How the poverty of stimulus solves the poverty of stimulus

The logical problem of language acquisition is the problem every child is facing when acquiring the grammar of its native language: it has too little evidence to uniquely determine which is the target grammar from the set of all grammars that would in principle be possible. The basic intuition that the grammars of natural languages are not learnable from available evidence is supported with a series of mathematical models. Here, we will focus our discussion on two such models: Gold (1967) and Nowak et al. (2001). These models are often interpreted as showing the necessity of strict, a-priori and innate constraints on the set of grammars a child needs to consider in the first place. The underlying assumptions of these “proofs” of Universal Grammar have been controversial. Gold, for instance, shows that context-free grammars are not learnable, if one assumes that the grammars are deterministic, that there is no negative evidence and that learnability corresponds to “identification in the limit”. Many have argued that it is unreasonable to assume that a child learns language in such a worst-case scenario (see e.g. Elman et al, 1996). Although we suspect that some of this criticism is in fact justified, we leave that issue as an empirical question. Instead, we study a computer model in which we make similar assumptions as in the mathematical models, evaluate the claims about Universal Grammar within that framework, and nevertheless arrive at very different conclusions. Our model consists of an evolving population of language learners, that learn a grammar from their parents and get offspring proportional to the success in communicating with other individuals in their generation. The grammar induction procedure is fixed; it is inspired by Kirby (2000). The details of the grammatical formalism (context-free grammars) and the population structure are deliberately close to Gold (1967) and Nowak et al. (2001) respec-