Peirce’s Diagrammatic Reasoning and Abduction

The mainstay of Peirce’s diagrammatic reasoning is deduction, for which he developed a comprehensive family of graphical logics termed existential graphs. He thought, however, that also the two other kinds of inferences, namely, abduction and induction, indirectly depend on diagrammatic reasoning, given that they depend for their justification on deductive reasoning. This chapter presents Peirce’s theory of diagrams from the wider philosophical and scientific perspectives. In particular, the chapter addresses the issue of how abductive modes of reasoning too rest on the theory and philosophy of diagrams and how abduction contributes to the value of diagrammatic reasoning in science. The chapter highlights two fields of science that have enjoyed renewed potential arising from their analysis in terms of Peirce’s theory of diagrammatic reasoning and abduction: cognitive science and exact mathematical and computational sciences.