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Noam Chomsky and other linguists and psychologists have suggested that human linguistic behavior is somehow governed by a mental representation of a transformational grammar. Challenges to this controversial claim have often been met by invoking an explicitly computational perspective: It makes perfect sense to suppose that a grammar could be represented in the memory of a computational device and that this grammar could govern the device's use of a language. This paper urges, however, that the claim that humans are such a device is unsupported and that it seems unlikely that linguists and psychologists really want to claim any such thing. Evidence for the linguists' original claim is drawn from three main sources: the explanation of language comprehension and other linguistic abilities; evidence for formal properties of the rules of the grammar; and the explanation of language acquisition. It is argued in this paper that none of these sources provides support for the view that the grammar governs language processing in something like the way a program governs the operation of a programmed machine. The computational approach, on the contrary, suggests ways in which linguistic abilities can be explained without the attribution of any explicit representation of rules governing linguistic behavior.