Chomsky (1965, 1986) presents a series of arguments for an innate syntactic component of the language faculty. Do the arguments proposed at that time still stand, or have they been overridden by newer proposals? The current paper emphasizes three research directions among the most recent advances in cognitive science. These directions lead to alternate proposals to the generative linguistic theory of language development. First, the 'item-based' theory of language development, which stresses that development of language knowledge goes from specific to general and is compatible with developing research in cognitive linguistics. Second, the apparent uniformity of adult linguistic competence, which is a fundamental tenet of generative linguistics theory, may be the product of literate cultures but not of invariants of the brain, as attested by the fundamental differences found between spoken and written language. Third, artificial neural networks provide evidence against the necessity to call on algebraic rules to explain language performance and this, in turn, argues in favor of the emergence approach and of the dynamic systems approach to language development. All this calls for a renewal of language development theories and for a separation between statistical, non-algebraic, non-conscious, item-based, and usage-based structures and processes dedicated to spoken language (and to automatized written language processes), and principle-and-rule-governed, algebraic structures and processes dedicated to conscious written or formal spoken language.