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		8 Environments

		Recall the component concepts of a learning paradigm:

		(a) a theoretically possible reality

		(b) intelligible hypotheses

		(c) the data available about any given reality, were it actual

		(d) a scientist

		(e) successful behavior by a scientist working in a given, possible reality

		Recursively enumerable languages and total recursive functions are the theoretically possible realities proper to the paradigms discussed so far. For both languages and functions, computer programs have been conceived as intelligible hypotheses.

		In Chapter 5 we examined alternative interpretations of item (d) by restricting the concept ''scientist" to subsets of the computable functions. Chapters 6 and 7 were devoted to a range of success criteria, in the sense of item (e). The present chapter concerns alternative construals of available data, item (c). Until now, the potential environments for a language or function have been equated with the class of all its texts. This equation embodies three assumptions about the character of the scientist's data, namely, that: (i) none are missing, (ii) those that reach the scientist are free of error, and (iii) they may arrive in any order. All three assumptions obviously misrepresent the circumstances of language acquisition. Thus, it is clear that children need not hear every sentence of their language in order to stabilize to an accurate grammar. They are also likely to face at least some ungrammatical intrusions (although perhaps not many; see [182]). There is also no doubt that children face a constrained order of sentences inasmuch as the speech addressed to them starts off simply. The same considerations apply to adult scientists conducting empirical inquiry. Their data are neither complete nor error-free, and the order of their arrival is constrained by such factors as cost. (Cheaper data arrive first!)

		In what follows, erroneous data will be conceived as intrusions into the interface between a language and a scientist. Error thus expands the class of texts for a given language. Allowing data to be omitted has a similar effect whereas constraints on order shrink the class of texts a scientist might face. These ideas are defined precisely in Sections 8.1 and 8.2. We subsequently discuss how scientists can exploit multiple sources of data about the same reality.