both a hypothesis space of grammars and the existence of an evaluation metric based on simplicity (Chomsky 1965). Indeed, it has been formally proven that an ideal learner incorporating a simplicity metric will be able to predict the sentences of the language with an error that approaches zero as the size of the corpus goes to infinity (Solomono¤ 1978; Chater and Vita`nyi 2007); in many more traditional approaches, the correct grammar cannot be learned even when the number of sentences is infinite (Gold 1967). However, learning a grammar (in a probabilistic sense) is possible, given reasonable sampling assumptions, if the learner is sensitive to the statistics of language (Horning 1969). In this article we propose a Bayesian framework for grammar induction, which can be used to quantitatively evaluate grammars with respect to one another by calculating an ideal tradeo¤ between simplicity and goodness-of-fit. Because the framework combines statistical inference mechanisms that can operate over structured representations of knowledge such as generative grammars, it can in principle apply to many interesting linguistic questions regarding representation and learnability. For instance, other work involving this framework suggests that structuredependence in language need not be innate: a rational learner could infer based on typical child-directed input that language is better captured by a hierarchical phrase-structure grammar than by a finite-state one (Perfors, Tenenbaum, and Regier, under review). Here we apply this framework to the issue of recursion by evaluating grammars of English with and without a particular set of recursive rules

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(NPs with relative clauses) as they apply to a specific corpus of actual spoken speech. Is a language with recursive NPs preferred by a rational learner over one without, even when the input does not contain sentences with many levels of embedding? Our results yield some surprising insights into the circumstances under which recursive rules might occur, and suggest that grammars that occupy a ‘‘representational middle ground’’ between fully-recursive and only non-recursive rules may be most preferred.

2. Method We cast the problem of grammar induction within a Bayesian framework in which the goal is to infer which grammar G is most likely to have generated some data D (a corpus of child-directed speech). The framework assumes a probabilistic generative model for linguistic utterances, which can then be inverted by the learner to infer aspects of the generating grammar from the language data observed. A linguistic corpus is assumed to be created by first picking a grammar G from a space of possible grammars, and then by generating D from the specific grammar G by drawing from the conditional distribution p(D|G). The inferences we can make from the observed data D to the specific grammar G are captured by the posterior probability p(G|D), computed via Bayes’ rule: pðGjDÞ pðDjGÞpðGÞ:

ð1Þ

This equation states that the posterior probability of a grammar given the data ( p(G|D)) is proportional to its prior probability ( p(G)) times the likelihood of the data given the grammar ( p(D|G)). The prior for a grammar p(G) is calculated assuming a generative model of grammars (a grammar for generating grammars) that assigns higher prior probability to simpler grammars. The likelihood p(D|G) reflects the probability of the corpus D given grammar G; it is a measure of how well the grammar fits the corpus data. The posterior probability p(G|D) thus automatically seeks a grammar that optimally balances the tradeo¤ between complexity (prior probability) and fit to the data (likelihood). In the following subsections we describe the specific grammars G, the corpus of data D, and the particulars of the computational framework.2

2. See Perfors, Tenenbaum, and Regier (under review) for a more detailed explanation of the corpus and the computational model, which are identical to the one used here.

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2.1. The grammars Each grammar consists of a set of production rules specifying how one non-terminal symbol (the left-hand side of the rule) in a string may be rewritten in terms of two other symbols, terminal or non-terminal. Each rule is associated with a probability, such that the probabilities of all rules with the same left-hand sides (i.e., all S rules, all NP rules, etc.) add to one and the probability of a complete parse is the product of the probabilities of the rules involved in the derivation. All grammars are context-free, since CFGs generate parse trees with hierarchical structure and are often adopted as a first approximation to the structure of natural language (Chomsky 1959). Probabilistic context-free grammars (PCFGs) are also standard tools in computational linguistics (Jurafsky and Martin 2000; Manning and Schu¨tze 1999). Although PCFGs do not capture the full complexity of natural language, we work with them because they are complex enough to allow for an exploration of the role of recursion, because they are easily defined in probabilistic terms, and because CFGs have been the focus of recent debate over the role of recursion as the allegedly uniquely human core of language (Hauser, Chomsky, and Fitch 2002; Fitch and Hauser 2004; Gentner et. al. 2006). All of our grammars can parse all of the sentences in the corpus, and all contain standard structures based in linguistic theory (including noun, verb, and prepositional phrases). We evaluate three main grammars that di¤er from each other only in whether some rules are recursive or not. The simplest grammar is the fully recursive R-CFG, which contains recursive noun phrases such as [NP ! NP CP] and is made up of 100 rules and 14 distinct non terminals. Since the reason recursive rules are costly is because they do not fit the data precisely, we design our other grammars so as to minimize overgeneralization. One grammar accomplishes this by eliminating recursive rules entirely; the other decreases the weight assigned to them by creating identical ‘‘shadow’’ rules that correspond to non-recursive expansions. For instance, a grammar with shadow rules retains a recursive rule like [NP ! NP PP] but also contains [NP ! NN PP], where NN only expands into simple noun phrases such as [NN ! Det N]. Rules in this grammar with right-hand-sides containing NP (such as [VP ! V NP]) are therefore also joined by rules containing NN (such as [VP ! V NN]). The grammar containing both recursive rules and non-recursive ‘‘shadow’’ rules is BCFG (‘‘B’’ for both: 126 productions, 15 non-terminals). The grammar without any recursive rules at all is identical to B-CFG

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Table 1. Sample rules from each of the three main grammars. These are chosen to illustrate the di¤erences between each grammar, and may not be an exhaustive list of all the expansions of any given non-terminal. Grammar with recursive rules (R-CFG) NP ! NP PP | NP CP | NP C | N | det N | adj N | pro | prop N ! n | adj N Grammar with both recursive and non-recursive rules (B-CFG) NP ! NP PP | NP CP | NP C | NN PP | NN CP | NN C | NN NN ! det N | N | adj N | pro | prop N ! n | adj N Grammar with non-recursive (depth-limited) rules (N-CFG) NP ! N2 PP | N2 CP | N2 C | NN P | NN CP | NN C | NN N2 ! NN PP | NN CP | NN C | NN NN ! det N | N | adj N | pro | prop N ! n | adj N

except that the recursive NP productions are eliminated and replaced with multiply-embedded non-recursive productions involving an additional new non-terminal, N2. This depth-limited non-recursive grammar, NCFG, can therefore only parse sentences with up to two nested relative clauses. Sample rules from each grammar are shown in Table 1.3 These three grammars do not capture the distinction between subject and object noun phrases, which have di¤erent syntactic properties, including di¤erences in the di‰culty of processing multiple recursive expansions. Recursive expansions of subject noun phrases (NPS ) results in the hard-tounderstand center-embedded sentences discussed earlier, but sentences with recursive expansions of object noun phrases (NPO ) are significantly easier: compare The cat that the dog that the boy petted chased eats to The boy petted the dog that chased the cat that eats (Miller and Chomsky 1963). We can examine the role of recursion in each type of NP by creating additional grammars like our three basic ones, except that they contain rules with distinct NPS and NPO left-hand sides. Nine (32) grammars 3. http://www.psychology.adelaide.edu.au/personalpages/sta¤/amyperfors/ research/lingrevrecursion/ contains the full grammars and corpora.

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result from all combinations of the three kinds of recursion (recursive-only (R), depth-limited (D), and both (B)) and two noun phrases (NPS and NPO). 2.2. The corpus The corpus consists of the sentences spoken by adults in the Adam corpus (Brown 1973) of the CHILDES database (MacWhinney 2000). Because grammars are defined over syntactic categories, each word is replaced by its syntactic category.4 For reasons of tractability, ungrammatical sentences and the most grammatically complex sentence types are removed from the corpus.5 The final corpus contains 21671 individual sentence tokens corresponding to 2336 unique sentence types, out of 25755 tokens in the original corpus, and includes interrogatives, wh-questions, relative clauses, prepositional and adjective phrases, command forms, and auxiliary and non-auxiliary verbs. 2.3. The probabilistic model Grammars were scored using a probabilistic scoring criterion based on Bayes’ rule, which combines the prior probability of a grammar G with the likelihood that the corpus D was generated by that grammar. 2.3.1. Scoring the grammars: prior probability A simplicity metric on a grammar may be derived in a principled way by defining the process by which the grammars themselves can be generated and then calculating each grammar’s relative prior probability based on 4. Parts of speech used included determiners (det), nouns (n), adjectives (adj), comments like ‘‘mmhm’’ (c), prepositions ( prep), pronouns ( pro), proper nouns ( prop), infinitives (to), participles ( part), infinitive verbs (vinf ), conjugated verbs (v), auxiliary verbs (aux), complementizers (comp), and wh-question words (wh). Adverbs and negations were removed from all sentences. Additionally, whenever the word what occurred in place of another syntactic category (as in a sentence like He liked what?), the original syntactic category was used; this was necessary in order to simplify the analysis of all grammar types, and was only done when the syntactic category was obvious from the sentence. 5. Removed types included topicalized sentences (66 individual utterances), sentences containing subordinate phrases (845), sentential complements (1636), conjunctions (634), serial verb constructions (460), and ungrammatical sentences (443).

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the distribution imposed by that process (Horning 1969). This process is a grammar-grammar, a generative model for grammars, in which each grammar is generated by making a series of choices. Longer grammars, which require more choices, will have a lower prior probability. If one were generating a grammar from scratch, one would first need to choose the number of non-terminals n, and for each non-terminal k to generate some number Rk of rules, each of which is associated with a production probability parameter yk. Each rule i also has Ni right-hand side items, and each of those items must be drawn from the grammar’s vocabulary V (set of non-terminals and terminals). If we assume that each righthand side item of each rule is chosen uniformly at random from V, the prior probability is given by: pðGjTÞ ¼ pðnÞ

n Y

pðRk Þpðk Þ

k¼1

Rk Y i¼1

pðNi Þ

Ni Y 1 : V j¼1

ð2Þ

We model the probabilities of the number of non-terminals p(n), rules p(Rk), and items p(Ni) as selections from a geometric distribution, which assigns higher probabilities to lower numbers; production-probability parameters p(yk) are sampled from a discrete approximation of a uniform distribution appropriate for probability parameters (Dirichlet). This prior gives higher probability to simpler grammars – those with fewer nonterminals, productions, and items. Because of the small numbers involved, all calculations are done in the log domain. 2.3.2. Scoring the grammars: likelihood Inspired by the work of Goldwater, Gri‰ths, and Johnson (2006), the likelihood is calculated assuming a language model that is divided into two components. The first component, the grammar, assigns a probability distribution over the potentially infinite set of syntactic forms that are accepted in the language. The second component generates a finite observed corpus from the infinite set of forms produced by the grammar, and can account for the characteristic power-law distributions found in language (Zipf 1932). In essence, this two-component model assumes separate generative processes for the allowable types of distinct sentences (defined here as sequences of syntactic categories) in a language and for the frequency of specific sentence tokens. The probabilistic grammar is only directly involved in generating the allowable types. One consequence of this approach is that grammars are analyzed based on individual sentence types rather than on the frequencies of di¤erent

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sentence tokens. This parallels standard linguistic practice: grammar learning is based on how well each grammar accounts for the types of sentence forms rather than their frequency distribution. Since we are concerned with grammar comparison rather than corpus generation, we focus in this work on the first component of the model. We thus take the data to consist of the set of sentence types (distinct sequences of syntactic categories) that appear in the corpus, and we evaluate the likelihoods of candidate probabilistic grammars on that dataset. The likelihood assigned to a grammar can be interpreted as a measure of how well the grammar fits or predicts the data. The penalty for overly general or flexible grammars is computed in the parsing process, where we consider all possible ways of generating a sentence under a given grammar and assign probabilities to each derivation. The total probability that a grammar assigns over all possible sentences must sum to one, and so the more flexible the grammar, the lower probability it will tend to assign to any one sentence. More formally, the likelihood p(D|G) measures the probability that the corpus data D would be generated by the grammar G. If we assume that each sentence type is generated independently from the grammar, this is given by the product of the likelihoods of each sentence type Sl, as shown in Equation 3. If there are M unique sentence types in the corpus, the corpus likelihood is given by: pðDjGÞ ¼

M Y

pðSl jGÞ:

ð3Þ

l¼1

The probability of any sentence type Sl given the grammar p(Sl |G) is the product of the probabilities of the productions used to derive Sl. Thus, calculating likelihood involves solving a joint parsing and parameter estimation problem: identifying the possible parses for each sentence in the corpus, as well as calculating the parameters for the production probabilities in the grammar. We use the inside-outside algorithm to integrate over all possible parses and find the set of production probability parameters that maximize the likelihood of the grammar on the observed data (Manning and Schu¨tze 1999; Johnson 2006). We evaluate Equation 3 in the same way, using the maximum-likelihood parameter values but integrating over all possible parses of the corpus. Sentences with longer derivations will tend to be less probable, because each production that is used contributes a multiplicative factor that is less than one. This notion of simplicity in derivation captures an inductive bias that favors sentences with more economical derivations.

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3. Results We first compare the three grammars R-CFG, B-CFG, and N-CFG, which di¤er from each other only in the recursive nature of some rules. As Figure 1 shows, the grammar with the highest posterior probability is B-CFG, which contains both non-recursive and recursive rules. It is neither the simplest grammar nor the one with the best fit, but o¤ers the best tradeo¤ overall. As expected, the grammar with recursive rules (R-CFG) is the simplest, but the gain in prior probability is balanced by a loss in the likelihood caused by overgeneralization due to (relatively high-probability) recursive rules. B-CFG contains recursive rules, but those rules have a small probability of expansion thanks to the non-recursive rules, which ‘‘absorb’’ much of the probability mass. Thus, B-CFG does not allocate as much probability mass to non-observed recursively-generated sentences and therefore over-generalizes less. The depth-limited grammar N-CFG over-generalizes

Figure 1. Log posterior probability of three grammars with three di¤erent types of NP rules. The grammar with both recursive and non-recursive rules (B-CFG) has higher probability than the either the depth-limited grammar (N-CFG) or the fully recursive grammar (R-CFG). Note that because log probability is negative, smaller absolute values correspond to higher probability. If two grammars have log probabilities that di¤er by n, their actual probabilities di¤er by e n. The grammar with the highest probability (B-CFG) is thus e63 times more probable than the grammar with the next highest (N-CFG). Note: log priors ¼ 1394 (B-CFG), 1471 (N-CFG), 1085 (R-CFG); log likelihoods ¼ 25827 (B-CFG), 25813 (N-CFG), 26375 (R-CFG).

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least of all since it lacks recursion entirely - but, as Chomsky predicted, such a grammar is more complex than the others, and it is penalized here on that basis. How might we interpret the preference for a grammar that contains recursive rules but also their non-recursive counterparts? Perhaps syntax, while fundamentally recursive, could usefully employ non-recursive rules to parse simpler sentences that recursive rules could parse in principle. This would not change the expressive capability of the grammar, but might dramatically decrease the cost of recursion. Indeed, if adult grammars contain both recursive and non-recursive rules, this (in addition to performance considerations) might partially explain the empirical lack of multiply-center-embedded sentences. Is the role of recursion di¤erent in subject and object noun phrases? There are several reasons to think it might be: people have much less di‰culty processing sentences with recursive object NPs, and the corpus contains many more recursively-generated object NPs than subject NPs. (For instance, the vast majority of subject NPs are pronouns or proper nouns, as in the sentences He fell or Bambi is home, whereas there are many more complex object NPs, as in the sentence Butch is a little boy who plays with Bozo the clown). Might the ‘‘shadow’’ recursive rules provide a benefit, then, only in the case of subject NPs? To test this we compare the grammars with distinct subject and object noun phrases. The results are shown in Figure 2. Several things are notable about these results. Interestingly, all of the grammars with distinct subject and object NPs have higher probability than any of the grammars without (in Figure 1). This supports the intuition that subject and object NPs have distinct properties. Also, as hypothesized, the ‘‘shadow’’ non-recursive elements provide a benefit when they occur in subject NPs, but not in object NPs. Indeed, grammars with only recursive NPO rules outperform grammars with both recursive and non-recursive NPO rules, which in turn outperform grammars without any recursive NPO rules at all. The story is di¤erent with subject noun phrases: there are so few recursive expansions of subject noun phrases in this corpus that grammars with only recursive productions perform extremely poorly. The depth-limited grammars have a somewhat higher probability, but (as before) do not fit the data well enough to compensate fully for their lower prior probability. The best-performing grammar of all, then, contains both recursive and non-recursive rules in subject NPs, but only recursive rules in object NPs, where the cost of recursion is far less.

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Figure 2. Log posterior probability of the nine grammars that systematically vary how recursion in NPS and NPO is represented. As before, because log probability is negative, smaller absolute values correspond to higher probability. Overall, the most probable grammar is the one whose subject NPs contain both recursive and non-recursive rules (B-CFG), but whose object NPs contain only recursive rules (R-CFG).

However, these results depend in an interesting way on the data. Because it is child-directed speech, the corpus contains many sentence fragments, including bare NPs. The results in Figure 2 occur when the grammar assumes that bare NPs are instances of subject noun phrases (a sensible choice, given the frequency and obligatoriness of subjects in English). If instead the sentence fragments are analyzed as instances of object noun phrases, the most preferred grammars contain depth-limited rules (i.e., no recursion) in the subject NP. This is reasonable since under such an analysis, none of the subject NPs in the corpus are of depth 2 or greater; a grammar with any recursive subject NP rules is therefore penalized in the likelihood while providing no benefit in prior probability. This suggests that the benefit of recursive rules occurs only if there is a high enough depth of embedding in the input. It also illustrates the sensitivity of our approach to the precise nature of the data, which is both a benefit and a limitation: a rational learner should be sensitive to the data, and our model is sensitive in reasonable and easily interpretable ways. However, it does underline the need for caution in interpreting these results: further investigation on a much wider range of corpora is necessary in order to

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draw strong conclusions about the nature of recursive rules in adult grammars of English.

4. Discussion This Bayesian framework for grammar induction can be used to quantitatively evaluate grammars with respect to one another (and a corpus of data) by calculating an ideal tradeo¤ between simplicity and goodness-offit. We employ this framework to evaluate the role of recursion, addressing whether a grammar with recursive noun phrases would be preferred by a rational learner even if the input – a corpus of typical child-directed speech – does not contain sentences with many levels of embedding. Our results suggest that depending on the distribution of recursively-generated sentences in the input, grammars that contain both recursive and corresponding non-recursive ‘‘shadow’’ elements may be most probable: these grammars maximize the tradeo¤ between simplicity (which favors recursive elements) and measures of goodness-of-fit (which generally do not). We are not claiming that adult grammars of English necessarily do contain shadow non-recursive rules. All of the grammars evaluated here are oversimplified in many ways, and our corpus consists of child-directed rather than adult-directed speech. Further work on a wider variety of corpora will therefore necessary to draw any definite conclusions. Our results do suggest that under some circumstances it may be rational to generalize beyond the input. In particular, we demonstrate that shadow rules may improve a grammar’s goodness-of-fit while allowing it to retain the expressive power (and some of the simplicity) of recursion. This suggests that a human learner might rationally conclude that particular rules have recursive versions given only finite, and realistic, input. That is, the knowledge that grammar can contain recursive rules need not be innate (although it could be, and a learner must be able to represent recursion so as to consider it as a hypothesis). In principle, future work based on these ideas could help to settle the debate over recursion in Piraha˜. One would need a representative corpus of Piraha˜ speech as well as (at least) two competing grammars of Piraha˜: one recursive and one non-recursive – as well as possibly others populating the representational middle ground we have explored here. Given this, an analysis directly analogous to the one we have pursued here would provide an objective basis for addressing this issue. This approach is valuable because it yields a rational, ideal standard by

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which it may be possible to judge human behavior, not because human learning is necessarily ideal. Bayesian methods o¤er what is arguably the best general way to formalize rational inductive inference (Jaynes 2003), and are consistent with an information theoretic perspective (Li and Vita`nyi 1997). Rational models of learning and inference based on Bayesian and information-theoretic statistical principles have been useful for understanding many aspects of human cognition (Anderson 1991; Chater and Oaksford 1999), including language (Chater and Manning 2006; Chater and Vita`nyi 2007; Dowman 2000). Even if human beings ultimately do not behave as a rational learner would, being able to establish how an optimal learner would perform provides an important means of evaluating how humans actually do perform, as it has here. References Anderson, John 1991 The adaptive nature of human categorization. Psychology Review 98 (3): 409–429. Bach, Emmon, Colin Brown, and William Marslen-Wilson 1986 Crossed and nested dependencies in German and Dutch: A psycholinguistic study. Language and Cognitive Processes 1: 249– 262. Brown, Roger 1973 A first language: The early stages. Cambridge, MA: Harvard University Press. Chater, Nick, and Chris Manning 2006 Probabilistic models of language processing and acquisition. Trends in Cognitive Sciences 10 (7): 335–344. Chater, Nick, and Mike Oaksford 1999 Ten years of the rational analysis of cognition. Trends in Cognitive Sciences 3: 57–65. Chater, Nick, and Paul Vita`nyi 2007 ‘Ideal learning’ of natural language: Positive results about learning from positive evidence. Journal of Mathematical Psychology 51 (3): 135–163. Chomsky, Noam 1956 Three models for the description of language. IRE Transactions on Information Theory 2: 113–123. Chomsky, Noam 1957 Syntactic structures. The Hague: Mouton. Chomsky, Noam 1959 On certain formal properties of grammars. Information and Control 2: 137–167.

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Chomsky, Noam 1965 Aspects of the theory of syntax. Cambridge, MA: MIT Press. Christiansen, Morten, and Nick Chater 1999 Toward a connectionist model of recursion in human linguistic performance. Cognitive Science 23 (2): 157–205. Dowman, Mike 2000 Addressing the learnability of verb subcategorizations with Bayesian inference. Proceedings of the 22nd Annual Conference of the Cognitive Science Society. Everett, Daniel 2005 Cultural constraints on grammar and cognition in Piraha˜: Another look at the design features of human language. Current Anthropology 46 (4): 621–646. Everett, Daniel 2007 Cultural constraints on grammar in Piraha˜: A reply to Nevins, Pesetsky, and Rodrigues (2007). http://ling.auf.net/lingbuzz/000427 Fitch, William Tecumseh, and Marc Hauser 2004 Computational constraints on syntactic processing in a nonhuman primate. Science 303: 377–380. Gentner, Timothy, Kimberly Fenn, Daniel Margoliash, and Howard Nusbaum 2006 Recursive syntactic pattern learning by songbirds. Nature 440: 1204–1207. Gibson, Edward 1998 Linguistic complexity: locality of semantic dependencies. Cognition 68: 1–76. Gold, E. Mark 1967 Language identification in the limit. Information and Control 10 (5): 447–474. Goldwater, Sharon, Thomas Gri‰ths, and Mark Johnson 2006 Interpolating between types and tokens by estimating power law generators. Neural Information Processing Systems 18. Hauser, Marc, Noam Chomsky, and William Tecumseh Fitch 2002 The faculty of language: What is it, who has it, and how did it evolve? Science 298 (5598): 1569–1579. Horning, James Jay 1969 A study of grammatical inference (Tech. Rep. No. 139). Stanford University. Jaynes, Edwin 2003 Probability theory: The logic of science. Cambridge: Cambridge University Press. Johnson, Mark 2006 Inside-outside algorithm. http://www.cog.brown.edu/~mj/code/ inside-outside.tgz Jurafsky, Daniel, and James Martin. 2000 Speech and Language Processing: An Introduction to Natural

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Language Processing, Computational Linguistics and Speech Recognition. Prentice Hall. Li, Ming, and Paul Vita`nyi 1997 An introduction to Kolmogorov complexity and its applications. New York: Springer Verlag. MacWhinney, Brian 2000 The CHILDES project: Tools for analyzing talk (3rd ed.). Lawrence Erlbaum Associates. Manning, Chris, and Heinrich Schu¨tze 1999 Foundations of Statistical Natural Language Processing. Cambridge, MA: MIT Press. Marks, Lawrence 1968 Scaling of grammaticalness of self-embedded English sentences. Journal of Verbal Learning and Verbal Behavior 5: 965–967. Miller, George, and Noam Chomsky 1963 Finitary models of language users. In Handbook of Mathematical Psychology, Vol. 2, R. Duncan Luce, Robert Bush, and Eugene Galanter (eds.), 419–492. New York: Wiley. Nevins, Andrew, David Pesetsky, and Cilene Rodrigues 2007 Piraha˜ exceptionality: A reassessment. http://ling.auf.net/lingBuzz/ 000411 Perfors, Amy, Joshua B. Tenenbaum, and Terry Regier under review The learnability of abstract syntactic principles. Cognition. Pinker, Steven, and Ray Jackendo¤ 2005 The faculty of language: What’s special about it? Cognition 95: 201–236. Solomono¤, Ray 1978 Complexity-based induction systems: Comparisons and convergence theorems. IEEE Transactions on Information Theory 24: 422–432. Weckerly, Jill, and Je¤rey L. Elman 1992 A PDP approach to processing center-embedded sentences. Proceedings of the 14th Annual Conference of the Cognitive Science Society, 139–156. Zipf, George 1932 Selective studies and the principle of relative frequency in language. Cambridge, MA: Harvard University Press.

Part III.

Evolutionary Perspectives

10.

Was recursion the key step in the evolution of the human language faculty?1

Anna R. Kinsella

1. Introduction Hauser, Chomsky and Fitch (2002) (HCF) propose that recursion is the core component underlying language, all other intricacies of our linguistic capacity the result of the recursive component interfacing with external systems of the brain called upon in the course of processing language. This article will assess HCF’s recursion-only hypothesis by asking four questions: (i) what do we mean by recursion?, (ii) is recursion unique to human language?, (iii) are there other unique properties in language?, and (iv) is language without recursion possible?

2. What do we mean by recursion? Definitions of recursion found in the linguistics and computer science literatures su¤er from inconsistency and opacity (Kinsella 2009). More importantly, they ignore two crucial details. Recursion is not the same as iteration, and there are di¤erent types of recursion. In natural language, representational recursion is exhibited by phrases embedded inside phrases of the same type: (1) Mary’s aunt’s brother’s dog’s ball is in the garden. [S[NP[NP[NP[NP[NPMary’s] aunt’s] brother’s] dog’s] ball] is in the garden]

1. This research was supported by a British Academy Postdoctoral Fellowship. Earlier versions of this work have been presented at EvoLang 6, held in Rome, April 2006, and at the RecHuL conference held at Illinois State University, April 2007. Thanks to the audiences there, and to three anonymous reviewers, for comments.

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(2) the man that kissed the girl that John met in the bar that Bill owns [NPthe man [CPthat kissed [NPthe girl [CPthat John met in [NPthe bar [CPthat Bill owns]]]]]] (3) The mouse the cat the dog chased bit ran. [SThe mouse [Sthe cat [Sthe dog chased] bit] ran] (1) and (2) exhibit tail recursion, phrasal embedding occurring at the beginning or end of the sentence/phrase. (3) exhibits nested recursion, embedding occurring in the center, such that material exists on both sides of the embedded component. In computing, a number of algorithms are best solved using procedural recursion. For example, to compute the factorial of an integer, the problem can be broken down into a smaller problem of the same type (the factorial of that integer minus 1). 2.1. Recursion versus iteration Iteration involves repetition of an action or object, where each repetition is entirely independent of those that come before and after. Recursion involves the embedding of an action or object inside another of the same type, each embedding being dependent in some way on the one it is embedded inside. Consider a non-linguistic example. In following recipe instructions such as stir the mixture until smooth, some action is completed over and over until a certain point is reached. This is iteration – each stirring action is a separate act, and does not rely on the preceding or following actions. Iteration allows for any repetition to be removed without the end result being altered. In cutting the resulting cake into eight even pieces, a recursive procedure is employed. First cut the whole cake in half, cut each of these two pieces in half, and cut each of those four pieces in half. An example of the divide-and-conquer method, the output of each action becomes the input to the next. Each division must take place in order, and unlike iteration, removing intermediate steps prevents the same result from being achieved. A crucial di¤erence between iteration and recursion is that only the latter involves keeping track or adding to memory using a pushdown stack. In baking the cake, we do not need to keep track of what point we are at. All we need to know is the terminating condition, at which point we can stop the stirring repetitions. When cutting the cake, if we lose track of what point we have reached, we do not know whether to divide the current piece or return to divide a piece left o¤ earlier.

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2.2. Tail versus nested recursion (1) to (3) introduced a distinction between two types of recursion. Like iteration, tail recursion does not require that we keep track. Further, it does not involve long-distance dependencies. These are implicated in nested recursion because embeddings occur in the middle of a sentence/ phrase. Nested long-distance dependencies entail the need to keep track in a stack fashion. Parsing (3), the NP the mouse must be held in memory and retrieved only once the element with which it agrees – ran – is reached. Only local dependencies are found in tail recursive structures. In parsing (1) the successive nouns that are encountered do not need to be pushed onto a stack, popping them o¤ when the head noun – ball – is reached. The memory requirements of nested recursion can also be framed in formal language theoretic terms. To generate nestedly recursive strings we require a type 2 context-free grammar, and the associated pushdown automaton (i.e., a finite automaton which makes use of a stack). Tail recursive strings can be generated by a less powerful type 3 machine, which does not incorporate a stack (Hopcroft et al. 2001). 2.3. Tail recursion versus iteration Consider (4) and (5): (4) Jack ate [NP1the sandwichNP1] and [NP2the doughnut NP2] and [NP3the appleNP3]. (5) [NP1 [NP2 [NP3John’sNP3] mother’s NP2] neighborNP1] bought the car. At the level of the string, both look to involve repeated NPs. The di¤erence only becomes clear at the level of the structure. Pragmatic issues aside, the labelled brackets reflect the typical structures assigned to such strings – flat for (4), recursively embedded for (5). The brackets are a proxy for the underlying semantics – the NPs in (4) are essentially independent of each other, while there are modification relations that hold between the NPs in (5). We can tell that these are the correct structural interpretations by considering what happens when the NPs are transposed. In (4), semantic equivalence holds, where this can be measured in terms of truth conditional semantics. In (5), the result is not semantically equivalent, the referent of the agent changing. Ordering constraints hold for (5), but not (4), identifying the former as tail recursion and the latter as simple iteration. Tail recursive algorithms can be coded iteratively, suggesting that tail recursion and iteration are equivalent. However, in

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natural language, semantics forces tail recursion and iteration to be understood di¤erently, indicating a di¤erence in structure not visible by considering strings alone. Clear definitions of iteration and recursion can now be formulated: Iteration: The simple, unembedded repetition of an action or object an arbitrary number of times. Recursion: The embedding at the edge (tail) or in the center (nested) of an action or object one of the same type. The output of the current embedded action or object will become the input to the next. Nested recursive embedding entails long-distance dependencies, and thus the need for keeping track or adding to memory.

3. Is recursion unique to human language? If recursion truly is unique to language, there are three places we should not find it: (i) human non-linguistic cognition, (ii) non-human non-communicative cognition, and (iii) non-human communicative cognition. 3.1. Human non-linguistic cognition A number of domains elsewhere in our cognition suggest themselves as recursive: number, navigation, vision, social cognition, music. Number must be ruled out as it may be intricately linked with language from an evolutionary perspective (Hurford 1987; Chomsky 1988). In navigation, the process of wayfinding can be conceived of along the lines of the algorithmic divide-and-conquer method. Visual decomposition of objects can be understood algorithmically in a similar fashion (Jackendo¤ and Pinker 2005). Music is hierarchically organized, but determining if musical phrases can be embedded inside each other recursively is impossible given that we are considering only strings with no pointer to the underlying structure. However, Hofstadter (1980) o¤ers a clearer case, where recursion is found in key change modulations. Complex pieces of music require the listener to push key changes onto a shallow stack, popping them o¤ once resolved. Our theory of mind provides perhaps the most uncontroversial example of non-linguistic recursion: I can embed the thoughts and knowledge of others within my own leading to recursively embedded conceptual structures.

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3.2. Non-human non-communicative cognition Possible recursive domains here include: number, navigation, complex action sequences, and social cognition. Number must be ruled out due to animals’ lack of understanding of the successor function, from which recursion stems. Studies within the travelling salesman paradigm (e.g., Cramer and Gallistel 1997) have yet to examine whether other species solve such tasks iteratively or recursively, but provide a starting point for investigating recursion in other species’ navigational abilities. Experimental research into other species’ complex action sequences (e.g., Byrne and Russon 1998; Whiten 2002) may also be a place to situate future research. Although theory of mind in other species is controversial, experimental research hints at the fact that non-human primates may have a level of social cognition that is recursive. Baboons classify themselves and their conspecifics into a linear hierarchy of dominance and matrilineal kin groups (Bergman et al. 2003), suggesting that they can form the conceptual structures represented in (6) and (7). These express tail recursive associations2 – phrases cannot be removed without a¤ecting the whole structure, nor re-ordered while maintaining the correct relations. (6) [X is mother of Y [who is mother of Z [who is mother of me]]] (7) [X is more dominant than Y [who is more dominant than Z [who is more dominant than me]]] 3.3. Non-human communicative cognition We can distinguish two types of animal communication system: (i) a nonhierarchically structured system with limited semantics, and (ii) a hierarchically structured system with no semantics. Examples of (i) include the honeybee dance, and the alarm call of the Campbell’s monkey (Zuberbu¨hler 2002), and examples of (ii) include the song of the Bengalese finch (Okanoya 2002), and the humpback whale (Suzuki et al. 2006). The lack of hierarchical embedding in (i) prevents recursion of any type. Recursion in (ii) is structurally possible. However, the lack of semantics prohibits

2. This assumes the baboons’ conceptual structures to be similar to ours. Although we think about our conceptual structures in linguistic terms, other species do not, making this correspondence somewhat uncertain.

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testing for tail recursion. Like music, we are looking only at strings, but a pointer to the underlying structure is required to distinguish tail recursion from iteration. However, complex enough strings could be used to identify nested recursion. It thus remains for future work to use these facts to narrow the research scope, designing experiments to diagnose the type of recursion in the type of system that is possible. Let us consider what we might look for in a hierarchically organized communication system to indicate nested recursion. Suzuki et al. (2006) report long-distance dependencies in humpback whale song. A birdsong system such as the following could plausibly also provide examples:

Figure 1. A birdsong system showing long-distance dependencies

The initial note determines the final note, no matter the notes that intervene. Importantly, this example, although clearly exhibiting a longdistance dependency, does not manifest nested recursion. In human language too long-distance dependencies can exist independently of nested recursion: er morgen fru¨h mit seiner (8) Das Kind ist froh, weil the child is happy because he tomorrow early with his Oma in den Park geht. grandmother in the park goes ‘The child is happy because he will go with his grandmother to the zoo tomorrow morning.’ Consequently, long-distance dependencies cannot be used as a diagnostic of nested recursion, making the problem of determining whether a hierarchically organized non-human communication system is recursive even more di‰cult.

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3.4. Answering the uniqueness question Although we cannot posit unambiguous positive evidence in many of the cases here, recursion appears not to be the defining factor in our uniqueness. A pointer to one of the features that may answer the uniqueness question can be found in the experiments of Fitch and Hauser (2004). Using a familiarisation/discrimination paradigm, human and tamarin subjects were exposed to strings generated by one of two grammars – a finite state grammar, (ab)n, and a context-free grammar, anbn – and later tested on their di¤erential reactions to new strings consistent with both the grammar they learned from, and the other grammar. The authors claim that while humans can learn both the finite state grammar and the more complex phrase structure grammar, tamarins are only capable of learning the finite state grammar. Despite claims of methodological flaws (Perruchet and Rey 2005), there may be an interesting alternative interpretation of these findings. If the (ab)n language was tail recursive, and the anbn language nestedly recursive,3 the di¤erence in processing abilities of humans and tamarins would not lie in phrase structure or in recursion, but in the di¤erence between tail and nested recursion. The hypothesis would be that although tamarins are capable of handling iterative or tail recursive strings, they cannot handle nestedly recursive strings which require a pushdown stack type of memory. Table 1 summarizes the findings of this section. What is particularly interesting is that while human cognition displays both tail and nested recursion, the suggested instances of recursion in non-human cognition are all of the tail variety. Perhaps the crucial step in the evolution of human language was not recursion, but an enhanced memory with the ability to store and retrieve in a stack fashion. 4. Are other properties unique to human language? HCF propose recursion to be ‘‘. . . the only uniquely human component of the language faculty’’ (1569). However, a list of features that are unique to language, and importantly, independent of recursion, can be formulated quite easily. 3. The meaningless syllables make it impossible to determine if the structure of the (ab)n strings is flat and iterative or hierarchical and tail recursive. The anbn strings could be processed nestedly recursively, or simply using a counter. The experiments would need to be redesigned to incorporate a pointer to the underlying structures.

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Table 1. Recursion in the cognitive systems of humans and animals Human Non-Communicative Cognition

Animal Non-Communicative Cognition

Animal Communication

Number

(

Number

X

Campbell’s Monkey

X

Navigation

?

Navigation

?

Honeybee

X

Games & Music

(*

Action Sequences

?

Bengalese Finch

X

Vision

(*

Social Cognition

?*

Tamarin

X

Theory of Mind

(*

Key: ( X ? *

recursion exhibited recursion not exhibited unclear if recursion is exhibited necessarily analysed as recursive

4.1. Structure dependence Berwick (1998) argues that structure dependence – the fact that sentences or phrases are not simply strings of linearly ordered words, but that the words and phrases that combine to make a sentence are related to, or dependent on, each other – falls out from the recursive combinatorial operation Merge assumed in Minimalist theories of syntax (Chomsky 1995). Yet it is far from clear that recursion in any sense can account for the facts seen in (9a–c). (9) a. The reluctant candidate should accept the position. b. Should the reluctant candidate accept the position? c. *The reluctant should candidate accept the position? The rule of subject-auxiliary inversion, employed in question formation in English, cannot simply count lexical items, but is sensitive to phrasal boundaries. This fact neither falls out of the Merge operation, or recursion as defined in section 2.3, making structure independence a feature unique to human language which is entirely independent of recursion. 4.2. Duality of patterning Duality of patterning – the fact that meaningful units of language (morphemes) can be broken down into units which are meaningless in isolation

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(phonemes), and which can be re-combined in di¤erent ways to give di¤erent meaningful units (Hockett 1960) – is a linguistic feature which seems to be absent from all other systems of communication and other human cognitive systems (Kinsella in press). It is further independent of recursion. It is true that we are dealing with the combination of meaningless units to give larger meaningful units in the same way that phrases are combined to give larger phrases or sentences, but there is no self-embedding of either phonemes or morphemes within themselves, and neither is there any sense of having to keep track of a phoneme while performing some other computation and then returning to that phoneme. 4.4. Syntactic devices Human language makes use of many syntactic devices which are both unique to language, and independent of recursion (Pinker and Jackendo¤ 2005). Case, agreement, pronouns, articles, quantifiers, articles, complementisers, auxiliaries, tense, and aspect all fall into this category. These devices will be absent in all cases of animal communication, as these communication systems cannot be said to have ‘syntax’ as it is defined for human language (Kinsella in press). In non-linguistic human cognitive domains, it is di‰cult to imagine what might constitute parallel mechanisms. Once more, these features of language are unrelated to the property of recursion. 4.5. The lexicon Lexical items are the core of language, yet fall outside the domain of recursion.4 They are not found elsewhere in cognition or in non-human communication. In our non-linguistic cognition, it might be suggested that facts are akin to lexical items. However, a lexical item consists of a form and a meaning, either of which can be used to look up the other, while facts lack this bi-directionality. Further, children learn lexical items in significantly di¤erent ways to facts – they rely on the mutual exclusivity bias when learning new words but not new facts (Markman 1989). It might be argued that vervet monkeys have a lexicon. Their alarm calls possess both form and meaning (or phonological and semantic 4. Pinker and Jackendo¤ (2005: 212) note that morphology ‘‘. . . constitutes the classical domain of recursion a` la HCF . . .’’ However, although lexical items can be formed by recursive processes, non-recursive processes abound – templates, a‰xation, umlaut, ablaut.

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features) – bidirectional units. However, there are no syntactic features associated with vervet alarm calls. Moreover, a human’s lexicon is immensely larger (even for a very young child) than a vervet’s. Quantitative does not necessarily imply qualitative di¤erence, but equating the lexicon of a natural language with what we find in other species seems somewhat extravagant. Furthermore, the lexicon is wholly learned by each and every generation using a particular language, in contrast to the innate vocabularies of other species (Oliphant 2000; Seyfarth and Cheney 1986).

5. Is language without recursion possible? Approaching the recursion-only hypothesis from another angle, we can ask if a communication system without recursion should be considered language. Recursion-less language would contradict the view of recursion as the defining property of language. Recent work (Everett 1986, 2005; Sakel & Stapert this volume) suggests that there may exist a language without recursive structures. Piraha˜ does not make use of CP-embedding or recursive possessors; juxtaposition, morphological markers, and pragmatic means are used to achieve the same results. Yet, Piraha˜ can express such concepts using alternative means. The implication of HCF that language with recursion is somehow better – ‘‘[i]n particular, animal communication systems lack the rich expressive and open-ended power of human language (based on humans’ capacity for recursion)’’. (1570) – thus fails if better is interpreted as more expressive. Fitch, Hauser and Chomsky’s (2005) claim that the status of Piraha˜ is entirely independent of the recursion-only hypothesis misses a crucial point. The Piraha˜ data tell us: (i) if the criterion for syntactic recursion is that there must be embedded inside a phrase one of the same type, Piraha˜ appears to lack syntactic recursion, (ii) Piraha˜ is a full human language – it cannot be equated with non-human communication systems, it exhibits uniquely human, uniquely linguistic features, that can only be acquired by the possessor of a human Language Acquisition Device, and (iii) ‘‘. . . Piraha˜ most certainly has the communicative resources to express clauses that in other languages are embedded . . .’’ (Everett 2005: 631). Faced with a full human language that can use alternate means to express recursive conceptual structures highlights the fact that recursion cannot be the one tool which serves to make language unique; it is just one in a larger set.

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6. Concluding remarks The take-home message is that recursion must be studied much more carefully. Even with conscientious analysis, many issues remain; however, the type of vague allusion evident in HCF, and the ensuing rejoinders, will only hamper progress in the field. The question posed in the title should be answered with a resounding no. Recursion exists in domains outside language in our species, and perhaps in other species too – recursion does not belong in the narrow language faculty. There are many properties of human language which are both specific to it, and independent of recursion – the narrow language faculty should thus be delineated di¤erently. Data from a full human language without recursion shows that recursion is not crucial to the communication system of our species. References Bergman, Thore, Jacinta Beehner, Dorothy Cheney, and Robert Seyfarth 2003 Hierarchical classification by rank and kinship in baboons. Science 302: 1234–1236. Berwick, Robert 1998 Language evolution and the minimalist program. In: James Hurford, Michael Studdert-Kennedy, and Chris Knight (eds.), Approaches to the Evolution of Language, 320–340. Cambridge: Cambridge University Press. Byrne, Richard and Anne Russon 1998 Learning by imitation: a hierarchical approach. Behavioral and Brain Sciences 21: 667–721. Chomsky, Noam 1988 Language and Problems of Knowledge: The Managua Lectures. Cambridge, MA: M.I.T. Press. Chomsky, Noam 1995 The Minimalist Program. Cambridge, MA: M.I.T. Press. Cramer, Audrey and Charles Gallistel 1997 Vervet monkeys as travelling salesmen. Nature 387: 464. Everett, Daniel 1986 Piraha˜. In: Desmond Derbyshire and Geo¤rey Pullum (eds.), Handbook of Amazonian Languages volume 1, 200–326. Berlin: Mouton de Gruyter. Everett, Daniel 2005 Cultural constraints on grammar and cognition in Piraha˜: Another look at the design features of human language. Current Anthropology 46: 621–646.

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Fitch, W. Tecumseh and Marc Hauser 2004 Computational constraints on syntactic processing in a nonhuman primate. Science 303: 377–380. Fitch, W. Tecumseh, Marc Hauser, and Noam Chomsky 2005 The evolution of the language faculty: Clarifications and implications. Cognition 97: 179–210. Hauser, Marc, Noam Chomsky, and W. Tecumseh Fitch 2002 The faculty of language: What is it, who has it, and how did it evolve? Science 298: 1569–1579. Hockett, Charles 1960 The origin of speech. Scientific American 203: 88–96. Hofstadter, Douglas 1980 Go¨del, Escher, and Bach: An eternal golden braid. London: Penguin. Hopcroft, John, Rajeev Motwani, and Je¤rey Ullman 2001 Introduction to Automata Theory, Languages and Computation (2nd edition). Reading, MA: Addison-Wesley. Hurford, James 1987 Language and number: The emergence of a cognitive system. Oxford: Blackwell. Jackendo¤, Ray and Steven Pinker 2005 The nature of the language faculty and its implications for evolution of language. Cognition 97: 211–25. Kinsella, Anna 2009 Language Evolution and Syntactic Theory. Cambridge: Cambridge University Press. Markman, Ellen 1989 Categorization and Naming in Children: Problems of Induction. Cambridge, MA: M.I.T. Press. Okanoya, Kazuo 2002 Sexual display as a syntactic vehicle: The evolution of syntax in birdsong and human language through sexual selection. In: Alison Wray (ed.), The Transition to Language, 46–64. Oxford: Oxford University Press. Oliphant, Michael 2002 Rethinking the language bottleneck: Why don’t animals learn to communicate? In: Kerstin Dautenhahn and Chrystopher Nehaniv (eds.), Imitation in Animals and Artifacts, 311–325. Cambridge, MA: M.I.T. Press. Perruchet, Pierre and Arnaud Rey 2005 Does the mastery of center-embedded linguistic structure distinguish humans from nonhuman primates? Psychonomic Bulletin and Review 12: 307–13. Pinker, Steven and Ray Jackendo¤ 2005 The faculty of language: What’s special about it? Cognition 95: 201–236.

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Seyfarth, Robert and Dorothy Cheney 1986 Vocal development in vervet monkeys. Animal Behavior 34: 1640–58. Suzuki, Ryuji, John Buck, and Peter Tyack 2006 Information entropy of humpback whale songs. Journal of the Acoustical Society of America 119: 1849–66. Whiten, Andrew 2002 Imitation of sequential and hierarchical structure in action: experimental studies with children and chimpanzees. In: Kerstin Dautenhahn and Chrystopher Nehaniv (eds.), Imitation in Animals and Artifacts, 191–209. Cambridge, MA: M.I.T. Press. Zuberbu¨hler, Klaus 2002 A syntactic rule in forest monkey communication. Animal Behavior 63: 293–299.

11.

When clauses refuse to be recursive: An evolutionary perspective1

Ljiljana Progovac

1. Introduction This article shows that even using the tools of Minimalism (e.g., Chomsky 1995) one can demonstrate that not all clause types are recursive. In particular, the argument is that even in English and other well-known languages there exists a structurally well-defined type of grammar which is not subject to syntactic subordination/recursion. This grammar is characterized by what I call Root Small Clauses (RootSCs), to be defined and discussed in more technical terms in Sections 5 and 6: (1) Everybody out! Family first! Me first! Case closed. Problem solved. Class in session. Point taken. Me in Rome. Him worry?! Her happy?! While these small clauses can be loosely attached to each other in some circumstances (2), they cannot embed one within another (3), and are not recursive in that sense: (2) Nothing ventured, nothing gained. Monkey see, monkey do. (3) *Him worry [me first]. *Her happy [case closed]. *Him worry [her happy [problem solved]]. (cf. He worries that I will be first. She is happy that the case is closed. He worries that she is happy that the problem is solved ).

1. For many good comments and discussions regarding various ideas in this paper, I am grateful to: Martha Ratli¤, Natasha Kondrashova, Eugenia Casielles, David Gil, Dan Seeley, Rafaella Zanuttini, Richard Kayne, John Locke, Tecumseh Fitch, Dan Everett, Eva Juarros-Daussa, as well as the (other) audiences at 2007 GURT, 2007 ILA, 2007 Max Planck Institute Workshop on Complexity, Leipzig, Germany, and 2007 Illinois State University Workshop on Recursion in Human Language. I am especially grateful to the three anonymous reviewers for their careful and stimulating comments.

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My conclusion will be that recursive subordination (i.e., embedding of one clause within another) is only possible with syntactically more complex clauses, in which some relatively specific functional glue/category is available (Section 4). If so, then the recursive power of language cannot be attributed to Merge alone, contra the hypothesis put forth in Chomsky (2005); Hauser, Chomsky, and Fitch (2002); and Fitch, Hauser, and Chomsky (2005). To put it another way, I will argue that it is possible to have a coherent human grammar which makes use of Merge, but which is not recursive. If so, then recursion cannot be the defining property of human language. Nor can Merge be considered the only evolutionary breakthrough for syntax. Furthermore, I hypothesize that the grammar instantiated by RootSCs in e.g., English can be seen as a vestige/‘‘living fossil’’ of an evolutionary stage of morpho-syntax which had Merge, but which utilized no functional categories necessary for embedding, and which, for that reason, could not exhibit (recursive) subordination (Section 2). This perspective opens up a new way of looking at some puzzling constraints in syntax, including Subjacency (Section 3).

2. Evolutionary perspective on small clauses and recursion My proposal is that the RootSC grammar is a vestige/‘‘living fossil’’ of an evolutionary stage of morpho-syntax which utilized no functional categories (such as Tense, structural case, complementizers) (see Progovac 2008a, 2009a, 2009b; see also Bickerton 1990 and Jackendo¤ 1999, 2002 for the notion of syntactic fossils).2 What I consider here to be preserved is the RootSC syntax, and our ability to tap into it, rather than any particular present-day realizations of such syntax. Once tense (and/or other functional categories) emerged, they were superimposed on RootSCs, letting them survive, albeit in marginalized roles.3 Crosslinguistically, small clauses are both pervasive and robust syntactic constructs, occurring in root contexts (as RootSCs, Sections 5, 6), as 2. According to Ridley (1993: 525), ‘‘living fossils’’ are species that have changed little from their fossil ancestors in the distant past, such as e.g., lungfish. 3. Similar stratification accounts have been proposed for brain development, as well as the development of complexity in general, where newly emerged patterns become dominant and ‘‘rework’’ older patterns into conformity with them (Rolfe 1996; Vygotsky 1981).

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integrated ECM small clauses (Section 4), as loosely attached adjuncts and conjuncts (Section 3), and they also serve as foundation for building full clauses, according to modern syntactic theory. Moreover, RootSCs (also ‘‘root infinitives’’) arguably characterize a stage in language acquisition and are frequently resorted to in agrammatic aphasia (e.g., Jakobson 1941; Bickerton 1990; Ouhalla 1991; Gil 2005; Kolk 2006).4 The so-called two-word stage in L-1 acquisition of e.g. English can be characterized as involving RootSCs, as well as by probable absence of Move (e.g., Radford 1990; Lebeaux 1988; Ouhalla 1991; Platzak 1990; Potts and Roeper 2006).5 In other words, the first syntactic, or proto-syntactic, stage of language may have been a stage where two words were combined into a single utterance (e.g., Bickerton 1990; Jackendo¤ 1999), with possibly mainly prosody serving to hold it together.6 It has been proposed that intonation and prosody, which are modulated analogically, rather than discretely, were available before syntax (Deacon 1997; Piattelli-Palmarini and Uriagereka 2004; Burling 2005). It is conceivable that such RootSC stage, basically a predication stage, was followed by a proto-coordination stage, a stage in which a functional category emerged, a proto-coordinator, whose sole purpose was to hold the utterance together by more than just prosodic means (see Progovac 2009b). It would have been only later that such proto-coordinators differentiated into specific functional categories, such as aspect, tense, or subordinators.

4. According to Studdert-Kennedy (1991) and Rolfe (1996), present-day views of ontogeny/phylogeny warrant the use of ontogeny, development in children, to corroborate hypotheses about phylogeny, development in species (see also Carroll 2005). As pointed out in Ridley (1993), the relationship between ontogeny and phylogeny has been a classic topic in evolutionary studies. 5. For references and discussion of alternative views, see e.g., Guasti (2002). 6. A reviewer wonders whether a binary pattern is necessary even in the absence of (complex) structure. This is an interesting question, about which I can only speculate here. Suppose that this essentially binary system of putting two words together (or two small clauses together, as in the examples such as [2; 4]), is cognitively the simplest type of grammar. If so, then it would stand to reason that this early stage of grammar would be characterized by binary merges only. In fact, this binary principle could have then intergraded into more complex grammars, once they became available, rendering all syntactic structure binary. This would then represent a case of continuity in the evolution of syntax.

