Learnability, Restrictiveness, and the Evaluation Metric

  • Howard Lasnik
Part of the Studies in Natural Language and Linguistic Theory book series (SNLT, volume 20)


At least in the last few decades considerations of learnability have played a guiding role in much linguistic research. In particular, there is fairly general agreement that restrictiveness is important. There is substantial controversy, however, over exactly what ought to be restricted and over the nature of the appropriate restrictions. I will explore the question of what has to be learned by the child and the implications for restrictiveness proposals, and I will discuss what I take to be the three major areas of concern: (1) properties of the evaluation metric; (2) restrictions on the class of grammars, particularly as they relate to the evaluation metric; and (3) restrictions limiting the type and amount of data required by the child.


Language Acquisition Human Language Negative Evidence Context Term Grammaticality Judgment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    The “incontrovertible learnability” mentioned by Levelt can, of course, only be con- strued as a remark about human learning. Although it is incontrovertible that human beings learn human languages, the question of whether the class of human languages is learnable in the technical sense of, for example, Gold (1967) has never even been formulated in a precise way, much less answered in the incontrovertible affirmative.Google Scholar
  2. 2.
    Note that a theory guaranteeing convergence in principle for the entire class of grammars would be of little use as a model of the language learner. Far preferable might be a theory guaranteeing rapid convergence for highly valued grammars but offering no convergence guarantee for the entire class of allowable grammars.Google Scholar
  3. 3.
    Wasow (1978) and Chomsky (1980) make this point also.Google Scholar
  4. 4.
    Under such a theory there would be only a finite number of grammars. While these grammars might generate nonrecursive sets of sentences, most recursively enumerable sets would not be generated.Google Scholar
  5. 5.
    Chomsky (1964) has the earliest argument for the principle of recoverability of deletion that I have been able to find. He claims that certain syntactic differences between relative clauses and wh questions can best be explained in terms of such a principle. Here too the argument is empirical.Google Scholar
  6. 6.
    Wasow (1978) has an interesting additional argument of this general sort based on observed properties of the operation of certain deletion rules.Google Scholar
  7. Wasow and many others have also presented a quasi-empirical argument for recursiveness. Following Putnam, Wasow indicates that speakers of a language have available a decision procedure for membership in the language. This point of view is presented particularly clearly in Levelt (1974). “Native speakers will in general be as capable of judging that a sentence belongs to their language as of judging that that is not the case. In other words, native speakers have an intuitive algorithm for the recognition of their language, and not only for accepting it” (vol. 2, p. 40).Google Scholar
  8. Such arguments seem to confuse competence and performance. What are the facts about grammaticality judgments? There seem to be three possibilities: (a) People in fact have judgments for all sentences and nonsentences, and these judgments are accurate. (b) Same as (a) except that the judgments are not invariably accurate. (c) Judgments are not always available. If (a) held, one would conclude that the sentences of a natural language form a recursive set. Is there any reason to believe that (a) holds? In everyday experience it seems not to hold. Further, even if it appeared to hold in normal experience, as Peters and Ritchie (1973) observe, this would simply be evidence that “the set of sentences acceptable to a speaker under performance conditions is recursive rather than an argument about the set of sentences specified as grammatical by the speakers’ competence” (p. 82). Grammaticality judgments are often incorrectly considered as direct reflections of competence. As Peters and Ritchie remark, responding to a grammaticality query is an instance of linguistic performance.Google Scholar
  9. Levelt’s elaboration of this argument is worth noting. He acknowledges that there are many unclear cases but dismisses their relevance: “If on the ground of this objection we drop the recursive enumerability of the complement of the language (the ungrammatical strings), on the ground of the same objection we must also drop the recursive enumerability, and therefore the type-0 character, of the language itself” (p. 40). But no one would claim that the evidence of unclear cases establishes that human languages are nonrecursive, merely that the two situations are compatible, just as unclear cases would be compatible with recursiveness. Hence, the argument collapses. Note too that people have the ability to recognize a wide range of nontheorems of arithmetic. In fact, for all practical purposes, a statement of arithmetic can be just as easily judged a nontheorem as it can a theorem, even though the set of theorems of arithmetic is not recursive.Google Scholar
  10. Finally, Levelt’s claim that it is “more elegant” to ascribe the existence of unclear cases to “psychological circumstances” is without force in the absence of an argument.Google Scholar
  11. Grammaticality judgments, then, provide no empirical basis for the claim that languages are recursive.Google Scholar
  12. 7.
    Or at least to limit the class of highly valued grammars.Google Scholar
  13. 8.
    Even if it turns out that all human languages are recursive, it might be that no formal constraint need stipulate this. Grammars for non-recursive languages might be ranked so low on the evaluation metric that the child would never entertain them as hypotheses. Whether this is so depends upon the correct formulation of the evaluation metric, which is clearly an empirical question.Google Scholar
  14. 9.
    As in the situation in fn. 8.Google Scholar
  15. 10.
    See Wexler and Culicover (1980, ch. 2) for useful discussion of this issue. “ See Wexler and Culicover (1980) for an extensive survey of this question.Google Scholar
  16. 12.
    A modification of this account will be considered later.Google Scholar
  17. 13.
    This same observation pertains to many functional explanations in the literature. The additional statement is needed because the potential utility of a hypothesized grammatical principle does not guarantee its existence.Google Scholar
  18. 14.
    There are implied variables in all possible positions. Thus NP NP is to be construed as X1 NP X2 NP X3, for example, where the X’s are variables.Google Scholar
  19. 15.
    The structure is simplified for expository convenience. All category labels are to be taken as abbreviations for projections of feature bundles.Google Scholar

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© Springer Science+Business Media Dordrecht 1990

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  • Howard Lasnik

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