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		Proof (of Proposition 5.8): For each , define . Let is recursive }. Clearly, .

		Suppose, however, that a consistent scientist M identifies . Let h be the function defined by the following equation:

		Since M must be total, h is clearly total recursive. Thus h satisfies the hypothesis of Lemma 5.9, so there is a recursive set S such that no is a characteristic function of S. But let i' be an index for S, and let  s ' be a locking sequence for M on Li'. Suppose . Then , which implies that . Now suppose . Then , since M is consistent so that . Thus is the characteristic function of S, contradicting the choice of S.

		We now consider the class version of consistency in which a scientist is required to be consistent only on the evidential states drawn from the languages under consideration.

		5.11 Definition (Barzdins * [13])

		We leave it to the reader to show the following proposition which establishes that the class version of consistency also restricts TxtEx.

		5.12 Proposition (Barzdins* [13]) .

		A natural question is how the global and class versions of consistency compare. As the of the proof of 5.8 is readily seen to be in [TxtEx]class-consistent, that proof also yields the following.

		5.13 Proposition .

		§5.2.3 Accountability

		We next consider scientists whose hypotheses always include some prediction about the state of affairs outside the data thus far seen.