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A reviewer points out that this, and similar evolutionary approaches to language, are ‘‘just-so-stories’’. But isn’t any hypothesis? And isn’t also Chomsky’s (2005) conclusion that syntax, in all its complexity and quirkiness, must have arisen through one single cataclysmic event, perhaps one gigantic mutation, which brought about Merge? Wasn’t the theory of evolution itself a just-so-story at one point? Interestingly, it has become almost automatic to derogate any evolutionary hypothesis about language as just-so-story, if one prefers a di¤erent story. Understanding how and why syntax evolved has to be a result of an investigation, rather than a prerequisite for it, and any such investigation can succeed only if it is open to exploring di¤erent and diverse hypotheses, or ‘‘stories’’, if one prefers to call them that. In addition to being able to shed light on the availability of various quirky syntactic constructions (seen here as evolutionary fossils), one good consequence of this particular ‘‘story’’ that I am exploring in this paper is that it can begin to make sense out of some abstract principles of syntax, such as Subjacency, the principle which has largely remained unexplained in syntactic theory, even though it has been in the spotlight for several decades. Ultimately, I believe, the strongest arguments for a gradualist evolution of syntax will be, not the ones that show that it is possible to derive syntax gradually, but the ones that show that syntax cannot be derived otherwise.

3. A di¤erent angle on Subjacency/Island e¤ects Although bare small clauses cannot embed one within another (Sections 1, 5, 6), they can participate in a loose paratactic relationship, as in e.g., proverbs or wisdoms:7 (4) Nothing ventured, nothing gained. / Easy come, easy go. / Monkey see, monkey do. These clauses have no auxiliaries or subordinators, and their expressive power is di‰cult to match with any finite counterpart (see Stump 1985 and references there for the same conclusion regarding absolute construc7. Notice that even this paratactic (loose) attachment (4) a¤ords the expression of temporal/causal relatedness, an interpretational possibility not available with just two isolated utterances in (i): (i)

Nothing ventured. Nothing gained.

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tions; see also Potts and Roeper 2006 on expressiveness). Of note is also that bare small clauses, whether paratactically combined (5b), or not (5a), cannot be manipulated by Move(ment): (5) a. b.

*Who(m) worry? *Where me? *What closed? *What ventured, nothing gained? / *How easy come, t go?

Neither Move nor recursion is an automatic consequence of Merge. One may be tempted to say here that small clauses such as Him worry or Me first do not involve ‘‘real’’ Merge (see e.g. Potts and Roeper 2006 for a discussion that can be interpreted along these lines; see also Progovac et al. 2006 for a response). But this is clearly a circular argument: in order to keep the claim that Move and recursion are automatically available with Merge, one has to conclude that, where a merger of two words into a clause does not license Move or recursion, it is not real Merge. Besides, these small clauses involve predication, and in Minimalism an argument is always considered to Merge with its predicate via ‘‘real’’ Merge, typically, in fact, in a small clause. If one concludes that the clauses in e.g. (1) are not constructed with ‘‘real’’ Merge, then one would have to draw the same conclusion for the beginnings of any clause, where an argument and a predicate initially combine in a small clause – see Progovac (2006) for arguments showing that the two types of small clauses are syntactically the same. Bare small clauses can also combine with finite clauses, either as paratactic attachments in adverbial (absolute) functions (6) (Jackendo¤ 2002) or with coordination (7) (Jespersen 1954):8 (6) [Us having left], he reverted to his old ways. (7) I am not going to have any woman rummaging about my house, and [me in bed]. The subjects of the small clauses in (6–7) do not receive structural case at all (note the default accusative on subject pronouns). The fact that these bare small clauses, whose subjects lack structural case (or any other means of being integrated into the matrix clause), can occur adjoined or coordinated suggests that coordination and adjunction still tolerate Merge of syntactically semi-integrated structures.

8. See also Stump (1985) and references there for a wealth of data illustrating the absolute constructions comparable to the one in (6).

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If constructions of varying degrees of integration into syntactic fabric can find themselves in the same sentence, this opens up a possibility to look at the principle of Subjacency in a completely di¤erent light. Subjacency is a principle taken to constrain Move(ment) out of certain syntactic ‘‘islands’’, such as conjuncts, adjuncts, subjects, wh-clauses, and relative clauses (Ross 1967). It may be that adjuncts and conjuncts, because they are not fully integrated into the sentence, do not allow movement to flow across their boundaries: (8) *What did Peter invite some guest over [and Lisa bought t]? (9) *What did Peter invite some guests over [after Lisa bought t]? Movement seems to require a well-defined hierarchical ladder of specialized functional projections along which the moved element can climb (cf. the notion of ‘‘extended functional projection’’), a ladder which may not be interrupted by an unintegrated link. If RootSCs introduced above have no relevant functional categories (see Sections 5, 6), then it is expected that they will not allow movement, whether they occur in isolation, or paratactically attached to another clause (the examples in [5]). Deutscher (2000) argues that the development of finite subordination in Akkadian led to higher inter-clausal cohesion. He reconstructs stages proceeding from least syntactically integrated (parataxis), to more integrated (coordination), to most integrated (finite subordination), which are typical stages reported in grammaticalization of finite subordination (e.g., Trauggot and Heine 1991 and references there). (10) He is crazy – you know it.

(Parataxis)

(11) He is crazy, and you know it.

(Coordination)

(12) You know that he is crazy.

(Subordination)

Languages that do not make use of finite subordination have been reported to exist today (e.g. Dixon 1995 for Dyirbal; Mithun 1984, this volume, for various Native American languages). Most recently, Everett (2005, 2007) has argued that Piraha˜ lacks recursion altogether, including subordination, the latter conclusion also reinforced by Sakel and Stapert’s work (this volume). Everett has also emphasized the reliance of Piraha˜ on the immediate context (his IEP), which also seems relevant for RootSCs in English and Serbian (Sections 5, 6). It will be shown in Section 4 that bare (i.e., unintegrated) small clauses are not licit in complement positions, complement positions being the

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freest not only when it comes to recursive subordination, but also when it comes to (long-distance) extraction: (13) What did Peter say [that Mary believed [that John’s friends bought t?]] If so, it may prove productive to look at Subjacency as an epiphenomenon of the degree of syntactic integration of various constructions, which in turn can be seen as a residue of evolutionary tinkering with syntactic structure (see Progovac 2008c for details). Contrary to the view that Subjacency cannot be captured by gradual emergence of syntax (see e.g., Lightfoot 1991), it may be that gradual emergence of syntax, and the residue of intermediate steps, is the only way to approach Subjacency. To date, there has been no satisfactory analysis of Subjacency as a principle in its own right (see e.g., Szabolcsi and den Dikken 2003); most accounts stipulate which syntactic nodes, and/or which combination of nodes, and/or nodes in which syntactic positions, constitute barriers to movement (some classic accounts are Huang 1982; Lasnik and Saito 1984; Chomsky 1986).9 In other words, instead of assuming that Move and recursion just become available automatically and freely with Merge, and then need to be constrained by certain abstract principles such as Subjacency (as monsters that need to be tamed, as put in Joshi 2007), it may well be that syntactic Move, as well as subordination and recursion in general, become possible (and indeed motivated) only upon the development of layer upon layer of functional structure, which Move serves to connect.

4. Types of embedded clauses Consider the following two types of subordination (i.e., embedding of one clause inside another), one which involves most syntactic structure, finite subordination with a CP (Complementizer Phrase) (14), and one which involves least structure, a small clause (SC) (15), abstracting away from intermediate cases, such as infinitive clauses.

9. Moreover, some of these obstacles are considered weak and some strong (see also Stepanov 2007). Belletti and Rizzi (2000) report an interview with Chomsky, in which he says that there is no really principled account of many island conditions.

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(14) Mary believes [that John knows [that the neighbors noticed [that he fell o¤ his motorcycle]]]. (15) a. b.

Let [it be]. Peter saw [Mike fall]. I consider [the problem solved]. ?I will let [John imagine [Peter see [Mike fall o¤ his motorcycle]]].

In contrast to finite subordination, which is recursive in the sense that one clause can be iteratively embedded inside another (14), potentially ad infinitum, small clause subordination shows limited recursion, as the marginal status of (15b) suggests (see also Verhagen, this volume). The commonly accepted analysis of small clauses (e.g., Stowell 1983, adopted in Chomsky 1995) treats them as projections of predicates, without any clausal functional projections such as T(ense) P(hrase) or CP.10 However, the subjects of embedded SCs have a structural (case) relationship with the matrix verb, the so-called ECM case,11 suggested by the required adjacency with the verb (no intervening adverbials) (16), and by the required determiner (17).12 (16) *Peter saw yesterday [Mike fall]. *I consider crucially [the problem solved]. (17) I consider [*(the) problem solved]. I consider [*(the) class in session]. Both types of embedding exploit some functional glue to ‘‘cement’’ the relationship between the two clauses: complementizers/subordinators (14) or structural case (15). Complementizer glue is more specific (typically only used for finite subordination), while structural case is used for other purposes as well. This may be one reason why recursion is freer with finite subordination (see also Deutscher 2000). It may be that finite subordination allows recursion more freely because it is more unambiguously marked for embedding than are small clauses. But can there exist clauses which avail themselves of even less specific functional glue, or of no

10. But see Cardinaletti and Guasti (1995) for di¤erent views. 11. ECM stands for Exceptional Case Marking: the verb here is assigning structural case to a noun phrase which is not its argument. 12. DP is taken to be required for structural case in e.g. English and Italian (Longobardi 1994; see also Section 5). For an elaborate argument with regard to small clauses in this respect, see Progovac (2006).

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syntactic glue at all, and which are consequently not able to embed (recursively) one within another? I argue that there are indeed such syntactic structures, even in wellknown present-day languages: these are small clauses whose subjects have no structural relationship with any case assigner, and instead surface in the ‘‘default case’’ (see Sections 5 and 6). Such clauses can be attached to other clauses by adjunction/parataxis or coordination (where I call them ‘‘bare SCs’’), as discussed in Section 3, but they are also found in isolation, in root contexts, where I call them ‘‘RootSCs’’, as discussed in the following two sections.

5. Root Small Clauses in English Here I present several types of Root Small Clauses (RootSCs), i.e., small clauses found in root contexts (in isolation), which all instantiate the same type of rudimentary but coherent grammar (see Progovac 2006, 2008a, 2009a, 2009b). Irrealis clauses (incredulity/imperative/optative) (18) Him worry?! Her happy?! Everybody out! Head first! Family first! Me first! Contextually situated or formulaic RootSCs (19) Case closed. Problem solved. Class in session. Point taken. Me in Rome. The clauses in (18–19) show no tense or structural case: the subject pronouns surface in the (default) accusative case, and the verbs, if used at all, surface in non-finite forms (e.g., non-agreeing worry or participle solved ).13 In the spirit of Stowell’s analysis of embedded ECM small clauses (examples in [15a], repeated below), I have analyzed RootSCs as tenseless syntactic constructs; however, in contrast to the ECM small clauses in (15), the subjects of the clauses in (18-19) are in the default case. (15) a.

Let [it be]. Peter saw [Mike fall]. I consider [the problem solved].

13. See Schu¨tze (2001) for a characterization of Default Case; see also Roeper’s (1999) notion of Default Grammar.

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Not only do subject pronouns in RootSCs (18–19) surface in the accusative case, without there being any accusative case assigner, but the nouns do not require articles, i.e., need not project a DP, the projection considered to be required for structural case-checking in ECM clauses (example [17], repeated below): (17) I consider [*(the) problem solved]. I consider [*(the) class in session]. One semantic consequence of no tense/TP is the preponderance of nonindicative/irrealis interpretations (e.g., incredulity, optative, imperative); another is reliance on context, typically that of the here-and-now (see also Section 6). One may be tempted to analyze what I call RootSCs, both in English and Serbian (Section 6), as finite clauses which have undergone deletion/ ellipsis of relevant categories, such as finite verbs and articles. In addition to facing the theoretical problem of constraining such deletion/ellipsis, an ellipsis analysis cannot even begin to explain either syntactic or semantic properties of these clauses, nor can it explain their resistance to recursion. Even though they are coherent semantic and syntactic structures, these bare small clauses cannot embed one within another, i.e., they are not recursive (see also Potts and Roeper 2006): (20) a. b. c. d. e.

*Him worry [(that) me first]?! *Her happy [(that) Peter retire]?! *If problem solved, (then) me first! *Me happy [(that) problem solved]/[(that) case closed]. *Him worry [me happy [case closed]].

It is also important to point out that these RootSCs are quite productive: every clause seems to have a RootSC counterpart. In fact, in modern syntactic theory, every clause (finite or non-finite) is taken to be derived from a small clause (for an evolutionary perspective on this, see Progovac (2008a, 2009a, 2009b).14 14. A reviewer wonders, if I understand correctly, whether these clauses should even be considered as syntactic creations, rather than as memorized chunks of language. It is true that many of these constructions are (semi-)formulaic, and they indeed may also be stored in the Lexicon as such, e.g. Case closed, Problem solved, etc. However, many such clauses clearly express novel propositions, such as the Serbian unaccusative clauses discussed in Section 6, as well as the English Him worry?!, John worry!?, Me in Rome, Peter in Japan, etc.

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6. Unaccusative Root Small Clauses in Serbian In addition to RootSC types illustrated in Section 5, Serbian also has unaccusative RootSCs, which are quite productive, and which provide an additional (word order) argument for RootSC syntax (see Progovac 2008b): (21) Stigla posˇta. /Pala vlada. / Dosˇla zima. / arrived.FSG mail fallen.FSG government come.FSG winter /Umro Petar. died.MSG Peter ‘The mail has arrived./The government has collapsed./The winter has come./Peter died.’ These clauses share two properties with the RootSCs of Section 5.15 First, they do not show tense, the auxiliary being missing.16 Second, the subjects are arguably in the default case, nominative serving as the default case in Serbian, as established on independent grounds. Unaccusative verbs (e.g., arrive, fall ) are crosslinguistically analyzed as taking an internal (theme) argument, which first merges as a complement (object) of the verb, and then remerges/moves to become the subject of the sentence/TP (Perlmutter 1978; Burzio 1986). Significantly, these unaccusative RootSCs in Serbian are only acceptable with this basic/underlying word order, in which the subject follows the verb. In contrast, the finite counterparts of these clauses, which feature an auxiliary verb, are grammatical with either word order. Progovac (2008b) attributes this word The interesting question is why so many RootSCs are formulaic, and frequently occur in proverbs as well. I believe that this is another instance of specialization between small clause syntax and finite syntax (see also Section 6): being shorter and more compact, small clauses are more likely to be selected as formulaic expressions. Moreover, given the evolutionary view I explore (Section 2), it is entirely possible that the proto-syntactic RootSC creations were not productive at first, but were subjected to memory, until a critical mass of such memorized clauses paved the way to productive syntax. What we are seeing then among the RootSCs of today is a mix of both types. 15. The closest counterparts to these in English would be frozen uses of come followed by the subject, in dependent clauses: (i) [Come winter], they will go to Florida. 16. The verb is in the non-finite participle form, which, like adjectives in Serbian, shows gender and number agreement with the subject, but not person agreement, which only surfaces on finite verbs.

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order curiosity of RootSCs in (8) to the lack of a TP projection, and thus to the lack of any motivation for subject movement. Crucially, these clauses cannot embed (23), in sharp contrast to their finite counterparts, which are fully recursive (22): (22) a.

Ja znam [CP da je posˇta stigla.] I know that AUX mail arrived [CP da je vlada pala.] that AUX government fallen [CP da je Petar umro.] that AUX Peter died ‘I know that the mail has arrived/ that the government has collapsed/ that Peter died.’

b.

Ja znam [CP da si ti video [CP da je posˇta I know that AUX you saw that AUX mail stigla.]] arrived

(23) *Ja znam [(da) stigla posˇta]. / *Ja znam [(da) pala vlada]. / *Ja znam [(da) umro Petar]. This shows that there are clauses which express propositional content, and which are in productive use, but which cannot embed/are not recursive. At first sight, it may seem that these clauses should be able to embed if the complementizer da is used, given that complementizers are supposed to provide the specific functional glue, as per the discussion in Section 4 (the same holds for the examples in [20] above). However, in syntactic theory it is considered that there is a hierarchy of functional projections such that each functional category selects the next (e.g. Abney 1987; Adger 2003). In this concrete case, a CP (Complementizer Phrase) is considered to select a TP (Tense Phrase). This means that if a clause does not have a TP to begin with, it cannot build a CP or use a complementizer/ subordinator. Serbian data illustrated in (22–23) conform to this pattern. The subordinate clauses with the tense auxiliary are introduced by the complementizer, and are fully recursive (22), while the clauses without the tense auxiliary cannot take a complementizer and cannot embed at all (23). Quite clearly, these data cannot be attributed to any cognitive restrictions: the ability to embed examples in (22), but not those in (23), depends

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solely on the structural properties of these two types of clauses. The significance of this for the evolutionary argument is that one may in principle be capable of recursive thought, but cannot express it through language if the structural properties of language are limited in this way. In addition, given these data and analysis, one can envision a gradualist approach to the evolution of syntax, leading to the development of recursion. Another restriction (and specialization of RootSCs), which also follows from the absence of grammatical tense, is that these RootSCs pertain only to the present situation, to the here-and-now (see Progovac 2008b), evoking Everett’s (2005, 2007) Immediacy of Experience Principle (IEP). These clauses cannot be used to refer to some remote past event: (24) ?*Me first three years ago!

?*Case closed three years ago.

(25) ?*Umro Petar pre tri godine. ‘Peter died three years ago.’

?* Pala vlada pre tri godine. ‘The government collapsed three years ago.’

Of note is also the redundancy in the system, i.e., the ability to express the same propositional content with both finite and RootSCs – all the clauses in (21) have perfectly available finite counterparts. This redundancy also invites evolutionary explanations (see Progovac 2008b for more on the division of labor between these two types of clauses, and for the frequent formulaic nature of RootSCs; see also Note 14). As put in Carroll (2005: 170–171), ‘‘multifunctionality and redundancy create the opportunity for the evolution of specialization through the division of labor . . .’’ In fact, each of the individual claims regarding lack of recursion that Everett makes for Piraha˜ seems to hold true of certain constructions in well-known languages as well. As argued in this paper, there is a coherent clausal grammar, the Root Small Clause grammar, which does not allow subordination/recursion even in English. There are also non-recursive possessive constructions across languages, including in Serbian. Moreover, subordination, as well as recursive possessives, are a rather late development in children, as has been reported in numerous references (e.g., Radford 1990; Potts and Roeper 2006; Verhagen, this volume; Hollebrandse and Roeper 2007). This situation on the ground is better approached by assuming that languages have an option to build recursive syntax for individual grammatical constructions (see also Perfors et al., this volume), by developing specialized functional glue, rather than by assuming that recursion is available everywhere and always in language.

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7. Concluding Remarks My first goal was to establish that there can exist, and does exist, a coherent human grammar, which can express propositions, and even combine propositions, but which does not allow recursion, or even subordination at one level. The rudimentary grammar I have identified here, based on small clauses, can be found in various constructions – it is a crosslinguistic and wide-spread phenomenon. My second goal was to construct an argument that this rudimentary grammar was, at some point in the evolution of human language, the only available grammar, which served as a foundation for building more complex grammars. What we witness today in various small clause constructions are fossils/traces of this evolutionary stage of grammar. Finally, if a human grammar with Merge, but without recursion (or Move), is possible, as I have argued, then recursion cannot be the defining property of human language, and neither can Merge alone be responsible for all the recursive power of language, contra the hypothesis put forth in Chomsky (2005); Hauser, Chomsky, and Fitch (2002); and Fitch, Hauser, and Chomsky (2005). While I agree with the claim that Merge must have been a major breakthrough in the evolution of syntax, the data and analysis in this paper point to the conclusion that Merge was not at all the only breakthrough, and that the advent of Merge did not automatically bring with it either Move or recursion. Merge is a necessary, but not su‰cient, condition for recursion. If so, then syntax must have developed through additional discrete stages, accreting layers of functional structure, which eventually yielded grammars with recursion.

References Abney, Steven P. 1987 The English noun phrase in its sentential aspect. Ph.D. diss, Massachusetts Institute of Technology. Adger, David 2003 Core Syntax: A Minimalist Approach. Oxford: Oxford University Press. Belletti, Adriana, and Luigi Rizzi 2000 An Interview on Minimalism, with Noam Chomsky, the University of Siena, November 8–9, 1999; revised March 16, 2000; available at: http://www.media.unisi.it/ciscl/pubblicazioni.htm.

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Bickerton, Derek 1990 Language and Species. Chicago: University of Chicago Press. Burling, Robert 2005 The Talking Ape: How Language Evolved. Oxford: Oxford University Press. Burzio, Luigi 1986 Italian Syntax: A Government-Binding Approach. Dordrecht: Kluwer. Cardinaletti, Anna, and Maria Teresa Guasti (eds.) 1995 Syntax and Semantics 28: Small Clauses. San Diego: Academic Press. Carroll, Sean B. 2005 Endless Forms Most Beautiful: The New Science of Evo Devo and the Making of the Animal Kingdom. New York: W. W. Norton & Company. Chomsky, Noam 1986 Barriers. Cambridge, MA: MIT Press. Chomsky, Noam 1995 The Minimalist Program. Cambridge, MA: MIT Press. Chomsky, Noam 2005 Three factors in language design. Linguistic Inquiry 36: 1–22. Deacon, Terrence W. 1997 The Symbolic Species: The Co-evolution of Language and the Brain. New York/London: W.W. Norton & Company. Deutscher, Guy 2000 Syntactic Change in Akkadian. The Evolution of Sentential Complementation. Oxford: Oxford University Press. Dixon, Robert M. W. 1995 Complement clauses and complementation strategies. In: Frank R. Palmer (ed.), Grammar and Meaning, 175–220. Cambridge: Cambridge University Press. Everett, Dan 2005 Cultural constraints on grammar and cognition in Piraha˜: Another look at the design features of human language. Current Anthropology 46.4: 621–646. Everett, Dan 2007 Cultural constraints on recursion. Paper presented at the Workshop on Recursion in Human Language, Illinois State University, Normal, IL, April 2007. Fitch, W. Tecumseh, Marc D. Hauser, and Noam Chomsky 2005 The evolution of the language faculty: Clarifications and implications. Cognition 97: 179–210. Gil, David 2005 Isolating-monocategorial-associational language. In: Henri

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Cohen and Claire Lefebvre (eds.), Handbook of Categorizaton in Cognitive Science, 347–379. Amsterdam: Elsevier. Guasti, Maria Teresa 2002 Language Acquisition: The Growth of Grammar. Cambridge, MA: MIT Press. Hauser, Marc, Noam Chomsky, and W. Tecumseh Fitch 2002 The language faculty: What is it, who has it, and how did it evolve? Science 298: 1569–1579. Hollebrandse, Bart, and Thomas Roeper 2007 Recursion and propositional recursivity. Paper presented at the Workshop on Recursion in Human Language, Illinois State University, Normal, IL, April 2007. Huang, James 1982 Logical relations in Chinese and the theory of grammar. Ph.D. diss, Massachusetts Institute of Technology. Jackendo¤, Ray 1999 Possible stages in the evolution of the language capacity. Trends in Cognitive Sciences 3.7: 272–279. Jackendo¤, Ray 2002 Foundations of Language: Brain, Meaning, Grammar, Evolution. Oxford: Oxford University Press. Jakobson, Roman 1941 Child Language, Aphasia and Phonological Universals. Translation published by Mouton, the Hague, in 1968. Jespersen, Otto 1954 A Modern English Grammar. Part III: Syntax. London: Allen and Unwin. Joshi, Aravind 2007 Uniform and non-uniform recursion. Paper presented at the Workshop on Recursion in Human Language, Illinois State University, Normal, IL, April 2007. Kolk, Herman 2006 How language adapts to the brain: An analysis of agrammatic aphasia. In: Ljiljana Progovac, Kate Paesani, Eugenia Casielles, and Ellen Barton (eds.), The Syntax of Nonsententials: Multidisciplinary Perspectives, 229–258. Amsterdam/Philadelphia: Benjamins. Lasnik, Howard, and Mamoru Saito 1984 On the nature of proper government. Linguistic Inquiry 15: 235– 289. Lebeaux, David 1988 Language acquisition and the form of grammar. Ph.D. diss, University of Massachusetts, Amherst. Lightfoot, David 1991 Subjacency and sex. Language and Communication 11: 67–69.

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Longobardi, Giuseppe 1994 Reference and proper names: A theory of N-movement in syntax and Logical Form. Linguistic Inquiry 25: 609–665. Mithun, Marianne 1984 How to avoid subordination. Proceedings of the Tenth Annual Meeting of the Berkeley Linguistics Society, 493–509. University of California, Berkeley. Ouhalla, Jamal 1991 Functional Categories and Parametric Variation. London: Routledge and Kegan Paul. Perlmutter, David 1978 Impersonal passive and the Unaccusative Hypothesis. Proceedings of the Fourth Annual Meeting of the Berkeley Linguistics Society, 159–189. University of California, Berkeley. Piattelli-Palmarini, Massimo, and Juan Uriagereka 2004 Immune syntax: The evolution of the language virus. In: Lyle Jenkins (ed.), Variation and Universals in Biolinguistics, 341– 377. Oxford: Elsevier. Platzak, Christer 1990 A grammar without functional categories: A syntactic study of early child language. Nordic Journal of Linguistics 13: 107–126. Potts, Christopher, and Thomas Roeper 2006 The narrowing acquisition path: From expressive small clauses to declaratives. In: Ljiljana Progovac, Kate Paesani, Eugenia Casielles, and Ellen Barton (eds.), The Syntax of Nonsententials: Multidisciplinary Perspectives, 183–201. Amsterdam/Philadelphia: Benjamins. Progovac, Ljiljana 2006 The syntax of nonsententials: Small clauses and phrases at the root. In: Ljiljana Progovac, Kate Paesani, Eugenia Casielles, and Ellen Barton (eds.), The Syntax of Nonsententials: Multidisciplinary Perspectives, 33–71. Amsterdam/Philadelphia: Benjamins. Progovac, Ljiljana 2008a What use is half a clause? In: Andrew D. M. Smith, Kenny Smith, and Ramon Ferrer i Cancho (eds.), Evolution of Language: Proceedings of the 7th International EVOLANG Conference, Barcelona, Spain, 12–15 March 2008, 259–266. New Jersey: World Scientific. Progovac, Ljiljana 2008b Root Small Clauses with Unaccusative verbs. In: Andrei Antonenko, John F. Bailyn, and Christina Y. Bethin, (eds.), Proceedings of FASL (Formal Approaches to Slavic Linguistics) 16, 359– 373. Ann Arbor: Michigan Slavic Publications.

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Progovac, Ljiljana 2008c Sex and syntax: Subjacency revisited. Presented at BALE (Biolinguistics: Acquisition and Language Evolution), University of York, England. To appear in the special issue of Biolinguistics. Progovac, Ljiljana 2009a Layering of grammar: Vestiges of evolutionary development of syntax in present-day languages. In: Geo¤rey Sampson, David Gil, and Peter Trudgill (eds.), Language Complexity as an Evolving Variable, 203–212. Oxford: Oxford University Press. Progovac, Ljiljana 2009b What is there when little words are not there: Possible implications for evolutionary studies. Proceedings of GURT (Georgetown University Roundtable) 2007, 99–108. Washington, DC: Georgetown University Press. Progovac, Ljiljana, Kate Paesani, Eugenia Casielles, and Ellen Barton 2006 Epilogue: Wherefrom and whereto? In: Ljiljana Progovac, Kate Paesani, Eugenia Casielles, and Ellen Barton (eds.), The Syntax of Nonsententials: Multidisciplinary Perspectives, 323–353. Amsterdam/Philadelphia: Benjamins. Radford, Andrew 1990 Syntactic Theory and the Acquisition of English Syntax. Oxford: Blackwell. Ridley, Mark 1993 Evolution. Oxford: Blackwell Scientific Publications. Roeper, Tom 1999 Universal bilingualism. Bilingualism: Language and Cognition 2 (3): 169–186. Rolfe, Leonard 1996 Theoretical stages in the prehistory of grammar. In: Andrew Lock and Charles R. Peters (eds.), Handbook of Human Symbolic Evolution, 776–792. Oxford: Clarendon Press. Ross, John R. 1967 Constraints on variables in syntax. Ph.D. diss, Massachusetts Institute of Technology. Schu¨tze, T. Carson 2001 On the nature of Default Case. Syntax 4.3: 205–238. Stepanov, Arthur 2007 The end of CED: Minimalism and extraction domains. Syntax 10.1: 80–126. Stowell, Timothy 1983 Subjects across categories. The Linguistic Review 2/3: 285–312. Studdert-Kennedy, Michael 1991 Language development from an evolutionary perspective. In: Norman A. Krasnegor, Duane M. Rumbaugh, Richard L. Scheiefelbusch, and Michael Studdert-Kennedy (eds.), Biological

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12.

The use of formal language theory in studies of artificial language learning: A proposal for distinguishing the di¤erences between human and nonhuman animal learners

James Rogers1 and Marc D. Hauser 2

1. Introduction Most of the articles in this collection reference, directly or indirectly, the conjecture from the abstract of Hauser et al. (2002): We hypothesize that FLN only includes recursion and is the only uniquely human component of the faculty of language. (Hauser et al. 2002: 1569)

While, this conjecture has been productive in sparking research, it was incidental to the primary focus of the original article. Rather, quoting from the conclusion, Hauser et al. presented three central points: First, . . . [to] move beyond unproductive debate to [a] more collaborative, empirically focused and comparative research program aimed at uncovering both shared (homologous or analogous) and unique components of the faculty of language. Second, although we have argued that most if not all of FLB is shared with other species, whereas FLN may be unique to humans, this represents a tentative, testable hypothesis in need of further empirical investigation. Finally, we believe that a comparative approach is most likely to lead to new insights about both shared and derived features, thereby generating new hypotheses concerning the evolutionary forces that led to the design of the faculty of language. (Hauser et al. 2002: 1578)

1. This work was undertaken while the first author was in residence at the Radcli¤e Institute for Advanced Study. 2. The authors would like to express their gratitude to Geo¤ Pullum for his extensive collaboration on this work and to Barbara Scholz and the referees for their helpful suggestions.

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Our goal here is to contribute to that research program by exploring criteria for experimental design of comparative studies across di¤erent populations, including di¤erent species, age groups, and subjects with neurological deficits, targeting capabilities relevant to the language faculty. The comparative method provides a way of analyzing evolutionary phenomena in the absence of genetic or fossil evidence, using empirical data concerning contrasts and parallels between traits in living species to draw inferences about their extinct ancestors. In particular, we are looking to identify shared and unique components of the faculty of language, to identify which of the shared traits are actually homologous rather than independently evolved under similar constraints, to distinguish whether current discontinuities in traits between species are the result of gradual divergence or reflect discontinuities in human evolution and to distinguish whether human traits evolved by gradual extension of common preexisting communication systems or were exapted away from previous non-language adaptive functions. Empirical tests of such issues require studies of di¤erential capabilities across species, in both communication and non-communication domains, including both spontaneous and trained behaviors. To set the stage for what follows, consider a study, cited in Hauser et al. (2002), reported in Fitch and Hauser (2004). This study employed familiarization/discrimination experiments to test the ability of cottontop tamarin monkeys to spontaneously generalize patterns of CV syllables spoken by a female (A) and a male (B) voice. The experiments were designed to contrast the ability of the subjects to recognize sequences of the form (AB) n, in which syllables of the two classes alternate, with the ability to recognize sequences of the form AnB n, in which there are equal numbers of syllables from each class, all those from one preceding all those from the other. The form (AB) n was chosen as an example of the class of Finite State stringsets, stringsets in which there is an a priori bound on the amount of information that must be inferred in distinguishing strings that fit the pattern from those that do not. The form AnB n was chosen as an exemplar of the class of Context Free stringsets, stringsets that can be generated by Context Free Grammars (CFGs) and for which, in principle, the amount of information required to distinguish strings that fit the pattern is proportional to the length of the string. Human languages are generally believed to be at least as complicated as Context Free stringsets. The ease with which the tamarins mastered the Finite State pattern, in contrast to their inability to master the Context Free pattern, suggests that the ability to generalize non-Finite-State patterns has evolved in humans

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since the divergence between their ancestors and the ancestors of tamarins. This result, again, has been fruitful in spawning further research, both in terms of comparative evidence and in terms of refining the potential underlying mechanism (Gentner et al. 2006; Perruchet and Rey 2005; Zimmerer and Varley 2007). But one of the things that is clear in reviewing the research thus far is that the problem of designing such experiments and, in particular, of interpreting their results, is extremely challenging. We turn next to a proposal for how one might beneficially continue this line of research, and in particular, set up a range of patterns or stringsets that enable more systematic explorations and discoveries of the underlying psychological mechanisms.

2. Formal design of recognition experiments While very di¤erent cognitive processes are involved, training experiments and familiarization/discrimination experiments have essentially the same formal structure. We will concentrate on the latter. In these experiments, subjects are familiarized with the intended stringset by exposure to some sample of the strings in the set. They are then tested with some sample of strings including both those in and those not in the intended set. The task of the subject, then, is to infer the pattern of a relatively large, possibly infinite, stringset from a small sample. As they are exposed to only positive examples, any stringset that includes this sample is consistent. Clearly the subjects cannot extract patterns that are more complicated than they are able to distinguish. Our expectation, as well, is that the subjects will not consistently fail to extract patterns of a given level of complexity if they are capable of recognizing them. Thus, the stringset they arrive at is an indicator of the capacity of the cognitive machinery they can bring to bear on the task. If a subject consistently, over a variety of strings, finds strings within the intended set to be ‘‘unsurprising’’ and those not in it to be ‘‘surprising’’ (where these terms refer to the relative novelty of the stimuli and the extent to which they trigger greater attention or more robust responses) then there is reason to conclude that they have generalized correctly. From such results, we are licensed to conclude that the target species has cognitive faculties su‰cient to recognize stringsets of at least this level of complexity. If a subject consistently, over a variety of strings, finds some string in the intended set to be surprising or some string not in the intended set to be unsurprising, then one can conclude that they have not

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Figure 1. Testing recognition of AnBn.

extracted the intended pattern. If subjects of a particular species do this consistently, over a variety of stringsets within a given complexity class, then we may plausibly conclude that the species does not have the cognitive faculties required to recognize stringsets of that level of complexity. The primary issue for the experimental design is determining which set the subject has generalized to. There will always be simpler sets that are consistent with the familiarization set (the set of all strings over the relevant alphabet, for example) and in general these will include both supersets and subsets of the intended set. The strings in the set AnBn, for example, have a variety of di¤erent features which could be generalized by the subject. For example, all of the As precede all of the Bs, the strings are all of even length and the number of As is equal to the number of Bs. In any finite subset, there will be additional features, upper and lower bounds on the number of As, for example. Figure 1 illustrates the situation when the subject has been exposed to just the string AAABBB. The set marked Am B n includes all strings in which the As precede the Bs, an extremely simple stringset (in fact, as described below, a strictly 2-local stringset). The set marked Ai B j 2jði þ jÞ is the subset of those that are of even length,3 a Finite State stringset. The set marked Ai B i i 3 is the finite subset of An B n in which n is no greater than three. The set marked jwjA ¼ jwjB is the set of all strings in which As and Bs are equinumerous,4 a Context Free stringset. In order to distinguish subjects that have generalized to An B n , and 3. The expression x| y denotes the property of y being an integral multiple of x. 4. The expression |w| denotes the length of the string w – the number of symbols it contains. The expression jwjA denotes the number of As it contains.

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therefore must be able to recognize at least some Context Free stringsets, from those that can recognize only stringsets of strictly lower complexity we need to expose them to strings that are in the set-theoretic symmetric di¤erence between the simpler sets and An B n . One can detect that the subject has generalized to a simpler set that is a subset of the intended set if there are strings in the intended set but not in the simpler set that are surprising to them. One can detect that the subject has generalized to a simpler set that is a superset of the intended set if there are strings in the simpler set but not in the intended set that are not surprising. Pairing AAABBB with AABBBB, for example, can reveal whether the subject has generalized to An B n or Ai B j 2jði þ jÞ and provides evidence of being able to recognize stringsets beyond the Finite State. Pairing it with AABBB, on the other hand, distinguishes subjects that have generalized to the strictly local stringset Am B n , but fails to distinguish Finite State from non-Finite-State; AABBB will be novel to both those that have generalized to An B n and those that have generalized toAi B j 2jði þ jÞ. Pairing AAABBB with AAAABBBB can reveal whether the subject has erroneously generalized to Ai B i i 3. Although one can never rule out the possibility that the subject has generalized to a finite subset of the intended set that happens to include both the strings in the familiarization set and those in the discrimination set that are in the intended set, one can be reasonably sure that they have not generalized to a finite set by including strings in the discrimination set that are longer than any in the familiarization set and therefore unlikely to be in any finite generalization. Thus, failure to perceive AAAABBBB as novel suggests that the subject has not generalized to any finite subset of An B n . Finally, AABBBA or ABABAB will appear novel even to subjects that can recognize only strictly local stringsets, although they will not appear novel to a subject that has overgeneralized to jwjA ¼ jwjB . Thus these strings fail to provide any evidence at all about the boundary between Context Free and simpler stringsets. The punch line here is straightforward: it is critical to the validity of these experiments that we have a clear idea not only of the intended stringset but also of the stringsets that it could, potentially, be mistaken for. Even with careful choice of stimuli there are still a variety of pitfalls in design and interpretation of these experiments that must be avoided. Examples of utterances of English that satisfy the patterns of Fitch and Hauser (2004) include (1a), of the form ðABÞn , and (1b), of the form An B n .5 5. These two examples are due to Geo¤rey K. Pullum.

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(1) a. b. c. d.

{(ding dong) n} {peoplen left n} {people who were left (by people who were left) n left} {people who were left (by people who were left)2n left}

The fact that (1b) is well-formed is usually not clear at first encounter for n greater than two or three. The paraphrase in (1c) is much easier to parse, but it is, in fact, Finite State. This points out one of the di‰culties of probing the boundaries of recognition capabilities in this way. Humans seem to be able to process, with no conscious e¤ort, many types of utterances which, as stringsets, are not Finite State. But there are many well formed utterances of the same sort that are utterly opaque without careful conscious analysis. The fact that, in humans, the same stimulus may be processed with potentially distinct faculties with di¤ering degrees of success demonstrates the di‰culty of isolating a particular faculty experimentally. This is one of the reasons for testing both spontaneous and learned behavior. A more fundamental issue is raised by the fact that (1d) represents a class of utterances that, while Finite State, is unlikely to be accurately identified by most English speakers without consciously searching for the key to the pattern (i.e., the number of prepositional phrases is required to be even). Thus, while (1a) and (1d) are both Finite State there seems to be a very dramatic di¤erence in the degree of di‰culty of recognizing them. The Finite State stringsets do not, in fact, present a uniform level of di‰culty of recognition. There is a rich hierarchy of classes of stringsets within the Finite State which corresponds to a range of gradations in cognitive capabilities. Viewed as an instrument for probing the boundaries of these capabilities, the pair of stringsets (AB) n and AnB n lack resolution. Thus it is not only important to understand which sets the subject may erroneously infer, it is also important to understand what ranges of complexity classes may be relevant to the faculties that are being explored. Finally, an issue of interpretation arises when the Fitch and Hauser (2004) result is taken as suggesting that one of the capabilities distinguishing humans from tamarins is a faculty for handling recursion. Fitch and Hauser do not claim that their results suggest that tamarins lack a capacity for handling recursion, per se, only that they cannot handle phrase structure, i.e., Context Free, patterns. In fact recursion is not actually necessary for recognizing the pattern AnB n. Algorithmically, one can recognize this using a single counter or by inferring a single binary relation over the input. Context Free grammars are not the only algorithmic mechanisms

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capable of generating or recognizing Context Free stringsets. Results establishing the definitional equivalence of distinct mechanisms are ubiquitous in Formal Language Theory (FLT), suggesting that there is no bound on the varieties of algorithmic mechanisms that are equivalent in the sense of defining the same classes of stringsets. Consequently, one cannot make inferences about cognitive mechanisms based on the details of any particular generative mechanism. Rather one is licensed only to make inferences based on the common characteristics of the entire class of equivalent mechanisms. The question is, how are those common characteristics to be determined?

3. Dual characterizations of complexity classes Most of FLT has developed from a foundation of abstract algorithmic processes: grammars, which generate strings, and automata, which recognize them (Hopcroft and Ullman 1979). The characteristics of these processes allow one to reason about the structure of the stringsets they define, establishing pumping lemmas,6 for example, or Nerode-style characterizations.7 An understanding of this structure is critical to the design of experiments of the sort we are interested in: How are the classes of stringsets related to each other? Which stringsets distinguish the classes? In parallel with these algorithmic characterizations, are descriptive characterizations, characterizations of classes of stringsets based directly on the properties of the strings they contain (Medvedev 1964; Bu¨chi 1960; Elgot 1961; Thatcher and Wright 1968; McNaughton and Papert 1971; Thomas 1982; Straubing 1994; Libkin 2004). When one specifies a stringset with properties such as ‘‘there are equal numbers of syllables from each class of syllables’’ one is specifying the stringset descriptively. Descriptive characterizations of classes of stringsets focus on the nature of the information required to distinguish strings that meet or do not 6. Pumping lemmas establish certain types of closure properties of stringsets: if a stringset includes strings with length exceeding an arbitrary but fixed bound then it also includes strings in which certain substrings are repeated arbitrarily many times. Shieber (1985) and Huybregts (1984) employed results of this sort to show that certain dialects of Swiss-German are not representable as Context Free stringsets. 7. These characterize the structure of stringsets in terms of the way in which certain relations on strings, which depend on the stringset, partition the set of all strings into equivalence classes.

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meet such patterns – the kinds of relationships between the components of the strings that must be detected if the patterns are to be recognized.8 The main strength of these characterizations, from our point of view, is that they do not presuppose any particular algorithmic mechanism. Any mechanism that can recognize or generate stringsets that fall properly within a descriptive class must necessarily be sensitive to the sort of information about strings that determines the class. Hence they provide a foundation for reasoning about the common characteristics of entire classes of formally equivalent mechanisms, be they abstract algorithmic mechanisms or concrete cognitive mechanisms realized in organisms. A second strength is their generality. Any description of strings that can be expressed within the means of a descriptive class defines a stringset within that class. By varying these means systematically we can cover an extremely broad range of seemingly disparate ways of specifying patterns with a relatively small set of descriptive classes. The fulcrum of the methodology we employ here is the deep fact that these two approaches to distinguishing classes of stringsets correspond. Descriptive classes can be characterized in terms of grammars and automata and vice versa. This allows us to use the descriptive characterizations as the basis for reasoning about cognitive mechanisms (avoiding the fallacy of basing such reasoning on the corresponding algorithmic mechanisms) while using the algorithmic characterizations to guide the experimental design.

4. The sub-regular hierarchy The range of complexity classes that falls between stringsets such as (1a) and (1d), the sub-regular hierarchy, has been largely overlooked by linguists in part because the Chomsky hierarchy starts with the Finite State and in part because, as human languages are widely assumed to be at least Context Free, there has been little motivation to explore sub-Finite-State classes in this context. But our interest is in recognition capabilities across many populations, including di¤erent species, age groups and neurological populations, targeting potential precursors to human faculties. Consequently, we are fundamentally interested in classes of stringsets that are simpler than human languages as these may well form some of the critical 8. We provide concrete examples of what we mean by ‘‘nature of the information’’ as we survey a range of descriptive classes in the next section.

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evolutionary and ontogenetic building blocks. More importantly, the classes in the sub-regular hierarchy correspond to a clear hierarchy of cognitive mechanisms and, since the classes in the hierarchy are defined purely in terms of types of relationships between positions in strings, that hierarchy of cognitive mechanisms will be relevant to any faculty that provides a syntax-like function, i.e., that processes stimuli solely as sequences of events, independent of meaning. The remainder of this section presents a brief overview of the formal aspects of the sub-regular hierarchy. Due to space limitations we skip most of the formal detail, presenting just the relevant characteristics of the classes of the hierarchy. We close the section with a list of criteria for the design and interpretation of acoustic pattern recognition experiments based on these classes. A more through exposition can be found in Rogers and Pullum (2007). 4.1. Strictly Local Stringsets The simplest definitions we will explore are those that specify strings solely in terms of the sequences of symbols that are permitted to occur adjacently in them, that is, in terms of the n-grams making up the string. Since our n-grams are not associated with probabilities we will refer to them with the standard FLT terminology: k-factors. A k-factor is just a length k sequence of symbols. A Strictly k-Local Definition is a set of k-factors drawn from some finite alphabet of symbols augmented with beginning of string (z) and end of string (y) markers. A string w satisfies a strictly k-local definition if and only if (i¤ ) the set of kfactors of the augmented string zwy is a subset of those included in the definition. A stringset is in the class SLk i¤ it can be defined with a strictly k-local definition, it is Strictly Local (SL) (McNaughton and Papert 1971) i¤ it is SLk for some k. The set of strings of the form (AB) n is an example of an SL2 stringset, being definable by the (minimal) set of 2-factors: ð2Þ

def

DðABÞn ¼ fzA; AB; BA; Byg;

which asserts that the string must begin with an A, end with a B, that every A is followed by a B and that every B other than the last is followed by an A. The set of strings licensed by this definition, denoted LðDðABÞn Þ, is fðABÞi j i > 0g. Membership in a Strictly Local stringset depends only on the k-factors

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in isolation: a string satisfies an SLk definition i¤ each of the k-factors in the string is independently licensed by that definition. From a cognitive perspective, all that is required to recognize a strictly k-local stringset is attention to each block of k symbols which occurs in the string. If the string is presented sequentially in time, this amounts to remembering just the last k consecutive events that have been encountered. The key to reasoning about the structure of SL stringsets in general is a theorem which characterizes them in terms of a property known as su‰x substitution closure: a stringset is SL i¤ there is some k for which it is closed under the substitution of su‰xes that begin with the same (k 1)-factor. This allows us to identify non-SL stringsets and to construct minimal pairs of stringsets which can be diagnostic of the ability to generalize SL patterns. One simple non-SL stringset is the set of strings of As and Bs in which there is at least one B, a stringset we call Some-B: ð3Þ

def

Some-B ¼ fw 2 fA; Bg j jwjB 1g:

To see that this is not SLk for any k, note that, for any k, strings of the form A . . . A A . . . A BA . . . A and those of the form A . . . AB |ﬄﬄﬄ{zﬄﬄﬄ} k1

A . . . A A . . . A are all in Some-B, but the result of substituting the su‰x |ﬄﬄﬄ{zﬄﬄﬄ} k1

of a string of the second form, starting at the marked sequence of k 1 As, for the su‰x of a string of the first form is A . . . A A ...A A...A |ﬄﬄﬄ{zﬄﬄﬄ} k1

which is not in Some-B. So, Some-B does not exhibit su‰x substitution closure and can not be specified with an SL-definition. 4.2. Locally Testable Stringsets In order to distinguish stringsets like Some-B it is necessary to di¤erentiate between strings on the basis of the whole set of k-factors that they contain, not just on the basis of the individual k-factors in isolation. Descriptions, at this level, are k-expressions, formulae in a propositional language in which the atomic formulae are k-factors which are taken to be true of a string w i¤ they occur in the augmented string zwy. More complicated k-expressions are built up from k-factors using the usual logical connectives, e.g., for conjunction (^), disjunction (_) and negation (:). Stringsets are Locally Testable (LT) (McNaughton and Papert 1971) i¤ they are definable by a k-expression, for some k. As an example, Some-B is defined

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by the following 2-expression, which is true of strings that either start with B or include AB: ð4Þ

def

’Some-B ¼ zB _ AB

The relation between strings and the k-expressions which holds i¤ the string satisfies the k-expression is denoted ; the set of strings licensed def by a k-expression ’, then, is Lð’Þ ¼ fw j w ’g. For the k-expression ’Some-B, L(’Some-B) ¼ Some-B. As this witnesses, k-expressions have more descriptive power than SLk definitions.9 Because membership in an LTk stringset depends on the whole set of kfactors that occur in a string k-factors can be required to occur as well as prohibited from occurring and they can be required to occur in arbitrary combinations – to occur together, to occur only if some other combination of k-factors does not occur, etc. On the other hand, membership in an LTk stringset depends only on the set of k-factors which occur in the string. Any mechanism which can distinguish strings on this basis is capable of recognizing (some) LTk stringset. Conversely, any mechanism that can distinguish members of a stringset that is LTk (but not SL) must be able to distinguish strings on this basis. Cognitively, this corresponds to being sensitive to the set of all kfactors that occur anywhere in the input. If the strings are presented sequentially, it amounts to being able to remember which k-factors have and which have not been encountered in the stimulus. An example of a stringset that is not LT is the set of strings over {A,B} in which exactly one B occurs: ð5Þ

def

One-B ¼ fw 2 fA; Bg j jwjB ¼ 1g

To see that this is not LT note that, for any k, AkBAk is in One-B while AkBAkBAk is not. Since these have exactly the same set of k-factors, however, there is no k-expression that can distinguish them. 4.3. FO(þ1) Definable Stringsets The next step in extending the complexity of the stringsets we can distinguish is to add the power to discriminate between strings on the basis of

9. It is easy to translate an SLk description into a k-expression defining the same stringset, so LTk is a strict superclass of SLk.

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the specific positions in which blocks of symbols occur rather than simply on the basis of blocks of symbols occurring somewhere in the string. Descriptions at this level are first-order logical sentences (formulae with no free variables) over a restricted string-oriented signature. Atomic formulae assert relationships between variables (x; y; . . . ) ranging over positions in the string: x / y (meaning that y is the next position following x), x y (x and y are the same position) and AðxÞ; BðxÞ; . . . (A occurs in position x, etc.). Larger formulae are built from these using the logical connectives and existential (9) and universal (8) quantification. A string w satisfies an existential (sub)formula ð9xÞ½’ðxÞ (i.e., w ð9xÞ½’ðxÞ ) i¤ some assignment of a position for x makes it true. It satisfies a universal (sub)formula i¤ all such assignments make it true. The class of stringsets definable in this way is denoted FO(þ1). As an example, One-B is FO(þ1) definable: ð6Þ

One-B ¼ fw 2 fA; Bg j w ð9xÞ½BðxÞ ^ ð8yÞ½BðyÞ ! x y g;

which asserts that there is some position x in which a B occurs and that all positions y in which B occurs are that same position. As One-B witnesses, FO(þ1) definitions are more expressive than k-expressions.10 It turns out that a stringset is FO(þ1) definable i¤ it is Locally Threshold Testable (LTT) (Thomas 1982). Such stringsets distinguish strings only on the multiplicity of the k-factors which occur in them and only relative to a threshold t above which multiplicities of the k-factors cannot be distinguished. This characterization is the key to identifying stringsets that are not FO(þ1) definable. An example of a non-LTT, hence non-FO(þ1)-definable, stringset is the set of strings over {A,B,C} in which some B occurs before any C: (7) def

B-before-C ¼ fw 2 fA; B; Cg j at least one B precedes any Cg 62 LTT: To see this, note that, for any k, AkBAk CAk and Ak CAkBAk have exactly the same number of occurrences of every k-factor and are therefore indistinguishable in the LTT sense for any threshold t.

10. Again, k-expressions can be easily translated into FO(þ1) formulae; so FO(þ1) is a strict superclass of LT.

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4.4. FO(<) Definable Stringsets We can, again, increase the complexity of the stringsets we can distinguish by, beyond just discriminating individual occurrences of k-factors, di¤erentiating between strings based on the order in which those k-factors occur. FO(<) descriptions extend FO(þ1) descriptions to include a precedence relation / which corresponds to < on the domain of the structure. An example of a FO(<) definable stringset that is not FO(þ1) definable is B-before-C: ð8Þ

B-before-C ¼ fw j w ð9xÞ½CðxÞ ! ð9yÞ½BðyÞ ^ y / x g:

This formula asserts that if there is a position x in which C occurs, then there is a position y in which B occurs which precedes x in the string. Strikingly, it turns out that extending the signature with the precedence relation in this way is exactly equivalent to adding a concatenation operator ( ) to the language of k-expressions. A stringset is Locally Testable with Order (LTO) (McNaughton and Papert 1971) i¤ it is definable with a k-expression augmented in this way. Note that we can define B-beforeC with ð9Þ

ð:ðzC _ AC _ BCÞ ðzBÞÞ _ :ðzC _ AC _ BCÞ;

which is satisfied either by strings which consist of a substring in which no C occurs followed by one which starts with B or by those in which, simply, no C occurs at all. If the strings are presented sequentially, this corresponds to being able to apply a fixed set of sequences of LTT-style threshold counting recognition strategies. E¤ectively, it corresponds to being able to count occurrences of events up to some threshold, coupled with the capacity to reset the counters some fixed number of times. The most useful abstract characterization of the structure of the FO(<) definable stringsets follows from an automata-theoretic characterization due to McNaughton and Papert (1971).11 In essence, a stringset is FO(<) definable i¤ there is some constant n > 0 for which, whenever a string in the set includes a block of symbols which is iterated at least n times, then it also includes all strings which are identical except that that block is iterated an arbitrary number of times greater than n. 11. A Finite State automaton recognizes an FO(<) stringset i¤ its syntactic monoid is aperiodic.

