Friday, September 28, 2012

Why this blog?


This blog is the direct result of an article by Tom Bartlett in the May 12, 2012 issue of the Chronicle of Higher Education. The article reports on a “debate” pitting Chomsky (“the discipline’s long-reigning king”) against Dan Everett (“the former missionary” and “true-blooded Chomskyan” whose belief in God and Chomsky “had melted away”). Everett’s claim is that Pirahã (an indigenous language spoken in Brazil) fails to display recursion and that this conclusively demonstrates that Chomsky’s conception of Universal Grammar (in which recursion is the defining property) is wrong.  Despite the fevered prose (Chomsky coverage is almost always breathless) it was pretty clear to me that given Everett’s reported views there could be no “debate” for the simple reason that Everett’s apparent understanding of ‘Universal Grammar’ had nothing to do with Chomsky’s (I contributed some comments on the website of the article to this effect under ‘nhornste’).  The “debate” was based on a misunderstanding and so a simple equivocation.  The article was apparently widely read and so a success for the Chronicle,  (a Chomsky take-down always makes for “good press”) but it had virtually no substance.

It did, however, have a consequence. The “debate” led me to appreciate how little linguistic outsiders (and even practitioners) know about the foundations and results of the Generative Enterprise initiated by Chomsky in the mid 1950s.  This blog is an attempt to rectify this. It will partly be a labor of hate; aimed squarely at the myriad distortions and misunderstandings about the generative enterprise initiated by Chomsky in the mid 1950s.  There is a common view, expressed in the Chronicle article, that Chomsky’s basic views about the nature of Universal Grammar are hard to pin down and that he is evasive (and maybe slightly dishonest) when asked to specify what he means by Universal Grammar (henceforth I’ll stick to the shorter ‘UG’ for ‘Universal Grammar’).  This is poodle poop!

The basic idea is simple and has not changed: Just as fish are built to swim and birds to fly humans are build to talk. Call the faculty responsible for this ability ‘the Faculty of Language,’ (FL for short).  The aim of the generative enterprise is to describe the fine structure of FL. The name we give to the proposed structure is ‘Universal Grammar’; ‘universal’ because it is intended to describe the capacity that all humans have and ‘grammar’ because grammars are compact ways of describing the words, morphemes, phrases, and sentences of a language. Over the years Chomsky and colleagues have made various proposals concerning the structure of UG.  It is not a daring hypothesis to propose that natural language grammars are recursive (it follows from the easily observed fact that there is no real upper bound on the size of a sentence) and so UG must allow for recursive grammars.  The interesting question is not whether there is recursion but the specific nature of the recursion that natural language grammars have. Studying the properties of natural language grammars should, we hope, shed light on how UG is constructed. So what’s UG?  It is the general recipe in FL that humans have to build grammars of natural languages.  What features does it have? Well, that is, as they say, an empirical question which this blog will discuss.  But reader be warned: as the central object of study within Chomskyan linguistics is the structure of UG and as the field is very active the details of the description change, or at least may appear to change to the untutored eye. I personally think that many of the central findings are pretty secure and that later theories have been conservative in that they have preserved the findings of earlier theories.  We intend to discuss some of this in the future.

The perspicuous reader will have noted the ‘we’ in the last sentence. I am one of many that will be writing here.  David Pesetsky is a co-conspirator. I have asked several others to contribute as well.  The contributors disagree on many issues.  However we all believe that there are no major empirical discoveries that have invalidated the Generative approach in linguistics initiated by Chomsky, no serious methodological failings concerning the practice of linguists and no conceptual incoherence in the leading assumptions upon which this practice is founded.  The details are all up for grabs. The basic perspective has more than proven its worth. 

Before ending some may be wondering about the equivocation that vitiated the “debate” in the Chronicle.  Well it’s this: Chomsky’s claim is that the distinctive characteristic of UG is that it contains recursion.  This is the defining property of FL, which, recall, is the human capacity to acquire language.  This does not imply that every human language grammar deploys recursion. It does imply that every human can learn a grammar that is recursive. The Pirahã may not deploy recursion when speaking Pirahã (though I should add here that Everett’s claim is likely false (c.f. Pirahã Exceptionality: A Reassessment in Language 2009:355-204) but Pirahã children have no trouble learning Brazilian Portuguese (an undisputedly recursive language) and so there is no evidence that their UGs are any different from anyone else’s.  Everett (and the Chronicle) interpreted UG to mean that every language must have recursive structures, while what Chomsky means is that recursion is a property of FL.  Whether Pirahã has recursion or not (and to repeat, it looks like it does) has no bearing on whether Pirahã speakers’ UGs have it or not.  This was the equivocation and this is why the “debate” was pointless.


  1. A great initiative, please keep this up!

  2. Oh dear, I've just discovered that a philosopher colleague who is an excellent though non-native speaker of English was afraid that the words "labor of hate" and "co-conspirator" were meant seriously, that is hostile-ly. I've tried to reassure her. But she was also concerned that if students and outsiders read this they'd get a very negative view of our field. (She already had the idea that "battles" among linguists are not pretty.) I have no way of knowing. I guess this is always a danger with any sort of satirical language in a purely written medium.
    But you certainly can't be asked to totally 'bleach' your language. I thought the closing "poodle poop" pretty unambiguously marks the style as good-humored. So I'll keep hoping that her fears are unfounded.

  3. Tongue firmly in cheek, check. Hopefully your friend will ahve read some of the posts and seen that we have (so far) been pretty low key. I confess to being surprised that a PHILOSOPHER would be worried about the level of polemic. I grew up in that world and kid gloves it ain't. That said, I am aiming for non rancorous mix-ups where views will be clearly aired. Humor is highly valued. Hope your friend keeps reading as there will be stuff there of interest, especially by Pietroski. Btw, thx again for the lectures. They were a real hit and I for one learned a lot.

  4. I am the philosopher who talked to Barbara Partee and I am really glad to learn that terms like ‘labor of hate’ do not imply in any way, shape or form, that people who disagree with Chomsky are hated. You invited me to look around. I did, and I found the tour informative. You say: “Humor is highly valued”. I sense you and I have a very different sense of humour. But, possibly you believe everyone (including your victims) is delighted by your jokes. So it may be informative to hold up a mirror and demonstrate how it is to be on the receiving end of your kind of condescending humor. To do this I borrow some of your strategies, like taking things you said out of context or using brutal analogies. Since I am a novice at this game my results will be a faint shadow of your masterpieces. I had written one longer post but was informed that I am only allowed 4096 characters, so I had to split it up in a few smaller sections. You will find them under several of your blogs.

