Learnability of a Language
A child must achieve competence with an infinite language based on a finite number of heard sentences. This is the essence of Noam Chomsky's "poverty of the stimulus" argument. As originally presented, it made a case for nativism, forcing empiricist theories to explain how such competence is achievable. In Stephen Pinker's Language Learnability and Language Development, he uses learnability both as a challenge to theories of language acquisition, and as a heuristic for evaluating them. Terrence Deacon, in The Symbolic Species, while dismissive of most of Chomskyan linguistics, still sees the learnability problem as a challenge to any theory that hopes to explain human linguistic knowledge. I will begin with a scrutiny of Pinker and Deacon's similar responses to the learnability problem, and will then examine Pinker's learnability criterion, which counters Deacon's aims.
The views of Deacon and Pinker overlap to a surprising extent. Some shared ground, and potentially shared ground, are to be found in their views on learnability. Both feel compelled to respond to the formal version of the poverty of the stimulus argument, as originally stated in a mathematical learning theory paper by E. Mark Gold. Gold proved that without feedback about hypothesized grammars or examples of ungrammatical constructions, it is impossible to inductively learn the unique grammar that produces an infinite language, even with a learning algorithm that remembers all observed data (Gold 1967).
A number of responses to Gold's theorem have been offered. Gold himself proposed a likely solution: that "the class of possible natural languages is much smaller than one would expect from our present model of syntax"...
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