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An example of a non-FO(<) definable stringset is the set of strings over {A, B} in which the number of Bs is even: ð10Þ

def

Even-B ¼ fw 2 fA; Bg j jwjB ¼ 2i; 0 ig 62 LTT

This set includes strings in which B is repeated at least n times, whatever value the constant n might have. But adding one more B to that block of Bs produces a string with an odd number of Bs. 4.5. MSO Definable Stringsets The next step in increasing the power of our descriptions is to introduce abstraction – to assign the occurrences of symbols in the strings to abstract categories and to discriminate between the strings on the basis of the sequence of categories rather than the sequence of symbols themselves. Categories of this sort can be captured in logical languages by allowing quantification over not just individual positions in the strings but over sets of positions, i.e, by adding Monadic Second-Order variables along with their quantifiers. An example of an MSO definition of a stringset is: ð9X0 Þ½ ð11Þ

ð8xÞ½:ð9yÞ½y / x ! X0 ðxÞ ^ ð8x; yÞ½x / y ! ðX0 ðxÞ $ :ðX0 ðyÞÞ ^ ð8xÞ½:ð9yÞ½x / y ! :ðX0 ðxÞÞ

This defines the set of all strings that are of even length: it asserts that there is a subset of positions in the string (X0) which includes the first position in the string, alternates between inclusion and exclusion of adjacent positions and does not include the last position.12 This formula can be modified to ignore everything except positions labeled B, which gives a definition of Even-B. So MSO is a proper superclass of FO(<). The assignments of positions in the strings to MSO variables is equivalent, in a strong sense, to the association of those positions with states in the runs of Finite State automata. And, in fact, the MSO-definable stringsets are exactly the Finite State stringsets (Medvedev 1964; Bu¨chi 1960; Elgot 1961). The abstract character of the MSO definable stringsets is a consequence of their characterization by Finite State automata. Two strings w and v 12. The reader should note the similarity between this definition and the SL2 definition of (AB) n (Equation 2).

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are Nerode Equivalent with respect to a stringset L over an alphabet (denoted w L v) i¤ for all strings u over , wu 2 L , vu 2 L. A stringset L is Finite State i¤ L partitions the set of all strings over into finitely many equivalence classes. These equivalence classes correspond to the categories (to the distinguished subsets) of the MSO definitions. Since the MSO definable stringsets extend the FO definable stringsets, the ability to discriminate between strings based on categorizing the events that comprise them in this way implies the ability to discriminate between them based on the multiplicity of their k-factors, counting up to a fixed threshold. As the definability of Even-B suggests, it extends this to the ability to distinguish strings based on the residues (remainders) of those multiplicities relative to some modulus, in essence to count modulo those thresholds, resetting the counters unboundedly often. It is, in fact, equivalent to using a finite set of counters that count modulo some threshold. It does not, on the other hand, provide the ability to count arbitrarily high; the stringset fAn B n j n > 0g, for example, is not MSO definable because the Nerode equivalence for the set is: ð12Þ

w An B n v , w; v 62 fAi B j j i; j 0g or jwjA jwjB ¼ jvjA jvjB :

for which there are infinitely many equivalence classes. Cognitively, the Finite State stringsets characterize an extremely broad range of mechanisms: whenever there is a fixed finite bound on the amount of information a mechanism can retain while processing a string the mechanism will be limited to recognizing at most Finite State – equivalently, MSO definable – stringsets. Note, though, that the fact that an organism can recognize non-Finite-State stringsets does not imply that the physical mechanisms they employ must have access to a store of unbounded size. The mechanisms may implement an algorithm which, in principle, requires unbounded storage which fails on su‰ciently long or su‰ciently complicated inputs. Or would if it ever encountered such. 4.6. Beyond Finite State The ability to recognize stringsets that are not Finite State implies discriminating between strings on the basis of information about the string the size of which depends on the length of the string – being able to count to values that are proportional to the length of the string, for example. The weakest class of the Chomsky hierarchy which properly extends the class of Finite State stringsets is the class of context free stringsets, those that can be generated by context free grammars. But there are many ways of

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Table 1. Distinguishing classes of the sub-regular hierarchy experimentally. Class

Example

In

Out

SL

ðABÞn

ðABÞiþjþ1

ðABÞ i BBðABÞ j

LT

Some-B

Ai BA j

Aiþjþ1

FO(þ1)

One-B

Ai BA jþkþ1

Ai BA j BAk

FO(<)

B-before-C

Ai BA j CAk

Ai CA j BAk

MSO

Even-B

B2i

B 2iþ1

CF

AnB n

AnB n

Anþ1 B n1

utilizing amounts of information that depend on the length of the string that do not provide the ability to recognize context free stringsets in general. The single counter that su‰ces to recognize AnB n can also recognize sets of well-nested brackets (the single bracket Dyck stringsets, D1), but it does not su‰ce to recognize D2, the two bracket Dyck stringsets, for example. There are, in fact, multiple hierarchies which partition the context free stringsets just as the sub-regular hierarchy partitions the Finite State stringsets. Experiments that are intended to di¤erentiate abilities beyond the Finite State will need to be based on formal analyses of this territory similar to the analysis of the sub-regular hierarchy we have provided here.

5. Recognition experiments Tables 1 and 2 summarize the conclusions that can be drawn about the cognitive capabilities of the subjects given the results of recognition experiments based on the sub-regular hierarchy. To test the recognition capabilities of a species relative to these classes one could use experiments based on patterns such as those given in the Example column of Table 1. Species with the ability to recognize patterns of that sort, having been familiarized to strings of the form given in the In column, should generally find novel strings of that form unsurprising while finding strings of the form given in the Out column surprising. If, on the other hand, subjects consistently fail to find strings of the form given in the Out column surprising after being familiarized to strings of

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Table 2. Cognitive significance of recognition results. Class

Outcomes

Cognitive significance

SL

Recognize (AB)n

Sensitive to a fixed length block of the immediately prior events

Fail Some-B

Only sensitive to the immediately prior events

Recognize Some-B

Sensitive to which fixed length blocks of events occur in the input, e¤ectively being able to recall sequences of events that occur at arbitrary points

Fail One-B

Insensitive to multiplicity or order of blocks

Recognize One-B

Sensitive to the multiplicity of events that occur in the input, at least up to some fixed threshold

Fail B-before-C

Insensitive to order of blocks

Recognize B-before-C

Sensitive to the multiplicity, up to some fixed threshold, of events that occur in the input and to the order in which a fixed number of events occur, in e¤ect counting to a threshold and resetting the counters up to a fixed number of times

Fail Even-B

Insensitive to order of events beyond some fixed number

Recognize Even-B

Capable of classifying the events in the input into a finite set of abstract categories and sensitive to the sequence of those categories. Subsumes any recognition mechanism in which the amount of information retained is limited by a fixed finite bound.

Fail AnBn

fixed finite bound, independent of the input, on amount of information retained

LT

FO(þ1)

FO(<)

MSO

the form given in the In column, this would be evidence that the target species is unable to distinguish patterns of that level of complexity. Table 2 summarizes the conclusions that can be drawn from such results. Recognize outcomes represent lower bounds on the species’ capacity. They indicate that the subject has at least the cognitive capabilities given in the Cognitive significance column. Fail outcomes represent upper bounds, evidence that the subject is limited in the way indicated in the Cognitive significance column.

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6. Conclusion Acoustic pattern recognition or artificial language learning experiments provide a powerful approach to understanding the ontogenetic and evolutionary building blocks of the human language faculty, distinguishing what is shared with other species and what is uniquely human. To design experiments of this sort with highly interpretable results, one must be clear about a bewildering array of formal considerations. These include the cognitive capacities that the experiment is designed to probe, the abstract structure of the classes of stringsets that those capabilities characterize, the structure of the stringsets the intended stringset may be confused with and what such confusion signifies about the capabilities of the subjects. The subregular hierarchy is a range of complexity classes that correspond to a range of cognitive capabilities that are, by virtue of the descriptive characteristics of the classes, necessarily relevant to any faculty that processes aural stimuli solely as sequences of events. As such it provides a clear framework for resolving these issues. We hope that our exposition of this hierarchy will facilitate continued experimentation of this type.

References Bu¨chi, J. R. 1960

Elgot, C. C. 1961

Weak second-order arithmetic and finite automata. Zeitschrift fu¨r Mathematische Logik und Grundlagen der Mathematik, 6: 66–92.

Decision problems of finite automata and related arithmetics. Transactions of the American Mathematical Society, 98: 21–51. Fitch, W. T. and M. D. Hauser 2004 Computational constraints on syntactic processing in nonhuman primates. Science, 303: 377–380. Gentner, T. Q., K. M. Fenn, D. Margoliash, and H. C. Nusbaum 2006 Recursive syntactic pattern learning by songbirds. Nature, 440: 1204–1207. Hauser, M. D., N. Chomsky, and W. T. Fitch 2002 The faculty of language: What is it, who has it and how did it evolve. Science, 298: 1569–1579. Hopcroft, J. E. and J. D. Ullman 1979 Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading, Mass.

The use of formal language theory Huybregts, R. 1984

Libkin, L. 2004

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The weak inadequacy of context-free phrase structure grammars. In G. J. de Haan, M. Trommelen, and W. Zonneveld, eds., Van Periferie Naar Kern, pp. 81–99. Foris Publications, Dordrecht.

Elements of Finite Model Theory. Texts in Theoretical Computer Science. Springer, Berlin/New York. McNaughton, R. and S. Papert 1971 Counter-Free Automata. MIT Press, Cambridge, MA. Medvedev, Y. T. 1964 On the class of events representable in a finite automaton. In E. F. Moore, ed., Sequential Machines – Selected Papers, pp. 215–227. Addison-Wesley, Reading, Mass. Originally in Russian in Avtomaty (1956), pp. 385–401. Perruchet, P. and A. Rey 2005 Does the mastery of center-embedded linguistic structures distinguish humans from nonhuman primates. Psychonomic Bulletin and Review, 12: 307–373. Rogers, J. and G. K. Pullum 2007 Aural pattern recognition experiments and the subregular hierarchy. In Mathematics of Language 10. UCLA. Shieber, S. 1985 Evidence against the context-freeness of human language. Linguistics and Philosophy, 8: 333–343. Straubing, H. 1994 Finite Automata, Formal Logic and Circuit Complexity. Birkha¨user, Boston. Thatcher, J. W. and J. B. Wright 1968 Generalized finite automata theory with an application to a decision problem of second-order logic. Mathematical Systems Theory, 2(1): 57–81. Thomas, W. 1982 Classifying regular events in symbolic logic. Journal of Computer and Systems Sciences, 25: 360–376. Zimmerer, V. and R. Varley 2007 Recursive syntax in patients with severe agrammatism. Recursion in Human Languages, Illinois State University, Normal, Illinois.

13.

Over the top: Recursion as a functional option1

Peter Harder

Abstract. The article presents a function-based account of recursion, arguing that recursion in language must be understood not only in a cognitive perspective, but also in the context of environmental a¤ordances for recursive processing. Rather than a direct correspondence between the three levels, there is a functional relationship: only some environmental a¤ordances are actually used by cognitive recursion, and only some recursive cognitive structures are encoded recursively. The key reason is processing load: recursion is a taxing process, which is o¿oaded whenever possible. The key cognitive ability, I argue, is to take one incremental step (of a recursively applicable kind) – not to go on forever. The nature of this incremental step comes out if recursion is viewed bottom-up, as the result of superimposing successive reapplications of an operation on a simple structure, forming gradually more complex wholes – rather than top-down, with the complex whole as the point of departure.

0. Introduction Most functional linguists do not devote a great deal of attention to recursion, and when asked about it, they tend to think that recursion as an issue in linguistics is an artefact of a Chomskyan formalism (cf., e.g., McGregor 2004). From a functionalist point of view, the mathematical properties of models used to describe languages do not automatically qualify as features of real languages: like everything else, human languages can be simulated by a formal model – but that does not entail that the properties of the model are also properties of the language, cf. Itkonen (1976). This foundational issue is important (cf. also Harder 2006), because formal-generative description is based on an understanding whereby abstract formal operations are part of language as an object of description, existing in the real world. The point is made explicitly by Hauser, Chomsky and Fitch (2002: 1569): 1. I would like to thank Michael Fortescue, the participants in the recursion symposium and three anonymous referees for valuable suggestions. Needless to say, remaining imperfections are my own responsibility.

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‘‘. . . it is important to distinguish between questions concerning language as a communicative system and questions concerning the computations underlying this system, such as those underlying recursion. . . . According to one view (1) [the note refers to Aspects of the Theory of Syntax, Chomsky 1965], questions concerning abstract computational mechanisms are distinct from those concerning communication . . .’’

According to the functional-cognitive view of language, language as an object of description exists as part of the constitution of human life – which (like weather systems, nuclear wars and everything else) can be simulated by abstract computational mechanisms, but does not inherently consist of abstract computational mechanisms. The point is discussed by Searle (1980, 1984): the fact that a physical object such as a pen behaves in a particular way – left to itself (to take Searle’s example), it remains in the same place, for instance – does not mean that in addition to behaving that way it also and additionally has an inherent formal, computational property (a function where location is a constant over time). This objection is sometimes seen as hair-splitting, because it is hard to know what something ‘‘really’’ is, and a working computational simulation may be the best handle we have. But the point in insisting on it is that it forces you to point to the actual skill that we posit recursion as a candidate feature of. I suspect there may be some lack of clarity also in Chomsky’s own thinking about what the central phenomenon is; in Chomsky (2000: 45–50), the property of ‘‘discrete infinity’’ is exemplified with the use of a very limited number of phonetic segments to express an infinity of ideas, and as pointed out in Pinker and Jackendo¤ (2005), recursion in the technical sense does not occur in phonology. However, no one disputes that languages like English possess syntactic mechanisms that can be formally modelled by recursion. For a functionalist linguist, this poses the challenge of considering whether recursion has a functional role in language. Recursion may not be the right way to account for linguistic creativity, but functionalists need to o¤er their own take on the issue – including the question strikingly raised by Piraha˜ (cf. Everett 2005) of what the precise relations are between recursion in culture, cognition and language. Accordingly, the account below will try to point to a precise type of functional ability in actual language use as that which underlies the properties that can be formally simulated by recursive systems. 1. The significance of the bottom-up perspective The standard definition of recursion (‘‘a procedure that calls itself ’’) views the phenomenon top-down. In a usage-based and functional approach,

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however, the bottom-up perspective is fundamental: more basic and concrete phenomena are prerequisites for more abstract and sophisticated ones (cf. e.g., Barlow & Kemmer 2000, Tomasello 2003). Approaching recursion bottom-up, I suggest that one can distinguish roughly between three stages of syntactic sophistication in sign systems. At the simplex stage, items are (morphosyntactically) unanalysable (ouch!). The second stage is that of constructional combinations, which are analysable into components but have a strong lexical flavour – reflecting the central tenet of construction grammar (cf. Goldberg 1995) that complex items are understandable as familiar routines with some optional add-ons, rather than fully compositional. The third and last stage of complexity is open-ended combination, where elements are combined in novel ways – and this is where recursion belongs. (This scale reflects some of the same intuitions as ideas advanced by Bickerton 1990 on ‘‘protolanguage’’, Wray 2001 on formulaic language and syntax, and Jackendo¤ 2002 on ‘‘linguistic fossils’’.) Two examples from di¤erent domains: (1) In terms for generations, the first stages are unanalyzable: mother, father, son, daughter. The next stage is constructional, with the frame grand-X yielding familiar but analysable items such as grandmother. From then on, however, new and progressively less familiar generations are denoted by recursion, as in great grandmother, great great grandmother and so on. (2) In the case of whole utterance meanings, the first stage is holophrases like yes and bye. Like son or mother, they are morphosyntactically unanalysable – but they di¤er in that they encode whole speech acts, and from that point of view they are functionally equivalent to whole sentences: in the proper context, yes is replaceable with I’ll come and bye historically arises from God be with you. The next stage is the home ground of construction grammar, with clause-level constructional combinations such as they sent her a present, which reflect constructional types that are familiar as wholes but analysable into parts – complex but not all that creative. The last stage goes beyond the standard formats, and includes cases of recursion such as he says she says it’s OK. One factor in this scale of complexity is processing e¤ort, cf. Pawley and Syder (1983) and Sinclair (1991): retrieval of familiar items is less costly than building from scratch. Thus one simplex element that will do the trick is the least costly solution; the next cheapest option is a combination of elements based on a familiar pattern. Only when there is no

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adequate alternative is it cost-e‰cient for speakers to resort to the most costly solution, that of open-ended combination, of which recursion is one salient type. Tomasello’s (2003) theory of language acquisition is a bottom-up theory in the sense reflected in this path: first simplex forms, then familiar whole constructions, which are subsequently analysed into freely combinable elements. The path of approach I suggest is also bottom-up in a di¤erent (though related) sense. In the top-down approach, recursion occurs when the structure of the whole recurs in the structure of a small part. In a bottom-up approach, we start with a smaller item and then superimpose a new operation of the same type on it. This operation is at work both in the generational and the clausal type of recursion: we can make a simpler structure more complex by prefixing another round of either great . . . or she says that . . . The resulting structures are the same whether we approach them top-down and bottom up, but the bottom-up perspective brings out an overlooked, and functionally interesting, mechanism: in moving upwards in the tree, we assign new functions to lower-down elements by integrating them in a new whole. The bottom-up approach, and the terminology of ‘‘prefixing’’ and ‘‘superimposing a new operation’’ may suggest a hypothesis about online processing – that speakers take the most deeply embedded constituent first and then move upwards. That is not the intention, however. Rather, it is assumed that syntactic structure and actual processing are only indirectly connected. As discussed in detail in Harder (2007), syntactic structure can be understood as ‘‘procedural knowledge’’ in a sense that is distinct from the structure of actual procedures – just as we may know how to cook a particular dish without carrying out the same operations in the same order on all di¤erent occasions. A fully competent speaker in some sense knows how to use a general compositional regularity to link up the canonical understanding of a less complex proposition P with the canonical understanding of a more complex proposition Mary says that P. This compositional regularity can be understood as neutral with respect to actual processing (productive or receptive); there is no reason why the whole apparatus of procedural knowledge needs to be put into action in the same way on all occasions.2 2. For the same reason, the claim that speakers know how to impose upgrading operations on simpler expressions does not rule out the existence of opacity phenomena that make certain constituents internally inaccessible to higherlevel operations. In fact, sealing expressions o¤ may be understood as part of

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From the top-down perspective, the most plausible function of recursion is to ‘‘specify reference to an object to an arbitrarily fine level of precision’’, cf. Pinker and Bloom (1990: 724) – because you can go on and on adding specifications to already existing constituents. Although potentially handy, this brings to mind the law of diminishing returns. In contrast, if we add new rounds of the same structures on our way up, we revamp and upgrade the existing linguistic expression – and this, I suggest, is the truly open-ended path of recursive modification. The re- prefix in recursion resembles the prefix in re-think, re-group, re-process: rather than being condemned to rest content with what he has got, the speaker knows how to upgrade his resources. With the examples given above: each time we add a new great we move another generation away from the base – and each time we add another he says that . . . we move the original message content onto a new stage of recontextualization. It follows from what I said above that in the individual processing situation, the point of departure does not have to be an ‘‘original message content’’ constituted by the most deeply embedded clause content – a speaker can start at any level of complexity he chooses. All that is claimed is that if we want to understand the relation between a hierarchy of structures with a simple clause at one end and the most complex recursive structure at the other end, then a functional approach suggests that we can understand a structure at complexity level X by seeing it as a development building on a structure at complexity level X minus one – and the structure of a simple clause does not presuppose any recursive embedding option. The bottom-up approach is not unheard of, naturally: Hauser, Chomsky and Fitch (2002: 1571) mention the operation of prefixing Mary said that . . . as the argument for why there is no longest sentence, and if the ‘‘merge’’ operation is regarded as recursive, it also instantiates an upward path (but there are arguments against viewing that as recursive, cf. Parker 2006). The point here, however, is the functional incentive to move upwards into recursion – i.e. to choose the more complex option when it is functionally motivated, and stay with the simpler option when it is not.

the e¤ort-reducing strategy discussed in section 3 with reference to Mithun (this volume). If an item can be handled as one inaccessible unit for higherlevel purposes, it yields the same functional advantage as container transport – you need not worry about what is inside while you subject it to the relevant external operations.

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2. Functional explanation and the contexts of recursion From a functional point of view, linguistic recursion must be understood in relation to a two-tiered context. The immediate context is cognition – but cognition in turn has a context in the form of an environment which o¤ers ‘‘a¤ordances’’ (cf. Gibson 1966) that the mind can grasp, i.e., goals which can be achieved by means of recursive processing. The centrality of recursion to cognitive processing depends on ways in which recursion brings home the bacon, as it were. This means that we need to distinguish between recursion as a feature of linguistic mechanisms, as a feature of a cognitive process, and as a functional a¤ordance o¤ered by the environment. There is a functional relationship between them: if some tasks are usefully solved by recursion, cognitive recursion confers an advantage – and if this needs to be communicated, a recursive linguistic encoding mechanism is the most direct outlet. Thus, if there is a family tree in the hall, beginning with (say) William the Conqueror, the question of how the present incumbent is related to him can be answered via a recursive cognitive procedure that adds generations on top of each other, encodable (in English) by a linguistic operator (great-) that matches the cognitive steps that you need to take.3 Similarly, because the content of a message can in fact be recursively recontextualized, it makes sense to think of it as undergoing such a recursive process, and accordingly encode it by prefixing the original utterance with X says . . . until the proper relationship is established. The relationship between recursion in the three domains that this account leads one to predict is that there are more a¤ordances for recursion than there are actual cognitive processes exploiting those a¤ordances – and there are more cognitive processes than there are recursive linguistic encodings matching them. This prediction seems to be borne out for recursion in numbers. The structure of the number system, cf. Hauser (2000), is such that recursive processing can start from zero: the ‘‘successor function’’, the ability to add one to the previous number, is the central numerical operation. But recursive cognitive use of numbers standardly does not begin from zero, because it is simpler to ‘‘subitize’’ small numbers, i.e. to use a mechanism of pattern recognition (analogous to using constructional patterns in language). We recognize pairs and threes without having to 3. My Copenhagen colleague Michael Fortescue o¤ers the following attested example: according to family tradition, Sir Richard le fort, knighted by William the Conqueror, was his great-great . . . (24 greats) . . . grandfather.

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‘‘decompose’’ their cardinality by counting, as in the case of dot patterns on dice. But this skill takes us only so far. As we approach what Miller called the ‘‘magical number seven, plus or minus two’’, subitization ceases to be practicable – leaving cognitive recursion, i.e. counting, as the only option. Yet the languages we use to encode cardinality do not ‘‘turn recursive’’ at this point. English only resorts to recursive encoding somewhere between twelve and twenty-one – and the base-ten number system only becomes recursive with the number ten. In other words, the extent of recursion in the three domains is matched by their relations of inclusion: linguistically coded processes form a subset of actually used cognitive processes, which form a subset of the options for dealing with the environment. 3. O¿oading recursion – and the essential cognitive skill that remains Suggesting a precise function for recursion requires a precise definition; but there is considerable confusion in the literature, cf. Parker (2006) about what recursion is, and how to tell it from iteration. The criterion I suggest, building on Parker’s lucid discussion, is that recursion requires that you ‘‘keep count’’ of the operations – while iteration can apply an untracked number of times until the target is reached (with Parker’s example (2006: 5.2.3), as when you ‘‘stir the mixture until it becomes smooth’’). When you add another great to a sequence that ends with grandmother, you do not know what person you are designating unless you keep count; and when you prefix Mary says that, if you lose count of the embeddings, you no longer know who says what to whom. Nevertheless, as Parker points out, recursive procedures other than centre-embedding can be transformed into iterative processes. The basic idea is that a chain of iterations, each of which refers back to the previous one, can do the same thing as one overarching recursive procedure. A linguistic illustration of the idea can be given by converting one sentence with multiple embeddings into a sequence of sentences with anaphoric reference: (1) He says she says it’s OK

(linguistic recursion)

(2) It’s OK. She says so. At least, that’s what he says (linguistic iteration) The fact that the English complementizer that is historically derived from a demonstrative suggests that there may at one point in the history of English have been a historical transition from iterative to recursive encoding of the same content. But it is not always unproblematic to encode the

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full recursive cognitive process by iterative means – and the cognitive process must be recursive, otherwise you ‘‘lose count’’ of who said what to whom. The mechanism of anaphoric encoding, however, points to a coping strategy: if each previous stage is repackaged as one single whole (referred to by that), it can be treated as given rather than part of a whole ongoing processing procedure. This ‘‘reification’’ of the input reduces processing cost (cf. also Mithun, this volume). Using this strategy, plus a strategy for putting information into the environment, it is possible to o¿oad recursion entirely from the cognitive system. The ‘‘prisoner’s tally’’ consists in adding one stroke every evening to the list on the wall – a wholly iterative procedure. The accumulated strokes then constitute what Hutchins (2005) calls a ‘‘material anchor’’ for cognition, enabling the prisoner to keep up without taxing his system with recursion (between counts). Using a number system, he could o¿oad all recursive processing by adding one to the previous total on the wall every night, writing X þ 1 ¼ Y , and on the next day Y þ 1 ¼ Z, etc. Recursion would then be only an ‘‘a¤ordance’’ built into the record on the wall. Only two things cannot be o¿oaded: the ability to grasp the end result (no procedure would help a prisoner with a one-year sentence without the ability to grasp the figure 365) – and the single incremental step (e.g., the successor function). What is cognitively significant, I hypothesize, is therefore the type of single step that is required to build a complex recursive operation. Two requirements must be met: there must be no pre-determined starting point (i.e., no stimulus control), and no fixed end-point (or the process could not be re-applied). Working bottom-up, ‘‘re-applying’’ means reapplying the same process to its own output (or at least to something that has undergone the same process at some lower stage). On this assumption, recursion depends on a mechanism that has a suggestive analogy both with what Edelman (1992) calls ‘‘re-entrant processing’’, and the kind of recurrence characteristic of ‘‘recurrent nets’’, cf. Elman (1993). The assumption that this is the crucial cognitive skill makes it possible to establish a link between formal recursion and complex hierarchical processing, an operation that it has often been confused with (cf. Parker 2006). Hierarchy does not inevitably bring about recursion, because new levels may have constituents of new types, cf. Ladd (this volume). But if we assume that the crux is mastery of processes that can be applied in an open-ended manner, formal recursion (where the same formal operations

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are re-applied higher up) and complex hierarchical processing are two instances of the same thing – re-processing the previous output as part of a complex problem-solving procedure.

4. Final remarks: recursion, functional explanation and Piraha˜ According to the account suggested above, recursion does not constitute one single cognitive skill, although it may well be that at some evolutionary stage the cognitive system more or less suddenly became powerful enough to handle recursive processing. The central ability is to take the single incremental step of applying a particular operation on the available input (of applying the great operator, or of prefixing Mary said (this:) . . . to an expression indicating what Mary said). Recursive application of this ability, on the theory I have outlined, is something that people do when and if it is functional for them and they have the necessary processing power. The gradual bottom-up development into recursive processing and encoding can be illustrated with the following findings from an ongoing elicitation.4 A range of informants from four to eight years plus an adult group were shown a cartoon where Donald Duck is standing with a partly shattered snowball on his head; behind him a snowman dressed as Donald Duck is posed with a snowball in his hand, as if to throw another snowball at him. Behind the snowman we see the nephews, Huey, Dewey and Louie, peeking out and laughing. Among the findings were a clear developmental sequence such that below 5, informants describe (more or less successfully) what meets the eye – for example at 4;3 one informant says the snowman is throwing snow all over the duck. Beginning at 5;5, single mental embeddings creep in (they’re making a snowman like Donald Duck

4. The elicitation presented a group of 58 Danish and 72 English children between four and eight (with adult groups for comparison) with a range of pictures and picture stories. The key object of investigation was the encoding of perspective, including di¤erent points of view that played a role for the picture or picture story. In the case of the Donald Duck picture, the focus of interest was on the ‘theory-of-mind’-inspired issue of the conflicting beliefs that enter into the humorous potential of the cartoon. Instructions were minimal, but varied depending on the readiness of the individual informant to respond to each stimulus.

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and then they pretend he’s throwing a snowball). Only in the adult groups do we find the multiple embedding (mental and linguistic) for which the picture constitutes an a¤ordance: they made it so it looks like it was the statue doing it, so that when he turns around he’ll think it’s the statue who’s done it. Rather than being at the bottom of the language ability, then, recursion is something you build up towards. In the case of the Piraha˜, the absence of linguistic recursion does not in itself show anything about cognitive processing; but as suggested by Everett (2005), there are cultural reasons why there may be less cognitive recursion than in communities found in the US and Europe. In my terminology, there is a functional link: since there are fewer a¤ordances for recursive processing than in America and other postmodern cultures, it is to be expected that Piraha˜ speakers do less of it: no arithmetic classes, etc. However, one would expect there to be recursive processing of mental attitudes to other people’s mental attitudes (cf. Verhagen 2005, this volume) on intersubjective co-ordination); for reasons argued above, linguistic markers like sai indicating given (‘‘reified’’) material (cf. Sakel and Stapert, this volume), marking reference to previous sentences, would be logical tools for this process. I have suggested that some forms of recursion have a functional role in o¤ering an open-ended, encodable path beyond entrenched routines: if your goal cannot be accomplished by staying in the trenches, you can go over the top. However, this view severs the privileged Chomskyan link between recursion and the notion of indefinitely long sentences (cf. Hauser, Chomsky and Fitch 2002: 1571) – if you view language as a functional-cognitive accomplishment. Discrete infinity is a property of natural numbers and of language, but only if both are understood in formal terms as sets of numbers and sets of sentences. This is where the functional-cognitive and the formal-generative perspectives diverge: language can be formally simulated by a device that specifies possible sentences of indefinite length, but this specification is not part of the human language skill. The key functional-cognitive accomplishment (in the area of language, as well as in the area of numbers) is the ability to take one incremental step beyond the given, not an ability to go on forever. The status of infinity is no di¤erent from what applies in the case of walking: having the walking competence enables us to set one foot in front of the other, and does not specify any constraints on how many times we can do it – but we are not born to take infinitely long hikes.

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References: Barlow, Michael and Suzanne Kemmer (eds.) 2000 Usage Based Models of Language. Stanford: CSLI Publications. Chomsky, Noam 1965 Aspects of the Theory of Syntax. Cambridge, Mass.: MIT Press. Edelman, Gerald M. 1992 Bright Air, Brilliant Fire. On the Matter of the Mind. New York: Basic Books. Elman, Je¤rey 1993 Learning and development in neural networks: The importance of starting small. Cognition 48: 71–99. Everett, Daniel L. 2005 Cultural Constraints on Grammar and Cognition in Piraha˜. Current Antropology 46 (4): 621–645. Gibson, James J. 1966 The Senses Considered as Perceptual Systems. Cambridge: Cambridge University Press. Goldberg, Adele E. 1995 Constructions: A Construction Grammar Approach to Argument Structure. Chicago: Chicago University Press. Harder, Peter 2006 Recursion in a functional-semantic grammar. In Timo Haukioja (ed.), Papers on Language Theory, 67–105 (Publications in General Linguistics 10.) Turku, Finland: University of Turku. Harder, Peter 2007 Grammar, flow and procedural knowledge: Structure and function at the interface between grammar and discourse. In Mike Hannay and Gerard Steen (eds.), Structural-Functional Studies in English Grammar. Amsterdam/Philadelphia: John Benjamins. 309–335. Hauser, Marc D. 2000 Wild Minds. What Animal Really Think. New York: Holt. Hauser, Marc D., Noam Chomsky and W. Tecumseh Fitch 2002 The faculty of language: What is it, who has it, and how did it evolve? Science 298: 1569–1579. Hutchins, Edwin 2005 Material anchors for conceptual blends. Journal of Pragmatics 37: 1555–1577. Itkonen, Esa 1976 The use and misuse of the principle of axiomatics in linguistics. Lingua 38: 185–220. Jackendo¤, R. 2002 Foundations of Language. Oxford: Oxford University press.

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McGregor, William 2004 Paper given at the symposium on recursion, Linguistic Department, University of Aarhus, March 25, 2004. Parker, Anna R. 2006 Evolution as a Constraint on Theories of Syntax: The Case against Minimalism. Ph.D. Dissertation: University of Edinburgh. Pawley, Andrew K. and Frances H. Syder 1983 Two puzzles for linguistic theory: nativelike selection and nativelike fluency. In Jack C. Richards and Richard W. Schmidt (eds.), Language and Communication, 191–226. London and New York: Longman. Pinker, Steven and Bloom, Paul 1990 Natural Language and Natural Selection. Behavioral and Brain Sciences, 13: 707–784. Pinker, Steven and Ray Jackendo¤ 2005 The Faculty of Language: What’s Special about it? Cognition 95 (2): 201–236. Sinclair, John M. 1991 Corpus, Concordance, Collocation. Oxford: Oxford University Press. Tomasello, Michael 2003 Constructing a Language. A Usage-Based Theory of Language Acquisition. Cambridge, MA: Harvard University Press. Verhagen, Arie 2005 Constructions of Intersubjectivity. Discourse, Syntax, and Cognition. Oxford: OUP. Wray, Alison 2001 Formulaic Language and the Lexicon. Cambridge: Cambridge University Press.

Part IV.

Recursion and the Lexicon

14.

Lack of recursion in the lexicon: The two-argument restriction1

Eva Juarros-Daussa`

1. Introducing the TAR Throughout this paper, argument structure is taken to be the level of linguistic representation which includes a predicate and all of its lexically encoded arguments, as well as any adverbial or specific semantic information associated with them (Hale and Keyser 2002). This is the narrow sense of the term, usually closely associated with the notion of the valence of a predicate. In contrast, a broader sense includes any wordform formed in the course of syntactic or discursive valence-changing operations (some of which will be discussed below), which may contain a larger or smaller number of event participants than those specified in its argument structure in the narrow sense. This paper explains the basic fact (apud Hale and Keyser 2002) of (narrow) argument structure that verbs cannot take more than three lexical arguments – more precisely, one subject, or external argument, and two objects, or internal arguments, as in the English verb give (1). (1) [The LinguistList] gave [nice prizes] [to the winners of the challenge] Introducing a conceivable additional participant without the help of a lexical preposition (such as for in (3) below) which contributes its own argument-taking abilities, results in ungrammaticality (2):2 1. Thanks to Chisato Kitagawa, Jean-Pierre Koenig, Tilman Lanz, Tom Roeper, Peggy Speas, Ellen Woolford, and two anonymous reviewers for their generous help. 2. Crucial to the paper is also the distinction between lexical argument and syntactic (or discursive) adjunct. Unfortunately, no set of necessary and su‰cient criteria has been universally agreed upon as the basis of the distinction between arguments and adjuncts (see recent proposals by Koenig et al. 2003, Boland 2005, and Randall, to appear, all of which include obligatoriness (apud Dowty 1991) as a minimum, but not su‰cient, fundamental criterion). For space reasons, I put aside justifying the argumental status of the elements considered as such in the examples presented throughout this article.

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(2) *[The LinguistList] gave [nice prizes] [to the winners] [the students] (3) [The LinguistList] gave [nice prizes] [to the winners] [for the students] In this article, I formulate the above observation as the Two-Argument Restriction (TAR): ‘‘A single predicate can have at most two internal arguments and one external.’’ I claim that the TAR is an unrestricted universal (in the sense of Croft 1990). I argue that the commonest valence-increasing operations, which result in applicative and causative constructions, while they present a challenge, however do not to violate the TAR. I further show that, since there is no known processing or discursive reason not to lexically associate more than three (strictly, two) participants to a predicate, the TAR is syntactic in nature, and it is one of a family of architectural constraints that determine and limit possible attainable languages (in this case possible argument structures). Following this idea, I show that the framework of lexical syntax put forth by Hale and Keyser (2002) is especially suited to derive the TAR at the theoretical level. Moreover, in my proposal, deriving the TAR crucially involves negating the existence of a recursive function in the domain of argument structure. 1.1. Challenges to the TAR Some data might seem to pose a problem to the TAR: I group them in three categories: applicative constructions, causative constructions, and bet-verbs. In many languages we find lexical processes that seem to add an argument to the basic argument structure of a predicate, known as valencechanging operations (Dixon and Aikhenvald 2000). Normally, they involve the promotion of a peripheral participant to core argument status. As a result, there is either a change of transitivity or a rearrangement of the argument structure of the predicate (Comrie 1985). The most usual ones result in applicative and causative constructions. Applicative constructions appear in many genetically unrelated languages (Dryer 2005). By far, the commonest type is the one that derives transitive forms of a primitive intransitive, as seen in the following examples from Hakha Lai (Peterson 2007: 22–23), in which the applicative morphemes and their meaning are in bold. Example (4) shows the primitive intransitive predicate, (5) shows the creation of a transitive through the addition of an applicative morpheme, and (6) shows that the introduction of the extra argument is dependent on the applicative morpheme:

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(4) ?a-thi? 3s-die2 ‘He died’ (5) ?a-ka-thi?-hno? 3s-1s-die 2-MAL ‘He died on me’ (6) *?a-ka-thi? 3s-1s-die 2 ‘He died ?? me’’ Applicative constructions can also create ditransitive predicates from basic transitive verbs, as exemplified by Bukusu below (Peterson 2007: 7): (7) wanjala a-a-kul-a Wanjala 3sS-TENSE-buy-FV ‘Wanjala bought a book’

sii-tabu C17-book

(8) wanjala a-a-kul-il-a omu-xasi sii-tabu Wanjala 3sS-TENSE-buy-APP-FV CL1-woman C17-book ‘Wanjala bought a book for the woman’ Crucially, however, several authors note that applicatives do not seem to be able to increase the valency of lexically ditransitive verbs. As Peterson (2007: 63) notes: ‘‘A ( . . . ) restriction that is rarely noted is the inability to use an applicative construction with trivalent bases. Such restrictions are explicitly noted for Yima (Foley 1997: 372), Alamblak (Bruce 1984: 232), and Sesotho (Machobane 1989: 111).’’ For example, in Sesotho, the applicative morpheme that freely appears with intransitive and transitive verbs cannot appear with a ditransitive verb to create a four-place predicate: (9)

ntate o-f-a bana lijo father AGR-give-FV children food ‘My father gives food to the children’

(10) *ntata o-f-el-a morena bana lijo father AGR-give-APP-FV chief children food ‘My father gives food to the children for the chief ’ If Peterson is correct, applicative constructions do not pose a challenge to the TAR. However, things might not be so simple, since other authors

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document the possibility in some languages to attach various applicative morphemes to a single root, as in the following example from Pajonal Campa (Dixon and Aikhenvald 2000: 170, apud Shaker 1971): (11) no-p-ako-ts-imo-tsi-ro-ri 1sg-give-REFERENCE.TO-EPENTHETIC-IN.PRESENCE.OFASPECT-3sgF-3sgM Irena Irocarto pano Irene Richard scarf ‘I gave Richard the head scarf in Irene’s presence’ Independently, Martin (2000: 400) notes: ‘‘we find that derivation in Creek can add as many as four arguments to a clause, in principle allowing seven-place verbs to be derived from basic three-place verbs’’. Although no examples are given of such monster predicate, if applicative morphemes are taken to indicate the argumental nature of the participants they introduce, and if Martin and others are right in that more than two internal arguments can thus be lexically associated to a single root, the generalization expressed by the TAR would be seriously challenged.3 It is hard to reconcile the contradictory claims about the possibility of creating larger than three-place predicates through applicative morphemes. Surely, a more detailed analysis of the construction is needed. Much work has been recently produced on the syntax and semantics of applicatives that might shed some light on the question (Marantz 1993; McGinnis 1998, 2001; Pylkka¨nen 2002; McGinnis and Gerdts 2003; Jeong 2007). Throughout these proposals, there seems to be a consensus that there are two kinds of applicative structures, which correspond to a di¤erent syntactic and semantic behavior of the arguments involved. Crucially, only one of these types is introduced below the VP level, the level of (narrow) argument structure that is the focus of this article. If the claim could (generally) be made that this kind of applicative is the one that presents no recursion, applicatives would cease to pose a potential problem for the 3. A reviewer correctly notes that the issue of whether three-argument verbs can take applicatives should be separated from the issue of multiple applicative derivations. For example, in Lander & Letuchiy (this volume), there are examples of the second kind in Adyghe, and it is argued that they instantiate recursion. The reviewer however notes that these are not standard applicatives in Peterson’s sense, for in this case applicatives do not change the initial argument structure. No cases of the first type are reported in Adyghe.

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TAR. For now, and leaving aside the question of identifying tests that elicit the di¤erent structures assigned to the particular applicative constructions for each particular language, I will adopt this working hypothesis, and thus keep maintaining that the TAR is a valid generalization, even in light of applicative phenomena. The other typologically extended valence-increasing operation is the causative. Dixon (2000: 30) defines it as a construction involving ‘‘the specification of an additional argument, a causer, onto a basic clause’’. Like applicatives, causatives prototypically apply to an underlying intransitive and form a derived transitive, as in the English verb trip: (12) John tripped (13) Mary tripped John The challenge to the TAR appears with serial causative constructions, which present two verbs in one predicate, especially in the case of causativization over ditransitives, as in the following Tariana example (Dixon 2000: 42): (14) phia kalisi Yuse isiu pi-kalite-de 2sg story Jose´ for 2sgA-tell-FUT ‘You will tell a story to Jose´’ (15) nuha pina kalisi Yuse isiu [nu-a-de nu-kalite-de] 1sg 2sg story Jose´ for 1sA-CAUS-FUT 1sgA-tell-FUT ‘I will make you tell a story to Jose´’ Other examples of causativization of three-place verbs are also documented for Creek (Martin 2000: 397), and Georgian (Dixon 2000: 56– 57). Even more puzzling is the appearance of multiple causative morphemes in a single root, as documented in Tsez by Comrie (2000: 369; see also Kulikov 1993; Lander and Letuchiy, this volume), who comments, ‘‘It is possible to have two causative su‰xes in sequence in Tsez, the semantic interpretation being the causative of a causative’’: (16) ucˇitel-a# uzˇi-q kidb-eq kecˇ teacher-ERG boy-POSS girl-POSS song.ABS q’ali-r-er-si sing-CAUS-CAUS-PAST.WIT ‘The teacher made the boy make the girl sing a song’

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Again, multiple causatives might pose a challenge to the TAR, if their analysis shows that all the participants of the predicate are indeed arguments dependent on a single root. It is beyond the scope of this paper to properly address this challenge; one suspects that, if it can be proven that the added arguments are always external (subjects), which are therefore not included in the lexical argument structure, a restriction like the TAR, which is concerned with the two internal arguments, is not contradicted by causative constructions. Tentatively, thus, and for the sake of the present argument, I will keep assuming that the TAR exists. Finally, beyond the productive constructions just reviewed, there is a small group of verbs that crosslinguistically appear to have a higher valence than the commoner ditransitive. They can be exemplified by the verb bet in English:4 (17) [I] bet [you] [three dollars] [that he comes back] While extremely limited in number, the existence of these verbs, and the argumental character of its dependents, is likely to be uncontroversial. They therefore pose a real counterexample to the TAR. I have nothing to say about them in the brief space allotted for this article, except that their violating a strong universal generalization might account for their rarity.5 In recapitulation: we have seen some potentially challenging data to the TAR. Further work is necessary to examine these cases in detail, and assess whether the generalization of there to be a maximum number of arguments lexically associated to a single predicate exists. Still, the prevalence of a three-argument upper limit is generally accepted in the literature, at least implicitly. Therefore, and having pointed out in some detail the challenges that will have to be addressed in order to fully prove the universal character of the restriction, let us assume that the TAR is valid, and argument structures, in their narrow sense, have a limit of three arguments – more specifically, one external and two internal ones. 2. Deriving the TAR Ideally, the TAR, as an empirical generalization, would follow from independent principles of grammar. To that purpose, it is useful to recall that, 4. I thank Jean-Pierre Koenig for pointing this group of verbs out to me. 5. A reviewer suggests that the fact that such verbs (at least in English) normally require a clausal complement might be the key for an explanation.

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in essence, what we are deriving here is the fact that argument structures are finite in a way that sentential structures are not: they limit the number of linguistically encoded participants, where at the level of sentences there is not such restriction. Now, it is well known that in many grammars recursion is the formal mechanism to attain this kind of infinitude at the sentential domain.6 Therefore, one obvious way to explain the lack of infinitude in argument structures is to simply claim that recursive mechanisms are not available in this grammatical domain. This apparently simple move only makes sense within a theory that otherwise assumes the same principles to apply for the levels of argument (lexical) structure and sentential structure – otherwise, the finitude of argument structures would be a fact incommensurable with the infinitude of sentences (they would just form two di¤erent grammatical systems, and their properties following from the same mechanisms would be no more than a coincidence). Hale and Keyser (2002) present such theory, and I next show that, when assuming it, the claim of there be no recursion in the building of argument structures precisely derives the facts captured by the TAR. 2.1. Hale and Keyser’s (2002) theory of lexical syntax Lexical syntax, as it is compiled from a series of formerly distributed articles in Hale and Keyser 2002 (henceforth H&K), is a theory of the grammatical level representing the relationships between the verb and its arguments, without taking into account their extended or functional projections. It assumes that a verb’s argument structure is not a mere enumeration of its arguments, but rather a structural representation that follows the same principles as sentential syntax. For example, H&K claim that the constrained nature of argument structure follows from the structural properties of the existing lexical categories. Two structural relations are taken as basic: whether the head category (h below, the root) has a specifier (spc) or not, and whether it has a complement (cmp) or not. (a is an unprojected head). Based on these parameters, H&K distinguish the following four lexical structural categories:

6. In strings captured by rules in which an element contains another element of its same type. For example, NP ! N PP and PP ! P NP, which results in potentially infinite NPs.

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Monadic [þcmp] [spc]

Basic Dyadic [þcmp] [þspc]

Composite Dyadic [cmp] [þspc]

Atomic [cmp] [spc] h

Argument structures are obtained by combination of the basic structural categories. Prototypically, the above configurations correspond to the following taxonomy in the verbal domain, respectively: (18) a. b. c. d.

monadic: unergative (John laughed ) or (pseudo)transitive (John made a fuss) basic dyadic: transitive (I shelved books) or ditransitive (I put books on the shelf ) composite dyadic: unaccusative (Many guests arrived; The screen cleared ) atomic: presumably weather verbs (It rains), although they are not discussed in H&K.

More complex argument structures are obtained by combining the basic lexical categories with each other. For example, the two possibilities in merging a basic dyadic and a monadic categories give the following two di¤erently behaved ditransitive verbs:7 (19) The pigs splashed mud on the wall / Mud splashed on the wall (20) The pigs smeared mud on the wall / *Mud smeared on the wall Crucially, in building argument structures H&K allow for unrestricted, recursive combination of the lexical categories. The result is that their system produces a potentially infinite number of argument structure types – which translates into a potentially infinite number of arguments associated with a single root. For example, in their argument structure for give, as in I gave the bottle to the baby, a basic dyadic category contains another basic dyadic category, a classical example of recursion (H&K 2003: 163): 7. For a treatment of these verbs, see Juarros-Daussa` (2006).

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(21)

In H&K, nothing prevents recursion of the lexical categories in this fashion; in fact, it seems that H&K’s model actually predicts that, in order to build the argument structures of verbs with two internal arguments (such as give above), recursive merging of the basic lexical categories is actually required. Driven to its ultimate consequences, this situation has the potential to create argument structures with an unlimited number of arguments, each one introduced by recursive combination of the basic lexical categories. Such structures would obviously be violating the TAR – something that does not occur in natural language. In order to solve this situation, I propose a general constraint that restricts the combination of the primitive lexical categories assumed in lexical syntax to one of each instance per argument structure. I call this the Uniqueness of Selection Hypothesis (USH): ‘‘An argument structure can contain two lexical categories x; y only if x A y’’. This principle amounts to negating the existence of a recursive function in the domain of argument structure, relegating such functions to other grammatical domains.8 The task is now to show that by adopting a simple restriction like that of the USH, the mystery of the TAR can be solved. I claim that this is so 8. While if the TAR is right, no language would make use of recursive mechanisms of this type in the domain of argument structure, languages could di¤er on the extent to which they use recursion in other domains: e.g., Progovac (this volume) identifies a layer of grammar without recursion in well-known modern languages, and Everett (2005) shows that a language like Pirahặ does not use recursion at all in its grammar.

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because the USH both derives the most complex argument structure (that of a verb with two internal arguments), and it accounts for the maximality of such structure: any larger structure would require recursive introduction of lexical categories, thus violating the USH. But first I will briefly discuss an interesting consequence of the USH, that of actually predicting the number of argument structure types that can occur in natural language. If argument structures are obtained by mere combination of the basic lexical categories assumed in the lexical syntax approach, and if the number of categories that can be present in a single lexical entry is restricted to one of each type by the USH, the interesting possibility presents itself of actually calculate, in an abstract manner, the number and structural configuration of all possible argument structure types potentially allowed in natural language. Brute mathematical calculation results in 64 possible structures.9 The importance of this number is not the quantity in itself; rather, that we have a strong prediction to test empirically. Interestingly for our purposes of deriving the TAR, amongst the abstract structures predicted in this fashion we find the one of two internal arguments attached to a root, which happens to be the largest structure allowed by the system (mainly, the one in which one instance of each lexical category appears, exhausting the combinatorial possibilities allowed by the USH). Next I show precisely how this is so. Many verbs have the maximal argument structure of a verb with two internal arguments: obligatory ditransitives like give, send, etc., optional ditransitives like write, kick, etc., prepositional verbs like put, splash, pour, etc.; and within the latter, many denominal verbs that have received special attention in the literature: butter, nail, spit, etc. (Jackendo¤ 1990; Randall in press; Juarros-Daussa` 2003). Take spit, which presents the following argumental possibilities: (22) a. When llamas get upset, they spit b. The volcano started spitting ash and lava c. The baby spat porridge on the table

[VP Vunergative] [VP Vtransitive NP] [VP Vresultative NP PP]

The latter example is one of the verb with two internal arguments. Here is a sketch of an analysis of this possibility that makes use of no recursion in the sense discussed above (based on Juarros-Daussa` 2003).

9. The calculation being: 1P: n ¼ 4; 2P: n(n 1) ¼ 12; 3P: n(n 1) (n 2) ¼ 24; 4P: n(n 1) (n 2) (n 3) ¼ 4! ¼ 24; Total: 64. I thank Gert Ho¤mann for mathematical advice.

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First, the root (spit is an atomic element which by itself would be realized as the noun spit:10 (23) [a (spit] In order to project a specifier for its argument, (spit merges with a composite dyadic category: (24) (The) spit of porridge

Next, a small clause analysis of the resultative construction is assumed (Stowell 1983, Bowers 1991)11, here implemented by a basic dyadic category: (25)

(spit merges this structure as its argument to form spit of porridge on the table: (26)

10. Presumably, by merging with the functional category D (Marantz 2000, Alexiadou 2001, McGinnis 2001, Borer 2005). 11. Note that Kratzer (2004) outlines an alternative analysis of resultatives as uniformly raising constructions, in the context of arguments being introduced by functional categories (see also Borer 2005).

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The complex is then embedded under a suitable monadic head to form the activity verb or nominal: (27) (The baby) spat porridge on the table / (The) spitting of porridge on the table

The crucial feature of (27) is that, assuming the USH, it exhausts the combinatorial possibilities of the lexical categories: there is one instance of each. This makes (27) the largest argument structure allowed in natural language. Since it is a structure in which two arguments are associated to one single root, the TAR is thus derived. A final note towards the lexical syntax of double object constructions: according to (27), the argument structure of give should be something in the lines of (28): (28) (Jaana) gave a present to Alexandra

3. Conclusion This article claims that the TAR exists; any other procedures of introducing additional arguments is syntactic or discursive, not lexical (and as

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such, it could allow recursion). As shown, a modified version of H&K can account for this restriction. In this proposal, the TAR crucially depends on the lack of recursion in the lexicon (in building argument structures), restricting the possibility of using this formal mechanism to the domain of sentential syntax (building of sentences).

References Alexiadou, Alexandra 2001 Functional Structure in Nominals. Amsterdam, John Benjamins. Boland, Julie E. 2005 Visual Arguments. Cognition 95. 237–274. Borer, Hagit 2005 In Name only. Structuring Sense. Oxford: Oxford University Press. Bowers, J 1991 The syntax and semantics of nominals. Proceedings from SALT I. Cornell Working Papers in Linguistics 10. 1–30. Comrie, Bernard 1985 Causative verb formation and other verb-deriving morphology. In Language Typology and Syntactic Description 3. T. Shopen (ed). 309–48. Cambridge: Cambridge University Press. Comrie, Bernard 2000 Valency-changing derivations in Tsez. In: R.M.W. Dixon and A. Aikhenvald (eds.). Croft, William 1990 Typology and Universals. New York: Cambridge University Press. Dixon, R.M.W. 2000 A typology of causatives: form, syntax and meaning’. In R.M.W. Dixon & A. Aikhenvald, (eds.). Dixon, R.M.W. and A. Aikhenvald (eds.) 2000 Changing Valency. Case studies in Transitivity. Cambridge, UK: Cambridge University Press. Dowty, David 1991 Thematic Proto-Roles and Argument Selection. Language 67, 3. 547–619. Dryer, Matthew S. 2005 Genealogical Language List. In M. Haspelmath, M. Dryer, D. Gil and B. Comrie (eds.) The World Atlas of Language Structures. Oxford, UK: Oxford University Press. 584–644. Everett, Daniel 2005 Cultural constraints on grammar and cognition in Pirahặ. Current Anthropology, 46.4: 621–646.