    You make some interesting claims. “Everyone believes that humans have a Universal Grammar (UG)”. I don’t remember you ever asked me – so how do you know I believe this? Quite a few people put in print that they don’t believe it (e.g., Deacon, 1997; Sampson, 1999; Tomasello, 2009; Everett, 2012; Lieberman, 2012). Do you think beliefs are innate cognitive structures that we have whether we know it or not? As philosopher and linguist you ought to know about the troubles of belief attribution and how easy it is to disprove categorical claims. All it takes one person who does not believe humans have a UG to prove you wrong. So never mind the experts cited above; how about pre-linguistic infants, members of indigenous tribes, high-school drop outs who have never heard of UG? Clearly, you could not have meant what you wrote but were joking.

    You write about people who claim “that Chomsky’s basic views about the nature of Universal Grammar are hard to pin down and that he is evasive (and maybe slightly dishonest) when asked to specify what he means by Universal Grammar”. And assure us: “This is poodle poop!” You do tell us who these poodle poopers are. But you are of course right: saying Chomsky is SLIGHTLY dishonest fails to recognize one of his most remarkable achievements. He has taken ‘misleading his audience and distorting his opponent’s view’ to previously unknown levels. The details are well documented in works we are both familiar with (e.g., Levine & Postal, 2004,; Postal, 2004, chapter 11; Postal, 2009,

    The lack of specificity accusation is similarly misguided. Like with the statues of Daedalus, it is not merely difficult but impossible to ‘pin down’ Universal Grammar. It is the product of Chomsky’s exceptionally active imagination, and as gifted artisan he can change it when no one is looking. He does not owe us any explanation why he continually alters some or all of its imaginary properties. People who expect otherwise just want to play a different game – the game called science.

    In case you feel I am unfair, may I remind you how you characterize opponents: their work shows “levels of silliness, stupidity and obtuseness [that are] left to plumb”, they develop “inane connectionist models”, “provide no theory beyond analogy combined with vague pragmatic principles”. And if they belong in the most terrible category of all - ‘empiricists’, your language becomes even more explicit: “This is classical empiricist dogma … “a form of insanity,” a species of “low input, high throughput, no output science.”
    Is it really surprising that I thought your blog is a labor of hate? How would you react if someone would use the above terms to refer to members of a minority or women? Outraged? Why then is it “funny” to use them for researchers who happen to disagree with your view?

  5. You are right, we do not share a sense of humor. However, this said:
    Everyone thinks that there is something special about humans that allows them to learn languages in the way they do: reflexively, unsupervised, quickly etc. The debate is what is special not whether there is something special. So in this sense, the one I made clear (thank god philosophers are still instilled with a principle of charity NOT!) there is no debate.

    The reason there is none is simple: it is a virtual observable that humans are to language what fish are to swimming, birds to flying and spiders to web design. It's what they do. It's part to human biological endowment. Again, what specifically is up for discussion. That there is something special here is not, at least in my opinion and ALL the people you site including Tomasello, Sampson, Everett etc. They disagree about what's special (bigger brain, capacity to imitate, whatever) not that there is something special.

    I disagree with Postal, strongly. And I stand by my view that his views are pretty easy to discern. Indeed, I set a pretty low bar: my view is that if I can understand it anyone can.

    The quote is not mine and it did not relate to empiricism but to a version of statistical investigation that has a nice home in an empiricist world view. There are more sophisticated versions of empiricism, but this is not one of them. The quote is from Brenner, though I completely agree.

    I have always thought that a (the) principle job of philosophy was as general purpose critic. You clearly disagree and find polemic distasteful. I don't. I love it and find that more often than not it clarifies matters. Clearly Tomasello, Postal, Everett, Sampson etc agree for they are not known for their kid glove treatment of what they don't like. It seems to me that pin this discussion your sensibilities are the outliers. I try not to take myself too seriously. You?

  6. Not seriously enough to suspect that the disappearance of the reply I had posted was some kind of censorship. There is no point to retype everything; just one question about your strong disagreement with Postal whom I had cited as someone who has documented Chomsky's lack of academic integrity. This passage seems quite convincing to me:

    Chomsky's 1957 claim that every transitive-looking clause permitted a passive analog was no mere mistake; for he was perfectly aware of its falsehood and had himself provided counterexamples in his unpublished 1955 study The Logical Structure of Linguistic Theory (finally published in 1975). There he cited e.g. this weighs three pounds/he got his punishment as "instances of actives with no corresponding passive".* Hence despite knowing at least two years before publication of Syntactic Structures that his claim about the passive rule was untrue, he produced an entirely unhedged and unrestricted 1957 account without reference to the earlier passage. That is, Chomsky knowingly published as part of a work introducing to the general public his conception of transformational grammar a false assertion about English syntax. [Levine&Postal, 2004] -

    What is your reason for disagreement? Have Levine & Postal omitted crucial evidence? If so what is this evidence?

    Should this post disappear as well i will take this as admission that there is no counter evidence and that Levine & Postal are correct.

  7. There are different standards depending on the audience. There is nothing wrong in smoothing the discussion to make a relevant point when addressing neophytes. Postal has made many incorrect claims in the literature, as Levine himself has pointed out in discussing Postal's discussion of parasitic gaps. Big deal. Charges of intellectual dishonesty are very serious and should not be made frivolously. Postal is all too prone to make them on the flimsiest grounds. Why is an issue for him and his shrink, not for me. What I do know is that Chomsky does not intentionally mislead. Indeed he is very generous in my experience, more so than he needs to be. Some might feel that he has overlooked their important contribution. My response is "suck it up. You are a grown up." This is the last comment I will make on this topic for of all the things you have harped on I find this to simply be odious.

    Last point. I did NOT delete your previous post. I notified you that it had not appeared when I went to check and reply.

  8. I am sorry to report that i did not receive your notification. Your position on 'the topic' has become perfectly clear and does not require any further elaboration. For the record I have never questioned Chomsky's generosity nor am I in any position to do so.

