The Poverty of the Stimulus and the Power of Statistical Learning

Some views of grammar learning suggest that children must have some kind of innate grammar learning mechanism - this might be "universal grammar" or a "language acquisition device." One of the strongest arguments in favor of this view is often called "the poverty of the stimulus," which suggests that language exposure alone is not sufficient for learning certain syntactic structures that children can nevertheless use correctly.

Recently, Lidz, Waxman & Freedman formalized this argument with an analysis of the word "one." Consider the phrase "I'll play with this red ball and you can play with that one." In this case, the word "one" refers to "red ball," not just "ball." Yet an analysis of natural language corpora suggests that only around one-fifth of one percent of the uses of the word "one" actually demonstrate this rule.

So, if children are aware of this rule, the poverty-of-the-stimulus argument suggests they cannot have learned it from their language exposure (in fact, grammatically incorrect uses of the word "one" outnumber anaphoric use of the word by a factor of 2). But how do we know they actually learn it at all?

To demonstrate that infants do learn the anaphoric use of the word "one," Lidz et al presented 24 18-month-olds with a given object accompanied by a voice recording ("Look! A yellow bottle!"). After presenting the object 3 times, a fourth display contained two objects: for example, a yellow bottle and a blue bottle. At this point, half the infants heard the phrase "Do you see another one?" and the other half heard a control phrase ("What do you see now?").

Only the infants who heard the phrase "Do you see another one" looked longer at the matching object (e.g., the yellow bottle) than at the non-matching new object (e.g., the red bottle), whereas the other group of infants looked longer at the new object (i.e., they demonstrated a novelty preference, a typical finding in infant studies). In other words, these 18-month-olds appear to understand the anaphoric use of "one" - otherwise, we would expect them to show a novelty preference, just like infants in the control group.

This finding, in combination with the analysis of language corpora, was used by Lidz et al. to support their argument that language learning must be enabled by some kind of innate grammar mechanism: since infants can understand the anaphoric use of "one," and since natural language contains an insufficient number of such uses, an innate grammar mechanism must underlie such knowledge.

Can you spot the problems in this argument?

This conclusion has been disputed by a number of researchers. In Tomasello's reply, he argues that "another one" (as used in the infant study) is significantly different from "one," and that the results demonstrate only that infants understand the purpose of the word "another," and not necessarily anaphoric constructions. (But based on evidence presented in Lidz & Waxman's subsequent reply, this explanation seems highly unlikely.)

A second reply, by Akhtar et al, points out three more problems:

1) By 18-months, infants have probably heard around 1 million sentences; this could translate into 33 anaphoric uses of the word "one." This is not clearly such a "poor stimulus" as we were lead to believe.

2) Language learners may also be capable of learning anaphoric use from contextual evidence - for example, other uses of the word "one," including phrases like "one of those."

3) The behavioral evidence does not unequivocally demonstrate that infants understand anaphoric "one," since the use of "now" in the control phrase ("What do you see now") may bias infants towards looking at the new object.

In a third reply, Regier & Gahl demonstrate how a Bayesian model with no innate grammar learning mechanism can acquire understanding of anaphoric "one" on the basis of negative or indirect evidence - in just a very few exposures (In a subsequent reply, Lidz & Waxman point out that this model's input is so highly constrained as to render the results somewhat meaningless, and also show that the model is in some ways inconsistent with current evidence on how anaphoric "one" is used in English).

Perhaps the two strongest theoretical reasons to doubt their account of anaphoric "one" are:

1) They do not convincingly demonstrate that the number of ungrammatical uses of "one" actually outweighs the number of grammatical anaphoric uses. For example, ungrammatical utterances will be essentially random, whereas even just a few anaphoric uses of "one" are clearly systematic. Young learners might be able to extract that regularity from the input, while ignoring random errors, even if the incidence of errors is higher than the incidence of anaphoric "one."

2) The authors claim to with Regier & Gahl agree that negative or indirect evidence can have a large impact on learning, but disagree with their model only in terms of implementation. However, they never show that negative evidence is insufficient to learn anaphoric "one" from language experience, as they must to claim the existence of an innate grammar mechanism.

Despite these limitations of the Lidz et al argument, a central challenge to empiricist perspective remains. If anaphoric "one" can be learned merely from language exposure, then what learning constraints must exist to produce it? Lidz et al have not provided the extraordinary evidence that should be required of extraordinary claims, particularly when relatively ordinary mechanisms might reasonably account for the observed results.