RECURSION IS AN ARTIFACT

 

0.  Introduction

    Several years ago, there appeared in the prestigious journal Science, which does not normally pay much attention to language, an article co-authored by Marc Hauser, Noam Chomsky and Tecumseh Fitch somewhat portentously entitled “The Faculty of Language: What Is It, Who Has It, and How Did It Evolve?”  (Hauser, Chomsky & Fitch 2002, henceforth HCF) The article was placed in that section of the journal titled “Science’s Compass,” and it was indeed designed to give directions to us poor benighted folks who (unlike the authors of the article) had actually been laboring in the quagmire of language evolution studies for a number of years.  The paper sought to derive the computational component of language (that is, what gives language its complexity) from a single process: recursion.

    The paper divided language into two parts: FLN (narrow faculty of language) and FLB (broad faculty of language)

•         FLB = all the parts of language either not unique to humans or human but not uniquely involved in language

•         FLN = all the parts of of language uniquely human and uniquely linguistic

The working hypothesis:of the paper was that the sole content of FLN is recursion.  Recursion, in turn, might well prove to be the exaptation of a faculty found in other species but used by them for non-linguistic purposes. Number, navigation, and social interaction were some of the functions suggested.

 
1. Some background

     In order to understand where HCF is coming from, some background information is necessary.

     Chomsky had for years avoided committing himself on language evolution.  During the 1990s he saw the field expanding, making him irrelevant.  The logic of minimalism forced him to become a player, but he needed leverage from biology to achieve a commanding position via the pages of Science.

     Prior to 2002, he and Hauser had been on opposite sides of most issues.  Hauser believed that language was on a continuum with animal communication and had emerged through natural selection.  Chomsky believed language was totally distinct from animal communication and did not believe that language had been specifically selected for.

     HCF represented a strategic compromise.  C yielded to H on most aspects of language but preserved what was most vital to him: a unique central process for syntax, one that had not been specifically selected for as a component of language, thus preserving intact his claim of uniqueness and independence from natural selection over a more limited domain.

 
2. Defining recursion

      But what exactly is recursion?  More than one commentator has expressed concern over the vagueness of HCF with regard to definitions.  The following are the clearest indications the paper offers:

     “..[Recursion] provid[es] the capacity to generate an infinite range of expressions from a finite set of elements…”

    “All approaches agree that a core property of FLN is recursion, attributed to narrow syntax in the conception just outlined. FLN takes a finite set of elements and yields a potentially infinite array of discrete expressions.”

     This differs from the usual definitions of recursion within a linguistic sphere of reference.  Three typical examples follow.

       “In fact, we can embed one sentence inside another again and again without limit, if we are so inclined! This property of syntactic rules is known as recursion.” (Phillips, n.d.)

      “In linguistics, this term refers to the fact that a sentence or phrase can contain (embed) another sentence or phrase -- much like a box within a box, or a picture of someone holding a picture. Common recursive structures include (1) subordinate clauses; e.g., He said that she left, where she left is itself a sentence; (2) relative clauses; e.g., She's the one who took the book.” (Levy 2007)

      “While iteration simply involves repeating an action or object an arbitrary number of times, recursion involves embedding the action or object within another instance of itself.”  (Parker 2007)

     A feature common to all these definitions (and many others in the literature) is the insertion of something within another thing of the same kind.  The resulting constructions are, of course, the major source of complexity in syntax.

     Publication of HCF gave rise to two pointless debates, which I will very briefly summarize.

 
3a.  First pointless debate

       The first debate, carried out in the pages of Cognition (Pinker and Jackendoff 2004,  Fitch, Hauser and Chomsky 2005, Jackendoff and Pinker 2005), limited itself to purely definitional issues: what were the proper contents of FLN and FLB.  PJ argued that many more things besides recursion should go into FLN; HCF argued that their limitation of FLN to recursion was a hypothesis not an empirical claim, and the burden of proof lay with those who would extend FLN to include other aspects of language, something they claimed PJ had failed to do.  Accordingly the debate was purely definitional; so issues of substance were involved.