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Foley, William 1997

Polysynthesis and complex verb formation: the case of applicatives in Yimas. In Complex Predicates. A. Alsina, J. Bresnan & P. Sells (eds.) 355–95. CSLI. Hale, Kenneth and S.J. Keyser 2002 Prolegomenon to a Theory of Argument Structure. Cambridge, MA: MIT Press. Jackendo¤, Ray 1990 Semantic Structures. Cambridge, MA: MIT Press. Jeong, Youngmi 2007 Applicatives. Amsterdam: John Benjamins. Juarros-Daussa`, Eva 2003 Argument structure and the lexicon-syntax interface. PhD dissertation, University of Massachusetts, Amherst. Juarros-Daussa`, Eva 2006 Why four kinds of V (DP) PP? In Brunting, J., S. Deasai, R. eachey, C. Straughn, and Z. Tomkova´ (eds.): CLS 42: 1: The Main Session. The Chicago Linguistics Society: Chicago. 87–101. Koenig, Jean-Pierre, Gail Mauner, and Breton Bienvenue 2003 Arguments for Adjuncts. Cognition 89. 67–103. Kratzer, Angelika 2004 Building resultatives. Ms., University of Massachusetts, Amherst. Machobane, M. 1989 Some restrictions on the Sesotho Transitivizing Morphemes. PhD. dissertation, McGill University. Kulikov, Leonid 1993 The ‘second causative’: a typological sketch. In B. Comrie and M. Polinsky (eds.), Causatives and Transitivity. 121¤. Marantz, Alec 1993 Implications of asymmetries in double object constructions. In S. Mchombo (ed.): Theoretical Aspects of Bantu Grammar. Stanford, CA: CSLI. 113–150. Marantz, Alec 2000 Words. Ms, MIT. Martin, J. 2000 Creek voice: beyond valency. In Dixon and Aikhenvald, (eds.). McGinnis, Martha 1998 Locality in A-movement. Ph.D. dissertation, MIT. McGinnis, Martha 2001 Variation in the phase structure of applicatives. In J. Rooryck & P. Pica (eds.): Linguistic Variations Yearbook. Amsterdam: John Benjamins. 105–146. McGinnis, Martha and D.B. Gerdts 2003 A phase-theoretic analysis of Kinyarwanda multiple applica-

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tives. Proceedings of the 2003 Annual Conference of the Canadian Linguistic Association. Montre´al, Universite´ du Que´bec. 154– 165. Peterson, D. 2007 Pylkka¨nen, L. 2002 Randall, Janet. In press Stowell, Tim 1983

Applicative Constructions. Oxford University Press. Introducing Arguments. Ph.D. dissertation, MIT. Linking: the geometry of argument structure. Springer. Subjects across categories. The Linguistic Review 2: 285–312.

15.

Kinds of recursion in Adyghe morphology

Yury A. Lander and Alexander B. Letuchiy

1. Introduction1 Since the early years of generative grammar, the concept of recursion in linguistics has been primarily associated with syntax (see, e.g., Tomalin 2007). Yet, if by recursion we understand application of a derivation to material containing the result of the same derivation, any language level employing derivations can theoretically show recursion. Therefore a generalization stating that recursion is mainly a syntactic property should be pretty non-trivial. One problem with such a generalization relates to polysynthetic languages, where morphology takes much work that is done by syntax in other languages. Perhaps because of this, polysynthetic morphology may manifest characteristics which are usually ascribed to syntax, at times including recursion. This is shown in the following example from Central Siberian Yupik, where we find two occurrences of the so-called postbase su‰x ‘ask to’, which presumably constitute two di¤erent layers of derivation:2 1. Most data presented here were collected in 2003–2006 in the village of Hakurinohabl (Republic of Adyghe, Russian Federation) within a project supported by the RGNF grants No. 03–04–18010e, 04–04–18008e, 06–04–00194a. The material presented in Section 3 relies partly on the work of Natalia Korotkova and Anna Kursakova. We are grateful to our language consultants for their help, especially to Zarema Meretukova for her contribution at the last stage of the preparation of a manuscript. Thanks also to other participants of the project for discussions and to George Hewitt and two anonymous reviewers for useful comments. All errors are ours. 2. Abbreviations used in glosses: a agent, abs absolutive, aux auxiliary morpheme, ben benefactive, caus causative, com comitative, cond conditional, dir directive, dyn dynamic a‰x, emp emphatic, fcl facilitive, fut future, hbl habilitive, inadv inadvertitive, indic indicative, instr instrumental, io indirect object, lnk linker, loc locative, neg negation, obl oblique case, opv general oblique preverb, pl plural, poss possessive, pot potential, pr possessor, pred predicative, pst past, ptcl particle, re reversive/refactive, rec reciprocal, sg singular, sml simulative, tmp temporal, trm terminative. Numbers denote persons.

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(1) iitghesqesaghiisqaa itegh-sqe-yaghtugh-sqe-aa come.in-ask.to-go.to-ask.to-indic.3sg ‘Hei asked himj to go ask himk to come in.’ (de Reuse 2006: 745) In this paper we argue, however, that even in such languages recursion may be allowed to di¤erent extents in di¤erent parts of the word and be highly constrained exactly in contexts that are considered prototypical for recursion. Hence this property is indeed not as natural for morphology as for syntax. Our arguments are based on the material of (Temirgoi) Adyghe, a highly polysynthetic language of the Northwest Caucasian family comprising, besides Adyghe, Kabardian, Abkhaz, Abaza and the now extinct Ubykh language. Figure 1 represents the general make-up of the Adyghe verb.3

Argument structure zone

Pre-stem elements

Causative marker(s)

Root (plus wordformation)

Propositional operators Endings

Stem Figure 1. Make-up of the Adyghe verb

The Adyghe verb consists of several zones, which are separated on the basis of functional and morphophonemic criteria which we cannot discuss in detail.4 The argument structure zone includes predominately cross-reference prefixes (as well as reflexive, reciprocal and relative prefixes, which have the same distribution) and markers providing information about the roles of participants of the situation. The pre-stem zone and the zone of endings mainly contain a‰xes that are responsible for the syntactic distribution of the form. The stem maximally consists of the prefixal causative marker(s), the root (sometimes together with undeniably word-formative a‰xes) and the zone of propositional operators which includes, in particular, su‰xes referring to the tense, aspect and modality. Consider the following example: 3. For the sake of simplicity, we disregard complex multi-stem forms, which comprise reduplicatives and certain tense forms discussed in Korotkova and Lander (Forthcoming). 4. For the relevant morphophonemic criteria see Smeets 1984; Arkadiev and Testelets (Forthcoming), and Korotkova and Lander (Forthcoming).

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(2) a-r Ø-je-mə-ŝ wa-ʁ-ew Ø-š’ə-tə-ʁ-ep that-abs 3sg.io-opv-neg-drink-pst-pred 3sg.io-loc-stand-pst-neg ‘He was not sober.’ (Literally: ‘He did not stand not being drunk.’) The dependent verb form je-mə-ŝ wa-ʁ-ew ‘not being drunk’ in (2) can illustrate most zones postulated above. The argument structure zone of the form includes the 3rd singular indirect object prefix (cross-referencing the undergoer of the formally intransitive bivalent root ‘drink’) introduced by the so-called general oblique preverb. Pre-stem elements are represented by the narrow scope negative prefix mə-. The root ŝ wa ‘drink’ is followed by the zone of propositional operators, which manifests itself with the past su‰x. The last morpheme -ew, which marks the form as dependent, belongs to the class of endings. Pre-stem elements and endings do not display recursion, but the argument structure zone and the stem do. These are considered in sections 2–4: in Section 2 we discuss recursion in the argument structure zone, in Section 3 recursion in the su‰xal zone is analyzed, and in Section 4 we consider multiple causatives. Section 5 discusses data given in previous sections. Section 6 presents conclusions.

2. Recursion in the argument structure zone: applicatives The initial part of the Adyghe verb contains prefixes cross-referencing arguments, applicative markers and a directive prefix; cf. Figure 2.5 The first slot is designed for prefixes cross-referencing absolutive arguments, i.e. intransitive subjects and undergoers of transitive verbs (note

Absolutive argument

Directive

Temporal argument

Adjuncts: applicatives

Agent argument

Figure 2. The argument structure zone 5. The arrangement shown in Figure 2 can be violated where the directive prefix is expected to precede the 3rd person plural applicative object prefix. In this case, the cross-reference prefix at surface may precede the directive marker rather than follow it (Smeets 1984: 182). We assume that this is a surface phenomenon which is not related to the overall structural organization of the zone.

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that Adyghe also has multivalent intransitive verbs whose undergoers are marked as indirect objects). This slot remains empty when the absolutive phrase is of the 3rd person. The directive prefix occupying the second slot has the meaning ‘hither’ with verbs of motion but also appears as an inverse marker with non-motion verbs. The third slot (‘‘temporal argument’’) is only observed in some temporal clauses and is not relevant for us. Next come applicatives expressing such relations as location, comitative, benefactive etc. Each applicative consists of a preverb indicating the role added to the argument structure, preceded by a person prefix filling this role. The last slot within the argument zone is reserved for the agent prefix, which appears in transitive verbs. The following example (artificial but accepted by consultants) demonstrates most parts of this zone, except for the temporal argument: (3) sə-qə-t-de-p-fə-Ø-r-a-ʁa-ǯe-š’tə-ʁ 1sg.abs-dir-1pl.io-com-2sg.io-ben-3sg.io-opv-3pl.a-caus-readaux-pst ‘They were making me read it to you together with us.’ Here we find the 1st person singular absolutive prefix, the directive prefix, three applicatives t-de- ‘with us’, p-fə- ‘for you’ and Ø-r- (the last introduces the undergoer of the caused situation treated in this case as indirect object), and the 3rd person plural prefix cross-referencing the agent/causer. Most parts of this zone do not allow for recursion. However, applicatives constitute an exception to this. Note that Adyghe applicatives add indirect objects rather than direct objects (as is common for applicatives cross-linguistically; see Baker 1988; Peterson 2007) and hence do not a¤ect the already established part of the argument structure. As (3) demonstrates, this makes it possible for a single verb to contain several applicatives, which form an applicative chain. The same is shown by the two alternative verb forms in (4): (4)

jeǯap ̣e-m rwəsλan mefeč ̣’ə-šx we school-obl Ruslan festival-big Ø-fə-Ø-š’-a-ṣ̂ə-ʁ / 3sg.io-ben-3sg.io-loc-3pl.a-make-pst Ø-š’ə-Ø-f-a-ṣ̂ə-ʁ 3sg.io-loc-3sg.io-ben-3pl.a-make-pst ‘They made a big festival for Ruslan.’

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The predicate in (4) contains two applicatives, namely the applicative introducing the beneficiary (Ruslan) and the applicative introducing the location (the school). As the example makes clear, the order of applicatives is not fixed (cf. Jakovlev and Asˇxamaf 1941: 356–357). The co-presence of several applicatives suggests recursion. In order to prove its presence, we should show that di¤erent applicatives represent the same kind of derivation and their chain is organized by layers. At first glance, all applicatives look alike: they are constructed in the same way and have the same morphosyntactic impact, namely the introduction of a new argument (albeit some applicative – root combinations became fixed). Still, they do not form a formally homogenous class. Thus, applicatives formed by the general oblique preverb, whose basic form is je-, must be distinguished from other applicatives (concrete applicatives, henceforth) on the basis of the fact that general oblique applicatives never swap places with concrete applicatives, with a few well-defined exceptions, must occur at the very end of that part of the argument structure zone that is reserved for applicatives and in some morphophonemic contexts even can omit the applicative marker;6 cf. (5a) and (5b): (5) a. b.

qə-Ø-š’ə-s-a-tə-ʁ dir-3sg.io-loc-1sg.io+opv-3pl.a-give-pst *qə-s-e-Ø-š’-a-tə-ʁ dir-1sg.io-opv-3sg.io-loc-3pl.a-give-pst ‘They gave it to me there.’

In (5a) we find a general oblique applicative ‘to me’ that is placed immediately before the agent prefix and follows a concrete applicative. Note that in this example the oblique preverb (which is normally represented by a vowel after the 1st and 2nd person prefixes), is reduced. In (5b), on the other hand, the general oblique applicative precedes the concrete applicative, and this makes this form infelicitous. Importantly, the contrast between general oblique and concrete applicatives also has a functional motivation. The general oblique preverb 6. In fact, there is no agreement in the literature on whether the general oblique morpheme should be regarded as applicative. Jakovlev and Asˇxamaf (1941), Kumakhov (1964) and Smeets (1984) state that indirect objects proper are expressed by single morphemes. However, Rogava and Kerasˇeva (1966) postulate the oblique preverb, and so do we. Some morphophonemic arguments for the latter view can be found in Arkadiev and Testelets (Forthcoming).

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introduces arguments that are closely related to the semantics of the stem.7 The roles of such arguments are often implied by the specific components within the semantics of the stem (as, for example, the recipient role is implied by the semantics of the verbs of giving), and this is probably the reason why the applicative prefix occasionally can be omitted in this case. Concrete applicatives, on the other hand, are functionally equivalent to adjunct postpositional phrases,8 they are formally optional and do not a¤ect the core argument structure, nor are the arguments introduced with concrete applicatives implied by the specific semantics of the stem. Despite these di¤erences, if we look at general oblique applicative chains and concrete applicative chains in isolation, we find good evidence that both of them instantiate recursion, i.e. their chains have layered organization.9 We will assume below that this can be shown by demonstrating that some applicatives can be sensitive to others. Thus, for multiple general oblique applicatives, it can be shown that their order is not accidental. This becomes most clear when we consider causative verbs formed from transitive stems: as we will see in more detail in Section 4, in this case, the causee is expressed by an indirect object introduced by a general oblique preverb. If a verb already contains a general oblique applicative, its causative derivative contains two general applicatives. As (6) demonstrates, the order of general oblique applicatives is relevant for interpretation, hence they are unlikely to have a flat structure:10

7. Following Lehmann and Verhoeven 2006, this kind of applicative can be characterized as extraversive, i.e., that type of applicative that introduces a semantically obligatory participant (or a participant closely related to the semantics of the stem), for instance, an undergoer or a recipient in situations like ‘give’. 8. In a detailed description of a similar system in Abaza, O’Herin (2001) suggested to treat such applicatives as incorporated postpositional phrases. For Kabardian, Colarusso (2006: 27) explicitly names applicatives adjuncts. 9. An alternative to this could be a template organization of applicatives such as that proposed by Kumakhov (1964: 152–154), but it does not accord with the facts of rearrangement in (4). Below, we attempt to argue against any model of this zone that presumes the flat structure of applicative chains. 10. To be sure, one can postulate that causative verbs derived from 3-place predicates with general oblique objects have a special template. In this case, however, a generalization will be missed that causatives add an indirect object causee after all indirect objects for any transitive stems, independently of their valence.

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(6) Ø-je-ŝ w-e-z-ʁe-tə-š’t 3sg.io-opv-2pl.io-opv-1sg.a-caus-give-fut ‘I will make you (plural) give it to him’; *‘I will make him give it to you.’ We propose, then, that general oblique applicative chains represent recursion. Nonetheless, it is worth noting that this recursion is somewhat restricted by the fact that any new general oblique applicative must be in a sense ‘‘licensed’’ by the stem, and in fact even in theory no more than three general oblique applicatives can appear in a single form. For concrete applicatives we have not found any well-established rule governing their order.11 Still, there is a preferred order of applicatives (e.g., locative applicatives tend to precede comitative and benefactive applicatives). Since no template can be proposed for this part of the verb, this suggests that applicatives are sensitive to the presence of other applicatives, and so the structure of the applicative chain is not flat either. Now, we find two curious constraints on multiple concrete applicatives in Adyghe. First, there is a constraint which prohibits two applicatives introducing the same role. Consider (7), with two identical preverbs: (7) s-a-fə-Ø-f-e-txe 1sg.abs-3pl.io-ben-3sg.io-ben-dyn-write ‘I write to him for their benefit.’ / ‘I write to them for his benefit.’ In (7), one of the preverbs conveys the benefactive meaning proper, whereas the other marks the addressee: despite the identity of complexes, they introduce di¤erent roles, so the readings like ‘I write for him for their benefit’ are excluded.12 It is worth emphasizing that at least for some speakers the order of applicatives is not restricted by their semantics, which suggests that no fixed positions can be provided for one or another semantic role.

11. Significantly, we have not found any strict dependencies between the arrangement of applicatives and their semantic contribution. In particular, we are not aware of any correlation between the order of concrete applicatives and the distinction discussed in detail by Pylkka¨nen 2008, whence applicatives are divided into high applicatives whose function is only to ‘‘add another participant to the event described by the verb’’ (p. 19) and low applicative, which bear a transfer of possession relation to the object. 12. See Letuchiy (Forthcoming a) for the discussion of various functions of the benefactive applicative.

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Second, applicative chains are occasionally blocked when ‘‘new’’ arguments are coreferential. For example, agents are sometimes ‘‘demoted’’ and introduced via applicatives.13 This phenomenon is observed, for example, in the case of the inadvertitive meaning ‘accidentally’ (8) and, remarkably, in the case of some reciprocals which are constructed via demotion of the agent and its subsequent reciprocalization (9):14 (8) s-ʔeč̣’e-wəʔa-ʁ 1sg.io-inadv-wound-pst ‘I accidentally wounded him.’ (9) tə-ze-re-wəʔa-ʁ 1pl.abs-rec.io-instr-wound-pst ‘We wounded each other.’ Importantly, a verb cannot contain several demoting applicatives. If such a reading is required, a single prefix referring to the argument can be introduced by a sequence of preverbs. Thus, in (10) the reciprocal prefix is followed by a sequence of the inadvertitive and instrumental preverbs: (10) tə-ze-ʔeč̣’e-re-wəʔa-ʁe-x 1pl.abs-rec.io-inadv-instr-wound-pst-pl ‘We wounded each other accidentally.’ In fact, it seems to us that both rules, namely the constraint prohibiting two applicatives and the constraint which can block several applicatives introducing coreferential arguments, can be stated without any reference to the structure. In particular, we hypothesize that the phenomena just discussed manifest the principle which prohibits multiple parallel expressions of the same semantic role.15 Thus, (7) cannot contain two applicatives

13. The treatment of these constructions as an instance of agent demotion is not widespread. Yet, for some parallel constructions in Abkhaz a similar treatment is presented in Hewitt 1979: 236. 14. Adyghe reciprocal constructions are described in Letuchiy 2007, but the present interpretation deviates from that presented in that paper in many respects. In particular, for the reasons that will become clear immediately below, we gave up the traditional analysis of the relevant reciprocal constructions, which postulates a single reciprocal prefix zere- (see Rogava and Kerasˇeva 1966; Hewitt 1979: 229, 235 inter alia). 15. By parallel expressions we mean expressions that do not reflect any di¤erences in either the semantic structure or the information structure.

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introducing the role of beneficiary because their appearance would lead to multiple parallel beneficiaries. Similarly, the introduction of the demoted agent in di¤erent applicatives would violate this principle if these applicatives are meant to interpret a role rather than to establish it, as they apparently are in (8) and (9). Notably, examples like (10) also pose the question of how such sequences of preverbs are organized. In fact, in Adyghe we find instances of complex applicatives that are definitely organized hierarchically. Thus, consider (11) where the instrumental preverb (here, with the meaning ‘through’) follows the locative preverb ‘inside’: (11) məzə-m Ø-ḳwec ̣ə-rə-č̣’ə-ʁe-x forest-obl 3sg.io-loc-instr-go-pst-pl ‘They went through the inner part of the forest.’ (Rogava and Kerasheva 1966: 133) Here the locative preverb together with the (null) cross-reference prefix refers to the reference point (‘inside it’) with respect to which the instrumental preverb is interpreted (‘through [inside it]’). This clearly points to a hierarchical structure (and e¤ectively, another kind of recursion). We are not ready to claim that this kind of structure applies to all complex applicatives, however.16 To conclude this section, we have tried to argue that multiple applicatives represent recursion. Furthermore, we have demonstrated that for concrete applicatives this recursion does not display any restrictions with the exception of very general ones, which presumably are not related to the structure of the verb.

3. Recursion in the su‰xal zone To the right of the root, we observe various su‰xes which modify the core proposition. Some su‰xes are shown in the following example: (12) a-š’ Ø-jə-wəne ə-ṣ̂ə-ž’ə-ŝ wə-ʁ that-obl 3sg.pr-poss-house 3sg.a-make-re-hbl-pst ‘S/he was able to repair his/her house.’ (Literally: ‘S/he was able to make his/her house back.’) 16. Spruit (1986: 22) notes that in the parallel complex locative applicatives in Abkhaz the second part can always function as a simple applicative marker. The same seems to hold for Adyghe.

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The verb in (12) contains three su‰xes, namely the refactive/reversive marker -ž’ə (‘back’), the habilitive marker -ŝ wə (‘is able to’) and the past marker -ʁ(e). While a few descriptions of the Adyghe morphology (e.g., Kumakhov 1964; Smeets 1984; Paris 1989) assumed that the arrangement of (classes of) su‰xes is determined by a template, Korotkova and Lander (2007; Forthcoming) argue against this model. In particular, they suggest that su‰xes function as semantic operators that take their base as an argument, hence the order of su‰xes is determined by their scope. For example, the semantics of the verb form in (12) can be represented as in (13): (13) pst [hbl [re [make]]] ¼ ‘There was a situation of [being capable of [back-[making]]].’ It is easy to see that the order of su‰xes in (12) is the mirror-image of the order of the operators in (13). The crucial argument of Korotkova and Lander is that the order of suffixes can vary together with their scope. This is demonstrated in (14), which contains the refactive marker and the simulative su‰x (‘seem’): (14) a.

b.

g wəŝ ẉ e-ŝ we-ž’ə-ʁ happy-sml-re-pst ‘It seemed again that s/he was happy.’ g wəŝ ẉ e-ž’ə-ŝ wa-ʁ happy-re-sml-pst ‘It seemed that s/he was again happy.’

In (14a) the simulative morpheme precedes the refactive marker and hence appears to be within the scope of the latter: this form is felicitous, for example, for describing a situation where the subject feigned his/her happiness and this was not the first time. In the second example, with the opposite order of the same two morphemes, the refactive operator is placed within the scope of the simulative operator: (14b) may apply, for example, to a situation where the subject feigned that s/he was happy again even if it was the first time s/he feigned it. The dependence of the position of a su‰x on its scope shows that this zone is organized by layers. There is no reason to claim that the simulative and refactive operators function in di¤erent ways, as would be the case if they required formally di¤erent bases or constructed stems displaying different behaviour. Hence examples like (14) can be thought to instantiate recursion: an application of an operator to the base that is constructed by an operator of the same class.

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An even clearer instance of recursion is observed for some su‰xes that are presumed to express the tense category and have been claimed obligatorily to close the stem (see Smeets 1984; Paris 1989: 198). Consider (15) and (16): (15) ade nebɤər-jə-pŝ-me nah deʁ w-ew ptcl person-lnk-ten-cond more good-pred ŝ wə-ŝ we-ž’ə-ʁa-ʁ ŝ wə-ŝxe-ʁa-ʁe-ba 2pl.abs-eat-pst-pst-emp 2pl.abs-drink-re-pst-pst ‘If you were ten persons, you had eaten and drunk nicely, had you not?’ (16) tə-qə-ze-sə-m 1pl.abs-dir-rel.tmp-reach-obl

ṣ̂əhafə-r subbotnik-abs

Ø-fe-wəxə-ʁe-xa-ʁ 3sg.io-ben-close-pst-trm-pst ‘When we came, the subbotnik17 had already ended.’ The matrix verbs in these examples contain two past su‰xes, a combination which is often treated as a complex pluperfect marker (see Rogava and Kerasˇeva 1966; Smeets 1984: 280, Paris 1989: 189 among others). While such a representation might look adequate for (15), it does not hold for (16), where the two temporal su‰xes are separated by a terminative su‰x meaning ‘already’. It can be argued, then, that multiple past suffixes represent di¤erent layers. Korotkova and Lander suggest that the real function of the so-called past su‰x is to shift the temporal value of the situation described by its base back on the time axis. In (15) and (16) this shift occurs twice, in order to show the precedence of the event described by the verbal forms to some other event and/or yielding the e¤ect of ‘‘discontinuous past’’ observed for such shifts in a number of languages (see Plungian and van der Auwera 2006). Consequently, this construction involves recursion both semantically (the shift applies to the temporal reference which resulted from another temporal shift) and morphologically (the successive appearance of two past markers). The past su‰x obviously can be considered an operator akin to the simulative and refactive markers. Hence we might expect that it could have narrow scope with respect to them just like they have narrow scope with respect to it in (14). This expectation is only partly borne out, 17. Subbotnik is a term for free weekend work occasionally organized since Soviet times.

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though. As the following examples show, stems whose temporal reference is already established overtly (with tense a‰xes) cannot take the refactive su‰x directly (17a), although the latter can attach to the base containing temporal a‰xes if it also includes additional morphology like the simulative (17b): (17) a.

b.

*g wəŝ ẉ e-ʁe-ž’ə-ʁ happy-pst-re-pst The intended meaning: ‘S/he again turned out to have been happy.’ g wəŝ ẉ e-ʁe-ŝ we-ž’ə-ʁ happy-pst-sml-re-pst ‘S/he seemed again that s/he had been happy.’

Since the refactive and simulative su‰xes belong to the same formal class, it is unlikely that the infelicity of (17a) relates to the categorial characteristics of the base of the refactive su‰x. We hypothesize that limitations of this sort are based on selectional restrictions of su‰xes. To sum up, Adyghe multiple su‰xation does indeed seem to instantiate recursion. Nonetheless, this kind of recursion is di¤erent from what we saw in Section 3 for applicatives, since it is limited by selectional restrictions among the operators.

4. Double causatives The causative marker ʁe- is placed immediately before the verbal root and normally adds a new argument (causer). The following examples demonstrate how causativization of an intransitive base works: (18) a.

b.

č̣’ale-r ma-ḳwe boy-abs dyn-go ‘The boy goes.’ pŝaŝe-m č̣’ale-r j-e-ʁa-ḳwe girl-obl boy-abs 3sg.a-dyn-caus-go ‘The girl makes the boy go.’

The sentence (18b) with a transitive predicate can be represented as derived from (18a) with a monovalent intransitive verb by causativization. As can be seen from these examples, such a causative construction marks the causer as the agent, whilst the causee remains absolutive.

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The next pair of examples demonstrates causativization of a transitive predicate: (19) a. č̣’ale-m g wəč̣ə-r j-e-wəfe boy-obl iron-abs 3sg.a-dyn-bend ‘The boy bends iron.’ b. pŝaŝe-m č̣’ale-m g wəč̣ə-r Ø-r-j-e-ʁe-wəfe girl-obl boy-obl iron-abs 3sg.io-opv-3sg.a-dyn-caus-bend ‘The girl makes the boy bend iron.’ These examples show that causativization of a transitive predicate makes its agent an indirect object, whilst the causer appears, again, as the agent. Despite the fact that in many examples the causative prefix immediately follows the causer prefix added to the argument structure and therefore resembles applicative preverbs, it should be emphasized that the causative construction is formally very di¤erent from the applicative construction. Thus, the causer prefix belongs to a special agent series of crossreference prefixes and the causer has all the formal properties of agents. Further, the causative marker can be separated from the argument structure zone by one of the pre-stem prefixes such as the dynamic prefix (see (18b) and (19b)) or the negative prefix: (20) se qe-sə-mə-ʁe-wəzə-n I dir-1sg.a-neg-caus-hurt-pot ‘I will not make it hurt!’ As (21) and (22) demonstrate, causativization can involve bases that already contain a causative prefix (see also Kumakhov 1964: 152;18 Smeets 1984: 273; Paris 1989: 182; Hewitt 2004: 138), such forms indicating causativization of an existing causative:19 18. Since Kumakhov operated with a rigorous template model, he had to postulate two homonymic prefixes with almost the same semantics for such examples. 19. Multiple causatives are certainly very common cross-linguistically, see Kulikov 1993 and Burgess 1995. It is important to note, however, that in Adyghe we do not find typologically widespread idiomaticization of causative repetition pointing to intensive and indirect causation, as, for instance, in Oromo: ra¤-is (sleep-caus) ‘put somebody to sleep (directly, e.g., by rocking)’ vs. ra¤is-iis- (sleep-caus-caus) with the meaning of indirect causation ‘make somebody sleep (e.g., by giving him/her a sleeping pill)’ (the example is from Kulikov 1993: 128). In fact, Hewitt (2004: 138) notices that the compositionality of double causatives in Northwest Caucasian languages distinguishes them from many other languages of the Caucasus.

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(21) Ø-je-s-e-ʁe-ʁa-ḳwe 3sg.io-opv-1sg.a-dyn-caus-caus-go ‘I make him/her make him/her go’. (22) Ø-r-Ø-je-z-ʁe-ʁe-λeʁ wə-ʁe-r 3sg.io-opv-3sg.io-opv-rel.a-caus-caus-see-pst-abs ‘the one who made him/her show it to him/her’ (literally: ‘the one who made him/her make him/her see it’) In (21) we find two causative prefixes with an intransitive root, while the relativized verb form given in (22) presents an example of double causativization based on a transitive root. In both forms, one of the causers is cross-referenced by an agent prefix, whilst the other is cross-referenced by an indirect object prefix. This is clearly an instance of recursion. Causative markers in (21) and (22) instantiate the same kind of derivation. Double causatives have a clear semantic structure and both causative prefixes add new arguments. These arguments, further, are expressed di¤erently, the one being introduced as an indirect object, the other being cross-referenced as the agent, which proves that the two causative markers are applied in turn. Nonetheless, we will see that this recursion is by no means as pure as it looks at first glance. First, no more than two causatives appear within a word: forms like (23) are considered infelicitous. (23) *Ø-r-Ø-je-s-e-ʁe-ʁe-ʁa-ḳwe 3sg.io-opv-3sg.io-opv-1sg.a-dyn-caus-caus-caus-go The intended meaning: ‘I cause himi to make himj make himk go.’ We have no explanation for this fact. In particular, we cannot account for this restriction by the processing complexity of the expression alone, because lexicalized causative – root combinations do not allow for the appearance of additional causatives either, despite the fact that the apparently word-formative causative should not a¤ect complexity here. Thus, consider the verb ʁeləǯə- ‘to tickle somebody/something’ (transitive) illustrated in (24b). Formally, it consists of a causative prefix and the root ləǯə‘to tickle’ (intransitive, of a body-part), whose use is shown in (24a). Since the causative verb can be used with animate causees and the bare root cannot be used with animate subjects, the meaning of the causative verb is non-compositional and lexicalized. Nonetheless, the stem ʁeləǯə- only takes one additional causative prefix, as (24c)–(24d) demonstrate:

Kinds of recursion in Adyghe morphology

(24) a.

277

a-r ləǯə-ʁ that-abs tickle-pst ‘It tickled.’ (Not: ‘S/he felt tickling.’)

b.

z-ʁe.ləǯə-ʁ 1sg.a-(caus.)tickle-pst ‘I tickled him/her.’

c.

Ø-je-z-ʁe-ʁe.ləǯə-ʁ 3sg.io-opv-1sg.a-caus-(caus.)tickle-pst ‘I made him/her tickle him/her.’

d.

*Ø-r-Ø-je-z-ʁe-ʁe-ʁe.ləǯə-ʁ 3sg.io-opv-3sg.io-opv-1sg.a-caus-caus-(caus.)tickle-pst The intended meaning: ‘I made him/her make him/her tickle him/her.’

Second, as was noted by Smeets (1984: 225, 273), double causation is occasionally expressed by a single causative marker. In this case, only the presence of an additional cross-referencing prefix indicates that the form indicates to causation of causation. Thus, compare the following two variants, with double causatives and with a single causative prefix: (25) pχexə-r s-jə-ʁe-ʁe-č’anə-ʁ / saw-abs 1sg.io+opv-3sg.a-caus-caus-sharp-pst s-jə-ʁe-č’anə-ʁ 1sg.io+opv-3sg.a-caus-sharp-pst ‘S/he made me sharpen the saw.’ (Literally: ‘She made me make the saw sharp.’) While the first form in (25) marks double causation explicitly by two causative prefixes, for the second form the double causation meaning can only be identified due to the presence of an ‘‘unexpected’’ indirect object prefix. The factors conditioning the choice of the first or the second variant are analyzed in Letuchiy (Forthcoming b). Briefly, the omission of the second causative marker could be considered an instance of haplology, which is to say, the deletion of a morpheme motivated by a phonologically identical context (Stemberger 1981). However, (25) shows that, for causatives, this process is optional, and in fact we do not observe it elsewhere in Adyghe. Further, it turns out that it can also relate to non-phonological factors. Indeed, it seems that explicit double causatives are more normal where

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some of the causers are treated as especially salient in the context (for example, where there is a 1st or 2nd person causer (as in (25)) or where one of the causers is relativized (22)). On the other hand, if all the causers are 3rd person, the presence of the second causative prefix is sometimes judged doubtful: (26) ʔ wefṣ̂aḳwe-m Ø-jə-ṣ̂wəz ṣ̂wəʔanə-r employee-obl 3sg.pr-poss-wife hoe-abs Ø-r-jə-ʁe-č’anə-ʁ / 3sg.io-opv-3sg.a-caus-sharp-pst ??Ø-r-jə-ʁe-ʁe-č’anə-ʁ 3sg.io-opv-3sg.a-caus-caus-sharp-pst ‘The employee made his wife sharpen the hoe.’ We conclude that the causative recursion is indeed somewhat restricted. In addition, it deviates from recursion proper in terms of both the possibility of non-compositional expression (whereby one causative marker is omitted) and dependence on pragmatic factors.

5. Discussion The previous sections have shown that recursion is allowed in various parts of the Adyghe verb form. Below we shall focus on di¤erences between the described phenomena and show that they are distinct in their recursability (i.e., their inclination to recursion). We identify three criteria for measuring recursability: – the quality criterion considers the number of combinations that similar operators can contract; – the quantity criterion determines how many times a given operation applies theoretically;20 – the explicitness criterion concerns overt and compositional expression of semantic operations.

20. We are making an assumption that we can distinguish between whether repeating an operation is grammatically prohibited or whether it results from processing complexities.

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Let us apply these criteria to the instances of recursion discussed above. Starting from concrete applicatives, as concerns the quality criterion, the appearance of a new applicative does not depend on the material to which it attaches until it violates some general constraints; hence, in principle, there are no potential limitations on the number of combinations. Concrete applicative derivations have no quantity restrictions either, at least formally, although in reality the number of applicatives only rarely reaches three. Last but not least, these derivations are always explicit and compositional. General oblique applicatives are very di¤erent. They do not interact with other similar derivations, and this restricts the number of their possible combinations to one. The number of general oblique applicatives crucially depends on the stem and does not seem able to exceed three. Finally, they allow for the omission of the applicative preverb in some contexts; hence this part of the word is not clearly compositional (although this fact is not related to recursion per se). The recursion in the su‰xal zone permits many di¤erent combinations, although it seems to be still more restricted in this respect than concrete applicatives due to the role of selectional restrictions. At the same time, this kind of recursion is not restricted formally as far as the number of operations is concerned. The role of the expliciteness criterion is less obvious in this case: whilst the semantics of this zone for the most part can be described as compositional, there is at least one aspect where this is disputable. Consider the following two examples: (29) a.

b.

ʁe-š’əne-ʁ weŝ ẉ ə caus-be.afraid-fcl ‘It is easy to frighten him.’ səmeǯe-ʁ weŝ ẉ ə-ʁ ill-fcl-pst ‘S/he promptly got ill.’ (Literally: ‘It was easy for him/her to get ill.’)

The comparison of these two examples, which both include the facilitive su‰x ‘easy’, demonstrates that the absence of temporal a‰xes may receive a probably unexpected present tense interpretation (as in (29a)). This is in spite of the fact that, as we argued above, temporal su‰xes ( just like, say, the facilitive su‰x shown in these examples) are part of a compositional structure; so the absence of tense morphology would not imply any

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Yury A. Lander and Alexander B. Letuchiy Recursability Causatives

General oblique applicatives

f Propositional operators

Concrete applicatives Combinations are limited by independent principles.

Quality

Only one recursive combination is possible.

Combinations are limited by selectional restrictions.

Quantity

Recursion is confined to two derivations.

No obvious restrictions on the number of derivations.

Explicitness

Operators can be suppressed.

Recursion is restricted by stem.

The absence of expression can be interpreted.

Overt expression is obligatory.

Figure 3. Kinds of recursion in Adyghe morphology

specific temporal meaning at all. Depending on the approach and relying on di¤erent arguments, the present tense interpretation here can be considered either a default value or the semantics of the bare stem that serves as a base for further temporal derivations.21 At least if the first interpretation is accepted, the su‰xal zone becomes somewhat less compositional. Finally, causative recursion shows the most idiosyncratic properties. It is only restricted to one combination and is limited to a sequence of two markers. In addition, one of the causative markers can be deleted, which leads to the violation of compositionality. These data are summarized in Figure 3, which suggests that concrete applicatives are the most recursable; the su‰xal zone is the next in order; then come general applicatives; and, finally, comes the causative. The fact that di¤erent morphological operations admit recursion to di¤erent extents is crucial, because it allows us to relate recursability to the properties of these operations. We propose that the following principle a¤ects recursability in Adyghe morphology.

21. Apparently, paradigms can hardly be constructed for su‰xal morphology, so the existence of null su‰xes is unjustified.

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(30) The more a derivation a¤ects the meaning of a stem, the less recursable it is.22 Consider causatives: while creating a situation of a new kind, the causative derivation a¤ects the meaning of a stem. Not any situation needs to be characterized as to whether it involves causation, and hence such information is highly marked significantly contributing to the semantics of the verb. Moreover, causatives partly determine the distribution of the stem (in particular, its combinability with some cross-referencing prefixes). Similarly, general oblique applicatives are closely related to the semantics of the stem, so that their appearance is in fact only possible where the semantics of the stem already implies that the corresponding participant is relevant. The appearance of an indirect object prefix in a sense should be licensed by some component within the semantics of the stem. It is, thus, not so surprising that sometimes such components can be ‘‘reconstructed’’ due solely to the presence of indirect objects, as we have seen in the case of double causation expressed with a single causative prefix. The su‰xal derivations too a¤ect the stem and its distribution. In particular, the appearance of some su‰xes can a¤ect the argument structure. An example of this is (29a) above, where the appearance of the facilitive prefix makes it possible to omit the agent prefix because the corresponding participant becomes irrelevant. At the same time, in most cases su‰xal operations only result in certain aspectual, temporal or modal interpretations (i.e., those interpretations that are not usually thought to touch upon the core lexical semantics). Finally, concrete applicatives while being ‘‘morphological adjuncts’’, prototypically bear only subsidiary information and hence a¤ect the stem to a lesser degree than other kinds of derivations. Given this picture, we find a neat correlation between the recursability of a derivation and the nature of its semantic contribution.

6. Conclusion In this paper we have described recursive morphological processes in Adyghe and have argued that their inclination to recursion depends on their semantic impact in the construction of a polysynthetic word. 22. This principle can be related to the concept of the relevance of morphological elements, as used by Bybee (1985).

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In Adyghe, as we have demonstrated, causative derivation is the least recursable, concrete applicative derivation is the most, and general oblique applicatives and propositional operators occupy an intermediate place. These results are remarkable because they contrast with our intuitions about syntactic recursion. In syntax, derivations similar to Adyghe concrete applicatives are the least prototypical instances of recursion, for they are ‘‘morphological adjuncts’’ and in some models (e.g., in dependency grammar) multiple adjunction is not considered an instance of recursion at all. Note also that concrete applicatives in Adyghe are typologically exceptional in nona¤ecting argument structure. Finally, it is our impression that morphological adjuncts belong to atypical phenomena for morphology, as they may show properties rather deviant from other kinds of derivations (see, for example, Newell 2005). Thus, we find that the least restricted recursion in Adyghe morphology is found with non-canonical derivations, and, in fact, this recursion is itself non-canonical. The most restricted recursion in Adyghe morphology is found in causative constructions, which in syntax easily allow for recursion. At the same time, morphological causatives seem to be far more widespread than, for example, applicatives and represent, in a sense, a more canonical morphological operation. The picture displayed by Adyghe cannot be captured by standard assumptions on both morphology and recursion. On this basis, we propose that morphology is indeed deficient as concerns recursion. This provides good evidence for the strong distinction between syntax and morphology even in such languages as Adyghe, where their functions may overlap.

References Arkadiev, Peter M. and Yakov G. Testelets Forthcoming O trex cˇeredovanijax v adygejskom jazyke [On three alternations in Adyghe]. In Aspekty polisintetizma: ocˇerki po grammatike adygejskogo jazyka, Yakov G. Testelets et al. (eds.). Moscow: Izdatel’stvo RGGU. Baker, Mark 1988 Incorporation: A Theory of Grammatical Function Changing. Chicago: University of Chicago Press. Burgess, Cli¤ord Spence 1995 Mapping multiple causatives. M.A. thesis, Simon Fraser University.

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Morphology: A Study of the Relation between Meaning and Form. Amsterdam: John Benjamins.

Colarusso, John 2006 Kabardian (East Circassian). Muenchen: LINCOM Europa. de Reuse, Willem J. 2006 Polysynthetic language: Central Siberian Yupik. In The Encyclopedia of Language and Linguistics, vol. 9, Keith Brown (ed.), 745–748. Oxford: Elsevier. Hewitt, George 1979 Aspects of verbal a‰xation in Abkhaz (Abzˇui dialect). Transactions of the Philological Society, 1979: 211–238. Hewitt, George 2004 Introduction to the Study of the Languages of the Caucasus. Muenchen: LINCOM Europa. Jakovlev, Nikolaj and Daud Asˇxamaf 1941 Grammatika adygejskogo literaturnogo jazyka [A Grammar of Literary Adyghe]. Moscow: Izdatel’stvo AN SSSR. Korotkova, Natalia A. and Yury A. Lander 2007 Logika polisinteticˇeskoj slovoformy: adygejskij material [ The logic of a polysynthetic word form: Data from Adyghe]. In Kontensivnaja tipologija estestvennyx jazykov: Materialy, 87–89. Makhachkala: DGU. Korotkova, Natalia A. and Yury A. Lander Forthcoming Deriving a‰x ordering in polysynthesis: Evidence from Adyghe. Morphology. Kulikov, Leonid I. 1993 The ‘second causative’: a typological sketch. In Causatives and Transitivity, Bernard Comrie and Maria Polinsky (eds.), 121– 154. Amsterdam: John Benjamins. Kumakhov, Mukhadin A. 1964 Morfologija adygskix jazykov [Morphology of Adyge languages]. I. Nal’chik: Kabardino-balkarskoe knizˇnoe izdatel’stvo.

Lehmann, Christian and Elisabeth Verhoeven 2006

Extraversive transitivization in Yucatec Maya and the nature of the applicative. In Case, Valency and Transitivity, Leonid I. Kulikov, Andrej Malchukov and Peter de Swart (eds.), 465– 493. Amsterdam: John Benjamins. Letuchiy, Alexander B. 2007 Reciprocals, reflexives, comitatives, and sociatives in Adyghe. In Reciprocal Constructions, Vladinir P. Nedjalkov (ed.), 773–811. Amsterdam: John Benjamins. Letuchiy, Alexander B. Forthcoming a. A‰ksy benefaktiva i malefaktiva: sintaksicˇeskije osobennosti i krug upotreblenij [Benefactive and malefactive a‰xes: syntactic

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features and sphere of use]. In Aspekty polisintetizma: ocˇerki po grammatike adygejskogo jazyka, Yakov G. Testelets et al. (eds.). Moscow: Izdatel’stvo RGGU. Letuchiy, Alexander B. Forthcoming b. Kauzativ, dekauzativ i labil’nost’ [Causative, anticausative and lability]. In Aspekty polisintetizma: ocˇerki po grammatike adygejskogo jazyka, Yakov G. Testelets et al. (eds.). Moscow: Izdatel’stvo RGGU. Newell, Heather 2005 Bracketing paradoxes and particle verbs: A late adjunction analysis. In Proceedings of ConSOLE XIII, Sylvia Blaho, Luis Vicente, and Erik Schoorlemmer (eds.). Leiden: Leiden University. O’Herin, Brian 2001 Abaza applicatives. Language 77: 477–493. Paris, Catherine 1989 Esquisse grammaticale du dialecte abzakh (tcherkesse occidental). In The indigenous languages of the Caucasus, vol. 2, B. George Hewitt (ed.), 157–260. Delmar: Caravan Books. Peterson, David A. 2007 Applicative Constructions. Oxford: Oxford University Press. Plungian, Vladimir and Johan van der Auwera 2006 Towards a typology of discontinuous past marking. Sprachtypologie und Universalienforschung 59: 317–349. Pylkka¨nen, Liina 2008 Introducing arguments. Cambridge (Mass.): The MIT Press. Rogava, Georgi V. and Zajnab I. Kerasˇeva 1966 Grammatika adygejskogo jazyka [A Grammar of Adyghe]. Krasnodar: Krasnodarskoe knizˇnoe izdatel’stvo. Smeets, Rieks 1984 Studies in West Circassian Phonology and Morphology. Leiden: The Hakuchi Press. Spruit, Arie 1986 Abkhaz studies. Ph.D. thesis, Leiden University. Stemberger, Joseph 1981 Morphological haplology. Language 57: 791–817. Tomalin, Marcus 2007 Reconsidering recursion in syntactic theory. Lingua 117: 1784– 1800.

16.

Recursion and the Lexicon*

Jan Koster 1. A critique of biolinguistics Current theorizing about the human language faculty, particularly about recursion, is dominated by the biolinguistics perspective. This perspective has been part of the generative enterprise since its inception and can be summarized as follows: The core of language is individual-psychological and may ultimately be explained in terms of human biology. A classical formulation of this program was Lenneberg (1967) and it was revitalized recently by Jenkins (2000) and particularly by Hauser, Chomsky and Fitch (2002) (henceforth: HCF). According to HCF, recursion (in the form of Merge) is the core of the human language faculty biologically conceived. The biological perspective is far from self-evidently correct and, in fact, goes against a long tradition that emphasized the cultural, conventional nature of language. This tradition goes back at least to Aristotle’s De Interpretatione and became the core idea about language since the late Enlightenment and Romanticism, thanks to the influence of Herder, Von Humboldt and others. Most early 20th-century views were o¤shoots of the great conceptions formulated around the turn of the 18th century. Thus, Ferdinand de Saussure followed German Romanticism in this respect, as did the great American structuralists Franz Boas and Edward Sapir. Saussure was also influenced by one of the founding fathers of sociology, E´mile Durkheim, who argued that certain social facts could not be reduced to individual psychology or biology.1 Also philosophers like Wittgenstein and Popper followed the European tradition, the former with his emphasis on the public and language game-dependent nature of linguistic rules, the latter by stipulating that language belongs to his (pseudo-technical) * This text is part of a paper presented on April 28, 2007, at a conference titled ‘‘Recursion in Human Languages,’’ sponsored by the Illinois State University, Normal, Illinois. I would like to thank the organizer, Daniel Everett, and the participants for discussion leading to several improvements of presentation. All remaining errors are my own. 1. See Durkheim (1982).

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conception of supra-individual human culture known as ‘‘world 3’’ (Popper 1972). None of these conceptions excludes a biological basis for language, for the trivial reason that all human culture and activity has a biological basis. Sapir (1921: 3), for instance, adheres to the cultural view of language: ‘‘[ . . . ] walking is an inherent, biological function of man’’ but ‘‘[ . . . ] speech is a non-instinctive, acquired, ‘‘cultural’’ function’’ (1921: 4). Clearly, however, this does not exclude biology for Sapir (1921: 9): Physiologically, speech is an overlaid function, or to be more precise, a group of overlaid functions. It gets what service it can out of organs and functions, nervous and muscular, that have come into being and are maintained for very di¤erent ends than its own.

Biological structures with a new, ‘‘overlaid’’ function is like what biologists Gould and Vrba (1982) call ‘‘exaptation.’’ I will argue, however, that culture involves particular forms of exaptation, namely those based on human agency. In the meantime, nobody really denies the non-biological, cultural aspects of language. In the framework of HCF, the biological core of language is separated from the rest by making an idealizing distinction between the faculty of language in the narrow sense (FLN) and the faculty of language in the broad sense (FLB). It is probably assumed that FLN is purely biological, while culture enters FLB. The essence of FLN, it is assumed, is recursive Merge. Suppose, counter to what I will ultimately conclude, that recursive Merge is the biological essence of language. Then an immediate further question arises, namely whether recursive Merge is, functionally speaking, unique to language in any sense. Interestingly, in both HCF and Chomsky (2007: 7) it is considered that recursive Merge is, ultimately, not languagespecific: The conclusion that Merge falls within UG holds whether such recursive generation is unique to FL or is appropriated from other systems. If the latter, there still must be a genetic instruction to use Merge to form structured linguistic expressions satisfying the interface conditions. Nonetheless, it is interesting to ask whether this operation is language-specific. We know that it is not. The classic illustration is ‘‘the mathematical capacity,’’ which troubled Alfred Russel Wallace 125 years ago because it ‘‘is wholly unexplained by the theory of natural selection, and must be due to some altogether distinct cause,’’ if only because it remained unused. One possibility is that it is derivative from language.

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This passage is worth reading twice because it considerably weakens the biolinguistics thesis: neither in its origins nor in its ultimate applications is Merge necessarily language-specific. At best, there is ‘‘a genetic instruction’’ to give Merge a linguistic function and perhaps the linguistic application has a certain genealogical priority over other applications such as in mathematics. The view cited comes close to what was called the Thesis of Radical Autonomy in Koster (1987, 1988, 1989): the computational core of language has no intrinsic linguistic function and its functional dedication to language is based on a purely human invention, namely the invention of words (or rather lexical items, including both words and morphemes). The main di¤erence between Chomsky’s view and my own is that Chomsky emphasizes ‘‘internal’’ functional dedication by a (so far undiscovered) ‘‘genetic instruction,’’ while I emphasize ‘‘external’’ functional dedication by invented words. Obviously, words do not belong to biology but to human cultural traditions, which presuppose individual psychology and biology but also have an existence external to the individual. It would be somewhat presumptuous to assume that the end of my life would be the end of Dutch! Although Chomsky has usually distanced himself from naı¨ve sociobiology (or evolutionary psychology), I believe that his emphasis on the (unknown) genetic instruction and his ignoring of culturally determined functionality brings his ideas closer to sociobiology than I consider desirable. I cannot do full justice to the topic here, but in general it seems to me that seeing cultural transparency in biological structures leads to views that Gould and Lewontin (1979) characterized as ‘‘panglossian,’’ after Dr. Pangloss in Voltaire’s Candide, who praised the human nose as a structure designed to support glasses.2 The panglossian view of language is confirmed by Chomsky’s longstanding tendency to see FLN as an organ, like the liver, the heart or the kidneys. This cannot be quite right, because there is a fundamental di¤erence between how organs acquire their functionality in the body and how recursive Merge (or the capacity underlying it) receives its function in language. The di¤erence is best described in terms of the distinction John Searle (1995: 20) makes between agentive and non-agentive functionality.

2. By ‘‘cultural transparency’’ I mean the idea that biological structures have an intrinsic cultural function, selected by evolution. In general, I believe that our biological structures have cultural functions thanks to our history of agentive function assignment, i.e., as a matter of free application.