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  10. Pointing out that Pirahã children should have no trouble in learning Portuguese is a good way of putting the debate about Daniel Everett’s claims about the Pirahã language and Universal Grammar (UG) in proper perspective. Norbert H. correctly points out that what is in question is not one or another “dictionary grammar” or description of Pirahã, even the most complete corpus of an ethnolingustic study that has catalogued the language use of the speech community. Rather, UG is about the language acquisition capacity. The fact that a given speech community, or many speech communities, may not deploy recursion does not count as negative evidence that falsifies UG or that recursion is a defining property of it. One would have to show that because of their cultural experience speakers of such a language can no longer learn a language with recursion, such that they would learn a pidginized version of it that does not implement any kind of embedding for example. To be a clear test, the experiment would need to be specific, not just children, but second language (L2) learners (children or adults) whose first language (L1) is Pirahã. Critics of UG, including Everett, would agree that a Pirahã child who acquired Portuguese as his or her L1 would in fact have no trouble mastering its grammar. Proponents of UG claim that there is nothing in “the culture” of a person that can block the acquisition of a grammar with recursion. Even in the case of primary language competence, there is nothing in the L1 of a speaker that will always block the acquisition of L2 features. Because L2 learning requires access to UG to at least some significant degree (the Poverty of Stimulus is still a problem for second languages, according to theory) successful L2 learning of Portuguese by L1 Pirahã speakers (not necessarily perfect native-speaker competence), having lived in the Pirahã culture, would show that they possess an intact UG-constrained language acquisition capacity. It is possible to imagine a L2 learner of Portuguese deploying the lexical resources of the target language in a way that avoids recursive patterns (e.g. at a certain stage of learning). Would the culture-determines-grammar theory predict that Pirahã learners of L2 Portuguese always impose this restriction as they advance in the mastery of the L2? What happens, by the way, when Pirahã-Portuguese bilinguals code-switch? Readers interested in a more complete motivation for this proposal (taking into account the second language learning/bilingualism factor) can find it in my recent study Bilingual competence and bilingual proficiency in child development, Chapter 6 (MIT Press, 2012), and the sequel, Bilingual development and literacy learning: East Asian and international perspectives, Chapters 2 and 3 (City University of Hong Kong Press, 2013).
    Thank you for posting this observation, Norbert F.

    1. Just a few thoughts regarding your interesting post, Norbert F.
      First, I agree that there are factual points that need clarification and that it will need take into account the specific claims by both proponents and opponents of UG. To draw attention to just one you mention: i am not aware that opponents of UG would claim cultural constraints that applied to L1 would block the acquisition of recursion in L2. As far as i understand the claims culture opens possibilities, it does not prohibit acquisition.

      Now note that your suggestion is neutral between the two hypotheses under consideration: if L2 learners are able to acquire this language as well as L1 it could be based on both LF or input. I remember that at least some proposals suggested the critical period is based on LF shutting down but alternatives are possible. What made the HCF 2002 paper interesting was that it made a scientifically testable prediction, namely that ALL human languages would have recursion [properly defined, there is some debate over what this means]. Everett's findings [if they turn out to be correct] would have refuted that hypothesis. It was in response to reports of Everett's results that the proposal was changed to recursion is one tool of LF and not all languages need to employ all tools. This proposal is no longer falsifiable; it is compatible with any evidence. Norbert H. thinks this is no problem because falsifiability is highly overrated, others disagree. In any event, no one disputes that recursion occurs is the vast majority of human languages, so the new proposal is not in opposition to what critics of UG believe regarding recursion.

      There is certainly room for disagreement on this topic. But I think, there should be no room for public name-calling, for engaging in 'labours of hate', for distortion, and the like.

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    3. Thank you Christina for these observations. I agree that there is still much that needs to be clarified in this discussion; for that reason it’s interesting. Let me respond first to some of the new issues that you’re raising in regard to the first language-second language factors. You correctly take note regarding the critical period question that when it is applied to L2 there are a number of different proposals without as yet a gathering consensus. In contrast, on the critical period question applied to L1, there is a much more broader agreement, even across theoretical lines (although researchers differ on the explanation). Regarding whether L2 learners are able to acquire language as well as L1, again there is a lively and still interesting debate on this question. Most if us would also agree with you that both factors internal to the Faculty of Language and input factors need to be considered. Interestingly here in regard to L2 learning, one proposal would say that this interaction between FL and input factors is different than in L1 acquisition. Some hypotheses favor an “FL-shutdown” and others favor the view that the FL remains intact during L2 learning (i.e. it never shuts down – recall from my posting that this is the one I favor). On the specific point about the “cultural influence” hypothesis (for lack of better name for now), I think you’re right that many if not most people who are generally favorable toward it view this hypothesis like you formulated it “culture opens possibilities.” But what distinguishes Everett’s claim it that it goes much further to be what we could call a very strong cultural influence hypothesis (my term). He does not use the term “block” but I think his proposal is pretty much along the same lines: try to “show how Pirahã rules out recursion in Pirahã grammar” (p. 14, Everett, in press, “The role of culture in the emergence of language” to appear in O’Grady & MacWhinney). That’s what sets his claim apart from others in the field. Hypotheses that are “very strong” are also hard to find supporting evidence in favor.
      I don’t want to address the issue of the “public name-calling” here because I posted on this separately on another thread, in response to a posting of yours.
      And allow me to address the other points you raised on another occasion before I run out of characters. Thanks again.

    4. Sorry, I didn't get the Everett quote exactly right. It reads:
      "show how Pirahã culture rules out recursion in Pirahã grammar."

    5. Here’s the second part of my reply. Falsifiability is important. And I think the hypotheses that we are considering are falsifiable. But a better way in my opinion to consider this problem is in terms of different kinds of evidence, for example positive, or conforming, evidence and negative, disconfirming evidence. The second is closer to the idea of falsifying evidence. In our line of work there is rarely a single experiment or other kind of study that we can perform that in one shot is capable of falsifying, just like that, a hypothesis that has accumulated a body of positive evidence. It’s a hard problem, and I’m not an expert in this area. But here are some examples of possible studies that could be carried out that might provide negative evidence for the proposal that a defining feature of the FL such as recursion forms part of the so-called “tool-kit” (this is not a bad metaphor) of UG, that is available for deployment but perhaps not implemented in actual language use in a given speech community. As an aside, I recall that this idea has been around for a while, not a recent innovation after the HCF (2002) article. Anyway, following Norbert H’s suggestion and my elaboration of it: Provide L1 speakers of Pirahã, socialized in the Pirahã culture, rich exposure of the naturalistic kind coupled with informal instruction in Portuguese (not formal classroom instruction which might, hypothetically, bias them to adopt recursion using non-FL means). After the learners progress in their L2 Portuguese, do the test: see if “Pirahã culture rules out recursion in their L2 Portuguese grammar.” “Ruling out” would imply that no recursive patterns would appear in production and well-formed sentences in Portuguese could not be understood correctly. This would be disconfirming evidence for the “tool-kit hypothesis.” If recursion appears in performance, in either expression or comprehension, this would be evidence in favor. A similar study could be carried out with bilingual speakers, (1) in mixed Portuguese-Pirahã speech are grammatical patterns completely lacking in recursive pattern? And (2) could examples be found in the performance of these bilinguals of inter-language transfer, specifically the transfer of L2 patterns to L1 speech? This last test is an example where negative (falsifying) evidence would not be conclusive, because bilinguals are known, famously sometimes, for their ability to keep the language sub-systems separate and suppress any and all kind of transfer including codeswitching. There are many other possible experimental designs that one could come up with. Now what is always posed in these cases is whether or not a given experiment is in fact valid test of falsification. This question is always an important consideration. Again, it’s a hard problem, but we make progress using these kinds of method little by little and part by part.

