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The central aim of this paper and its projected successors is to prove in detail that stimulus-response theory, or at least a mathematically precise version, can give an account of the learning of many phrase-structure grammars. Section 2 is concerned with standard notions of finite and probabilistic automata. An automaton is defined as a device with a finite number of internal states. Section 3 presents a treatment of the stimulus-response theory. In Section 4 the most important result of the paper is proved; namely, any finite automaton can be represented at asymtote by an appropriate model .of stimulus-response theory. In Section 5 some extensions of these results to probabilistic automata are sketched, and an example from arithmetic is worked out in detail. The central idea is to show that by applying accepted, principles of conditioning an organism may theoretically be taught by an appropriate reinforcement schedule to respond as a finite automaton. (RP)