This paper sketches a theory of scientific discoveries that is mainly based on two concepts that Charles Peirce developed: abduction and diagrammatic reasoning. Both are problematic. While “abduction” describes the process of creating a new idea, it does not, on the one hand, explain how this process is possible and, on the other, is not precisely enough defined to distinguish different forms of creating new ideas. “Diagrammatic reasoning,” the process of constructing relational representations of knowledge areas, experimenting with them, and observing the results, can be interpreted, on the one hand, as a methodology to describe the possibility of discoveries, but its focus is limited to mathematics. The theory sketched here develops an ex-tended version of diagrammatic reasoning as a general theory of scientific discoveries in which eight different forms of abduction play a central role.