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		§3.1.2 Human Languages and Comparative Grammar

		Turning to the developmental context, languages in our technical sense may be conceived as representing human languages like Chinese or German that must be mastered by children in the course of their development. Within this perspective, human languages are conceived in a manner familiar from the theory of formal grammar (see Hopcroft and Ullman [82, Chapter 1]) where a sentence is taken to be a finite string of symbols drawn from some fixed, finite alphabet, and a language is construed as a subset of all possible sentences. This definition embraces rich conceptions of sentences, for which derivational histories, meanings, and even bits of context are parts of sentences. Since finite derivations of almost any nature can be collapsed into strings of symbols drawn from a suitably extended vocabulary, it is sufficiently general to construe a language as the set of such strings. By coding strings numerically (see Section 1.4.1), a human language may then be conceived as a subset of the natural numbers N. However, not just any subset of N can play this role. Since human languages are generally considered to have grammars, and since grammars are intertranslatable with Turing Machines, we restrict attention to the recursively enumerable subsets of N—that is, to "languages" in our technical sense.

		Now it seems evident to many linguists (notably, Chomsky [40, 43]) that children are not genetically prepared to acquire any arbitrary language on the basis of the kind of casual linguistic exposure typically afforded the young. Instead, a relatively small class of languages may be singled out as "humanly possible" on the basis of their amenability to acquisition by children, and it falls to the science of linguistics to propose a nontrivial description of . Specifically, the branch of linguistics known as "comparative grammar" is the attempt to characterize the class of (biologically possible) natural languages through formal specification of their grammars; and a theory of comparative grammar is such a specification of some definite collection. Contemporary theories of comparative grammar begin with Chomsky (e.g., [38, 39]), but there are several different proposals currently under investigation (see Wasow [190] and Lasnik [124]).

		Theories of linguistic development stand in an intimate relation to theories of comparative grammar. For if anything is certain about natural language, it is this: children can master any natural language in a few years' time on the basis of rather casual and unsystematic exposure to it. This fundamental property of natural language can be formulated as a necessary condition on theories of comparative grammar: such a theory is true only if it embraces a collection of languages that is learnable by children. For this necessary condition to be useful, however, it must be possible to determine whether