Using form in the sense of abstract structure, the focus of my interest in this investigation is limited to the formal properties of inquiry processes.  Among their chief constituents these include all the thinking and unthinking processes that support the ability to learn and to reason.  This formal apology, the apologetics of declaring a decidedly formal intent, will be used on numerous occasions to beg off a host of material difficulties and thus avoid the perceived necessity of meeting a multitude of conventional controversies.

Category Double-Takes

The first use of the formal apology is to rehabilitate certain classes of associations between concepts that would otherwise go down as category mistakes.  This conversion can be achieved in each detailed case by flipping from one side of the concept’s dual aspect to the other as the context demands.  Thus it is possible in selected cases to reform the characters of category mistakes in the manner of categorical retakes or double-takes.

Conceptual Extensions

The second use of the formal apology is to permit the tentative extension of concepts to novel areas, giving them experimental trial beyond the cases and domains where their use is already established in the precedents of accustomed habit and successful application.

This serves to dissipate the “in principle” objection that any category distinction puts a prior constraint on the recognition of similar structure between materially dissimilar domains.  As a result, it leaves this issue as a matter to be settled by a post hoc judgment, one that is directed to the question of what fits best “in practice”.

Explosional Recombinations

Another obstacle to inquiry is posed by the combinatorial explosion of questions that can arise in complex cases.  This embarrassment of riches is deceptively deadly to the ends of inquiry in the very measure that it seems so productive at first.  The formalist strategy provides a way to manage this wealth of material diversity by identifying formal similarities among materially different domains, permitting the same formal answer to unify many contentious questions under a single roof, overall reducing the number of distinct topics that need to be covered.

Interpretive Frameworks

Iterations of this recombinatorial process will generate an alternative hierarchy of categories that helps to control the explosion of parts in the domain under inquiry.  If by some piece of luck this alternative framework is uniquely suited to the natural ontology of the domain in question, then it becomes advisable to reorganize the whole inquiry along the lines of its topic headings.

But a complex domain seldom falls out that neatly.  The new interpretive framework will not preserve all the information in the object domain, but typically capture only another aspect of it.  In order to take the maximal advantage of all the different frameworks that might be devised, it is best to quit depending on any one of them exclusively.  Thus, a rigid reliance on a single hierarchy to define the ontology of a given domain passes over into a flexible application of interpretive frameworks to make contact with particular aspects of one’s object domain.