opper, 1963; Wisdom, 1952). This information itself is produced by applying current scientific classification schemes to raw data in an attempt to structure and interpret it. The reasoning is deduction, whether formal deductive logic or other deductivist analytical procedures. Models play an important, though indirect, role in analytic inference (Hanson, 1958; Kuhn, 1970; Toulmin, 1960). The quantitative and symbolic information and the identifications, descriptions, predictions, and explanations which are the outputs of analytic inferences are derived from detailed knowledge such as equations, formulas, laws, and theories. However, standing behind this detailed knowledge is a fundamental model of the "deep structure" of the world which, in effect, provides a rationale for applying that particular kind of detailed knowledge to that specific data. For instance, the kinetic-molecular theory of gases is one such fundamental model whose scientific function is to provide a rationale for searching and then applying a particular kind of detailed knowledge about gases. Figure 3.7 shows the input/output structure of analytic inference.
Inductive inferences are logical patterns for moving from quantitative or symbolic information about a restricted portion of a domain to universal statements about the entire domain (Cohen, 1970; Good, 1977; Hilpinen, 1968; Horton, 1973; Lehrer, 1957, 1970; Rescher, 1961; Salmon, 1967; Skyrms, 1966). There are two somewhat different aspects of inductive inference: Inductive generalization and abstraction. In inductive generalization, some finite set of measurements of an independent variable and its dependent variable are generalized into a mathematical function which holds for all possible values of those variables. Alternatively, in abstraction, some finite set of symbolic representations of just a few members of some domain is the basis for inferring some abstractive characteristic common to all members of the domain. Examples of abstraction include moving from a set of white objects to the concept of "white," and inferring from the information that all observed ravens are black; the principle that being black is a defining characteristic of ravens. As was the case with analytic inferences, models play an important though indirect role (Hanson, 1958; Kuhn, 1970; Toulmin, 1960). These models serve to restrict the range of mathematical functions or abstractive concepts that can characterize a domain, hence, they focus the inductive inference from information to generalization. For instance, we know that Robert Boyle was guided in the processing of pressure and volume data by a model of gases that required volume to decrease while pressure increased (Toulmin, 1961). Figure 3.8 suggests the input/output structure of inductive inference.
Abductive inferences are logical patterns for moving from an input set that includes: ? some theoretical structure T consisting of models, theories, laws, concepts, classification schemes, or some combination of these, ? some prediction P derived from T by means of an analytic inference, and ? some set of quantitative or symbolic data D which contradict P (D = not -P),
ANALYTIC PROCESSOR = ( JSALYTIC PRTCEDURES
Figure 3.7. - Analytic inference.
?
