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if such languages are admitted as human, perhaps as special cases. Exact identification would then, once again, be the appropriate standard of learnability. |
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Computable scientists occupy center stage in our theory of scientific inquiry. To study them we extend our conception of Turing Machines so that they also represent functions from SEQ to N and from SEG to N. The choice of domain depends on whether we consider natural numbers as codes for SEQ or for SEG. In either case, the class of computable scientists is indexed as Mi. |
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A wide variety of paradigms are defined and analyzed in the chapters to follow. For concision, each is associated with a symbolic name that refers to the family of collections of languages or functions that can be identified within them. For example, Lang is the family of all collections of languages that can be identified in the sense of Section 3.4, and Func is the family of all identifiable collections of functions in the sense of Section 3.9.4. Restricting attention to computable scientists, these paradigms become TxtEx and Ex, respectively. |
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Introducing the computability constraint on scientists limits the collections that can be identified. In particular, it was shown that both Lang - TxtEx and Func - Ex are nonempty. When computability is considered in conjunction with other characteristics of scientists, the impact on identifiability is not straightforwardly deducible from the impact of each characteristic considered separately. This was illustrated by considering the kinds of collections of languages that can be identified by scientists who are either computable, memory-limited, or both. |
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Real scientists have flexibility that is not represented by functions from SEQ or SEG to N. In particular, scientists can often take account of background knowledge communicated to them from an external source such as colleagues or professors. To incorporate this feature of empirical inquiry into our theory we consider "parameterized scientists" who receive an additional, numerical input. The input is conceived as a code for a class of languages or functions that delimit the possible realities that the scientist must envision. Given a set of such codes, we ask whether there exists a computable, parameterized scientist that can identify the class associated with any code in the set. Two kinds of codes were considered, one for communicating classes of languages to scientists, the other for communicating classes of functions. |
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Finally, we returned to the study of comparative grammar and observed that the class of human languages is generally defined as including all and only the languages |
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