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		of notation in slightly ambiguous fashion. Officially, a symbol like Lang denotes a class of collections of languages. However, we also use it unofficially to denote the associated paradigm, that is, an ensemble of definitions concerning possible realities, scientists, and so forth. This allows us to make reference to "the paradigm" Lang. We take the same liberty with Func and the other names to be introduced.

		§4.2 Language Identification by Computable Scientist

		§4.2.1 The Paradigm TxtEx

		We now introduce the paradigm TxtEx. The symbol Txt signifies that the paradigm concerns the identification of languages on texts. Ex signifies that the success criterion is the one specified in Section 3.4, namely, convergence to a single index for the language of the incoming text (Ex stands for Explains). Notice that no part of the name TxtEx refers explicitly to the computable nature of scientists. This is because the restriction to the computable case will henceforth be a feature of all the paradigms to be introduced.2 The only difference between TxtEx and Lang is this: "scientist" now means a computable function — either partial or total — from SEQ to N. All other aspects of the paradigm are the same as before, including the criterion of success given in Definitions 3.10-3.12. Here is the official definition:

		4.2 Definition (Gold [80])

		(a) Let M be a computable scientist and let . M TxtEx-identifies L (written: ) just in case M identifies L.

		(b) .

		So, TxtEx(M) in the above definition denotes the collection of all languages identified by M. Considered as classes of collections of languages, what is the relation between Lang and TxtEx? Since the computable scientists are a subset of the class of all scientists, it follows that . Now we consider whether the inclusion is strict.

		2 TxtEx has other names in the literature, e.g., INT and Lim. The terminology TxtEx is due to Case and Lynes [33].