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in a language thus consists in knowing the function that maps one representation onto the other. Under suitable encoding, this competence amounts to knowing which member of  effects the mapping embodied by the language. The class of human languages corresponds to only a proper subset of  , possibly quite narrow. (Variants of this basic framework are possible; see Wexler and Culicover [194] for discussion.) |
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Within this perspective, language acquisition proceeds as follows. Nature (in the guise of parents) selects some function f from the human subset of  and presents the child with the sentences corresponding to f. Contextual clues give the child access to the underlying representation of these sentences, whereas their superficial representations are made available acoustically. She thus receives, in effect, an enumeration of the graph of f. In response she produces a series of conjectures about f, hoping to stabilize on an accurate program for it. |
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 thus corresponds to 3.1a, in our list of concepts to be specified by any paradigm of empirical inquiry. We proceed now to specify the others. |
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§3.9.2 Function Identification: Hypotheses, Data |
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Since theoretical possibilities are members of  , we conceive of "intelligible hypotheses" as programs for computing functions. As usual, it is simpler to assimilate such hypotheses to the indexes associated with programs (see Chapter 2). Item 3.1b thus reduces to N though we shall continue to use "program" as an informal synonym for "index" in the context of function identification. Note the following detail. Whereas only total functions are possible realities, many programs compute properly partial functions. Such programs are legitimate conjectures, but within the present paradigm they are necessarily inaccurate. (Their existence will be crucial to more refined models of empirical inquiry, treated later, e.g., in Chapters 5 and 6.) |
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We turn now to 3.1c, the data that Nature makes available about any given function, f. The totality of all such data is conceived as a list of the graph of f in Some arbitrary order. For simplicity, we do not allow pauses in the presentation of data, so # does not appear. Officially:2 |
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(a) We extend the concept of "text" (see Definition 3.4) to include any single-valued infinite sequence over N × N, i.e., any infinite list of pairs of numbers such that, for each |
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2 In what follows it will be helpful to recall the modern interpretation of a function, which identifies it with its "graph." See Chapter 2. |
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