    6. Thank you for the interesting comments Norbert F. I admit I have not read the paper you cite from, so I can't comment. I had read Everett's commitments differently, I thought his claim was that several facts about Piraha grammar that cannot be explained if Piraha has recursion. So this is a claim about E-language not about the putative language faculty and certainly not a claim about an ability [or lack thereof] to acquire languages that have recursion. Note that virtually all our knowledge about the structure of language comes from what Chomsky calls E-language, not from brain research [which is still far too crude to make the very find distinctions that would be needed]. Note also that even if Piraha kids [or adults] could acquire as L2 a language that has recursion it would be desirable to know why Piraha hasn't [given that recursion continues to be called the essence of language]

      As for falsifiability: I certainly agree that one should not throw out a theory that has great explanatory power the first time some counter evidence is found. So I had no principled objections to the part of the Nevins et al. paper that challenged whether Everett's interpretation of the data is correct: we are all humans and can make mistakes. But i do believe a theory should be at least in principle falsifiable - so saying either a language has recursion or it has not is not interesting from a scientific point of view because it is true no matter what we find. I further think if someone [like Norbert H.] is not prepared to consider the possibility his theory could be wrong no matter what empirical facts are discovered, then this person is not doing science.

    7. I found the Everett chapter on LingBuzz (2014-05). It’s an interesting presentation of his theory in part because he now introduces the concept of I-Language (defined in a different way than most other authors). In this chapter I think he does start to suggest, though I may be wrong (not sure), that Pirahã culture affects what some of us call the “mental grammar.” In any case, I agree with you that it would be interesting to study why languages like Pirahã either (1) haven’t implemented recursion or (2) don’t exhibit the kinds of recursion that appear widely in the languages of the world. Nevins et al. (2009) present evidence that in actual performance (1) is not correct. Either way, I think this is a viable research problem that in addition is interesting. I do think that it will help us get a better understanding about what modules and other kinds of cognitive domain “make up” the FL(narrow) and FL(broad), and help us get a better idea of what recursion is. So, studying language use (aspects of ability or performance) will contribute to this inquiry; that’s my view. We also agree, I think, on the way you put it: a theory should be at least in principle falsifiable. At the same time I don’t think it’s fair to say that researchers such as Norbert H. and other supporters of UG who share his view are not prepared to consider the possibility that their theory could be wrong. There are legitimate differences among researchers on what counts as negative (“falsifying”) evidence and the strength of a particular instance of negative evidence. Sometimes we come to be very strongly convinced that a certain hypothesis is correct and argue forcefully in favor of it. That’s OK, and it’s not a sign of an unscientific approach. In my case I happen to agree with the main idea that he is presenting, and equally convinced of the overall UG critique of Everett’s findings. Where we may differ, perhaps, is about the point I made above about what may be interesting in studying languages like Pirahã. We’re all doing science though; Everett is doing science too.

    8. @Norbert F. I am traveling, so just a quick comment: I do not claim that Norbert H. is not doing science because he defends a view I think is incorrect. After all I could be the one who is wrong. But I asked him on this blog what empirical evidence he would accept as proof that his/Chomsky's theory is wrong. He replied he could not imagine any. The conversation was quite a while back but I am sure you still can find it, Norbert H. stopped talking to me some time ago...

    9. Confirming and disconfirming evidence, evidence favoring and evidence disfavoring is a difficult problem in science. Sometimes we say “proving” or “disproving” a theory, but this is usually more of an informal way of talking about the problem. We should let Norbert H. speak for himself about what he meant. I’ve caught myself sometimes saying some evidence is “proof” that a theory is correct or that it’s wrong. But I realized right away that I didn’t mean it in the precise way that we normally use this term. I’ve said, informally, that such and such theory has been “proven,” suggesting that it’s settled and that there is no more evidence that needs to be sought. And of course there are lots of claims in science that have been proven in this way. I think it’s important to remember that this is a blog, and we often post opinions that are not formulated with the same precision that we use in papers edited for publication. So I think we should take each other’s comments in this spirit. The default setting should be that all of us who work in this field try the best we can to apply the methods of science, and that no one in our profession should be written off or excluded, unless there is clear and unambiguous evidence of willful fraud. The other exclusion involves those who explicitly reject the methods of science and try to deliberately subvert rational inquiry. Sadly, there is still plenty of this in academic where entire departments have been colonized by proponents of postmodern critique and radical social-constructivism. There is the place where we will find truly anti-scientific and unscientific methods, opening proclaimed as such by their supporters. In the meanwhile, we should cut each other some slack.

    10. @Norbert F.: apologies for the delayed reply [and the slightly cryptic comment I wrote when in a hurry]. We agree of course that [a] it is often not easy to specify what would be disconfirming evidence vs. evidence that may require just an adjustment of the theory and (b) that one should not lightly accuse anyone of unscientific conduct.

      Now regarding [a], I have often found that researcher A will claim researcher B's theory has been disproven because of evidence E. To which B will reply: "Well, A just does not understand my theory, it is perfectly compatible with E". Since this seems to happen in debates about generative grammar rather frequently, I think it is counterproductive to tell others what would disconfirm their theory. Instead, I ask them what they would accept as disconfirming evidence. One would assume they understand their own theory and are in a position to know what would disconfirm it. Yes, there might be grey areas. But there should be also clear cut cases. For example I do not believe that language acquisition depends on an innate domain specific LF. But if someone discovers such a faculty in a human brain and provides a full bio-physiological description of it I would admit that I was wrong. [Note this is very different from specifying something I expect to be discovered in the imminent future].

