One of the fundamental properties of human language is that it can be used to create an unlimited number of utterances given a limited number of pieces. At the syntactic level, this property follows directly from a mathematical property of language called recursiveness. We’re all familiar with recursiveness (even if not with the term). It is found in language , and computer programs, and even in children’s stories, as in (1). In (1), the process or rule that creates a relative clause (here, the clauses beginning with that) has applied repeatedly to the noun phrases inside other relative clauses. This repeated application of the same rule to create more and more complex sentences is an example of recursiveness. The children’s story is amusing precisely because we all know that there is no theoretical limit to the application of this rule. Any speaker of English can add to the story by generating another relative clause at the beginning, as in (2). The only limitations on th...
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