 
3b.  Second pointless debate

      The second debate, triggered by a sympathetic article in the New Yorker (Colapinto 2007) involved Dan Everett (Everett 2005, 2007) and a number of generativists (see e.g. Nevins, Pesetsky and Rodriguez 2007).  Everett. a longtime student of the Piraha language, claimed that Piraha had no recursion, and that therefore recursion could not form part of universal grammar (and maybe, if FLN was just recursion, then there was NO universal grammar.)  His opponents insisted that he had misanalysed his data and that Piraha did indeed have recursion.  Both sides entirely missed the point that while a biological capacity enables behaviors, it dos not enforce them.  The absence of recursion from Piraha grammar says no more about universal grammar than the absence of prenasalized consonants or verb serialization from English grammar.

     In neither debate did anyone question the status of recursion as central to FLN, let alone whether or not recursion really was a language process.

 
4.  The birth of recursion in premature analyses

      So where does the idea of recursion come from?  The idea that syntax is a recursive process originated in early forms of generative grammar, but quickly came to be accepted by everyone.  It seemed so self-evident that it has never yet, to my knowledge, been questioned.

     The idea arose initially from the analysis in Chomsky (1957).  At this time, his theory was known as “Transformational-generative grammar” and since transformations formed the most novel (and to many the most salient) aspect of it, it was widely referred to as “Transformational grammar” tout court.  The grammar however was divided into two components, phrase structure and transformations.  Phrase-structures were supplied only for simple sentences, leaving complex sentences to be built out of these by means of the transformational component.  Phrase structures were derived from a series of “re-write rules”, which produced strings of abstract symbols consisting of category labels, S(entence), N(oun) P(hrase). V(erb) P(hrase), N(oun), V(erb). P(reposition) etc.  Rewrite rules included:

.                 S -->  NP VP

                  NP -->  (Det) N

                  VP -->  V (NP) (PP)

                  PP -->  P NP

Strings that provided descriptions of simple sentences then served as input to the transformational component.

     However, for heuristic purposes the operations were frequently described as if they operated on real (surface structure) sentences.  Thus “The man you saw yesterday is Harry’s brother” might be described as being produced by insertion of “You saw the man yesterday” into “The man is Harry’s brother” to yield “The man [you saw (the man) yesterday] is Harry’s brother” with subsequent deletion of the repeated “the man”.

     Thus the Syntactic Structures model involved recursion only in the transformational component, when one prefabricated S was inserted in another prefabricated S.

      However, this picture was changed radically in Chomsky (1965).  The new model introduced “generalized phrase markers”; so that complex sentences were now generated directly by means of expanded rewrite rules.  Consequently, recursion was no longer seen as part of the transformational component but formed a core element of phrase structure:

                    S -->  NP  VP

                    NP -->  (Det) N  (PP) (S)

                    VP -->  V  (NP) (PP) (S)

(The second rule above generates relative clauses, the third generates complement clauses—in both cases referred to as “embedded” sentences.)  Consequently “the man you saw yesterday is Harry’s brother” would be generated from the generalized phrase-marker _S[ _NP[Det N _S[ NP  VP]]  _VP[V  _NP[ N _NP[N]]]] which featured one case of S within S  and two cases of NP within NP.

      Accordingly both S-within-S and NP-within-NP seemed to constitute clear cases of recursion.  Note, however. that recursion is now deduced from a post-hoc, static description and no longer assumed to form part of any sentence-building process.   This might already make recursion look dubious as a process that humans had to execute in order to evolve language. But at this point, of course, a quarter century had to elapse before linguists could even bring themselves to think about evolution.

 
5.  Recursion lingers on while the theory marches on

      Subsequent changes would make generative theory differ even more radically from its beginnings.  Transformations continued to be reduced in number, being replaced by a small number of interacting principles that achieved similar results at less cost, until finally there was only one (“Move alpha”).  With the arrival of the Minimalist Program, the deep-structure/surface-structure dichotomy gave way to a single structural level with two interfaces, the phonological and the semantic (“logical form”).  Processes were reduced to two (“Move” and “Merge”, with attempts to reduce the former to a special case of the latter).  “Merge” “takes a pair of syntactic objects and replaces them by a new combined syntactic object” (Chomsky 1995, 226).  Whether or not any two such objects can be merged depended on “feature-checking” (determining whether properties and dependencies of objects to be merged matched one another).

