It is no accident that the beginnings of generative linguistics coincided with the first work in what became known as formal language theory (FLT). The generative perspective takes grammars, rather than collections of sentences, to be the scientifically central objects: rather than compact summaries of observed regularities in collections of sentences, grammars are mental systems that determine the status of sentences, from which the observed regularities follow as consequences. FLT is the study of the kinds of regularities that arise from grammars that are structured in various ways. Without FLT, there were no hypotheses about what mental grammars might look like that could be connected to predictions about the regularities that would be observed.
Nowadays the connections are less apparent between research in generative syntax and formal systems of the sort that facilitated Chomsky's early work, and there is a perception that FLT has little relevance to a properly mentalist approach to linguistics. This is an overreaction to certain much-discussed linguistic shortcomings of specific details of the original "Chomsky Hierarchy". The important underlying ideas transcend these details, and a sharper understanding of contemporary syntactic frameworks comes from seeing how they instantiate those same underlying ideas in new ways.
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