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10
Learning with Additional Information |
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Scientific inquiry almost never starts from scratch. Previous inquiry, common sense, or mere intuition cut back the range of potential realities that scientists are willing or able to consider. In the favorable case, reducing the search space leaves reality among the possibilities still under consideration. (Otherwise, the door is wide open for frustration.) In the case of linguistic development, there is broad agreement that successful language acquisition depends upon limitations in the class of potential languages that the child is willing to impute to her caretakers. Indeed, if all r.e. sets were genuine candidates for natural languages, the child might get stuck conjecturing the finite set of sentences heard to date! |
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It is clear that our models of inquiry (either scientific or developmental) should represent such a priori restrictions on the class of possible hypotheses. To the present point in our discussion, however, such restrictions have been handled in the crudest possible way. We have simply declared a particular collection of functions or languages to be relevant to scientific success, and allowed the scientist to fail with impunity on the others. For example, to say that  is identifiable means that if the class of possible realities is limited to  , then some scientist can reliably determine which member of these potentialities is actual. The curtailment of possible reality to  is modeled by including no more than  in the criterion of successful inquiry. In this way it is possible to ask whether success can be guaranteed if reality is pinned down a priori to  . For  the answer is Yes; the answer is negative for many other collections of functions and languages — which is what makes the subject interesting. Nevertheless, much is missing from our account of the scientist's starting point. Not every collection of functions or languages need constitute a feasible or meaningful restriction on hypotheses, yet our theory provides no natural means for enforcing such a distinction. |
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The issue of scientific starting points is so fundamental and complex that we cannot hope to provide much insight at the present stage of theory construction. (Perhaps the reader will consent to visit us again when the book is in its fourth or fifth edition?) We would nonetheless like to discuss one aspect of the topic for which some results have been obtained. The class of plausible hypotheses that come to the mind of a scientist might interact with the character of the true hypothesis. In other words, since the scientist is |
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