     Merge seems not to have been devised as a description of how sentences are actually produced, but it could serve as such; the process of linking words with one another successively is something that a primate brain once equipped with a large lexicon should be able to do with little change beyond some additional wiring. The process is derivational not representational: that is to say it builds structures from scratch, bottom up, rather than starting with a completed string of category labels.  It has no preconceived structure: the complex structures of X-bar theory, projecting triple layers of X, X-bar, XP. is abandoned.  Its trees consist exclusively of binary branching: ternary branching is excluded, since nodes can have only one sister, and non-branching nodes are excluded because they cannot, by definition, result from applications of Merge.

 
6.  Deriving complexity via Merge

      Accordingly, let us derive “The man you saw yesterday is Harry’s brother” via Merge:

        saw + e -->  [saw  e]                     Harry’s + brother à-->  [Harry’s brother]   

      (e represents the empty category to be interpreted as co-referential with “man”)

        [saw e] + yesterday -->  [[saw e] yesterday]

         is + [Harry’s brother]  -->  [is [Harry’s brother]]

         you +  [[saw e] yesterday]  -->  [you [[ saw e] yesterday]]

       man + [you [[ saw e] yesterday]]  -->  [man [you [[ saw e] yesterday]]]

         The + [man [you [[ saw e] yesterday]]] -->

                              [the [man [you [[ saw e] yesterday]]]]

         [the [man [you [[ saw e] yesterday]]]] + [is [Harry’s brother]] -->

         [[the [man [you [[ saw e] yesterday]]]]] [is [Harry’s brother]]]

Where’s the recursion?  We have constructed the sentence by means, not of a recursive, but of an iterative procedure, consisting of repeated applications of an identical process.

     What is true for relative clauses is equally true for complement ckauses:

 “Bill thinks that Mary said that John liked her.”

         liked +  her -->  [liked her]

         John + [liked her] -->  [John + [liked her]]

         that +  [John + [liked her]] --> [that [John [liked her]]]

         said +  [that [John [liked her]]]  --> [said [that [John [liked her]]]]

         Mary + [said [that [John [liked her]]]] -->

                                    [Mary [said [that [John [liked her]]]]]

         that  +  [Mary [said [that [John [liked her]]]]] -->

                      [that  +  [Mary [said [that [John [liked her]]]]]]

         thinks  + [that [Mary [said [that [John [liked her]]]]] -->

                      [thinks [that [Mary [said [that [John [liked her]]]]]]]

         Bill + [thinks [that [Mary [said [that [John [liked her]]]]]]  -->

              [Bill [thinks [that [Mary [said [that [John [liked her]]]]]]]]

 Again there is no case of recursion as it is normally defined

      The irony is that Chomsky is the sole person responsible both for the appearance and disappearance of recursion.  His 1957 analysis, created the notion that syntax required recursion.  Hs 1995 analysis removed the necessity for assuming recursion. So how is it that Chomsky in HCF is still proposing recursion as the central, perhaps sole content of FLN?

 

7.  Recursion versus iteration

        Let’s look again at the definition of recursion in HCF  

a)     “..[Recursion] provid(es) the capacity to generate an infinite range of expressions from a finite set of elements…”

b)    “All approaches agree that a core property of FLN is recursion, attributed to narrow syntax in the conception just outlined. FLN takes a finite set of elements and yields a potentially infinite array of discrete expressions.”

     It’s worth noting that both definitions avoid any reference to the insertion of syntactic objects into other syntactic objects of the same class.  And, as we have seen, Merge is in fact an iterative not a recursive process.  Why didn’t HCF bite the bullet and replace “recursion” with “iteration”?

     I think the reason can only be that iteration alone cannot generate “infinite arrays of discrete expressions”.  Iteration of the numbers 1-9 produces no “discrete expressions’ but just a string of unrelated numbers (387964421765988…) Only an additional process coupled with iteration can do this.  If we add multiplication to iteration, we can indeed generate an “infinite array of finite descriptions”

      5 x 7 = 35  35 X 2 = 70  2 x 9 = 18  18 x 70 = 1360  9 X 7 = 54…..

And so on, ad infinitum. 

     What process could one add to iteration to produce such an array in language?

