“Theoric Transformations” and a New Classification of Abductive Inferences

Abstract

Based on a definition of "abductive insight" and a critical discussion of G. Schurz's (2008) distinction of eleven "patterns of abduction" that he organizes in four groups, I suggest an even more comprehensive classification that distinguishes 15 forms in an alternative structure. These forms are organized, on the one hand, with regard to what is abductively inferred—singular facts, types, laws, theoretical models, or representation systems—and, on the other, with regard to the question whether the abductive procedure is selective or creative (including a distinction between "psychologically creative," as in school learning, or "historically creative"). Moreover, I argue that theoretical-model abduction—which seems to be the most important form of abduction—depends on two preconditions: first on the availability of an adequate system of representation, and second on finding a new "perspective" on a given problem, as Peirce described it with the notion of a "theoric transformation." To understand the significance of theoric transformations—especially in mathematics—it is necessary to analyze in some detail Peirce's main example for a theoric transformation: the proof of Desargues's theorem.