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Cultural functionality involves human decisions and is therefore agentive, for instance when we use a stone as a paper weight. The functionality of the heart and other organs, in contrast, is assigned in a very di¤erent way, namely completely independent of human interference. It is essentially a genetically driven, fully automatized biological process. So, what kind of functionality is involved in the human language faculty? How does recursive Merge get its function? The capacity at issue would remain completely dormant and linguistically functionless without the purely human invention mentioned, i.e., the invention of lexical items. Lexical items belong to a culture and, as such, are external to the individual. More importantly, lexical items are invented artifacts and therefore involve an undeniable element of human agency. Since recursive Merge only has linguistic functionality thanks to this human invention, the capacity in question is not properly characterized as a language organ but, not unlike a paper weight, something that receives its functionality the agentive way. In other words, language, even in the narrowest sense, is more properly characterized as a technology than as some organ-like part of human biology. I just follow Sapir and the tradition in this respect and consider the fully biological interpretation of FLN an error. What about poverty-of-the-stimulus arguments, one might object. I consider poverty-of-the stimulus arguments completely irrelevant for the issues at hand, because poverty-of-the-stimulus arguments are about innateness, not about the nature of functional dedication. Clearly, the fact that we learn so much in such a short time, on the basis of so little evidence (‘‘Plato’s problem’’) shows that something is innate (cf. Chomsky 1986). That much of the Chomskyan view stands unchallenged, as far as I am concerned. However, the arguments in question show at best that the capacity for recursive Merge is innate, not whether this capacity is functionally dedicated to language in the manner of organs or by applying it thanks to human invention. Innateness considerations only apply to the components of language as such, not to what makes these components part of language, namely their culturally mediated combination into a linguistically functional whole. As emphasized by Saussure, the essence of language is the bridge function between publicly accessible and supported signs and the corresponding elements of our conceptual-intentional world, between external signifiants and internal signifie´s (Saussure 1916). None of the components of language is in its own right, in abstraction from the relevant functional combination, linguistic in any sense. Thus, many innateness issues have been discussed in relation to the sounds of speech (for instance, as in Mehler,

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Jusczyk, Lambertz, Halsted, Bertoncini & Amiel-Tison 1988) or even similar elements of sign language (Petitto 2005). It is very well possible, and even likely, that rapid and smooth access to such elements evolved to facilitate its use in language. But note that there is nothing inherently linguistic about speech sound. Speech is not even a necessary condition for language, as in many cases the public aspect of language is not represented by speech sounds (or signs) but by written words or print. What is necessary for language is an external, publicly accessible medium. Speech happens to be such a medium, but not a necessary one. The word that comes to mind in connection with speech is ‘‘facilitation.’’3 Obviously, speech is facilitated in ways that writing is not. Similarly, it is very well possible (and even likely) that rapid and smooth access to the recursive mechanisms underlying grammar were also facilitated by evolution. But once more, this is irrelevant for the question whether language is a biological phenomenon or a form of technology. Riding a bike or playing the piano is a cultural function, based on technologies, but largely exploiting genetically determined aspects of our biology. The same is, trivially, true about language, the only di¤erence being that the components of language are probably more facilitated by evolution than the physical and biological elements underlying biking and piano playing. A related issue is whether language should be seen as E-language or Ilanguage, as something external or internal to the human mind (see Chomsky 1986). It seems to me that this is a false dichotomy, as language, even in the narrowest sense, has both external, public aspects and internal aspects.4 The idea of a narrow language faculty (FLN, recursive Merge) as I-language does not make sense because there is nothing about recursive Merge per se that makes it linguistic. It is only in combination with external, invented cultural objects -lexical elements- that our capacities for recursion have any linguistic relevance at all. In some sense, then, words are closer to the essence of language than syntax, which is a matter independent of the fact that syntactic theories are often more profound that theories about words. 3. By ‘‘facilitation’’ I mean that the ease and speed of access and use of mechanisms has been increased in the course of evolution. Unlike playing the piano, the elements of speech and the recursive mechanisms of language are readily available to all children at an early age, while the use of these mechanisms is instantaneous and reflex-like rather than di‰cult and showing huge di¤erences in individual talent. 4. See also Muysken (2002).

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More generally, FCH seem to discuss language as if they were discussing fish without taking into account that fish swim in water. One crucial di¤erence between humans and apes is that we live in symbiosis with an external, supra-individual and shared symbolic culture. Mentally speaking, humans can only be understood as symbionts with a shared culture.5 This culture is a record, among other things, of earlier successful agentive assignments of functionality, language among them. This external culture is, no doubt, possible thanks to internal developments of our brains in comparison to other primates, but it has led to an entirely di¤erent organism that is not properly understood within the confinements of primate biology. Summarizing so far, we can say that culturally invented, not biologically given, words are the primary carriers of linguistic functionality. Words are not individual properties of organisms but belong to a shared culture, which has an existence external to the individual. Linguistics is the study of the unique technology embodied by our words, including the internal factors that make possible the complex properties of our most important cultural objects. Recursion is a case in point.

2. A critique of Merge It is now more than 50 years ago that Chomsky’s Syntactic Structures appeared and started having its revolutionary impact on linguistics, making the field the intellectual adventure it has been until the present day. In retrospect, however, it must be said that the view expounded on syntax in this seminal little book was based on an error, ironically precisely where it deviated from a linguistic tradition of more than 2000 years. According to Egli and Egli-Gerber (1992), it is one of the oldest insights of linguistics (at least since the Stoics) that syntax realizes the combinatorial properties of words. Since the 19th century, German linguists and others studied combinatorial properties of words under the label ‘‘Rektion’’ (cf. ‘‘government’’) and the various 20th-century structuralists were often discussing matters in terms of the ‘‘valency’’ of words.6 Syntactic Structures deviated from 5. For the idea of humans as symbionts, see Donald (1991). For related reasons, I am skeptical about the notion mind/brain. The brain is an individual biological part of humans, while for the mind, being a symbiotic structure, no sharp distinction can be made between the individual and the supra-individual. 6. See, for instance, Tesnie`re (1959).

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this tradition by introducing a form of syntax that was no longer wordoriented, but largely independent of words. This new approach was borrowed from the theory of formal systems, in which complex expressions are generated with the terminals (‘‘words’’) as elements of an alphabet, without internal properties.7 I consider this approach to the syntax of natural language fundamentally flawed. At the time, Aspects of the Theory of Syntax (Chomsky 1965) was often seen as the next step forward, but in retrospect it can be said that it was a correction of the mistaken view of Syntactic Structures and the first step of a gradual return to more traditional insights, particularly the view that the lexicon plays a crucial role in natural language syntax. Aspects added a lexicon to generative grammar, with selectional restrictions and subcategorization frames. Subcategorization frames are nothing other than more or less explicit versions of the combinatorial properties of words, which were seen as the core of syntax since Antiquity (‘‘valency,’’ etc.). The addition of a lexicon with said properties clearly revealed what was wrong with a grammar based on lexicon-independent rules: the same information was stated twice in the grammar, once in the subcategorzation frame (1a) and once in the possible outputs of phrase structure rules (as in 1b): (1) a. b.

see: [þV, NP] [VP [V see] NP]

In other words, a redundancy problem was introduced in grammar, as was clearly realized by Chomsky right away and formulated not too long ago as follows (1981, 31): Thus information concerning the class of subcategorization frames is in e¤ect given twice in the grammar: once -implicitly- in the lexicon, as a property of the class of lexical items in its totality; and once -this time directlyby the rules of the categorical component.

In Chomsky (1970), X-bar theory was introduced as a response to the redundancy problem (and also as a response to the well-known endocentricity problem, which I will ignore here). However, X-bar theory was nothing really new but one of the structuralist formulations of valency properties (in this case going back to Harris 1951), in line with the tradition since Antiquity to see grammar as a theory about the combinatorial properties of words. 7. See Tomalin (2002).

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Thanks to Emonds’s idea of structure-preservingness (1970), the revolutionary nature of generative grammar came even more under fire: if the outputs of transformations have exactly the same form as the outputs of phrase structure rules, why would one need transformations in the first place? If the kind of structure generated by PS-rules is all there is, everything could be reduced to X-bar theory (a theory of lexical properties) and therefore to a form of grammar completely compatible with the tradition. In the 1970s, many syntacticians came to that kind of conclusion in one way or another, leading to more or less transformation-free variants of generative grammar (Brame 1978, Hoekstra, Van der Hulst and Moortgat 1980, Bresnan 2001, HPSG, Koster 1978, 1987). Mainstream generative grammar, however, insisted on the transformational residue ‘‘move alpha,’’ which eventually disappeared but lives on in current minimalist theories as ‘‘internal Merge.’’ I have argued elsewhere why I do not find this ongoing derivational tradition convincing (see, for instance, Koster 2007). Although I do not see X-bar theory as formulated in the 1970s and 1980s as the last word, I find the leading idea basically correct, namely that syntactic structures are projected from lexical items. Given a word, its possible syntactic environments are predictable, which can be seen as a reflection of the tacit knowledge of the native speaker of a language. Lexicon-independent theories of sentence generation inevitably lead to the redundancy problem, indicating that something is wrong. Within the minimalist framework, lexicon-independent sentence generation made a come-back in the form of the operation Merge. Merge di¤ers from phrase structure rules but partially runs into the same problems: it combines lexical elements that are not dummies but that, even before Merge has applied, have full-fledged combinatorial properties that fully specify the hierarchical configurations that are redundantly generated once more by Merge. Even if Merge interacts with independent information at the interfaces, the fact remains that this interface information is partially the same as what is introduced by Merge, so that the redundancy problem fails to disappear. In fact, theories based on Merge can hardly be evaluated because it is almost never made explicit what happened to combinatorial lexical information.8 It can certainly not be reduced to semantics, because it is 8. A positive exception is Adger (2003), but his treatment of subcategorization of verbs as the elimination of N-features (for objects) leaves the impression that bare phrase structure plus this kind of feature elimination is a notational variant of X-bar theory.

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generally agreed upon that c-selection cannot be reduced to s-selection (see, for instance, Odijk 1997). Although these considerations strongly argue against Merge as a sentence-generation device, it is still possible that Merge is a more abstract background mechanism, accounting for certain properties that all projectable lexical frames have in common. In this view, recursive Merge would be a non-linguistic, functionless capacity, which is assigned a function by its application in the combinatorial frames of words. This approach would be conceptually less problematic than the standard approach, but it runs into the empirical problem that the creation of hierarchical structure and the combination of the properties of elements does not run exactly parallel in natural language. Traditional phrase structure rules created hierarchical structures but left the combination of properties to other mechanisms, such as the amalgamation rules of Katz and Fodor (1963) and construal rules of Chomsky (1981). To the extent that Merge combines these two functions, it runs into new empirical problems, for instance with idioms, which often have normal hierarchical structure but not the standard combination of properties as found in normal compositionality. Therefore, although I am sympathetic to the idea that recursion is part of an unapplied, non-linguistic background capacity, I believe that Merge does not quite fit the bill. The theory we are looking for separates the account of hierarchical structure (primary computation) from the varying ways of combining properties that exploit this hierarchical structure (secondary computation).

3. Concluding remarks So far, I have distanced myself from current biolinguistics, from notions such as I-language and from the idea that sentences are directly generated by Merge. The conclusion of the first section was that language, no matter how narrowly construed, has an inalienable external element. There is not the slightest reason to call our capacity for Merge or any other biological capacity ‘‘linguistic.’’ The essence of language is not in our biology but in the technology we have developed to apply our biology, possibly including our capacity for recursion. The technology in question mediates between our inner, conceptual-intentional world and the external, public world we share with others. The core of our linguistic technology has been the invention of words. Particularly with respect to their spoken form, the invention of words is probably facilitated by our genetic endowment, but

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this does not seem to be the case at all for written words, which are equally valid, and often even the most frequently used interface elements in modern societies. It is even possible that the ‘‘instinct’’ to connect inner forms with outer signs is based on a genetic instruction, but this should be a matter not of stipulation but of discovery. Since words and lexicons are cultural objects, their properties, including recursion, are properties of our culture as well. Even if our capacity for recursion is innate, its application to cultural objects was the result of invention, and therefore a matter of agentive functionality. Agentive assignment of functionality can be a conscious process but does not need to be. More generally, linguistics (narrow or not) cannot be reduced to biology, in the same way that biology itself cannot be reduced to physics. The reason, in both cases, is that there is no intrinsic connection between form and function. That an existing physical form can be given a function is a matter of good luck and of what happens to work in an infinite and unpredictable set of ever changing contexts. The non-agentive function assignments are what Jacob (1982) called a matter of ‘‘tinkering,’’ which he sees as the most typical aspect of biological evolution. Due to its accidental nature, successful tinkering cannot be preserved as a matter of physical law and therefore required something new and unknown before the emergence of life: a memory in the form of DNA. Humans are constrained but not determined by their biology. Thanks to our capacity of agentive function assignment -also- in ever changing contexts, we are able to give an infinite and unpredictable number of applications to our innate biological structures. We have a strong creative impulse in this respect and it liberates us from our biology to some extent, even in spectacular ways sometimes. Just as successful non-agentive functionality is preserved via DNA, successful agentive function assignment is preserved in another innovative memory structure, our cultural record. Words and their properties are the most important elements of our nonindividual cultural memory, giving infinite potential to otherwise meaningless structures of our brain. References Adger, David 2000

Core Syntax: A Minimalist Approach. Oxford: Oxford University Press.

Brame, Michael 1978 Base Generated Syntax. Seattle: Noit Amrofer.

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Bresnan, Joan 2001 Lexical-Functional Syntax. Malden, Mass.: Blackwell. Chomsky, Noam 1957 Syntactic Structures. The Hague: Mouton. Chomsky, Noam 1965 Aspects of the Theory of Syntax. Cambridge, Mass.: MIT Press. Chomsky, Noam 1970 Remarks on nominalization. In R. Jacobs & P. Rosenbaum, (eds.), Readings in English Transformational Grammar, 184–221. Waltham, Mass.: Ginn and Company. Chomsky, Noam 1981 Lectures on Government and Binding. Dordrecht: Foris. Chomsky, Noam 1986 Knowledge of Language. New York: Praeger. Chomsky, Noam 2007 Approaching UG from below. In Uli Sauerland and HansMartin Ga¨rtner, (eds.), Interfaces þ Recursion ¼ Language?, 1– 29. Berlin: Mouton de Gruyter. Donald, Merlin 1991 Origins of The Modern Mind. Cambridge, Mass.: Harvard University Press. Durkheim, E´mile 1982 What is a social fact? In E´mile Durkheim, The Rules of the Sociological Method. Edited by Steven Lukes; translated from the French original (1895) by W.D. Halls, 50–59. New York: Free Press. Egli, Urs & Renata Egli-Gerber 1992 Sprachsysteme: logische und historische Grundlagen der erweiterten Phrasenstrukturgrammatik. Konstanz: Fachgruppe Sprachwissenschaft Universita¨t Konstanz. Arbeitspapier 28. Emonds, Jospeh 1970 Root and structure preserving transformations. Ph.D. Dissertation, MIT. Gould, Stephen Jay and Richard Lewontin 1979 The spandrels of San Marco and the panglossion paradigm: a critique of the adaptationist programme. Proceedings of the Royal Society of London. B 205 (1161): 581–598. Gould, Stephen Jay and Elisabeth Vrba 1982 Exaptation: A missing term in the science of form. Paleobiology 8: 4–15. Hoekstra, T. et al. 1980 Lexical grammar. Dordrecht. Harris, Zellig 1951 Methods in Structural Linguistics. Chicago: University of Chicago Press.

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Hauser, Marc D., Noam Chomsky, & Tecumseh W. Fitch 2002 The faculty of language: what is it, who has it, and how did it evolve? Science 298: 1569–1579. Jacob, Franc¸ois 1982 The Possible and the Actual. New York: Pantheon Books. Jenkins, Lyle 2000 Biolinguistics. Cambridge., Mass.: MIT Press. Katz, Jerrold J. en Jerry. A. Fodor 1963 The structure of a semantic theory. Language 39: 170–210. Koster, Jan 1978 Locality Principles in Syntax. Dordrecht: Foris. Koster, Jan 1987 Domains and Dynasties: The Radical Autonomy of Syntax. Dordrecht: Foris. Koster, Jan 1988 Doelloze structuren. Inaugural Lecture, University of Groningen. Dordrecht: Foris. Koster, Jan 1989 How natural is natural language? In Jens Erik Fenstad, Ivan T. Frolov and Risto Hilpinen (eds.), Logic, Methodology, and Philosophy of Science VIII, 591–606. Amsterdam: Elsevier. Koster, Jan 2007 Structure-preservingness, internal merge, and the strict locality of triads. In Simin Karimi, Vida Samiian, & Wendy K. Wilkins, (eds.), Phrasal and Clausal Architecture: Syntactic Derivation and Interpretation, 188–205. Amsterdam/Philadelphia: John Benjamins. Lenneberg, Eric 1967 Biological Foundations of Language. New York: John Wiley & Sons, Inc. Mehler, Jacques, P. Jusczyk, G. Lambertz, N. Halsted, J. Bertoncini, & C. AmielTison 1988 A precursor of language acquisition in young infants. Cognition 29: 143–178. Muysken, Pieter 2002 Waar is de taalwetenschap? Inaugural lecture, Radboud University. Nijmegen. Odijk, Jan 1997 C-selection and s-selection. Linguistic Inquiry 28: 365–372. Petitto, Laura-Ann 2005 How the brain begets language: On the neural tissue underlying human language acquisition. In James McGilvray, (ed.), The Cambridge Companion to Chomsky, 84–101. Cambridge: Cambridge University Press. Popper, Karl R.

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Popper, Karl R. 1972 Epistemology without a knowing subject. In Karl R. Popper, Objective Knowledge: An Evolutionary Approach, 106–152. Oxford: Oxford University Press. Sapir, Edward 1921 Language: An Introduction to the Study of Speech. New York: Harcourt, Brace & World. Saussure, Ferdinand de 1916 Cours de linguistique ge´ne´rale. C. Bally & A. Sechehaye (eds.). Lausanne and Paris: Payot. Searle, John R. 1995 The Construction of Social Reality. London, etc.: Penguin Books. Tesnie`re, Lucien 1959 E´lements de syntaxe structurale. Paris: Editions Klincksieck. Tomalin, Marcus 2002 The formal origins of syntactic theory. Lingua 112: 827–848.

Part V. Recursion outside Syntax

17.

A note on recursion in phonology1

Harry van der Hulst 1. Introduction Recursion is widely postulated or questioned as a property of human language, in particular of syntactic and morphological expressions, i.e. as a property of Martinet’s first articulation (Martinet 1960). What about the second articulation? It is quite common to read that phonology is not recursive. To illustrate this point it is often mentioned that, for example, we do not find ‘syllables inside syllables’; cf. Pinker and Jackendo¤ (2005: 10): ‘‘Recursion consists of embedding a constituent in a constituent of the same type, for example a relative clause inside a relative clause (. . . .). This does not exist in phonological structure: a syllable, for instance, cannot be embedded in another syllable.’’

On the other hand, Ladd (1986, 1996) argues that higher-level prosodic structure allows (limited) recursion, while Hunyadi (this volume) argues that intonational structure displays recursion, even center-embedding. Several other authors have discussed the notion of recursion in phonology, both with reference to syllables and feet (i.e. lower prosodic structure) and prosodic words, phonological or intonational phrases (i.e. higher prosodic structure). In this chapter I o¤er a general discussion of the notion recursion in phonology. As stated in van der Hulst (this volume), recursion is possible when combinations of units that can be included in larger combinations are of the same complexity. Thus in syntax, XPs can occur inside XPs and this then allows for the kind of recursion that Pinker and Jackendo¤ refer to: we can find a phrase of a certain categorical type (e.g. a NP) inside a phrase of the same type.2 A common characterization of phonotactic 1. This material was first included in my introductory article to this volume. Several readers suggested developing it as a separate chapter. I wish to thank Marcel den Dikken, Anthi Revithiadou and Marina Viga´rio for comments on an earlier draft of this chapter. 2. In syntax, this type of direct recursion is perhaps limited to adjunction structures. In morphology, however, we readily find, for example, nouns that are directly dominated by the category noun, as in [[child]hood].

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structure is that it adheres to the ‘Strict Layer Hypothesis’ (Selkirk 1980, 1984, 1986, 1995; Nespor and Vogel 1986) which precludes a phrase from containing a phrase of the same complexity. The kind of structure that the Strict Layer Hypothesis allows can be characterized by the following rule schema (see van der Hulst, this volume):3 (1) Phrasen þ1

%

Phrase n þ Phrase n

Given this rule format, prosodic structure can not be recursive, which confirms the point that hierarchical structure as such does not entail recursion. However, the ban on recursivity has not been taken to be absolute. The phonological literature contains proposals for recursive feet, recursive phonological words, recursive phonological phrase and recursive intonational phrases. We also, although less common, find proposals to allow intrasyllabic recursion, which allow syllables inside syllables, or, at even lower levels of organization, onsets within onsets, or rhymes within rhymes. In the next two sections I will briefly discuss proposals of this sort, starting in section 2, with the lower prosodic units (i.e. syllables and feet). Section 3 will be devoted to the higher prosodic units. In what follows I will assume that phonotactics is just as much a combinatorial system as morphotactics and that combinations involve both basic units and units that themselves are combinations. My general conclusion will be that there is no reason to expect that phonology is not recursive. Rather, adopting the notion of Structural Analogy (Anderson 1992; van der Hulst 2005b) which suggests that both articulations (i.e. morphotactics and phonotactics) appeal to the same kinds of structural relations, we would not expect recursion to discriminate between the two. Rather, then, I will promote the idea that recursion is part of the ‘tactic planes’ of language. Being within the reach of our human cognitive capacities, both phonotactics and morphotactics make use of it, albeit it to di¤erent degrees. It is important to keep in mind that morphemes, the basic units of morphotactics, are meaningful units, whereas phonemes, the basic units of phonotactics (loosely ‘phonology’), are not4. The ‘other side’ of phonemes 3. I refer to Itoˆ and Mester (2009) for a detailed discussed of the formal aspects of the prosodic hierarchy as it was originally understood. They also discuss subsequent views within Optimality Theory and their own proposals which I discuss in section 3.1. 4. I use the term ‘phonotactic structure’ to cover syllabic, and metrical/prosodic structure.

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is not ‘semantic substance’ as it is for morphemes, but rather ‘phonetic substance’. Thus the basic units in both articulations di¤er substantially. There is therefore no reason to expect that phonotactics will display the same degree of recursive structure as morphotactics for the simple reason that the kinds of structures that are employed in both modules do not exist in a vacuum, but rather are formed to iconically (i.e. isomorphically) accommodate whatever it is that these structures stand for. This view point reflects the idea that both tactic planes are ‘grounded in their substances’ (Anderson 1997). If we assume that certain aspects of semantic substance are inherently recursive (such as second degree intentionality5 ), we expect morphotactics to try and mimic this as much as possible. Of course, principles, if any, that are inherent to morphotactics may impose limits on the degree of isomorphy that morphotactic structures can attain. Additionally, it is conceivable that these structures, at the same time, also try to accommodate something other than strictly semantic substance, such as information structure (i.e. the organization of given and new information, etc.). If, on the other hand, phonetic substance is not inherently recursive there is no need for phonotactics to produce recursive structures in an attempt to be isomorphic. As I would like to claim, phonetic substance indeed does not appear to be recursive. Rather it would seem that phonetic substance, being the result of motoric actions, is essentially ‘sequential, iterative and rhythmic’6, which seems be mimicked by phonotactic structures that display strict layering. Why then would phonotactics nonetheless display recursion? I suggest that there are two reasons. Firstly, if strict layering is guided by binarity (as I will assume here, although the matter, of course, warrants more discussion) we need a procedure for incorporating (i.e. adjoining) ‘stray units’ when the string to be organized consists of an odd number of units; this produces degree-1 recursion; cf. below. Secondly, at higher levels of organization, phonotactic structure tries to match (be isomorphic to) morphotactic structure (and therefore indirectly semantic structure). This stimulates recursion wherever the morphotactic structure is recursive. In this case, however, recursion of phonological structure is counterbalanced by the fact that the phonetic

5. Second degree intentionality involves intentions that are about intentions. 6. These terms would obviously have to be more precise to explain the correlation between phonetic stu¤ and ‘flat structures’. For the moment, I will not try to do that and appeal to a more intuitive and informal understanding of this point.

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grounding stimulates adherence to the strict layering which, in turn, may give rise to recursion resulting from adjunction. I will demonstrate the first source of recursion by referring to the fact that rhythmic structures (as exemplified in music and language, and other areas) impose a binary or ternary structure on sequential events such that an even number of events is grouped in binary units (cf. 2a), whereas an uneven number of events would have to deal with one stranded unit, (2b): (2) a. b. c. d.

(x (x (x (x

x) x) x) x)

(x x) (x x) (x x) x ((x x) x) (((x x) x) x)

I suggest that the most likely manner for a stranded unit to be adjoined to an adjacent binary structure is as in (1c), which, then, creates a recursive structure. However, even though recursion is thus possible (and perhaps the only way to go), we would not expect to find multiple recursion, as in (2d), because an even number of units can be more rhythmically parsed as in (2a). One would only expect to find (2d) if some other external force than rhythm demands it. I will argue below that, in phonotactics, this other force could be the ‘desire’ for phonotactic structure to be isomorphic to morphotactic structure, but I will also show that, while rhythm may give in to isomorphy ‘a little’, rhythm is strong enough to prevent phonotactic structure to be fully isomorphic to morphotatic structure, which is the reason for why phonotactic structures are usually flatter than morphotactic structures. Thus, summarizing, I will argue that phonotactics does produce recursive structures to (a) incorporate stranded units and (b) achieve isomorphy to morphotactic and thus semantic structure. With reference to the latter, what would perhaps be optimal recursion in phonology (from the view point of achieving maximal isomorphy) is counterbalanced (i.e. flattened) by the inherent sequential, rhythm and iterative drive of the phonetic substance. Anticipating the discussion in section 3, I add here an important distinction, made explicit in Wagner (2005), which is that the question of recursion in phonotactic structure must be distinguished from the e¤ect of phonological rules applying cyclically to (potentially recursive) syntactic structures. If, for example, a cyclic phonological rule lengthens the rightmost vowel in a syntactic phrase, it is easy to see that this cannot be an argument in favor of recursive phonological grouping-structure, or, for that matter, phonological grouping-structure of any kind, unless the argument could be made that the ‘phrases’ that the rule refers to are phonolog-

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ical (‘prosodic’) rather than syntactic. Even if, let us say, a phrasal accentuation rule applies cyclically to increasingly larger syntactic phrases, this, again, does not mean that these rules create recursive phonological structures unless one would argue that the notion phrasal accent is formalized in terms of a phonological grouping structure. The latter point of view would be taken within standard metrical theory (Liberman and Prince 1977, and maintained in Ladd 2008). However, if phrasal accentuation rules simply assign ‘an accent’ (i.e. grid mark), there is no sense in which the result is a recursive structure.7

2. Syllables (and feet) With the preceding remarks in mind, let us start with a discussion of syllable structure which is the lowest level of organization, imposing a grouping on the linear string of phonemes. I will assume that phonemes indeed group into syllables, although this is not generally accepted. For example, in all varieties of Government Phonology (see Scheer 2004 for an overview), the syllable is not recognized as a phonotactic constituent. Instead, phonemes are grouped into onsets and rhymes (some of which are emptyheaded; cf. below), which in the standard variety of Government Phonology (Kaye, Lowenstamm and Vergnaud 1990), depending on the language, are allowed to branch once, so that each contains maximally two phonemes. In this view, syllabic constituents combine only basic units (i.e. phonemes) which, then, rules out recursion because recursion can only exist if combinations can be included into larger combinations (cf. section 1). In a more widespread view, the one adopted here, syllables are recognized as constituents, which entails grouping of units that themselves can be combinations. In this view recursion is possible, at least in principle, and, as we will see, it does, contrary to popular belief, occur.8 The issue involves the analysis of so-called codas.

7. Schreuder, Gilbers and Quene´ (2009) argue in favor of phonological recursion on precisely these grounds, but it would seem that they only show that accent assignment in phrases can be cyclic. 8. As is well-known, Chomsky and Halle (1968) did not postulate syllables. In the approach taken by Blevins (2003) arguments in favor of the syllable, based on their alleged necessity for the statement of phonotactic restrictions and allophonic e¤ects are questioned. I will assume here without further discussion that phonotactic arguments remain valid; cf. van der Hulst and Ritter (1999).

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It is generally stated that syllables are projections from vowels. Since the consonantal skeleton of lexical items can be said to be the primary expression of the lexical meaning of these items (especially in templatic languages like the Arabic languages), while vowels are less crucial in this respect and indeed often the expression of inflectional categories, we can think of the latter as ‘functional’ units and the former as ‘lexical’ units, and as such, heads that take consonants as complements. Hence a CVCVCV word can be parsed into three syllables:9 (3)

This way of looking at vowels and consonants, whatever its merit, is congruent with the traditional idea that vowels are syllable heads because they are the most sonorous phonemes. Thus, syllable heads are sonority ‘maxima’ (optimally vowels, perhaps more generally sonorants), while their consonantal dependents are sonority minima (optimally obstruents, more generally consonants). Sonorant consonants fall within the intersection of sonorants and consonants and can thus be either heads or dependents. I take the labels ‘C’ and ‘V’ (in 3) to be category labels of phonemes (analogous to labels such as Noun and Verb for morphemes). Feature structures that capture the ‘content’ of phonemes can belong to the category V or to the category C in which case we refer to them as ‘vowels’ and ‘consonants’, respectively. In addition to C and V we can postulate subcategories such as ‘C;V’ for ‘sonorant consonants’.11 The term ‘syllable’ is just an informal label for a complex unit that belongs to the category V; likewise, the term ‘nucleus’ can be used for a basic (non-

9. Henceforth I will add subscript labels such as ‘syll(able)’ that correspond to traditional labels. These subscripts have no formal status in the proposal discussed here, but they help the reader to relate the structures used here to more informal traditional ones. 10. In van der Hulst (2005a) I present an extensive discussion of such phoneme categories which traditional feature systems capture in terms of ‘major class features’. 11. These intermediate categories can be characterized in terms of dependency structures as proposed in Anderson and Ewen (1987); cf. van der Hulst (2005a) for an elaboration of these ideas.

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complex) V and the term ‘onset’ can be used as an informal label for units that belong to the category C.12 When a string of phonemes is more complex than a regular CV alternation, we need more than one round of grouping before all phonemes have been organized into syllables. We can think of the way in which a string of phonemes can be analyzed in terms of syllables and subsyllabic units in the following manner. First we locate the ‘lexical units’ (onsets). As ‘complements’ to a head (cf. 3) we expect onsets to be potential projections themselves and in languages that allow so-called branching onsets that is what they are. It is tempting to think of onsets (at least in languages that allow branching onsets) as units defined in terms of rising sonority, just like syllables as a whole, which, in fact, would allow us to see the syllable as a recursive unit in that onsets would be ‘syllables inside syllables’. Although I think that this perspective has some merit, it seems to entail that in such complex onsets, the more sonorous consonant is the head. However, because onsets are sonority minima, the least sonorous consonant (optimally an obstruent) counts as the typical member of the complex onset. For this reason it makes more sense to regard the least sonorous phoneme as the head as is proposed in Anderson (1986) and in Kaye, Lowenstamm and Vergnaud (1990):13 (4)

If we now assume that all Cs that are not followed by a sonorant form onsets on their own, the next step after (4) is to combine onsets with their functional heads to their right, the V units.

12. Whether obstruents can be syllable heads, like vowels can be onsets (as ‘glides’), is controversial. This point, however, is not absolutely crucial to the following discussion. 13. Here and below, the strings of phonemes do not present actual words in any specific language.

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(5)

Here we face the question what to do with stray ‘onsets’, i.e. C’s or C;V’s that are not followed by a V; such ‘onsets’ are usually called ‘codas’. In approaches such as Government Phonology (Kaye, Lowenstamm and Vergnaud 1990), some of these stray ‘onsets’ are taken to be followed by an empty V (a V unit that has no vowel content associated to it), while others are analyzed as proper codas, i.e. as direct dependents of the V to their left (if certain conditions are met). Let us say, however, that these alleged codas are, in fact, always onsets followed by an empty ‘nucleus’ (cf. Lowenstamm 1996, Scheer 2004). The next question is then how such ‘syllables’ are integrated into the phonotactic parse. There are two options. In (6a) the vowel takes a following ‘coda’ as the direct dependent and the preceding onset as an indirect dependent. This creates the familiar ‘onset – rhyme’ division. The other possibility would deliver (6b) which would correspond to a moraic theory of syllable structure which also has certain arguments going for it (cf. Hyman 1985): (6) a.

b.

I will assume here that the onset – rhyme structure is the correct one because (a) phonotactic combinatorial constraints refer more often to the vowel and the following ‘coda’ than to the vowel and the preceding onset

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and (b) the poetic convention of rhyming and as well as slips of the tongue and language games also more often presuppose this structure rather than its rival in (6b). This then would lead to the syllabic grouping in (7) for the string in (5): (7)

The representation of ‘codas’ as degenerate syllables is not unique to the proposal made here, and indeed is common in varieties of Government Phonology. However, to place this unit as subordinate to the preceding vowel (‘nucleus’) is not found in these approaches, nor in any other proposal that I am aware of. But that does not mean that the proposal at hand is not a possible contender. It is precisely this possibility that invokes the kind of recursion that is generally held impossible: a syllable inside a syllable. Syllables are commonly taken to involve a kind of constituent structure that is quite analogous to the syntactic structure of sentences, or perhaps phrases: (8) a.

b.

This analogy, indeed, invites the question why ‘complements’ within the syllable are not syllables, just like complements within syntactic phrases are themselves phrases? It would seem that the apparent lack of recursion within the syllable is an artifact of using the labels that we traditionally

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use. If the ‘right’ labels are used we see that codas are syllables (albeit, so far, with an empty rhyme), and thus that ‘codas’ are ‘syllables inside syllables’. We can exemplify all this by focusing on the complex syllable trim in (9) in which I have informally labeled the ‘coda’ as ‘syl-cd’: (9)

This account of syllables structure raises a further question.14 Why do syllables inside syllables (i.e. codas) need to be empty-headed? Why can’t we have the syllable /pa/ inside the syllable /ko/? A sequence /kopa/ would ‘normally’ be regarded as a branching foot, as in (10a). However, I submit that (10b) is, again, a possible contender: one syllable with a syllable inside it: (10) a.

b.

14. Other phonologists have proposed structures for the syllable that involve recursion: Smith (1999), Garcia-Bellido (2005), Po¨chtrager (2006). For the sake of brevity I refrain from making a comparison to these other proposals, some aspects of which overlap with the present proposal.

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In this proposal ‘feet’ are syllables that happen to contain another syllable. Why would we prefer (10a) over (10b)? (10b) would seem to be extremely adequate given the often observed equivalence between a closed syllable and a branching foot (cf. McCarthy and Prince 1986). In the proposal made here, these two objects are structurally identical (cf. 6a and 10b), here both repeated for convenience: (11) a.

b.

Again we can invoke poetic rhyming in support of (11b). In ‘feminine rhyme’ (hocus – pocus), the initial consonant of the foot falls outside the rhyming unit which indeed is a unit in (10b), but not in (10a). The structures in (11) are so-called trochaic ‘feet’. Iambic ‘feet’ could have the following structure, with one light syllable pre-adjoined to a heavy syllable:15 (12)

15. In case of so-called ‘minor syllables’ as in Kammu the head of these adjoined syllables is empty (cf. van der Hulst and Ritter 1998). Below I argue that this structure can be used for triconsonantal ‘onsets’ in English too.

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That trochaic ‘feet’ and iambic ‘feet’ quite di¤erent ‘entities’ has been argued for a variety of reasons (Hayes 1986, van der Hulst 2000; van de Vijver 1995). The present proposal provides a basis for a di¤erentiation. Adjunction, of course, also creates recursion. Returning to trochaic patterns, let us now ask whether syllables that are contained in syllables can contain syllables, i.e. recursion of the second degree? In other words can the string in (13) be parsed as one syllable? (13)

I suggest that (13) is possible and, in fact, represents what elsewhere has been called ‘a ternary foot’ (sometimes called ‘superfoot’), which is a perfectly legitimate object in, for example, English (winnepe-saukee, hippopotamus).16 It is interesting that the initial consonant of the such structures is indeed external to the whole sequence as is evidenced by the poetic dactylic rhyming convention: [h]ickeldy – [p]ickeldy. The structure in (13) captures the special position of the initial onset (which can or must be different), as opposed to the other more deeply embedded onsets (which must be identical). It is generally the case, in syntax, that recursive structures can either result from complement structures or from adjunction. Again, there is no 16. Below I propose that this structure can also be used to accommodate complex ‘codas’.

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a priori reason to reject the same two options in phonology. In fact, our proposed structure for trochaic and iambic ‘feet’ di¤er in precisely this way. The trochaic structure is recursive because the complement (i.e. dependent) of a head is identical to the maximal projection of the head. This is the kind of recursion that is illustrated in (8) and in (9), (10b), (11b) and (13). The dependent, which causes recursion, is subjoined to the head. The recursive structure in (12), on the other hand, results from adjunction. Here recursion is caused by the fact that the head contains an instance of itself after an element has been adjoined. This is what is commonly called ‘Chomsky-adjunction’. Recursion following from adjunction has been proposed more generally and almost always underlies the claim that a specific phonological unit is recursive. Indeed, work in metrical theory has used ternary feet in which the right-most ‘extra’ CV unit at the end is seen as being adjoined to the foot formed by the first two syllables, rather than being incorporated as the deepest unit: (14)

This is also the structure that Dresher and Lahiri (1991) proposed for the ‘Germanic foot’, with the first CVCV unit being called the ‘subfoot’. If adjunction creates a legitimate (and also recursive) structure (as it does for iambic ‘feet’), the structure in (12) is, perhaps, a possible structure, possibly necessarily arising when extrametrical syllables, which are independent syllables, not contained in any other syllable, are incorporated into the phonotactic structure. I will leave undecided here whether both types of structures (i.e., 12 and 14) are independently needed for ternary feet. Perhaps the structure in (14) has been used in cases where that in (13), unavailable in current models, would be more appropriate. I will make another suggestion bearing on this distinction in the concluding section. Let us now ask whether there are limits on recursion in phonology: Can a sequence of four CV units be parsed as in (15), as a quaternary ‘foot’?

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(15)

Although formally perfectly correct (if recursion is available), it would seem that (15) creates a dis-rhythmic structure: SWWW, i.e., a lapse that can be avoided by adding an extra beat which would not create a clash. Indeed, a string of four CV units is more likely to be parsed as a sequence of two feet (SWSW), which together form a phonological word which is either left-headed or right-headed. Here I display the former option, which expresses the initial primary accent: (16)

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(16) is ‘flatter’ than (15) and this, I suggest (merely making implicit what most phonologists would take for granted) is a consequence of the rhythmic nature of the ‘phonetic substance’ that phonotactic structure represents, which seems to be better expressed by an iterative rather than by a recursive structure. Beyond the ‘magic number’ 3, recursion gives in to rhythm (cf. the discussion surrounding 1 in section 1). In other words, I suggest that recursion is perfectly possible in phonology if it does not make the phonotactic structure dis-rhythmic. From a rhythmic point of view ‘4’ is just too much (hence we see ‘flattening’), ‘1’ is too little (hence we see subjunction or adjunction), which makes ‘2’ and ‘3’ rhythmically wellformed, i.e. binary and ternary rhythm, respectively. Syllables have been said to display an even greater complexity than considered so far. In English, onsets can contain three consonants (/spr/) and rhymes can be of even greater complexity (/ink/).17 The extra consonants (/s-/ and /-m/) would constitute degenerate syllables by the above algorithm, and I will assume that they can be structurally represented as in (17):18 (17)

17. This ignores so-called coronal appendices /s/, /st/): warm-st ‘warmest’ which I will analyze as clitics; cf. van der Hulst (2005b). 18. Kuryłowicz (1952) proposes such bare onsets for Slavic initial clusters, although he does not unite this bare onset with the following syllable. A similar

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The /s/ is adjoined as a ‘degenerate syllable’, making use of the iambic structure proposed in (12). The /k/, on the other hand, makes use of the subjunctive structure that was introduced (13).19 Subjunction brings the rhyme to the maximum structure of three ‘nuclei’, while adjunction brings the onset to the maximum of three consonants. The recursive options stretch the limit of rhythm from 2 to 3, a limit that has been reached in English. We thus predict that languages could not be more complex than this because beyond ‘3’ we have enough material to group into 2’s. This prediction faces challenges, as we know, some of which are discussed in van der Hulst and Ritter (1999). The discussion in this section challenges the idea (or prejudice) that phonology is not recursive at the ‘level’ of the syllable. What we have argued is that the notion ‘foot’, at least the trochaic and dactylic foot, emerges naturally from allowing ‘syllables inside syllables’, whereas other forms of recursion (involving iambic feet as well as trisegmental onsets) can be modeled in terms of adjunction. What needs further study is ‘how recursive’ the domain of the syllable/foot can be and whether indeed rhythmic principles impose absolute limits, or rather make degree 3 and beyond unlikely, although not impossible.

3. Higher prosodic levels In this section I will discuss some proposals for recursive structure at the level of prosodic words and prosodic phrases. I refer to Fox (2000, chapter 6) for a good overview of di¤erent proposals for prosodic organization, including work that was inspired by Selkirk (1978), which culminated in the seminal Nespor and Vogel (1986). The review that Fox o¤ers makes it clear that the question of recursion in prosodic is not a recent one. He refers to earlier work (e.g. by the linguists Kenneth Pike and Paul Tench) who distinguish between basic units in the hierarchy and ‘expansions’: ‘‘the expansion is a group of units whose role is the same as that of the analysis could be used for minor syllables in Khmer languages; cf. van der Hulst and Ritter (1999). As mentioned, in Government Phonology such bare onsets are taken to be followed by an empty-headed rhyme. Kaye (1992) proposes an onsetless empty headed rhyme with /s/ as the coda. This unit could still be adjoined as in (17), although this is not what Kaye assumes. There are other proposals on /s/ which involve seeing S þ obstruent as a complex segment. This proposal would entail a much deeper adjunction of /s/, in fact below the C terminal of the onset head (cf. van de Weijer (1996). 19. These possibilities were pointed out to me by Marcel den Dikken.

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basic unit which constitutes its head’’ (Fox 2000: 351). In this view, a complex onset is an expansion of a single consonant forming an onset, just like unaccented syllables form an expansion to the accented syllables (making a foot). The spirit of these proposals clearly is that prosodic categories display recursion. We must note, however, that the recursion that follows from ‘‘expanding’’ the head corresponds to what is here called ‘recursion following from adjunction’. Indeed, in section 2 we have seen that recursion can take two forms (cf. also van der Hulst, this volume). The category of the complex units can be identical to the head (adjunction) or to the dependent, i.e. complement of the head which is the kind of recursion that results, in morphotactic structure, from complement phrases having the same category as the phrase that they are contained in. We have called this ‘recursion following from subjunction’. In section 2 I have suggested that the latter kind of recursion can be attributed to syllable/foot structure if codas and weak syllables are represented as dependents of the preceding syllable nucleus. Subjunctive recursion is what, in morphotactics, is referred to as the prototypical case of recursion (‘a unit of type A within a unit of type A’), while adjunctive recursion is usually not mentioned as such. However, in (14) I displayed a recursive foot which involves adjunctive recursion in contrast with (13) which displays subjunctive recursion. As we will see in this section all recursion at higher prosodic levels is of the adjunctive kind, even when it claims to be isomorphic to subjunctive morphotactic structure. In section 4 I briefly consider the possibility of subjunctive recursion at levels of organization above the syllable/foot. 3.1. The prosodic word Leaving the syllable and foot level behind us now, let us turn to the Phonological or Prosodic Word and higher levels, adopting, for convenience, the label F(oot) as it is commonly used. If prosodic structure is driven by rhythm which calls for flat binary grouping, we expect that Prosodic Words contain 2, at most 3 feet and that longer morphosyntactic words will correspond to more than one prosodic word: (18) a.

b.

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Whereas the English word apalachicola can be one PrW containing three feet, a word consisting of four feet would have to be parsed as two prosodic words; cf. also Helsloot (1993, 1995) who explicitly argues on similar grounds that prosodic words are not ‘endless’. Note that the structures in (18), on the assumption that the highest node is PrW, both display recursion, although with a di¤erence. I will return to the structure in (18b) below. First, let us take a closer look at the structure in (18a). Structures of this kind (albeit without the lower PrW label) were proposed in metrical theory (Liberman and Prince 1977). As shown in van der Hulst (this volume) the view embodied in this kind of structure seems to be that the phonological structure of PrWords can be characterized by an inductive definition: (19) Phonological words (recursive definition) a. PrWord % foot (base case) b. PrWord % PrWord þ Foot (inductive step) According to (19) a foot is a (minimal) prosodic word and every structure that results from adjoining a foot to a prosodic word is also a prosodic word. In later versions of metrical theory, however, PrWords have been characterized in terms of an iterative structure so that indeed (20a) and (20b) both occur in the metrical literature: (20) a.

Iterative definition

b. Inductive definition

The ‘flat’ representation in (20a) has also been proposed (e.g., in Halle and Vergnaud 1987) in the guise of so-called ‘bracketed grids’. The question is which representation accounts best for the properties of phonological words. (20b), for example, can be said to express di¤erent degrees of prominence of feet, about which (20a) has nothing to say. In other words, just like semantic properties may be more adequately expressed in recursive morphotactic structures, phonetic properties may be more adequately expressed in recursive phonotactic structures. However, an unbounded recursive structure does rather poorly as a predictor of rhythm, since there is

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no structural basis for the fact that a long sequence of feet will display rhythmic alternation (SWSWSW etc.) and a structure as that in (20b) is therefore likely to be broken up as in (23): (21)

In analyses of languages with long words, Halle and Vergnaud (1987) in fact postulate binary grouping of feet in, what they call, cola (sing. colon). However, if recursion is available there is in fact no need for postulating new phonological categories each time we need more structure than the strict layering model allows. The question should rather be whether the larger unit that is added displays the same kinds of properties as the smaller unit that it contains. In this regard, as we will see below, serious claims have been made that combinations of PrWs do indeed form a specific prosodic category, rather than simply being recursive PrWs. If correct, this would cast doubt on the structure in (18b), here repeated as (22b). Let us now return to the structures in (18) which suggested that recursion in phonology can take two di¤erent forms (both not being of the subjunctive type): (22) a.

b.

(Recall that the ‘foot’, as per section 2, is a kind of syllable.) In a strict layering model, both structures are considered ill-formed. In (18) I tentatively suggested both structures as possibilities for monomorphemic words, although the likelihood of finding a quadric-podal morpheme might be rather slim. We could call (22a) an unbalanced recursive prosodic

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structure, whereas (22b), then, would be a balanced recursive prosodic structure. The former arises from adjunction which creates ternary structures as in (18a), whereas the latter result from the need to express rhythm in terms of a layered structure. In both cases, the detailed structure is inherently phonological because the words, by hypothesis, lack any kind of morphotactic structure. In a sense, these structures involve a mismatch between the prosodic structure and the morphotactic structure in that a single morphotactic word is parsed into a prosodic word ‘and a bit’ or two or even more prosodic words. One would perhaps expect that the reverse is also possible, i.e. a polymorphic structure that corresponds to a single prosodic word. This, of course, is precisely what we find when we deal with a‰xes that are what are called ‘cohering’ or ‘integrating’. These a‰xes (roughly the level I su‰xes in English; cf. Allen 1978) ‘integrate into the prosodic domain that is formed by their base’ (Booij 1996): (23) a.

b.

Whether or not words that are formed with integrating a‰xes form one or two prosodic words depends on their length, if it is true that the PrW is not an endless domain. As suggested in Helsloot (1993), if there are more than two feet a single prosodic word unit cannot comprise the whole word, as in (23b), where we still leave the matter undecided as to whether the whole unit is a PrW. However, when we start dealing with units that are bigger than single morphemes (or bigger than simplex words), another type of motivation for phonological structure comes into play, namely the drive for phonological structure to be isomorphic to the morphotactic-semantic structure.

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In line with this, as it is frequently claimed (as in Kabak and Revithiadou 2009), every morphotactic word (belonging to a major lexical category; cf. below) wants to be a prosodic word. The drive for isomorphy would lead to another structure for the words in (23): (24) a.

b.

Technically, these structures emerge when metrical organization is assigned cyclically (Kiparsky 1979). A reflection of such cyclic application would be the fact that primary accents of embedded words are preserved as ‘cyclic non-primary accents’. If this is how prosodic structure behaves, it would seem that prosodic structure mimics the recursion that is present in the morphotactic plane. Note, however, that the prosodic structure does not mimic the morphotactic structure in one important respect. Whereas in the latter structure newly added material (su‰xes) are heads (because su‰xes determine the category of the complex word), the idea that prosodic domains corresponding to more deeply embedded words are contained in prosodic domains of less deeply embedded words suggests that the more deeply embedded domains are heads to which the new material is adjoined as dependent material. This assumption (which may be misguided) leads to the fact that the recursion that we find in the prosodic hierarchy is adjunctive recursion, while the recursion in the morphotactic hierarchy is subjunctive recursion. I will return to this point in section 4. The cyclic-isomorphic account can be enforced derivationally in terms of cyclic application or, non-derivationally, in terms of constraints that

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demand alignment of morphotactic edges with prosodic edges or, more straightforwardly, demand each morphotactic word (or phrase) to be a prosodic word (or phrase). The question arises, however, to what extent, phonology serves isomorphy? Kiparsky (1979) demonstrates that cyclic structure is changed into rhythmic structure in case the primary accent of the embedded word is adjacent to the primary accent of the su‰x, thus avoiding a clash: (25) a.

invı´te P `ınvite´e

b.

Likewise, restructuring is likely to happen if the primary accent of the embedded word is non-initial since, in English and other languages, initial syllables attract the secondary accent: (26) a.

renu´merate P re`numera´tion

b.

It would seem then that unbalanced recursive structure within the prosodic word tends to be replaced by balanced recursive structure. Another area where unbalanced recursive prosodic word structure arises above the level of the morphotactic word, i.e. ‘in the syntax’, occurs when lexical items belonging to closed categories ‘cliticize’ to a host to their right or left. The resulting structure, which some have termed the clitic group, has been identified as a recursive prosodic word (Peperkamp 1997):

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(27)

But when more than one clitic is added, as in (28), we need to ask whether the structure remains recursive (and thus isomorphic), or whether it will be ‘flattened’: (28)

Peperkamp (1997) compares various Italian dialects in terms of the e¤ect that clitics have on the rhythmic structure of words and it would seem that in some dialects the restructuring in (28) applies while other perhaps tolerate the unflatted structure. This seems to mean that the conflict between rhythmic grouping and isomorphy can be resolved by giving precedence to one over the other. If the multiple recursive structure in (28) is a possible structure this implies that phonology allows more recursion in case of morphotactically complex expressions than for simplex words, simply, we would have to assume, in order to maintain isomorphy and this again raises the question how recursive (and thus disrhythmic) phonology is willing to be in order to comply with the demands of isomorphy. Turning to morphological compounds, it would seem that, at least in English, their prosodic structure is isomorphic to their morphotactic structure, each member of the compound forming its own prosodic word. However, how are these prosodic words organized into larger prosodic units? The original strict layer hypothesis would require that a compound is a phonological phrase. This kind of structure, then, would also be likely for words derived with ‘heavy’ su‰xes like –hood, which have often been claimed to display the same kind of prosodic structure as compounds:

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(29) a.

b.

In fact, even non-compound words that apparently display the phonotactic structure of compounds would be represented in this way. Such words may be loan words or ‘old (hidden) compounds’. However, rather than taking this step, other researchers (Kabak and Revithiadou 2009, Itoˆ and Mester 2008) have suggested that such complex words have balanced recursive structures: (30) a.

b.

Vogel (2009), on the other hand, proposes that compounds are more like ‘clitic groups’ (which she calls ‘composite groups’ to express the idea that the unbalanced recursive prosodic word covers more than clitic structures): (31) a.

b.

A third kind if proposal can be found in Viga´rio (to appear) who proposes that the prosodic unit formed by compounds (and compound-like structures) is a new category that she calls the Prosodic Word Group. One argument for recruiting a new category rather than a recursive structure is that the relevant unit has properties that can be quite distinct from the properties of prosodic words. A property that Viga´rio discusses is the fact that compounds often have a prominence pattern that di¤ers from that of words and that of phrases, which suggests that this unit should not be identified with either.

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Here I will remain neutral on which proposal is more appropriate, although, perhaps, more than one should be allowed, albeit for di¤erent kinds of data. The structures in (31) would attribute less prosodic autonomy to the right-hand compound member which may apply to certain languages or be the result of diachronic ‘weakening’ from balanced structures. Whatever the case may be, when compound structures get more complex morphotactically, the question arises again to what extent the phonological structure stays isomorphic or will be subjected to ‘flattening’. The evidence suggests that flattening is very likely to occur (Giegerich 1985, Visch 1999). Thus, while the structure in (32a) is isomorphic and still rhythmic (being ternary), the even longer compound in (32b) is likely to be subject to flattening so that we get (32c) instead:20 (32) a.

b.

20. Here I adopt Viga´rio’s Prosodic Word Group, assuming that this category tolerates unbalanced (as in 32a and b) and balanced (as in 32c) occurrences for compounds consisting of more than two terminal words.

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c.

