Mind, Body, World- Foundations of Cognitive Science, 2013a

found that informant learning permitted context-sensitive and context-free grammars
to be identified in the limit.
Gold’s (1967) research was conducted in a relatively obscure field of theoretical
computer science. However, Steven Pinker brought it to the attention of cognitive
science more than a decade later (Pinker, 1979), where it sparked a great deal of
interest and research. This is because Gold’s computational analysis revealed a paradox
of particular interest to researchers who studied how human children acquire
language.
Gold’s (1967) proofs indicated that informant learning was powerful enough
that a complex grammar can be identified in the limit. Such learning was not possible
with text learning. Gold’s paradox emerged because research strongly suggests
that children are text learners, not informant learners (Pinker, 1979, 1994, 1999). It
is estimated that 99.93 percent of the language to which children are exposed is
grammatical (Newport, Gleitman, & Gleitman, 1977). Furthermore, whenever feedback
about language grammaticality is provided to children, it is not systematic
enough to be used to select a grammar (Marcus, 1993).
Gold’s paradox is that while he proved that grammars complex enough to model
human language could not be text learned, children learn such grammars—and do
so via text learning! How is this possible?
Gold’s paradox is an example of a problem of underdetermination. In a problem
of underdetermination, the information available from the environment is
not sufficient to support a unique interpretation or inference (Dawson, 1991). For
instance, Gold (1967) proved that a finite number of expressions presented during
text learning were not sufficient to uniquely determine the grammar from which
these expressions were generated, provided that the grammar was more complicated
than a regular grammar.
There are many approaches available for solving problems of underdetermination.
One that is most characteristic of classical cognitive science is to simplify
the learning situation by assuming that some of the to-be-learned information
is already present because it is innate. For instance, classical cognitive scientists
assume that much of the grammar of a human language is innately available before
language learning begins.
The child has an innate theory of potential structural descriptions that is sufficiently
rich and fully developed so that he is able to determine, from a real situation
in which a signal occurs, which structural descriptions may be appropriate to this
signal. (Chomsky, 1965, p. 32)
If the existence of an innate, universal base grammar—a grammar used to create
phrase markers—is assumed, then a generative grammar of the type proposed by
Chomsky can be identified in the limit (Wexler & Culicover, 1980). This is because
learning the language is simplified to the task of learning the set of transformations
74 Chapter 3