Abstract

Charles Peirce insisted that creativity is essential both in deductive and in non-deductive reasoning. For the latter, he developed the well-known inference form of abduction. Less studied with regard to creativity in deductive reasoning is in particular one concept: what he called late in his life a “theoric step” or a “theoric transformation” which consists in changing the perspective on a problem. Whereas abduction focuses on explanatory hypotheses for phenomena that call for an explanation, problems call for a solution. Reacting to Peirce’s “wish [that] a historical study were made of all the remarkable theoric steps and noticeable classes of theoric steps,” the present contribution provides three case studies from the history of mathematics. With these cases I will (1) show how certain problems in mathematics can be solved by finding a theoretical model by means of which the solution can be deduced; (2) conceptualize the corresponding process of reasoning as “theoric transduction”; and (3) provide a proposal to capture the inferential structure of theoric transduction and a preliminary typology of its forms. All this will enrich our understanding of human reasoning and creativity and might be useful for the design of artificial intelligence (AI).