The focus of this chapter is the sort of abduction that is only achievable by means of the unique, generative process capable of producing original ideas. The authors discuss Kapitan’s (1997) theses as a framework for understanding Peirce’s theory of abduction. They then return to Peirce’s concepts of phenomenology and normative science to explore the relationships between these philosophical concepts (and that of mathematics) with the development of a model for Peirce’s concept of abduction. They conclude with an in-depth description of Relational thinking, which includes algorithms (based upon Chiasson’s notational system) for three of the many types of operations performed by Relational thinkers.
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By creative abduction, we mean a particular generative process that incites and nourishes (rather than implements) an incipient idea and which can lead to the creation of a unique outcome. Thus, creative abduction describes feats of a particular kind of imagination—the kind that many would call “fanciful” (Peirce, 1932, Vol. 1, para. 46-48). In this sense, abduction is a means-directed (as opposed to a goal-directed) process,1 and thus requires a significantly different relationship of means to ends (Peirce, 1935, Vol. 5, para. 129) than does deduction (which is premise driven) or induction (which is category related). Even the sort of inference to the best explanation type of abduction discussed in the previous chapter (and in Peirce’s early syllogism [Peirce, 1935, Vol. 5, para. 189]) has a specific problem-solving purpose, which, as a sort of goal, directs the selection and rejection of options, thus limiting possibilities. From the perspective of creative abduction, a unique relationship between means and ends holds the clue for explicating the mystery of abduction.
In terms of the Relational Thinking Styles (RTS) model, the abductive-like process of Relational thinking does not necessarily engage the retroductive-like recursive process (Chiasson, 2005) of Multi-relational thinking. The former moves in an exploratory way outward from means towards potential ends (yet without a specific end in view) and the latter begins with the abductive acquisition of a hypothesis or goal and proceeds to explicate and test to support (or eliminate) this possibility (Chiasson, 2005). There are indeed Multi-relational (retroductive-like) thinkers and, though rare, such thinkers (who are capable of operating within any of the style patterns for a given purpose) may choose a habitual thinking pattern from any style, unless some thing or idea emerges to sufficiently capture their attention long enough to engage in full-scale retroduction (Chiasson, 2005).
The focus of this chapter is the sort of abduction that is only achievable by means of the unique, generative process capable of producing original ideas. We discuss Kapitan’s (1997) theses as a framework for understanding Peirce’s theory of abduction. We then return to Peirce’s concepts of phenomenology and normative science to explore the relationships between these philosophical concepts (and that of mathematics) with the development of a verifiable model for Peirce’s concept of abduction. We conclude with an in-depth description of Relational thinking, which includes algorithms for three of the types of operations performed by Relational thinkers.