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		4. constraints on the relation between conjectures.

		The next four sections treat each of these in turn.

		Relative to any given constraint a further distinction often arises. As an example, consider the requirement that conjectures must be consistent with the data that give rise to them. Formally, scientists satisfying this requirement have the property that on evidential state  s  they output the index of a language that contains content( s ). Observe, however, that this requirement can be interpreted in the following two different ways.

		1. Global consistency: A collection of languages, , is identifiable by a globally consistent scientist just in case there exists an M that is consistent on all and M identifies . Such collections of languages are denoted [TxtEx]consistent.

		2. Class consistency: A collection of languages is identifiable by a class-consistent scientist just in case there exists an M that is consistent on all evidential states drawn from languages in and M identifies . Such collections of languages are denoted [TxtEx]class-consistent.

		Of course, the question immediately arises whether [TxtEx]consistent is a proper subset of [TxtEx]class-consistent. (See Proposition 5.13 below.) For many strategies, considering both the global and class versions is meaningful, whereas for other strategies only one version makes sense.

		§5.2 Constraints on Potential Conjectures

		From the premise that M identifies , one can deduce no information about the nature of M( s ) for any particular . For example, is M( s ) consistent with  s ? This section considers the effects on identification of various constraints on ways in which learners respond to evidential states.

		§5.2.1 Totality

		The most elementary constraint on a conjecture is that it exist. This requirement may be formulated as follows.

		5.1 Definition

		(a) M is always defined on L just in case, for every  s  with , we have .