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		§3.1.1 Languages as Scientific Possibilities

		Consider a scientist studying periodicity in the arrangement of atoms packed into the microstructure of a certain class of alloys. She poses the question: For what natural numbers n are there alloys from the class that exhibit periodicity n? Let us call this latter set periods. The results of her observations can be summarized by statements like:

		3.2 , , , , , . . .

		or more compactly by:

		3.3 3, 41, 17, 53, 75, . . .

		The scientist's goal is to transform these data into an accurate and stable conjecture about periods. A language L in this setting corresponds to one possible reality, namely, the reality in which periods = L.

		In what follows we shall assume the set periods to be recursively enumerable. It is possible that Nature is not so kind as to guarantee the machine acceptability of sets of integers that correspond to physical processes. However, to keep our topic manageable, we shall limit attention to situations in which the recursive enumerability of the underlying reality is a reasonable assumption; let us take it to be so in the periods example.

		In the simplified metaphysics that governs our analysis of science, we always assume that Nature selects exactly one underlying reality to be actual. However, not every logically possible reality need be assumed a genuine alternative. Rather, attention may be focused on some proper subset of the class of all languages. Such a focus amounts to stipulating that the theoretically possible alternatives are limited to , other languages being mere logical possibilities ruled out on scientific grounds. Stipulations of this kind allow us to frame questions such as the following: ''Suppose that it is known in advance that periods falls in . What kinds of scientists (if any) are sure to discover which member of is equal to periods?"

		A scientist might obtain assurance that periods is limited to a subclass of languages in two ways. On the one hand, prior research carried out by other scientists (e.g., her professors) might allow certain languages to be ruled out of the class of genuine alternatives. On the other hand, it is possible that human genetic endowment imposes certain true beliefs about Nature's choice of language, making languages discrepant with these beliefs seem highly implausible.