(32c) results when rhythm (the phonology-inherent force) takes over from isomorphy.21 Note, however, that in both cases we have recursive structure on the assumption that compounds, no matter how complex, form prosodic word groups rather than phonological phrases. Recapitulating, we have seen two types of recursive prosodic word structures, unbalanced and balanced. Both structures are recursive and both can be subject to flattening. Structures of this sort have been put to use in recent studies by Kabak and Revithiadou (2009), Itoˆ and Mester (2009) and Viga´rio (to appear). Itoˆ and Mester (2009) suggest that recursive structures are limited in the following manner: (33)

(As we will see below, they propose the same scheme for the phonological phrase.) By allowing adjunction (creating recursive structure), Itoˆ and Mester claim that we can avoid unprincipled proliferation of prosodic categories. The suggestions made here concur with the ideas of these authors and it is interesting that they limit the adjunction scheme to precisely the point where further adjunction would create a quaternary and this disrhythmic structure. 21. This prosodic structure is ambiguous in that a di¤erent compound [[arm chair] [factory director]] ‘an armchair kind of factory director’ (i.e. he doesn’t have much practical experience), has this same structure, albeit that in English the second ‘S’ would be the primary compound accent in that case.

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3.2. The phonological phrase (and beyond) Climbing up the prosodic hierarchy, the next unit is the phonological phrase and here too, as we expect, isomorphy (to morphotactic structure) plays an important role. Much has been written on the formation of prosodic phrases and their relationship to syntactic phrases (starting with Selkirk 1978, 1980, Nespor and Vogel 1986 followed by a lot of further work; cf. Truckenbrodt 2007 and Elordieta 2008 for overviews). Firstly, a distinction must be made between phrases with a lexical head and phrases with a functional head. The latter typically do not project prosodic phrases, but instead are adjoined to prosodic phrases that are projected from lexical heads; depending on the language, the host of adjunction is either the complement of the functional category, as in (34) (which preserves isomorphy), or not: (34)

Returning to the notion of clitic group (interpreted as a recursive prosodic word), one might ask whether functional words can adjoin at the prosodic word level or at the prosodic phrase level. Di¤erent authors take di¤erent points of view, although adjunction at the level of the PrW seems to be the more popular approach (Booij 1996). Turning now to lexical phrases that recursively contain lexical phrases, we might ask whether prosodic phrases (analogously to prosodic words) allow various levels of adjunction, thus forming recursive prosodic structure that is isomorphic to the morphotactic structure. Itoˆ and Mester (2008, 2009) suggest that it does and they propose the following structure: (35)

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This still leaves open what the prosodic status of ‘X’ is in such cases: (36)

Selkirk (1986) and others have shown that whether or not complement phrases form their own prosodic phrases depends on the ‘weight’ of the phonological material of the syntactic complement. In addition, however, languages may simply be di¤erent in this respect. Di¤erent types of prosodic phrases (such as minor and major phrases; Beckman and Pierrehumbert 1986) have been distinguished. One would have to re-examine all these proposals, but it is possible, as Itoˆ and Mester suggest, if not likely, that these distinctions are simply specific instances of recursion within the prosodic phrase, e.g.: (37)

If we allow the recursive structure in (37) we might again ask how much recursion in prosodic structure is tolerated. If, let us say, two levels of embedding are added, do we get (38a) or (38b)? (38) a.

b.

Giergerich (1985: 235 ¤.) already proposed that with increasing phrasal embedding, isomorphic (recursive) prosodic structure gives way to a flatter

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rhythmic balanced grouping so that (38b) is preferred over (38a) as evidenced by the two possible rhythmic structures of the phrases here informally represented with Ws and Ss.22 With reference to (38b) one could furthermore ask whether a conjunction of two phonological phrases necessarily means that the combination is a higher prosodic category, such as the Intonational Phrase. Would instead of (39a), (39b) also be possible? b.

(39) a.

If the structures that group phonological phrases are analogous to those that group prosodic words, we would expect that a case can be made for either structure. As in the previous section, it would seem that structures as in (40a), balanced structures, are needed in addition to the one in (40b), unbalanced structures: (40) a.

b.

Ladd (1996: 244) indeed proposes balanced structures of this kind (with specific reference to the Intonation Group) which he calls compound prosodic domains. Besides providing empirical evidence for his proposal, he also motivates this type of structure by pointing out that repeated flattening of recursive structures would lead to an undesirable proliferation of prosodic categories unless balanced recursion of categories is invoked. Again the view concurs with what is suggested in this chapter. Let us conclude then that prosodic structure displays recursion which is either unbalanced (and isomorphic to morphotactic structure) or balanced (resulting from flattening when unbalanced embedding exceeds degree 2). In the 2nd edition of 22. See Schreuder, Maartje, Dicky Gilbers and Hugo Quene´ (2009) for a recent study showing that the accentual patterns in phrases can reflect the recursive morphotactic structure of these phrases which means that rhythmic adjustment is not always obligatory.

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his book on intonation, Ladd (2008) writes: ‘‘. . . many researchers now accept that some form of recursion and/or indeterminate depth of structure must be incorporated into our understanding of prosodic structure . . . Many details, though, remain to be worked out.’’

4. Concluding remarks In this chapter, I have explored the (potential) use of recursive structures in phonology. My starting point was that recursion is not, as Hauser, Chomsky and Fitch (2002) believe, limited to the syntactic module. Following Anderson’s notion of Structural Analogy, my working hypothesis has long been that the same kinds of structures are available in all modules of grammar. (In fact, I believe that recursion is a general faculty of the human mind, employed in language where needed.) In discussing the notion of recursion, we have first looked at levels of organization where isomorphy with morphotactic structure plays no role. Kabak and Revithiadou (2009) suggest that these lower levels of organization are fundamentally di¤erent from the higher levels of prosodic organization. They conclude from this that recursion at these levels is unexpected, but this is fueled by their belief that recursion is phonology must be morphotactically motivated. While I accept that this is true for higher levels of prosodic organization (surrounding the prosodic word and the prosodic phrase), I have suggested that ‘feet’ can be analyzed as resulting from recursion, either because syllable heads (nuclei) can take syllables as ‘complements’ which leads to subjunctive recursion, or as a result of adjunction. It may very well be that syllables (in the extended sense proposed here, i.e. including foot structure) display a kind of recursion that is di¤erent from what we find at higher levels, a finding that further illustrates the parallelism between these basic phonotactic units and the basic morphotactic units (i.e. syntactic phrases), a point to be developed below. Proceeding with a discussion of higher prosodic levels (the prosodic word and the prosodic phrase) we have seen that the idea of strict layering has been widely abandoned, being replaced by two types of recursive structures, unbalanced and balanced. Unbalanced recursion always appears to follow from adjunction, whereas balanced recursion results from conjunction. Thus neither type of prosodic recursion results from subjunction. At this point I return to the question why this should be so. Let us look back at the examples in (24). Why do we think of prosodic words that occur inside extended prosodic words as heads and of the added material as dependent? If prosodic structure tries to be isomorphic to morphotactic

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structure why aren’t su‰xes, for example, prosodically strong? After all, some su‰xes literally are prosodically strong in that they will receive primary accent or at least attract the accent in their direction. It would seem that the headedness of the extended prosodic word is actually irrelevant, at the very best. What matters is the formation of domains within which certain rules, for example accent rules, may apply. However, in many cases, in particular, languages with so-called lexical accent systems, there is reason to believe that the accentual properties of a‰xes predominate over the accentual properties of their base such that the accent of the last added a‰x that has a lexical accent predominates. Systems of this sort require a default statement which assigns an accent if no morpheme in the word brings in a lexical accent. In languages where only su‰xes may have accentual properties, the facts can be accounted for by saying that the primary accent lies on the rightmost accented morpheme or, if no lexical accent is present on the last or first syllable. A case in point is Russian which indeed has primary accent on the rightmost accented syllable and initial accent if there is no lexical accent. English works like this too, but here there is no default clause since, whereas su‰xes may be accented or unaccented (or even pre-accented), there are no accentless stems. If we would choose to capture the rightmost e¤ect in terms of headed prosodic structure we would then represent the su‰xes (as prosodic entities) as heads that take the prosodic unit forms by their base as a ‘complement’. This leads to an adaptation of the structure in (24) as in (41); in these structures headedness is indicated by vertical lines: (41) a.

b.

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For the su‰xes I have chosen a ‘categorial’ prosodic category ‘P\P’ which stands for ‘takes a prosodic word to form a prosodic word’).23 In other words, the relevant su‰xes are subcategorized for taking a prosodic word as their base and forming a prosodic word when attached. With a representation of this sort, in which a‰xes are prosodic heads, we provide a basis for the fact that their accentual properties, if present, prevail. What this ‘exercise’ demonstrates is that the recursion in the prosodic hierarchy does not have to be of the adjunctive kind (as in 24). In fact, we can get mileage out of displaying it in terms of subjunctive recursion. Finally, there is one other important issue that we need to address which specifically regards higher prosodic structure. We have seen that if prosodic structure wishes to be isomorphic to morphotactic structure, this structure will have to allow, especially unbalanced, recursion (as in 24 or 41). The evidence for this isomorphic prosodic structure comes from ‘rules’ (segmental rules and ‘stress’ or ‘accent’ rules). Then, there is other evidence, specifically involving rhythm which suggests that the prosodic structures appear to be ‘flatter’ and thus much less isomorphic. Now let us recall a point that was made in section 1 (following Wagner 2005), namely that evidence from rules which seem to respect recursive morphotactic structure do not automatically support the idea that there is a prosodic structure which is also recursive. Rules of this sort could simply make direct reference to the morphotactic structure which would make them irrelevant as evidence for any kind of prosodic structure, recursive or not. Here we need to bear in mind that the existence or need for prosodic structure that is isomorphic to morphotactic structure is hard to prove on principled grounds. Assuming that the morphotactic structure is independently needed, if phonological rules can simply be applied with reference to this structure, postulating additional isomorphic prosodic structure is uncalled for.24 The crucial evidence would have to come from cases where the alleged prosodic structure di¤ers (perhaps only minimally) from the morphotactic one. Indeed, much of the original motivation for 23. I actually explored a proposal of this sort in van der Hulst (1982). I here also refer to Wheeler (1981) who develops a categorial approach to phonology which captures this kind of isomorphism between morphotactic and phonological structure. 24. By thus increasing the isomorphy between the morphotactic structure and the phonotactic structure, as in (41), we make this case for a separate prosodic structure even weaker. We can state the generalization that the accentual properties of su‰xes prevail directly in terms of the morphotactic structure in which su‰xes are heads.

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prosodic structure took this form (cf. Nespor and Vogel 1986), although many of the case studies had or have been analyzed with rules that refer to syntactic structure (Kaisse 1985, 1990; Odden 1987). Now, we have also considered the fact that next to recursive prosodic structures which are isomorphic or perhaps near-isomorphic to morphotactics, there is evidence, specifically rhythmic evidence which suggest a di¤erent much flatter organization. Following earlier proposals (e.g. Giegerich 1985) I took it for granted that there are prosodic transformations which map unbalanced recursive structures that exceed degree 2 embedding by balanced recursive structures. In van der Hulst (2003, 2009) I suggest a perspective that allows a di¤erent view on the clash between recursive structures and rhythmic structures. The basic idea is that there are most likely two phonological hierarchies, one which is very close, if not identical to the morphotactic organization (and, as such, it is perhaps really the morphotactic representation) and another one which is driven by the distribution of (word and phrasal) accents (which have been assigned in the first mentioned ‘phonological’ hierarchy) and purely rhythmic. I will use the term phonotactic hierarchy for the first level and reserve the term prosodic hierarchy for the second level. The exact nature of the rhythmic prosodic organization is not fully clear. However, being rhythmically driven we expect unbalanced (adjunctive) recursion to accommodate ternary rhythms and otherwise balanced recursion. In this dual view, I would consider the structure of syllables and feet (as discussed in section 2) to be part of the first phonotactic hierarchy. In other words, phonotactics (understood as the syntax of segments; the so-called ‘second articulation’) forms one plane with the morphotactic hierarchy (the ‘first articulation’) which explains that both systems are structurally so much analogous, displaying the same kinds of subjunctive recursion (syllable inside syllable; phrases inside phrases). Whether at higher levels we need a phonotactic plane that is near isomorphic, but not identical to the morphotactic plane remains an open question, as we have just seen. The proposals of Itoˆ and Mester (2008) and Kabak and Revithiadou (2009) demand a very high degree of isomorphy and this suggests that, perhaps, we are really dealing with morphotactic structure here and that rules referring to higher levels are direct reference rules. With reference to the structures in (41), I further add that the phonotactic structure coinciding with the morphotactic structure may be even more isomorphic to is usually assumed. The prosodic plane, however, is fully independent from the morphotactic plane and belongs to ‘utterances’ rather than abstract linguistic expressions. It provides the context for fast-speech rules and the fine details of intonational con-

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tours or, more generally, for phonetic implementation (cf. Pierrehumbert 1980). The prosodic hierarchy ranges from the lowest units (segments, or even gestures) to the highest (utterances) and thus has units which are somewhat like the phonotactic syllables discussed in section 2, which I will call prosodic or phonetic syllables. Perhaps prosodic syllables are less structured, flatter (as in Kahn 1976), forming iterative rather than recursive patterns (cf. van der Hulst 2003). By invoking two phonological levels (the (phonoPmorpho)tactic level and the prosodic level) we can dispense with restructuring rules that ‘flatten’ unbalanced recursive structures that exceed degree-2 embedding. In phonetic interpretation, rhythmic beats respect primary word and phrasal accents that have been assigned at the (phonoPmorpho)tactic level, but they can ‘overwrite’ the potential impact of the more deeply embedded ‘cyclic’ accents which are inherent to the phonotactic hierarchy (cf. van der Hulst, in prep.). The resulting model is much in the spirit of Kaisse (1990), which admits two kinds of phonological rules. Firstly, there are ‘direct reference’ rules which operate in terms of the abstract grammatical tactic structure. Then, there are the prosodic rules operating in terms of prosodic domains which belong to actual utterances. In fact, Nespor and Vogel (1986) also admitted both levels, while the idea that all phrasal phonology is prosodic (‘indirect reference’) was promoted in Hayes (1990).25 The diagram in (42) captures the idea of there being two phonologies: (42)

25. Frota (to appear) provides an overview of ‘prosodic’ structure, making explicit reference to the fact that di¤erent hierarchies have been suggested, for di¤erent purposes. Whether, these di¤erent hierarchies can be reduced to one, as has usually been assumed, is, as she says, an empirical issue.

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So, while it is true that Martinet’s second articulation (‘phonology’) exists below the level of the first articulation (‘morphology and syntax’), the two being sequential, it is, at the same time true that there is a phonological organization that is fully parallel with the entire morphotactic structure (although I would say ‘with the entire tactic structure’). This view, as pointed out in van der Hulst (2003, 2009) resolves ‘structure paradoxes, especially with reference to lower levels of organization and provides a home to ‘phonological (i.e. phonotactic) syllables and feet and ‘phonetic’ (i.e. prosodic) syllables and feet. The exact nature of the prosodic hierarchy remains to be determined. It could be arboreal (tree-based), displaying ‘Abercrombian feet’ (see van der Hulst 2009 for discussion) or it could be purely grid-based, or both (as in Nespor 1990 who proposes two di¤erent planes as in Liberman and Prince 1977, or Halle and Vergnaud 1987 who use ‘bracketed grids’). If the prosodic hierarchy is not arboreal (as suggested in Prince 1984 and Neeleman and van der Koot 2006)26 it is perhaps less appropriate to speak of recursion since there would be no containment relations defined over nodes. It seems to me that the authors cited here who argue in favor of recursion at higher levels, at least in part, study phenomena that fall within the tactic realm rather than the prosodic realm. We have seen that at this level, phonotactic structure displays considerable recursion, firstly at the syllable/foot level and, secondly, at the word and phrase level. In the case of word or phrase level recursion it remains to be seen whether the recursive structure isn’t really the morphotactic structure. However, the syllable/foot level recursion, albeit limited, is inherent to the phonotactic structure. Whether the prosodic phonology also displays recursion should be seen as a separate issue, but if intonation domains belong to the prosodic hierarchy, as suggested in Rischel (1982) there are grounds for accepting that the prosodic hierarchy also displays (both unbalanced and balanced) recursion. This is also confirmed by the work of Ladd (1986, 1996), Hunyadi (this volume) and Fox (2000: 317–320) who all describe the inclusion of intonation domains within larger intonation domains.

26. Both proposals do not distinguish between the two phonologies (phonotactic and prosodic), however. Hence, I think that, Neeleman and van der Koot are not right in denying recursion to (phonotactic) syllable, but they may be right in their assessment of higher levels of organization provided that they are talking about the prosodic hierarchy.

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References Allen, Margaret 1978 Morphological investigations. PhD, university of Connecticut. Anderson, John M. 1986 Suprasegmental dependencies. In: Jacques Durand (ed.). Dependency and non-linear phonology, 55–133 London: Croom Helm. 1992 Linguistic representation: Structural analogy and stratification. Berlin and New York: Mouton de Gruyter. 1997 A notional theory of syntactic categories. Cambridge: Cambridge university Press. Anderson, John M. and Colin J. Ewen 1987 Principles of Dependency Phonology. Cambridge: Cambridge University Press. Beckman, Mary, and Janet Pierrehumbert 1986 Intonational structure in English and Japanese. Phonology Yearbook 3: 255–310. Blevins, J. 2003 The independent nature of phonotactic constraints: an alternative to syllable-based approaches. In: C. Fe´ry & R. van de Vijver, eds., The Syllable in Optimality Theory, 375–403. Cambridge: CUP. Booij, Geert 1996 Cliticization as prosodic integration: the case of Dutch. The Linguistic Review 13: 219–242. Chomsky, N. and M. Halle 1968 The sound pattern of English. New York: Harper and Row. Dresher, B.E. & A. Lahiri 1991 The Germanic foot: Metrical coherence in Old English. Linguistic Inquiry 22: 251–286. Elordieta, Gorka 2008 Segmental phonology and syntactic structure. In: Gillian Ramchand and Charles Reiss (2008). The Oxford Handbook of Linguistic Interfaces. Oxford: Oxford University Press, 125–177. Fitch, W. Tecumseh, Marc D. Hauser, and Noam Chomsky 2005 The evolution of the language faculty: Clarifications and implications. Cognition 97: 179–210. Frota, Sonia To app. Prosodic structure, constituents and their representations. In: Abigail Cohn, C. Fougeron and M. Hu¤man (eds.). Handbook of Laboratory Phonology. Oxford: Oxford University Press. Garcia-Bellido, Paloma 2005 The morphosyntax and syntax of phonology: The svarabhakti construction in Spanish, Estudios de Lingu¨´ıstica del Espan˜ol, Vol. 22.

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Giegerich, Heinz J. 1985 Metrical Phonology and Phonological Structure. Cambridge University Press, Cambridge. Gussenhoven, Carlos 1984 On the grammar and semantics of sentence accents. Dordrecht: Foris. Halle, M. and J.-R. Vergnaud 1987 An essay on stress. Cambridge, Mass.: MIT Press. Hauser, Marc D., Noam Chomsky, and W. Tecumseh Fitch 2002 The faculty of language: What is it, who has it, and how did it evolve? Science 298: 1569–1579. Hayes, Bruce 1986 A revised parametric metrical theory. NELS 17: 274–289. 1990 Precompiled phrasal phonology. In: Sharon Inkelas and Draga Zec (eds.). The Phonology-syntax connection. Chicago and London: The university of Chicago Press, 85–108. Helsloot, Karijn 1993 The prosodic word: an endless domain? Proceedings 17. Institute of Phonetic Sciences. University of Amsterdam, 129–146. 1995 Metrical prosody. A template-and-constraint approach to phonological phrasing in Italian. HIL disserations #16. Hulst, Harry van der 1982 Een lexicaal-prosodische analyse van klemtoon in het Nederlands [A lexical-prosodic analysis of Dutch stress. Presented at Linguistics in the Netherlands, Amsterdam, January 23rd, 2008. 2000 Issues in foot typology. In: M. Davenport and S.J. Hannahs (eds.). Issues in Phonological Structure, 95–127 Amsterdam: John Benjamins Publishing Company. 2003 Structure paradoxes in phonology. In: Stefan Ploch (ed.), Living on the edge. A festschrift for Jonathan Kaye, 75–94. Berlin: Mouton de Gruyter. 2005a The molecular structure of phonological segments. In: Headhood, elements, specification and contrastivity. P. Carr, J. Durand and C. Ewen (eds.), 193–234. Amsterdam: John Benjamins Publishing Company. 2005b Why phonology is the same. In: H. Broekhuis Norbert Corver, Riny Huybregts, Ursula Kleinhenz & J. Koster (eds.), The organization of grammar. Studies in Honor of Henk van Riemsdijk. Berlin/New York: Mouton de Gruyter, pp. 252–262. 2009 Two phonologies. In: Janet Grijzenhout and Baris Kabak (eds.), Phonological domains: universals and deviations, 315–352. Berlin: mouton de Gruyter. In prep Word accentual systems. Ms. University of Connecticut. To app. Dependency-based Phonologies. In: J. Goldsmith, A. Yu and J. Riggle (eds.). The Handbook of Phonological Theory. Second Edition. Oxford: Blackwell.

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Hulst, Harry van der and Nancy Ritter 1998 Kammu minor syllables in Head-driven Phonology. In: E. Cyran (ed.). Structure and interpretation. Studies in phonology. Lublin: Folium, 163–182. 1999 Theories of the syllable. In: Hulst, Harry van der & N. Ritter (eds.), The syllable: views & facts, 13–52. Berlin: Mouton de Gruyter. Hyman, Larry 1985 A theory of phonological weight. Dordrecht: Foris. Itoˆ, Junko and Armin Mester 2008 Prosodic adjunction in Japanese compounds. Formal approaches to Japanese Linguistics. Proceedings of FAJL 4. MIT Working Papers in Linguistics 55, 97–112. 2009 The extended prosodic word. In: Janet Grijzenhout and Baris Kabak (eds.), Phonological domains: universals and deviations, 105–194. Berlin: mouton de Gruyter. Jackendo¤, Ray and Steven Pinker 2005 The nature of the language faculty and its implications for evolution of language (Reply to Fitch, Hauser, and Chomsky). Cognition 97: 211–25. Kabak Baris and Anthi Reviathiadou 2009 An interface approach to prosodic and word recursion. In: Janet Grijzenhout and Baris Kabak (eds.), Phonological domains: universals and deviations, 105–134. Berlin: mouton de Gruyter. Kahn, Daniel 1976 Syllable based generalizations in English phonology. Doctoral dissertation, MIT. Published by Garland, New York. Kaisse, Ellen 1985 Connected speech. The interaction of syntax and phonology. Orlando: Academic Press. 1990 Toward a typology of post-lexical rules. In: Sharon Inkelas and Draga Zec (eds.), The phonology-syntax connection, 127–144. CSLI, Stanford University. Kaye, Jonathan 1992 Do you believe in magic?: The story of s þ C sequences. SOAS Working Papers in Linguistics and Phonetics 2: 293–313. [Also in: Henryk Kardela & Bogdan Szymanek (eds.). A Festschrift for Edmund Gussmann from his friends and colleagues, 155–176. Lublin: The Catholic University of Lublin Press. 1996.] Kaye, Jonathan, Jean Lowenstamm and Jean-Roger Vergnaud 1990 Constituent structure and government in phonology. Phonology Yearbook 7: 193–231. Kiparsky, Paul 1979 Metrical structure assignment is cyclic. Linguistic Inquiry 10, 421–441.

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Kuryłowicz, Jerzy 1952 Uwagi o polskich grupach spo´łgłoskowych. Biuletyn Polskiego Towarzystwa Je˛zykoznawczego 12: 221–232. Ladd, D. Robert 1986 Intonational Phrasing: The Case for Recursive Prosodic Structure. Phonology Yearbook 3: 311–340. 1996 Intonational Phonology. Cambridge: Cambridge University Press. [2nd edition 2008] Liberman, Mark, and Alan Prince 1977 On stress and Linguistic Rhythm. Linguistic Inquiry 8: 249–270. Lowenstamm, Jean 1996 CV as the only syllable type. In: Durand, J. & Laks, B. (eds.), Current trends in phonology: models and methods, vol. 2. Manchester: European Studies Research Institute. 419–442. Martinet, Andre´ 1960 Elements of general lininguistics. London: Faber and Faber Ltd. Neeleman, Ad, and Hans van der Koot 2006 On syntactic and phonological representations. Lingua 116/10, 1524–1552. Nespor, Marina 1990 On the separation of prosodic and rhythmic information. In: Sharon Inkelas and Draga Zec (eds.), The phonology-syntax connection, 243–258. CSLI, Stanford University. Nespor, Marina, and Irene Vogel 1986 Prosodic phonology. Foris Publications, Dordrecht. Odden, David 1987 Kimatuumbi phrasal phonology. Phonology 4: 13–26. Peperkamp, Sharon 1997 Prosodic words. LOT/HIL dissertation #34. The Hague: Holland Academic Graphics. Pierrehumbert, Janet 1980 The phonology and phonetics of English intonation. [Unpublished Ph.D. dissertation, MIT, Cambridge, Massachusetts.] Pinker, Steven and Ray Jackendo¤ 2005 The faculty of language: What’s special about it? Cognition 95: 201–236. Po¨chtrager, Markus Alexander 2006 The structure of length. PhD dissertation. Universita¨t Wien. Rischel, Jorgen 1982 On unit accentuation in Danish – and the distinction between deep and surface phonology. ARIPUC 16, 191–239. Scheer, Tobias 2004 A Lateral Theory of Phonology. What is CVCV, and why should it be? Berlin/New York: Mouton de Gruyter.

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Selkirk, Elisabeth 1978 On prosodic structure and its relation to syntactic structure. In: T. Fretheim (ed.), Nordic Prosody 2, 111–140. Trondheim: TAPIR. 1980 Prosodic domains in phonology: Sanskrit revisited. In: M. Arono¤ and M.-L. Keans (eds.), Juncture, 107–129. Saratoga, Ca.: Anma Libri. 1984 Phonology and Syntax. The Relation between Sound and Structure. MIT Press, Cambridge, Massachusetts. 1986 On derived domains in sentence phonology. Phonology Yearbook 3: 371–405. 1995 Sentence Prosody: Intonation, Stress, and Phrasing. In: John Goldsmith (ed.), The handbook of phonological theory, 550–569. Cambridge, MA and Oxford, UK: Blackwell. Schreuder, Maartje, Dicky Gilbers and Hugo Quene´ 2009 Recursion in phonology. Lingua 119/9: 1243–1252. Smith, N.S.H. 1999 A preliminary account of some aspects of Leurbost Gaelic Syllable structure. In H.van der Hulst & N. Ritter (eds), The syllable: views and facts, 557–630. Berlin: Mouton de Gruyter. Truckenbrodt, Hubert 2007 The syntax – phonology interfaced. In: Paul de Lacy (ed.). The Cambridge Handbook of Phonology, 435–456. Cambridge: Cambridge University Press. Viga´rio, Marina To appear Prosodic structure between the prosodic word and the phonological phrase: recursive nodes or an independent domain. Vijver, Ruben van den 1995 The Iambic issue. Iambs as a result of constraint interaction. HIL dissertation 37. The Hague: Holland Academic Graphics. Visch, E. 1999 The rhythmic organization of compounds and phrases. In H. van der Hulst (ed.). Word prosodic systems in the languages of Europe. Berlin and New York: Mouton de Gruyter, 161–232. Vogel, Irene 2009 The status of the clitic group. In: Janet Grijzenhout and Baris Kabak (eds.), Phonological domains: universals and deviations, 15–46. Berlin: mouton de Gruyter. Wagner, Michael 2005 Prosody and recursion. Ph.D. diss., Massachusetts Institute of Technology, Cambridge, MA. 2007a Prosodic Evidence for Recursion? Ms. Cornell University. 2007b Prosody and Recursion in Coordinate Structures and Beyond. Ms. Cornell University.

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18.

Cognitive grouping and recursion in prosody1

La´szlo´ Hunyadi 1. Introduction2 In their article on the faculty of language Hauser, Chomsky, and Fitch make a distinction between FLN (the faculty of language in its narrow sense) and FLB (the faculty of language in its broad sense) and hypothesize that FLN only includes recursion and is the only uniquely human component of the faculty of language (Hauser, Chomsky, and Fitch 2002, p. 1569). According to their hypothesis the core computational mechanisms of recursion in FLN appear in narrow syntax and the mappings to the interfaces and are uniquely human. In contrast, they suggest that much of the complexity of language derives from complexity in the peripheral components of FLB that have an ancient evolutionary history. These peripheral components of FLB include the sensory-motor system, a conceptual-intentional system and other possible systems. In their view, FLN, the abstract linguistic computational system is independent of the other systems with which it interacts and interfaces, but, being a component of FLB, its underlying mechanisms are some subset of those underlying FLB. It is this key component of FLN that generates internal representations and maps them into the sensory-motor interface by the phonological system, and into the conceptual-intentional interface by the formal semantic system. Apart from numerous arguments against this restricted understanding of FLN (that only recursion is special to language; cf. Pinker and Jackendo¤ 2005, Jackendo¤ and Pinker 2005), it is also arguable whether recursion is specific to narrow syntax alone. Phonology and morphology 1. This article was supported by OTKA grant No. 69042. An earlier version was presented at the conference Recursion in Human Languages in Normal, Ill., April 27–29, 2007. 2. I would like to express my thanks to the following people for their valuable comments and suggestions on previous versions of this paper or parts of it: Zolta´n Ba´nre´ti, Vale´ria Cse´pe, Ray Jackendo¤, Ilona Kassai, Andra´s Kerte´sz, Katalin E´. Kiss, and Shalom Lappin.

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are among the possible candidates to be also included in the faculty of language as specific to humans, but if any of them shows properties of recursion, the question arises how recursion found in them is related to syntactic recursion and whether their computational mechanism is specific to humans only. The question is important since the issues raised in Hauser, Chomsky, and Fitch 2002 are directly related to the evolutionary history of human language and any findings regarding recursion in other humanspecific areas of language may broaden and refine our understanding of the place of human language in the history of evolution. In this article it will be shown that a. prosody, as part of phonology shows properties of recursion and b. the mechanism behind prosodic recursion is related to a broader, non-linguistic cognitive capacity of abstract grouping. These findings have the potential to be seen as a challenge to the original hypothesis of Hauser, Chomsky, and Fitch 2002 regarding the structure and evolutionary status of the narrow language faculty.

2.

On the syntax-prosody interface

It is not the aim of this article to give a detailed overview of the large body of work on the issue of how syntactic structure is reflected in prosodic structure. For our purpose it will su‰ce to mention that in a syntax-based grammar (as has been the accepted approach in much of the generative tradition) syntactic relations are phonologically and semantically interpreted through interface relations and one would expect that a. this interpretation is as perfect as possible and b. the phonological and the semantic sides of this interface express but relations contained in the syntactic structure proper. That is, whereas in such a view syntax is autonomous, the phonological and semantic interfaces are not. Restricting ourselves just to the interface between syntax and phonology, however, it has long been observed that the two do not fully match. It was already shown in Chomsky and Halle 1968 that there is a mismatch between syntactic and phonological (prosodic) phrase boundaries; cf. (1) – the inserted vertical bars showing where phonological phrase boundaries occur: (1) [|This is [the dog |that chased [the cat |that killed [the rat |that ate [the malt |that lay in [the house that Jack built.|]]]]]] This mismatch is considered to be the result of attempting to match one kind of structure onto another – suggesting that rules governing structures on the two sides of the interface are not necessarily identical.

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Moreover, it has been found that – in addition to certain limitations of prosodic structure – the latter can, in turn, ‘‘repair’’ limitations of syntactic structure as well: as Price et al. 1991 showed, syntactical ambiguity (verb-preposition vs. verb-particle) is disambiguated by prosody via the di¤erentiating use of phrase final lengthening; cf. (2) vs. (3): (2) [The Vikings won] % [over their enemies.] % (3) [The Vikings won over] % [their enemies.] % It has also been shown that prosodic phrasing can disambiguate syntactic/ semantic ambiguities (e.g. scope ambiguities in Hungarian resolved by prosody; cf. Hunyadi 2002); cf. (4) and (5): (4) JA´NOS la´tott mindenkit. John-nom. saw everyone-acc. ‘It was John that, for every x, x ¼ person, John saw x.’ (5) JA´NOS la´tott MINDENKIT. John-nom. saw everyone-acc. ‘For every x, x ¼ person, it was John that saw x.’ In view of these and similar mismatches one may suggest that the structural/computational mechanisms behind syntax and prosody are not necessarily identical. In fact, it has been argued (cf. Nespor and Vogel 1982, Selkirk 1984) and widely accepted afterwards that mismatches like those demonstrated in (1) are accounted for by the fact that prosody is ‘flatter’ than syntax due to the lack of recursion in prosody. Namely, according to Selkirk’s Strict Layer Hypothesis (SLH), in a prosodic tree, any domain at a given level of hierarchy consists exclusively of domains at the next lower level of the hierarchy. As a consequence of SLH, then, a prosodic tree has a limited depth. As such, prosody is hierarchical but is not recursive. This view was partially challenged in Ladd 1986, 1992, 1996 by the introduction of the so-called Compound Prosodic Domain allowing for restricted recursion in cases like (6) and (7) and giving a structural account for perceived di¤erences in boundary strength in these structures: (6) [A and B [but C]] (7) [A [but B and C]] Here, a prosodic domain of a given type X has immediate constituents of the same type X, an evidence for a mechanism to generate an indeterminate depth of prosodic structure (even if only restricted to coordination).

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Another way to allow for certain, restricted cases of prosodic recursion was suggested by Selkirk 1995 and Peperkamp 1997, namely, that the constraint against recursion can be maintained by allowing some other constraints to force its violation and produce recursive structure. This position was also adopted by Truckenbrodt 1999 in his analysis of data from Kimatuumbi. Wagner, following Ladd’s proposal, has recently shown (Wagner 2005) that translating recursive syntactic phrase boundaries into recursive boundary length di¤erences (size of a pause) in the production of prosodic segmentation is perceptually valid and indicative of recursive structure. The observation, however, that the boundary length preceding and following an embedded syntactic phrase is perceived and calculated locally, i.e., relative to one another rather than across a complete syntactic hierarchy (cf. Clifton, Carlson, and Frazier 2002) suggests that there can be additional (prosodic) factors that influence the perception and evaluation of embedding. Such a view is further supported by Watson and Gibson 2004 showing that pauses do not always occur at intonational phrase boundaries and, in addition, syntactic structure does not determine the size of a pause, although it may a¤ect the probability of a boundary. In view of such observations and results we may rightly ask how and to what extent prosody with its limited symbolic inventory (lexicon) of just pitch, intensity and duration (pause) can contribute to the generation of prosodic structure. Since, as we have seen, there is no necessary direct relation between syntactic and pausal phrasing, we might want to turn our attention to prosodic phrasing brought about by variation of pitch and intensity, and, as a result, tonal phrasing and find out how tonal and pausal phrasing participate in their joint venture of representing prosodic (and syntactic) phrases. Finally, as it was shown by Ladd 1996 that prosodic structure is not as flat as predicted by Selkirk’s Strict Layer Hypothesis, we may want to test the generative power of prosodic recursion even beyond coordination. By presenting next the results of our experiments, we will suggest that tonal phrasing is mandatory for prosodic phrase formation and that its full generative capacity is based on recursion. 3. Properties of tonal phrase formation vs. recursion 3.1. Experiments In computational terms recursion is usually defined as a procedure that calls itself; structurally, as a result of recursion a constituent will contain another constituent of the same kind with the potential to generate

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unbouded sequences. Recursion is always hierarchical, although the existence of hierarchy does not by itself define a structure as recursive (cf. the understanding of the prosodic tree according to the SLH). Recursion always involves repetition of some operation(s), but it is clearly distinct from iteration, the latter being non-hierarchical. Recursion has several kinds (for a systematic typology of recursion see Parker 2006). Among them the most interesting for us will be instances of embedded (nested) recursion as contrasted to tail recursion. In the case of embedded recursion chunks of a phrase/sentence are embedded within a larger material, whereas cases of tail recursion are characterized by their phrase/sentenceinitial or sentence-final position. The latter bear some similarity to iteration but the two are not identical. The distinction between embedded and tail recursion is important for us beyond their descriptive di¤erence. From a computational/procedural point of view, embedded recursion involves access to memory (storage and retrieval): according to Liu and Stoller 1999 (cited in Parker 2006: 175), ‘‘[r]ecursion refers to computations where the execution of a function or procedure calls itself and proceeds in a stack fashion.’’ Iteration, on the other hand, has a di¤erent relation to memory: it is performed in looping,, i.e., involving keeping track of the times the same operation has been performed. We hypothesize that if the performing of prosodic recursion and iteration has any cognitive relevance, then there will be a meaningful di¤erence in the way (embedded) recursion and iteration access memory, and this di¤erence will be manifested in some prosodic features of the given utterances. In order to test this hypothesis, instances of utterances of sentences with embedded recursion as well as of sentences with iteration were recorded, analyzed and compared with special emphasis on their tonal and durational (pausal) realization. Below, we will present the results of experiments with recursion (3.2), discuss tonal continuity as the prosodic principle to denote recursion (3.3), show that this principle applies to discontinuous phrases in general (3.4) and, presenting the results of experiments with iteration, discuss how the procedural di¤erence between recursion and iteration is manifested in prosody (3.5). 3.2. The prosodic structure of utterances with central embedded (nested) recursion3 The fundamental units of the prosodic structure of an utterance have a strong tonal character. According to Beckman and Pierrehumbert 1986, 3. For all analyses, the program Praat v. 4.5.16 was used on an Apple PowerBook G4 computer.

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the edge of the intonation phrase is marked by a phrase tone and a boundary tone, whereas the intermediate phrase by a phrase tone only. Edges of phrase tone contours are, however, often associated also with pauses in a meaningful way: according to Cooper and Paccia-Cooper 1980, the duration of a pause following a tonal break may even reflect the given hierarchical syntactic boundary. It is also widely held that intonation phrase boundaries themselves can be determined on the basis of possible or obligatory pauses (cf. Selkirk 1984, Taglicht 1998, Downing 1970). Next, we will examine the role of phrasal tones and pauses in prosodic segmentation by asking which of the two (if any) has priority over the other in denoting prosodic phrase boundaries. First, we will look at the role of pauses and see how pauses match the structure of a Hungarian sentence (4): (8) A macska, amit a kutya, ami megveszett, megharapott, elszaladt. the cat that the dog that was rabid bit ran away ‘The cat that the dog that was rabid, bit, ran away.’ The above sentence is an example of embedded recursion. Interestingly, as for pausal phrasing, we found a significant di¤erence among the four speakers (the four numbers represent the pauses on the four syntactic phrase boundaries): Speaker 1: 0.065, 0, 0, 0.158 Speaker 2: 0.050, 0.187, 0.075, 0.075 Speaker 3: 0.164, 0.072, 0.046, 0.217 Speaker 4: 0.844, 0, 0, 0.125 As the data show, no unified way was found to represent all embedded syntactic boundaries by pauses. What they all agreed in was to represent by pause the major embedding only.4 Three out of the four speakers (Speaker 1, Speaker 2 and Speaker 3) agreed in indicating the boundaries of the major embedding (A macska . . . elszaladt ‘The cat . . . ran away’) so that the pause before embedding (i.e., following the phrase A macska) was shorter than the one before de-embedding (i.e., before elszaladt), whereas

4. This observation coincides with Truckenbrodt 2007, who, following Downing 1970 points out that root clauses (not embedded inside another clause), and only those, are bounded by obligatory intonation phrase brakes.

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an opposite temporal relation for the same embedding was measured for Speaker 4. For Speaker 2 and Speaker 3, those representing by pause the second level embedding as well, the latter was represented by a pause shorter than the first one. Speaker 1 and Speaker 4 did not appear to represent the inner embeddings by pause at all. Whereas pausal phrasing showed a quite varied picture, tonal phrasing proved to be highly systematic. It was found consistent with all speakers that a. each of the embeddings was performed at a lower pitch level (speaking range) than the phrase it was embedded into and b. the corresponding de-embedding was performed by an upstep, in fact, by a return to the very same pitch level (speaking range) before the given embedding. Lowering the speaking range of an embedding was consistent with the recursive application of embedding: the deeper the embedding in the syntactic hierarchy, the deeper speaking range for the given embedded phrase was chosen. This tonal representation of the recursive syntactic structure is shown in the next figures as follows: Figure 1 represents the pitch contour of the overall utterance of (8) by Speaker 1. Figure 2 represents (8a) where the pitch contour of the innermost embedding of the same recording (8) is removed, and Figure 3 represents (8b) with the pitch contour of both inner embeddings of the same recording (8) removed. It is noteworthy that, as suggested above, the removal of an embedding and the subsequent concatenation of the remaining halves of the utterance results in perceptually continuous tone at the point of concatenation, proving that whereas embedding is realized by the lowering of the speaking range of the overall embedded phrase, as a result of de-embedding the tone returns to the final pitch before embedding. Importantly, the return of the tone to the final pitch before embedding suggests that downdrift, the general tendency of the lowering of the pitch contour across an utterance does not apply. It is this e¤ect that, after the removal of the intervening material, results in the perception of the concatenation of the two remaining halves as a single prosodic phrase5 (in the figures to follow, an arrow indicates the place of concatenation after the removal of an embedded phrase): (8) A macska, amit a kutya, ami megveszett, megharapott, elszaladt. the cat that the dog that was rabid bit ran away ‘The cat that the dog that was rabid, bit, ran away.’ 5. The original recordings and the results of their manipulations can be found at https://ling.arts.unideb.hu/recursion.

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Figure 1

(8) a.

A macska, amit a kutya [. . .] megharapott, elszaladt. the cat that the dog [ . . . ] bit ran away ‘The cat that the dog [ . . . ] bit, ran away.’

Figure 2

(8) b.

A macska [. . .] elszaladt. the cat [ . . . ] ran away ‘The cat [ . . . ] ran away.’

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Figure 3

The English equivalent of the above utterance shows the e¤ect of a similar prosodic mechanism; cf. (9) and (9a)–(9b) and Figure 4, Figure 5 and Figure 6, respectively: (9) The cat that the dog that was rabid, bit, ran away.

Figure 4

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(9) a.

The cat that the dog [. . .] bit, ran away.

Figure 5

(9) b.

The cat [. . .] ran away.

Figure 6

The mechanism that produces the continuation of the tone of discontinuous chunks of an utterance will be called tonal continuity.

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3.3. Tonal continuity and the bookmark e¤ect Tonal continuity is a prosodic principle of long-distance dependency characterizing two discontinuous prosodic segments A and B as a single prosodic phrase [A. . .B]. It applies when a prosodic phrase C of the same type intervenes in [A. . .B], such as [ACB]. The discontinuous segments A and B of [A. . .B] have tonal properties identical to those of a sequence of A and B within a continuous prosodic phrase, [AB]. Tonal continuity has three important e¤ects: a. downdrift, the general tendency of the lowering of the pitch contour across an utterance does not apply to the intervening phrase C within [A. . .B]; b. phrase C is tonally realized in a di¤erent (usually lower) tonal space (the term used in the sense of Ladd 1992), i.e., at a lower overall speaking range), and c. deembedding takes the form of an upstep of B to the initial tonal space of A. Since tonal continuity can repeatedly apply to another prosodic phrase of the same type embedded within the embedded C itself with yet another similar e¤ect (the relative lowering of the tonal space at the point of embedding and an upstep at the point of de-embedding to the initial tonal space of the given embedding, thus creating a hierarchy of tonal spaces), its repeated application is recursive. As a consequence, the application of tonal continuity to prosodic phrases of the same type shows that prosodic phrases can be generated recursively. Consequently, the mechanism of generating prosodic structure is suggested to include recursion. We assume that there is a cognitively significant computational process underlying tonal continuity. Tonal continuity, i.e. the principle behind long-distance tonal dependency obviously overrides the principle of downdrift, the default tonal movement across an utterance so that instead of a continuous downdrift the tonal parameters of two discontinuous segments will match: in the above sequence [ABC] C is not downdrifted, instead, it matches A tonally as if they formed a single continuous phrase. We assume that this process heavily relies on memory: it involves storing the prosodic state before embedding (embedding C in our case) and restoring it after embedding. It serves as a sort of a memory aid which, therefore, we will call the bookmark e¤ect. Although tonal continuity is an important diagnostic characteristic of central embedding, it is not restricted to it: it is also the prosodic realization of any kind of insertion, as shown in the next section. 3.4. Tonal continuity in non-recursive discontinuous phrases The prosodic realization of insertion demonstrates that the principle of tonal continuity is not restricted to prosodic recursion: it equally applies

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to cases of insertion as well; cf. (10) and (11), examples from Hungarian and English (the corresponding F0-contours are shown in Figure 7 and Figure 8 for (10) and (10a), and Figure 9 and Figure 10 for (11) and (11a), respectively: (10) Meg tudna´d mondani, hogy – az e´n o´ra´m mega´llt – Vpref you-could tell that the my watch stopped ha´ny o´ra van? how many hour is ‘Could you tell me – my watch has stopped – what time it is?’

Figure 7

(10) a. Meg tudna´d mondani, hogy [. . .] ha´ny o´ra van? Vpref you-could tell that [ . . . ] how many hour is ‘Could you tell me [ . . . ] what time it is?’

Figure 8

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(11) Why don’t you – I said – go and find it?

Figure 9

(11) a.

Why don’t you [. . .] go and find it?

Figure 10

Both (10a) and (11a) clearly demonstrate the bookmark e¤ect: a continuous tone at the point of concatenation, similarly to what was previously

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found in the case of recursive structures. Since (10a) and (11a) are instances of insertion, we can conclude that tonal continuity is a prosodic principle applied to discontinuous prosodic phrases in general. Its function is to denote that two long-distance discontinuous prosodic chunks are structurally related forming a single phrase. Although insertion cannot be applied recursively, embedding can. As such, tonal continuity, applied to recursive embedding, results in the recursive lowering of the tonal space and the recursive application of upstep to the next higher tonal space. 3.5. Recursion vs. iteration As mentioned earlier, recursion always involves repetition of some operation(s), but it is clearly distinct from iteration, the latter being nonhierarchical. Since tonal continuity was found to be related to discontinuous structures, iteration being sequential we do not expect the bookmark e¤ect and, consequently, tonal continuity to apply to it. Recordings of iterative structures in Hungarian support such an expectation; cf. (12) and (13) (compare their respective F0-contours in Figures 11 and 12): (12) Ja´nos egy nagyszerű, jo´kedvű, jo´ humoru´ ember. John an excellent cheerful good-humored man ‘John is an excellent, cheerful, good-humored man’

Figure 11

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(13) Egy, kettő, ha´rom, ne´gy, o¨t, hat, he´t, nyolc. one two three four five six seven eight ‘One, two, three, four, five, six, seven, eight’

Figure 12

As we saw in 3.3, prosodic recursion involving central embedding follows the principle of tonal continuity, characterized by the lack of downdrift at the juncture of A and B inside the phrase [A. . .B], the presence of a change (usually lowering) of the tonal space for embedding, and the presence of upstep at the point of de-embedding to the original tonal space at B. Iteration, as shown in both (12) and (13), does not have any of these properties: first, there is a continuous downdrift across the whole utterance, second (as a consequence of the overall downdrift), there is no change of the tonal space, and third, the slight upstep observed at the beginning of each phonological word is not an upstep to the very same pitch level of a previous, discontinuous chunk of prosody but an upstep to the downdrifted initial pitch of each copy of the iterated prosodic segments (looking at it from a di¤erent angle, one can observe here the e¤ect of downstep, the stepwise lowering of pitch at specific pitch accents; cf. Pierrehumbert 1980).6 We can thus conclude that prosodic structures with central em6. Carefully observing the pitch contour of (13) we can note an upstep with continuation rise after ne´gy ‘four’. This upstep, however, not associated with a previous downstep is not the e¤ect of tonal continuity. Instead, it is the e¤ect of inherent grouping, a property of grouping in general, to be discussed in Section 4 below.

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bedded recursion and those with iteration are derived by di¤erent prosodic mechanisms: such recursive prosodic structures (and non-recursive discontinuous structures in general, as shown in 3.4) are derived by tonal continuity, whereas iterative structures follow downdrift. Tail recursion is similar to central embedded (nested) recursion in that it also involves embedding and generates a hierarchical structure. But in an important aspect it is di¤erent: its assumed computational mechanism does not need to store information on a stack in the way central embedding does, since there is no need to return to the pre-embedding state. As for its prosodic realization, then, we can expect that it does not display the bookmark e¤ect, i.e. it does not involve a change (lowering) of (and return to) the initial tonal space by a pair of a specific downstep and an upstep. Instead, we can expect the sequence of prosodic material to follow downdrift across the utterance. This is exactly what we find in (14), a case of tail recursion in Hungarian (see its corresponding F0-contour in Figure 13): (14) Ja´nos tala´lkozott Anna fe´rje bara´tja´nak John met Anna husband (poss) friend (poss) a la´nya´val a moziban. the daughter (poss) the cinema (in) ‘John met Anna’s husband’s friend’s daughter in the movie.’

Figure 13

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The observed downdrift at points of embedding takes exactly the same prosodic form as the one observed in iteration (cf. (12) and (13)) – thus giving a prosodic support for the assumption that iteration and tail recursion are not structurally distinguishable. 3.6. Recursion and pausal phrasing Although it seems to be su‰cient to di¤erentiate nested recursive and iterative prosodic structures on the basis of their tonal properties alone, there is still one more aspect of prosody, duration (pausal phrasing) that is worth considering. The di¤erence in their use of pausal phrasing is equally telling. We find that in nested prosodic recursion, pausal phrasing is structural (it follows hierarchical relations), whereas in iteration it is rhythmical. Accordingly, in recursive structures at least the major (first level) embedding is generally preceded and followed by a pause (the same for cases of single insertion) with some tendency for the pause before the embedding to be shorter than after de-embedding (in three out of our four cases; cf. Section 3.2). We found pausal segmentation at structural positions only, even though pauses were less articulate (if at all) at lower levels of the hierarchy. In contrast, an utterance containing iteration was found to be characterized by a eurhythmic organization of the sequence of iterated constituents denoted by the rhythmical distribution of pitch accents rather than the use of pauses (more on eurhythmics cf. Hayes 1984, see also Liberman and Prince 1977). A computational model of recursion, as mentioned earlier, involves access to memory: one has to store information on a stack and it has to be retrieved later on. In recursive speech prosody there are two kinds of information to be taken care of in memory (and to be shown in the bookmark e¤ect): structural (to keep track of the hierarchical position of the given constituent) and phonological (to keep track of the tonal position of discontinuous segments following the principle of tonal continuity).7 The storing and retrieving of both kinds of information need access to memory and, consequently, require processing time. One might want to suggest that pauses in recursive structures are then reflections of such a mental operation.

7. Our observations based on the role of tonal continuity both in instances of recursive and non-recursive long-distance dependences suggest that, contrary to Parker 2006: 185, a single center-embedding also has the memory requirement of keeping track in a stack fashion.

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However, the fact that pausal phrasing in speech utterances only occurs at some but not all structural positions indicates that access to memory is too short to be directly reflected by a pause. As such, the presence of a pause cannot then be the consequence of such a memory access, it is rather a formal means to express some structure. However, since pauses do not necessarily occur at all hierarchically significant positions whereas tonal phrasing is present in all utterances, we may conclude that pausal phrasing is, to some extent, secondary to tonal phrasing. If the above mentioned obvious prosodic di¤erence between nested recursion and iteration (pausal vs. rhythmic phrasing) cannot be justified on grounds of di¤erences in memory requirements, we have to suggest that pausal and rhythmic phrasing are actually two di¤erent formal means for the prosodic representation of two di¤erent types of structure, together with their di¤erences in tonal phrasing as well. The question remains whether these prosodic means of expressing structure are purely linguistic or have some more general, cognitive basis. The aim of the following two sections is to o¤er a possible answer to it. Surface di¤erences apart, all sentences agree that any syntactic structure is based on the grouping of words and phrases of a given sentence. The prosodic segmentation of a sentence is also based on a similar grouping. Similarly to the fact that the number of underlying types of syntactic phrases is finite (and limited), one may also assume that the infinite prosodic surface variation of utterances can also be generalized as instances of a finite (and limited) number of underlying prosodic phrases. It will be assumed that these abstract underlying prosodic phrase types represent the fundamental types of grouping in general (coordination and subordination) and that rules of generating complex prosodic phrases include but are not limited to recursion. In order to identify the underlying, abstract properties of prosodic grouping, we carried out two kinds of experiments: those involving the grouping of abstract prosodic patterns with no linguistic (syntactic or semantic) content and those involving the grouping of abstract visual patterns even with no prosodic content. With these experiment we expected to identify those abstract tonal and pausal (durational) means of grouping which are general enough to underlie grouping in speech prosody. Furthermore, we assumed that if the tonal and pausal properties of speech prosody will be found to share in common the basic corresponding properties of abstract prosodic/visual grouping, then we can make the conclusion that prosodic phrasing is based on more general principles of

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cognition rather than language alone. Below, we will examine the grouping of abstract prosodic patterns (in Section 4) and the grouping of abstract visual patterns (in Section 5) – the data and analyses referred to here are taken from a more extensive study on grouping; cf. Hunyadi 2006.

