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		of noncomputable scientists thereby facilitates the analysis of proofs, making it clearer which assumptions carry the burden. This issue will be revisited in Chapter 11.

		On the other hand, Chapters 9 and 10 will discuss senses in which our present conception of scientist is too narrow. Note, for example, that scientists as defined here cannot make decisions on a random basis by including the outcome of a coin-toss as an additional input.

		§3.4 Language Identification: Scientific Success

		Languages, hypotheses, texts, and scientists are the dramatis personae of the identification paradigm. To develop its story-line we turn now to the criterion of successful inquiry, 3.1e, which is defined in three steps.

		§3.4.1 Identifying Texts

		3.10 Definition Let scientist F, text T, and be given.

		(a) F converges to i on T (written: ) just in case for all but finitely many , F(T[n] = i. If there exists an i such that , then we say ; otherwise we say F(T) diverges (written: ).

		(b) F identifies T just in case there is such that F converges to j on T, and Wj = content(T).

		So, to identify T, F's conjectures must eventually stabilize to a single grammar for content(T). This is impossible, of course, if T is for a non-r.e. set. In the case of interest, however, T is for some language , hence there are infinitely many grammars for content(T).

		Suppose that F identifies T. Definition 3.10 places no finite bound on the number of times that F "changes its mind" on T. In other words, the set may be any finite size; it may not, however, be infinite. Similarly, the smallest such that WF(T[m]) = content(T) may be any finite number, so F's first correct guess may occur arbitrarily late in T. It is also permitted that for some , WF(T[n]) = content(T), but . That is, F may abandon correct conjectures, provided that F eventually sticks with some correct conjecture. Observe that to identify a text, a scientist can be undefined on at most a finite number of its initial sequences.