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		required to convert data of a happenstance character into the understanding (implicit; or explicit) that renders his world predictable and intelligible.

		It is not surprising that so little is known about the mental processes responsible for children's remarkable intellectual achievements. Even elementary questions remain the subject of controversy and inconclusive findings. For example, there is little agreement about whether children use a general-purpose system to induce the varied principles bearing on language, social structure, etc., or whether different domains engage special-purpose mechanisms in the mind.2

		The disparity just noted for intellectual development has also been observed in the acquisition of scientific knowledge by adults. Like the child, scientists typically have limited access to data about the environment, yet are sometimes able to convert this data into theories of astonishing generality and veracity. At an abstract level, the inquiries undertaken by child and adult may be conceived as a process of theory elaboration and test. From this perspective, both agents react to available data by formulating hypotheses, evaluating and revising old hypotheses as new data arrive. In the favorable case, the succession of hypotheses stabilizes to an accurate theory that reveals the nature of the surrounding environment. We shall use the term ''empirical inquiry" to denote any enterprise that possesses roughly these features.

		It is evident that both forms of empirical inquiry — achieved spontaneously in the early years of life, or more methodically later on — are central to human existence and cultural evolution. It is thus no accident that they have been the subject of speculation and inquiry for millenia.3 The present book describes a set of conceptual and mathematical tools for analyzing empirical inquiry. Their purpose is to shed light on both intellectual development and scientific discovery. They may also be of use in guiding the development and evaluation of artificial systems of empirical inquiry (such as those described in Langley, Simon, Bradshaw, and Zytkow [123]).

		Since the pioneering studies of Putnam [155], Solomonoff [184, 185], Gold [80], and the Blums [18] a large technical literature has been devoted to the development and use of the tools at issue here. Papers within this tradition are spread over journals and books in mathematics, computer science, linguistics, psychology, and philosophy. Our topic has variously been called "The Theory of Scientific Discovery," "Formal Learning Theory," "The Theory of Machine Inductive Inference," "Computational Learning Theory," and "The Theory of Empirical Inquiry." We shall use all these terms to describe the collection of definitions, examples, and theorems that emerge from the literature. Our goal is to

		2 For discussion, see Chomsky [40], Pinker [148], and Osherson and Wasow [142].

		3 See Russell [163] for an historical overview.