      I think anyone proposing theory T should be in a position to say; "If E is discovered then T is false". So I did not tell Norbert what I thought would disconfirm minimalism but asked him what he would accept. That he had no answer to this question should surprise anyone who assumes [as I did] he is doing science.

    11. I don’t want to speak for Norbert H. He will have to clarify this misunderstanding (I suspect that’s what it is). But yes, I agree. Hypotheses and claims that are put forward for further investigation need to consider as part of the research proposal what kinds of evidence would support them and what kinds of evidence would disconfirm them. One thing to consider (like you mentioned, this not a simple straightforward yes-no, prove-disprove, matter): it’s very important to be specific. What can be taken as falsifying evidence for *specific* claims, the more circumscribed the better. For example, if the domain we’re considering is too broad (e.g., an entire research program – like “biolinguistics”) then it’s very hard to get a grip on what exactly can be tested. And like you said, it’s not unusual that there are debates about whether a given test was valid or not in the first place, and not just about claims in linguistics. In any case, anyone can propose a test of a claim, proponent or opponent, and then make the best argument for it. If a researcher puts forward a hypothesis and is not willing to give or can’t think of possible negative evidence, then critics of the hypothesis are given a valuable opportunity, to do just that, propose an experiment or other kind of study that might indeed shed light on its viability. In these kinds of debate, we should try to be just as well informed of opposing theories as we are of theories that we favor. We need to still assume that all of us here are doing science, even when misunderstandings arise or replies are given that may be incomplete or ambiguous.

  11. I wonder why the Piraha culture is where it is. If the information available on the Web (Nimuendaju 1948, and Wikipedia) is correct, there was a people of Mura, of which Piraha was a dialect, with roughly fifty thousand members some two hundred years ago. At present there are 300 or so speakers of Piraha (and perhaps a few thousand other descendants of the Mura people who don’t speak the Mura language any more). What has happened to Mura people can be viewed as a cultural shock.

    Note that an individual could lose their speech completely due to a shock and yet it could hardly be argued, referring to such an accident, that having language is not universal to humans. I find this analogy telling though not necessarily quite fair (because cultural shocks may be a way culture does develop).

    Now I’m getting to my point, which is based on what can be seen in the Brazilian jungle from Europe with a naked eye (so I’d rather apologize for it in the first place): If we assume that Piraha are not much different from the rest of Mura (or at least were not so before the cultural shock), then the answers to some of Norbert Francis’ June 16, 2014 questions might perhaps be obtained via inspecting the rest of the present-day Muras without a need for experimentation with L2 learners.

  12. Vilem proposes another interesting test of the presence of a design feature of language (in the mental grammar of speakers): the emergence of a dialect that branches off, becoming isolated but remaining closely related to other dialects. If in the case of the descendants of the Mura, who according to reports have shifted completely to Portuguese, there then would present itself another possible comparative study. Identify a number of similar language shift situations (this is the term that our colleagues in sociolinguistics use, which a I think is especially apt) among indigenous languages of the region, some whose ancestral language deployed the design feature and some that didn’t (e.g. recursion). The best comparison would be in situations of recent language shift. Then ask the question: did two significantly distinct variants of Portuguese emerge from the respective shifts traceable to the original difference in ancestral language? Vilem suggests a related problem that we have tried to understand better in the work of our project in Mexico: rapid and abrupt shift, related to a kind of demographic/cultural “shock.” Setting aside for now the cases of demographic collapse result of genocide or disease, interesting questions about the nature of the Faculty of Language are posed. Traditionally the study of these cases has been the purview of anthropology and sociology, but cognitive science has a spoon in this dinner as well. As a tentative proposal, we put forward the Replacing Language (RL) hypothesis, which posits the preservation of the FL (preserved access to UG) to explain the different kinds of language ability outcome resulting from these situations of “language loss,” better understood, if the RL hypothesis turns out to be correct, as "replacement."

    1. Everett 2013, lingbuzz/000994, p. 20 quotes himself: “Pirahã babies certainly can learn languages with recursion”. So there’s no need for the kind of research we’ve discussed above. The point is much simpler: Those grown up in a closed cellar with no one to talk to or in an isolated small group of people who utter only simple sentences will not learn much of what is standard elsewhere. The only question then is what is behind Genie’s fate or Piraha’s history. For the latter case, Everett’s answer is ’culture’. OK, but what do we know about its history?

    2. I think no one has denied that infants can learn the language of the community they grow up in regardless of who their biological parents are. So the Everett quote is neutral between what Norbert H. calls empiricists and rationalists. Further, Everett does not claim Piraha language is simple; so i would be very careful with comments like they "will not learn much of what is standard elsewhere" that seem to imply Piraha people are lesser beings than speakers of English.

      The questions Norbert F. raises above are certainly very interesting. But we should remember that UG/LF was supposed to account for true language universals that are common to all human languages BECAUSE they are provided by our biological endowment. So if it is possible that one language has no recursion because of culture it is logically possible that no language has recursion but recursion still is a universal. Something like that that has been proposed as I-universals:

      I-universals … need not be observable … the mere fact that every language displayed some property P does not imply that P is a universal in the I-sense. Put more paradoxically, the fact that P holds universally does not imply that P is a universal. Conversely, some property can be an I-Universal even if only manifested in a single human language. The only thing that makes something an I-universal on this view is that it is a property of our innate ability to grow language (Hornstein & Boeckx, 2009, 81).

      One can't empirically discover these I-universals but has to rely on Norbert H's or Chomsky's or... intuitions. One can of course do this but in my books one no longer does science when one relies on entities that can neither be confirmed nor disconfirmed empirically.

    3. @ Christina

      So Norwegians' capacity for production and darkening of Melanin (tanning) is unobservable until they happen to take a vacation. Does this unobservability mean that melanogenesis and melanin darkening in Norwegians is not part of their biological endowment? Culturally-derived traits?