4. Grouping in abstract prosodic patterns A group of 23 university students were presented with a sequence of linearly arranged letters such as A, B, C, and D. They were instructed that in some patterns pairs of parentheses were used to denote various kinds of grouping. They were asked to observe the given patterns and then, following the pattern, read them out pronouncing the names of the letters. Each reading was recorded and its tonal and pausal phrasing analyzed. A strong consistency was found among subjects in the tonal representation of patterns; cf. (15) and (16): (15) A B C D a. rise rise rise fall (14) b. fall fall fall fall (6) c. rise fall rise fall (2) d. fall rise fall fall (1) The above pattern had a simple internal structure: the coordination of four abstract elements. Whereas the tone of D was determined by its pattern-final position to be a fall, A, B and C were also pronounced using the same rise or fall tone in 20 out of the 23 cases representing the equal structural status of the four elements. It was only in 3 cases that there was a tonal variation on B, suggesting a structural division between B and C. (16) (AB) (CD) a. fall rise fall fall (15) b. rise fall fall fall (5) c. high_level high_level low_level low_level (2) d. rise fall rise fall (1) The parentheses in this pattern suggest two groups: AB and CD, and this grouping is tonally represented by most (18) subjects applying a change in the direction of the tone or level of the pitch at the group boundary. Even

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in the remaining 5 cases (response type b.) there was a significant lowering of the tonal space following the first fall (i.e., after B).8 Tonal phrasing in (17) with a recursive pattern resulted in more variation: (17) A(B(CD))E a. rise rise fall rise fall (12) b. rise rise fall fall fall (6) c. rise fall fall fall fall (3) d. fall rise fall fall fall (2) In 12 of the cases tonal phrasing was used to represent embedded structure (with rise at a phrase boundary). The rise on B and the fall on C were initiated at an overall pitch level lower than the previous tonal space, corresponding to what was found earlier for recursive embedding in speech prosody as well. In 6 cases the main recursive embeddings between A and B, and between B and C were tonally represented in a similar way, but the de-embedding following D was tonally ‘‘missed’’. The last two groups of subjects used tonal phrasing less consistently for the denotation of this abstract recursive structure. If we look at pausal phrasing manifested in the above patterns, we find a strong consistency among all subjects in representing the given patterns by temporal structure (cf. Figure 14 for (15) and (16) and Figure 15 for (17):

Figure 14

Figure 15

The figures above demonstrate the expected pausal phrasing of (16): the segments (AB) and (CD) are both short and their values fairly close, 8. Ladd 1996 notes a similar tonal e¤ect at a major boundary: the initial peaks of a clause at a major boundary were higher than those at a minor boundary. See also H-tone insertion in Truckenbrodt 1999.

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whereas the pause between B and C is represented by a significant increase of segment length (in other words: boundary strength). Although we would expect equal durations for all segments in (15), there is still a slight increase of duration found between B and C (essentially due to the 3 subjects who also performed a tonal segmentation in (16). This is no mistake, however, but it indicates that grouping is, as a default, inherently present in our perception of structure in general. The pausal phrasing in (17) appears quite systematic: on one side of the embedding, the deeper the embedding the shorter the segment (boundary length), and on its other side, de-embedding is represented by a boundary longer than the corresponding embedding. Accordingly, embedding denoted by segment b between B and C is shorter than the embedding above it denoted by segment a between A and B, whereas segment c between C and D is the shortest with no embedding inside. Finally, the longest segment d represents the boundary between D and E, a boundary of deembedding corresponding to the highest embedding between A and B. The comparison of tonal and pausal phrasing in speech prosody and abstract prosodic grouping shows important similarities and certain di¤erences as well. They are similar in that, first, they agree in using both tonal and pausal phrasing to represent structural relations, and, second, and most importantly, they agree in applying recursion in structure generation. They di¤er in the extent they use tonal and pausal phrasing. Whereas in the case of abstract prosodic patterns pausal phrasing was highly consistent with all subjects, and tonal phrasing, however strongly present, had a secondary role, in speech prosody there was a reverse relation between the two kinds of phrasing: the use of tonal phrasing was systematic in all utterances, whereas pausal phrasing was, in some cases, less articulate. We will o¤er an account for this di¤erence after showing how grouping in abstract visual patterns is realized.

5. Grouping in abstract visual patterns A group of 50 university students were presented a set of patterns consisting of a series of dots like ‘‘ e ’’ arranged linearly. (For proper comparison, these dots were arranged in patterns essentially identical to those presented in the experiment on abstract prosodic grouping.) Subjects were instructed that in some patterns pairs of parentheses were used to denote various kinds of grouping. They were asked to observe the given patterns and then, following these patterns, represent them by mouse clicks. The

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onset time of each click was recorded on the computer and the resulted durations analyzed. A strong consistency was found among subjects in the durational representation of all patterns; cf. (18), (19) and (20) (below, Figure 16 shows the corresponding temporal segmentation of (18) and (19) and Figure 17 that of (20), respectively: (18)

eeee

(19) ( e e )( e e ) (20)

e ( e ( e e )) e

Figure 16

Figure 17

A comparison of the above data on pausal phrasing in abstract visual grouping with those in abstract prosodic grouping show important similarities and certain di¤erences as well. They agree in the systematic role of pausal phrasing and, most importantly, the use of recursion in the durational (pausal) representation of recursive structure. They di¤er in two aspects. First, pausal segmentation in visual grouping appeared to be more exact: the two short segments (boundaries) in (19) proved to be virtually identical in abstract visual grouping, more than in abstract prosodic grouping. Although we might find an explanation for it in the more precise nature of mouse clicks, it does not account for the second di¤erence: inherent grouping observed in (18), where no overt grouping was denoted in the visual pattern, was shown more articulate than in the case of abstract prosodic grouping. These two di¤erences may receive the following common explanation: if a modality has a single means of grouping (such as pausal phrasing in visual grouping), this means needs to be applied as closely as possible. However, if a modality has more than one means of grouping (such as tonal and pausal phrasing in abstract prosodic grouping), they can share their responsibility in denoting grouping. As a consequence, these means do not necessarily participate in denoting

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grouping equally. Our experiments allow us to suggest that a means more specific to the particular modality assumes a more prominent role in grouping. Accordingly, pausal phrasing, universal across the three modalities studied (speech prosody, abstract prosodic grouping and abstract visual grouping), is less specific to prosodic modalities since what makes the latter, prosodic modalities specific is their use of tones in phrasing. However, tonal phrasing was found to have more preference over pausal phrasing in speech prosody than in abstract prosodic grouping. (The specific role of tones in speech was also shown by Lickley 1994 who, examining disfluencies found that, in case pause was absent at the point of disfluency, both phoneme-level and tonal cues could still contribute to identifying disfluencies.) This finding can be related to the increased overall role of tones in speech: whereas in abstract prosodic grouping (where the use of tones is an added specificity as compared to the highly abstract nature of visual grouping) tones are only used to denote abstract grouping relations, tones in speech prosody, while preserving their role in denoting abstract grouping relations, also assume a language-specific role, that of expressing language-internal modalities. This increased specificity of tones in speech prosody is what gives tonal phrasing a stronger preference over less specific pausal phrasing than what we find in the case of abstract prosodic grouping.

6. Summary and conclusions: recursion in prosody and its cognitive status We have shown that the computational mechanism of recursion can be identified in prosody in two forms: in tonal and pausal phrasing. As for tonal phrasing, the principle behind nested recursive prosodic phrase generation is tonal continuity. Since tonal continuity involves a change (usually the lowering) of the tonal space of the embedded phrase, applied recursively it results in the recursive unidirectional change (continuous relative lowering) of the tonal space.9 It was shown that the computational di¤erence between nested recursion and iteration has its prosodic correlate. Namely, recursion is characterized by the lack of downdrift, whereas 9. It is useful to note that such a change of the tonal space for recursive embedding appears to correspond to key change modulation in recursive musical phrase formation observed in Hofstadter 1980. We may also note that a special case of key change in music is fifth tone change, an ancient way of modulation in pentatonic music, among others in Hungarian.

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iteration by the presence of downdrift. Upstep is also conditioned by different processes: it is a phonetic requirement for tonal continuity in recursion and a phonetic consequence of downdrift in iteration. It was also shown that the principle of tonal continuity is not restricted to prosodic recursion: it underlies any structure involving discontinuous prosodic phrases, including insertion and appears as the bookmark e¤ect. As for pausal phrasing, it was found to be structure-dependent and, as such, suitable for denoting hierarchical phrase boundaries in recursive embedding. It was also found that iteration, being non-hierarchical, does not make use of pausal phrasing, instead, it uses a rhythmic organization of the sequence of iterated constituents based on the rhythmic (metrical) distribution of pitch accents. It was also found that tail recursion that is computationally similar to iteration has the same prosodic realization as iteration: the principle of tonal continuity does not apply to it. The question that is of theoretical importance is whether recursion in prosody is the e¤ect of an interface-relation between syntax and prosody or has at least some other sources for its origin. Experiments involving grouping in abstract prosodic patterns as well as grouping in abstract visual patterns demonstrate the recursive use of tonal and pausal phrasing in a fashion similar to those found in speech prosody. Their di¤erences, especially regarding the relative preference of means of grouping across di¤erent modalities based on their modality-specificity suggest that grouping in prosody has its cognitive basis in the grouping of less specific, more abstract, nonlinguistic elements. That recursion in prosodic grouping is exactly the same mechanism as the one found in the grouping of less specific, more abstract, non-linguistic prosodic and visual elements suggests that recursion in prosody cannot be the e¤ect of an interface relation between syntax and prosody, instead, it is the manifestation of a more general, more universal computational mechanism found beyond linguistic structure. Suggestions of the similarity of tonal continuity (the recursive handling of tonal space) to a change of key modulation as well as pentatonic fifth tone modulation) in music point in this direction. In their reply to Pinker and Jackendo¤ 2005, Fitch, Hauser, and Chomsky 2005: 201 consider what consequences it would have on the theoretical and evolutionary status of the narrow faculty of language (FLN) if phonology were eventually found recursive. They ask the following questions: ‘‘is it [a recursive mechanism in phonology] the same as or different from that in phrasal syntax?’’, ‘‘is it a reflex of phrasal syntax perhaps modified by conditions imposed at the interface?’’ and ‘‘is phonological recursion the same as or di¤erent from that in musical phrases?’’.

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They conclude that ‘‘If the answer to all of these questions were ‘‘same’’, we would reject our hypothesis 3, possibly concluding that FLN is an empty subset of FLB, with only the integration of mechanisms being uniquely human.’’. Even though some of these questions cannot be answered within the confines of this article, based on the fact that recursion is identified in prosody and important properties of prosodic recursion are found in cognitive systems beyond language, the present article may have o¤ered further arguments for a possible answer in this direction.

References Beckman, Mary E., and Janet Pierrehumbert 1986 Intonational structure in English and Japanese. Phonology Yearbook 3: 255–310. Chomsky, Noam and Morris Halle 1968 The Sound Pattern of English. New York: Harper and Row. Clifton, Charles, Jr., Katy Carlson, and Lyn Frazier 2002 Informative prosodic boundaries. Language and Speech 45 (2): 87–114. Cooper, William and Jeanne Paccia-Cooper 1980 Syntax and Speech. Cambridge, MA: Harvard University Press. Hauser, Marc D., Noam Chomsky, and W. Tecumseh Fitch 2002 The faculty of language: What is it, who has it, and how did it evolve? Science 298: 1569–1579. Downing, Bruce T. 1970 Syntactic structure and phonological phrasing in English. Ph.D. diss., University of Texas Austin. Fitch, W. Tecumseh, Marc D. Hauser, and Noam Chomsky 2005 The evolution of the language faculty: Clarifications and implications. Cognition 97: 179–210. Hayes, Bruce 1984 The phonology of rhythm in English. Linguistic Inquiry 15: 3– 74. Hofstadter, Douglas R. 1980 Go¨del, Escher, Bach: An Eternal Golden Braid. London: Penguin. Hunyadi, La´szlo´ 2002 Hungarian Sentence Prosody and Universal Grammar. Frankfurt/ New York: Peter Lang. 2006 Grouping, the cognitive basis for recursion in language. Argumentum 2: 67–114. University of Debrecen.

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Jackendo¤, Ray and Steven Pinker 2005 The nature of the language faculty and its implications for evolution of language (Reply to Fitch, Hauser, and Chomsky). Cognition 97: 211–25. Ladd, D. Robert 1986 Intonational Phrasing: The Case for Recursive Prosodic Structure. Phonology Yearbook 3: 311–340. Ladd, D. Robert 1992 An introduction to intonational phonology. In: Gerard J. Docherty and D. Robert Ladd (eds.), Papers in Laboratory Phonology. Vol. II: Gesture, segment, prosody, 321–334. Cambridge: Cambridge University Press. Ladd, D. Robert 1996 Intonational Phonology. Cambridge: Cambridge University Press. Liberman, Mark and Alan Prince 1977 On stress and linguistic rhythm. Linguistic Inquiry 8: 249–336. Lickley, Robin, J. 1994 Detecting Disfluencies in Spontaneous Speech. Ph.D. Dissertation, University of Edinburgh. Liu, Y. Annie and Scott D. Stoller 1999 From recursion to iteration: What are the optimizations? ACM Sigplan Notices 34: 73–82. Nespor, Marina and Irene Vogel 1982 Prosodic domains of external sandhi rules. In: Harry van der Hulst and Norval Smith (eds.), The structure of phonological representations, Vol. I, 225–255. Dordrecht: Foris. Parker, Anna R. 2006 Evolution as a Constraint on Theories of Syntax: The Case against Minimalism. Ph.D. Dissertation, University of Edinburgh. Peperkamp, Sharon 1997 Prosodic words. HIL Dissertations 34. The Hague: Holland Academic Graphics. Pinker, Steven and Ray Jackendo¤ 2005 The faculty of language: What’s special about it? Cognition 95: 201–236. Pierrehumbert, Janet 1980 The phonology and phonetics of English intonation. Ph.D. thesis, MIT, published 1988 by Indiana University Linguistics Club. Price, P.J., M. Ostendorf, S. Shattuck-Hufnagel, and C. Fong 1991 The use of prosody in syntactic disambiguation. Journal of the Acoustical Society of America 90: 2956–2970. Selkirk, Elisabeth 1984 Phonology and Syntax: the relation between sound and structure. Cambridge, MA: MIT Press.

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Selkirk, Elisabeth 1995 The prosodic structure of function words. In: Jill Beckman, Laura Welsh Dickey, and Suzanne Urbanczyk. (eds.), Papers in Optimality Theory, University of Massachusetts Occasional Papers 18, 439–469. Amherst, MA: Graduate Linguistic Student Association. Taglicht, Joseph 1998 Constraints on intonational phrasing in English. Journal of Linguistics 34: 181–211. Truckenbrodt, Hubert 1999 On the relation between syntactic phrases and phonological phrases. Linguistic Inquiry 30: 219–255. Truckenbrodt, Hubert 2007 The syntax-phonology interface. In: Paul de Lacy (ed.), The Cambridge Handbook of Phonology, 435–456. Cambridge: Cambridge University Press. Wagner, Michael 2005 Prosody and recursion. Ph.D. diss., Massachusetts Institute of Technology, Cambridge, MA. Watson, Duane and Edward Gibson 2004 The relationship between intonational phrasing and syntactic structure in language production. Language and Cognitive Processes, 2004, 19 (6): 713–755.

19.

Becoming recursive: Toward a computational neuroscience account of recursion in language and thought

Simon D. Levy 1. Introduction First you curse . . . and then you recurse. – Harry Mairson, ‘‘In Praise of the Research University’’

After remaining more or less in the background for several decades, the issue of recursion in human languages has returned to the fore. The current, vigorous debate is about not just recursion, but the very idea of linguistic universals as a coherent scientific notion, and the nature of language itself. The prevailing view is that recursion – the ability to produce an unbounded number of well-formed sentences through the combinatorial operations of syntax – is a fundamental property of the ‘‘faculty of language in the narrow sense’’ (FLN), i.e., that recursion is what di¤erentiates human language from other forms of animal communication (Hauser, Chomsky, and Fitch 2002). As an explicit challenge this view, Everett (2005) has documented the syntax of Piraha˜, a language that appears to have no embedded clauses, recursive possessives, or other syntactic structures suggesting this capacity. Everett o¤ers Piraha˜ as a fatal counter-example to the universality of recursion, and questions the utility of searching for other sorts of linguistic universals as well. Although this debate has involved linguistics, and sometimes politics, we suggest that it might also be fruitfully informed by neuroscience. In particular, we will present a model of event semantics based on neurally plausible role/filler bindings, and describe how recursion, like other syntactic processes, can be viewed as the by-product of ‘‘unpacking’’ and serializing the contents of these representations. A rough outline of our argument: we start by enumerating some basic assumptions or ground rules about what any model of human language and cognition should look like. We then provide a review of simple vector arithmetic for the benefit of readers unfamiliar with this branch of mathematics, and we

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show how high-dimensional vectors can be used as a plausible model of role/filler semantics and other mental representations without violating any of our stated assumptions. Next we sketch the rudiments of a model of language that treats grammar as a process of transduction between these mental representations and sequences of symbols. We present a brief account of how this language model can be related to traditional syntactic categories like agent and theme, and conclude by setting the model in the context of current research on the sources of linguistic universals.

2.

Basic assumptions

We believe that any theory of language or other mental activity must be constrained by a basic set of ground rules. Some of these rules come from general scientific principles, others from concerns specific to cognitive linguistic modeling. The most basic principle is Occam’s Razor: entities should not be multiplied without necessity. In more modern terms, a model with N components that explains a phenomenon adequately should be favored over one with N þ k components, for positive integers N and k. We are thinking here of the fact (noted by others in this volume) that although recursive grammars can generate infinitely long sentences and sentences with unbounded recursive embedding, ordinary spoken language consists of short sentences with little or no recursion. A standard account of this somewhat embarrassing fact posits an infinite ‘‘competence’’ grammar constrained by a ‘‘performance’’ component such as short-term or working memory (Chomsky 1965). Perhaps because of the popularity of the concept of short-term memory in psychology as a whole, this two-component model has become the standard justification for recursive grammars, despite the strange empirical predictions they make. Though we do not wish to dispute the usefulness of concepts like short-term memory as high-level descriptions, we would argue for the advantages of a model in which the limitations on embedding and related operations arise from the same component or substrate that supports these operations. Second, we take it as a given that all human beings think recursively, i.e., that they can and often do have thoughts about the thoughts or mental states of others. Further, we note that many human languages express these thoughts recursively (I think that you think that you’re smarter than me.) As the title of our article suggests, we therefore take it as an important challenge to our research program to account for how

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languages might come to represent recursive thoughts in recursive symbol sequences. Our third basic assumption is that the task of grammar or any grammar-like model is to provide a mapping between structured meanings and sequences of symbols. By structure we mean the whole apparatus of semantic roles and fillers, variable binding, and unification that has been used by linguists and cognitive scientists to represent ‘‘who did what to whom’’ event semantics, logical propositions, and the like. Though it may not seem controversial, this assumption bears mentioning here. There is a long-standing generative tradition, echoed in recent connectionist modeling, that views languages as sets of strings and the task of a grammar for a language as generating all and only the strings belonging to the set. Such a model need take no account of the (propositional) meanings conveyed by these strings. Following a suggestion by Pullum and Scholz (this volume), we choose instead to model grammars as transducers between form and meaning. The constraints that our model places on recursion and other processes will fall out as the consequence of the limitations that our representations impose on the transduction process. The issue of representation brings us to our final assumption: the primitives of our model, and the operations supported by these primitives, should be biologically plausible. More strongly: in the words of Kanerva (2008), we ask what kinds of things suggested by the architecture of the brain, if we modeled them mathematically, could give some properties that we associate with mind ? By architecture we take Kanerva to refer not to specific anatomical structures, but instead to general properties of how the brain seems to represent conceptual information. Among such properties we would include content-addressability, robustness / graceful degradation in the presence of noise, and low-precision encoding distributed over a large number computing elements with a high degree of interconnection. These properties are notably absent in the representations employed in traditional symbol-manipulating systems like generative grammars and symbolic programming languages (LISP, Prolog), and in the ubiquitous symbol-manipulating devices called digital computers. First, manipulation of representations in such systems requires ‘‘chasing down pointers’’ to get at content (e.g., tracing from the root of a tree structure to its leaf nodes). Second, because representations in a computer memory are stored locally at specific addresses, small changes to the representation can cause performance to degrade catastrophically. For example, changing the value of a single bit of the representation can produce a ‘‘dangling pointer’’, causing arbitrarily large amounts of structure to become inacces-

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sible. Third, implementing theoretically unbounded recursion in a finite, discrete device makes recursion work perfectly up to some arbitrary, fixed memory limit, after which it fails completely (stack overflow). In the next section we describe a representational scheme that exhibits the desired architectural properties.

3. Vector-based architectures for symbol manipulation Insofar as linguists know about connectionist/distributed models of language, they typically are aware of the work of Rumelhart and McClelland (1986) on learning the past tense of English verbs, and the work of Elman (1990) on learning structure via sequence prediction. Though we share with these ‘‘connectionists’’ an appreciation of the appeal of distributed representations, we note that (1) neither model addresses the encoding and transduction of propositional meaning that concerns us here; (2) both models rely on the back-propagation algorithm (Rumelhart, Hinton, and Williams 1986), which is generally considered biologically and psychologically implausible (Crick 1989); and (3) as stated above, we consider symbol manipulation essential to cognition. We therefore agree with Holyoak and Hummel (2000), Marcus (1998), and others that the ‘‘eliminative connectionism’’ of Rumelhart and McClelland, Elman, et al. cannot account for the phenomena that interest us here. In the remainder of this section we present recent work in connectionism that we feel holds significant promise for providing such an account. Because this work builds on vector arithmetic, we start with a very brief overview of that topic. Readers familiar with vector arithmetic may want to skip to section 3.2. 3.1. Review of vector arithmetic For our purposes here, a vector can be defined as an ordered list of items or elements. The number of items in the vector is called the vector’s dimensionality. Anyone who has taken high-school trigonometry will be familiar with the two-dimensional vectors of numbers that make up the Cartesian plane. Such vectors can be visualized either as points, or as line segments with an arrow on the end. Visualizing the vectors as points helps us to see the relationships (e.g., clustering) among a large number of vectors. Visualizing the vectors as line segments helps us to compare the directions represented by a small number of vectors, using a familiar trigonometric

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Figure 1. Two-dimensional vectors: (a) represented as points and (b) as line segments. (c) A pair of mutually orthogonal vectors.

function like cosine. Figure 1 shows these two di¤erent methods of visualization. If the cosine between two vectors is zero (i.e. they are at a right angle to each other), the vectors are said to be mutually orthogonal. Mutual orthogonality is very useful property: if we are using vectors to represent symbols, then mutually orthogonal vectors help to keep the symbols for di¤erent concepts distinct. Conversely, two similar concepts can be represented by vectors with a higher cosine (degree of similarity), as in the method of Latent Semantic Analysis (Foltz and Laham 1998). 3.2. Computing with high-dimensional, low-precision vectors Although two- and three-dimensional vectors are easily visualized, they make a poor choice for representing large numbers of symbols: to distinguish among a large number of vectors we need a high degree of numerical precision, and there are, for example, only four mutually orthogonal directions for vectors in two-dimensional space. As discussed earlier, high-precision representations are biologically unrealistic and non-robust in the presence of noise. For this reason, we use high-dimensional vectors, typically 10,000 dimensions or more, with a very low numerical precision for each element. The lowest precision possible (one bit of precision, in information-theoretic terms) distinguishes between only two values. If the choice of value is made randomly for each element (‘‘flipping a coin’’), we can obtain very large numbers of mutually orthogonal vectors that are highly robust to noise. A surprisingly large number of the elements in a given vector can be arbitrarily changed before the vector becomes more similar to another vector than to its original form (Kanerva to appear).

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Single-bit precision is most often associated with the numerical values 0 and 1. For the purposes of symbol manipulation, however, the values 1 and þ1 give the vectors a useful property: every vector is its own multiplicative inverse; i.e., multiplying a vector by itself elementwise produces a vector of all 1’s. This allows multiplication to act as a very fast form of associative memory. If we wish to associate two vectors A and B, we simply take their elementwise product, which we represent as A d B. The item associated with A can then be retrieved by multiplying this association vector by A; that is, A d B d A ¼ B. In a similar manner, multiplying by B retrieves A. This very general method of association can be used to bind semantic roles to their fillers, to associate a concept with the word representing it, etc. To represent several pairs of associations, we can simply add them together elementwise; e.g., the sum A d B þ C d D þ E d F represents simultaneously the association of A with B, C with D, and E with F. Summing vectors in this way produces values other than 1 and þ1, but as the cosine function is not sensitive to magnitude, such values do not a¤ect the basic operation of association. (To maintain realistically low precision, we can also normalize the sum to a small number of fixed values in the interval [1, þ1].) As with ordinary algebra, multiplication has precedence over and distributes over addition, and both operations are commutative and associative: for three vectors A, B, and C of the same dimensionality, A d B ¼ B d A, A þ B ¼ B þ A, (A d B) d C ¼ A d (B d C), (A þ B) þ C ¼ A þ (B þ C), and A d (B þ C) ¼ A d B þ A d C. These properties make such representations easy to work with. 3.3 Cleanup memory Summation does however introduce noise into the representation. Consider, for example, the result of retrieving the value associated with A from the summation A d B þ C d D þ E d F: (1)

A d (A d B þ C d D þ E d F) ¼ B þ A d C d D þ A d E d F

This operation correctly retrieves the value B, but also retrieves the undesired associations A d C d D and A d E d F. These bogus associations can be removed from the retrieved vector by passing it through a ‘‘cleanup memory’’ that stores only the meaningful vectors (A, B, C, D, E, F). Cleanup memory can be implemented in a biologically plausible way as a Hopfield network (Hopfield 1982) that maps each meaningful

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vector to itself, a variant of Hebbian learning (Hebb 1949). Such networks can reconstruct the original form of a vector or image from a highly degraded exemplar, via self-reinforcing feedback dynamics. How the meaningful vectors come to be in the memory is a topic of current research. A cleanup memory enables other interesting operation as well; for example, the crucial operation of variable substitution used in the unification algorithm. Unlike classical unification, however, this vector-based substitution supports simultaneous substitution of an arbitrary number of new values. Consider for example a vector representing the association of the element X with A and Y with B. Say we wish to substitute P for A and Q for B. We can do this by multiplying our original vector by a vector that encodes the substitutions as pairwise representations: (2)

(X d A þ Y d B) d (P d A þ Q d B) ¼ XdAdPdA þ XdAdQdB þ YdBdPdA þ YdBdQdB ¼ XdP þ XdAdQdB þ YdBdPdA þ YdQ ¼ X d P þ Y d Q þ noise

where noise is material that is not in the cleanup memory and hence will be removed by it. Crucially, none of the operations (association, summing, cleanup) changes the dimensionality of the vectors, unlike earlier forms of vectorbased associative memory (e.g. Smolensky 1990). Such fixed-size representations also have a higher degree of biological plausibility than classical symbolic (tree, graph) representations, where the storage required increases with the amount of information being represented. It is even possible to implement such high-dimensional vector representations as spiking neurons (Eliasmith 2004). Just as important, however, is the fact that everything (symbols, associations, sets of associations) is represented by objects (vectors) of the same size. This uniformity of representation leads to an extraordinary flexibility in the behavior of systems built this way: combinations can act as entities in their own right, symbols can serve as both variables and constants, fillers can act as roles, etc. This behavior opens up possibilities for exploring issues like analogy, metaphor, and learning, as well as grammaticalization and other forms of language change, in a novel way (well beyond the scope of the present article). 3.4. Embedding More to the point of the volume in which this article appears, the uniform representation of conceptual entities opens the door to embedding linguis-

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tic and conceptual entities inside similar entities, i.e., to recursion. We start with simple embedding. Suppose that instead of associating one symbol with another, we wish to associate a symbol with an entire set of associations – as for example, the predicate believe embeds an entire proposition. This can be done by introducing a symbol representing the embedded set. Consider, for example a vector containing: (3) A d B þ C d D þ E d (P d Q þ R d S þ T d V) where E is a symbol used to embed the association of P with Q, R with I, and T with V. From this vector we can retrieve the item associated with A by multiplying the vector by A, giving us B plus noise. The same goes for retrieving the items associated with B, C, and D. If however we try to retrieve the item associated with P by multiplying the vector by P, we get back nothing but noise, because no part of the resulting product reduces to a single symbol: (4)

P d (A d B þ C d D þ E d (P d Q þ R d S þ T d V)) ¼ PdAdB þ PdCdD þ PdEdPdQ þ PdEdRdS þ PdEdTdV ¼ PdAdB þ PdCdD þ EdQ þ PdEdRdS þ PdEdTdV ¼ noise

We can think of this situation as analogous to infelicity of an exchange in which someone is told John wonders whether Bill likes Mary and responds by asking WHO does Bill like? If we wish to retrieve the item associated with P, we must instead multiply by EdP; in other words, by the embedded representation of P: EdPd(AdB þ CdD þ Ed(PdQ þ RdS þ TdV)) ¼ EdPdAdB þ EdPdCdD þ EdPdEdPdQ þ EdPdEd RdS þ EdPdEdTdV ¼ EdPdAdB þ EdPdCdD þ Q þ EdPdEdRdS þ EdPdEdTdV ¼ Q þ noise

(5)

3.5. Recursion and permutation With a model of embedding in place, we can turn our attention what happens when a symbol embeds itself; i.e., recursive embedding. As a simple example, consider the vector (6) Ed(A þ Ed(B þ C)) Careful readers may already have anticipated the problem that arises here: the symbol E cancels itself out, losing the inner embedding of B and C:

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Ed(A þ Ed(B þ C)) ¼ Ed(A þ EdB þ EdC) ¼ EdA þ EdEdB þ EdEdC ¼ EdA þ B þ C

One way of overcoming this problem is to apply a permutation (re-ordering) operator to the vector representation of an embedding before adding it to the vector representing the non-embedded material (Gayler 1998). A permutation is just a re-ordering of the elements of the vector; hence, like the other operators, permutation does not change the dimensionality of the vector. Typically, a random re-ordering is used, though systematic orderings like left- or right-shift work equally well. Functionally, permutation as like a quoting or bracketing operation that insulates the embedded material from the e¤ects of self-cancellation. We can use the Greek letter P to represent permutation; hence, the self-embedding expression above could be represented as Ed(A þ P (Ed(B þ C))). For greater depth of embedding, more permutations can be used: (8) Ed(A þ P1 (Ed(B þ C þ P2 (Ed(D))))) where the subscript on P indexes a di¤erent permutation (and hence the depth of embedding). The permuted material can be made available for retrieval by applying the inverse permutation appropriate to that stage of retrieval. A few points about this permutation-based recursive encoding are worth noting. First, despite the functional similarity that permutation and its inverse bear to pushing and popping operations in a traditional stack automaton, in no sense is the representation of the embedded structure ‘‘contained’’ inside or below the representations of the higher-level material. All representations are spread across an entire, single vector. Second, permutation distributes over addition and multiplication, and (with the degenerate exception of the identity permutation) the composition of a permutation with itself is another permutation di¤erent from the original. Hence, a single permutation su‰ces to encode arbitrarily many levels of recursion; for example: (9)

P (A þ (P (B þ P (C)))) ¼ P (A) þ P (P (B)) þ P (P(P (C))) ¼ P (A) þ PoP (B) þ PoPoP (C) ¼ P1 (A) þ P2 (B) þ P3 (C)

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Figure 2. Hypothetical neural circuit for recursive embedding. See text for explanation.

where o stands for operator composition, and Pi (X ) is the ith permutation of vector X. Finally, although permutation may seem like an ad-hoc solution to a technical problem, it has a good deal of neural plausibility. In a biological neural network, each neuron typically computes the sum (integral) over the input from many others (Dayho¤ 1990). Hence, it is reasonable to model the mapping between two layers of neurons (each corresponding roughly to a hyperdimensional vector) as a sum of permutations from the first layer to the second. Recursive structure can then be built from the bottom up, using a feedback circuit like the one shown in Figure 2. This circuit accepts three vectors as inputs, computes the sum of the second two, multiplies this sum by the first (embedding) vector, permutes the resultant product, and passes the permuted vector back as the third input on the next pass. It can be used to encode right-branching recursive structures like the ones above. 3.6. Representing sequences Thus far we have shown how sets of symbolic associations, including recursively structured sets, can be encoded using the vector operations multiply, add, and permute. What if we wanted to encode not just sets, but ordered sets; i.e., sequences, such as the sequences of words in a sentence? Vector addition by itself is insu‰cient owing to its commutativity: (A þ B þ C) is the same as (A þ C þ B), (B þ C þ A), etc. Following Plate (2003), we can use a positional or ‘‘trajectory’’ encoding for sequences in which the position of each element is represented as a position vector mul-

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Figure 3. Hypothetical neural circuit for decoding sequences. See text for explanation.

tiplied by that element. The sequence A, B, C can be encoded P1 dA þ P2 dB þ P3 dC, and in general, for an arbitrary vector Pi , the product Pi d X can be used to represent the element (symbol, association, set of associations, etc.) X being in the ith position in a sequence. An actual temporal sequence can be generated from such an encoding by multiplying it by the successive Pi, running the result through the cleanup memory, and outputting the cleaned-up result. If the product of Pi and the cleaned-up output is subtracted from the sequence vector on each such iteration, the values in the vector will eventually reach zero, allowing the process to halt. In this way the vector can be considered an abstract ‘‘motor program’’ for producing the sequence. A hypothetical neural feedback circuit implementing this algorithm is shown in Figure 3.

4. Language transduction with the multiply-add-permute architecture Having outlined our multiply-add-permute framework for symbol association, embedding, and sequencing, we can start applying it toward building a transduction model for language. Our general approach will be to model associations between propositional content and symbol sequences as multiplicative bindings. The simplest associations are between individuals and their names: johndJohn, marydMary, etc., where john and mary are vectors representing those persons and John and Mary are vectors representing their names. The next step is to build associations

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between propositions concerning such individuals and the sequences of symbols used to convey those propositions in sentences; for example: (10) (actiondkiss þ agentdmary þ patientdjohn)d (P1 dMary þ P2 dkissed þ P3 dJohn) The first half of this association is a purely conceptual, nonlinguistic vector representation of an event or logical proposition. Other researchers (Eliasmith and Thagard 2001) have used just this sort of representation to model analogical reasoning, independent of language. To produce a sentence representing this event, we multiply this vector by the association vector, yielding the vector (P1 dMary þ P2 dkissed þ P3 dJohn) by selfcancellation. Passing this vector through the circuit in Figure 3 produces the sequence Mary kissed John. The knowledge that speakers have of their language can be represented as the set of such associations stored as a content-addressable memory containing the sum of the associations, along with a cleanup memory. Of course, mappings of this form, specific to a single predicate and set of arguments, ignore the sorts of generalizations that we expect any model of grammatical knowledge to represent. Instead of idiosyncratic mappings like this one, we would like the model to contain more general ones in which the predicates and arguments are abstracted as variables. Even better would be a model capable of acquiring the general mappings based on exposure to specific instances. Our model’s ability to meet these challenges derives from a crucial feature of the multiply-add-permute vector framework that we alluded to earlier: because all entities are vectors of a fixed size, there is no underlying distinction between constants and variables. As we saw in the examples above, the association/substitution mechanism behaves as if there were variables, but these are merely a notational convenience that we use to characterize the mechanism’s behavior. As noted by Kanerva (to appear) this fact leads to a very powerful ability to acquire a general pattern quickly from even a single instance. The example below illustrates this principle, showing how the correct generalization be derived from exposure to a single mapping involving John and Mary (and the relevant individual concept/word associations), via the multiplicative association operator and self-cancellation. (In this and subsequent examples we assume an implicit noise term, which we leave out to avoid clutter. We also make liberal use of ad-hoc semantic roles and categories for the sake of illustration. We have no commitment to any particular view of semantic roles, an issue orthogonal to our interests here).

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(actiondkiss þ agentdmary þ patientdjohn)d (kissdkissed þ johndJohn þ marydMary)d (P1 dMary þ P2 dkissed þ P3 dJohn) ¼ (actiondkissed þ agentdMary þ patientdJohn)d (P1 dMary þ P2 dkissed þ P3 dJohn) ¼ P1 dagent þ P2 daction þ P3 dpatient

This construction can then be used to generate the appropriate symbol sequences for other propositions: (12)

(P1 dagent þ P2 daction þ P3 dpatient)d (insultdinsults þ freddFred þ billdBill )d (actiondinsult þ agentdfred þ patientdbill) ¼ P1 dFred þ P2 dinsults þ P3 dBill

Before moving on to syntactic recursion, we would like to highlight a few points about this model. First, what appears as multi-step algebraic derivations in these examples is just another notational convenience. In an actual implementation the entire set of substitutions takes place at once, using elementwise vector multiplication and addition followed by cleanup. Second, the position vectors could equally well represent other sorts of linguistic encoding than sequencing, such as inflectional endings in a language with freer word order than English. Third, the model is by no means restricted to stereotypical transitive constructions. The contentaddressable memory could just as easily contain intransitives, ditransitives, noun phrases, etc.: (13)

(P1 dexperiencer þ P2 dstate-change) [John died ]

(14)

(P1 dagent þ P2 daction þ P3 dbeneficiary þ P4 dtheme) [Mary gave Bill presents]

(15)

(P1 didentity þ P2 dattribute þ P3 dentity) [a tall man]

Fourth, we have used the English simple past tense in these examples to illustrate the overall behavior of the model, but it would be straightforward to extend the model to generalize over tense, aspect etc, via lexical associations like kissdpastdkissed. Finally, we are not the first to take a data-driven approach to generalizations of this sort. There is a growing literature in this area, mainly using traditional representations like parse

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trees and grammatical rules (e.g., Bod and Scha 1997; Batali 2002). Our contribution here is to show how this approach can be grounded in a neurally plausible framework.

5. Phrase structure, embedding, and recursion In an earlier section we presented an account of embedding in which the vector representations of embedded material were permuted to prevent the self-cancellation of recursive structure. In this section we discuss how this mechanism can be exploited in our transduction model. Consider a representation of the proposition expressing one person’s belief about the beliefs of another: (16)

experiencedbelief þ experiencerdx þ themedP (experiencedbelief þ experiencerdy þ themedP(p))

where x and y are individuals, p is a proposition, and P a permutation operator. Even with the permutation operator, a problem arises when we try to use these mappings in the context of the corresponding transduction mappings like (P1 dexperieriencer þ P2 dexperierience þ P3 dtheme) and (P1 dagent þ P2 daction þ P3 dpatient): multiplying these mappings together results in the self-cancellation of each position vector, obliterating the sequencing information. 5.1. Syntax as planning The origin of this problem lies in the oversimplified way in which we are associating semantic content with syntactic form. In section 4 above, we alluded to a content-addressable memory that supports this association, but gave no details. To flesh out the details of such a device, we begin by noting that it is unrealistic to expect it to supply the entire set of associations for a given propositional meaning at once, especially when the proposition contains embedding. Instead, following recent work by Steedman (2002), we might view the associative memory as a kind of planning mechanism. This mechanism would retrieve the appropriate mapping for a given semantic content before retrieving the mapping for any part of that content. The execution of intermediate plans – here, the serialization of embedded semantic content – would be accomplished by means of a

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mechanism that gives precedence to intermediate plans as they are retrieved. Because of the way that we are encoding sequences, ‘‘embedded’’ here refers to any material requiring its own internal sequencing, including noun phrases. As shown in (Levy 2007), such a mechanism can be modeled in a neurally plausible way using the fixed-size vector apparatus described here. Its operation can be understood by analogy with the foregrounding and backgrounding of visual images. As new images (plans) are overlain onto the fixed-size image bu¤er, they are foregrounded by amplifying them by some constant. For visual images, this operation manifests itself as greater prominence of the foregrounded image. For sequential plans like the ones we are working with here, an additional mechanism is needed, to store the current position vector and reset it after the current plan is completed. If we use the sort of low-precision neural encoding that we mentioned in our introduction, we obtain a realistic ‘‘soft limit’’ on the number of such plans that can be superimposed in this way. We also obtain a prediction about the relative ease of processing tail-recursive constructions (the stick that beat the cat that ate the goat) as compared with the di‰culty of center-embedded constructions (the goat that the cat that the stick beat ate). As more position vectors are added together and the sums normalized to a fixed precision, it becomes increasingly di‰cult to recover earlier plans. In terms of our initial discussion, this means that competence and performance derive from the same source, namely, the mathematics of highdimensional, low-precision vectors. 5.3. Grammatical categories as attractor basins Given our use of ad-hoc semantic roles and grammatical constructions, the reader might wonder about the status of grammatical categories (lexical, phrasal) in our model. Rather than positing such categories as primitives, we see them as emergent properties of the coordination between meaning and form that is accomplished by our associative mappings. Specifically, they are the attractor basins (Abraham and Shaw 1992), or stable patterns, that emerge in the Hopfield network of the associative cleanup memory as it is exposed to exemplars of such mappings during language acquisition. Repeated exposure to common patterns like (P1 dagent þ P2 daction þ P3 dpatient) induces (metaphorically) deep, wide attractor basins for such patterns that make them easier to reconstruct from degraded or incomplete data. In practical terms this means that when pre-

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sented with a novel sequence, such as (P1 da þ P2 dlarge þ P3 dglarph), the associative memory will be derive a representation for glarph that is in the vector ‘‘neighborhood’’ for concepts that in English are expressed by nouns. This graded interpretation of grammatical categories is reminiscent of the syntax-lexicon continuum of cognitive/construction grammar (Croft and Cruse 2004). Our contribution here is to propose a biologically plausible mechanism supporting such a continuum. 5.4. Becoming recursive Our model puts not just grammatical categories, but also recursion itself, in a new light. Because the model makes it necessary to encode all sorts of structure using permutations, there is no overt representation or special status given to ‘‘true’’ recursion, e.g., occurrence of a predicate in the scope of an identical predicate (John knows that Bill knows that Mary kissed Fred ). Because the model is based on transduction between concrete patterns, as opposed to abstract categories, sets, and rules, the contentious question about whether all (or any) human languages are ‘‘infinite’’ does not arise. Eschewing such traditional mechanisms and their resulting distinctions encourages us to explore the issues surrounding recursion in a novel way. For example, the role of recursion in language evolution can be recast as the question of how a mechanism used to represent events, states, roles, fillers, and other relational semantic information came to be coupled with a mechanism for planning sequential actions. Perhaps the sequence-processing ability was exapted from other modalities, as one researcher has suggested for the sense of smell (Lorig 1999). With respect to language acquisition, our model gives no reason to expect constructions traditionally viewed as recursive (like relative clauses) to be more di‰cult to acquire than non-recursive structure of comparable syntactic complexity. This view is consistent with recent experiments in the acquisition of English relative clauses, which found adult-like competence for relative clauses by age three or four (Fragman, Goodluck, and Heggie 2007). If recursion per se does not constitute a fundamental leap in language evolution or acquisition, the absence of recursion in a language would likely be due to non-linguistic constraints; for example, a cultural prohibition on certain forms of utterance. This is precisely the situation that Everett (2005) describes for Piraha˜.

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6. Conclusions and future work In this article we have presented a view in which recursion is not a single faculty or property of language, but rather the result of the way that ‘‘quasi-recursive’’ mental representations and processes are used (quoting Pinker and Bloom 1990) for the transmission of propositional structures through a serial interface. Though other researchers have taken approaches similar to ours, we feel that our model di¤ers in significant respects. Tabor, Juliano, and Tanenhaus (1996) present a back-propagation network model in which lexical and phrasal categories emerges as basins of attraction in the network dynamics, but their task consists of predicting word sequences without modeling the event semantics described by the sequences. Chang, Dell, and Bock (2006) describe a connectionist network that ‘‘becomes syntactic’’ by learning to predict roles and their fillers; however, they too use the biologically implausible back-propagation algorithm, and don’t deal with recursive constructions. Dominey, Hoen, and Inui (2006) model the processing of grammatical constructions using a network that relates roles and fillers to sequences in a way similar to ours. Their network uses a localist indexing scheme and works with relative clauses; it is not clear how well the model would extend to other sorts of embedded/recursive structures. The view we have sketched is naturally quite tentative, and much work remains to be done. Relative clauses and conjuncts present a challenge for us because they can associate the same role with two di¤erent fillers (The cat chased the rat that chased the mouse; Mary kissed John and John kissed Fred ). It is not clear how to represent the semantic structure conveyed by such utterances, let alone the mapping to a syntactic construction, in the permutation-based approach we have taken here. Finally, we note the immense gap in explanatory capacity between our model and the rich theoretical apparatus provided by more traditional frameworks like generative grammar. The latter has had five decades to develop accounts of subjacency, word-order universals, and other important phenomena that we have not even begun to address. Rather than being a single, unitary alternative to this framework, we see our model as part of an overall approach that seeks to explain language patterns as arising from the interaction of multiple biological, psychological, social, and cultural constraints on communication and adaptation. (See, for example, Berwick and Weinberg’s (1984) parsing account of subjacency, Hawkins’

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(1994) performance theory of word-order universals, and Kirby’s (2002) communication-bottleneck model of the emergence of recursive syntax.) We hope to have made some small contribution here to this ongoing and worthwhile e¤ort.

Acknowledgments The author thanks Ross Gayler and Harry Howard for extensive discussions and advice on the material presented in this article, and two anonymous reviewers for helpful comments. References Abraham, Ralph and Christopher D. Shaw 1992 Dynamics: The Geometry of Behavior. Reading, Massachusetts: Addison Wesley. Batali, John 2002 The negotiation and acquisition of recursive grammars as a result of competition among exemplars. In Ted Briscoe (ed.), Linguistic Evolution through Language Acquisition: Formal and Computational Models. Cambridge: Cambridge University Press. Berwick, Robert C., and Amy S. Weinberg 1984 The Grammatical Basis of Linguistic Performance: Language Use and Acquisition. Cambridge, Massachusetts: MIT Press. Bod, Rens and Remko Scha 1997 Data-oriented language processing: An overview (Technical Report 38). Amsterdam: NWO Priority Programme in Language and Speech Technology. Chang, Franklin, Gary S. Dell, and Kathryn Bock 2006 Becoming syntactic. Psychological Review 113 (2): 234–272. Chomsky, Noam 1965 Aspects of the Theory of Syntax. Cambridge, Massachusetts: MIT Press. Crick, Francis 1989 The recent excitement about neural networks. Nature, 337: 129– 132. Croft, William A. and D. Alan Cruse 2004 Cognitive Linguistics (Cambridge Textbooks in Linguistics). Oxford: Oxford University Press. Dayho¤, Judith 1990 Neural Network Architectures. New York: Van Nostrand Reinhold.

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Dominey, Peter F., Michel Hoen, and Toshio Inui 2006 A neurolinguistic model of grammatical construction processing. Journal of Cognitive Neuroscience 18: 2088–2107. Eliasmith, Chris 2004 Learning context sensitive logical inference in a neurobiological simulation. In Simon D. Levy and Ross Gayler (eds.), Compositional Connectionism in Cognitive Science: Papers from the AAAI Fall Symposium, 17–20. Menlo Park, California: AAAI Press. Eliasmith, Chris and Paul Thagard 2001 Integrating structure and meaning: a distributed model of analogical mapping. Cognitive Science 25 (2): 245–286. Elman, Je¤rey L. 1990 Finding structure in time. Cognitive Science 14: 179–211. Everett, Daniel L. 2005 Cultural constraints on grammar and cognition in Piraha˜. Current Anthropology 46 (4): 621–646. Foltz, Thomas K. and Darrell Laham 1998 Introduction to latent semantic analysis. Discourse Processes 25: 259–284. Fragman, Cathy, Helen Goodluck, And Lindsay Heggie 2007 Child and adult construal of restrictive relative clauses: Knowledge of grammar and di¤erential e¤ects of syntactic context. Journal of Child Language 34 (2): 345–380. Gayler, Ross W. 1998 Multiplicative binding, representation operators, and analogy [Abstract of poster]. In Keith J. Holyoak, Dedre Gentner & Boicho N. Kokinov (eds.), Advances in Analogy Research: Integration of Theory and Data from the Cognitive, Computational, and Neural Sciences. Sofia: New Bulgarian University. Hauser, Marc D., Noam Chomsky, and W. Tecumseh Fitch 2002 The faculty of language: What is it, who has it, and how did it evolve? Science 298 (5598): 1569–1579. Hawkins, John 1994 A Performance Theory of Order and Constituency. Cambridge: Cambridge University Press. Hebb, Donald O. 1949 The Organization of Behavior. New York: John Wiley and Sons. Holyoak, Keith J. and John E. Hummel 2000 The proper treatment of symbols in a connectionist architecture. In E. Dietrich and A.B. Markman (eds.), Cognitive Dynamics: Conceptual and Representational Change in Humans and Machines. Mahwah, New Jersey: Lawrence Erlbaum Associates. Hopfield, John J. 1982 Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences 79: 2554–2558.

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Kanerva, Pentti to appear Hyperdimensional computing: A tutorial on computing in distributed representation based on high-dimensional random vectors. Cognitive Computation. Kanerva, Pentti 2008 Encoding meaning with high-dimensional random vectors. Guest lecture delivered 9 December 2008, Redwood Center for Theoretical Neuroscience, Berkeley, California. Available at http://www. archive.org/details/ucbvs298_neural_comp_2008_12_09. Kirby, Simon 2002 Learning, bottlenecks and the evolution of recursive syntax. In Ted Briscoe (ed.), Linguistic Evolution through Language Acquisition: Formal and Computational Models, 173–204. Cambridge: Cambridge University Press. Levy, Simon D. 2007 Continuous states and distributed symbols: Toward a biological theory of computation (Poster). Proceedings of Unconventional Computation: Quo Vadis? Santa Fe. Lorig, Tyler S. 1999 On the similarity of odor and language perception. Neuroscience & Biobehavioral Reviews 23 (3): 00041–4. Marcus, Gary. F. 1998 Rethinking eliminative connectionism. Cognitive Psychology 37: 243–282. Pinker, Steven and Paul Bloom 1990 Natural language and natural selection. Behavioral and Brain Sciences 13 (4): 707–784. Plate, Tony 2003 Holographic Reduced Representation: Distributed Representation for Cognitive Science. Stanford, California: CSLI Publications. Rumelhart, David E. and James L. McClelland, James L. 1986 On learning the past tenses of English verbs. In James L. McClelland, David Rumelhart, and the PDP research group (eds.). Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Volume 2: Psychological and Biological Models. Cambridge, Massachusetts: MIT Press. Rumelhart, David E., Geo¤rey E. Hinton, and Ronald J. Williams 1986 Learning internal representations by error propagation. In Rumelhart and McClelland (1986). Smolensky, Paul 1990 Tensor product variable binding and the representation of symbolic structures in connectionist systems. Artificial Intelligence 46, 159–216. Steedman, Mark 2002 Planning, a¤ordances, and combinatory grammar. Linguistics and Philosophy 25: 723–753.

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Tabor, Whitney, Cornell Juliano, and Michael K. Tanenhaus 1997 Parsing in a dynamical system: An attractor-based account of the interaction of lexical and structural constraints in sentence processing. Language and Cognitive Processes 12 (2/3) 211–271.

20.

Recursion in severe agrammatism

Vitor Zimmerer and Rosemary A. Varley

1. The recursion module in language and cognition In an influential article, Hauser, Chomsky and Fitch (2002, in the following referred to as HCF ) suggested that the ‘‘abstract linguistic computational system’’ (p. 1571) consists only of a recursion module, making recursion the defining feature of syntax. Furthermore, it has been claimed that the same mechanism that embeds phrases into other phrases might also be important for other cognitive systems. For example, Theory of Mind, the ability to attribute mental states to others, might be based on the recursive embedding of one belief into another: We believe what a second person believes a third person believes (Corballis 2003; Hurford 2004; de Villiers 2007). Similarly, HCF claimed that in the domain of mathematics, the very same recursive system might be necessary to understand that adding 1 to a number creates another number, making it possible to compute exact numbers of arbitrary size. In this way, the capacity for recursion may be the feature that distinguishes humans from other animals. This view that several cognitive systems interact with one recursion module is an alternative to more traditional theories that regard recursion simply as the preferred solution of all complex systems, and thus a property of several cognitive areas (Pinker and Jackendo¤ 2005: 230). HCF’s theory can contribute to three areas of investigation in human cognition. The first is evolution: If the recursion module is unique to humans, it explains a wide range of cognitive di¤erences between the species. The second is the development of the human mind: A child’s development in several cognitive domains might be tied to the maturation of the recursion module. The third is the workings of the mature mind: Di¤erent cognitive faculties can, by accessing the recursion module, attain greater power. The aim of this article is to show how research on agrammatic aphasia can contribute to this last area of research. Data from agrammatism show dissociation between the ability to embed phrases in language and perform non-linguistic tasks claimed to be recursive, and thus presents

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Vitor Zimmerer and Rosemary A. Varley

evidence against the claim that the system used for syntactic recursion is a core mechanism of non-language cognitive domains.

