"Theoric Transformations" and a New Classification of Abductive Inferences

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.