    4. @William Matchin: Thank you for drawing our attention to a very important difference between biological properties that have been confirmed and those that have not. We could test Norwegians for N-acetyl-5-methoxytryptamine before they take vacations [besides they do get sunshine in Norway, so please take some sunscreen if you take a trip]. So [to use the Chomskyan analogy]: performance [skin darkening] is not needed to confirm competence [availability of N-acetyl-5-methoxytryptamine which under the right conditions can cause skin darkening]

      The situation is very different for the postulated LF. If you have followed the discussions on this blog you know that each time I ask for biological properties of LF defenders of the Chomskyan view fall silent. At this point the biological LF is inferred from data that have been gathered from language performance and analysis of these data by competent linguists. But there is no "Merge" equivalent to N-acetyl-5-methoxytryptamine that we could test in Piraha speakers.

    5. @ Christina

      Yes there is sun - but before the arrival of tan beds I don't think any of them resembled the cast of Baywatch.

      The problem is that nobody knows the biological properties of any cognitive faculty, because we don't know much about how neurons relate to cognition. This is the famous nematode example - 400 neurons, and we don't know how it works. This doesn't mean we can't intelligently investigate the cognitive underpinnings of complex behavior. This is all of psychology, is it not? E.g., auditory processing. Psychophysicists determine the underlying properties of the auditory system by experimentation, observation, etc. Many of the postulated properties are unobservable in the nervous system, but nobody cries foul. Are you denying the legitimacy of all of experimental psychology?

    6. Christina wrote: “Everett does not claim Piraha language is simple”

      Yes, he doesn't and nor do I. But remember Everett’s “You drink. You drive. You go to jail. Where’s recursion?” Simple sentences (this is what I did say) don’t really imply simple language. (Note that Watumull et al. in “On recursion” even claim that it is recursion in discourse what counts.) But according to Everett, Piraha is somehow special, so much special that he sees “The Shrinking Chomskyan Corner”. I just wonder what it is.

    7. I think maybe I’m sensitive to assertions of who should be counted as doing science and who shouldn’t because of a discussion in another thread of this blog (Elivicious) - I'll respond to the other points in another post - Norbert H. brought up the case of Marc Hauser. Even though a Harvard University committee charged with investigating allegations of fraud and misconduct found that he was guilty, we in the profession should refrain from assuming that these allegations are true because none of us have actually seen the evidence. I agree. Under the circumstances, to accuse him publicly that he is a fraud or is guilt of research misconduct would be irresponsible. To try to exclude him in any way, for example, by insinuation, would be unacceptable. Christina responded with a post that called attention to a similar situation: the accusations of fraud and misconduct against Daniel Everett. The post reminded me of the case, in which no one has yet brought forward or pointed to any evidence (e.g. the findings of a committee of inquiry). I in turn replied asking for this evidence and asking for clarification of the widely circulated charge of fraud.

    8. @Norbert F. and VilemK.
      Thank you Norbert F. for the reminder that still no one has provided any evidence for the charges that Daniel Everett is a charlatan, apparently made by Chomsky in Folha de Sao Paulo. And to the charges that have been made on several blogs that Everett is a racist. Now above Vilem actually likened the language of the Piraha to that of the severely abused, language input deprived girl Genie:

      "The point is much simpler: Those grown up in a closed cellar with no one to talk to or in an isolated small group of people who utter only simple sentences will not learn much of what is standard elsewhere."

      I sincerely hope this was an unintended likening and I hope even more that no one will accuse Vilem of racism because he made this comparison. So maybe a good idea to think more than twice before circulating further charges against Everett. [@Vilem: I do not agree with everything Everett writes, so you would have to ask him about the work you refer to]

      Regarding Norbert H's attitude towards science: I think he is certainly capable to clarify his position. In fact he has done so in this post [and a number of follow ups]

    9. Christina, you seem to indicate there is a reason to accuse me from racism. If so it’s a dirty game that I don't wish to play with you or anyone else.

    10. Everett is very clear that the Piraha can and do use discourse to get the same effects as syntactic recursion, & I can't under stand why Vilem thinks that Christina is suggesting that he's a racist. Furthermore, true, Nazi-style racism is not at issue here, because nobody is suggesting that there's anything generic about the Piraha that's responsible for the way their language is, according to Everett; what seems to be at stake is a confusion between actual racism and potentially derogatory observations about other people's cultures, a completely different matter (since anybody who believes in the possibility of self-improvement believes that such criticisms when directed at themselves and their culture are sometimes true and capable of being fixed).

      I think where the quarrel between Everett & the generativists lies is in what kinds of predictions generative theory ought to be able to make correctly in order to claim to be scientifically justified; he's taking a particularly simple minded view that it predicts that we ought to be able to find clearly recursive structures in every human language; I think that this is too simple-minded and wrong, but the amount of effort that people have directed towards trying to show that he's wrong about Piraha suggests to me that his claim is 'morally correct' (some generativists are really eager to have all languages show clearly recursive syntax) even if technically wong (nothing in Minimalism or any other version of GG actually requires this to be the case).

      Note that this discussion presupposes that there is a difference between syntax (sentence structure) and discourse, which seems to be true but doesn't logically have to be (and it would be nice to have a more detailed story about what it is), and that, independently of clausal recursion in Piraha, there is also the issue of how they learn not to say things "John's friend's canoe", since, unlike with the restrictions on prenominal possessives in German, there is no simple alternate construction to express the forbidden combinations, but only complicated periphrases, so it's a lot less clear how for example some kind of statistical preemption could work. So there is a learning theory problem there, independently of any wider issues.

    11. Before I reply to some of the other questions raised above, as I said I would, I just want to underline the observation here by Avery: the suggestion that an argument or comparison was made in this thread that could be taken as racist is simply a misunderstanding. There was no suggestion of this kind, and no one has made an argument that remotely can be construed in this way. It wasn't Christina's intention to suggest this, if you read carefully her remarks.
      On the separate point here, there is something important to consider that is often forgotten. Let's agree for argument sake with Avery that Everett's broader claim about finding evidence disproving UG is not founded. But there still may be important research questions to ask that Everett has touched on. Why, for example, do we find such remarkable features in the Pirahã grammar as it has come to be implemented (so to speak). This of course is a question of language use or language ability, that perhaps belongs to the domain of FL(broad). But this may lead us to discoveries that are interesting from the point of view of getting a better understanding of the FL as a whole. From all the descriptions of Pirahã I have seen, what this speech community has come to deploy does seem to me as remarkable and worthy of study.