     The answer lies in the difference between words and numbers. Numbers have no dependencies.  Each number (like an animal call, incidentally) is complete in itself and has no special relations, negative or positive, with any other number.  Words, to the contrary, have dependencies.  If I utter the word “leopard” in isolation, with no expressive intonation, you would know that I was making some kind of reference to an African animal, but you would not know if I was warning you about a leopard, or asking if you had seen one, or denying that there were any around, or merely listing major predators.  “Leopard” has to have other words with it if it is to mean anything significant.  There has, probably, to be a verb of which it is subject or object.  But it cannot be the subject of just any verb; it can be subject of “run” or “kill”, but not of “sing’ or “rust” or “dissolve”.    In turn, if we started with “dissolve”, its subject could not be “leopard” or “clock”; it could be “clouds” but not “cloud”, since “dissolve” does not agree with singular nouns in number.  Thus the dependencies of words result from their properties, and those properties may be semantic, categorial or grammatical (most times, all three).  Indeed, as shown by the feature-checking process in the minimalist program, the iterative procedure in Merge has to proceed along with the process of satisfying the requirements of the various words that are merged: (e.g. liked = Vtrans = requires object; her = 3rd pers. Fem. Sing. Acc. = possible object; liked her = predicate requiring subject; Mary = proper noun, no case = possible subject, and so on.) 

 
8.  Why Chomsky can’t jettison recursion

      So why didn’t HCF simply say that DLN consisted of iteration plus the satisfaction of lexical requirements?

     Because iteration, unlike recursion, cannot be described as a process required only by language.  Iteration is a process that lies within the capacity of a wide range of species.  In consequence, either (a) FLN would be void or (b) it would consist solely of a lexicon and its requirements.  However, Chomsky since the beginning of his career had been wholly committed to the idea that the central part of language is syntax.  His compromise with Hauser would not have worked if he had been forced to abandon the centrality of syntax.  To preserve that, FLN had to be retained (thus avoiding (a)) and the content of FLN had to be syntactic not lexical (thus avoiding (b)).  These goals could be achieved only by appealing to a process that was almost universally supposed to operate in syntax, recursion, even though the most recent developments in Chomsky’s own theory showed that the generation of even the most complex sentences did not require it.

     A fall-back position might seek to equate recursion with the Merge process.  The definition of recursion in HCF seems almost designed to make such a move possible.  It might be claimed that since FLN “takes a finite set of elements and yields a potentially infinite array of discrete expressions”, Merge alone satisfies this definition and therefore must be recursive.  But any such attempt would simply remove any real content from the term ‘recursion’, as well as obliterating the distinction between iteration and recursion.. 

 
9. How (and why) complexity evolved

      A more rational response would be to adopt an altogether different model of language evolution.  Such a model would claim that, given the kind of lexicon typical of any human language, a purely iterative process that fulfilled the requirements of that lexicon would suffice for the development of structure to whatever level of complexity the language might require.  A language might, for reasons of its own, develop only a very low level of complexity, as has been claimed for Piraha, but essentially similar mechanisms would be in play, and nothing in language itself would preclude developing higher levels.

     The apparent fitting of one structural element (NP or S) inside another of the same type is simply epiphenomenal, arising from the fact that (other than those imposed by individual lexical items) there are absolutely no restrictions on iterative process that generates sentences, which is also undetermined by prior applications of that process.

     Goes this mean that there is no unique biological basis for language, no universal grammar?  Certainly not.  Following Deacon (1997), we can assert that symbolic units are unique to humans and that aspects of the lexicon are genuine universals.  After all, the theta-grids of verbs appear to be universal; we know that if we meet a verb in some hitherto unknown language that translates as “sleep”, it will take a single argument, while one that translates as “crush” will take two and one that translates as “tell” will take three.  Other things that do not appear to require learning include the rules that determine the reference of empty categories; indeed, since these have no physically-perceptible expression, it is unclear how, even in principle, they could ever be learned. And we have as supporting evidence the fact that no other species can acquire a human language.

      Clearly some kind of universal grammar is required for the production of complex sentences.  But there is no real evidence that any truly recursive process need be included in that grammar.  Rather than the unique content of FLN, recursion in language appears to be no more than an artifact of analysis.

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