Abstract
Two kinds of formal models need to be distinguished: data models derived from patterned observations and theory models derived from theories about processes that produce the patterned observations. These correspond to the difference between the phenomenal domain of observations and the ideational domain of theories. Explanation can be characterized by isomorphism between data models and theory models. The physical, biological and cultural domains differ by what constitute the relevant structuring processes for each of these domains. The cultural domain associated with human societies is far more complex than the other two because the domain of observation must include cultural idea systems. One of the primary roles of formal models for cultural idea systems is to determine the necessary consequences (through mathematical reasoning) of processes hypothesized to provide their internal coherency.
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