    12. Thank you to Vilem and Christina for finding and commenting on the actual quote from Everett regarding the ability of Pirahã children to learn recursive patterns in Portuguese (if Portuguese is their L1, as in for example early bilingual acquisition - the shorthand we use in the field is 2L1). As I mentioned in my first post to this thread, I assumed that this would be Everett’s view, but didn’t have the citation. As Christina put it, the Everett quote is “neutral” between the two opposing theories. Taking note of this “common position” is more important than might appear at first glance. It’s important in discussions like this to see clearly where there is agreement on data or prediction. That’s the way we can have more clarity in the debate. This was the reason that I proposed that a test of Pirahã speakers’ access to recursion should involve L2 learners. By the way, the findings from such a study could offer disconfirming evidence for the recursion-as-a-design-feature-of-language hypothesis. If L1 Pirahã speakers consistently fail to learn the recursive patterns of L2 Portuguese, I WOULD HAVE TO ADMIT that this is evidence that contradicts the hypothesis that I favor.

    13. I want to call readers’ attention to a recent study that I just came across which gathered bilingual speech data from L1 Pirahã speakers – from the author’s account mainly lexical insertion of Portuguese in Pirahã. Recall that this was the example I gave earlier of a possible test of what effect exposure to L2 grammar might have on language use patterns in Pirahã when bilinguals engage in borrowing and codeswitching. The author gathered a large corpus, over 10 hours, and it will be interesting to see further studies from her on this question. In the meanwhile, I have to say that one example (p. 42) at least shows evidence of recursion, if the analysis of the author is correct (DM = discourse marker). I suppose the analysis here all hinges on the function of DM ("Ai")

      Example (3)

      Ai Pao’ai hi ’abóp-ap-ao TÓPAGAI
      DM Dan 3SG return-PUNCT-temp technical.V.Engl

      kóbai-kói TREVISÃO.
      watch-EMPH television.Pt
      ‘At the point of time when Dan has returned we will watch videos.’ [GK1]

      Jeannette Sakel (2012). Transfer and language contact: the case of Pirahã. International Journal of Bilingualism,16(1): 37-52.

  13. Another Sakel's paper "Acquiring Complexity: The Portuguese of Some Pirahã Men" 2012 (available on the Web) may be of interest to you.

  14. Yes, I just checked it out. This is an interesting paper with lots of examples, L2 Portuguese-beginner level (sounds like my Portuguese) and one intermediate-level learner (GK2) with analysis and discussion by the author that is very suggestive, parallel to findings we're seeing in other bilingual indigenous language situations in Latin America. Thanks for the posting!

    1. Thanks for the interesting comments. I have a point of clarification and 2 questions:
      Vilem; I did NOT suggest you are a racist and apologize if what I said seemed to imply this to you. I reminded you that Everett has been called a racist for making claims about Piraha that were of a similar nature as the claims you made. It IS noteworthy that those who have accused Everett of racism still have not either defended their allegations or apologized...

      My questions:
      1. for Avery: You say Everett is taking a simple minded view of what minimalism predicts. Can you please clarify for us what exactly ARE the scientifically testable predictions of minimalism, so we all are on the same page when talking about them?

      2. for Norbert F. [but really for everyone defending innatism]:
      I find the discussion of L2 quite interesting but, at the same time, it does not offer any help in deciding between E- and R- views: if Piraha kids can learn a language with recursion from the input it is an open question whether they can do so because of innate endowment or because the required information is in the input.

      Now one would expect that IF we have some innate language faculty and if we have speakers that have been acquiring the same language L over many many generations, eventually their LF would have been selected for acquiring L and that those speakers would have difficulties acquiring any L2. Yet, to my knowledge this seems not to be the case and, furthermore, one claim innatists seem to agree on is that every infant can learn any language regardless of his/her biological parents. We know from other biological traits [e.g. ability to bind more oxygen in the blood of people who live in high altitudes] that the time required to establish innate differences between human populations is much shorter than the time LF allegedly mutated into existence [or even the time some tribes have been isolated from contact with other human languages]. So why is there no human group that has [innate] difficulties acquiring a L2?

    2. The simplest prediction (true) would be that multiword expressions will show evidence of phrasal structure, since Merge sticks things together in pairs. More subtly, that if you look hard enough, you will find evidence that this structure is binary brancing rather than at least sometimes n-ary (not so clear, but not completely implausible either). Of course the problem with the simple prediction is that all of Minimalism's serious competitors predict this too, in one way or another (but differ on binarity, either a merit or a demerit of LFG for example, in the end),, & we are too empirically ignorant and mathematically incompetent to work out the best way of getting the right predictions.

      But the endeavor does chug along, I think. Forex Stabler, Kobele, Graf et al seem to me to be making excellent progress on showing that syntax is mildly context-sensitive (by coming up with ways of converting many apparently different ways of formulating grammatical rules of kinds that linguists have found useful to formats that are provably so).

      To get past the 'incredibly hazy and primitive' stage, one thing we need is really effective learning theories to which we can present data and get a prediction via a mathematics, say, what I knew about Icelandic in 1974 as input, and the existence of (or at least a high probability of the existence of) the evidence that shows that that language really has non-nominative subjects, including covert ones in Equi and Raising constructions. This does not yet exist, as far as I can see, but it is a coherent aspiration.

    3. And for Q2 (me being a moderate innatist), recursion is never in the data, because the data is always a finite list. For a specific example based on syntax teaching experience, if students are given data such as:

      John yelled
      the little girl yelled
      the girl yelled
      John's brother yelled
      the girl's brother yelled

      Some of them can be counted on to produce a non-recursive grammar such as:

      S -> NP VP
      VP -> yelled
      NP -> {PN, Det (Adj) N, {PN, Det N)}'s N}

      trying to 'hug the data' because they don't see an adjective inside a possessor phrase. So there needs to be a bias of some kind to predict that 'the little girl's brother yelled' will also be OK.

      This bias does not of course have to be something specific to language, but could be general cognitive, but without a bias, there really is nothing in the data.

      The issue of different groups having different abilities is intriguing: I don't think we really know that people of exclusively mainland southeast asian ancestry don't have some kind of deficit in picking up heavily inflected languages such as Russian or Kayardild, or that that speakers of these latter languages might be a little bit worse at learning to infer semantic roles from context, since there's no way to do the required experiments ethically, or, indeed at all (the little asians growing up in Russia or Mornington Island would probably be treated a bit differently than the majority population, thereby wrecking the results).

      But if the original Advanced Human Language speakers came up with some toolkit of language-specific cognitive tricks, then facilities in it that aren't used by certain populations would have to atrophy in order to become unavailable to the the descendents of those populations, and my impression is that atrophy takes some time.

