Empirical restrictions on the power of transformational grammars
In their article "On the Generative Power of Transformational Grammars", Peters and Ritchie (1971) argue that given any recursively enumerable set there exists a transformational grammar that will produce that set. They claim that the deletion rule used in their proof (b → ø) is a recoverable deletion rule. This deletion rule obligatorially deletes all occurrences of a terminal symbol b from every sentence of a context-sensitive language related to the original recursively enumerable set. As a result of such a transformation, there exists no surface sentence with b. The terminal symbol b is only recoverable because in their formulation the grammar that produces the b's is already determined. There is, however, no evidence in the surface strings of the language for any b.
Given the assumption that speakers do not have rules for which there is no empirical evidence, the type of deletion rule found in Peters and Ritchie's proof would never be found in any human language. In terms of language acquisition, the deletion rule is not recoverable. Given such an empirical condition on grammars, the types of rules found in the grammars of natural languages would be restricted on the basis of empirical evidence. Peters and Ritchie's proof fails to meet this empirical condition and is therefore invalid.
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