Chomsky's KNOWLEDGE OF LANGUAGE addresses certain conceptual questions about the foundations of generative linguistics that center on a 'skeptical paradox' that Kripke attributes to Wittgenstein. Chomsky's discussion offers an extended defense of his psychological conception of grammar against this challenge. This essay argues that Chomsky's response to the skeptical paradox is inadequate, but instructively so. The inadequacies of Chomsky's reply surface as a destructive dilemma for the psycholinguist conceptually committed to the generative paradigm in such a way as to reveal a conceptual incoherence in that paradigm. Specifically, the essay exhibits the dilemma as it arises for the performance theory of Berwick and Weinberg (1986). While modification of the philosophical foundations of generative linguistics may show the working psycholinguist the way out of the dilemma, this essay leaves the dispute unresolved, making only the negative point