    4. Just a very brief reply to your last point, Avery:

      "if the original Advanced Human Language speakers came up with some toolkit of language-specific cognitive tricks, then facilities in it that aren't used by certain populations would have to atrophy in order to become unavailable to the the descendents of those populations, and my impression is that atrophy takes some time"

      It seems you get your evolution story backwards here: unless the first language spoken by the small tribe in Africa [from which all owners of an innate LF descend] used ALL the tools in the kits it makes no sense to postulate tools that have not been used. Maybe a human designer would provide tools that have no task at the moment but could be used later - but evolution does not work that way. I think for that reason the basic idea behind minimalism [to have as few innate tools as possible] is good. The problem with that idea is that it can no longer account for acquisition ...

    5. Thank you Christina for the clarification and the questions (these in particular bring a new facet of the discussion to this thread that we haven’t considered yet). Just briefly on the clarification, important it is that you reminded readers of the insinuation of racism directed against Everett that to my knowledge has never been supported by an example, even though it has been repeated frequently on the internet, often as an aside or passing tidbit of interesting information. But I don’t want to comment on this issue here as it belongs in the thread on misconduct and ethics (Evilicious) where Christina and I called attention to the as of yet unsubstantiated accusations against Everett.
      In regard to the questions, here is where we can first start with a common ground I’m pretty sure: both emergentist/functionalist theories and generativist theories agree that there is an innate foundation to language in humans. I think Everett would also agree. We all account for human exceptionality by assuming a unique capability that humans possess, which doesn’t reside in how human infants are socialized, but rather in our biology. The divergence is that the former prefer to look for this capability in domain-general cognitive capabilities, the latter look for domain-specific competencies. In the other words the empirical question will come down to tests of one or another modularity hypothesis. Just to lay my cards on the table, I think that these hypotheses are subject to tests that can show them to be false, or conversely provide positive evidence in favor. In my view the jury is still out. For UG, the problem is tied to the closely related research question of Poverty of Stimulus. From where I’m looking at things, this question is at the heart of the generativist research program. If future investigation severely weakens or shows that the PoS hypothesis is not correct, there is no more reason to think in terms of a domain-specific UG or modular FL. This is all related to our other discussion of evidence. Both modularity and PoS are falsifiable (this of course is a simplification on my part: we have to consider very specific claims of specific versions of each. In my view, for example, some versions of the modularity hypothesis are not even plausible). All of this is relevant to the questions that we have been considering in the case of Pirahã and similar languages, like how to understand bilingualism and second language learning in these situations.

    6. @Christina: yes, entire task specific toolkit developed in one population, which spreads. Which implies I think that it's pretty small, everything else having independent cognitive uses for critters with our general lifestyle. Admittedly a bit surprising, but so are the actual phenomena (case-stacking in Kayardild, anyone?).

      This is independent of PoS arguments, which illustrate the need for some bias in how to interpret the data, regardless of where that bias comes from.

    7. @Avery: I fear I do not understand this paragraph:

      "This is independent of PoS arguments, which illustrate the need for some bias in how to interpret the data, regardless of where that bias comes from."

      Are you suggesting the familiar POS slogan 'what cannot be learned from the input must be innate' no longer applies? Then what are Norbert H. and Alex C. at times rather fiercely arguing about? Even if there are merely some 'biases' that account for acquisition, these still need to be accounted for in the domain-specific 'genetic endowment' story or you have nothing left that distinguishes nativists from emergentists/constructivists. And, as you said above: recursion can not be learned from finite input [I am not sure why this is the case but you're the expert], so the recursive mechanism needs to be innate as well.

      The problem should be familiar by now: we have 2 incompatible stories: one for evolution [where as little as possible is innate - so it could have popped into existence by one chance mutation] and another for acquisition [where a lot must be innate because only the innate endowment can overcome the alleged POS].

    8. Wrt the POS, I'm thinking for example slide 10 of the document where the right side shows innate biases divided into domain specific and domain general, the former (upper right quadrant) characterized by Pearl as constituting Universal Grammar, which I'd prefer that people called 'Narrow Universal Grammar', with 'Broad Universal Grammar' being the entire right side of the diagram.

      POS means no bias, no learning (of anything), but it doesn't have to be domain specific, that's an empirical question for language learning. Phrase structure for example might be learned through biases that our evolutionary ancestors found useful for parsing each other's activities to figure out what they were up to and get the drop on them.

      And no recursion without a bias because without a bias, a wide range of nonrecursive analyses are always available from finite data (not an expert point - anybody who teaches syntax will see many practical examples if they assign problems with recursive NP structures).

      It would be excellent if we knew more about how much evidence of complex NP structures children get in their input, and what kinds of outputs they produce at various ages as a result of their exposure. Perhaps something could be done with the Pearl and Sprouse Childes treebank, in fact. Maybe even by me, since, as a retired person, I ought to be able to find time to do it.

    9. This comment has been removed by the author.

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    11. [revision of deleted comment]. So, modulo the effects of errors in my search techniques and the parsing of the corpus (which exist), in the 170,770-odd CDS utterances, there are about 265710 NPs, 150233 of them non-pronominal, of which about 2111 have non-pronominal possessors, and 25 of those have non-pronominal possessors (a lot more than the 1 I found at first). The non-initial nouns don't seem to get more than one modifiers (Auntie Marian's (new) puppy's (dog) name) fits the pattern OK, but more than two full NP possessors don't seem to occur, and no 'group genitives' either (the man from Snowy River's horse). The statistics seem to be that a bit more than 1% of NPs that aren't personal pronouns (PRP in the corpus structures, I didn't try to exclude other kinds of putatively pronominal NPs) have full NP possessors, so that the corpus would have to be about 100 times bigger before we'd really expect to see some with three possessors instead of just two.

      So all this could be done with various kinds of nonrecursive 'bad student analyses', such as:

      NP = (Det) (MOD) N (POS (MOD) N) (POS (MOD) 'name')

      (in the doubly-possessed ones, the last item is always 'name'. all but 3 of them are in the brown-sarah corpus, including 022 and 023 when sarah was pretty young)

      Such formulations are of a kind depressingly familiar to people who teach intro syntax to undergraduates, indicating to me that there does need to be a bias that favors recursion (and is missing from the faculty of science-learning of the weaker students).

  15. Thanks, Christina, for your June 28, 2014 at 1:40 AM clarification.