2. Recursion in agrammatism Aphasia is an acquired language disorder caused by lesions to perisylvian cortex, usually in the left hemisphere. It can be quite diverse with regard to which aspects of language are a¤ected, and the severity of the impairment. One outcome is severe agrammatism, in which most, if not all sensitivity to syntactic structures is lost. The capacities of people with agrammatism may provide a valuable window on the role of syntactic recursion. The data presented here are from PR. At the time of this investigation PR was a 62 year old english-speaking male who su¤ered a stroke seven years earlier. He had a large lesion across left perisylvian language areas, resulting from a left middle cerebral artery infarct. A CT scan revealed damage to the inferior frontal gyrus, insula and underlying deep white matter. The superior temporal, supramarginal and angular gyri were lesioned, with damage extending to the inferior border of the intraparietal sulcus. PR’s language production consists of high-frequency words (numbers, days of the week) and few phrasal constructions (e.g., I don’t know) which he does not modify and therefore might be completely lexicalized. His comprehension is also severely impaired. While PR understands many words, he is unable to comprehend any utterances in which the meaning cannot be extracted solely from the semantic content of the words, such as conditional clauses. This applies for both auditory and visual modalities. Despite this, PR’s communication can be seen as prolific. It involves an abundance of hand gestures, written words or drawings. He conveys information about a wide range of topics, including more elaborate events involving causal references and multiple agents. Language assessment tests (for further information see Varley et al. 2005) confirm these observations. PR’s scores are extremely low in all language production tasks, while he achieves high scores in lexical comprehension tests such as spoken and written word-picture matching tests or synonym judgments. In tests assessing syntactic processing, PR performs at chance level. In understanding reversible sentences like The man kills the lion or The lion kills the man, he fails to correctly assign thematic roles even in active, canonical sentences. In grammaticality judgment tasks, he accepts severe violations, such as sentences with a misplaced or missing

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VP. Whether recursion is only postulated for the embedding of clauses, or additionally at the level of merging single lexical units (e.g. Chomsky 1995), PR shows no evidence for recursive operations in syntax. According to HCF and others, one might expect PR’s cognitive impairment to go far beyond communication. However, this cannot be observed. In experiments assessing his mathematical skills, he showed no impairment in understanding of integers, decimal numbers or in basic computational procedures (Varley et al. 2005). He was able to calculate the result of expressions involving syntactic brackets, some of them featuring double embedding [e.g., 50 ðð4 þ 7Þ 4Þ]. Solving these expressions requires recursive processes due to hierarchical nature of the computation. PR was also able to solve a non-linguistic Theory of Mind task (for the experimental methods, see Varley and Siegal 2000). For example, on a first-order false belief test, he was presented with a familiar container with unusual contents (a video case for the movie ‘‘Superman’’ containing a book instead of the tape). When asked what a third person who had not viewed the contents would think was within the case, PR, unable to produce the word superman, hummed the theme tune from the 1960s television series ‘‘Batman’’. He was also able to respond correctly to probes as to the actual content of the container (by drawing a book), and also to trials which probed true beliefs (i.e., Russian Babushka doll containing further dolls). While PR was only tested for first-order Theory of Mind, Apperly et al. (2006) found intact second-order Theory of Mind in an aphasic patient described as having severe agrammatism. Beyond his performance in the experiments, PR’s sophisticated social behavior strongly indicates that he has no di‰culty in understanding the mental states of others.

3. Is agrammatism a competence or performance issue? Artificial grammar learning in agrammatism 3.1. Competence vs. performance The evidence from agrammatism and the extent to which it can inform debates on relationships between language and other domains of cognition is sometimes dismissed on the basis that the patients are not ‘‘truly’’ agrammatic, but merely su¤er from performance deficits (Newton and de Villiers 2007, Chomsky 2007). Under this view, agrammatic patients might per-

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form well in recursive non-linguistic tasks because they can recruit their retained syntactic competence in domains in which performance is less impaired. Syntax in language does not only require knowledge about syntactic operations, but also a range of other resources. One such capacity is working memory (WM) (Blaubergs and Braine 1974). Claims for di¤erent kinds of performance-related WM are made, such as phonological WM (Friedmann and Gvion 2002) and structural WM (Gibson and Thomas 1999). Complexity of syntactic structures is generally correlated with WM load, which means that it is limited by WM capacities. However, agrammatism can be independent from WM resources. Friedmann and Gvion (2002) investigated the comprehension of relative clauses in three patients with conduction aphasia, whose phonological WM was impaired, and three agrammatic patients who performed well in WM tasks. In the patients with conduction aphasia, the comprehension of relative clauses was dependent on phonological distance between antecedent and gap. By contrast, the syntactic impairment of agrammatic patients was consistent regardless of phonological WM demand. It is undeniable that PR su¤ers from performance impairment. For example, his language production is severely limited in comparison to his comprehension in that he can understand many words that he cannot produce. Also, his verbal WM is below average. In a recognition version of a digit span test, (PALPA 13, Kay et al. 1992), in which the subject listens to two strings of numbers and has to decide whether they are the same (e.g., 387 387) or di¤erent, PR shows a digit span of 4 (the average span in an age-matched control group was 8; Ankerstein et al., in preparation). However, PR does not comprehend syntax even in very short sentences, and also fails at tests that use the written modality. If PR’s cross-modal impairment is a performance issue, the impaired performance system must be involved in both written and spoken language. The question that remains is whether PR su¤ers from competence impairment in addition to his performance impairments. Standardized tests o¤er little to address this question. Grammaticality judgment and sentence comprehension tasks do not measure only competence, but performance. Even when administered across modalities they require more than just pure syntax in a Chomskyan sense, as lexical and semantic content has to be activated and mapped to the syntactic structure. In this report, we explore whether the artificial grammar learning (AGL) paradigm can be used to explore syntactic capacities in a person with severe

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Figure 1. Center-embedding interpretation of An B n (Fitch and Hauser 2004).

aphasia, and the extent to which such tasks can provide insight into the syntactic abilities of such individuals. 3.2. Artificial grammar learning Artificial grammar learning (Reber 1967) can be regarded as a test of grammatical competence. In the usual AGL experiment, a subject is exposed to strings of nonsense items which follow certain grammatical rules. After the training phase, the subject engages in a decision task and has to decide whether new strings are grammatical or not. It is assumed that the subject learns the grammar from the training phase and applies it to make the grammaticality decision. By using stimuli free of semantic content and with a relatively low memory load it becomes possible to investigate syntax isolated from other linguistic processes. Neuroimaging studies show that brain activation during AGL can be compared to the activation during tasks involving natural language syntax (Petersson et al., 2004; Friederici et al., 2006). Demonstrating that subjects can spontaneously apply recursive rules in AGL tasks has proven to be di‰cult. An established problem is that strings resulting from a tail-embedding grammar can be described by iterative, finite-state grammars (Hurford 2004). AGL experiments therefore need to look at center-embedding. Fitch and Hauser (2004) exposed subjects to strings of the grammar An B n , which they present as a centerembedding, phrase-structure grammar that is learned through the rule S ! AðSÞB (Fig. 1). While recursion is not mentioned in their experimental report, they use AnBn to investigate ‘‘[t]he capacity to generate a limitless range of meaningful expressions from a finite set of elements’’ (p. 377)

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Vitor Zimmerer and Rosemary A. Varley

and also refer to the Chomsky hierarchy of formal languages (Chomsky 1957). HCF discuss the experiment as one empirical approach to investigating recursion (p. 1573). In the training phase of the Fitch and Hauser experiment, participants listened to An B n strings in which n was either 2 or 3 (AABB, AAABBB). For each A or B, one spoken CV syllable was presented. Class A syllables were spoken by a female, and class B syllables by a male speaker. In the test phase, participants had to distinguish grammatical strings from strings that violated An B n . In human subjects, 85% of the judgments were correct. Cotton-top tamarins on the other hand failed to learn An B n . This result was seen as evidence for competence in humans and a lack of competence in the monkeys. However, center-embedding strategies are not the only way of learning An B n . The grammar has been described as ‘‘counting recursion’’ (Christiansen and Chater 1999: 160–161) as it is possible to count and compare the number of As in the first block with the number of Bs in the second block (both have to be equal), while knowing that all As appear before the Bs. Further investigations provide evidence for the use of counting rules in An B n (de Vries et al. 2008, Zimmerer et al. submitted). Despite di¤erent explanations for the acquisition of An B n , two experiments using the grammar were designed in order to reveal more about PR’s syntactic competence. In a first experiment PR was exposed to 72 strings of An B n in which n could be 2, 3 or 4. For each of the classes A and B, eight low-frequency, non-word CV syllables were used. Just as in Fitch and Hauser, class A was spoken by a female, and class B by a male speaker. The syllables were edited for equal duration (400 ms) and intonation, using Audacity.1 Between each syllable in a string there was a 200 ms pause, between each string there was a pause of 4.5 sec. The training phase was divided into three blocks of equal length. The stimuli were presented through stereo speakers connected to a laptop. The presentation was written in DMDX.2 PR was told just to pay attention and listen. In the test phase, PR listened to 120 new strings, half of which were grammatical. The remaining half consisted of five types of ungrammatical strings. Each type occurred in 12 trials:

1. http://audacity.sourceforge.net/ 2. http://www.u.arizona.edu/~kforster/dmdx/dmdx.htm

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– Type 1 (e.g., AABBB) violated the legal total number of items in the string and the number of As compared to Bs. – Type 2 (e.g., AAAABB) violated the legal number of As compared to Bs. – Type 3 (e.g., BBBAAA) had a wrong initial item, final item, and contained the illegal bigram *BA. – Type 4 (e.g., BABAAB) had a wrong initial item, contained the illegal bigram *BA and violated block consistency (items of one class did not appear together). – Type 5 (e.g., ABBABA) had a wrong final item, contained the illegal bigram *BA and violated block consistency. The di¤erent types of ungrammatical stimuli allowed for a more precise identification of response strategies that varied from the acquisition of the target grammar. For instance, if a subject rejected all string types except for the grammatical strings and strings of Type 1 and 2, this would indicate that performance was driven by rejecting the illegal bigram *BA. PR made his decisions using a two-button mouse with a green sticker on one button and red on the other. He pressed green for accepted strings, and red for rejected strings. When presented with auditory stimuli, 53% of PR’s judgments were correct. While this performance is not significantly above chance, an analysis by string types revealed that he correctly rejected 83% of the Type 1 violations (above chance; p ¼ 0:039), and was at chance level in all other test string types. This suggested that, while PR was not able to acquire the target grammar, his behavior was not completely random. It is probable that he counted the total number of items and rejected a string if the number did not correspond to the number of items in a grammatical string (4, 6 or 8). Because the stimuli were spoken syllables, it is likely that PR’s performance was a¤ected by phonological WM limitation and/or auditory perceptual impairment. Seven weeks after the first experiment, he completed a second experiment in which the phonological stimuli were replaced by abstract shapes. All other components of the experimental design were unchanged (including the same item order). For A, 8 blue, rounded shapes were used, for B, 8 red, angled shapes. All stimuli were presented on a laptop screen, with a light grey background. PR’s judged 57% of all strings correctly, which was still not significantly above chance level. However, he correctly rejected 79% of the counting violations Type 1 and Type 2 (above chance, p ¼ 0:007). The results suggested that with the visual

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Vitor Zimmerer and Rosemary A. Varley

stimuli, in addition to rejecting strings in which the total number of items was incorrect, PR consistently rejected each string in which the number of A-shapes did not match the number of B-shapes. However, he showed no sensitivity to sequence. For example, PR would accept a string like ABBABA. PR’s ‘‘pure counting’’ performance is very unusual compared to control data. Each experiment was run on ten non-aphasic English native speakers who were aged 50 or older. The mean age of the group participating in the auditory experiment was 57 (range 50–66). The mean percentage of correct judgments in the test phase was 69.8% (SD ¼ 16.47, SE ¼ 5.21). In the visual experiment, the mean age of the control group was 62 (range 50–78). The mean percentage of correct judgments was 88.5% (SD ¼ 15.7, SE ¼ 4.96). An independent samples t-test revealed that the di¤erence of mean scores between modalities was significant ½tð18Þ ¼ 2:599; p ¼ :018, with the superior performance in the visual modality. The response strategies of each control participant were also analyzed. No healthy individual in either the auditory or visual experiment showed PR’s pattern of responses. Controls who rejected strings violating the counting rule also rejected at least the sequential violations of type 4 and 5, if not all violations, thus showing at least some sensitivity to sequence. There are several ways by which to account for PR’s response strategy of counting in absence of sequence awareness. It is possible to describe his behavior by a center-embedding, recursive grammar (e.g., Cohen 1991: 259–262). However, such a grammar is considerably more complex than the center-embedding rule that describes An B n . For the claim that PR used recursion to stand, it would require an explanation as to why the easier An B n was not learned. It is more likely that PR solved the task using counters. He was able to discern the two classes within stimulus strings and assigned to each a counter. With both counters operating in parallel, he then accepted strings in which the final numbers matched. Alternatively, he might operate with a single counter which increments on As and decrements on Bs, and accepted a string if the state at the end of the string matched that of the state before the string. In either scenario, PR did not put the stimuli into a syntactic context. The results of the experiments suggest that on tasks which minimized linguistic performance components, he still displayed marked impairment in processing sequential information, supporting the claim of a loss of competence. However, PR’s performance cannot be explained with pure-counting

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alone. If PR had used counting as the sole criterion, he would have not only rejected counting violations, but also consistently accepted all other string types. But his performance in other string types, including grammatical strings, was at chance level. This suggests that when the number of As matched the number of Bs, he used an additional strategy which could not be identified, did not contribute to the learning of the target grammar and might as well have been guessing. Future experiments will continue to explore PR’s AGL capabilities. Fitch and Hauser (2004) reported on cotton-top tamarins and their inability to learn An B n , deeming them competence-less. Under the same criteria and considering the current data, PR’s atypical behavior also needs to be described as evidence for impaired syntactic competence. Preliminary data from other severely agrammatic patients show a similar trend. 4. Discussion This article is, to our knowledge, the first to discuss di¤erent recursive processes in a patient with severe agrammatism. The evidence from language assessment tests, mathematics, Theory of Mind and AGL suggests two things. First, aphasic patients can su¤er from a loss of competence. Second, despite their loss, they show recursive thinking in non-linguistic areas. Aphasia is not the only phenomenon that suggests an independence of non-linguistic recursion from syntax. It is claimed that while the Amazonian Piraha˜ tribe lacks clause embedding in its language (Everett 2005), discourse data show that the Piraha˜ engage in recursive thinking (Stapert and Sakel in this volume). But what would the e¤ective use of recursion in non-linguistic domains by a severely agrammatic patient mean for the role of syntactic recursion? We o¤er two explanations. First, syntactic recursion might be important for the development of the human mind, but only to spawn new recursive procedures. As soon as recursion in other areas is enabled, maturation makes them independent from syntax. Syntax would still be the ‘‘mother of recursion’’, but once lost in the mature mind, recursion in other areas is not a¤ected. Second, the data are also in accord with the views of Pinker and Jackendo¤ (2005). Recursion might be a general property of the human mind. If this was the case, it would not be surprising to see recursive procedures appear in cognitive areas where it is beneficial. All types of recursion would simply be di¤erent incarnations of a very prevalent neuronal architecture.

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Evidence from patients with focal brain lesions can be used to develop hypotheses regarding the localization of cognitive processes, such as recursion, within the brain (Mu¨ller and Knight 2006). Such an approach however should be used with caution as the extent of functional lesion or hypometabolism may extend well beyond the boundaries of the structural lesion (Metter et al. 1981). The possibility of inferring structure-function relationships is further limited in cases such as PR where there is extensive damage across the left perisylvian region. At first sight, the evidence from agrammatism seems to contradict the results from recent dual-task studies that appear to show that verbal shadowing disrupts performance in certain non-language cognitive domains. It has been observed that the ability to apply Theory of Mind (Newton and de Villiers 2007) is significantly disturbed when the subjects have to simultaneously shadow continuous speech. This is explained by the language system being occupied with the shadowing task, illustrating the dependency of non-linguistic systems on language. However, shadowing does not only recruit syntactic resources – the e¤ect might be due to conceptual systems being overloaded by the dual-task demand. While experimenters employ non-language shadowing tasks such tapping rhythms in an attempt to control for the general processing demands of dual-tasking, it is unlikely that the monitoring of meaningless inputs engages semantic-conceptual systems in the same way as shadowing linguistic material. There are unresolved issues with AGL itself. Since acquiring An B n does not require center-embedding and possibly involves counting even in healthy controls, other grammars might be better suited for future studies. An B n does not completely match many descriptions of natural grammars such as X-Bar and the Minimalist Program, since its merging is not binary and there is no consistent head rule: The constituent AðSÞB is an S even if the optional, embedded S is absent. Also, it is not clear how much AGL indeed reveals implicit processes, since the grammaticality decision takes place o¿ine. It can never be ruled out that syntactic recursion still lurks inside even a severely aphasic brain, and that new studies will reveal it. However, the null-hypothesis should be that a patient not showing recursion in syntax does not have it, since there can be no evidence for absence. While the performance deficit claim should not be completely dismissed, it becomes weaker the severer the damage to the brain is. If competence cannot be disrupted by brain injury, it is not a property of the brain. It is plausible that, in a case such as PR, syntactic competence is destroyed, and the

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evidence suggests that such damage has insignificant implications for recursive abilities in the non-linguistic domains explored to date. Acknowledgements We thank PR for his willing participation in this investigation. We also thank the three anonymous reviewers for their comments and suggestions. The research was funded by an ESRC Professorial Fellowship. References Ankerstein, Carrie A., Victoria Peace, Joanne Evans, and Rosemary A. Varley In prep. Digit span in recall and recognition. Apperly, Ian A., Dana Samson, Naomi Carroll, Shazia Hussain, and Glyn Hum2006 phreys. Intact first- and second-order false belief reasoning in a patient with severely impaired grammar. Social Neuroscience 1 (3–4): 334–348. Blaubergs, Maija S., and Martin D. S. Braine 1974 Short-Term Memory Limitations on Decoding Self-Embedded Sentences. Journal of Experimental Psychology 102 (4): 745–748. Chomsky, Noam 1957 Syntactic Structures. The Hague: Mouton & Co. Chomsky, Noam 1995 The minimalist program. Cambridge: MIT Press. Chomsky, Noam 2007 Approaching UG from below. In: Uli Sauerland and HansMartin Ga¨rtner (eds.), Interfaces þ Recursion ¼ Language?, 1–30. Berlin: Mouton de Gruyter. Christiansen, Morten H., and Nick Chater 1999 Toward a connectionist model of recursion in human linguistic performance. Cognitive Science 23 (2): 157. Cohen, Daniel I.A. 1991 Introduction to Computer Theory. Revised Edition. New York: John Wiley & Sons, Inc. Corballis, Michael C. 2003 Recursion as the Key to the Human Mind. From mating to mentality: Evaluating evolutionary psychology, Kim Sterelny, and Julie Fitness (eds.), 155–172. New York: Psychology Press. Everett, Daniel L. 2005 Cultural Constraints on Grammar and Cognition in Piraha˜. Another Look at the Design Features of Human Language. Current Anthropology 46 (4): 621–646.

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Fitch, W. Tecumseh, and Marc D. Hauser 2004 Computational Constraints on Syntactic Processing in a Nonhuman Primate. Science 303: 377–380. Friederici, Angela D., Jo¨rg Bahlmann, Stefan Heim, Ricarda I. Schubotz, and 2006 Alfred Anwander The brain di¤erentiates human and non-human grammars: Functional localization and structural connectivity. PNAS 103 (7): 2458–2463. Friedmann, Naama, and Aviah Gvion 2002 Sentence comprehension and working memory limitation in aphasia: A dissociation between semantic-syntactic and phonological reactivation. Brain and Language 86: 23–49. Gibson, Edward, and James Thomas 1999 Memory Limitations and Structural Forgetting: The Perception of Complex Ungrammatical Sentences as Grammatical. Language and Cognitive Processes 14 (3): 225–248. Hauser, Marc D., Noam Chomsky, and W. Tecumseh Fitch 2002 The Faculty of Language: What Is It, Who Has It, and How Did It Evolve? Science 298: 1569–1579. Hurford, James R. 2004 Human uniqueness, learned symbols and recursive thought. European Review 12 (4): 551–565. Kay, Janice, R. Lesser, and M. Coltheart 1992 Psycholinguistic Assessment of Language Processing in Aphasia. Hove: Psychology Press. Metter, E. Je¤rey, Claude G. Wasterlain, David E. Kuhl, Wayne R. Hanson, and 1981 Michael E. Phelps FDG positron emission computed tomography in a study of aphasia. Annals of Neurology 10: 173–183. Mu¨ller, Notger G., and Robert T. Knight 2006 The functional neuroanatomy of working memory: Contributions of human brain lesion studies. Neuroscience 139: 51– 58. Newton, Ashley M., and Jill G. de Villiers 2007 Thinking While Talking. Adults Fail Nonverbal False-Belief Reasoning. Psychological Science 18 (7): 574–579. Petersson, Karl Magnus, Peter Forkstamm, and Martin Ingvar 2004 Artificial syntactic violations activate Broca’s region. Cognitive Science 28: 383–407. Pinker, Steven, and Ray Jackendo¤ 2005 The faculty of language: what’s so special about it? Cognition 95: 201–236. Reber, Arthur S. 1967 Implicit learning of artificial grammars. Journal of Verbal Learning and Verbal Behaviour 6: 855–863.

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Varley, Rosemary A., and Michael Siegal 2000 Evidence for cognition without grammar from causal reasoning and ‘theory of mind’ in an agrammatic aphasic patient. Current Biology 10 (12): 723–726. Varley, Rosemary A., Nicolai J. C. Klessinger, Charles A. J. Romanowski, and 2005 Michael Siegal Agrammatic but numerate. PNAS 102 (9): 3519–3524. de Villiers, Jill 2007 The interface of language and Theory of Mind. Lingua 117: 1858–1878. de Vries, Meinou H., Padraic Monaghan, Stefan Knecht, and Pienie Zwitserlood 2008 Syntactic structure and artificial grammar learning. The learnability of embedded hierarchical structures. Cognition 107: 763– 774. Zimmerer, Vitor C., Patricia E. Cowell, and Rosemary A. Varley Subm. Learning of an artificial, non-finite grammar.

Subject index Absolute constructions (see also small clauses) 197 Abstract grouping 344, 365 –Prosodic 363–365 –Visual 364 Abstract visual patterns 360–361, 363–366 Abstraction 39, 97, 155, 226 Acceptability 122, 148 Accessibility 12 Acquisition 102, 188, 195, 236, 385– 386, 398–399 Adjective 44, 115, 118, 123, 166, 203 Adjunct/adjunction xlii, xlvii, 44, 130, 144, 195, 197, 198, 200, 265, 268, 281–282, 247, 301, 304, 312–317, 320–321, 327, 330, 332–333 Adverb 7–8, 44, 46, 48–97, 118, 123, 131, 166 Adverbial clauses xxxvi–xxxviii, 10, 19–20, 22–23, 30–32, 36–37, 39, 76–78, 99, 107 A‰x order 267–269, 272–273, 280 A¤ordances 233, 238, 240, 242 Agentive 287–288, 290, 294 Agrammatism 393–396, 400–403 Alarm calls 183, 187–188 Amalgamation rules 293 Ampliative reasoning 118, 123 Anaphor 123, 239–240 Animals xvii, xIiii, 93–95 Animal communication 95, 183–184, 186, 187–188, 371 Anthropology 124 Aperiodicity 225 Aphasia xlix, 195, 393–397, 401 Applicative constructions xliv, xlvi, 38, 51, 248–251, 265–271, 274, 275, 279–282 Apposition xxiv, 33, 43, 46–48, 75 Argument structure xliv, 247–248, 250, 252–259, 264–268, 275, 281– 282

Argument vs. Adjunct 247 Arithmetics 119, 142 Artificial Grammar Learning (AGL) xlix, 395–397, 400–402 Attractor basins 385 Automata xlix, 152, 181, 219–220, 225–226 Auxiliary verb 101, 166, 186, 203–204 Balanced recursive prosodic structure 319–320, 324 Basic verb 105 Bayesian framework xl, 162–163, 172–173 B-before-C 224–225, 228–229 Behavior 93, 98, 128–129, 173, 214, 218, 395, 399–401 Behaviorism 127 Benefactive 266, 269 Bet-verbs 248 Bigrams 128–129 Bilingualism 9–10 Binary pattern xxvii, 120, 152, 195, 218, 304, 315, 317, 319, 402 Binding theory 123 Biolinguistics 285–287, 293 Biology 285–290, 293–294 Birdsong 184 Bookmark e¤ect 353, 355, 358, 366 Borrowing xxxvi, 8–10 Bottom-Up vs. Top-Down 35, 233– 237, 240–241 Boundary xlviii, 129, 345–346, 348, 361–363 –Length of 346, 363 –Strength of 345, 363 Brain 125, 148, 179, 194, 290, 294, 373, 397, 402 Branching degree 117, 131 Branching onsets 307 Case – default 197, 200–201, 203 Case – structural 194, 197, 200–202

408

Subject index

Category labels 306 Causative constructions xxxviii, xliv, xlvi, 34–35, 38–39, 100–102, 248, 251–252, 264–265, 268, 274–278, 280–282 Chaining 31, 47, 147 Chomsky Adjunction 313 Clause combining xxxv, 20, 69–89 Clitic Group 322, 324, 327 Closure 140–144, 219 Coda xlvii, 305, 308–310, 312, 316, 317 Cognition xvii–xviii, xxxvii, xl, xlvii– xliv, 7, 17, 27, 39, 93, 98, 101–102, 106, 108, 128–139, 204, 219, 221, 238, 240, 343–344, 347, 353, 361, 365–366, 374, 393–396, 401–403 Cognitive processing xxviii, xxxii, xliv, xlix, 51, 63, 79, 165, 170, 179, 185, 235–242, 276, 278, 359, 385–388, 400, 402 Combinatorial properties of words 290–293 Comparative method 214 Competence xxxii–xxxiv, xlix, l, 84, 102, 121, 148–149, 242, 372, 385– 386, 395–398, 400–402 Complement xxviii, xxxiii, xxxvi– xxxvii, xli, 57, 60, 65, 102–108, 198, 203, 253 –In phonology 306–309, 312–313, 317, 327–328, 330–331 –Clausal 18–39, 70–74, 77–81, 121, 123, 130–132, 252 Complementizer xlii, 6, 21–22, 24, 30, 37, 72–74, 82, 187, 194, 200, 204, 239 Complementizer phrase (CP) xlii, 6, 199–200, 204 Complex action sequences 183 Compositionality 275–280, 293 Compound prosodic domains 329, 345 Compound xli, xlv, 323–325, 329 Computation xxxii, xlii, xlix, 99, 104, 121, 234, 287, 293, 343–347, 353, 358, 365–366, 395

Computational linguistics 51, 150, 164 Computational simulation 233–234 Concatenation xxi, 225, 349, 355 Conceptual-intentional system 288, 293, 343 Conditional clause 5, 394 Conjunct xxxv, 53, 142–144, 195, 198, 222, 329–330, 387 Conjunction 9, 46–48, 51, 53, 73, 76, 82, 97, 130, 166 Connectionism 374 Constraints xxxii, xliii–xliv, 43, 45, 50, 53–65, 109, 123, 125, 127, 144, 149, 181, 194, 214, 242, 248, 255, 269– 270, 279, 308, 321, 346, 373, 386– 387 Construal rules 293 Constructed data 85 Construction network 103 Content-driven memory 98 Content-restriction 101, 107 Context free stringsets 214–220, 227– 228 Context-sensitivity 120–121 Coordination xxxix, 46–47, 73, 114– 115, 117, 130–132, 195, 197–198, 200–201, 345–346, 360–361, 385 Cost-advantage 99 Cottontop tamarin monkeys 93, 185– 186, 214–215, 218, 398, 401 Countable infinity 117, 149 Creativity, linguistic 126–127, 129, 132 C-selection 293 Cultural evolution xxxviii, 108–109 Culture xl, xliv, 48, 64, 234, 242, 285– 290, 294 Cyclicity 304–305, 321–322 De-embedding xlviii, 348–349, 353, 357, 359, 362–363 Demonstratives xxxvii, 28–30, 239 Denominal verbs 256 Dependency structures 306

Subject index Derivation xlv, 34, 38–39, 120–121, 125, 130, 149, 164, 168, 250, 263, 267, 276, 279–282 Descriptive complexity classes 219 Determiner Phrase (DP) 200, 202 Diachrony 18, 21–22, 131, 325 Direct reference xlvii, 332–334 Direct speech 6 Discontinous phrases 347, 353–356 Discontinuous segments 353, 359 Discontinuous structures xlvii, 356, 358 Discourse 6, 19, 27–30, 33, 38–39, 69– 71, 79, 83–85, 131, 401 Discourse marker xxxv, 6, 9, 38–39, 71, 82 Discrete infinity xxii, xxxix, 96, 113– 114, 117, 147, 153, 160, 234, 242 Disjunction 142, 144, 222 Ditransitive clause 100, 249, 251–252, 254, 256 Downdrift 349, 353, 357–359, 365– 366 Downstep 357–358 Dyck stringsets 228 Economy of Description 143 E¤ability 141, 196 E-language 125, 289 Ellipsis 202 Embedding xxiv–xlviii, 4, 8, 19, 33– 35, 43, 45, 47, 50–65, 94–95, 97–98, 100–102, 103–104, 106–107, 160, 165, 170, 179–182, 183–194, 199, 200, 346–349, 353, 356–360, 362– 363, 365, 374, 379, 385, 397–398, 400, 402 –Center-embedding xxiv–xlviii, 43, 50–65, 94–95, 97, 103–104, 107, 160, 165, 170, 301, 359, 385, 397– 398, 400, 402 –Depth of 56, 70, 73, 77–81, 114, 171, 379 –Maximal degree of 53, 63 –Mulitple center-embedding xxv,

409

55–56, 58, 60, 63 –Tautocategorial 142–143 –Self-embedding xxiv, xxix, xxxiv, l, 51, 54–56, 65, 160, 187, 379 Endocentricity xli–xlii, 291 Entrenchment xxxvi, 18, 103, 105– 106, 144, 242 Enumeration 49, 145, 253 Environment 98 Esoteric/exoteric communication 3, 12–13 Essentially infinite language 155 Eurythmics 359 Even-B 226–229 Evidentiality 6–8 Evolution xviii, xxxviii, xl–xliii, 39, 95, 98–99, 131, 107–109, 131, 182, 185, 194–196, 202–206, 213–214, 221, 230, 241, 287, 289, 294, 343–344, 366, 386, 393 Exaptation 286 Exceptional Case Marking (ECM) 195, 200–202 Experiments xvii, xliii, xlviii, xlix, 4–6, 63, 183–185, 214– 221, 228–229, 346–347, 360, 363–366, 386, 395, 397–403 Expliciteness criterion 279 Extension 125–127 Facilitation 289 Facilitive 279, 281 Faculty of language xv–xvii, xxxix, xliii, 17, 69, 85, 147, 153, 159, 185, 213– 214, 230, 285–289, 330, 343–344, 366 Faculty of Language in Broad sence (FLB) xvii, 286, 343–344 Faculty of Language in Narrow sence (FLN) 189, 213, 286–289, 343–344, 366, 371 Finite clause 23, 46, 64, 73, 76, 100, 102, 123, 130, 132, 197, 202 Finite state model 96 Finite state stringsets 214, 216–218, 226–228

410

Subject index

Finiteness 37, 53, 100, 132 First articulation 301, 333, 335 First-order (FO) 124, 224, 395 Fitness 99 Fixed expressions 72, 102, 103 Flattening l, 315, 325–326, 329 FO(þ1) definable stringsets 223–224 FO(<) definable stringsets 225–226 Foot xxx, xlvii, 310–320, 330, 335 Formal completeness 141–142 Formal language theory (FLT) 51, 150, 155, 162, 219 Formal systems xxxi, 122, 127, 291 Formulaic xxxvi, 3, 12, 106, 201–202, 203, 205, 235 Fossil xlii, 194, 196, 206, 235 Free modification 44–45 Free NP 75 Frequency 11, 99, 102–103, 105, 108, 167–168, 171, 394 Functional categories/projections xlii, 9, 194–195, 198–200, 204, 253, 206, 257 Functional head 307, 327 Functionality 205, 287–288, 290, 294, 299 Generalized Phrase Structure Grammar (GPSG) 121, 123 Generative capacity 96, 125, 150, 346 Generative linguistics 123, 132, 147 Genetic endowment 293 Goodness-of-fit xxxix, 162, 172 Government Phonology 305, 308–309, 316 Grammar xvi–xvii, xix–xxiv, xxvi, xxxi–xxxii, xxxiv, xxxvi, xxxviii, xxxix, xl, xlii–xliv, xlix, 13, 44, 50, 52, 85, 94–96, 99, 100, 107–109, 114, 117, 120–133, 139, 147–156, 159– 173, 185, 193–195, 201, 205, 206, 219–220, 235, 252–253, 289, 291– 292, 330, 344, 372–373, 386, 397–402 –Axiomatic grammars 128 –Context free grammars (CFGS) xxvi, xxxi, 121, 149–150, 153, 156, 160, 164, 181, 185, 214, 218, 227

–Default Grammar 201 –Dependency grammar xxxi, 282 –Finite state grammar (FSG) xxxi, 94–95, 160, 162, 185, 397 –Generative grammar xix, xxxix, xl, 51, 117, 120–129, 132–133, 162, 263, 291–292, 373, 387 –Intonational grammar xlviii –Phrase Structure Grammar (PSG) 94–95, 162, 185, 397 –Stochastic grammars 128–129 –Strictly Local (SL) grammars 128– 129 –Transformational grammar 121, 132 –Tree grammar 152–153 Grammaticality 115, 148, 394, 396– 397, 402 Grammaticalization 32, 71, 74, 198, 377 Habilitive marker 272 Haiku 126–127 Haplology 277 Head-driven Phrase Structure Grammar (HPSG) 123 Here and now (see also immediacy; see also immediacy of experience principle (IEP)) 202, 205 Hierarchy 218, 240, 316, 347, 353, 359 –Chomsky 95, 220, 227, 398 –Social (in non-human primate societies) 183 –Syntactic 204, 237, 293, 346, 349 –Sub-regular xliii, 220–221, 228, 230 –Prosodic xxii, 302, 321, 327, 332– 335, 345 Holophrase 235 Human agency 286, 288 Hypotaxis 129–130 Iamb 311–313, 316 Idealization 127 Identity requirement 107 Idiomatic expression 48, 105, 275

Subject index If . . . Then . . . Construction 97 I-language 125, 289, 293 Immediacy of experience principle (IEP) (see also here and now) 198, 205 Inadvertitive 270 Inductive Generalization 118–119, 140 Infinitude Claim xxii, xxxviii–xxxiv, 113–133, 139–145, 253 Information structure 35, 45, 270, 303 Inherent grouping 357, 364 Innateness xvi, xl, 162, 172, 188, 288, 294 Integers 119, 123, 142, 145, 180, 372, 395 Intension 125 Intensity 346 Interfaces 292, 343–346, 387 –Sensory-motor xvi, 343 –Syntax-phonology interface 344 –Syntax-prosody interface 344–346, 366 Intermediate phrase 348 Internal vs. External argument xliv, 247–248, 250, 252, 255–256 Inter-translatability 132 Intonation xxiii, xxix, xxxi, xlviii, l, 24–27, 30–31, 37, 39, 195, 301, 330, 333, 335, 346, 398 Intonational Phrase 301–302, 329, 346, 348 Intransitive 18, 100, 248–249, 251, 265, 274, 276, 383 Invention 287–288, 293–294 Islands (see also Subjacency) 196–199 Isomorphy xxiii, xxx, xlvii, l, 303–304, 317, 320–333 Iteration xxiii–xxiv, xxviii, xxxi, xxvii, xliv, xlvii, 33–35, 43–52, 140, 179– 182, 184, 239–240, 347, 356, 357– 360, 365–366, 381 Juxtaposition 10, 13, 131, 188 k-expressions 222–225 k-factors 221–225, 227

411

Language contact 4, 8–10 Left-branching xxvi, xxxv, 43–44, 50, 54, 60, 64, 78, 160 Length of sentences 47, 51, 96–97, 114, 116, 118–119, 123, 127, 148– 149, 242 Lexical bundles 44 Lexical items xix, xx, xxxiv, xxxviii, xliii, 32, 38, 103, 186, 187, 287–294 Lexical syntax 248, 253–259 Lexicalized multiword expressions 44 Lexicon xviii, xliii–xliv, 121, 131, 187– 188, 202, 247–259, 291–294, 346, 385 Likelihood 162–163, 166–171 Linearization 44–45 Linguistic experience 102–103, 108– 109 Listing xxiv, 43, 46, 49 Literacy xxxviii, 85, 108 Loanword 9 Locally Testable stringsets (LT) 222– 223 Locally Testable with Order (LTO) 225–226 Locally Threshold Testable (LTT) 224 Location 38, 266–267 Long distance dependency xxvi, xxviii, xxxii, xxxvii, 94–97, 104–105, 181– 182, 184, 199, 353, 356, 359 Markov model 96 Material anchor 240 Mathematical induction 118–119, 123, 140 Mathematical logic 50, 124, 126 Mathematics 114–115, 118, 287, 393, 395 Memory xxxvii, 51, 63–64, 79, 84, 98– 99, 160, 180–182, 185, 203, 294, 347, 353, 359–360, 372–374, 376–377, 381–386, 396–397 –Working memory 99, 160, 372, 396 Mental verb constructions 7 Merge 186, 194, 196–197, 199, 206, 237, 285–294

412

Subject index

Minimalism xvi, xix, 121, 186, 193, 292, 402 Minor syllable 311, 316 Modality-specificity 364–366 Modeling xxxi, xxxix–xl, l, 63, 69, 96, 113, 115, 119, 123, 129, 140–141, 147–156, 233, 282, 313, 372–373, 387 Monadic Second-Order (MSO) 226 Monolingualism 9 Mora 126–127 Moraic theory of syllable 308 Morphemes xx, 73, 186–188, 287, 302–303, 306, 319–320, 331 –Applicative 38, 250, 265–271 –Causative xlvi, 34–35, 38–39, 251, 264–265, 274–278 –Negative 265, 275 –Nominalizing 18, 20 –Quotative 6, 74 –Reciptrocal 264 –Refactive 272–274 –Reflexive 264 –Relative 264 –Simulative 272–274 –Tense xlvi, 34 Morphological compounds 323–324 Morphology xviii, xx, xxxvi, xli, xlv– xlvii, 13, 17, 34–35, 38–39, 127, 131, 186–188, 263–282, 301, 323–324, 335, 343 Morphotactics xxiii, xxx, 302–303, 317, 333 Move 195, 197–199, 206, 292 Movement xxxviii, xliv, 104, 107, 123, 195, 197–199, 203–204, 206, 236, 292 –Wh-movement xxxviii, 104–105, 107 MSO definable stringsets 226–229 Multiply-add-permute architecture 381–384 Music 182, 184, 186, 304, 365–366 Mutation 196 Mutual belief 144

Narrow syntax 96, 343 Navigation xvii, 182–183, 186 Negation 142, 166, 222, 265, 275 Nerode equivalence 227 Newspaper text 102–104 N-grams 221 Nominalization xxxvi, 18–20, 37, 39, 57, 60, 64, 131 Non-agentive functionality xliv, 287, 294 Non-discreteness 71 Non-finite verb xxxvi, 21, 24, 64–65, 201, 203 Non-finite clause 100, 102, 130, 202 Non-hierarchical 347, 366 Non-recursive structures xvii, xxxiv, xl, l, 8, 11–13, 108, 131, 160–165, 169–173, 205, 353, 358, 386 Number system 108, 117–119, 142, 145, 182, 183, 186, 238–240, 242, 393, 395 Olfaction 386 One-B 223–224, 228, 229 Onset-rhyme structure 305–316 Ontogeny 195 Organs 286–290 Panglossian view 287 Paraphrase 143 Parataxis 11, 130, 132, 196–198, 201 Particle xxxv, xxxvi–xxxvii, 22, 27– 32, 37–38, 71–74, 76, 345 Pausal duration xlviii, 346–348, 359– 360 Pausal phrasing 346–349, 359–366 Pausal segmentation 359, 364 Pause xlviii, 26, 74, 76, 346–349, 359– 366 Peano’s axioms 119 Performance xxxii–xxxiv, xlix–l, 83– 84, 148–149, 154, 160, 170, 372–373, 385, 388, 395–396, 399–403 Peripheral components 343 Perspective-taking 102, 107

Subject index Philology 124 Phonemes 187, 302, 305–307 Phonological Phrase 302, 323, 326– 330, 344 Phonology xv, xviii, xxi, xxix–xxxi, xxxiv, xlvii–xlviii, l, 126–127, 144, 187, 234, 277, 301–335, 343–367, 396, 399 Phonotactic hierarchy 333–334 Phonotactic restrictions 305 Phonotactics xxxi, 127, 302–305, 308, 313, 315, 318, 324, 330, 332–335 Phrasal accentuation xlvii, 305 Phylogeny 195 Pitch xlviii, 24–26, 31, 76, 346, 349, 353, 357, 359, 361–362, 366 Pitch accents 357, 359, 366 Pitch contour 349, 353, 357 Planning 384–386 Plato’s problem 288 Pluperfect 273 Polysynthesis xlvi, 263–264, 281 Population 99, 107–109 Possessive 18–20, 205, 371 Poverty-of-the-stimulus argument 288 Pragmatics 11, 82–83, 127, 188, 278 Precedence 44, 225, 273, 323, 376 Predication 30, 35, 75, 195, 197 Prepositional phrase xxi, xxxv, 43, 50, 57, 60, 107, 114, 164, 218 Prior probability 162–163, 166–171 Procedural knowledge 236 Procedural recursion 180 Productivity 18, 20, 33, 49–50, 55, 60– 61, 64, 96, 103, 108, 120, 153–154, 202–204 Proper classes 144 Propositions 126, 132, 202, 206, 236, 271, 373, 378, 381–384, 387 Propositional operators xlvi, 264–265, 280, 282 Prosodic domain 320–321, 329, 334, 345 Prosodic hierarchy xxii, 302, 321, 327, 332–335

413

Prosodic modalities 365 Prosodic phrase 316, 327–330, 346, 348–349, 353, 356, 360, 365–366 Prosodic segmentation 346, 348, 360 Prosodic segments 353, 357 Prosodic state 353 Prosodic structure xxii, xlvii, 301– 302, 317, 320–335, 344–347, 353, 357–360 Prosodic tree 345, 347 Prosodic Word Group 324–326 Prosodic word 317, 326–332 Prosody xxii, xxxvi–xxxvii, xlvii– xlviii, 27, 30, 39, 75, 195, 301–302, 305, 316–335, 343–367 Proto-coordination 195 Protosyntax 195, 203 Prototype 102, 105 PS-rules 292 Psychology xxxix, 127–129, 285, 287, 372 Pumping lemmas 219 Push down stack 99, 180, 185 Quality criterion 278–279 Quantity criterion 278 Quotative construction xxxvi, 6, 18, 21, 37, 39, 73–74 Quoted speech 6, 131 Random generation 122 Rational principles xl, 159 Reciprocalization 264, 270 Recursability xlvi, 278, 280–281 Recursion xxxv, 3, 45, 49, 52–55, 70, 106, 114, 119–121, 124, 126–127, 130, 132–133, 140, 150–151, 179– 182, 289–294, 343–349, 353, 356, 358–360, 363–367, 371 –Adjunctive 317, 321, 333 –Clausal xxxv, 52–55, 70, 106 –Computational model of 359 –Direct 35 –Embedded 347–348, 362, 366 –Multiple tail-recursion 64

414

Subject index

Recursion (cont.) –Nested embedding 94 –Nested recursion 50, 63, 180–182, 184–185, 347, 359–360, 365 –In argument structure 253 –Noun phrase recursion 17, 21, 3335 –Indirect 34 –In intonation 301 –In morphology 34–35, 263–281 –In phonology 301 –In syntax 49, 344, 349, 359 –Prosodic recursion 344–347, 353, 357, 365–367 –Subjunctive 321 –Tail recursion 64, 101, 180–185, 347, 358, 366 Recursive Merge xliv, xlviii, 286–289, 293 Recursive prosodic structure 320, 327– 328, 358–359 Recursive prosodic word 322 Recursive unidirectional change 365 Reductio ab absurdum 140 Redundancy problem 291–292 Redundancy 205 Reduplication 48 Referential specification 107 Relative clause 11, 12, 107 Repetition 48–49 Reportative 6 Representational recursion 179 Resources 99 Reversive 272–274 Rhyme 311 Rhyming 309, 312 Rhythm 315 Rhythmic organisation 359, 366 Rhythmic phrasing 359–360 Rhythmic structures 304 Rhythmical distribution of pitch accents 359, 366 Right-branching 50, 78 Routinization xxxvii, 39, 108 Rules 120, 126, 128, 253, 285, 291– 293, 304–305, 331, 332–334

Scope ambiguities 345 Scope, of a‰xes 265, 272–273 Second articulation 301, 333, 335 Second degree intentionality 303 Segment length 363 Selection 98–99 Selective pressure 107 Semantic ambiguities 345 Semantic cohesion 10 Semantics xxiii, xxx–xxxi, xlviii–xlix, l, 83, 85, 95, 127, 132, 181–183, 187, 202, 247, 250, 251, 268, 269, 270, 272, 273, 276, 278, 279–280, 281, 292, 303–304, 318, 343, 344–345, 371–373, 375–376, 382, 384–187, 394, 396 Sentence 71, 74–76, 148–149, 153– 154, 159–172, 186–187, 224, 235, 292–293, 309, 372, 382, 394 Sequential arrangement 44–46 Sets 144 ‘‘shadow rules’’ 164, 170, 172 Shared attention 102 Sign language 289 Simplicity xxxix, 161–162, 166, 168, 172 Size-increasing operations 140–143, 145 Small clause (SC) xlii, 12, 193–206, 257 Social cognition 182–183, 186 Sociobiology 287 Sociolinguistics 124 Some-B 222–223, 228–229 Specialization 203, 205 Spoken language xxxiii, xxxv, 11, 13, 43, 53, 55, 59–60, 70, 71, 74, 77, 84– 85, 372, 396 S-selection 293 Stacking 60 Starlings xvii, 94, 107 Strict Layer Hypothesis (SLH) 302, 323, 345–347 Strictly k-local definition 221–222 Strictly Local stringsets (SL) 217, 221– 222

Subject index

415

Strong generative capacity 150 Structural Analogy 302, 330 Structural positions 359–360 Structure-preservingness 292 Subcategorization frames 291 Subitizing 238–239 Subjacency xliii, 194, 196–199, 387 Subjectivity 106 Subjunction xlii, 315–317, 319 Submodification 60 Subordinating conjunctions 9, 51, 53 Subordination xxxvi, 5–6, 9–11, 97– 100, 117, 127, 129, 130–133, 166, 193–200, 204–206, 309, 360 Succession xxiv, 43, 46, 49 Successor function 49, 119, 183, 238, 240 Su‰x substitution closure 222 Superfoot 312 Syllable heads 306–307, 330 Syllable structure xlvii, 305–316 Symbionts 290 Syndetic coordination 46–48, 130–131 Syntactic category 100, 154, 166–168, 372 Syntactic phrase 304–305, 309, 327, 330, 346, 348, 360 Syntax xx, xxiii–xxiv, xxxi, xxxiii– xxxvi, xlii–xliii, xliv, xlvii, xlix, 3–4, 8, 11, 13, 17, 35, 37, 43–63, 73–85, 96, 113, 115, 118, 121, 123–124, 127–128, 130–133, 156, 170, 186– 188, 193–206, 234–236, 247–248, 250, 258–259, 263–264, 267, 282, 289–292, 301, 304–305, 309, 312, 322, 327, 330, 333, 335, 343–345, 366, 371, 384, 386, 388, 393, 395– 397, 401–402

Tense xlii, xlvi, 34, 187, 194, 195, 201– 205, 264, 273–274, 279–280, 374, 383 Tense phrase (TP) 200, 203–204 Termination condition 51 That-omission 11–12 Theory of mind xxiii–xxiv, xlix, 182– 183, 186, 241, 393, 395, 401–402 Thesis of Radical Autonomy 287 Tinkering (evolutionary) 199, 294 Token frequency 102 Tone xlvii–xlviii, 346–366 –Tonal continuity xlvii–xlviii, 347, 352–359, 365–366 –Tonal parameters 353 –Tonal phrasing xlvii, 346, 349, 360–363, 365 –Tonal properties 353, 359 –Tonal representation 349, 361 –Tonal segmentation 363 –Tonal space 353, 356–358, 362, 365–366 –Tonal variation xlviii, 361 Transducer 122, 373 Transduction xlix, 372–374, 381–384, 386 Transformations 122, 123, 127, 292, 333 Transitive clause 100 Transitivity 18, 248–251, 254, 265– 266, 268, 274–276, 383 Trees xix, 120–121, 150–153, 164, 384 Trochee 311–313, 316 True recursion xxxvii, 99, 103–104, 107–108, 386 Two argument restriction xliv, 248, 258 Type-frequency 103 Type-token 103

Technology 288–290, 293 Template xxxviii, 105–106, 187, 268, 269, 272 Temporal relation 98, 349 Temporal segmentation 364 Temporal structure 362

Unaccusative 202, 203, 254 Unbalanced recursive prosodic structure 319–326, 329–330, 332–335 Unboundedness xxi, xxxix, 97, 114, 117, 126, 131, 154, 160, 227, 318, 371–372, 374

416

Subject index

Undecidability 121 Uniqueness xlviii, 185 Uniqueness of Selection Hypothesis (USH) 255 Universals xxxviii, xliv, xlix, 17, 113, 116, 132–133, 151, 248, 271–372, 387–388 Upstep 349, 353, 356–358, 366 Usage xxxviii, 85, 98–100, 104–106, 109, 234 Utterance xxxiv, xlii, 6, 95, 114, 122, 163, 235, 333–334, 347, 349, 351– 353, 357–360, 363, 386–387, 394

Vector arithmetic 371, 374 Verb serialization 47, 166 Verbal shadowing 402 Vision 182, 186 Visual grouping 360, 364–365

Valency 290–291 Valency-changing operations xliv, 249

Zero 108

Weak generative capacity 125, 150 Whale song 184 Written language xxxiv–xxxvi, 11–12, 43, 48, 53, 55, 58, 63–64, 74, 85, 102, 108, 289 X-bar Theory xliii, 123, 291–292, 402

Language index Abaza 264, 268 Abkhaz 264, 270–271 Adyghe xlvi, 250, 263–282 Akkadian 131, 198 Alamblak 249 Amazonian languages xvii, 3, 130– 131, 159, 401 Australian aboriginal languages 130 Bukusu 249 Cariban languages 131 Central Alaskan Yup’ik xxxvi, 17–20, 22–23, 33–39 Central Siberian Yupik 263 Chinese 75 Creek 250–251 Danish 53 Dutch 97–98, 100–101, 103–105, 287 Dyirbal 130, 198 English xxviii, xl, xlii, xliv, xlv-xlvi, 6, 7–8, 11–12, 53, 55, 68, 71, 96–98, 100, 105, 115–119, 123, 128–129, 140, 142, 198, 202, 234, 239, 247, 251–252, 311–318, 320–326, 331, 351, 354, 374, 383, 386, 394, 400 Finnish xxxv, 11, 53, 59–62, 69–81, 84 Georgian 251 German 53, 55–57, 59, 81, 219 Greek 53, 58 Hakha Lai 248

Hixkarya´na 131 Hungarian 345, 348–350, 354, 356– 359, 365 Indo-European languages 70, 130 Iroquoian family 38 Japanese xxxv, 11, 69–79, 81–84, 126 Kabardian 264, 268 Khalkha xxxvi, 20–23, 33–39 Latin 53 Mohawk 23–39 Mongolian 20–23, 33–39 Native-american 198 Oromo 275 Pajonal campa 250 Piraha˜ xvii, xxiii, xxxvi, xl, 3–13, 44, 70, 72, 130–131, 159–160, 172, 188, 198, 205, 234, 241–242, 255, 371, 386, 401 Portuguese xxxvi, 4, 8–11 Proto-Uralic 130 Sanskrit 50 Serbian 198, 202–205 Sesotho 249 Swedish 47–49, 53, 61 Tamil 50 Tariana 251 Tsez 251 Ubykh 264 Wargamay 130 Yima 249

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