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organize part of this material, and to render it accessible to students and researchers interested in empirical inquiry. Along the way we shall provide pointers to areas given little coverage in these pages. |
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The material to be presented facilitates the definition and investigation of precise models of empirical inquiry. Such models are often referred to as "paradigms." A paradigm offers formal reconstruction of the following concepts, each central to empirical inquiry. |
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1.1 (a) a theoretically possible reality |
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(b) intelligible hypotheses |
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(c) the data available about any given reality, were it actual |
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(d) a scientist |
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(e) successful behavior by a scientist working in a given, possible reality |
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The concepts figure in the following picture of scientific inquiry, conceived as a game between Nature and a scientist. First, a class of "possible worlds," or possible realities, is specified in advance; the class is known to both players of the game. Nature is conceived as choosing one member from the class, to be the actual world; her choice is initially unknown to the scientist. Nature then provides a series of clues about the actual reality. These clues constitute the data upon which the scientist will base his hypotheses. Each time Nature provides a new clue, the scientist may produce a new hypothesis. The scientist wins the game if his hypotheses ultimately become stable and accurate. Whether the scientist can win the game depends on the breadth of the set of possible worlds. The more constrained Nature's choice of actual world, the more likely the scientist is to discover it. |
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Different paradigms formalize this picture in different ways, resulting in different games. To fix our ideas, let us now examine some simple paradigms, without concern for rigor at this point. |
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§1.3 Some Simple Paradigms |
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Call a set of positive integers "describable" just in case it can be uniquely described using an English expression. For example, the set {2, 4, 6, 8, . . .} is one such set since it is |
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