A demonstration of the uncomputability of parametric models of language acquisition and a biologically plausible alternative
The logical problem of language acquisition has been at the forefront of psycholinguistics and behavioral neuroscience for decades. One of the most influential answers to the problem of how successful acquisition occurs on the basis of noisy input suggests that the child is aided by innate principles and parameters (P&P). These are conceived aspart of our biological endowment for language. Previous work on the computability of parametric models has focused on the process of parameter-setting,leaving settability unaddressed. Settability is a key notion in parametric models since it provides an answer to the logical problem of language acquisition: the setting of one parameter carries implications for the settability of others, minimizing the child’s task. However, a mathematical analysis of the expected probability of successful computation of settability relations has not been carried out. We report results from a novel program developed to calculate the probability of successful computation of a network of 62 linguistic parameters as attested in 28 languages, spanning across 5 language families. The results reveal that some parameters have an extremely low probability of successful computation, such that trillions of unsuccessful computations are expected before a successful setting occurs. Using the same program, we performed an additional second analysis to a different network, covering 94 parameters from58 languages and 15 language families. In this case, the estimated number of expected unsuccessful computations rose from trillions to quadrillions. These results raise concerns about the computational feasibility of the highly influential P&P approach to language development. Merging insights from various acquisition models, including some developed within P&P, a biologically plausible alternative is offered for the process of deciphering a target grammar in the acquisition of both spoken and signed languages. Overall, our analysis of the P&P approach to language acquisition centers learnability and computability constraints as the major factors for determining the psychological plausibility of grammar development.
Keywords: acquisition, language, learnability, Universal Grammar, computability